Home

The MAGAN Project Magan 3.1 User's Manual by A. Schettino

1. Equation 22 becomes N Gns y 2Gp7 arctan de Gig Gi 23 n 1 a Expression for x in terms of z are similar to that discussed previously eq 14 We can write x a z B 24 where an and B are given by eq 15 17 Finally substitution in Eq 23 provides gt T efs A arctan Gnn Se N 2 Ei Eni Y 2Gp B e402 c c qf gt Swat 81 3 Gwa Si a ree _ ata l _ arctan e l a VE G n l En 25 The first two terms in parentheses of summation give zero after summation Therefore 5 Sw S1 gt Gy Si 26 n l y 260 Pee ape at arctan Sea ntl aran E Grasi Gii This solution implies that the gravity of a body in a two dimensional problem only depends upon the coordinates of the vertices of a polygon that approximates its cross section Vertex coordinates C in Equation 26 can be replaced by quantities r and 0 illustrated in Fig 6c In fact E 6 0 arctan 27 n In this instance the solution assumes the following simple form N A i 2603 t o A Q 0 90 l gt na F6 3 Gwa G 28 n l n n 18 Therefore the normal gravity of a two dimensional problem depends upon the distances of the polygon vertices from the observation point and from the angles that the radii r make with the horizontal Angles 0 are calculated through Eq 27 by calling the atan2 C library function This call may lead to improper evaluatio
2. deg Spacing of modelling station points along the flow line km Identifier in the user defined rotation model of plate at positive offsets Identifier in the user defined rotation model of plate at negative offsets Chron of ridge extinction or C1n for currently active ridges Chron associated with the oldest block in the left side magnetization model Chron associated with the oldest block in the right side magnetization model Offset of origin in flow line list Offset of currently selected node in flow line list RGB code of current background color X window coordinates of spreading ridge symbol end points Y window coordinates of spreading ridge symbol end points Flag indicating if a background image is currently displayed Flag indicating if ship track data points are currently displayed Flag indicating if projected data points are currently displayed Flag indicating if ship track data points are aeromagnetic data Integer which specifies the flow line sorting criterium 0 1 2 32 Table 1 Continued Parameter Keyword Value Projection_Distance Geomag_Params Version Axial_Magnetization Obliquity Asymmetry Pen__Size_ k Pen_Color_ k Maximum original distance of projected data points from the current flow line Full path of an ASCII file containing geomagnetic field parameters txt Version of Magan which created the project Default axial magnetization A m Default obliquity of the magnetized blocks
3. log I 0 os O OX Cra Sn O 0 P Oz Ox R r Oz Ox R 25 2 3 Forward Modelling We now face the problem of applying the previous equations to the forward modelling procedure of marine magnetic anomalies The crustal magnetization model is started with a sequence of m linear prisms draped on bathymetry having constant height h equal to the user defined magnetized layer thickness and width w proportional to the corresponding chron duration w VvAt 54 where v is the default full spreading rate and Az is the duration in Myrs of the i th chron The magnetization direction for each prism is determined on the basis of APWPs that are calculated through an user supplied rotation model or if the user doesn t specify one on the basis of the local geographic latitude and direction of spreading In plate kinematics the magnetization direction of a prism cannot be chosen as coincident with the present day reference field F not even when the data ages encompass the last 2 3 Myrs In fact assuming that the rock magnetization is entirely of NRM type even in the case of rocks that formed during the last polarity chron the average magnetization direction would be aligned with the time averaged geomagnetic field for the last 0 78 Myrs which is a GAD field Therefore in this instance the paleomagnetic direction in 38 and 39 would be J 90 D 0 and not that of the local IGRF field i e Jo and Do
4. as shown in Fig 22 The structure of rotation model files has been discussed above This field is not mandatory If the user does not specify any rotation model then the plate identifier fields are disabled and the program uses a constant axial pole Z 90 D 0 for all magnetization directions This could be an appropriate choice for profiles that encompass the last 4 5 Myrs However it gives a very crude approximation in the case of profiles on old crust at low latitudes When a rotation model has been specified the user must also fill the plate identifier fields with appropriate numbers and those plates must exist in the rotation model Magan uses these information to build an APWP for the plates on the two flanks of the spreading ridge and determine the direction of remnant magnetization of any block in the model The Default Full Spreading Rate mm yr and Default Spreading Asymmetry fields are used to specify constant velocity and spreading asymmetry values for the construction of the initial magnetization model The Default Magnetization A m and Default Axial Magnetization A m fields allows to specify respectively a value of default magnetization for all blocks older than Cln and a value of default magnetization for the blocks associated with Cln 43 Set Global Parameters Rotation Model for APP calculations E Lab Data Ship_Tracks Peme40 rot Browse Default Full Spreading Rate mm yr 18 0 Mean declination
5. standard Geomag70 format see p 60 is specified through the dialog of Fig 39 59 Import Do lo along flow line Input IGRF DG F Total Field Data File at Survey Time JE Lab Data Ship_Tracks 01 030165 IGRF_01030165 tst Browse Output Geomagnetic Parameters Data File ENLab D ata Ship_Tracks 010301 65 params_01030165 2 txt Browse OK Figure 39 Dialog for the generation of a geomagnetic field parameters file Tools Project ship track data This is a key command of Magan which allows to project a ship track data set onto the current flow line Figure 40 shows the dialog that is displayed after the execution of this command I remind that Magan requires flow lines in which successive nodes have either monotonically increasing longitudes or monotonically increasing latitudes This information is supplied to the program in the projection dialog through the Output Data Sorting option In the Decimation distance along x axis km control the user specifies the minimum distance between projected points along the flow line Therefore the program performs data averages in order to assure the desired output resolution Project Ship Track Data Output Data Sorting Decimation distance along x axis km as Max Allowed Distance from Flow Line km 30 0 cnt Figure 40 Dialog for the projection of ship track data onto flow lines C Increasing Latitudes Increasing Longitudes Finally in the Max A
6. 30 lt w lt 150 with respect to flow line Default spreading asymmetry If k lt 8 this is the size of a pen in graphics e g velocity track lines etc If k lt 8 this is the RGB code of a pen in graphics e g velocity track lines etc File gt Save As This command saves the current project in a different file File gt Close This command closes the current project File Print This command generates a printout of the window content File Page Setup This command allows the user to select the printer and setup the printer page File gt Exit This command terminates Magan 33 3 2 Edit Menu Edit gt Flow Line gt Generate from Euler pole This command automatically generates a flow line as a small circle arc about an Euler pole The command opens a dialog window Fig 12 where the user specifies the coordinates Lat Lon of the Euler pole the opening angle in degrees and if the rotation is clockwise or counterclockwise It should be noted that Magan only accepts flow lines in which successive nodes have monotonically increasing longitudes or flow lines in which successive nodes have monotonically increasing latitudes Therefore the selection of the correct direction of rotation about the Euler pole is essential Euler Pole Pole Latitude Pole Longitude Total Opening Angle 20 Sort output data by Counterclockwise Rotation C Clockwise Rotation Node
7. Lon Lat pairs associated with each node in the flow line ordered list Such a file has a filename with the fl prefix in the current folder flname txt Files having a pr prefix prname txt are generated after the projection of magnetic data onto the current flow line They have the same table structure as the anname txt but only projected points are included in these files Finally the execution of the command Parameters Time Scale determines the immediate creation of an internal table containing the magnetization and velocity model This file has name mdname txt and has an entry for each chron in the selected time scale 4 2 Future versions Magan will be updated periodically as soon as people find bugs or after suggestions of improvements by the public Please do not hesitate to contact me if necessary A first improvement for the next version could be the capability of importing more NGDC track lines at a time rescaling the total field anomaly to a common time Another improvement could be represented by a more sophisticated de spiking algorithm 4 3 Acknowledgments The Magan project had its origin in the necessity of new software tools for a comprehensive re examination of the central Atlantic magnetic anomalies I give special thanks to my PhD student Luca Tassi who helped me both in the design and debug of Magan The extensive use of the software for his research project on the central Atlantic plate kinematics allowed
8. Spacing 0 1 Set Close Figure 12 Dialog for the automatic generation of flow lines from Euler poles 34 The selection of a node spacing in this dialog window Fig 12 determines the angular distance of the flow line nodes about the Euler pole When all the parameters have been inserted you must press the button Set and return to the project window without closing the dialog Here you click at the assumed location of the flow line origin and the program immediately generates a flow line passing through that point A successive click at a different location deletes the previous flow line and forces the creation of a new list You may even change one or more parameters in the dialog press the Set button again and come back to the project window When you are satisfied press the Close button to close the dialog and return to the current project Edit Flow Line Generate from rotation model This command automatically generates a flow line as a sequence of small circle arcs using the algorithm of Shaw 1987 To this purpose the program opens a dialog Fig 13 where the user specifies a rotation model the plate identifiers at negative and positive offsets the age of the oldest point Start Time and the age of the youngest point End Times The buttons Set and Close have the same meaning of the previous command Generate Flow Line from Rotation Model Source path to rotation file
