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1. Chapter 4 where D is the standard normal cumulative function M and M are the minimum and maximum characteristic magnitudes respectively and EM and s are parameters defining the distribution of M EM can be interpreted as the expected value of the characteristic earthquake and s as its standard deviation 4 0 is the exceedance rate of magnitude M o In addition an slip predictable behavior can be modeled assuming that EM grows with time elapsed since the last characteristic event 700 in the following fashion E M D F In T00 4 Of course if F is set to zero then EM D independently of time elapsed 4 4 Generalized Non Poissonian model This type of seismicity description allows for direct specification of the required probabilities that is the probabilities of having 1 2 Ns earthquakes of given magnitudes in a given location during the next Tf years This information is given to CRISIS by means of a binary file with extension nps non Poisson seismicity which has the following format Number of point sources TotSrc Integer Number of magnitude bins Nbin Integer Number of time frames Nt Integer 4 Maximum number of events for which Prob i j is given al Dre S Magnitude representative of M 1 Double 8 Magnitude values are useful bin 1 only if parametric attenuation models are used They are not used in Magnitude representative of generalized attenuation bin Nbin pes Double d models Time frame 1 Tf 1 Do
2. 96 3490 15 5260 15 0000 96 0000 15 5000 15 0000 95 0000 15 1970 15 0000 95 0000 15 9100 30 0000 96 2670 16 2570 30 0000 81 Chapter 11 REGION 16 Subducci n Oaxaca 1 Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 97 3540 15 6700 15 0000 96 3490 15 5260 15 0000 96 2670 16 2570 30 0000 97 2100 16 4430 30 0000 REGION 17 Subducci n Oaxaca 2 Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 97 8770 15 7750 15 0000 97 3540 15 6700 15 0000 97 2100 16 4430 30 0000 97 6550 16 5280 30 0000 REGION 18 Subducci n Oaxaca Oeste 82 Chapter 11 Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 98 2420 15 8730 15 0000 97 8870 15 7750 15 0000 97 6550 16 5280 30 0000 98 0350 16 5910 30 0000 REGION 19 Subducci n Ometepec Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 99 6630 16 3430 15 0000 98 2420 15 8730 15 0000 98 0350 16 5910 30 0000 99 4380 17 0100 30 0000 REGION 20 Subducci n San Marcos Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc 83x Chapter 11 Area source Number of vertex 4 Long Lat De
3. Brune 1970 0 00381 1 15130 Singh et al 1980 0 00564 1 15130 55 Chapter 10 Wells and Coppersmith 1994 Strike slip 0 01100 1 03616 Wells and Coppersmith 1994 Reverse 0 00571 1 12827 Wells and Coppersmith 1994 Normal 0 02072 0 94406 Wells and Coppersmith 1994 All 0 01015 1 04768 10 6 2 Line sources In this case the fault length L in km is related to magnitude through L5 K e The corresponding built in set of constants taken from Wells and Coppersmith 1994 are Surface Rupture Length SRL Strike Slip 0 00028 1 70391 Surface Rupture Length SRL Reverse 0 00138 1 45063 Surface Rupture Length SRL Normal 0 00977 1 15129 Surface Rupture Length SRL All 0 00060 1 58878 Subsurface Rupture Length RLD Strike Slip 0 00269 1 42760 Subsurface Rupture Length RLD Reverse 0 00380 1 33550 Subsurface Rupture Length RLD Normal 0 01318 1 15129 The built in sets of constants presented in the previous tables are given in file CRISIS2008 rpr located in the installation directory of the CRISIS executable file These constants can be edited or new constants can be manually added to this file The general format for a new constant would be in a single row separated by commas the following Author K K K E Where Author is a string used for identification purposes normally indicating the author of the corresponding relation and K p K K K are the given constants For area sources it is required
4. The following is an example of the res file Basically it contains all the data given by the user to define source geometry source seismicity and attenuation characteristics as well as other global parameters DLELLLLLLLLLLLLLLLLLLLLLELLLLLLLLLLLLLLLLLLLLLLII CRISIS 2009 Version 3 4 2 0 15 04 2010 07 33 20 p m La Arbolada Jalisco 69 Chapter 11 VALUES OF PARAMETERS FOR THE PRESENT PROJECT Number of regions or seismic sources 45 Number of attenuation models 3 Number of structural periods 9 Number of intensity levels 15 Number of magnitudes for integration 9 Type of computation sites Lista Max dist of integration 500 000 Min distance Triangle size ratio 5 000 Minimum triangle size km 7 000 INTENSITIES ITD A00 AU I UNITS 1 1 00E 02 1 00E 00 1 50E 03 2 1 50E 01 1 00E 00 4 00E 03 3 3 00E 01 1 00E 00 3 30E 03 4 5 00E 01 1 00E 00 2 20E 03 5 1 00E 00 1 00E 00 1 30E 03 6 2 00E 00 1 00E 00 7 50E 02 7 3 00E 00 1 00E 00 6 00E 02 8 4 00E 00 1 00E 00 4 00E 02 9 5 00E 00 1 00E 00 3 00E 02 TIME FRAMES ITF I 1 5 00E 01 70 Chapter 11 INITIAL GRID OF POINTS File of list of sites C Crisis 2008 Extra Pruebas M xico CD_3Ciudades TXT THE INITIAL GRID WAS MODIFIED WITH THE FOLLOWING POLYGONS Number of polygons 1 Polygon 1 Number of vertex 16 LONG LAT 117 7324 32 7306 116 4633 27 6343 113 8458 24 3694 110 0386 21 7417 104 1692 17 0435 97 5065 14 1769
5. Within the CRISIS development team this combination is known as Peruzza type since Prof Laura Peruzza suggested its implementation an used it in her calculations in the context of project S2 2008 2010 funded by the Italian Civil Protection Authority Option 3 In this option source geometry is a line or an area but ground motion characteristics are described with a generalized attenuation model This option is impossible due to the fact that generalized attenuation models are associated to known fixed hypocentral locations while line or area sources contain implicitly uncertainty about future hypocenters Thus these source attenuation choices are incompatible with each other In addition generalized attenuation models contain information about individual events with known although irrelevant magnitudes Since each event is associated to a fixed value of magnitude occurrence probabilities for each of the events contained in the attenuation model cannot be computed for continuous arbitrary values of magnitude with the information provided by parametric seismicity descriptions as earthquake magnitude exceedance rates It must be remembered that starting with magnitude exceedance rates occurrence probabilities in given time frames can only be computed for magnitude intervals magnitude bins and not for point values Option 4 AQ Chapter 6 In this option the source is a line or an area seismicity is described with a
6. 1984 as a tool to capture and quantify the uncertainties associated with the inputs required to perform such an analysis and they have since become a standard feature of PSHA Coppersmith and Youngs 1986 Reiter 1990 Handling uncertainties is a key element of SHA Seismic Hazard Analysis Distinction is made between two types of uncertainty in seismic hazard assessment and these are given the adjectives aleatory and epistemic e g Budnitz et al 1997 terms used to replace and distinguish between the terms randomness and uncertainty whose use has become ambiguous Bommer 2003 Uncertainties that are related to an apparent randomness in nature such as the scatter associated with empirical relationships are referred to as aleatory variability If the aleatory variability can be measured usually by fitting observations to an assumed probability distribution it is then straightforward to incorporate this variability directly into the hazard calculations The most important aleatory variability in SHA is that associated with ground motion prediction equations which is generally represented by the standard deviation of the logarithmic residuals of the predicted parameter Standard practice in PSHA is now to integrate across this aleatory variability within the hazard calculations Uncertainties reflecting the incomplete knowledge of say seismicity rupture characteristics and seismic energy excitation are referred to as epistem
7. 2008 Attenuation relationships for PGA and 5 damped PSA Brief description for shallow crustal earthquakes in active tectonic enviroments worldwide 106 Chapter 12 Number of parameters Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values 7 Data Vs30 Ground type and Geom mean of V s30 Units coefficient 1E 20 to 1E 20 Sigma truncation 1E 20 to 1E 20 Geometric mean of Vs30 NEHRP Class Boundaries rounded Based on Measured Velocities in NGA Flatfile Suggested Vs30 in Boore 2003 Measured amp Inferred Vs30 in NGA Flatfile Measured Vs30 in NGA flatfile Fault type Thrust reverse Normal Strike slip Unspecified Ground type NERHP E NERHP D NERHP C NERHP B NERHP A Vs30 1E 20 to 1E 20 Reference D Boore and G Atkinson Ground Motion Prediction Equations for the Average Horizontal Component of PGA PGV and 5 Damped PSA at Spectral Periods between 0 01 s and 10 0 s Earthquake Spectra Volume 24 1 pages 99 138 February 2008 12 4 Cambell and Bozorgnia 2003 Class name Distance metric Valid distance range Valid magnitude range Valid period range Original units Intensity dimension Residual distribution Short name Brief description Number of parameters Crisis2008 ExtraGMPE CampbellBozorgnia04 JyB to
8. Long 13 7 Cities file The city file is in ASCII format and must contain the following data Number of cities Name of the state name of the city longitude and latitude of the city 1 line for each city Example 2 Number of cities GUERRERO Acapulco 99 900 16 850 AGUASCALIENTES Aguascalientes 102 300 21 883 13 8 Map file The map file must contain the following data Number of polygons For each polygon Name of the polygon Number of vertex of the polygon For each vertex Latitude and longitude Example 2 Number of polygons State 1 Name of polygon 1 121 Chapter 13 122
9. ModGRN 56 Nbytes Nx2 Ny2 moment NumMoments Grid for DIN ModGRN 56 Nbytes Nx2 Ny2 measure 2 moment 1 Grid for usps ModGRN 56 Nbytes Nx2 Ny2 290 Chapter 5 Description Type Length Comments measure 2 moment 2 Grid for intensity measure 2 moment NumMoments ModGRN 56 Nbytes Nx2 Ny2 Grid for Then the actual georeferenced probabilistic intensity measure ModGRN 56 Nbytes Nx2 Ny2 i Numint intensity values follow moment 1 Grid for intensity measure Numlnt moment 2 ModGRN 56 Nbytes Nx2 Ny2 Grid for intensity measure E Ka N t ModGRN 56 Nbytes Nx2 Ny2 moment NumMoments 5 4 Adding new built in GMPM In addition to attenuation tables and generalized attenuation models CRISIS admits built in GMPM which are given to the code in the form of classes compiled in a Dynamic Link Library dll 30 Chapter 5 CRISIS includes a number of built in GMPM which can be consulted in this link However this collection can be extended by way of writing code for user defined GMPM Each new GMPM must be a new class that implements at least the following methods No Method type ReadOnly Property 2 ReadOnly Property 3 ReadOnly Property 4 ReadOnly Property 5 ReadOnly Property 6 ReadOnly Property 7 ReadOnly Property 8 ReadOnly Property 9 ReadOnly Property Method name BriefDescription DistanceT ype MaximumV alidDistance MaximumV alidMagnitude Mi
10. Possible values E420 to 1E 20 silde Chapter 12 Reference D Garc a S K Singh M Herr iz M Ordaz and J Pacheco Inslab Earthquakes of Central Mexico Peak Ground Motion Parameters and Response Spectra Bulletin of the Seismological Society of America Vol 95 No 6 pp 2272 2282 December 2005 12 15 Youngs et al 1997 Class name Distance metric Valid distance range Valid magnitude range Valid period range Original units Intensity dimension Residual distribution Short name Brief description Number of parameters Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Crisis2008 NewA ttenuation A ttenuationC lasses Y oungs97 Rrup 10 to 500 Km 5 to 8 5 0 to 3 sec cm s s Crisis2008 New Attenuation DimensionClasses Acceleration LogNormal Youngs et al 1997 Ground motion prediction model for subduction zone earthquakes interface and intraslab determined with world wide data 4 Units coefficient 1E 20 to 1E 20 Fault location Intraslab Interface Sigma truncation 1E 20 to 1E 20 Soil type Soil Rock Reference R R Youngs S J Chiou W J Silva and J R Humphrey Strong Motion Attenuation Relations for Subduction Zone Earthquakes Seismological Research Letters Vo 68 No 1 pp 58 73 January February 1997 115 116 Chapter 13 13 File Formats The following is a description of the various f
11. SEA99 A Revised Ground Motion Prediction Relation for Use in Extensional Tectonic Regimes Bulletin of the Seismological Society of America 89 5 pp 1156 1170 October 1999 See also P Spudich and D M Boore ERRATUM to SEA99 A Revised Ground Motion Prediction Relation for Use in Extensional Tectonic Regimes Bulletin of the Seismological Society of America 95 3 p 1209 June 2005 12 12 Arroyo et al 2010 Class name Distance metric Valid distance range Valid magnitude range Valid period range Original units Intensity dimension Residual distribution Short name Brief description Number of parameters Parameter name Possible values Parameter name Possible values Crisis2008 ExtraG MPE Arroyoetal09 Rrup 16 to 400 Km 5 to 8 5 0 001 to 5 sec cm s s Crisis2008 NewA ttenuation DimensionClasses Acceleration LogNormal Arroyo et al 2010 Spectral horizontal accelerations 5 damping on rock for Mexican subduction zone interface earthquakes 2 Units coefficient 1E 20 to 1E 20 Sigma truncation 1E 20 to 1E 20 12 13 Atkinson and Boore 2003 Class name Distance metric Valid distance range Valid magnitude range Valid period range Original units Intensity dimension Residual distribution Crisis2008 ExtraGMPE AtkinsonBoore03 Rrup 1 to 300 Km S to 8 5 0 01 to 3 03 sec cm s s Crisis2008 New Attenuation DimensionClasses Acceleration LogNormal 113 Chapter 12 Short name Atkinson
12. 0000 16 2000 30 0000 95 0000 15 9000 30 0000 95 0000 17 2000 100 0000 96 0000 18 3000 100 0000 97 0000 18 8000 100 0000 98 0000 18 9000 100 0000 99 0000 19 1000 100 0000 90 Chapter 11 REGION 33 Prof int Este nueva Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model NormalDaniel RRup 5 Trunc CR2007 Area source Number of vertex 6 Long Lat Depth km 95 0000 15 9000 30 0000 94 0000 15 4000 30 0000 92 3000 14 0800 30 0000 91 5000 14 9000 100 0000 94 0000 16 5000 100 0000 95 0000 17 2000 100 0000 REGION 34 Petrolera Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 10 Long Lat Depth km 92 5000 18 5000 30 0000 92 0000 19 0000 30 0000 93 0000 19 1250 30 0000 94 0000 19 2500 30 0000 96 0000 19 5000 30 0000 96 0000 18 5000 30 0000 95 5000 18 0000 30 0000 25 Chapter 11 95 0000 17 5000 30 0000 94 0000 17 5000 30 0000 93 0000 17 5000 30 0000 REGION 35 Golfo Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 6 Long Lat Depth km 96 5000 21 0000 15 0000 96 5000 20 2000 15 0000 96 0000 19 5000 15 0000 92 0000 19 0000 15 0000 91 0000 21 0000 15 0000 94 0000 21 0000 15 0000 REGION 36 Eje volc nico Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 8 Lo
13. 02 2 01E 01 3 62E 01 6 81E 02 1 23E 02 3 04E 02 5 99E 02 1 10E 03 9 69E 04 2 42E 03 4 84E 03 1 78E 03 4 03E 05 1 01E 04 2 02E 04 2 87E 03 8 43E 07 2 11E 06 4 22E 06 4 64E 03 8 60E 09 2 15E 08 4 30E 08 7 50E 03 4 31E 11 1 08E 10 2 15E 10 11 3 Example FUE file This file gives of the contribution of each source to the exceedance probabilities at a site In the example below for a single site values of probability of exceedance generated by each of the 2 sources present in the model are shown for 2 different intensity measures ten different intensity values and three different rime frames The user should remember that probabilities are not additive This means that for the same site intensity measure intensity level and time frame the addition of the exceedance probabilities associated to all the individual sources does not give the total probability of exceedance Please see the basic theoretical background in order to know how the arithmetic of exceedance probabilities works Site 0 2 0 25 Intensity 1 T 0 050 Time frame 1 Tf 10 000 Level Region 01 Region 02 1 00E 02 5 64E 01 5 64E 01 1 54E 02 2 21E 01 2 21E 01 2 39E 02 4 98E 02 4 98E 02 3 68E 02 6 34E 03 6 34E 03 5 69E 02 4 39E 04 4 39E 04 8 79E 02 1 64E 05 1 64E 05 1 36E 03 3 48E 07 3 48E 07 2 10E 03 4 83E 09 4 83E 09 3 24E 03 4 99E 11 4 99E 11 102 Chapter 11 5 00E 03 4 05E 13 4 01E 13 Intensity 1 T 0 050 Time frame 2 Tf 25 000 Level Region 01 Region 02 1
14. 127 12 2 Akkar and Bommer 2007 Class name Distance metric Crisis2008 ExtraGMPE AkkarBommer07 JyB 105 Chapter 12 Valid distance range 1 to 100 Km Valid magnitude range 5 to 7 6 Valid period range 0 to 4 sec Original units cm s s Intensity dimension Crisis2008 New Attenuation DimensionClasses Acceleration Residual distribution LogNormal Short name Akkar and Bommer 2007 Bion DOR Attenuation relation obtained from 532 accelerograms from the strong motion databank of Europe and Middle East Number of parameters 5 Parameter name Units coefficient Possible values 1E 20 to 1E 20 Parameter name Damping Possible values 30 20 10 5 2 Parameter name Sigma truncation Possible values 1E 20 to 1E 20 Parameter name Fault type Possible values Unspecified Reverse Normal Parameter name Ground type Possible values Suff Soil Soft Soil Otherwise Reference Akkar and J Bommer Prediction of elastic displacement response spectra in Europe and the Middle East Earthquake Engineering and Structural Dynamics Pages 1275 1301 February 2007 DOI 10 1002 eqe 679 12 3 Boore and Atkinson 2008 Class name Crisis2008 ExtraGMPE BooreA tkinson08 Distance metric JyB Valid distance range 1 to 200 Km Valid magnitude range 5108 Valid period range 0 to 10 sec Original units g Intensity dimension Crisis2008 NewAttenuation DimensionClasses Acceleration Residual distribution LogNormal Short name Boore and Atkinson
15. 60 Km 5to7 5 0 03 to 4 sec g Crisis2008 NewAttenuation DimensionClasses Acceleration LogNormal Campbell and Bozorgnia 2003 Equations developed for and tectonically active shallow crustal regions located troughout the world for 5 damping ratio 7 107 Chapter 12 Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Component Vertical Horizontal Units coefficient 1E 20 to 1E 20 Sigma truncation 1E 20 to 1E 20 Fault type Generic unknown Reverse or thrust Thrust Reverse Strike slip or normal Ground type BC boundary Generic rock Generic soil Firm rock Soft rock Very firm soil Firm Soil PGA type Uncorrected Corrected Standard deviation calculate By Mw By PGA recomended Reference K Campell and B Bozorgnia Updated Near Source Ground Motion Attenuation Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and Acceleration Response Spectra Bulletin of the Seismological Society of America Vol 93 1 pages 314 331 February 2003 12 5 Cauzzi and Faccioli 2008 Vertical 5 damped Class name Distance metric Valid distance range Valid magnitude range Valid period range Original units Intensity dimension Residual distribution Short name Brief description Number of para
16. 88 0000 16 3000 10 0000 REGION 45 Polochic 3 Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 4 Long Lat Depth km 94 0000 16 0000 15 0000 93 0000 15 2000 15 0000 89 5500 15 2000 15 0000 88 0000 16 3000 15 0000 SEISMICITY Gutenberg Richter sources 07 Chapter 11 Source name MO Lambda0 E Beta c Beta E Mu D Mu Baja California intraplaca nor 4 500 1 14E 00 0 970 0 097 5 800 0 000 Baja California intraplaca sur 4 500 1 21E 00 0 933 0 036 5 800 0 000 Baja California interplaca nor 4 500 2 51E 00 1 782 0 093 7 700 0 300 Baja California interplaca cen 4 500 7 26E 01 1 637 0 168 7 400 0 400 Baja California interplaca sur 4 500 2 09E 00 1 674 0 082 7 200 0 600 Sierra Madre Occidental 4 500 1 16E 01 2 880 0 030 5 600 0 000 Cuencas y Sierras 4 500 2 69E 01 2 880 0 030 5 600 0 000 Cuenca de Burgos 4 500 1 87E 01 2 880 0 030 5 600 0 000 Interfaz Pac fico Rivera 4 500 3 41E 00 1 736 0 088 7 200 0 000 Sismicidad difusa 1 4 500 6 58E 01 2 880 0 030 5 600 0 000 Sismicidad difusa 2 4 500 1 80E 01 2 880 0 030 5 600 0 000 Centroam rica 4 500 4 97E 01 1 942 0 180 7 700 0 300 Jalisco nuevo 4 500 2 01 E 00 1 827 0 110 7 200 0 000 Gro Mich nuevo 4 500 4 79E 00 1 547 0 077 7 200 0 000 Oaxaca nuevo 4 500 6 72E 00 1 847 0 063 7 200 0 000 Chiapas nuevo 4 500 1 89E 01 2 059 0 037 7 200 0 000 Prof Interm Oeste nueva 4 500 2 16E 00 1 699 0 097 7 800 0 200 Prof
17. Focal 2 Epicentral 3 Joyner and Boore 4 Closest to rupture area Rrup For each of the NT different intensity measures the following blocks of lines T J SLA J 0 AMAX J COEFH Structural period of j th spectral ordinate It is used only for identification purposes and to T J plot the uniform hazard spectrum so in the cases in which structural period has no meaning it can be just a sequential number Standard deviation of the natural logarithm of the j th measure of intensity A value of SLA J 0 given after the table of SA values AMAX J See Probabilistic interpretation of attenuation relations for a definition of this quantity COEFH Depth coefficient See explanation below SLA J 0 lt 0 implies that the user will give standard deviations that vary with magnitude In this case the corresponding o values one for each of the VMAG magnitudes has to be Some modern attenuation relations have a coefficient to make the intensity explicitly dependent on focal depth This information is given with coefficient COEFH so that MED A M R SA M R exp COEFH H 5 where MED A M R is the depth dependent median value of intensity for given values of magnitude M and distance R SA M R is the median intensity given in the table for the same values of magnitude and distance and H is focal depth e Chapter 5 Matrix of median intensities associated to a magnitude row and a distance column SA 1 1 1 SA L 1 2
18. Number of vertex 10 Long Lat Depth km 117 0000 33 9900 7 0000 116 3050 33 0680 7 0000 115 6100 32 1450 7 0000 114 9150 31 2230 7 0000 114 2200 30 3000 7 0000 113 5300 30 8200 7 0000 114 2230 31 7430 7 0000 114 9150 32 6650 7 0000 115 6080 33 5880 7 0000 116 3000 34 5100 7 0000 REGION 4 Baja California interplaca centro Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source 75 Chapter 11 Number of vertex 6 Long Lat Depth km 114 2200 30 3000 10 0000 113 3600 29 1550 10 0000 112 5000 28 0100 10 0000 111 8100 28 5300 10 0000 112 6700 29 6750 10 0000 113 5300 30 8200 10 0000 REGION 5 Baja California interplaca sur Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 7 Long Lat Depth km 108 0000 22 0000 10 0000 107 1000 23 0000 10 0000 108 6500 25 0000 10 0000 110 5500 27 6100 10 0000 111 8600 28 4800 10 0000 112 5000 28 0000 10 0000 110 2500 25 0000 10 0000 REGION 6 Sierra Madre Occidental Gutenberg Richter SOURCE IS ACTIVE 76 Chapter 11 Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 5 Long Lat Depth km 110 0000 29 0000 20 0000 110 5500 27 6100 20 0000 108 6500 25 0000 20 0000 106 0000 25 0000 20 0000 106 0000 29 0000 20 0000 REGION 7 Cuencas y Sierras Gutenberg Richter SOURCE I
19. events of magnitude M in the next Tf years due to the effect of the whole fault Pr M Tf would be given by P i M Tf exp AX M Tf 1 239 Chapter 6 where AA M is the Poissonian magnitude occurrence rate of earthquakes with magnitudes in the vicinity of M for the whole source This occurrence rate can be written as AX M In P i M Tf Tf 2 In the case of Poissonian occurrences occurrence rates are additive Thus the occurrence rate corresponding to a sub source of relative size Wi would simply be AX M ANM W 3 J J Note that for all sub sources Zw 1 Now we can go back to compute the occurrence probability associated to sub source j P i M Tf expCA M Tf exp N 4M Tfw exp n PG M Tp w 4 J J J J from which we gather that P i M Tf P i M Tp 5 Note that as we had mentioned if only the occurrence probabilities for the whole source are specified there is not a unique way to specify occurrence probabilities associated to sub sources However the path chosen by CRISIS is in our view reasonable and exact for the case of Poissonian sources The only compatibility restriction when using this option is that the file that contains the generalized non Poissonian occurrence probabilities must stipulate in the nps file that the number of sources is equal to 1 that is only a set of occurrence probabilities is given See this link in order to see where this parameter is stipulated
20. into a data file normally with extension dat Although data are written in a plain text file care must be taken when editing this file by hand 10 3 Map and cities file selection Button e Menu Input Maps Give the name and path of the map file and the cities file Both files are optional By double clicking in the text box you can choose an existing file The map and cities information is a helpful visual reference but has not any influence on the computations 10 4 Grid or list of sites Button e Menu Input Grid of sites This screen allows you to input the grid or list of sites for which seismic hazard will be computed There are two options Grid of sites 53 Chapter 10 Compute for a grid defined by its origin longitude and latitude increments and number of lines in both directions Hazard will be computed at the nodes of this grid List of sites Select this option if you want to compute hazard for a list of sites with given coordinates Double click in the box to read the name of the file that contains the list of sites The format of this text file is the following Number of cities State_1 City_1 Longitude_1 Latitude_1 State_2 City_2 Longitude_2 Latitude_2 Grid reduction It is possible to modify the basic rectangular grid by using optional polygons Introducing one or more boundary polygons can reduce the initial rectangular grid of points If polygons are given the computation of haz
21. that N Nm v a 2 Y AA M Pr A a M R 16 k i l Note that n a the well known Poissonian intensity exceedance rate does not depend anymore on T In the limit the inner sum of equation 16 can readily be recognized as the integral with respect to magnitude that is present in the conventional Esteva Cornell approach to compute Poissonian seismic hazard The outer sum in equation 16 is simply the aggregation of intensity exceedance rates due to all sources In other words N Nm L M v a y VM k i l Pr 4 gt a M R JAM 17 2 dA M v a gt ee M R dM 18 a dM Note that due to the definition we used for Dl M in equation 9 its sign changed when we converted it to its differential form We have then shown that equation 7 derived for the general non Poissonian case is also valid for the Poissonian case leading to the well known Esteva Cornell expression to compute seismic hazard 2 2 Spatial integration procedure CRISIS assumes that within a source seismicity is evenly distributed by unit area area sources or by unit length line sources For point sources of course all seismicity is assumed to be concentrated at the points In order to correctly account for this modeling assumption CRISIS performs a spatial integration by subdividing the original sources Once subdivided into sub sources CRISIS assigns to a single point all the seismicity associated to a sub source and then
22. the appropriate data 10 9 1 For the Gutenberg Richter model GR Model Threshold magnitude M ni The catalog of earthquakes is assumed to be complete for M M o Earthquakes with M lt M gare absolutely ignored Lambda MO Exceedance rate of magnitude M o The units are earthquakes year Expected value of beta Expectation of the b value for the source given in terms of the natural logarithm Coefficient of variation of beta Coefficient of variation of the b value for the source given in terms of the natural logarithm Parameters defining Mu Expected value Expected value of the maximum magnitude for the source See details 258 Chapter 10 Uncertainty range A number indicating that the maximum magnitude will have a uniform probability density function centered at its expected value plus minus this number See details 10 9 2 For the characteristic model Median value of the times between characteristic earthquakes with M gt M o This is the inverse of the exceedance rate for M gt M o Standard deviation of the magnitude of the characteristic earthquake It is assumed independent of time Minimum possible magnitude of a characteristic earthquake Earthquakes with M lt M o are absolutely ignored Maximum magnitude of the characteristic earthquake to be used in the integration process Parameters D and F define the expected magnitude as a function of time as in the slip predictable model It is assumed that E M
23. these options result in very similar nodes E Chapter 8 An important principle to follow in setting up a logic tree but not always taken into account is that the options represented by the branches extending from a single node should encompass the complete range of physical possibilities that particular parameter could be expected to take This is consistent with the objective of the logic tree in capturing epistemic uncertainty which arises from lack of knowledge The branches should be set up so that as knowledge improves mainly through the gathering of more and better data revised estimates for the parameters should fall within the bounds expressed by the logic tree branches In the context of CRISIS each branch of a logic tree is formed by one data file usually with extension dat along with a measure of the degree of belief that the analyst has on each of the branches being the true one Results from the different branches along with the weights assigned to each branch are computed using the combination rule that will be described in the following paragraphs Assume that the probability of exceeding level a of a intensity measure A at a site in the i th time frame accoring to the j th branch of a logic tree is y Aa Assume also that the probability of being the true one Then the expected value of PA gt a once all branches have been accounted for P A gt a is given by N P A gt a Pi A gt a w
24. 0 000 0 270 7 000 8 400 Subducci n Michoac n 25 600 6 000 7 500 0 000 0 270 7 000 8 400 Subducci n Colima 1 47 500 18 000 7 500 0 000 0 270 7 000 8 400 Subducci n Brecha de Colima 56 700 183 000 7 500 0 000 0 270 7 000 8 400 Subducci n Jalisco 19 800 57 000 7 500 0 000 0 270 7 000 8 400 EEES ok oke ok ok ok k ok ok ok ok ok ok ok K ols ok ok ok ok ok oft ok olk ok ok ok ok ok ok ok ok ok ols K ok ok ok ok oke ok ok 2K ok WARNINGS ABOUT MAGNITUDE DISTANCE RANGES VALIDITY Region 3 Baja California interplaca norte The maximum magnitude in the region is larger than the maximum valid magnitude of GMPE Abrahamson y Silva No HW S S 7 7 gt 7 5 99 Chapter 11 Region 12 Centroam rica The maximum magnitude in the region is larger than the maximum valid magnitude of GMPE Abrahamson y Silva No HW S S 7 7 gt 7 5 Region 40 Motagua 1 The maximum magnitude in the region is larger than the maximum valid magnitude of GMPE Abrahamson y Silva No HW S S 7 8 gt 7 5 Region 41 Motagua 2 The maximum magnitude in the region is larger than the maximum valid magnitude of GMPE Abrahamson y Silva No HW S S 7 8 gt 7 5 Region 42 Motagua 3 The maximum magnitude in the region is larger than the maximum valid magnitude of GMPE Abrahamson y Silva No HW S S 7 8 gt 7 5 Region 43 Polochic 1 The maximum magnitude in the region is larger than the maximum valid magnitude of GMPE Abrahamson y Silva No HW S S 7 8 gt 7 5 Region 44 Polo
25. 00E 02 8 74E 01 8 74E 01 1 54E 02 4 64E 01 4 64E 01 2 39E 02 1 20E 01 1 20E 01 3 68E 02 1 58E 02 1 58E 02 5 69E 02 1 10E 03 1 10E 03 8 79E 02 4 10E 05 4 10E 05 1 36E 03 8 71E 07 8 71E 07 2 10E 03 1 21E 08 1 21E 08 3 24E 03 1 25E 10 1 25E 10 5 00E 03 1 01E 12 1 00E 12 Intensity 1 T 0 050 Time frame 3 Tf 50 000 Level Region 01 Region 02 1 00E 02 9 84E 01 9 84E 01 1 54E 02 7 12E 01 7 13E 01 2 39E 02 2 25E 01 2 26E 01 3 68E 02 3 13E 02 3 13E 02 5 69E 02 2 19E 03 2 19E 03 8 79E 02 8 18E 05 8 19E 05 1 36E 03 1 74E 06 1 74E 06 2 10E 03 2 41E 08 2 42E 08 3 24E 03 2 49E 10 2 50E 10 5 00E 03 1 99E 12 2 00E 12 Intensity 2 T 0 150 Time frame 1 Tf 10 000 Level Region 01 Region 02 1 00E 02 8 60E 01 8 60E 01 1 62E 02 5 27E 01 5 27E 01 2 61E 02 1 92E 01 1 92E 01 4 22E 02 3 95E 02 3 95E 02 6 81E 02 4 46E 03 4 46E 03 1 10E 03 2 62E 04 2 62E 04 1 78E 03 7 68E 06 7 68E 06 2 87E 03 1 13E 07 1 13E 07 4 64E 03 9 20E 10 9 20E 10 103 Chapter 11 7 50E 03 5 02E 12 5 02E 12 Intensity 2 T 0 150 Time frame 2 Tf 25 000 Level Region 01 Region 02 1 00E 02 9 93E 01 9 93E 01 1 62E 02 8 46E 01 8 46E 01 2 61E 02 4 13E 01 4 13E 01 4 22E 02 9 58E 02 9 58E 02 6 81E 02 1 11E 02 1 11E 02 1 10E 03 6 55E 04 6 55E 04 1 78E 03 1 92E 05 1 92E 05 2 87E 03 2 82E 07 2 82E 07 4 64E 03 2 30E 09 2 30E 09 7 50E 03 1 25E 11 1 25E 11 Intensity 2 T 0 150 Time frame 3 Tf 50 000 Level Region 01 Region 02 1 00E 02 1 00E 00 1 00E 00 1 62E 02 9 76E 01 9 76E 01 2 61E 02 6 55E
26. 01 6 55E 01 4 22E 02 1 82E 01 1 82E 01 6 81E 02 2 21E 02 2 21E 02 1 10E 03 1 31E 03 1 31E 03 1 78E 03 3 84E 05 3 84E 05 2 87E 03 5 64E 07 5 65E 07 4 64E 03 4 60E 09 4 60E 09 7 50E 03 2 50E 11 2 51E 11 104 Chapter 12 12 Appendix GMPM currently supported by CRISIS 12 1 Abrahamson and Silva 1997 Class name Distance metric Valid distance range Valid magnitude range Valid period range Original units Intensity dimension Residual distribution Short name Brief description Number of parameters Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Crisis2008 New Attenuation A ttenuationClasses AbrahamsonA ndSilva97 Rrup 0 1 to 200 Km 4 to 7 5 0 01 to 5 sec cm S s Crisis2008 NewA ttenuation DimensionC asses Acceleration LogNormal Abrahamson and Silva 1997 Horizontal spectral accelerations for shallow crustal earthquakes in tectonically active regions world wide 5 Units coefficient 1E 20 to 1E 20 Site is in the hanging wall True or False Sigma truncation 1E 20 to 1E 20 Soil Type Deep soil Rock or shallow soil Style of fault Other including strike slip Reverse Oblique Reverse Reference N A Abrahamson and W Silva Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes January February 1997 Seismological Research Letters vol 68 num 1 pp 94
27. 1 Give the exceedance probability that will be used to draw a hazard map or a uniform hazard spectrum 10 15 6 Intensity value Fixed intensity Give the fixed intensity value that will be used to draw a map with show exceedance probabilities associated to fixed values of time frame and intensity or to draw a spectrum showing the exceedance probabilities associated to a fixed value of spectral intensity and time frame as a function of period 10 15 7 Save hazard map a Give a name to the file in which the hazard map will be saved and the format for the map There are three format options Bitmap The file saved will be simply a bitmap image of the map shown in CRISIS hazard map screen DSSA Surfer ASCII format Taken from SURFER 8 Help file DSSA grid files contain five header lines that provide information about the size and limits of the grid followed by a list of Z values See details XYZ file This is an ASCII file containing longitude latitude hazard sets for all the nodes in the computation grid 10 15 8 Draw hazard map El Draws the hazard map with the selected options 64 Chapter 10 10 15 9 Site Selection Click into a point of the hazard map in order to see 1 The hazard curve for the selected intensity measure and time frame 2 Depending on whether the fixed intensity or the fixed probability switch is selected e The uniform hazard spectrum e A graph showing the exceedance probabilities asso
28. 1 j 1 Results of the logic tree combination will be given in the form of a new hazard model with an associated dat file that will have the base name of the file that described the combination but with the extension dat This new hazard model can be loaded into CRISIS and the corresponding hazard results can be analyzed with CRISIS hazard maps exceedance probability curves uniform hazard spectra as if they were the results of a regular dat file Disaggregation results however can not be obtained for the hazard resulting from the logic tree combination 48 Chapter 9 9 Hazard disaggregation Magnitude distance disaggregation Consider the basic hazard computation equation see the basic theoretical background ar N Nm Pr A lt a T Pr 4 lt a M T k D l where Pr A a T is the probability of not exceeding intensity a at a site in the next T years when subjected to a seismic regime composed by N point sources each of which produces darthquakes of magnitudes M M pM NM It can be noted that the product in equation 1 is composed by many terms each of which corresponds to a particular magnitude value M and to a specific source to site distance which is the one from source k to the site for which hazard is being computed In view of this the contributions to Pr A a T or to Pr A gt a T could be grouped for a range of magnitudes say from M Lo M 2 and a range of distances This is the magnitu
29. 170 15 0000 103 8680 18 3000 15 0000 103 6120 18 7610 30 0000 104 1820 19 1730 30 0000 REGION 26 Subducci n Jalisco Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 8 Long Lat Depth km 104 4570 18 7170 15 0000 104 1820 19 1730 15 0000 105 0000 20 0000 15 0000 105 1300 20 2560 15 0000 105 5000 21 0000 30 0000 106 0000 21 0000 30 0000 86 Chapter 11 105 7000 20 0000 30 0000 105 0000 19 1000 30 0000 REGION 27 Jalisco nuevo Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 8 Long Lat Depth km 106 0000 21 0000 15 0000 105 7000 20 0000 15 0000 105 0000 19 1000 15 0000 104 0000 18 4000 15 0000 103 7300 18 8400 30 0000 104 0000 19 0000 30 0000 105 0000 20 0000 30 0000 105 5000 21 0000 30 0000 REGION 28 Gro Mich nuevo Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 11 Long Lat Depth km 104 0000 18 4000 15 0000 EA Chapter 11 103 0000 17 6000 15 0000 102 0000 17 1500 15 0000 101 0000 16 8000 15 0000 100 0000 16 4500 15 0000 99 0000 16 1000 15 0000 98 8200 16 8100 30 0000 100 0000 17 2000 30 0000 101 0000 17 5000 30 0000 102 0000 17 9000 30 0000 103 7300 18 8400 30 0000 REGION 29 Oaxaca nuevo Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source