9. a two dimensional problem The polygon approximating the body cross section has vertices v which are ordered clockwise 21 The unit vector associated with the magnetization direction can be written as n cos sina n cosI cosa 36 n sinI Therefore for any scalar field p constant in the y direction the directional derivative of along direction n results to be ov V a a sin Z 37 b n cos sin a n Ox Oz It is easy to determine the vertical and horizontal components of the anomalous field combining Equations 35 and 37 We obtain HoM og HoM 2 cos sina Esin 7 38 4nGp On 4nGp ox OZ MoM s Holt 2 ST sin 39 AnGp n 4nGp ax OZ Quantities g and g can be calculated respectively using Equation 28 because g y and a similar formula for g These formulae can be written as follows 2Gp Xo Ske 2Gp gt Z 40 n l n 1 22 where B Tat l X a log 0 0 41 n l a n 8 n l J B Tit l Z log a 9 9 42 n 1 02 g r A n l e Therefore substituting these expressions into Equations 38 and 39 we get M amp 3X X AF E ee ee z sin 43 2r Z O Oz N AF Hole gt 22 cos I sina OL sin Z 44 eT ac OX Oz Figure 9 Components of the Earth s reference field F in a local frame of reference H is the horizontal component X and Y are respectively the North
10. are located along the full range of x offsets associated with the user defined flow line as far as an user specified cut off distance is reached In this way the algorithm tries to minimize boundary effects which generally determine unreliable results towards the profile edges Once the quantities AT have been calculated for all the station points the program displays the resulting plot in a model profile window Fig 2 along with the magnetization model and observed anomalies Then the user can select one or more blocks at a time by mouse clicking and change remnant magnetization or full spreading rate during the corresponding chron The model is automatically changed after these operations Figure 11 Geometry and numbering of magnetized prisms The program starts building the magnetized blocks from the youngest e g Cln and stops when a block lies at offsets located outside the flow line cutoff distance For each chron the algorithm tries to build two conjugate blocks Note that block walls always dip towards the spreading axis 29 Chapter 3 Magan Commands 3 1 File Menu File New Project This command creates an empty project A new project window is open ready to receive further commands and flow line editing The default background image is the low resolution 5 min Terrainbase grid which has worldwide coverage and is available from NGDC The flow line editing rules are simple a A single mous
11. basis of the current rotation model In this instance if Q is the stage angle and AT is the chron duration and if Ox is the angular distance of a small profile segment from the stage pole during this stage then the linear distance Ax travelled by a point during the time interval A7 is scaled to angular distance Aag QyAT about the stage pole by the following relation Ao lt 58 Rsin where R is the Earth s radius The brown line in Fig 31 shows the time angular distance plot T T q predicted on the basis of the current rotation model Conversely black dots in Fig 31 show the T T a plot associated with the current magnetization model Therefore the user can compare the two plots and decide if the current block model is viable Time Distance Model DEK Figure 31 Mean Age Angular Distance window Vertical scale is in Ma whereas the horizontal scale is in deg Each point black dots represents the predicted mean crustal age at any angular distance from the origin according to the current magnetization model The brown line displays the plot T T amp accoring to the current rotation model 53 3 5 Tools Menu Tools gt Measure Distance This command is available from project windows Once you have launched the command click at the location of a starting point on the background image A small dialog opens which displays the distance in km and angular from the selected starting point as you m
12. et al 2004 M series time scales 40 Parameters Background Image This command allows to specify a background image to be used in the current project window A dialog opens where the user selects the path to a 256 colors bitmap file bmp containing the raster image Fig 19 Magan only reads Microsoft Windows indexed color bitmaps having a color depth of 8 bits per pixel The file must be accompanied by an ASCII header file hdr having the the same file name but different extension with the following rows ncols number of columns nrows number of rows xllcorner longitude of lower left corner yllcorner latitude of lower left corner cellsize bitmap resolution deg per pixel Magan assumes that the map projection of the background image is a simple planar geographic projection The parameters included in this header file are used not only for the appropriate display of the background image but also in a number of other computations Therefore it is essential that the user specifies correctly the parameters of the background image Windows Bitmap Selection Filename JE Lab Article 15 Data Ship_Tracks Background bmp OK Cancel Figure 19 Dialog for the definition of a background image 41 Parameters Background Color This command allows to specify a background color for the current project window when the background image is hidden A dialog opens where the user selects the RGB values of t
13. me to improve considerably the program design 70 References Blakely R J 1995 Potential Theory in Gravity and Magnetic Applications 441 pp Cambridge University Press Cambridge UK Cande S C amp Kent D V 1995 Revised calibration of the geomagnetic polarity timescale for the late Cretaceous and Cenozoic J Geophys Res 100 B4 6093 6095 DeMets C Gordon R G Argus D F amp Stein S 1994 Effect of recent revisions to the geomagnetic reversal time scale on estimate of current plate motions Geophys Res Lett 21 20 2191 2194 Gradstein F Ogg J G amp Smith A G 2004 Geologic Time Scale 2004 500 pp Cambridge University Press Cambridge UK Schettino A 1998 Computer aided paleogeographic reconstructions Computers amp Geosciences 24 3 259 267 Schettino A amp Scotese C R 2005 Apparent polar wander paths for the major continents 200 Ma Present Day A paleomagnetic reference frame for global plate tectonic reconstructions Geophys J Int 163 2 727 759 Schettino A 2012 Magan A new approach to the analysis and interpretation of marine magnetic anomalies Computers amp Geosciences 39C 135 144 doi 10 1016 j cageo 2011 07 007 Shaw P R 1987 Investigations of relative plate motions in the South Atlantic using SEASAT altimeter data J Geophys Res 92 B9 9363 9375 Talwani M Worzel J amp Landisman M 1959 Rapid gravity computations for
14. of reference field deg 18 200 Default Spreading Asymmetry 0 0 Mean inclination of reference field deg 54 800 Default Magnetization A m 5 0 Last Chron Cin Default Axial Magnetization A m 50 First Chron Left Side C5r 3r Magnetized Layer Thickness km o5 First Chron Right Side C5r 3r Block Walls Dip deg oao Model Res km 0 200 Survey Altitude km 0 0 Default Spreading Obliquity deg 115 0 Cutoff Distance o0 Plate Identifier at positive offsets Fo Plate Identifier at negative offsets 101 Figure 22 Dialog for the definition of the global parameters The Magnetized Layer Thickness km field specifies the thickness of the magnetized layer The default 0 5 km value should be appropriate for most situations The Block Walls Dip deg parameter specifies the inclination of the block walls The default value 90 is a correct choice in the case of normal to fast spreading ridges However according to Tivey 1996 prisms should have dipping polarity boundaries especially in the case of slow spreading rates e g Red Sea Therefore Magan allows to specify an angle other than 90 for the dip of block walls The Survey Altitude km allows to specify the altitude of the observation points Use a positive value in the case of aeromagnetic surveys zero default for most marine surveys a negative value when the magnetometer is towed at significant depth The Cutoff Distance field is used to accelerate
15. project windows Set a background raster image e g gravity in a ship track window Create a flow line where the magnetic data can be projected Import Kp index data and generate Kp index windows Generate magnetic and bathymetric profiles for the projected data Assign and change the ship track zero offset location in a project window Set inclination and declination of the reference field at the survey time along the flow line Set the block wall dip Load a rotation model for the calculation of synthetic Apparent Plar Wander Paths APWP Set default full spreading rate and asymmetry Specify a crustal thickness for the magnetized layer along the profile View magnetization models and model measured profiles in model profile windows Set the magnetization function along the profile Set the full spreading rate function along the profile Set the spreading asymmetry and obliquity functions along the profile Specify ridge jump locations Export model profiles Save anomaly crossing points along the profile Generate velocity windows Generate T x age distance and T a age angular distance windows Perform a stage analysis of age distance plots Figure 1 Project Window elements A flow line brown line parallel to existing fracture zones is used to project magnetic anomaly data of a ship track white line in the central Atlantic The background image shows the gravity anomalies pattern in this zone Ridge axis orienta
16. the calculation of model anomalies of long profiles This is the maximum distance in km at which the anomalous field generated by a block may influence an observation point The default value 50 km may be appropriate during the initial phase of forward modelling but should be substituted by a larger value e g 100 km when the model only needs few refinements The Mean declination inclination of reference field deg fields allow to specify the mean geomagnetic field direction at the survey time in the case of small scale surveys You can use the NGDC web server at http www ngdc noaa gov geomagmodels IGRFWMM jsp to calculate these parameters If the survey area is large more than 200 km it is possible to import a geomagnetic field direction for 44 each point in the flow line In this instance Magan calculates the model anomaly at a point using the declination and inclination of the closest flow line point The field Last Chron is used to specify the name of the chron of extinction of a spreading ridge or if it is still active Cln default value Similarly First Chron Left Side and First Chron Right Side specify the chron that will be associated to the oldest magnetized block respectively along the left and right side of the flow line If you leave one of these fields empty the program will assume that the oldest chron along the corresponding side of the profile coincides with the oldest chron included in the selecte
17. to avoid the projection of points that are too far away from the flow line the user specifies a maximum allowed distance of the data from the flow line It should be noted that a reliable analysis of marine magnetic anomalies requires that data do not cross fracture zones Therefore the user should select with care this parameter before launching the projection procedure When the ship track is highly oblique with respect to the azimuth of the surrounding fracture zones it is not appropriate to build a flow line as described above because this approach would require a large distance of projection Therefore in this instance it is convenient to create a flow line which interpolates the real ship track trend and use the global spreading obliquity parameter to set the angle between magnetized prisms and profile strike This trick allows Magan to perform correctly the computation of model anomalies The next chapter discusses the basic procedures adopted by Magan for the calculation of model anomalies starting from a projected ship track data set and a flow line Chapter 2 Calculation of Model Anomalies 2 1 Magnetic Anomalies A total field anomaly is calculated from total field measurements by subtracting a reference regional field usually the IGRF and eventually applying a diurnal correction which removes those components of the measured field associated with solar and ionospheric activity If T T r t is the measured magnit
18. trend of the flow line Then the components of the vector AF in the local frame of reference can be easily obtained by the following simple transformation AF AF sinB AF AF cosB 45 AF AF Zz It should be noted that the anomalous field vectors don t have y components in the x y z reference frames whereas they have non zero Y components with respect to the standard X Y Z coordinate system Therefore the total field anomaly at an observation point r AT is given by AT AF F AF F AF F AF cos 1 AF cos D AF sin D AF sin I 46 Evaluation of derivatives in formulae 43 and 44 is simple Z ae e i Ga G Tie Oz l log 8 41 0 P 47 P Q Furthermore OZ am E O 6 Gai 2G Fasl a R an S ox iz y Fai SaaS n n n l n n n 0 0 eRe ig eee Finally ox AOR 6 log Fai Cm oc 0 fa P ax R a nd where R IA y Fera b y 2 2 2 R r Tad n Sind 7 GAGs c ea a ae 6n Gaa Gea Zi Gra Gai Ga J SG oe 5 co AAAG 6 Ela 6n Cra Ena R r 2 n n l 48 49 50 SD 52 53 Also in this case the evaluation of angles 0 through the atan2 C library function must take into account of three special situations The first two conditions are the same of the gravity case whereas the third one is now if En 1 then 2 2 OZ ae OZ 2 O 6
19. two dimensional bodies with application to the Mendocino submarine fracture zone J Geophys Res 64 1 49 59 Talwani M amp Ewing M 1960 Rapid computation of gravitational attraction of three dimensional bodies of arbitrary shape Geophysics 25 1 203 225 71 Tivey M A 1996 Vertical magnetic structure of oceanic crust determined from near bottom magnetic field measurements J Geophys Res 101 B9 20 275 20 296 Won IJ amp Bevis M 1987 Computing the gravitational and magnetic anomalies due to a polygon Algorithms and Fortran subroutines Geophysics 52 2 232 238 12
20. D77 MGD77T MAG88T trackline file and you must have loaded a Kp geomagnetic activity indices table The graphic content of these windows can be saved as compressed PNG Portable Network Graphics files or standard Microsoft Windows bitmaps or printed Bathymetric Profile Figure 26 Projected bathymetric profile window Vertical scale is in mt whereas the horizontal scale displays the offset in km along the flow line starting from the origin View gt NGDC Source Data Submenu This submenu allows to open windows displaying respectively the magnetic bathymetric or Kp profile of an entire NGDC track line or an imported XYZ magnetic data set These windows are similar to those displayed in Figs 24 26 and 27 but in this case the horizontal scale displays the offset along the flow line starting from the beginning of the ship track 49 iQ Kp Index Profile Figure 27 Projected Kp index profile window Vertical scale is dimensionless 0 100 whereas the horizontal scale displays the offset in km along the flow line starting from the origin Figure 28 Velocity model window Vertical scale is mm yr whereas the horizontal scale is in Ma 50 View Velocity Model This command opens a new window displaying the current velocity model if any as shown in Fig 28 In this window each chron in the magnetization model is represented by a point whose horizontal error bar indicates the chron duration in Myrs Also
21. Data gt NGDC Trackline This command of the Tools Import Data submenu allows to import NGDC GEODAS MGD77 MGD77T trackline files a77 m77t and the new MAG88T m88t aeromagnetic data format into Magan Fig 34 You should consult the NGDC GEODAS site at http www ngdc noaa gov mgg geodas geodas html for more information about these data formats NGDC trackline files are the primary data source for which Magan has been designed although you may wish to import standard trackline data in ASCII format see below Open Look in 03110001 NRM e ex EB Filename 03110001 a77 Files of type MGD77 File a77 Figure 34 Dialog for the selection of an NGDC track line file to import If the operation is successful Magan displays the imported track line and is ready for data projection provided that a flow line has been loaded The magnetic and bathymetric data can be displayed through the View gt NGDC Source Data submenu Tools gt Import Data gt XYZ ASCII File This command allows to import any XYZ ASCII table xyz containing Lon Lat Anomaly triples when an MGD77 MGDC77T MAG88T file is not available Fig 35 In this case the bathymetric and Kp index profiles cannot be displayed through the View NGDC Source Data submenu 56 XYZ ASCII File Selection Filename C Magan Tests Red Sea Profile 1 mag xyz OK Cancel Figure 35 Dialog for the selection of an XYZ magne
22. E Lab Anticle 15 Data Ship_Tracks Pemed40 rot Browse Plate Identifier at Negative Offsets f 01 Start Time 1 20 Plate Identifier at Positive Offsets 71 4 End Time id an Figure 13 Dialog for the automatic generation of flow lines from rotation models 35 Magan follows the Paleomap Project conventions regarding rotation models Therefore a rotation model is an ASCII table rot whose rows have the field structure listed in Table 2 Table 2 Fields of a rotation model Field Name Value Plate 3 digit plate identifier 999 for comment lines Time Age of reconstruction pole Ma Lat Latitude of finite Euler reconstrruction pole deg Lon Longitude of finite Euler reconstrruction pole deg Angle Angle of finite rotation deg Ref Plate 3 digit reference plate identifier References Up to 50 characters of comment dT 208 0 nT Figure 14 Elements of a modelling window A simplified version of the Schettino amp Scotese 2005 rotation model is included in the Magan distribution package A tutorial on rotation models and their definition can be found at http www serg unicam it Tutorial html 36 Edit Velocity Submenu This set of commands is only available when the active window is a modelling window They may also be executed pushing the buttons on the right side control bar Fig 14 When you have selected one or more blocks they appear bounded by a red frame as
23. The MAGAN Project Ver 3 1 July 2013 Magan 3 1 User s Manual by A Schettino e mail antonio schettino unicam it University of Camerino Printed at the University of Camerino Copyright 2010 2013 Antonio Schettino All Rights Reserved Table of Contents 1 Introduction 1 1 Purpose 1 2 General Overview 1 3 Flow Lines 2 Calculation of Model Anomalies 2 1 Magnetic Anomalies 2 2 Modelling of Marine Magnetic Anomalies 2 3 Forward Modelling 3 Magan Commands 3 1 File Menu 3 2 Edit Menu 3 3 Parameters Menu 3 4 View Menu 3 5 Tools Menu 3 6 Window Menu 3 7 Help Menu 4 Miscellaneous 4 1 Magan Files 4 2 Future Versions 4 3 Acknowledgments References Il N e 10 26 30 30 34 40 46 54 67 68 69 69 70 70 71 IV Chapter 1 Introduction 1 1 Purpose The main objective of the Magan project is to design and implement a new free software package for the analysis and interpretation of marine magnetic anomalies Schettino 2012 The software is available to marine geophysicists with new advanced features with respect to older programs in an attempt to improve the reliability of anomaly identifications in plate kinematics studies In particular the program allows to VVVVVVVVVVVV VVVVVV VV VV VV Load a time scale of magnetic polarity inversions Import NGDC ship track data or other magnetic anomaly data Create load and save projects Manage ship track
24. These parameters can also be used for rocks of Pliocene Pleistocene age but in general older crust requires a different approach The along track magnetic anomaly is computed applying Equation 46 to the vector summation of the anomalous fields associated with each block in the magnetization model In order to determine the quantities J and a in Equations 43 and 44 we start from a palaeopole location or the geographic North pole if an APWP is not available and calculate the inclination using the well known GAD or dipole formula tan 7 2cot p 55 26 where p is the local palaeo colatitude of the profile If an APWP has not been defined the inclination is calculated using the present day geographic colatitude Calculation of a requires a knowledge of the site declination Let B be the local strike of the spreading axis 0 lt B lt 360 measured clockwise from the North Fig 10 Let D be the palaeopole declination If an APWP is not available then we set D lt 0 It can be easily shown that o is given by a D B 180 56 The previous calculations assume that a palaeopole location A is available for calculating inclination Z and declination D of remnant magnetization for the given prism Conversely quantities J and D are determined using the prism geographic colatidude 0 in the GAD formula and assuming D 0 when an APWP cannot be calculated However if an APWP is available for one of the two con
25. and East components Z is the vertical component positive if downward directed Declination Do is the angle between the North direction and the horizontal projection of the field measured clockwise The angle between projection H and the field is the inclination Io positive if F is downward directed We have shown that the total field anomaly can be easily calculated by projecting the vector AF onto the present day reference field axis Eq 3 Let Do and Jp be respectively the declination and 23 inclination of the reference field Fig 9 The components of the anomalous field vector AF that are calculated through Eq 43 and 44 are expressed in the local x y z frame of a prism In order to combine the contributions of several blocks through the superposition principle we must represent the anomalous vector components in a common reference frame Then the expected total field anomaly AT associated with the crustal field AF AF r can be calculated by projecting the vector AF onto the axis of the present day reference field F which has declination Do and inclination Jo in the X Y Z local reference frame of Fig 9 Therefore it is convenient to express the components of the anomalous magnetic field vectors generated by each block in the standard X Y Z coordinate system Let B 0 lt B lt 360 be the local strike of the y axis measured clockwise from the North As it is shown below this quantity is determined by the local
26. and locations of the ship track points and parameters txt is the name of the output file 62 The locations table must have 5 fields for each record according to the Geomag70 syntax for instance 1974 39 D KO 36 9433 25 9418 1974 39 D KO 36 9421 25 9448 1974 39 D KO 36 9409 25 9478 1974 39 D KO 36 9397 25 9508 Please read the Geomag70 syntax documentation available through the NGDC web server in order to set appropriately these fields Tools Spike Filtering This command is available when the active window is a projected magnetic profile window e g Fig 41 It allows to remove spikes that could result from solar activity measurement errors ship track data projection etc Magan uses a moving average algorithm for spike removal which substitutes the magnetic anomaly at any point along the profile with the average in a data window surrounding the point The window size is selected through the dialog window shown in Fig 42 This command does not automatically update the projected profile in the main project window To this purpose you must execute the command Tools Update Project Set Filter Size Moving Window Size Figure 42 Dialog for the definition of the window size in the despike algorithm 63 Tools Update Project This command is available when the active window is a projected magnetic profile window in which the magnetic anomalies have been modified by de spike filtering or a m