30. 2 2 61E 02 4 22E 02 6 81E 02 1 10E 03 1 78E 03 2 87E 03 4 64E 03 7 50E 03 Intensity 3 0 2 T 0 050 Time Frame 1 Time Frame 2 Time Frame 3 8 10E 01 3 93E 01 9 72E 02 1 26E 02 8 78E 04 3 28E 05 6 97E 07 9 66E 09 9 99E 11 8 06E 13 T 0 150 Time Frame 1 Time Frame 2 Time Frame 3 9 80E 01 7 77E 01 3 47E 01 7 74E 02 8 90E 03 5 24E 04 1 54E 05 2 26E 07 1 84E 09 1 00E 11 T 0 300 Example gra file 0 25 9 84E 01 7 13E 01 2 26E 01 3 13E 02 2 19E 03 8 19E 05 1 74E 06 2 42E 08 2 50E 10 2 01E 12 1 00E 00 9 76E 01 6 55E 01 1 82E 01 2 21E 02 1 31E 03 3 84E 05 5 65E 07 4 60E 09 2 51E 11 101 Site coordinates 1 00E 00 9 17E 01 4 00E 01 6 16E 02 4 38E 03 1 64E 04 3 48E 06 4 82E 08 4 98E 10 3 99E 12 1 00E 00 9 99E 01 8 81E 01 3 32E 01 4 37E 02 2 62E 03 7 68E 05 1 13E 06 9 20E 09 5 01E 11 This block gives hazard values for the same site Probability of exceeding the level of intensity number 1 indicated in the first column in three different time frames Probability of exceeding the level of intensity number 2 indicated in the first column in three different time frames Chapter 11 Level Time Frame 1 Time Frame 2 Time Frame 3 Probability of exceeding the level of intensity number 3 1 00E 02 9 62E 01 1 00E 00 1 00E 00 ota in three different time frames 1 62E 02 7 33E 01 9 63E 01 9 99E 01 2 61E 02 3 38E 01 6 43E 01 8 72E 01 4 22E 02 8 60E
31. 56 65 56 85 07 89 81 74 53 51 69 70 00 54 19 62 27 74 51 55 95 55 42 71 21 74 63 63 14 44 99 13 5 Surfer 6 Binary Grid file format This section has been taken from SURFER 8 Help File char single byte short 16 bit signed integer float 32 bit single precision floating point value double 64 bit double precision floating point value The Surfer 6 format has the following layout id z11 z12 Z217 222 z31 z32 char short short double double double double double double float gt float float float 4 byte identification string DSBB which identifies the file as a Surfer 6 binary grid file number of grid lines along the X axis columns number of grid lines along the Y axis rows minimum X value of the grid maximum X value of the grid minimum Y value of the grid maximum Y value of the grid minimum Z value of the grid maximum Z value of the grid first row of the grid Each row has a constant Y coordinate The first row corresponds to ylo and the last row corresponds to yhi Within each row the Z values are ordered from xlo to xhi second row of the grid third row of the grid all other rows of the grid up to yhi 120 Chapter 13 13 6 Data Types Type of stored variables has the following codes _ Value Comments 1 Byte Short 2 Integer Corresponds to character D This Single 68 code is used for compatibility with binary Surfer 6 format Double
32. 6 5000 20 2000 20 0000 97 0000 34 0000 20 0000 REGION 11 Sismicidad difusa 2 Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 6 Long Lat Depth km 116 3000 34 5100 20 0000 113 5300 30 8200 20 0000 O Chapter 11 111 8100 28 5300 20 0000 110 5500 27 6100 20 0000 110 0000 29 0000 20 0000 110 0000 34 0000 20 0000 REGION 12 Centroam rica Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 4 Long Lat Depth km 88 2000 15 8000 5 0000 85 3000 15 8000 5 0000 85 3000 17 0000 5 0000 88 2000 17 0000 5 0000 REGION 13 Subducci n Chiapas Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 94 0180 14 5270 15 0000 92 6670 13 6200 15 0000 92 3010 14 0690 30 0000 80 Chapter 11 93 6130 15 1000 30 0000 REGION 14 Subducci n Brecha de Tehuantepec Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 5 Long Lat Depth km 95 0000 15 1970 15 0000 94 0180 14 5270 15 0000 93 6130 15 1000 30 0000 93 9870 15 3920 30 0000 95 0000 15 9100 30 0000 REGION 15 Subducci n Oaxaca Este Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 5 Long Lat Depth km
33. 89 8128 13 7787 86 1642 18 9546 85 6883 23 2546 90 7646 22 9361 94 3339 21 0250 95 8409 27 3157 100 5999 31 1380 105 8348 32 6509 111 9422 33 4472 117 0185 33 9250 ATTENUATION MODELS 225 Chapter 11 Model 1 ATCOSTAm Trunc Of class Crisis2008 NewA ttenuation A ttenuationClasses AttenuationTable Brief description Not available Original units Not available Dimension Acceleration Spectral period range 0 005 to 6 Valid distance range 5 to 500 Valid magnitude range 4 to 8 5 Type of distance metric Focal Residuals distribution LogNormal Parameter Units coefficient 1 Parameter Attenuation Table C Crisis 2008 Extra Pruebas M xico ATCOSTAm Trunc ATN Model 2 Abrahamson y Silva No HW S S Of class Crisis2008 New Attenuation A ttenuationClasses AbrahamsonA ndSilva97 Brief description Model by Abrahamon and Silva Original units cm s s Dimension Acceleration Spectral period range 0 01 to 5 Valid distance range 0 1 to 200 Valid magnitude range 4 to 7 5 Type of distance metric Rrup Residuals distribution LogNormal Parameter Units coefficient 1 Parameter Site is in the hanging wall False 299 Chapter 11 Parameter Sigma truncation 1 Parameter Soil Type 0 Parameter Style of fault 2 Model 3 NormalDaniel RRup 5 Trunc CR2007 Of class Crisis2008 NewAttenuation A ttenuationClasses AttenuationTable Brief description Not available Original units Not available Dimension A
34. A gt a M H 1 F Te js M HD 4 8 Q 0 a gt Te Tc 0 35 Chapter 5 In this case ABS Tc K is interpreted as the number of standard deviations for which integration will be performed Hence the integration will be performed between the lower limit and A ud both given in the previous table Therefore l Fa MD MED OO m Pr A gt a M H 417 Fala A H 15 M H Us 0 a gt Ano Depending on the distribution chosen Ana takes the values indicated in the previous table Note that in this case the actual truncation value for A depends on magnitude and distance In the following graph the effect of the different truncation schemes can be observed 1 00E 01 Free A truncated to 1000 gal 1 00E 02 A truncated to 500 gal A truncated to 3 Siqmas 1 00E 03 1 00E04 Exccedance rate 1 y ear 1 00E 05 200 400 600 800 1000 5 9 Measuring distances suggested by Dr R Secanell In CRISIS there are four ways of measuring site to source distances 1 Focal Rp 2 Epicentral Ripp 3 Joyner and Boore closest distance to the projection of the fault plane on the Earth s surface Ro 4 Closest distance to rupture area R up The following figure illustrates the different distances 36 Chapter 5 H is the focal depth Computation of Ry and Rip deserves no further comments Computation of Rb Up and Rg however require the specification of a rup
35. Acceleration Residual distribution LogNormal Short name Sabetta and Pugliese 1996 fault distance Developed using Italian strong ground motion data Original Ke coefficients are for PGA and spectral pseudovelocities the Brief description latter have been converted to pseaudoaccelerations This version uses Joyner and Boore distance Number of parameters 3 Parameter name Units coefficient Possible values 1E 20 to 1E 20 Parameter name Sigma truncation Possible values 1E 20 to 1E 20 Parameter name Soil type Possible values Deep alluvium Shallow alluvium Rock Reference F Sabetta and Pugliese Estimation of Response Spectra and Simulation of Nonstationary Earthquake Ground Motions Bulletin of the Seismological Society of America Vol 86 2 pages 337 352 April 1996 12 10 Sabetta and Pugliese 1996 Epicentral distance Class name Crisis2008 ExtraGMPE SabettaPugliese96EpicDist Distance metric Epicentral Valid distance range 1 to 100 Km Valid magnitude range 4 6 to 6 8 Valid period range 0 to 4 sec 111 Chapter 12 Original units Intensity dimension Residual distribution Short name Brief description Number of parameters Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values cm s s Crisis2008 New Attenuation DimensionClasses Acceleration LogNormal Sabeta and Pugliese 1996 epicentral Distance Developed using Ita
36. Chapter 1 CRISIS 2008 USER S MANUAL Chapter 1 1 Introduction 1 1 Brief description CRISIS gives a friendly environment to calculate seismic hazard The program computes seismic hazard using a probabilistic model that considers the earthquake occurrence probabilities attenuation characteristics and geographical distribution of earthquakes A friendly graphical interface facilitates data input Hazard results are given for each computation site in terms of probabilities of exceeding a given intensity value in different time frames Details on the hazard computation algorithm can be found following the link Some of the main features of CRISIS are 1 1 1 Earthquake occurrence Earthquake occurrence can be modeled either as a Poissonian process or as a non Poisson process For the Poissonian case CRISIS admits two type of magnitude frequency relations modified Gutenberg Richter law and Characteristic Earthquake For Non Poissonian occurrences CRISIS can work with a generalized model with which earthquake occurrence probabilities are explicitly given for various time frames 1 1 2 Source geometry CRISIS versions although the new point sources permit new modeling options 1 1 3 Attenuation models Attenuation models also called Ground Motion Prediction Models or GMPM relate in probabilistic terms the earthquake characteristics e g magnitude hypocentral location and the site location relative to the source with the inte
37. ISIS probabilistic relations between magnitude source site distance and intensities Each attenuation table must be in a different file and must contain the following information Attenuation table header This is a new part of the attenuation table starting with CRISIS2008 All the lines of this portion are optional so as to keep back compatibility with older attenuation tables The reader however must be aware of the default values that are used for the parameters that will be described in this numeral This header can contain up to 4 lines that give different characteristics of the attenuation table lines can be given in any order Field names including capital letters are fixed All header lines have the following format Field name Field value The following table gives the four possible header fields recognized by CRISIS 2912 Chapter 5 A string giving a brief description of the attenuation table Description This information is for A usually includes author date of E Not Description Soe presentation purposes in the publication type of earthquakes for pro E available which the model was derived and so _ on The original units will appear for information purposes in the Attenuation Data screen A string giving the units for which However o tne Not Units Sen might be relevant if a Units the model was developed uu HE A ras available Coefficient is given in order to convert from these o
38. Number of vertex 10 Long Lat Depth km 99 0000 16 1000 15 0000 98 0000 15 8000 15 0000 97 0000 15 6000 15 0000 96 0000 15 5000 15 0000 95 0000 15 2000 15 0000 95 0000 15 9000 30 0000 96 0000 16 2000 30 0000 97 0000 16 4000 30 0000 98 0000 16 6000 30 0000 98 8200 16 8100 30 0000 SRR Chapter 11 REGION 30 Chiapas nuevo Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 5 Long Lat Depth km 95 0000 15 2000 15 0000 92 6700 13 6200 15 0000 92 3000 14 0800 30 0000 94 0000 15 4000 30 0000 95 0000 15 9000 30 0000 REGION 31 Prof Interm Oeste nueva Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model NormalDaniel RRup 5 Trunc CR2007 Area source Number of vertex 14 Long Lat Depth km 105 5000 21 0000 30 0000 105 0000 20 0000 30 0000 104 0000 19 0000 30 0000 102 0000 17 9000 30 0000 101 0000 17 5000 30 0000 100 0000 17 2000 30 0000 89 Chapter 11 99 0000 16 8500 30 0000 99 0000 19 1000 100 0000 100 0000 19 2000 100 0000 101 0000 19 1000 100 0000 102 0000 19 2000 100 0000 103 3000 19 3000 100 0000 104 0000 19 8000 100 0000 105 0000 21 0000 100 0000 REGION 32 Prof int centro nueva Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model NormalDaniel RRup 5 Trunc CR2007 Area source Number of vertex 10 Long Lat Depth km 99 0000 16 8500 30 0000 98 0000 16 6000 30 0000 97 0000 16 4000 30 0000 96
39. PM CRISIS recognizes three families of GMPM Attenuation tables In these tables relations between earthquake characteristics and intensities at a site are given in terms of the following parameters magnitude structural period source site distance and depth For the first moment usually the median of a lognormal distribution the attenuation relations are matrices in which the rows run for the magnitude and the columns run for the distance Note that when using attenuation tables the relations between magnitude distance and intensity do not need to be of parametric nature since the intensity medians are given point by point for magnitude distance combinations Built In models These are popular models published in the literature in which magnitude distance and intensity are probabilistically related by usually a set of formulas or parametric equations There is a set of built in models ready to use in CRISIS and there is also the possibility of adding new models Generalized models Generalized attenuation models are non parametric probabilistic descriptions of the ground motions produced by an earthquake In the context of CRISIS a generalized attenuation model is a collection of probabilistic footprints one for each of the events considered in the analysis Each footprint gives in probabilistic terms the geographical distribution of the intensities produced by this event 5 1 Attenuation tables These tables give CR
40. S ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 7 Long Lat Depth km 110 0000 34 0000 20 0000 110 0000 29 0000 20 0000 106 0000 29 0000 20 0000 106 0000 25 0000 20 0000 104 0000 25 0000 20 0000 104 0000 29 0000 20 0000 105 0000 34 0000 20 0000 REGION 8 Cuenca de Burgos Gutenberg Richter wu Chapter 11 SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 4 Long Lat Depth km 104 0000 27 5000 20 0000 104 0000 22 0000 20 0000 99 5000 22 0000 20 0000 99 5000 27 5000 20 0000 REGION 9 Interfaz Pac fico Rivera Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 6 Long Lat Depth km 110 0000 18 5000 5 0000 106 0000 18 5000 5 0000 106 0000 20 0000 5 0000 108 0000 20 0000 5 0000 108 0000 22 0000 5 0000 110 0000 22 0000 5 0000 REGION 10 Sismicidad difusa 1 Gutenberg Richter SOURCE IS ACTIVE Sn Chapter 11 Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 14 Long Lat Depth km 105 0000 34 0000 20 0000 104 0000 29 0000 20 0000 104 0000 27 5000 20 0000 99 5000 27 5000 20 0000 99 5000 22 0000 20 0000 104 0000 22 0000 20 0000 104 0000 25 0000 20 0000 108 6500 25 0000 20 0000 106 0000 21 5000 20 0000 105 5000 20 0000 20 0000 105 0000 21 0000 20 0000 100 2800 20 5400 20 0000 9
41. SA J K L SA NT NMAG NRAD SA J K M Median value of the intensity for the J th spectral ordinate the K th magnitude and the L th distance Only if SLA J lt 0 SLA J 1 SLA J 2 SLA J NMAG Example In this example an attenuation model for NT 2 periods or measures of intensity is given Description Sample attenuation file constructed for illustration purposes 2008 Units cm sec sec Distribution EZ Dimension Acceleration 4 5 8 5 5 5 magnitudes between 4 5 and 8 5 5 0 500 0 10 1 10 distances log spaced between 5 and 500 Km focal distance 0 0 0 7 0 0 0 0 Period 0 Sigma 0 7 Amax 0 no truncation CoefH 0 1193 197 5 70 3 45 3 26 8 14 7 n3 3 2 1 1 0 3 202 5 165 6 119 4 76 9 45 5 24 9 12 4 5 4 IS 0 5 344 0 281 2 202 7 130 6 HAES 42 3 21 1 9 1 Bee 0 8 584 1 477 6 3443 221 8 131 2 71 9 2519 15 5 5 4 Es 992 0 811 1 584 7 376 7 Dorn 1224 60 9 26 4 9 1 p 0 2 0 7 0 0 0 0035 Period 0 2 Sigma variable with M Amax 0 no truncation CoefH 0 0035 250 4 203 2 1452 92 7 54 2 29 4 14 5 6 2 2 1 0 5 420 4 341 3 244 0 155 7 91 2 49 4 24 3 10 4 3 6 0 8 708 3 575 2 411 3 262 6 153 8 83 4 41 1 17 6 6 0 1 4 1193 5 969 6 6938 443 3 2599 141 0 69 5 29 7 10 2 2 4 2014 4 1637 1 1172 1 749 4 439 6 238 6 117 7 50 4 17 3 4 1 0 830 5 values of magnitude dependent Sigma one for each magnitude 0 784 0 615 0 623 0 514 24 Chapter 5 5 2 Built in attenuation models These are popular att
42. Site location Longitude Latitude Site Choose the desired intensity measure usually a spectral ordinate associated to a structural period time frame and epsilon value in the Options frame Optins gt Period epsilon eps 0 0 vi Choose in the Intensity Return period frame the value of intensity for which disaggregation results will be presented or choose the desired exceedance probability CRISIS will compute exceedance probability if intensity is given or intensity if exceedance probability is given Intensity Retrun period Intensity 1 000E03 Exc O prob Use the Grid options frame to define the size of the disaggregation chart giving the limits for magnitude and distance as well as the number of cells in each direction 66 Chapter 10 Grid options N Min Max M 10 4 4 75 mm R 10 S JO 400 00 In general disaggregation charts will be redrawn every time a parameter change is made Results will be shown in a disaggregation chart like the following Total probability in chart 1 000E 00 100 007 of total Autoscale q Qc F 1 e wech LO a i a bi E 00 JUE 01 89 133 178 222 267 311 356 400 Focal distance Km The value in each cell is the probability that the selected intensity level is exceeded in a given time frame if only earthquakes with magnitudes and distance within the cell s range are accounted for T
43. T00 max M D F LN T00 where 700 is the time elapsed since the last characteristic event Of course if F is set to zero then D becomes the expected time independent magnitude of the characteristic earthquake 10 9 3 For the Non Poisson model Give by double clicking the name of the nps file that stores the non Poissonian earthquake occurrence probabilities associated to this source 10 10 Attenuation data Button Menu Input Attenuation data This screen allows entering information about the attenuation relations to be used in the hazard analysis In general an attenuation relation describes the probabilistic link between earthquake magnitudes source to site distance and intensity see Probabilistic interpretation of attenuation relations In general CRISIS must know what relation to use to attenuate earthquakes generated in each source In principle each source could have its associated attenuation relation In practice only a few different attenuation relations are used in a particular analysis e g one for subduction events and another for shallow crustal earthquakes CRISIS can perform a simultaneous hazard analysis for several intensity measures e g PGA and spectral accelerations for different periods Therefore CRISIS must also know for how many different intensity measures the analysis will be carried out and the associated attenuation relations Frequently the different intensity measures are spectral re
44. a source Number of vertex 7 Long Lat Depth km 93 0000 15 2000 5 0000 92 4000 14 4500 5 0000 90 0000 14 5000 5 0000 89 0000 14 5000 5 0000 88 0000 15 1000 5 0000 88 0000 16 3000 5 0000 89 5500 15 2000 5 0000 REGION 41 Motagua 2 Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 7 Long Lat Depth km 93 0000 15 2000 10 0000 92 4000 14 4500 10 0000 90 0000 14 5000 10 0000 89 0000 14 5000 10 0000 88 0000 15 1000 10 0000 88 0000 16 3000 10 0000 89 5500 15 2000 10 0000 95 Chapter 11 REGION 42 Motagua 3 Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 7 Long Lat Depth km 93 0000 15 2000 15 0000 92 4000 14 4500 15 0000 90 0000 14 5000 15 0000 89 0000 14 5000 15 0000 88 0000 15 1000 15 0000 88 0000 16 3000 15 0000 89 5500 15 2000 15 0000 REGION 43 Polochic 1 Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 4 Long Lat Depth km 94 0000 16 0000 5 0000 93 0000 15 2000 5 0000 89 5500 15 2000 5 0000 88 0000 16 3000 5 0000 96 Chapter 11 REGION 44 Polochic 2 Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 4 Long Lat Depth km 94 0000 16 0000 10 0000 93 0000 15 2000 10 0000 89 5500 15 2000 10 0000