27. ational potential of a linear body such that illustrated in Fig 7 can be written as pla z dx dy dz V x 0 z G R Ve x f ty z 2 f 00 dy G p x z dx dz pel apo Gfplv2 im f in je s T uyr ty G p x z himliog a VP a log at VP a hicaz S 2 2 G plx z lim log lavde 19 o a r a where r a xY z zy and S is the cross section of the volume R orthogonal to the y axis Clearly as a the limit in 19 diverges and the potential approaches infinity This problem is overcome by changing the definition of the potential for infinitely extended bodies The potential of an infinite body is defined to be zero at a unit distance from the body r 1 This is accomplished by adding a constant quantity to the previous equation ao 2 2 2 Hs Gf in a vrt a 5 at vlt a Jove 2 S log atvrt a at vl a 2G p x y log ede 20 5 r 16 If we move the observation point to the origin of the reference frame and assume a constant density p the vertical component of gravity will be given by _ OV ante 2Gp 21 5 Oz Pfr z Integration over x yields y 2Gpfae arctan arctan 23 2Gp arctan dz 22 2 Z amp B S Z where and 2 are function of z and B S is the boundary of S As before we now approximate the perimeter of S with an N sided polygon having vertices 61 61 62 62 6n 6n
28. be displayed after that a Kp index table has been imported Tools gt Import Data Geomagnetic field parameters The default survey time geomagnetic field direction Do o which is used in Eq 46 to calculate model total field anomalies is specified through the global parameters dialog see p 43 However in the case of large ship tracks the model reference field e g the IGRF at survey time may change considerably across the survey area In this instance a more accurate computation of the model anomalies can be performed using a different geomagnetic field direction Do o for each point along the flow line This operation is enabled through the import of a sequence of geomagnetic field directions for the set of points composing the flow line In this case Magan calculates the model anomaly at a point using the declination and inclination of the closest control point The name of the ASCII txt file that will contain the geomagnetic field directions Do o for each control point Lon Lat along the flow line is specified through the dialog of Fig 39 The rows of the file that is generated by this command have the following 4 fields format Lon Lat Dec Inc This information is then used in modelling windows to generate the magnetic anomalies that form model profiles The Do o pairs are calculated starting from a table of reference field records which can be generated using the NGDC routine Geomag70 This table which must have the
29. c storms Determination of these components in Eq 1 can be performed using magnetic observatory data and or a special design of the survey tracks Unfortunately as most marine surveys lack these kinds of data the calculation of marine magnetic anomalies is simply performed by subtraction of the reference field Let AF be the perturbation of the main reference field caused by a crustal magnetic source If we ignore the external contribution then the observed field at location r and time f will be given by e g Blakely 1995 T r t F r t AF r 2 Figure 5 Relationship between main field F observed field T and anomalous field AF The relationship between observed and reference fields with the vector anomaly is illustrated in Fig 5 We note that the total field anomaly AT is not equivalent to the magnitude of the anomalous field AF because AT F AF F AF Note that in Equation 2 the anomalous field vector is considered as time independent which is only approximately true because a small component of time varying induced magnetization is always present in AF In order to understand the meaning of total field anomalies AT we must consider that under the typical conditions of crustal studies F gt gt AF In this instance we can write AT F AF F VF F 2F AF F F pa F2 3 FAR oo pA A F F F F F Therefore the total field anomaly AT approximately coincides with
30. d time scale The Model Res km entry is used to specify the spacing in km that Magan must use to generate model profiles Uses a small value e g 0 5 km when you want to gain a better look at the details of a profile Finally the Default Profile Obliquity deg allows to specify a common value of the profile obliquity angle yw for all blocks This value must be set according to the conventions illustrated in Fig 15 This parameter can be also used to analyze ship tracks that are too oblique with respect to the true flow lines of motion thereby preventing a correct projection of the magnetic data In this instance it is convenient to manually generate a flow line which interpolates the ship track independently from the real trend of the fracture zones and project the magnetic data Then it is possible to use the default spreading obliquity parameter to allow Magan to perform a correct computation of the strike of each magnetized prism Parameters Pen Styles This command allows to change the appearance of line features in all Magan windows A dialog opens where the user specifies thickness and color of flow lines ship tracks model magnetic anomalies etc Fig 23 Customize Pen Styles Curve Plot Pen Size Ti 2 a Green o Blue o Figure 23 Dialog for the selection of line styles thickness and color 45 Parameters Set Origin This is the last command in the Parameters m
31. ds in the case of W E flow lines Edit Add Ridge Jump This commands is only available when the active window is a modelling window and a single block is selected It allows to introduce a ridge jump in the magnetization model The command opens a dialog window Fig 16 where you can specify the number of blocks n that are jumped at the end of the current chron The jump direction is specified through the sign of the n a positive integer implies a rightward jump whereas a negative integer means leftward jump 38 Set Ridge Jump Number of Blocks iq Cancel Figure 16 Dialog for the addition of ridge jumps For instance if you select the block C18n 2n on the left side of the origin and specify n 43 then at the end of this chron the ridge is moved rightwards at the right side of C19n Therefore the left side block sequence would be modified as follows C20n C19r C19n C18r C18n 2n C18n 2n C18r C19n C18n 1r C18n 1n Conversely the sequence of blocks from C18n 2n to C19n would be missing on the right side of the origin positive offsets and the normal sequence would be substituted by the following C18n 1n C18n 1r C19r C20n Remove Ridge Jump Chron of Ridge Extinction EAEn carl Figure 17 Dialog for the removal of ridge jumps Edit Remove Ridge Jump This commands is only available when the active window is a modelling It allows to remove an existing rid
32. e axis 1 3 Flow Lines Flow lines are an important feature of Magan which allows the user to generate them manually or in two automatic ways These are lines where the ship track or aeromagnetic data must be projected before a forward modelling window can be open Fig 1 They could be locally parallel to the true flow line of motion as indicated by existing fracture zones or simply have a unique strike coincident with the average strike of the ship track In fact in most cases a track line swings irregularly about a definite direction Therefore generally the user will trace flow lines as arbitrary projection lines that interpolate the ship tracks In some cases it will be possible to project different neighboring survey lines onto a unique line of projection in order to generate an averaged magnetic profile A flow line can be simply defined by a pair of points generated by a couple of mouse clicks In this instance magnetic and bathymetric data are projected onto the great circle arc connecting the two points Alternatively the user may trace a more refined flow line which is parallel to the existing fracture zones if a background raster has been defined Each point in a flow line can be moved by dragging it onto a new location or deleted by a right mouse click The user may select a flow line node by clicking on it The current selected point appears as a red node The insertion of new points always occur after the currently select
33. e click far away from the current chain of nodes inserts a new point after the selected point b Clicking on an existing node causes the selection of the point The currently selected node is represented by a red circle After insertion of a new node this point becomes the selected node c A right click deletes an existing node d The selected node can be moved to another location by dragging it across the window e A flow line can be deleted at any time by pressing the key Del Available commands when the active window is a project window are e All File menu commands e Edit gt Flow Line which allows automatic creation of flow lines e All Parameters menu commands which allow to set the global parameters of a model 30 e View gt Zoom in Zoom out which allow to zoom over a window region or return to the previous view e View gt Background image which displays or hide the background image e View gt Ship Track data points which displays or hide locations of ship track data Of course this command is available when a ship track has been imported e View gt Projected data points which displays or hide the data after their projection onto the flow line e All View gt Projected Data menu commands These commands are available when an NGDC or other ship track data set has been imported and data have been projected e All View gt NGDC Source Data menu commands These commands are avai
34. ed node One of the points of a flow line must be assigned the role of profile origin zero offset point Of course such a point should be located on an active or extinct ridge It is important to note that Magan works correctly if and only if successive nodes in a flow line have either monotonically increasing longitudes or monotonically increasing latitudes When the user wants to analyze a short profile across a spreading ridge it is possible that the flow line is represented by a simple small circle arc about the current stage pole If the location lat lon of this stage pole is known for instance from global plate motions models such as NUVEL 1A DeMets et al 1994 then the user may ask Magan to automatically generate the flow line In this instance the user only needs to click at the location of the origin and the program generates automatically all the other points In the case of longer profiles which encompass several stages the flow line has a more complex geometry which can be assimilated to a sequence of small circle arcs In this instance the user may trace manually and eventually edit a line which is parallel to existing fracture zones or ask Magan to generate one starting from a preliminary rotation model Again the automatic generation of flow lines requires a click at the assumed location of the origin Once a flow line has been defined the user can project the ship track magnetic and bathymetric data onto it In order
35. enu It allows to specify that the current flow line node in a project window which appears in red must be considered as the profile origin which has zero offset This point should be located on the ridge axis and its position can be changed after inspection of the observed and model magnetic anomaly profiles Magan marks the flow line origin by a red line If the location of the origin is subsequently changed dragging the corresponding node across the window it is necessary to launch this command again Such a procedure generally represents the first step of forward modelling It has the objective to position correctly the axial model anomaly relatively to the observed profile 3 4 View Menu View Zoom in out These commands allow respectively to select a region of the current project window for closer inspection or return to the previous view View Background Image This command allows to display or hide the current background image View gt Ship Track data points This command allows to display or hide the nodes of a ship track line 46 View Projected data points This command allows to display or hide the relocated ship track data on the current flow line View Projected Data Submenu This sub menu allows to open windows displaying respectively the magnetic bathymetric or Kp profile of a projected data set Therefore these commands are only available after projection of ship track data onto the curren
36. eparated by newlines 31 File Save Project This command saves the current project Projects are ASCII files containing a sequence of rows with the format param value where param is a project parameter name and value is the current value Allowed keywords and values for project parameters are listed in Table 1 The order of inclusion in the project file is non influential Table 1 Parameter keywords and allowed values in project files Parameter Keyword Value Time_Scale RotModel Background_Image Project_Folder Basement_Grid Velocity Magnetization Thickness Dip Altitude Cutoff D I Mod_Res PosOffsetPlateId NegOffsetPlateId Last_Chron First_ChronL First_ChronR Origin Selected Background_Color Spr1_X Spr2_X Spr1_Y Spr2_Y BmpOverlaid ShipTrackPoints ProjectedPoints Aeromag Data_Sorting Full path of an ASCII file containing the time scale txt Full path of an ASCII file containing the rotation model rot Full path of a 256 colors raster to be used as background image bmp Path to the folder where the project data are stored Full path of a single precision floating point grid containing basement depth data flt Default velocity mm yr Default magnetization A m Block thickness km Dip of block walls 30 lt lt 90 Altitude of survey km Cut off distance for model anomalies calculation Declination of reference field deg Inclination of reference field
37. es of the crossing point By convention Magan writes the positive offset crossing point row first 64 Tools gt Reset gt Current Model This command is available from modelling windows It resets the current model to the initial values of spreading velocity asymmetry magnetization and obliquity It also removes any ridge jump Tools Reset Left Side This command is available from modelling windows It resets the current model to the initial values of spreading velocity asymmetry magnetization and obliquity along the left side only It also removes any ridge jump Tools Reset gt Right Side This command is available from modelling windows It resets the current model to the initial values of spreading velocity asymmetry magnetization and obliquity along the right side only It also removes any ridge jump Tools gt Rebuild Current Model Alos this command is available from modelling windows It simply rebuilds and displays the current model when some global parameter has been changed from the main window Tools Generate Crossing Points File This command is available when the active window is a modelling window and generates a crossing point file having the structure discussed above see the command View Age Distance model 65 Tools Find Stages This command is available when the active window is an age distance window in the mean age mode see the com
38. ferent from those associated with the current profile the command fails and an error is displayed Figure 37 shows the import dialog for this command Distance Anomaly ASCII File Selection Filename C Magan Tests Red Sea ffProfile_1 tet OK Cancel Figure 37 Dialog for the selection of an XZ filtered profile to import Tools gt Import Data Kp Geomagnetic activity indices This command allows to import UKSSDC ASCII tables txt containing sequences of Kp indices which are available from the UK Solar System Data Centre at http www ukssdc ac uk The first 8 rows of these files are ignored by Magan The renaining rows must have the following format YYYY MM DD Time Index where YYYY is the year MM is the month DD is the day Time is the three hour time and Index is the Kp geomagnetic index in the range 0 90 A Kp index file Kp index_1960 Jan 01_2009 Feb 28 txt for the time interval from 1960 through February 28 2009 is already included in the Magan distribution package Figure 38 shows the import dialog for this command 58 Kp Index UKSSDC ASCII File Selection Filename C Magan Data Kp index_1960Jan 01_2009 Feb 28 txt OK Cancel Figure 38 Dialog for the selection of a Kp index file to import Kp index profiles which are available for NGDC data sets through the commands View gt NGDC Source Data gt Kp Index Profile and View Projected Data gt Kp Index Profile can only
39. ge jump in the magnetization model The command opens a dialog window Fig 17 where you can select the chron at the end of which a ridge jump must be removed 39 Edit Set Chron Grouping Mode Also this commands is only available when the active window is a modelling It allows to simplify the construction of a block magnetization model through the grouping of blocks within chrons in single selections In other words a single click allows to select the parameters of all the blocks within a chron e g C2An 1n C2An 1r C2An 2n C2An 2r C2An 3n and C2Ar within chron C2A and change the their parameters Similarly the navigation keys TAB SPACE etc now operate on chrons and not on the single subchrons 3 3 Parameters Menu Parameters Time Scale This command allows to specify the time scale that must be used in the construction of the magnetization model A dialog opens where the user selects the path to an ASCII table file containing the time scale Fig 18 Time Scale File Selection Filename E Lab Article 15 Data Ship_Tracks CK GTS2004 txt OK Cancel Figure 18 Dialog for the definition of the time scale A time scale table must be composed by three fields rows that specify top age base age and name of each chron from the youngest Cln to the oldest The time scale CK GTS2004 txt included in the Magan distribution package is a combination of the Cande amp Kent 1995 C series and Gradstein
40. he new background color Fig 20 Set Background Color Background Color el th Red 200 HE Green 255 HARAR Blue 200 Cancel Figure 20 Dialog for setting a background color Parameters Bathymetry Basement grid This command allows to specify the path to a 32 bits floating point file flt containing basement or bathymetric depths as negative real numbers representing the depth in meters The file can be easily generated using any GIS software e g GlobalMapper It must be accompanied by an header file having the same structure of the header files which are attached to background images Figure 21 shows the dialog that is used to select a basement bathymetry grid 42 32 Bits Floating Point File Selection Filename JE Lab Article 15 Data Ship_Tracks Catl fl OK Cancel Figure 21 Dialog for the definition of a basement bathymetric grid Magan uses the information included in this file to determine the geometry of all magnetized blocks in a model Therefore it is mandatory to specify a basement bathymetry grid before opening modelling windows Furthermore the program could generate run time errors if the the geographic extent of the selected grid is not sufficient to cover the location of all the blocks Parameters Global parameters This command allows to specify the global parameters of a block model A dialog opens where the user enters the values of the new parameters
41. hron in the time table Velocities are initially set to a unique default value vy v k 1 2 7 but the user generally changes these quantities interactively during the forward modelling procedure Similarly the default spreading obliquity y is initially set to 90 for all blocks but the user can change this value when the observed magnetic stripes are oblique with respect to the local fracture zone trend Finally the algorithm accepts a sequence of magnetization amplitudes Mg k 1 2 7 Also these quantities are initially set to a unique value Mg M which is typically changed during the subsequent modelling phase Figure 10 Local coordinate system for a prism at location Q along a flow line FL starting from a present ridge axis R ppp is the palaeopole location for the prism calculated from the mean age of the associated chron z axis not shown points downwards The modelling algorithm starts with the generation of a crustal magnetization model according to the selected time scale and full spreading rates 1 Fig 11 The model consists of a sequence of polygons Px k 1 2 8 S lt 2T having vertices ak n Ekn G kn that are computed from the bathymetric data the spreading velocities and the magnetized layer thickness Although the algorithm computes magnetic anomalies for the restricted range of x offsets where projected ship 28 track data are available calculations are accomplished using blocks that
42. iles are created by executing the File Save Project and File Save as commands You may edit these files directly using a text editor for instance if you want to change a file path Once you have created a project the folder where you have stored the project file becomes the project folder and Magan uses this location to store any other internal file If you import an NGDC GEODAS MGD77 trackline file having file name name a77 where name is any string allowed by the operating system Magan creates an ASCII table having the following file name a77_name txt which contains the same information of the original file but can be easily read by a spreadsheet program such as Microsoft Excel Similarly when you import an NGDC GEODAS MGD77 trackline file having file name name m77t Magan creates an ASCII table having name m77t_name txt Finally a file having name m88t_name txt is created when you import an NGDC GEODAS MAG88 file having file name name m88t In the latter case altitudes are converted from feet to meters These files are not used by Magan they are only created for your convenience However the execution of the command Tools Import Data gt NGDC Trackline determines the creation of another file which is for internal use only and should not be edited by the user Its name has the an prefix in the current folder anname txt 69 Another Magan internal file is generated after the creation of a flow line It simply stores the
43. in this case the graphic content can be saved as compressed PNG Portable Network Graphics files or standard Microsoft Windows bitmaps or printed Time Distance Model 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 Figure 29 Age Distance window Vertical scale is in Ma whereas the horizontal scale is in km In this example the redu curve refers to the eastern side positive offsets whereas the blue curve represents ages along the western side negtive offsets View gt Age Distance model This command opens a new window displaying age distance plots as shown in Fig 29 These curves show the predicted crustal age at any orthogonal distance from the spreading axis according to the current velocity model It should be noted that in these windows the distance x corresponding to any given time T is always calculated as an offset from the ridge along a theoretical flow line of motion assuming obliquity y 90 independently from any user defined flow line and obliquity angles Conversely modelling windows show an age distance relation which depends from both the 51 spreading rates and the obliquity of the magnetized prisms with respect to the flow line In the case of symmetric spreading the two age distance curves overlap In the example of Fig 29 the magnetic profile reaches 1200 km offset from the origin along the eastern side and 3000 km along the weste