45. alue of the grid ylo yhi ylo is the minimum Y value of the grid yhi is the maximum Y value of the grid zlo zhi zlo 1s the minimum Z value of the grid zhi 1s the maximum Z value of the grid grid row 1 These are the rows of Z values of the grid organized in row order Each row has a constant Y coordinate Grid row 1 corresponds to ylo and the last grid row corresponds to yhi Within each row the Z values are arranged from xlo to xhi grid row 2 grid row 3 The following example grid file is ten rows high by ten columns wide The first five lines of the file contain header information X ranges from 0 to 9 Y ranges from 0 to 7 and Z ranges from 25 to 97 19 The first Z value shown corresponds to the lower left corner of the map and the following values correspond to the increasing X positions along the bottom row of the grid file This file has a total of 100 Z values DSAA 10 10 0 0 9 0 0 0 7 0 25 00 97 19 91 03 77 21 60 55 46 67 52 73 64 05 41 19 54 99 44 30 25 00 96 04 81 10 62 38 48 74 57 50 63 27 48 67 60 81 51 78 33 63 92 10 85 05 65 09 53 01 64 44 65 64 52 53 66 54 59 29 41 33 94 04 85 63 65 56 55 32 73 18 70 88 55 35 76 27 67 20 45 78 97 19 82 00 64 21 61 97 82 99 80 34 58 55 86 28 75 02 48 75 91 36 78 73 64 05 65 60 82 58 81 37 61 16 89 09 81 36 54 87 119 Chapter 13 86 31 77 58 67 71 68 50 73 37 74 84 65 35 95 55 85 92 55 76 80 88 75 56 74 35 72 47 66 93 75 49 86 39 92 10 84 41 55 00 74 77 66 02 70 29 75 16 60
46. and Boore 2003 Relations for subduction zone interface and inslab Brief description earthquakes for the Cascadia and other regions with 5 damping ratio Number of parameters 5 Parameter name Units coefficient Possible values 1E 20 to 1E 20 Parameter name Sigma truncation Possible values 1E 20 to 1E 20 Parameter name Fault type Possible values In Slab Interface Parameter name Ground type Possible values NERHP E NERHP D NERHP C NERHP B Parameter name Zone Possible values Japan Cascadia General Reference G Atkinson and D Boore Empirical Ground Motion Relations for Subduction Zone Earthquakes and Their Application to Cascadia and Other Regions Bulletin of the Seismological Society of America Vol 93 4 Pages 1703 1729 August 2003 12 14 Garc a et al 2005 Class name Crisis2008 New Attenuation A ttenuationClasses DGarcia05 Distance metric Rrup Valid distance range 0 1 to 400 Km Valid magnitude range 5 to 7 5 Valid period range 0 to 5 sec Original units cm s s Intensity dimension Crisis2008 NewA ttenuation DimensionClasses A cceleration Residual distribution LogNormal Short name Garc a et al 2005 Ground motion prediction model for the horizontal spectral Brief description acceleration produced by intra slab subduction earthquakes obtained with intermediate depth Mexican earthquakes Number of parameters 2 Parameter name Units coefficient Possible values E 20 to 1E 20 Parameter name Sigma truncation
47. and Faccioli 2008 for 5 damping and unspecified ground and fault types Number of parameters 2 Parameter name Units coefficient Possible values 1E 20 to 1E 20 Parameter name Sigma truncation Possible values 1E 20 to 1E 20 Reference C Cauzzi and E Faccioli Broadband 0 05 to 20 s prediction of displacement response spectra based on worldwide digital records J Seismol 12 Pages 453 475 April 2008 DOI 10 1007 s10950 008 9098 y 2008 12 7 Cauzzi and Faccioli 2008 Full model Class name Crisis2008 NewA ttenuation A ttenuationClasses CauzziFaccioli08 Distance metric Focal Valid distance range 6 to 150 Km Valid magnitude range 5 to 7 2 Valid period range 0 033 to 20 sec 109 Chapter 12 Original units cm s s Intensity dimension Crisis2008 New Attenuation DimensionClasses Acceleration Residual distribution LogNormal Short name Cauzzi and Faccioli 2008 Empirical equations for attenuation of horizontal spectral Brief description accelerations for crustal earthquakes in tectonically active zones Number of parameters Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values Parameter name Possible values worldwide 6 Damping ratio 30 20 10 5 Units coefficient 1E 20 to 1E 20 Ground type D C B A Unspecified In this case Vs30 applies Fault type Strike slip Reverse Normal Unspecif
48. aps exceedance probability curves and uniform hazard spectra with the following options 10 15 1 Types of hazard maps Two types of hazard maps can be generated 1 If switch is selected the map will show intensities associated to a fixed exceedance probability in a given time frame Give the required exceedance probability and time frame the corresponding boxes 2 If switch 4e is selected the map will show exceedance probabilities associated to fixed values of time frame and intensity Give the required values of time frame and intensity in the corresponding boxes In both cases the map will be generated for the intensity measure chosen in the box Intensity 10 15 2 Intensity measure Int T 0 040 Select in this combo box the intensity measure for which maps and hazard curves are to be generated 63 Chapter 10 10 15 3 Time frame i Tf250 0 WENS Select in this combo box the time frame for which maps and hazard curves are to be generated 10 15 4 City Selection City Select a city of the list in order to see 1 The hazard curve at the city for the selected intensity measure and time frame 2 Depending on whether the fixed intensity or the fixed exceedance probability switch is selected e The uniform hazard spectrum e A graph showing the exceedance probabilities associated to a fixed value of spectral intensity and time frame 10 15 5 Exceedance probability Exceed prob 1 00E 0
49. ard will be performed only for those points of the grid which are inside at least one of the polygons The polygon must be described in counter clockwise order Select the Start polygon command to start drawing the polygon Each click of the mouse defines a point of the polygon Choose End polygon command to close the polygon Command Delete selected polygon allows you to remove the selected polygon To see the selected polygon choose a polygon number and press the command draw The polygon with the widest line is the selected polygon 10 5 Geometry of the sources Button amp Menu Input Source Geometry This screen allows entering the geometry of each seismic source Sources can be areas lines or points 10 5 1 Source operations Add Area Use this button to add an area source to the hazard model Add Fault Use this button to add a line source to the hazard model Delete Delete the active source Rename Rename the active source Import Import fault geometry from a shape file or from an ssg file Name Select the active source using this combo box 54 Chapter 10 Source is alive Select if the source is alive or not A source that is not alive is simply ignored in the hazard computations The total number of sources and the number of the active source will be shown in the corresponding labels 10 5 2 Source vertex For area or line sources use this grid control to give the coordinates of the vertex of the active so
50. cceleration Spectral period range 0 005 to 6 Valid distance range 0 01 to 500 Valid magnitude range 4 to 8 5 Type of distance metric Focal Residuals distribution LogNormal Parameter Units coefficient 1 Parameter Attenuation Table C Crisis 2008 Extra Pruebas M xico NormalDaniel RRup 5 Trunc CR2007 atn PROPERTIES OF THE SOURCES REGION 1 Baja California intraplaca norte Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S 73 Chapter 11 Area source Number of vertex 10 Long Lat Depth km 119 2500 34 5600 10 0000 118 1250 33 0600 10 0000 117 0000 31 5600 10 0000 115 8750 30 0600 10 0000 114 7500 28 5600 10 0000 113 5800 29 4400 10 0000 114 7050 30 9400 10 0000 115 8300 32 4400 10 0000 116 9950 33 9400 10 0000 118 0800 35 4400 10 0000 REGION 2 Baja California intraplaca sur Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 10 Long Lat Depth km 114 7500 28 5600 10 0000 113 6250 27 0600 10 0000 112 5000 25 5600 10 0000 111 3750 24 0600 10 0000 110 2500 22 5600 10 0000 109 0800 23 4400 10 0000 110 2050 24 9400 10 0000 74 Chapter 11 111 3300 26 4400 10 0000 112 4550 27 9400 10 0000 113 5800 29 4400 10 0000 REGION 3 Baja California interplaca norte Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source
51. chic 2 The maximum magnitude in the region is larger than the maximum valid magnitude of GMPE Abrahamson y Silva No HW S S 7 8 gt 7 5 Region 45 Polochic 3 The maximum magnitude in the region is larger than the maximum valid magnitude of GMPE Abrahamson y Silva No HW S S 7 8 gt 7 5 The integration distance Rmax is greater than the maximum valid distance of GMPE Abrahamson y Silva No HW S S 500 gt 200 ok oke ok ok ok akk ok ok ok ok oke ak ok ok ok ok ok ok oke oke ok ok ok ok ok ok ok ok oke oft ok ok ok ok ok ok ok ok K ok ok ok ok ok ok ok oke oke ok ok ok ok ok ok ok oke oke ok ok ok ok ok ok ok ok oke ok ok 2K ok 11 2 Example GRA file This files gives hazard results in terms of probabilities of exceeding intensity values in different time frames In the following example we show the portion of the file that corresponds to only one site In the cases of computations for several sites blocks of data similar to the one presented will be written for each site The example presented was computed for 3 intensity measures each with 10 intensity levels and for 3 different time frames CRISIS 2009 E Program name and version 17 12 2009 00 00 03 58 55 a m Date and time of the run File header Prueba No Poissoniana Name of the run 100 Chapter 11 Site Intensity 1 Level 1 00E 02 1 54E 02 2 39E 02 3 68E 02 5 69E 02 8 79E 02 1 36E 03 2 10E 03 3 24E 03 5 00E 03 Intensity 2 Level 1 00E 02 1 62E 0
52. ciated to fixed values of time frame and spectral intensity 10 15 10 Zoom Tools es Use these tools to zoom in and zoom out from the map or to define a rectangular area to zoom in 10 15 11 Draw options Draw options Grid Sources C Site effects Check in this frame the drawing items that will appear in the hazard map 10 15 12 Color scale AutoScale 65 Chapter 10 Select in this section whether or not you want CRISIS to auto scale the colors associated to the map In case that auto scale is not chosen the user must give upper and lower values for the scaling process Also moving the mouse along the color scale will indicate the numerical values associated to a particular color 10 16 Magnitude Distance disaggregation results CRISIS can generate exceedance rates disaggregated by magnitude distance and epsilon value The program presents these values graphically in the disaggregation screen To see disaggregation results in this screen the following operations are needed Select the site for which results are desired by pointing to 1t with the mouse in the right hand side picture box which shows either the computation grid or the list of sites The actual point used for the disaggregation computations will be the one belonging to the grid or list of computation sites that is the closest to the point clicked by the user The actual point used for disaggregation will be indicated in the Site Location frame
53. complexity 5 3 Generalized attenuation models Generalized attenuation models are non parametric probabilistic descriptions of the ground motions produced by an earthquake Ground motions descriptions obtained when using traditional attenuation models also called ground motion prediction equations GMPE are generally functions of earthquake magnitude and source to site distance 25 Chapter 5 But generalized attenuation models are not explicit functions of magnitude and distance They are simply probabilistic footprints of the ground motions produced by an individual event In the context of CRISIS a generalized attenuation model is a collection of probabilistic footprints one for each of the events considered in the analysis Each footprint gives in probabilistic terms the geographical distribution of the intensities produced by this event For a given event the footprint consists of several pairs of grids of values Each pair of grids is associated to one of the intensity measures for which hazard is to be computed CRISIS needs two grids for each intensity measure because as with other ground motion prediction models the intensity caused by the earthquake is considered probabilistic so CRISIS requires two statistical moments in order to fix a probability density function of the intensity caused by an earthquake at a particular location For instance assume that one generalized attenuation model will be used to describ
54. d K 4 are constants given by the user or chosen from a built in set of constants In the case of area sources and point sources CRISIS will assume that the earthquake takes place in a plane defined by the source geometry and that the rupture area will be a circle within this plane with area A and in consequence with radius r A n 3 In the case of line sources CRISIS will assume that the earthquake takes place along a line defined by the source geometry and that the rupture length will be centered at the hypocenter CRISIS recognizes also a particular type of magnitude rupture size relation indicated by K 1 for area sources and K 1 for line sources This type of source breaks completely for every earthquake regardless of magnitude value In view of this there is only one hypocenter associated to the area or to the line This hypocenter is the point within the source closest to the computation site 238 Chapter 6 6 GeoSeismAtt Combinations The different geometry seismicity attenuation models give raise to the combinations listed in the following table Follow the link to obtain a more detailed explanation of each combination In the table Normal attenuation refers to attenuation tables or user coded models while General refers to generalized attenuation models Also GR and C seismicity refer to Gutenberg Richter and Characteristic Earthquake models respectively while NP denotes non Poissonian mod
55. de distance disaggregation These results indicate which combinations of magnitude and distance contribute more to the seismic hazard at a site for a given intensity measure for a given time frame and at certain level of intensity a in this case Let s say that hazard has been disaggregated leading to a matrix of Ng rows one for each magnitude range and Nr columns one for each distance range The contents of each cell must be such that the following relation is satisfied Nr Nm Pr A al7 II Pim 2 WA m 1 In other words the original non exceedance probability must be equal to the product of the non exceedance probabilities disaggregated for each magnitude distance bin This means that oppositely to what happens with intensity exceedance rates which are additive non exceedance probabilities or exceedance probabilities are not additive but multiplicative in the sense expressed by equation 2 above In view of this when seeing CRISIS disaggregation results the user must not expect that the exceedance probabilities associated to each cell used for the disaggregation add up to the total exceedance probability computed for the same site intensity value and time frame As shown by the previous paragraphs arithmetic of exceedance probabilities is more complex to that of intensity exceedance rates used in conventional hazard studies Epsilon disaggregation In occasions it is interesting to know which portions of the intensity pr
56. e Numbering of the vertex of the polygon must be done counter clockwise in this plane when looked from above the surface of the Earth If there are vertical planes CRISIS will try to triangulate the area in the XZ plane so numbering of vertex must be done counterclockwise in this plane Finally CRISIS will try to triangulate in the YZ plane There are some bizarre source geometries that cannot be well resolved by CRISIS for instance an L shaped vertical plane In these cases an error will be reported 13 Chapter 3 3 2 Line source This option defines the active source as a fault line source Line sources are in general polylines defined by the 3D coordinates of their vertexes The example below shows a fault source of 4 vertexes located in the XZ plane with varying depth 3 3 Point sources This option defines the active source as a collection of point sources in which each vertex will be a point source Each point is a potential earthquake hypocenter and is defined in the newer versions of CRISIS in terms of the following parameters 1 Longitude latitude and depth in Km of the point 2 A unit vector normal to the rupture plane associated to each point source This unit vector is relevant only when the ground motion prediction model associated to this source uses distance measures for which the rupture area is relevant that is Bag or Rep see the definition of source to site distances in this link Since poin
57. e the intensities caused by 10 different earthquakes Also assume that the hazard analysis is being made for seven intensity measures for instance the response spectral ordinates for seven different structural periods For this example each event will be described by 14 different grids two for each intensity measure the first one giving the geographical distribution of the median intensity and the second one given the geographical distribution of the standard deviation of the natural logarithm of the intensity Hence a total of 140 grids will form the generalized attenuation model of this example It would be natural that all the 140 grids covered exactly the same region however there are no restrictions at this respect From this description it is clear that it would be extremely difficult to perform a hazard study of regional or higher size using generalized attenuation models Usually a hazard model of regional size contains thousands of events and the task of geographically describing the intensities caused by all of them in non parametric form would be titanic Rather generalized attenuation models will very likely be used for local studies for which the relevant earthquakes are few and can be clearly identified In this case the grids of required values geographical distribution of statistical moments of one or more intensity measures for each event can be constructed using for instance advanced ground motion simulation techniqu
58. ecompute branches that have already been computed Results of the logic tree combination will be given in the form of a new hazard model with an associated dat file that will have the base name of the ltc file that described the combination but with the extension dat NU Chapter 10 This new hazard model can be loaded into CRISIS and the corresponding hazard results can be analyzed with CRISIS hazard maps exceedance probability curves uniform hazard spectra as if they were the results of a regular dat file Disaggregation results however can not be obtained for the hazard resulting from the logic tree combination 10 14 Validate data save and start execution Button B Menu Run Validate and Run This command allows you to execute a run after you have finished with the input If data are still required when this command is executed CRISIS will issue a message showing the data required Enter the data needed save the data file and choose Run to initiate execution Also in some cases CRISIS will issue a set of warnings pointing to possible inconsistencies in the input data While these warning do not prevent the user from computing hazard CRISIS issues them so the user is aware of potential problems After a successful run a success screen appears showing which output files were generated and where they are located 10 15 Hazard maps This command is enabled after a successful CRISIS run and allows seeing hazard m