44. initely thin laminas Then the boundary of each lamina is approximated by a polygon Fig 6 The observation point is placed at the origin of a reference frame Let s consider first the calculation of the gravity of a mass distribution 10 8 7 9 Na tl Fn oe N Tig x Figure 6 Stack of laminae in the Talwani amp Ewing s 1960 method of calculation The potential V of the distribution is given by V G Place 4 R where R is the region containing the mass distribution p p r is the local density and G is the gravitational constant The gravity associated with this potential is g VV cf py F dyaz 5 We are generally only interested to the vertical component of gravity because gravity meters just measure this quantity If we indicate this component by y then ee pla L zdxdydz 6 R x y EZ irn This equation has the general form y f olx y zyx y zMxdydz 7 R where the function Zz yix y z G 8 x y z paye is called a Green s function We now assume that the density is constant within the region R 12 In this instance Equation 6 reduces to dxd S a l J ye e Gp T z zdz 9 S z x y 27 Kl Zi where T z 10 dale a y an zy The integral I z represents a surface integral over a single horizontal lamina of the body As shown in Fig 6b it can be converted into a line integral around the pe
45. is profile are crustal expressions of existing chrons in the selected time scale The user can locally change the magnetization amplitude or the full spreading velocity and obliquity of any block He she can set a spreading asymmetry simply specifying different velocities for conjugate blocks Ridge jumps can be introduced clicking on a block and assigning a jump width in terms of number of blocks and direction Once the user has obtained the desired match between theoretical and observed profiles crossings corresponding to stage boundaries can be exported for future construction of isochrons Figure 2 illustrates the main features of a forward modelling window z Magnetization Model DER Model Anomalies 100 Magnetization Model Figure 2 Forward modelling Windows Individual blocks can be selected to change magnetization amplitude or full spreading velocity The model is automatically updated when velocity and or magnetization are changed Another important and innovative feature of the program is represented by its capability to calculate the correct anomalous field generated by each block according to the following criteria 1 The strike of each prism is calculated locally along the user defined flow line This means that the spreading direction is not considered as constant for the whole profile Instead this quantity is calculated independently for each block in the model 2 A rotation model supplied by the user
46. is used to generate a synthetic apparent polar wander path APWP for each conjugate plate These data are used in turn to determine inclination and direction of remnant magnetization for each block in the model The quality of an interpreted data set can be assessed on the basis of a magnetic disturbance index during the survey Magan can generate a plot of the Kp index along any NGDC ship track allowing an evaluation of the data at local scale at 3 hours intervals Once a magnetic profile has been interpreted two additional plots can be generated namely a full spreading rate curve for the profile Fig 3 and a time distance plot showing the mean age at any distance from the spreading center Fig 4 Time Ma 40 Figure 3 Full Spreading Rates Windows Each point represents the full spreading rate during a user defined stage Error bars represent stage widths Finally it should be noted that this software does not include a module for the computation of finite reconstruction poles and associated statistics starting from a data set of crossing points Such a module will be included in the free distribution of PCME Schettino 1998 which should be released in 2012 The following section discusses the importance of flow lines in the forward modelling approach adopted by Magan Figure 4 Time Distance Windows The two lines show the crustal age on each flank of a spreading center at any distance from the ridg
47. jugate plates quantities Z and D must be determined also for the other plate when the flow line is symmetric with respect to the present day or exinct spreading axis Let 7 and D be respectively the inclination and declination of magnetization along the conjugate prism Clearly the two blocks formed at the same latitude Therefore we can assume that I Conversely the declination will be different for the two conjugate prisms However knowing the local strike B of the conjugate block it is possible to calculating D through Equation 56 because the strike o is the same for the conjugate prisms D a f 180 57 The algorithm of calculation of model magnetic anomaly profiles has in input a time table t ti 1 X J 1 2 7 the rows of which specify top and base in Ma of each chron and its formal name e g C2n Each chron name must terminate with an n or an r according to the chron polarity The program uses this information to determine the orientation of magnetization Also the algorithm requires to specify offset d and altitude h of the observation points in km Altitudes h have a unique default value h h which is generally zero in the case of ship track data However the user may wish assigning to this quantity a different value in the case of aeromagnetic surveys or special situations A sequence of T values of the spreading rate is the third input data set 27 one for each c
48. lable when an NGDC or other ship track data set has been imported e View gt Velocity model which opens a velocity vs time window This command is only available when a time scale has been loaded and a flow line origin has been defined e View gt Age Distance model which opens a crustal age vs distance window This command is only available when a time scale has been loaded and a flow line origin has been defined e Tools gt Measure Distance which allows to measure a distance over the background map e Tools gt Theoretical Profile which allows to generate theoretical magnetic anomaly profiles according to specified parameters e All Tools gt Import Data menu commands e Tools gt Project ship track data which allows to project raw magnetic and bathymetric data onto a flow line e Tools gt Set magnetic layer depths from gridded data which allows to define the depth of track line magnetic data from gridded bathymetry e Tools gt Export magnetic profile for filtering which allows to generate an ASCII table of magnetic data and offset that can be filtered by an external program e Tools gt Forward Modelling which opens a new modelling window File Open Project This command opens an existing project and creates a project window for editing or running modelling windows velocity windows or age distance windows Magan projects are ASCII files containing a sequence of param value pairs s
49. llowed Distance from Flow Line km control the user specifies the maximum distance from the flow line that a data point must have in order to be projected All other 60 data are discarded This command may be executed again if the resulting projected data set is incomplete for instance if the user selected a too large distance from the flow line or when the decimation distance was incorrect Tools Set magnetic layer depths from gridded data I admit that this command is not much useful It simply substitutes the depth of the magnetic source at the location of each projected datum by a new value which is extracted from a grid For instance the user may want to use true basement depths instead of bathymetry However the command is uninfluential for the construction of the magnetization model because modelling windows always employ user supplied basement bathymetry grid Therefore it is only useful when the user wants a display of the magnetic profile through the command View Projected Data gt Bathymetric Profile and the correct depth to basement must be shown The grid file selection occurs through the dialog of Fig 21 Tools Export magnetic profile for filtering This command allows to export a projected data set as an ASCII XZ table containing Offset Anomaly pairs Then the file can be sent to other computer programs e g Autosignal for filtering procedures For instance you could want to remove the profile tre
50. mand View Mean Age Linear Distance It opens a dialog window where the statistical parameters of a linear spline regression fit of the mean age distance curve are displayed Fig 43 Time Distance Model Stage Analysis RMS Error Myrs Anomaly MOr Knot Km Time Ma 725 01 2502 74 Velocity mm yr 45 34 Close 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 Figure 43 Linear splines fitting of a mean age distance plot Red points are the user defined regression knots The dialog shows the rms error of regression and the stage parameters anomaly time mean stage velocity location Then the program waits for the insertion of knot locations which is performed clicking at a point where a change of dip occurs Only the x coordinate of the clicked screen location is important for the definition of new knots Conversely deletion of a knot requires a precise right click on the corresponding regression curve node After each knot insertion or deletion the program updates the content of the report dialog with the new rms error of regression and list of stage boundaries For each stage are displayed the anomaly name of the old boundary the anomaly time and the mean stage velocity The user can browse other stage parameters by selecting other knot locations 66 3 6 Window Menu Window Cascade This c
51. n of these quantities when the observation point is located between C and Cn 1 Therefore the following tests are performed if sgn C sgn Cn4i then if G Gn41 lt En 1Gn and Cn 1 0 then 0 lt 0 27 else if EnGn41 gt En iGn and Gn 2 0 then On41 lt lt On41 27 else if GnGn 1 amp 41Gn then y lt 0 j if 6n Gr 0 or amp n 1 Gas 0 then y lt 0 if En En 1 then 1 b 2 oe ves Oo Ona a 0 By log QO r n Tal The typical conventions for the calculation of normal gravity through Eq 28 require clockwise polygons and a downward directed z axis as shown in Fig 7 Consider now the problem of calculating the magnetic anomaly generated by a magnetized 2 dimensional body This anomaly can be easily computed by the Poisson s relation using the previous equations Consider a body with uniform magnetization M and density p A small element of the body can be considered as a single dipole having magnetic moment m Mdxdydz If the observation point is placed at the origin then a dipole at location r generates a small magnetic field dB which is approximately given by dB 2 A ies Jaa 29 r 5 An r where uo is the vacuum magnetic permeability uo 420x107 H m 19 Therefore the potential dV is given by av H MT dedy YOM v i jae 30 4 An r T r Integrating Equation 30 over the region R occupied by the body gives the total magnetic poten
52. nQ Gu Ga52 arctan Q E 6 2 17 n l 14 where Q x y z eB 0 2 18 xhi a k B 022 B2 ix y 2 Substituting the solution 17 into equation 9 provides the vertical component of gravity in the origin In general integration over z can be performed using standard numerical techniques and should not constitute a problem The basic idea of converting a surface integral into a line integral around the surface boundary also represents the starting point of the method proposed by Talwani Worzel amp Landisman 1959 for calculating the gravity anomalies of two dimensional bodies A geological structure having a linear trend for example a long horizontal cylinder generates linear magnetic or gravity anomalies and can be modelled by sources respectively magnetic or gravitational that are invariant along the direction parallel to the long side In this case the y axis is often chosen parallel to the invariant direction Fig 7 leaving calculations to be performed only with respect to the x and z dimensions We say that the corresponding problem is two dimensional This class of forward modelling problems can be solved by approximating the cross section of the body by an N sided polygon in a way similar to that illustrated in Fig 6c As the density of a two dimensional source does not vary along the y dimension we can set p p x z Figure 7 Geometry of a two dimensional problem 15 The gravit
53. nd through a Fourier filtering algorithm Use the command Tools Import Data gt Filtered magnetic profile to import the filtered data set Fig 41 shows the data set of Fig 24 after a high pass filtering which removed a 100 nT constant component 61 Z Magnetic Profile Figure 41 Magnetic profile of Fig 24 after external high pass filtering Tools Set ship track anomalies from IGRF DGRF data This command is available from project windows when an NGDC ship track has been loaded into the current project It allows to recalculate and set the ship track anomalies on the basis of an updated Earth s magnetic field model It is particularly useful when some ship track records specify the total field value but not the corresponding magnetic anomaly which is obtained subtracting a reference field value The command assumes that you have compiled a table of reference field records containing a set of field parameters for each ship track location The format of this table must coincide with the standard output of Geomag70 namely Date Coord System Altitude Latitude Longitude D_deg D_min I deg I min H_nT X_nT Y_nT ZnT F_nT dD_min dIl_min dH_nT dX_nT dY_nT dZ_nT dF_nT You can easily generate such table using the following Geomag70 syntax Geomag70 model f locations txt parameters txt where model is the name of an IGRF model e g igrf1 cof locations txt is the name of a table which specifies dates
54. odelling window after any change of velocity or magnetization In the former case the program updates the projected magnetic anomalies In the case of modelling windows the program updates an internal table that is used for the construction of velocity windows age distance windows etc Tools gt Forward Modelling This command is available from the main project window It launches the forward modelling procedure through the construction of a magnetization model and the progressive match between observed and model anomalies Fig 2 The program allows to save the graphic content of these windows as compressed PNG Portable Network Graphics files or standard Microsoft Windows bitmaps The graphic content can also be printed Finally the user can save an ASCII txt text table with the observed and model magnetic anomaly profiles using the commnd File Save as This kind of windows also allows to generate crossing point files through the command Tools gt Generate Crossing Points File These files are ASCII tables txt containing as much rows as are the magnetized blocks in the model Each row has the following five fields Chron name Top age Offset Longitude Latitude Chron name is the name of a chron e g C6n according to the current time scale Top age is the upper age of the corresponding chron Offset is the anomaly distance along the flow line starting from the origin Longitude and Latitude are the geographic coordinat
55. ommand stacks all open windows and overlaps them so that part of each underlying window is visible Window gt Tile vertical This command arranges your open windows from left to right so that they display next to each other If there are more than three open windows Magan arranges them in a manner that allows more height than width Window Tile horizontal This command arranges your open windows from top to bottom without overlapping one another If there are more than three open windows the IDE arranges them in a manner that allows more width than height Window Arrange icons his command rearranges any icons on the desktop The rearranged icons are evenly spaced beginning at the lower left corner of the desktop This command is useful when you resize your desktop that has minimized windows It is unavailable when no windows are minimized Window Close all This command closes all open windows 67 3 7 Help Menu Help About Magan This command displays the Magan version and contact information 68 Chapter 4 Miscellaneous 4 1 Magan Files All Magan files are simple ASCII text files As already mentioned project files contain a sequence of rows with the format param value where param is a project parameter name and value is the current value Allowed keywords and values for project parameters are listed in Table 1 The order of inclusion in the project file is non influential These f
56. ove the mouse Click again to close this dialog and switch back to the editing mode Tools Theoretical Profile This command allows to generate theoretical magnetic anomaly profiles e g for teaching and testing purposes It is available when a time scale has been defined Once you have launched the command the following dialog window allows to specify the profile parameters Fig 32 Set Theoretical Model Parameters _ Depth to source fm j4000 Present day strike deg joo Full Spreading Rate mm yr 200 Declination of reference field deg bo Intensity of Magnetization A m 50 Inclination of reference field deg oo Magnetized Layer Thickness km o5 Last Chron Ein Altitude of observation km joo Oldest Chron C34 Paleostrike of normal polarity prisms deg joo Model Resolution kml hoo Paleo Latitude deg o0 Profile Obliquity deg 30 0 OK Cancel Figure 32 Dialog for the selection of the parameters of construction of theoretical magnetic anomaly profiles 54 The Depth to source m field specifies the depth of the magnetized layer zero is sea level The default 4000 m value should be appropriate for most simulations Full spreading rate intensity of magnetization thickness altitude declination and inclination of the reference field first and oldest chrons model resolution and profile obliquity have the same meaning of equivalent global parameters see Fig 22 Paleo
57. rimeter of the lamina In fact let x1 y1 and x2 y2 be respectively the points having absolute minimum and maximum of y within the region S z We also assume that the region S z has not relative maxima or minima for variable y In this instance the boundary of S z can be represented by two functions x y and x la y connecting x1 y1 to x2 y2 For any function f x y on the surface of the lamina it results eias dy eoi falele 0 9 Fe O y Foy an S z yw 4 y yy B z where B z is the boundary of S z Therefore the quantity I z in Eq 10 assumes the following expression T z ch dy 12 This integral can be calculated by approximating the perimeter B z of the lamina through a polygon having vertices 1 C1 2 C2 EnGn aS Shown in Fig 6c This is equivalent to 13 approximate the functions y and lo y by piecewise first order polynomials Therefore the line integral 12 will be converted into a sum of simple integrals 13 N Cn P T z dy Cna S z x 42h ty gc N 1 The variable x in this equation can be easily expressed in terms of y because the path is composed by straight line segments x a ytB 14 where a 1 aF Q nt gt n z n Z0 n 15 Cosy aF p S Finally substitution in Eq 13 provides n l N Sna a y E OD See 3 Nu 1 16 9 x y z 2 fo 1 20 B B 2 P i The solution of these integrals gives z X arcta
58. rn side Time Distance Model DER 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 Figure 30 Mean Age Distance window Vertical scale is in Ma whereas the horizontal scale is in km Each point represents the mean crustal age at any distance from the origin where the average is performed between the two flanks of the spreading ridge View gt Mean Age Linear Distance This command is only available when the active window is an age distance plot Fig 29 It calculates the average crustal age T x at each offset x and displays a point for each chron in the model Fig 30 It is used for the detection of tectonic stages characterized by approximately constant spreading velocity through the command Tools Find Stages Use the command again to switch back to the standard view View gt Angular Distances This command is only available when the active window is an age distance plot in the mean age mode Fig 30 It allows to convert the linear distances expressed in km into angular distances about the sequence of stage poles which are independent from the location of the profile Magan 52 uses the rotation model specified through the Global Parameters dialog Fig 22 to calculate the angular distance corresponding to each top age of the block model Assume that each chron in the time scale forms a stage whose stage pole can be calculated on the
59. shown in Fig 14 You can increase or decrease the velocity on the side where the block is located during the corresponding chron by the specified amount This operation does not affect the velocity on the opposite flank of the ridge Therefore both the average full spreading rate and asymmetry during the selected chrons change after this operation To select a single block simply click on its area In order to select a set of blocks not necessarily adjacent each other hold the SHIFT button pressed while clicking successive blocks When you want to select a sequence of adjacent blocks from both flanks of a ridge it is more convenient to select the first block and then press repeatedly SHIFT TAB to select all the successive blocks Finally when you want to select a sequence of adjacent blocks from one flank only press repeatedly ALT Gr TAB or the SpaceBar to select all the successive blocks Edit gt Magnetization Submenu This set of commands is only available when the active window is a modelling window They may also be executed pushing the buttons on the right side control bar Fig 14 When you have selected one or more blocks you can increase or decrease the magnetization on both sides of the ridge during the corresponding chron by 1 A m Therefore this operation affects the magnetization of the blocks on both sides of the ridge even if you have selected only one block Edit gt Obliquity Submenu Also this set of commands is onl
60. strike of normal polarity chrons allows to specify the parameter a strike of magnetized prisms at the time of formation that will be used to calculate the anomalous field through 43 and 44 Note that this quantity is the strike of a magnetized block measured counterclockwise from the paleomagnetic North to the negative y axis Fig 8 The paleolatitude parameter will be used by Magan to determine the inclination of magnetization J Finally the present day strike specifies the parameter B of Fig 10 It is the local strike of the y axis measured clockwise from the North Once you have pressed OK a new window opens which shows the magnetization model and the corresponding theoretical magnetic anomaly profile The user interface of these windows is similar to that of the modelling windows Fig 33 i i sm Magan Sr Fie Ean ow Hei llk Cin v 20 00 mm yr M 5Ajm Obi 90 Ses Magnetization Model v 10 AAIRIRIATIT ENI MAL AIPA TTT OE Te i im T 50 50 Ma x 505 0 Km dT 82 0 nT Figure 33 User interface for theoretical magnetic anomaly profile windows Also in this instance you can click a block in the block model to obtain information corresponding chron name velocity etc Finally you can change the spreading velocity magnetization and profile obliquity using the control bar on the right pane 55 Tools gt Import