59. ects are present then 4 5 7 1 1 Note that while the median intensity is modified to account for site effects the uncertainty in the intensity after site effects is the same that it was before site effects The user has to give CRISIS means to obtain the amplification factors A S 7 These factors are given to CRISIS by means of two binary files that will be described in the following paragraphs Both files must have the same base name but different extensions 1 Predominant period file This is a binary grid file in Surfer 6 binary format grd The main purpose of this file is to locate in space the grid for which amplification factors are given as well as to give the grid s resolution This grid contains as z values the predominant ground periods associated to each point of the grid Points with positive periods are interpreted as part of the area for which site effects are known Points with negative periods are interpreted as outside the area for which site effects are known Hence for these points the amplification factor will always be 1 regardless of period and ground motion level Extension grd is required for this file For instance MySiteEffects grd 2 Amplification factors file This is also a binary file with extension ft For instance MySiteE ffects ft This file contains the amplification factors themselves As we have indicated amplification factors depend on site location structural period and ground motion le
60. els Option 1 This is an old CRISIS option which is valid always Option 2 In this new option a source is geometrically modeled as a line or as an area which means that every point that belongs to the source has the same probability of being a hypocenter this is the usual assumption when using line or area sources in CRISIS Attenuation as in older CRISIS option is modeled with a parametric description a normal GMPM However the new option permits stipulation of earthquake occurrence probabilities with a generalized non Poissonian model and not through a parametric frequency magnitude relation Gutenberg Richter or Characteristic Earthquake The occurrence probabilities given in the non Poissonian seismicity file correspond to the whole source that is they are the probabilities of having and earthquake of given magnitude and in a given time frame in anywhere in the source Using its standard spatial integration scheme CRISIS will sample the source in order to compute hazard accounting for all possible locations of the earthquake within the source Note however that when probabilities are specified for the whole source probabilities associated to segments of the source or sub sources are not univocally defined The following approach is adopted by CRISIS in order to define the occurrence probabilities associated to sub sources of known sizes Assume first that we have a conventional Poissonian source The probability of having i
61. ents of classes internal to CRISIS The tenth method is more complex and it is the core of the GMPM Its purpose is to determine the probabilistic intensity that is generated given hypocentral characteristics that include hypocentral location and earthquake magnitude and receiver location Function getA cceleration requires the following parameters Period Double The value of the period for which intensity is requested The location of the site for which intensity is being determined expressed SiteKn PointType in the form of x y and z distances in Km with respect to the first vertex of the source to which the hypocenter belons SiteInDegrees PointType The location in degrees of the site for which intensity is being determined An element of class hypocenter defining the location and properties of the h t H t NE DU f Een Li hypocenter that generates the event for which intensity is being determined Again in column Type of variable returned of the previous table the variable types written in green are elements of classes internal to CRISIS A detailed fully documented example of the construction of a ground motion prediction model implementing the methods just described is presented in the form of VB Net project GMPETutorial that is distributed as part of CRISIS instalaltion package with the name GMPETutorial zip 5 5 Units coefficient All GMPM used by CRISIS attenuation tables built in models and generalized models give p
62. enuation equations published in the literature that the user can choose as GMPM for CRISIS These models relate in probabilistic terms earthquake magnitude and a certain distance metric with the intensity at a site CRISIS can handle 4 types of distance metrics Also many of these attenuation equations require specification of additional parameters that the user must select such as style of faulting and soil type The following GMPM are built in into CRISIS Models for active tectonic regions with shallow seismicity e Abrahamson and Silva 1997 e SEA99 1999 e Cauzzi and Faccioli 2008 Full model e Akkar and Bommer 2007 e Boore and Atkinson 2008 e Campbell and Bozorgnia 2003 e Cauzzi and Faccioli 2008 Simple version e Cauzzi and Faccioli 2008 Vertical 5 damping e Sabetta and Pugliese 1996 Fault Distance e Sabetta and Pugliese 1996 Epicentral Distance e Pasolini et al 2008 Macroseismic intensity Subduction zones e Arroyo et al 2010 e Youngs et al 1997 e Atkinson and Boore 2003 e Garcia et al 2005 Note that besides the parameters that each GMPM uses such as soil type or style of faulting all built in GMPM contain two extra parameters called Units coefficient and Sigma truncation The first one is used to change the original units of the model see details while the second one is used to truncate the probability distribution of the residuals see details level of
63. es Generalized attenuation models are given to CRISIS in the form of binary generalized attenuation files GAF The reason for requiring the GAF s to be in binary format is the computational need of having random access to individual intensity values This need is basically dictated by computational speed The following tables illustrate the detailed format of GAF s Custom file Give a synthetic description of the main String Variable features of the GAF description Original Units String Variable Intensity physical String Variable dimension 26 Chapter 5 Description Data type short integer single double long Probability distribution assigned to intensity normal lognormal beta gamma Number of intensity measures number of periods Number of sources locations Number of magnitudes per location Number of statistical moments of intensity stored Period 1 Period 2 Period Number of Intensity measures Magnitude representative of bin 1 Magnitude representative Type Integer Integer Integer Integer Integer Integer Double Double Double Double Double Length 27 Comments Period values are required because the user might want to compute for arbitrary periods Magnitude values are required to compute occurrence rates when GR or Characterisitic models are used When a non Poissonian seismicity file is given these magnitudes are irrele
64. gation charts can be saved using button Save which will save in a text file the currently displayed chart settings as well as the matrix of disaggregated hazard values 10 17 Help Opens the help file of CRISIS 68 Chapter 11 11 Output Files Upon the user s selection CRISIS can generate several output files The possible output files are Results file res This file contains a printout of the name of the run the values assigned to the variables characteristics of the attenuation models geometrical and seismicity description of the sources the data defining the computation grid etc It also gives a summary of the computations for each site indicating which sources are of interest the site and which sources were skipped The computer times are also written If the users chooses to do so this file also gives the final results that is exceedance probabilities for each time frame site and type of intensity See an example of the res file Graphics file gra This file contains a brief identification header and the exceedance rates for the types and levels of intensity requested This file can be used as input file to plot intensity versus exceedance rate curves See an example of the gra file Source by source results fue fue file Additionally CRISIS will generate binary files one for each intensity measure used in the analysis to be able to generate its own maps 11 1 Example RES file
65. generalized non Poissonian model an ground motion characteristics are given with a generalized attenuation model This option is the only one in which generalized attenuation models can be used Note that when using this type of ground motion model locations of earthquake hypocenters are in principle unknown and irrelevant In consequence specification of a source location is also in principle irrelevant However there are two reasons why a source location must be specified 1 when constructing a hazard model with CRISIS interface it is useful for the analyst to have a visual feedback of the source location and 2 for hazard disaggregation purposes CRISIS must know the location to which the hazard coming from all events has to be assigned For the purpose of dissaggregation earthquake location is conventionally considered to be the geometrical center of the source area or line On the other hand since also earthquake magnitudes are fixed and irrelevant in generalized attenuation models and each set of grids represents an individual event it would be impossible to associate to this events seismicity parameters using parametric descriptions In view of this the only possibility is that earthquake occurrence probabilities are assigned using non Poissonian generalized models Compatibility conditions in this option are the following 1 The number of sources in the generalized attenuation model gaf must be the same that the number
66. he color scale will adjust automatically if Autoscale is selected The user however can change the upper red color and lower white color limits of the scale once the Autoscale option is disactivated On top of the disaggregation chart CRISIS shows the following legend Total probability in chart 0 000E 00 100 00 of total This legend indicates that with the current grid settings magnitude and distance limits and the selected epsilon level the total probability of exceedance is a certain percentage of the total exceedance probability for all magnitudes and distances and epsilon equal to minus infinity However the total probability is computed by interpolation of a previously computed hazard curve for the site If computation of this hazard curve was made for a small number of intensity levels the interpolation will not be exact and percentages reported by the legend could be somehow inexact To solve this problem simply compute the hazard curves with a larger number of intensity levels 67 Chapter 10 When seeing CRISIS disaggregation results the user must not expect that the exceedance probabilities associated to each cell used for the disaggregation add up to the total exceedance probability computed for the same site intensity value and time frame As shown in this link arithmetic of exceedance probabilities is more complex to that of intensity exceedance rates used in conventional hazard studies Disaggre
67. here Pr A a M R p is the probability that intensity a is exceeded given that an earthquake of magnitude M took place at source k that is separated from the site of interest by a distance R Please note that this probability depends only on magnitude and source to site distance and it is normally computed giving a probabilistic interpretation to intensities predicted by ground motion prediction models or attenuation relations We also note that implicit in equation 1 is the assumption that exceedances of intensity values at source k given that an earthquake of magnitude M occurred are independent from each other This is the reason why the non exceedance probability of a given that s events of magnitude M took place at source k can be computed as 1 Pr 4 gt a M ROP Seismic hazard contained in equation is more easily expressed in terms of non exceedance probabilities Chapter 2 Ns Pr 4 lt a M T k Y P s M T Pr 4 lt a M R 2 s 0 Equation 2 gives the non exceedance probability of intensity value a given that only earthquakes of magnitudeM took place The non exceedance probability of a associated to the occurrence of earthquakes of all magnitudes at source k in the next T years can be computed as Nm Pr 4 lt a T k Pr 4 lt a M T k 3 i where Nm is the number of magnitude bins into which the earthquake occurrence process has been discretized Again we have used the independence hypothesis among earthquake
68. hquake with magnitude M took place at a distance R from the site is given by Pe a T M R 1 expl A4 M T p a M R 1 where p alM R is the exceedance probability of intensity level a given that a magnitude M event occurred at a distance R from the site and AA M is the Poissonian magnitude exceedance rate associated to the magnitude range also called magnitude bin characterized by magnitude M Note that p 1 a M R depends only on magnitude and site to hypocenter distance This probability does not depend on earthquake occurrence probabilities In turn AA M can be computed as AAM AM AM 2 A M AM I2 2 where it is implicit that the magnitude bin characterized by magnitude M goes from M AM 2 to M AM 2 For the modified Gutenberg Richter model the earthquake magnitude exceedance rate is given by xp 4M exp BV MM A expl T Expl PM M SM lt M 3 exp 8M exp 8M 17 Chapter 4 where A is the exceedance rate of magnitude M B is a parameter equivalent to the b value for the source except that it is given in terms of the natural logarithm and M is the maximum magnitude for the source CRISIS can account for uncertainty in both B and M In this case the user must give the coefficient of variation of D and give parameters that describe the uncertainty in the maximum magnitude 4 2 Uncertainty in the maximum magnitude CRISIS regards M E the maximum magnit
69. ic There are many epistemic uncertainties in any seismic hazard assessment including the characteristics of the seismic source zones be these area zones or specific faults the model for the recurrence relationship and the maximum earthquake magnitude In PSHA the established procedure is to incorporate the epistemic uncertainty into the calculations through the use of logic trees The logic tree is set up so that for each of the steps in which there is epistemic uncertainty separate branches are added for each of the choices that the analyst considers feasible To each of these a normalized weight is assigned that reflects that analyst s confidence that this is the most correct model and the weights are generally but not necessarily centered on a best estimate The hazard calculations are then performed following all the possible branches through the logic tree each analysis producing a single hazard curve showing ground motion against annual frequency of exceedance The weighting of each hazard curve is determined by multiplying the weights along all the component branches For every branch added to a logic tree a penalty is paid in terms of additional calculations if there are multiple branches for each component of the hazard analysis the total number of hazard calculations can rapidly become very large For this reason it is advisable to avoid using branches with very small differences between the options that they carry in cases when
70. ic hazard in the newer versions is the probability of experiencing peak ground acceleration greater or equal than 0 2 g in the next 50 years at a given location This change was made in order to allow users to introduce in the computations probabilities of earthquake occurrences derived from non Poissonian models Poissonian computations however are still possible since one can regard this case as a particular case of the non Poisson computations We will se later how to compute the probabilities now required by CRISIS from conventional Poissonian models In order to compute seismic hazard the territory under study is first divided into seismic sources according to geotectonic considerations in most cases it is assumed that within a seismic source an independent earthquake occurrence process is taking place For each seismic source earthquake occurrence probabilities are estimated by means of statistical analysis of earthquake catalogs In the more general case earthquake occurrence probabilities must stipulate the probability of havingsevents s 0 1 Ns of magnitude M in the following 7 years at a given source k We will denote these probabilities as P SM T D they completely characterize the seismicity of source k Seismic hazard produced by an earthquake of magnitude M ata single point source say the k th and for the next d years can be computed as Pr 4 gt a M T k 1 Y P s M T 1 Pr 4 gt a M R 1 s 0 w
71. ied Sigma truncation 1E 20 to 1E 20 Vs30 1E 20 to 1E 20 Reference C Cauzzi and E Faccioli Broadband 0 05 to 20 s prediction of displacement response spectra based on worldwide digital records J Seismol 12 Pages 453 475 April 2008 DOI 10 1007 s10950 008 9098 y 2008 12 8 Pasolini et al 2008 Class name Crisis2008 ExtraGMPE PasoliniEtA108 Distance metric Epicentral Valid distance range 0 to 140 Km Valid magnitude range 4 to 7 Valid period range 0 to 0 sec Original units Mercalli Cancani Sieberg Intensity Crisis2008 NewA ttenuation DimensionClasses MCSI Residual distribution Normal Intensity dimension Short name Pasolini et al 2008 Relationships for attenuation of seismic intensity in Italy Bu uet using the Parametric Catalog of Italian Earthquakes CPTI04 and the related database of macroseismic intensity observations in Italy DBMIO4 110 Chapter 12 Number of parameters 0 Reference Pasolini et al The Attenuation of Seismic Intensity in Italy Part II Modeling and Validation Bulletin of the Seismological Society of America V ol 98 2 pages 692 708 April 2008 DOI 10 1785 0120070021 12 9 Sabetta and Pugliese 1996 Fault distance Class name Crisis2008 ExtraGMPE SabettaPugliese96FaultDist Distance metric JyB Valid distance range 0 to 100 Km eu ASES Valid period range 0 01 to 4 sec Original units cm s s Intensity dimension Crisis2008 New Attenuation DimensionClasses