61. t flow line Note that the bathymetric profile could not be available This is the case when NGDC bathymetric data are missing or when the magnetic data have been imported as simple XYZ files In this instance you can use the command Tools Set magnetic layer depths from gridded data to assign a depth value to each projected data point The difference between standard and unsorted magnetic profiles is associated with the procedure of projection onto a flow line In general a standard magnetic profile Fig 24 is used to display the final result of the procedure of projection and averaging of several segments of a ship track onto a flow line In fact depending on the maximum distance of projection see the command Tools Project ship track data one or more track segments can be combined to form a magnetic profile that will be subsequently used in the forward modelling procedure Such a profile is ever displayed in the modelling windows along with the model profiles calculated by Magan However you may wish to generate a plot of the projected magnetic data independently from the modelling procedure In this case you can use the command View Projected Data Magnetic Profile to open a window which displays the result of the projection procedure as shown in Fig 24 When different segments of the same ship track are combined some care must be put in using the averaged profile in the forward modelling procedure In fact because of naviga
62. the projection of the anomalous field onto the reference field axis In other words AT approximates the component of the field generated by the crustal sources in the direction of the regional field Typical total field anomalies range from a few nT to thousands of nT with an rms value of 200 300 nT Therefore the condition F gt gt AF is usually met Note that in general AT is not a function of the position only even if we consider AF as a time independent vector quantity because it is obtained by projecting AF onto a time varying field direction 2 2 Modelling of Marine Magnetic Anomalies In general the forward modelling procedure of identification of marine magnetic anomalies requires the calculation of the vector field AF AF r associated with a distribution of magnetized blocks of oceanic crust Then total field magnetic anomalies are calculated for the survey time and compared with the observed anomalies A best match is found by trial and errors varying the spreading rate function hence the width of crustal blocks having normal or reversed magnetization Consider now the problem of calculating the gravitational or magnetic field generated by a distribution of mass or respectively magnetization The method described here was first proposed by Talwani amp Ewing 1960 and subsequently modified by Won amp Bevis 1987 to improve the computational efficiency In this approach a body is represented by a stack of inf
63. tial V vato MT pave Ho vf Jae GD Ane r An RA R This formula is similar to solution 4 for the gravitational force of a mass distribution if the body density is constant In fact in this instance Equation 4 gives V Gp l dxdydz 32 R g VV Gpy Jaya 33 r R Therefore the magnetic potential of a uniformly magnetized body having constant density can be written as HoX V M g O H 34 4nGp 2 4nGp j a 20 where y is the magnetic susceptivity and H is the inducing geomagnetic or palaeomagnetic field This Equation is called the Poisson s relation It states that the magnetic potential of a uniformly magnetized body having constant density is proportional to the component of the gravity field in the direction of magnetization Therefore taking the gradient of Eq 34 we obtain that the anomalous field of a body in a 2 dimensional problem can be written as AF VV UM Og Lox Og 4nGp n 4nGp n 35 where n is the direction of induced or remnant magnetization This solution implies that unlike the gravity anomaly the magnetic anomaly also depends on the strike of the body as this affects the direction of magnetization Let J and a be respectively the mean palaeomagnetic field inclination in the survey area and the strike of the body measured counterclockwise from the paleomagnetic North to the negative y axis Fig 8 Magnetic North Figure 8 Conventions and geometry of
64. tic profile to import Tools gt Import Data gt Projected XYZ Data This command is similar to the previous one except that in this instance the data are considered as already projected data and the ship track coincides with the flow line Therefore a flow line coinciding with the track is implicitly loaded along with the track and there is no need to project further the data Also in this case an XYZ ASCII table xyz containing Lon Lat Anomaly triples is supplied by the user through the dialog shown in Fig 35 Tools gt Import Data gt XY ASCII Flow Line This command allows to import any XY ASCII table txt containing Lon Lat pairs of a flow line for instance when this line has been generated through a GIS software Figure 36 shows the import dialog for this command XY ASCII File Selection Filename C Magan Tests Red Sea Profile_1 txt Figure 36 Dialog for the selection of an XY flow line to import 57 Tools gt Import Data gt Filtered magnetic profile This command allows to import any XZ ASCII table txt containing Offset Anomaly pairs It is assumed that the user has first exported the current magnetic profile of projected data through the command Tools Export magnetic profile for filtering and that the data have been filtered through an external program Then this command substitutes the original magnetic data set by filtered data at the same offsets If one or more data offsets are dif
65. tion errors up to 10 km different track segments could not be correlable thereby the final magnetic profile would be affected in an unpredictable way by the combination of various data sets Therefore if you are using complex ship tracks it is good practice to generate an unsorted magnetic profile in order to test the self correlation of the ship track segments and detect incoherencies of the averaged profile This is done using the command View Projected Data gt Unsorted Magnetic Profile Fig 25 47 shows an example of good self correlation of up to four ship track segments The averaged magnetic profile is shown in Fig 24 Magnetic Profile 600 Figure 24 Projected magnetic profile window Vertical scale is in nT whereas the horizontal scale displays the offset in km along the flow line starting from the origin Magnetic Profile Figure 25 Unsorted projected magnetic data Vertical scale is in nT whereas the horizontal scale displays the offset in km along the flow line starting from the origin This plot shows that the magnetic profile of Fig 24 has been generated combining several up to 4 ship track segments 48 The other two kinds of windows that can be opened through the View Projected Data submenu are the bathymetric and the Kp index plots of a projected data set Figs 26 27 In order to display Kp index profiles the current data set must have been imported from an NGDC GEODAS MG
66. tion is calculated automatically once the user has defined the profile origin 1 2 General Overview The program manages two basic kinds of windows ship track project windows and forward modelling windows The first kind of windows allows the user to set the general parameters of a project ship track data flow line origin inclination declination of the reference field at survey time block walls dip background image basement grid and optionally a rotation model and eventually change some default parameters e g full spreading rate magnetization The window can show a ship track line on a background bathymetric gravity or magnetic anomalies image The user can manually trace and edit a flow line parallel to fracture zone trends which will be used later to project ship track data Alternatively the user can ask the program to generate automatically a flow line using an existing rotation model Figure 1 illustrates the elements of a project window through a real example from the central Atlantic The user must also select an origin for the reference frame blue circle which will be used for calculating the distance from the spreading center Forward modelling windows are the primary interactive tool for the analysis of magnetic anomalies These windows display both the calculated and measured magnetic anomaly profiles along the selected flow line They also display the magnetization profile The individual blocks composing th
67. ude of total field at location r and time t which can be obtained by scalar magnetometer surveys F F r f is the reference field at the same point and time e g the IGRF or DGRF field and AS AS r f is a diurnal correction then the total field anomaly is defined as AT r t T r t F r t AS r t 1 The IGRF or DGRF reference field is predominantly a long wavelength field component which roughly represents the influence of the core magnetic field and its secular variation although its truncated spherical harmonic series at order n 10 for dates preceding year 2000 and n 13 from 2000 onward still includes small crustal contributions This field varies from being horizontal and of magnitude about 30000 nT near the Equator to vertical and about 60000 nT near the poles the root mean square rms magnitude of the vector over the surface is 45000 nT The field also varies in time on a time scale of months and longer This is the so called secular variation SV which has a global rms magnitude of about 80 nT yr Another contribution to the observed magnetic field comes from electric currents in the ionosphere and magnetosphere and from the associated induced fields generated by currents induced in the crust The so called solar quiet S fields determine daily variations having primarily frequencies of 24 12 8 and 6 hours and amplitudes of few tens nT However these external contributions can reach 1000 nT during magneti
68. y available when the active window is a modelling window They may also be executed pushing the buttons on the right side control bar Fig 14 When you have selected one or more blocks you can increase or decrease the obliquity y of the magnetic stripe with respect to the local trend of the flow line on both sides of the ridge by 1 or 10 In this instance the effective distance of an observation point having offset x from the block is reduced to xsiny The default value is y 90 whereas the range of accepted values is 30 lt y lt 150 In order 37 to assign correctly this parameter you should take into account that the computation of the anomalus field components through Equations 43 44 is performed assuming an x axis which is oriented towards increasing flow line offsets This axis is locally tangent to the flow line only when the obliquity angle wy is 90 Therefore y is the angle between the positive y axis namely the magnetized stripe axis and the positive flow line direction The following Figure illustrates an example of appropriate attribution of the spreading obliquity angle Figure 15 Example of determination of the spreading obliquity angle w In this example a W E directed flow line parallel to the fracture zones has obliquity y gt 90 with respect to the strike of the magnetic stripes as evidenced by the background pattern of magnetic anomalies Note that the y axis is always directed southwar

The MAGAN Project Magan 3.1 User's Manual by A. Schettino

Contents

Download Pdf Manuals

Related Search

Related Contents