72. ile formats in use by CRISIS 13 1 Format of modGRN grids modGRN format is an extension of binary Golden Surfer 6 format While binary Golden Surfer 6 format consists on a header and a succession of values stored as 4 byte single numbers modGRN format allows to store the values with other types of variables The only difference between modGRN and binary Golden Surfer 6 formats is the first byte in the header that in the case of the modGRN format indicates what type of variables are being stored The structure of a modGRN binary file is the following Header ZU ZOON 7219732 GridHeader Grid header The type is that indicated by grid First grid row Each row has constant Y header byte ID It can be byte value First row corresponds to Ylo and short integer single double or the last row corresponds to Yhi Within a long row values are ordered form Xlo to Xhi The type is that indicated by grid header bye D Second grid row The type is that indicated by grid a header byte ID ur iud The type is that indicated by grid The remaining rows until reaching that header byte ID corresponding to Y hi 13 2 Grid Header This is the header of modGRN files Its structure 1s very similar to that of the header of binary Surfer 6 files except that the first byte indicates what type of variable will be stored IDD Ny Xlo Byte Short Short Double The first byte indicates what type of variables will be stores See c
73. in file This description was taken from ESRI Shapefile Technical Description an ESRI White Paper July 1998 See this report for further information on shapefiles 13 4 Surfer 6 ASCII Grid Format This section has been taken from SURFER 8 Help File DSSA grid files contain five header lines that provide information about the size and limits of the grid followed by a list of Z values The fields within DSSA files must be space delimited The listing of Z values follows the header information in the file The Z values are stored in row major order starting with the minimum Y coordinate The first Z value in the grid file corresponds to the lower left corner of the map This can also be thought of as the southwest corner of the map or more specifically the grid node of minimum X and minimum Y The second Z value is the next adjacent grid node in the same row the same Y coordinate but the next higher X coordinate When the maximum X value is reached in 118 Chapter 13 the row the list of Z values continues with the next higher row until all the rows of Z values have been included The general format of a DSSA grid file is Id The identification string DSAA that identifies the file as an ASCII grid file nx ny nx is the integer number of grid lines along the X axis columns es ny is the integer number of grid lines along the Y axis rows xlo xhi xlo is the minimum X value of the grid xhi is the maximum X v
74. inimum Distance Triangle Size ratio 4 2 2 2 Line sources In this case the subdivision is performed by bi partition of a fault source segment again until one of the following criteria are met 1 The size of the line is smaller than the value Minimum triangle size given by the user 2 The ratio between the site to source distance and the line size is larger than the value Minimum Distance Triangle Size ratio given by the user The site to source distance is measured from the computation site to the midpoint of the line whose possible subdivision is being examined The size of the line is simply its length The seismicity associated to each centroid is proportional to the line s length 11 12 Chapter 3 3 Source geometry In general sources are the portions of the Earth in which it is possible that earthquakes take place CRISIS accepts source geometries of the following three types 1 Areas polygons 2 Faults polylines 3 Points 3 1 Area source This option defines the active source as an area source In general area sources are polygons defined by the 3D coordinates of their vertex In the example below we have a 3D polygon with 8 vertexes simulating a dipping plate with varying dip angle Vertical planes are allowed In the case of area sources in order to perform the spatial integration CRISIS will divide the polygon into triangles It first checks if triangulation can be made in the XY plan
75. int centro nueva 4 500 1 71E 00 1 576 0 110 7 900 0 200 Prof int Este nueva 4 500 2 78E 00 1 761 0 087 7 800 0 200 Petrolera 4 500 6 05E 01 3 050 0 209 6 700 0 500 Golfo 4 100 1 05E 01 2 704 0 459 6 500 0 500 Eje volc nico 4 500 2 49E 01 1 884 0 223 7 200 0 300 Intraplaca 4 500 1 44E 00 1 889 0 124 6 500 0 500 Chiapas Volc n 4 500 1 61E 00 2 005 0 119 7 000 0 200 Profundos Chiapas 4 500 2 52E 00 2 207 0 093 7 500 0 300 Motagua 1 5 000 2 77E 01 2 234 0 309 7 800 0 000 Motagua 2 5 000 2 77E 01 2 234 0 309 7 800 0 000 98 Chapter 11 Motagua 3 5 000 2 77E 01 2 234 0 309 7 800 0 000 Polochic 1 5 000 1 20E 01 2 187 0 105 7 800 0 000 Polochic 2 5 000 1 20E 01 2 187 0 105 7 800 0 000 Polochic 3 5 000 1 20E 01 2 187 0 105 7 800 0 000 Characteristic model sources Source name Med T TO D F sM MO Mu Subducci n Chiapas 18 700 20 000 7 500 0 000 0 270 7 000 8 400 Subducci n Brecha de Tehuantep 24 700 200 000 7 500 0 000 0 270 7 000 8 400 Subducci n Oaxaca Este 24 800 26 000 7 500 0 000 0 270 7 000 8 400 Subducci n Oaxaca 1 39 400 13 000 7 500 0 000 0 270 7 000 8 400 Subducci n Oaxaca 2 77 900 63 000 7 500 0 000 0 270 7 000 8 400 Subducci n Oaxaca Oeste 104 700 23 000 7 500 0 000 0 270 7 000 8 400 Subducci n Ometepec 26 700 9 000 7 500 0 000 0 270 7 000 8 400 Subducci n San Marcos 89 900 29 000 7 500 0 000 0 270 7 000 8 400 Subducci n Guerrero 39 700 80 000 7 500 0 000 0 270 7 000 8 400 Subducci n Petatl n 52 600 12 000 7 500
76. lian strong ground motion data Original coefficients are for PGA and spectral pseudovelocities the latter have been converted to pseaudoaccelerations This version uses epicentral distance 4 Units coefficient 1E 20 to 1E 20 Sigma truncation 1E 20 to 1E 20 Ground type Deep Alluvium Sites Shallow Alluvium Sites Otherwise Type of Coefficients Smooth Raw Reference F Sabetta and Pugliese Estimation of Response Spectra and Simulation of Nonstationary Earthquake Ground Motions Bulletin of the Seismological Society of America Vol 86 2 pages 337 352 April 1996 12 11 SEA99 Spudich et al 1999 Class name Distance metric Valid distance range Valid magnitude range Valid period range Original units Intensity dimension Residual distribution Short name Brief description Number of parameters Parameter name Possible values Parameter name Crisis2008 NewAttenuation AttenuationClasses SEA99 JyB 0 1 to 100 Km 5 to 7 5 0 to 2 sec cm s s Crisis2008 New Attenuation DimensionClasses Acceleration LogNormal Spudich et al 1999 SEA99 Horizontal spectral accelerations 5 damping for events in extensional tectonic regimes world wide 3 Units coefficient 1E 20 to 1E 20 Sigma truncation 112 Chapter 12 Possible values Parameter name Possible values 1E 20 to 1E 20 Soil type Soil Rock Reference P Spudich W B Joyner A G Lindh D M Boore B M Margaris and J B Fletcher
77. meters Parameter name Possible values Parameter name Crisis2008 ExtraGMPE CauzziF accioli08 Vertical Focal 6 to 150 Km 5 to 7 2 0 05 to 20 0000000000001 sec cm s s Crisis2008 N ew Attenuation DimensionClasses Acceleration LogNormal Cauzzi and Faccioli 2008 vertical SA Empirical equations for attenuation of crustal earthquakes worldwide for vertical the vertical component of the spectral acceleration for 5 damping 3 Units coefficient 1E 20 to 1E 20 Ground type 108 Chapter 12 Possible values D C B A Parameter name Sigma truncation Possible values 1E 20 to 1E 20 Reference C Cauzzi and E Faccioli Broadband 0 05 to 20 s prediction of displacement response spectra based on worldwide digital records J Seismol 12 Pages 453 475 April 2008 DOI 10 1007 s10950 008 9098 y 2008 12 6 Cauzzi and Faccioli 2008 Simple version Class name Crisis2008 ExtraGMPE CauzziFaccioli08Simple Distance metric Focal Valid distance range 6 to 150 Km Valid magnitude range 5 to 7 2 Valid period range 0 033 to 20 sec Original units cm s s Intensity dimension Crisis2008 NewAttenuation DimensionClasses Acceleration Residual distribution LogNormal Short name Cauzzi and Faccioli 2008 simple version Empirical equations for attenuation of crustal earthquakes in tectonically active zones worldwide This simple version Brief description does not require parameters and corresponds to the complex GMPM of Cauzzi
78. n CRISIS will use the general attenuation model of the source It must be noted that if site effects grids are given the amplification factors will be applied on top of the intensities computed either with the general attenuation model assigned to the source or with attenuation models assigned to special attenuation regions 5 8 Probabilistic interpretation of attenuation relations In general given a magnitude and a distance intensity A is assumed to be a random variable with a given probability distribution usually lognormal Attenuation relations also called ground motion prediction models or GMPM give the two first statistical moments of 4 given a magnitude and a distance that is A M R These two moments usually describe the mean or median value of A M R and a measure of its uncertainty Up to now CRISIS supports three probability distributions that can be used to describe intensities These distributions are presented in the following table along with the two statistical moments that have to be given in order to correctly describe 4 M R as a random variable 34 Chapter 5 Standard m Lognormal Median of the natural 0 p exp Ku 1 logarithm Gamma Mean Standard deviation 0 eae le Normal Mean Standard deviation infinity p Kp As part of the hazard computations CRISIS requires to compute the probability that intensity 4 at a given site exceeds a known value a given that at some hypocentral location H an ear
79. n level NL i B Period 1 and so on Amplification function for NT doubles The order of the sites is the ground motion level 1 same than for the associated Amplification function for NAT lenen predominant period grid ground motion level 2 that is starting from the NT doubles low left corner and Amplification function for NT doubles OCO ground motion level NL l wr OG GUTER In other words sites are described following the order of cross sections of constant y Amplification function for NT doubles Nx and Ny are the number ground motion level 1 of grid lines along the X Amplification function for NT doubles 8Xi columns and the ground motion level 2 number of grid lines along NT doubles the Y axis rows given in Amplification function for fne Sne pens NT doubles period grid file ground motion level NL The first column of the following table presents an example of the contents of a site effects file with extension ft We recall however that this file must be in binary format Value 1 3 5 20 100 300 0 0 0 2 0 5 Comments A number 1 reserved for future use 3 ground motion levels 5 different structural periods First ground motion level Second ground motion level Third ground motion level First period for which amplifications are given Second period for which amplifications are given Third period for which amplifications are given 45 Chapter 7 1 0 Fourth period for which amplifications are given Fifth pe
80. ng Lat Depth km 105 5000 20 0000 15 0000 103 1500 18 5000 15 0000 EENG Chapter 11 99 0000 18 5000 15 0000 96 0000 18 5000 15 0000 96 0000 19 5000 15 0000 96 5000 20 2000 15 0000 100 2800 20 5400 15 0000 105 0000 21 0000 15 0000 REGION 37 Intraplaca Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source Number of vertex 7 Long Lat Depth km 103 1500 18 5000 15 0000 97 0000 16 0000 15 0000 95 0000 16 2000 15 0000 94 0000 16 0000 15 0000 93 0000 17 5000 15 0000 96 0000 18 5000 15 0000 99 0000 18 5000 15 0000 REGION 38 Chiapas Volc n Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model Abrahamson y Silva No HW S S Area source 93 Chapter 11 Number of vertex 6 Long Lat Depth km 93 0000 17 5000 15 0000 94 0000 16 0000 15 0000 91 8000 14 0000 15 0000 89 0000 14 0000 15 0000 88 0000 16 0000 15 0000 90 2500 17 2500 15 0000 REGION 39 Profundos Chiapas Gutenberg Richter SOURCE IS ACTIVE Base Attenuation model NormalDaniel RRup 5 Trunc CR2007 Area source Number of vertex 7 Long Lat Depth km 96 0000 18 3000 100 0000 95 0000 17 2000 100 0000 94 0000 16 5000 100 0000 91 9000 15 1500 100 0000 91 6000 15 5000 200 0000 93 3000 16 7500 200 0000 95 0000 18 0000 200 0000 REGION 40 Motagua 1 Gutenberg Richter SOURCE IS ACTIVE 94 Chapter 11 Base Attenuation model Abrahamson y Silva No HW S S Are
81. ng exceedance rate curves 10 7 5 Upper limit for intensity level See Points defining exceedance rate curves 10 7 6 Units The units of the intensity measures for reference only 10 7 7 Number of levels of intensity for which seismic hazard will be computed See Points defining exceedance rate curves 10 8 Points defining exceedance probability curves Lower limit upper limit and number of levels for hazard computation Exceedance probabilities will be computed for the number of levels selected and between the lower and upper limit given by the user with logarithmic spacing For instance 1f 10 levels of intensity PGA in this case are chosen between say 1 gal and 300 gal the exceedance probabilities will be given as shown in the following figure 57 Chapter 10 0 1 0 01 so AN RI CN 0 0001 i 0 00001 Exccedance rate 1 yr PGA gal There is always a compromise between speed and precision the larger the number of points to define the curve or the larger the intensity range the slower the computation time Usually not more than 20 points are required to accurately define the exceedance probability curves 10 9 Seismicity Button Menu Input Source seismicity This screen allows you to enter the information about the seismicity of each source 1 Select an occurrence model Gutenberg Richter Characteristic Earthquake or Non Poisson See Seismicity models used for more details 2 Give
82. nimumV alidDistance MinimumV alidMagnitude OriginalUnits PhysicalDimension ResidualDistribution ste Type of variable returned String TipoDistancia Double Double Double Double String Dimensione TipoDistribucion Purpose Returns a brief description of the main model characteristics in order to inform the user about it The distance type which the attenuation model works with Returning value must belong to enumeration TipoDistancia Returns the maximum valid distance of the model Returns the maximum valid magnitude of the model Returns the minimum valid distance of the model Returns the minimum valid magnitude of the model Returns original units of the model in text form E g cm s s Returns the physical dimension of the intensities described in the ground motion model Returns the type of random variable with which the residuals of this GMPE are Chapter 5 modeled Returns intensity 10 Public Function getAcceleration VariableAleatoria value for given parameters Of all the methods presented in the previous table the first nine do not require parameters and are very simple For instance ReadOnly Property MinimumV alidDistance must return a Double number that gives the value of the minimum distance for which the model under definition is considered valid In column Type of variable returned of the previous table the variable types written in green are elem
83. nown as Warner type since Warner Marzocchi suggested its implementation an used it in his calculations in the context of project S2 2008 2010 funded by the Italian Civil Protection Authority 41 Chapter 6 Option 7 In this option source geometry is a collection of points but ground motion characteristics are described with a generalized attenuation model This option is considered impossible because generalized attenuation models contain information about individual events with known although irrelevant magnitudes Since each event is associated to a fixed value of magnitude occurrence probabilities for each of the events contained in the attenuation model cannot be computed for continuous arbitrary values of magnitude with the information provided by parametric seismicity descriptions as earthquake magnitude exceedance rates It must be remembered that starting with magnitude exceedance rates occurrence probabilities in given time frames can only be computed for magnitude intervals magnitude bins and not for point values Option 8 Note that this option is similar to option 4 except that source geometry in option 8 is of the point source type In principle this option could have been regarded a valid since when using generalized attenuation models source geometry is irrelevant However we felt that option 4 in which the source is an area of a line that is given only for the purpose of visual feedback and dissaggregation
84. ns produced by an earthquake In the context of CRISIS a generalized attenuation model is a collection of probabilistic footprints one for each of the events considered in the analysis Each footprint gives in probabilistic terms the geographical distribution of the intensities produced by this event Use the following buttons to create and edit the collection of attenuation models Add Model Edit model Delete model 10 10 2 Assignment of attenuation models Once one or several attenuation models have been added the user must assign one attenuation model to each source See special attenuation models for a more complex use of attenuation models 10 11 Site effects Button Menu Input Site effects Add or delete site effects grids to be used in the hazard analysis See the format of the site effects grids in this link 60 Chapter 10 10 12 Global parameters Button 2 Menu Input Global parameters This screen allows you to enter information concerning The spatial integration procedure The value of the time frames for which seismic hazard will be computed The distance to be used for M R disaggregation 10 12 1 Integration parameters Parameter controlling the integration process All sources or sub sources farther away than this number in Km will be ignored in the spatial integration process Minimum triangle size Sources will be subdivided into sub sources whose characteristic size will not be les
85. nsities produced at the site by the earthquake CRISIS admits three families of GMPM Attenuation tables furnished by the user built in parametric models and generalized attenuation models These possibilities give CRISIS great flexibility to perform the hazard computations 1 1 4 Spatial integration procedure CRISIS operates with a dynamic integration procedure which allows fast computation of hazard in extended areas 1 2 About CRISIS CRISIS has been mainly developed at Instituto de Ingenier a UNAM Mexico It has been developed by M Ordaz II UNAM Mexico E Faccioli Politecnico di Milano Italia Chapter 1 F Martinelli INGV Italia A Aguilar II UNAM Mexico J Arboleda II UNAM Mexico C Meletti INGV Italia V D Amico INGV Italia Development of CRISIS 2008 has been funded between 2008 and 2010 by the Department of Civil Protection Government of Italy All rights reserved 1987 2010 Chapter 2 2 General Overview 2 1 Basic theoretical background The purpose of this section is not to describe in detail the techniques to compute seismic hazard However we will rapidly describe some of their main aspects Starting with CRISIS 2008 the code does not work anymore with intensity exceedance rates as measures of seismic hazard The more recent versions give seismic hazard in terms of probabilities of exceedance of intensity values in given time frames For instance a valid measure of seism
86. obability density function contribute most to the seismic hazard at a given site Consider the following equation which is equation 1 but written in terms of exceedance probabilities 49 Chapter 9 N Nm Pr 4 gt a 7 1 TI Saaz aM r pl 6 k i l For given magnitude time frame and source location the term Pr 4 gt a Mi Tj k will be computed by calculating the area shown in green in the following figure Sa gal The shape of the probability density function of Sa shown in black in the previous figure depends on magnitude distance and ground motion prediction model employed while a is an arbitrarily fixed value the one for which seismic hazard is being computed However it is sometimes of interest to know how much of the probability marked in green comes from the high percentiles of the distribution For instance how much of the probability comes from the area to the right of value L shown in blue in the previous figure Normally L is indexed to an epsilon e value such that L MED A M T k exp e0 y A M P Ei e where MED A Mi Tj k and o ind Mi Tj k are respectively the median and the logarithmic standard deviation of A given magnitude Mi at source k the value of e is kept fixed for the whole analysis In view of 50 Chapter 9 this when an epsilon disaggregation is required exceedance probabilities required to evaluate equation 4 are computed with Pr 4 gt a M T k pau z Da
87. odes in the following table 4 identification bytes Number of columns in the X direction Number of rows in the Y direction Minimum longitude of the grid 117 Chapter 13 Xhi Double 8 Maximum longitude of the grid Ylo Double 8 Minimum latitude of the grid Yhi Double 8 Maximum latitude of the grid Zlo Double 8 Maximum Z value in the grid Zhi Double 8 Minimum Z value in the grid The first byte indicates what type of variables will be stores according to the following codes Name Vale Comments 1 Byte Short 2 Integer 3 Single 68 Corresponds a character D This code is used for com patibility with binary Surfer 6 format Double 5 Long 6 13 3 SHP files A shapefile stores non topological geometry and attribute information for the spatial features in a data set The geometry for a feature is stored as a shape comprising a set of vector coordinates An ESRI shapefile consists of a main file an index file and a dBASE table The main file is a direct access variable record length file in which each record describes a shape with a list of its vertices In the index file each record contains the offset of the corresponding main file record from the beginning of the main file The dBASE table contains feature attributes with one record per feature The one to one relationship between geometry and attributes is based on record number Attribute records in the dBASE file must be in the same order as records in the ma
88. of sites in the generalized non Poissonian seismicity file nps 2 The number of magnitudes in the generalized attenuation model gaf must be the same that the number of sites in the generalized non Poissonian seismicity file nps Within the CRISIS development team this combination is known as of type Stupazzini Villani type since Marco Stupazzini and Manuela Villani are the two researchers in charge of developing this type of model in the context of project S2 2008 2010 funded by the Italian Civil Protection Authority Option 5 In this option source geometry is given in terms of points there is a normal attenuation model and a parametric seismicity description either of Gutenberg Richter or Characteristic Earthquake type This is an old CRISIS option which has no compatibility restrictions Option 6 In this option source geometry is given in terms of points a normal ground motion prediction models is used and earthquake occurrence probabilities are given with a generalized non Poissonian seismicity model This option is mainly used to model the so called smoothed seismicity but now with probabilities obtained with arbitrarily complex non Poissonian models The only compatibility restriction in this option is that the number of vertex given in the point sources description must be equal to the number of sources given in the non Poissonian seismicity file Within the CRISIS development team this combination is k
89. on occurrence process is taking place for earthquakes of all magnitudes Under this assumption P AC M T 7 takes the form of precisely a Poisson probability distribution s 8 where Dl M is the number of earthquakes of magnitude M that per unit time take place at source k In other words this quantity is the conventional exceedance rate of earthquakes in the range of magnitudes represented by M that 1s AA M 4 M AM 2 A M AM 2 9 Replacing equation 8 in equation 2 we obtain Pr A lt a M T k gaon evol Am ur evol A4 Qr per s Pr 4 a A SP 10 Note that now the sum extends to infinity since in the Poisson process the possible range of values of s is 0 to infinity The sum in equation 10 has analytical solution Pr 4 a M T k expI A4 M T l Pr A a M R 11 Pr A Xa M T k expt AA M JT Pr A2 a M R 12 Hence from equation 7 we get that N Nm Pr 4 gt a T 1 expt 4 M T Pr A2 a M RO 13 El i l N Nm l Pr 4 gt a T 1 em H gt AA MT Pr 42 a M R d r 14 i l Chapter 2 But under the Poisson assumption for the earthquake occurrences the process of intensity exceedances is also a Poisson process for which the exceedance probability of intensity a during the next T years would be given by Pr A a T expi v a T 15 where n a is the exceedance rate of intensity a Comparing equations 14 and 15 we obtain
90. parameters Minimum triangle size 11 Km Minimum Distance Triangle Size ratio 3 The following graph shows the resulting subdivision of a squared source of size 1 x1 when the computation site is located at the center of the source using the default integration parameters ESSE IS Ss SSES NNNNNINININ NNNONINNININ NNNNINNININ BS SUN NS AINA NINA NN Figura 2 1 Source subdivision with Minimum triangle size 11 Km Minimum Distance Triangle Size ratio 3 NN EN Chapter 2 Figure 2 shows the same subdivision but with Minimum triangle size 5 Km Minimum Distance Triangle Size ratio 3 Note how this subdivision yields smaller triangles in the neighborhood of the computation site Figura 2 2 Source subdivision with Minimum triangle size 5 Km Minimum Distance Triangle Size ratio 3 Figure 3 shows the same case but with Minimum triangle size 5 Km Minimum Distance Triangle Size ratio 4 Note that the smaller triangles cover now a wider area around the computation site Figura 2 3 Source subdivision with Minimum triangle size 5 Km Minimum Distance Triangle Size ratio 4 Finally Figure 4 shows the resulting subdivision with Minimum triangle size 0 5 Km and Minimum Distance Triangle Size ratio 4 Note how the density of triangles varies radially as we get away from the computation site 10 Chapter 2 Figura 2 4 Source subdivision with Minimum triangle size 0 5 Km M
91. perhaps irrelevant They would be irrelevant for instance if an attenuation model based on focal distance is going DEED to be used for the hazard computations If the unit vector normal to the fault 5 650 45 250 11000 plane is described with 0 0 0 a horizontal plane will be the default 5 650 45 350 11000 5 650 45 450 11000 5 650 45 550 11000 5 750 44 450 11000 5 750 44 550 11000 ELT 16 Chapter 4 4 Seismicity models used Speaking generally CRISIS expects to have the seismicity described by means of the probabilities of having 1 2 Ns earthquakes of given magnitudes in a given location during the next Tf years As can be noted this is the most general description of seismicity that can possibly be given In order to get this information CRISIS admits three types of seismicity models The first two were already contained in older CRISIS versions and both are related to Poissonian occurrences although they differ in the way in which they define the earthquake magnitude exceedance rate The third model is generalized non Poissonian model that gives explicitly the required probabilities See details of the three models in the following links Modified Gutenberg Richter model Characteristic earthquake model Generalized non Poissonian model 4 1 Modified Gutenberg Richter model This model is associated to Poisson occurrences so the probability of exceeding intensity level a in the next T years given that an eart
92. power of this dimension Provides a number specific to the class Checks if the types have same power for MKSA elements describing dimensions Public MustOverride ReadOnly Property name As String Public Overrides Function Equals ByVal obj As Object As Boolean Classes constructed that implement these methods must be compiled to the form of a dll which must be ste in CRISIS application directory In addition file CRISIS2008 dim must be edited to add the new classes The geral format of the lines of this file is the following Full class name Assembly name 5 7 Special Attenuation Models In the most frequent case only one attenuation model will be assigned to a source However there is the possibility to assign one ore more special attenuation models to a source which will be effective only for sites located inside corresponding polygons called special attenuation regions given by the user If special attenuation models are given then CRISIS will proceed in the following way When computing hazard from a source CRISIS will check if this source has special attenuation models If it does not then it will use the general attenuation model for the source If the source was assigned special models then CRISIS will check if the site of computation is inside one of the user given polygons If affirmative CRISIS will use the model assigned to this source site combination If the site is not inside any of the special polygons the
93. pth km 100 0620 16 4730 15 0000 99 6630 16 3430 15 0000 99 4380 17 0100 30 0000 99 8360 17 1430 30 0000 REGION 21 Subducci n Guerrero Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 101 0050 16 7970 15 0000 100 0620 16 4730 15 0000 99 8360 17 1430 30 0000 100 8100 17 4370 30 0000 REGION 22 Subducci n Petatl n Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 84 Chapter 11 101 7010 17 0440 15 0000 101 0050 16 7970 15 0000 100 8100 17 4370 30 0000 101 4990 17 7090 30 0000 REGION 23 Subducci n Michoac n Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 103 1350 17 7010 15 0000 101 7010 17 0440 15 0000 101 4990 17 7090 30 0000 102 9160 18 3930 30 0000 REGION 24 Subducci n Colima 1 Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 103 8680 18 3000 15 0000 103 1350 17 7010 15 0000 102 9160 18 3930 30 0000 ERS lt Chapter 11 103 6120 18 7610 30 0000 REGION 25 Subducci n Brecha de Colima Characteristic model SOURCE IS ACTIVE Base Attenuation model ATCOSTAm Trunc Area source Number of vertex 4 Long Lat Depth km 104 4570 18 7
94. riginal units to user units given in the Intensities screen Supported values are MEC Normal 1 In integer number indicating the Distribution probability distribution assigned to Lognormal 2 2 Lognormal the residuals of the attenuation model Beta 3 Gamma 4 A string giving the physical f a E th f physical Dimension dimension of the intensities described ns i o ha x Acceleration i dimension in this link in the attenuation table pcc ei Parameters defining the magnitude limits 1 line MINF MSUP NMAG MINF Lower limit of magnitude given in the table MSUP Upper limit of magnitude given in the table NMAG Number of magnitudes for which intensity is given CRISIS assumes than intensities are given for magnitudes M K where M K MINF K 1 DMAG 1 DMAG MSUP MINF NMAG 1 2 Parameters defining the distance limits and type 1 line RINF RSUP NRAD TYPE 22 Chapter 5 RINF Lower limit of distance given in the table RSUP Upper limit of distance given in the table NRAD Number of distances for which intensity is given An integer indicating the type of distance used by TYPE the attenuation table CRISIS assumes than intensities are given for distances R K where log R K log RINF K 1 DLRAD 3 DLRAD log RSUP log RINF NRAD 1 4 In other words distances are supposed to be logarithmically spaced TYPE can have the following values depending on the type of distance to be used 1 or blank
95. riod for which amplifications are given 2325332019 E as factors one for each structural period for ground motion Five amplifications factors one for each structural period for ground motion level 2 Five amplifications factors one for each structural period for ground motion level 3 2325332019 E factors one for each structural period for ground motion Five amplifications factors one for each structural period for ground motion level 2 Five amplifications factors one for each structural period for ground motion level 3 2 2 2 4 3 2 1 9 1 8 2 12 3 9 11 4177 2 22 4 3 2 1 9 1 8 2 52 53 99 2107 46 Chapter 8 8 Logic trees The following paragraphs giving a brief introduction to logic trees in the context of seismic hazard analysis have been taken from On the Use of Logic Trees for Ground Motion Prediction Equations in Seismic Hazard Analysis by Julian J Bommer Frank Scherbaum Hilmar Bungum Fabrice Cotton Fabio Sabetta and Norman A Abrahamson Bulletin of the Seismological Society of America Vol 95 No 2 pp 377 389 April 2005 doi 10 1785 0120040073 Logic trees are widely used in probabilistic seismic hazard analysis as a tool to capture the epistemic uncertainty associated with the seismogenic sources and the ground motion prediction models used in estimating the hazard Logic trees were first introduced into probabilistic seismic hazard analysis PSHA by Kulkarni et al
96. robabilistic relations between earthquake properties site characteristics and intensities at a site These relations are given in terms of the first and second statistical moments of the intensities given some earthquake and site parameters For instance for the GMPM in which the residuals are lognormally distributed the GMPM gives the median and the standard deviation of the natural logarithm of the intensity given a set of earthquake and site parameters The GMPM are constructed to express the intensities in certain units These units are called the original units However the user of CRISIS might want to perform calculations for intensities expressed in other units For instance a user could be using a model whose original units are cm sec but he wants to make 2894 Chapter 5 hazard calculations for intensities expressed as a fraction of the acceleration of gravity g In these case the g units will be called the user units which are given by the user in the Intensities Screen The Units Coefficient UC is a positive number used to change from the model s original units to the user units using the following relation user unit UC original units 1 For instance in the example given above since the original units are cm sec and the user units are fractions of g we would have that 1 g UC cm sec and hence UC 981 because 1 g 981 cm sec 5 6 Physical dimension In order to have tighter checks of the compatibilit
97. s of all magnitudes But seismic sources are usually points lines areas or volumes so a spatial integration process must be carried out to account for all possible focal locations We will assume that the spatial integration process leads to N sources So finally assuming that earthquake occurrences at different sources are independent from each other we obtain that the non exceedance probability of intensity a in the next d years due to earthquakes of all magnitudes located at all sources can be computed with e Pr 4 lt a T Pri4 lt a T k 4 k l N Nm Pr 4za T Pas c 5 kel iel N Nm Ni Pr 4 lt a T gt s M 7 Pr 4 lt a M RT 6 k i l s 0 Finally N Nm Ns Pr 4 gt a T 1 gt R G M r PrC4 a1 M RT 7 k i s 0 Equation 7 is the one used by CRISIS to compute seismic hazard for situations in which the sources are spatially distributed A 1 N there are earthquakes of various magnitudes M i 1 Nm and the earthquake occurrence probabilities in known time frames T at source k are given by P AS M T D that is the probability of having s events of magnitude M in the next 7 years at source k Chapter 2 The equations presented here are in general applicable to non Poisson occurrence process But they are also applicable to the Poisson process Let us see what results we obtain if we assume that the occurrence process is Poissonian Let us assume that at all sources a Poiss
98. s than this number For area sources the characteristic size is the square root of its area For a fault source the characteristic size is its length Minimum Distance Triangle size ratio Sources will be subdivided until the ratio between source site distance and characteristic size of the sub source is larger than this number 10 12 2 Time frames for which hazard will be computed Give in this table the values of the time frames for which hazard will be computed These values must be coherent with those given in the non Poissonian seismicity files nps associated to the sources 10 12 3 Distance used for M R disaggregation The M R disaggregation results give for a site intensity measure and intensity level the distribution of exceedance rates as a function of magnitude and distance Choose which distance will be used as the argument of this M R distribution 10 13 Logic tree computation Button D This screen allows definition of a logic tree a tool that is frequently used to account for epistemic uncertainty in the computation of seismic hazard 61 Chapter 10 In the context of CRISIS each branch of a logic tree is formed by one data file usually with extension dat along with a measure of the degree of belief that the analyst has on each of the branches being the true one Therefore this screen allows construction of the logic tree by way of informing CRISIS which dat files form the branches of the tree and
99. sponse values for different periods so a uniform hazard spectrum can be constructed 59 Chapter 10 In view of this the general operations that have to be performed in this screen are e Select and add the attenuation models to be used in the analysis e Assign one of these models to each source 10 10 1 Selection of attenuation models CRISIS admits three families of attenuation models Attenuation tables In these tables relations between earthquake characteristics and intensities at a site are given in terms of the following parameters magnitude structural period source site distance and depth For the first moment usually the median of a lognormal distribution the attenuation relations are matrices in which the rows run for the magnitude and the columns run for the distance Note that when using attenuation tables the relations between magnitude distance and intensity do not need to be of parametric nature since the intensity medians are given point by point for magnitude distance combinations Built In models These are popular models published in the literature in which magnitude distance and intensity are probabilistically related by usually a set of formulas or parametric equations There is a set of built in models ready to use in CRISIS and there is also the possibility of adding new models Generalized models Generalized attenuation models are non parametric probabilistic descriptions of the ground motio
100. t sources are generally used to geometrically describe potentially thousands of hypocentral locations information about this type of source is given to CRISIS by means of an ASCII file usually with extension ssg with the following structure ID Header Header String Number of point sources TotSrc Integer Geometry record for source 1 Geom 1 Geometry record Geometry record for source 2 Geom 2 Geometry record 14 Chapter 3 Geometry record for source TotSrc Geom TotSrc Geometry record The following table describes the structure of a geometry record h X in degrees Hypocentral location h Y in degrees h Z in Km always positive Unit vector describing the orientation el x of the fault plane SE These three values describe a unit vector normal to the E fault plane X is longitude Y is latitude and Z is depth The following table gives and example of a point source geometry file where 16 point sources are geometrically described Griglia Marzocchi Header line for identification purposes 16 16 points are described 5 550 44 950 11 000 5 550 45 050 11000 5 550 45 150 11 000 5 550 45 250 11 000 5 650 44 650 11000 5 650 44 750 11000 These lines give the longitude latitude and depth 11 Km in this case always 5 650 44 850 11000 positive for the 16 sources 5 650 44 950 11000 Note that the coordinates of the unit vector normal to the fault plane are given as 5 650 45 050 11000 0 0 0 This means that they are unknown or
101. that K f K Pa while for line sources it is required that K ac K 0 10 6 3 References Donald L Wells and Kevin J Coppersmith 1994 New Empirical Relationships among Magnitude Rupture Length Rupture Width Rupture Area and Surface Displacement Bulletin of the Seismological Society of America Vol 84 No 4 pp 974 1002 August 1994 S K Singh E Bazan and L Esteva 1980 Expected Earthquake Magnitude from a Fault Bulletin of the Seismological Society of America Vol 70 No 3 pp 903 914 June 1980 10 7 Data on spectral ordinates Button k 56 Chapter 10 Menu Input Spectral ordinates This screen allows entering the parameters for each spectral ordinate or in general intensity measure for which seismic hazard will be computed 10 7 1 Total number of spectral ordinates Is the total number of different intensity measures for which hazard is to be computed Frequently the different intensity measures refer to spectral ordinates for different structural periods In this case spectral attenuation relations are needed 10 7 2 Actual spectral ordinate Use this control to move from one intensity measure to the other 10 7 3 Structural period of spectral ordinate This is the value of the structural period associated to this measure of intensity The values given in the attenuation tables must be coherent with the period values given here 10 7 4 Lower limit of intensity level See Points defini
102. the spatial integration adopts a summation form The subdivision procedure will be briefly described in the following paragraphs Chapter 2 2 2 1 Area sources These sources are originally given by the user as 3D polygons the user gives the coordinates longitude latitude and depth of the N vertex defining the area source First the area source is subdivided into N 2 triangles These triangles will be further subdivided until one of the following two conditions are met 1 The size ofthe triangle is smaller than the value Minimum triangle size given by the user That is the triangle is subdivided if it is still big 2 The ratio between the site to source distance and the triangle size is larger than the value Minimum Distance Triangle Size ratio given by the user In other words the triangle is subdivided if the site is still not far enough The sub sub divisions are performed by means of a recursive function The site to source distance is measured from the computation site to the centroid of the triangle whose possible subdivision is being examined The size of the triangle is simply the square root of its area The seismicity associated to each centroid is proportional to the triangle s area If CRISIS decides that a triangle has to be subdivided this is done dividing the triangle into four new ones whose vertexes are the mid points of the three sides of the original triangle CRISIS uses the following as default
103. thquake of magnitude M took place that is Pr 4 gt a M H If no truncation is applied to intensity values this probability is computed with the following expression Pr 4 gt a M H 1 F as n M HM HIJ 1 where u M H and uM H are the first and second moments respectively of intensity A given that at hypocentral location H an earthquake of magnitude M took place Depending on the probability distribution assigned to A the first and second moments have the interpretation presented in the previous table F 4 a u i M H u OM H is the probability distribution of A also called the cumulative probability function whose form depends on the type of distribution chosen The moments of A M R that is u M H and u OM H are given by the user by means of attenuation relations or GMPM In many cases truncation is specified in the GMPM trough a parameter called Sigma truncation 7c This means that the integration across the attenuation relation uncertainty implied in the previous equations is not carried out up to infinity but up to a certain value Tc Depending on the value of the truncation coefficient given in the GMPM the following considerations are made Tc 0 In this case no truncation is applied so Equation 1 is used Tc 0 In this case a truncated distribution between the lower limit of A and Tc is assumed regardless of magnitude and distance Hence 1 Fla 44 M E g ML E a Tc Pr
104. ture area In CRISIS the area is specified with the following criteria The rupture area is assumed to be circular with radius r which depends on magnitude in a way specified by the user see Relation between magnitude and fault radius The circular fault is contained in the plane defined by the triangle resulting from source subdivision whose centroid is assumed to be the hypocentral location Note that if the site is within the projection of the fault in the Earth s surface R p70 and Reup H The user must indicate to CRISIS what type of distance he wishes to use depending on the characteristics prediction models GMPM Computation of the exact values of distances R and R is cumbersome To save computation time the exact values are approximated with simpler formulas that produce small errors 5 10 Relation between magnitude and fault size In CRISIS attenuation relations can be specified in terms of 4 different measures of distance If distances R RUPEL R pare used CRISIS must have means to know the rupture area or the rupture length as a function of magnitude in order to compute the required distances In general CRISIS assumes that the relation between area rupture length and magnitude is 2376 Chapter 5 A K exp K M for area sources A in Km 1 L K exp K M for line sources L in Km 2 where 4 is the source area in km L is the rupture length in km M stands for magnitude and K p K K 3 an
105. u 5 max where p AM Tj 0 is the probability density function of 4 given magnitude Mi at source k and Laa MAax L a 6 Interpretation of e for other probability distributions Usually intensity A is assigned a lognormal probability distribution so Equation 4 can be used to compute the lower integration limit L However admits the possibility of using four different types of probability distributions Lognormal Gamma Normal and Beta In the three last cases the meaning of e is not unambiguously defined In CRISIS the following interpretations of e are adopted For the Gamma distribution L E A M T k 0 A M T k L20 7 For the Normal distribution L E A M T k 8e0 4 M T k 8 For the Beta distribution L E A M T k 0 A M T k OSLSI 9 In the three cases above E A Mi Tj k and c A Mi Tj k are respectively the expected value and the standard deviation of A given magnitude Mi at source k 5 LSD Chapter 10 10 Building a data file CRISIS data files are constructed via a user graphic interface that is comprised of several screens and menu items See below what pieces of information are given in each screen 10 1 Open an existing input file Button ZS Menu File Open This command triggers an open file dialog to open an existing data file usually with extension dat 10 2 Save data to a file d Button S Menu File Save As This command allows saving data
106. uble 8 Time frame Nt Tf Nt Double 8 Seismicity record for source 1 Seis 1 pe 8 8 Ns Nt record 19 Chapter 4 Seismicity Seismicity record for source 2 Seis 2 EE 8 8 Ns Nt Seismicity record for Ee Seis TotSrc n 8 8 Ns Nt source TotSrc Seismicity record Description Variable Type Length Comments Prob 1 1 Double 8 Probability of having 1 2 Ns Prob 1 Double 8 Block associated to events in time frame 1 Le time frame 1 Prob Ns 1 Double Prob 1 2 Double 8 Probability of having 1 2 Ns Prob 2 2 Double 8 Block associated to events in time frame 2 ee time frame 2 Prob Ns 2 Double 8 Prob 1 Nt Double Probability of having 1 2 Ns Prob 2 Nt Double 8 Block associated to events in time frame Nt Ka time frame Nt Prob Ns Nt Double 8 Total 8 Ns Nt length Oe Chapter 5 5 Ground Motion Prediction Models GMPM In general ground motion prediction models also called attenuation relations establish probabilistic relations between earthquake characteristics and intensities at a site of interest These relations are probabilistic since for given earthquake characteristics the intensities are regarded as random variables whose probability distribution is completely fixed by the GMPM In most of the cases this means that at least the first two statistical moments e g the median and the standard deviation of the natural logarithm in the lognormal case of the probability distribution must be furnished by the GM
107. ude as an unknown quantity We assign to this variable a uniform probability distribution between M and M which are informed to CRISIS in terms of two values the expected value of the maximum magnitude E Mu and DM such that M 1 and M 5 are given by M E Mu DM 1 M E Mu DM 2 Thus maximum magnitude is considereder equally likely for all values between M 1 and M gt 4 3 Characteristic earthquake This model is associated to Poisson occurrences so the probability of exceeding intensity level a in the next T Years given that an earthquake with magnitude M took place at a distance R from the site is given by Pe a T M R 1 exp AA M T p a M R 1 where p a M R is the exceedance probability of intensity level a given that a magnitude M event occurred at a distance R from the site and A2 M is the Poissonian magnitude exceedance rate associated to the magnitude range also called magnitude bin characterized by magnitude M Note that D a M R depends only on magnitude and site to hypocenter distance This probability does not depend on earthquake occurrence probabilities In turn AA M can be computed as AAM AM AM 2 A M AM I2 Q where it is implicit that the magnitude bin characterized by magnitude M goes from M AM 2 to M AM 2 For the Characteristic earthquake model the earthquake magnitude exceedance rate is given by M qucd a UM A z y A EMT J M EM S S MEM SM 3 18
108. urce Use the right mouse button to insert or delete columns Depths are always positive In the case of point sources vertex coordinates cannot be edited from this screen and all changes must be made in their corresponding ssg file 10 5 3 Fault length rupture radius Give parameters that relate magnitude to rupture length or rupture radius 10 5 4 Draw options Choose whether the map cities and computation sites will appear for your reference in the graphs Choose also if the triangularization of the area sources will appear in the graphs 10 5 5 Sources to draw Active Graphs will show only the active source Selection Graphs will show only the sources selected Range Graphs will show all sources with numbers in the range Start to End Long Lat plane See the sources selected to draw in the horizontal longitude latitude plane Several planes See the sources selected to draw in the three different planes 10 6 Rupture Area Rupture Length CRISIS allows choosing for each source the parameters that relate rupture area or rupture length with magnitude These parameters can be either given by the user or chosen from a set of constants 10 6 1 Area sources or Smoothed seismicity geometries The general relation is the following A Ket where A is the source area in km M stands for magnitude and K E and K are constants given by the user or chosen from a set of constants CRISIS has the following built in sets of constants
109. vant Chapter 5 Description Type Length Comments of bin 2 Magnitude representative Double 8 of last bin Magnitude values are required to compute occurrence rates when GR or Characterisitic Scenario name Char 40 models are used When a non Poissonian seismicity file is given these magnitudes are irrelevant Grid for intensity measure 1 moment 1 Grid for intensity measure 1 moment 2 ModGRN 56 Nbytes Nx1 Nyl ModGRN 56 Nbytes Nx1 Nyl Grid for intensity measure 1 ModGRN 56 Nbytes Nx1 Nyl moment NumMoments Grid for intensity measure 2 moment 1 Grid for intensity measure 2 moment 2 ModGRN 56 Nbytes Nx1 Nyl ModGRN 56 Nbytes Nx1 Nyl Grid for intensity measure 2 ModGRN 56 Nbytes Nx1 Nyl moment NumMoments 28 Chapter 5 Description Type Length Comments Grid for intensity En measure ModGRN S6 NbytestNxl Nyi_ Ten the actual georeferenced probabilistic Numint Y moment 1 Grid for intensity measure ModGRN 56 Nbytes Nx1 Nyl Numlnt moment 2 Grid for intensity EN ModGRN 56 Nbytes Nx1 Ny1 moment NumMoments Magnitude values are required to compute occurrence rates when GR or Characterisitic Char 40 models are used When a non Poissonian seismicity file is given these magnitudes are irrelevant Scenario name Grid for DIN MOdGRN 56 Nbytes Nx2 Ny2 measutenl es moment 1 Grid for intensity ModGRN 56 Nbytes Nx2 Ny2 measure 1 moment 2 Grid for intensity measure 1
110. vel Dependence on ground motion level is included 43 Chapter 7 to account for non linear soil behavior In view of this amplification factors are given by means of a 4 index matrix The first two indexes are used to sweep through space that is rows and columns of a grid please note that the size and location of the grid of amplification factors are exactly the same than for the grid of predominant periods The third index sweeps through structural periods while the fourth index sweeps through ground motion levels In principle amplification factors for a given site and period can be different depending on the size of the ground motion In general CRISIS uses as an indicator of this size the intensity for the shortest period available for the GMPM that is used to compute the intensity without site effects In most of the cases but not always this intensity corresponds to peak ground acceleration The format in which amplification factors must be given is described in the following table A4 Chapter 7 For site Nx Ny Block For site 1 1 For site 1 2 Variable Size Comments Amplification function for NT doubles The amplification function ground motion level 1 for a given site and ground Amplification function for NT doubles Motion level is a collection ground motion level 2 of NT numbers one for NT doubles each structural period The Gn ER ee first number is associated to ground motio
111. was more useful and we inhibited this one to avoid confusion 42 Chapter 7 7 Site Effects CRISIS permits inclusion of local site effects in hazard computations Site effects are given to CRISIS in terms of amplification factors that depend on site location structural period and ground motion level in order to account for soil non linearity Amplification factors are interpreted by CRISIS in the following way Suppose that during the hazard computations CRISIS requires to compute the median of the intensity at structural period T that would take place at site S due to an earthquake of magnitude M originating at hypocenter A We will denote this intensity as S T M H Normally S T M H is computed using the attenuation relation or ground motion prediction model that the user has selected for the source to which H belongs or using the special attenuation model that the user has assigned to the source site combination to which S and H belong The value so computed is interpreted by CRISIS as the median intensity without site effects But if site effects are given then the median intensity that CRISIS will use for the hazard computations JI is the product of S T M HI and the amplification factor given by the user which depends on site location structural period and ground motion level 7 o We will denote this amplification factor as A S TI y In other Words L S T M H IS T M H AST 1 Clearly if no site eff
112. what weight is assigned to each of the branches The functions provided for this aim are the following d Use this option to create a new logic tree Use this option to open a previously created logic tree Logic trees are defined in text files usually with extension ltc logic tree combination that contains for each branch the name path included of the CRISIS input data file associated to this branch as well as the weight assigned to each branch in the form of a numerical integer This weight normalized by the sum of the weights of all branches is interpreted as the probability of being the true one The format of the text file is the following FileNamel dat Weight 1 FileName2 dat Weight 2 FileNameN dat Weight N Note that the file name and its associated probability must be separated by a comma 2 Use this option to save a logic tree usually in a text file with extension ltc A Add a new branch to the logic tree S Delete the selected branch of the logic tree d Change the weight of the selected branch La Perform the logic tree combination Before proceeding to do the logic tree computations CRISIS will perform the following checks 1 That all dat files exist and contain data of a valid hazard model 2 That there is coherency among the various dat files Also CRISIS will only recompute the branches whose associated dat files have changed since the last execution In other words CRISIS will not r
113. y among different ground motion prediction models GMPM when performing logic tree computations each GMPM must be assigned aphysical dimension of the measures of intensity the model is describing The physical dimension of most GMPM is acceleration because they are usually constructed for PGA and the response spectral ordinates at selected periods but other physical dimensions are also accepted CRISIS so far accepts the following physical dimensions which correspond to classes defined for this purpose Acceleration Crisis2008 New Attenuation dll Velocity Crisis2008 New Attenuation dll Displacement Crisis2008 New Attenuation dll MMI Crisis2008 New Attenuation dll MCSI Crisis2008 New Attenuation dll Ductility Demand ExtraDimensions dll ISDrift ExtraDimensions dll Although only these physical dimensions are recognized by CRISIS it is relatively simply to construct additional classes associated to other intensity measures To do so the constructed class must implement the following methods Returns an integer indicating Public ReadOnly Property distancePow As Integer the distance power of this dimension Returns an integer indicating Public ReadOnly Property forcePow As Integer the force power of this dimension Returns an integer indicating Public ReadOnly Property timePow As Integer the time power of this dimension e Chapter 5 Returns an integer indicating Public ReadOnly Property chargePow As Integer the charge

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