User`s guide
Contents
1. ICO2 and ICO3 for the two response components in this case apparent resistivity and phase since IMOD 1 and the data weights used in the inversion A data component can be omitted if its column index is set to zero ICO1 0 or ICO2 0 Likewise weights are not read at all if ICO3 0 as in the example above The remaining NOF lines define 12 the column formatted data frequency FREQ Hz the measured apparent resistivity Ohmm and the phase component deg The maximum amount of frequencies or loop spacings is 80 and the header text is used as a second line in the response graph title If the header text line is empty the default title in the FDEMINV DIS file is used instead The frequencies or loop spacings must be either in an ascending or descending order Note also that the data file can contain several data columns from which one or two are read for the interpretation This means that the same data file can contain for example measurements along a profile Manual editing of the column indices is currently required to choose the correct data column for the FDEMINV program Data values equal to zero are omitted and thus used for missing data values Although there is no need to edit model files manually the following example illustrates the format of the model files FDEMINV 1 4 model file 0 10000E 03 0 10000E 03 0 10000E 01 1 1 1 500 00 1 00 0 000000 0 23 2 000000 3 000000 4 500000 6 750002. max 40 characters Note that to mimic depth sounding the response lies on the horizontal x axis and the vertical y axis is the parametric frequency or loop spacing axis Note also that by default the graph does not contain the actual names and units of all the thirteen different the response types Instead generic names e g Resp 1 and Resp 2 are provided and the response type is shown in the description text in the top right corner of the graph page defines Manual editing of the FDEMINV DIS file is required if graphs are going to be prepared for presentation purposes The DISLIN graphics allows using special characters in graph texts The instructions are placed between and characters For example the text Resistivity M2 W M1 m will produce Resistivity Qm Superscripts and subscripts can be initiated using control characters hat and _ underscore Text will be reset to baseline after control character dollar See the DISLIN documentation for further information 6 Additional information Originally I made the FDEMINV program at the University of Oulu in December 2001 when I worked as a researcher funded by a grant from Outokumpu Foundation addressed to Prof Sven Erik Hjelt Afterwards I ve updated the program every now and then The forward computation is based on the well known solution for magnetic dipole sources above 1 D layered earth e g Keller and Friscknecht 1967 The convoluti
3. also that there is no need to edit model files manually when interpreting field data The following example illustrates the format of the input data file Synthetic data 1 Lt 1000 0 12 2 3 30 4 00 0 14219E 01 0 30574E 02 8 00 0 12220E 01 0 23876E 02 16 00 0 15243E 01 0 18217E 02 32 00 0 22128E 01 0 14607E 02 64 00 0 32212E 01 0 13006E 02 128 00 0 63994E 01 0 13824E 02 256 00 0 17812E 02 0 18135E 02 512 00 0 47480E 02 0 27415E 02 1024 00 0 10998E 03 0 42078E 02 2048 00 0 17153E 03 0 58351E 02 4096 00 0 10288E 03 0 50792E 02 8192 00 0 93610E 02 0 45630E 02 The first line defines a header text max 30 characters to be shown in the response graph The third line defines the source type ISYS response type IMOD and sounding type IOPT The source is either a VMD ISYS 1 or a HMD ISYS 2 or 3 The response type is one of the nine possibilities MOD 1 2 or 13 defined in the Using the program chapter The sounding type is either frequency sounding IOPT 1 or geometric sounding IOPT 2 The 4 th line defines either the loop spacing LOOP m or frequency FREQ Hz used in the frequency or geometric soundings respectively The second parameter on the 4 th line defines the height HEI m of the dipole dipole system from the surface of the earth The source and the receiver are always on the same height level above or on the surface The 5 th line defines the number of frequencies NOF and the column indices ICO1
4. are shown below 40 32 32 26 26 1 2 1 1 0 Oo 0 370 350 0 600 0 850 0 830 FDI EM sounding Test model Response 1 Response 2 Frequency Hz Loop spacing m NORrRNEF comp comp meas meas System and model description Resist Ohmm Thickness m Depth m Susc SI The 1 st line defines five character heights The first one is used for the main title and the graph axis titles the second height is used for the axis labels the third height is used for the plot legend text the fourth height is used for the model description text and the last height is used for the axis labels in the model view The 2 nd line contains integer valued parameters that define 1 is the info text is shown 2 is the model view is drawn 3 in which corner the legend is drawn 4 are the grid lines visible 5 is widescreen mode is active 6 normalization plain percent ppm for some response modes 7 how phase data is shown radians or degrees and 8 how error bars are drawn The 3 rd line defines parameters that define the x horizontal and y vertical position of the origin of the main graph in pixels the length of the x and y axis relative to the size of the total width and height of the total plot area eg 0 5 50 of the width or height which is equal to 2970x2100 pixels landscape A4 and the screen aspect ratio for widescreen mode 15 e The remaining lines define various text items of the graph
5. evenly spaced on a logarithmic scale The Error bars menu is used to hide or show the 95 confidence limits in the model view Error bars can be shown as a cumulative minimum and maximum curves b vertical and horizontal sticks c rectangular boxes as in Fig 3 The Exit menu has two items The first one can be used to restart the GUI and swap between traditional 3 4 display mode and a widescreen mode giving an aspect ratio between 0 5 0 9 The second item is used to confirm the exit operation On exit the latest model is saved in the FDEMINV INP file and the results are saved in the FDEMINV OUT file Errors that are encountered before the GUI starts up are reported in the FDEMINV ERR file When operating in GUI mode run time errors arising from illegal parameter values are displayed on the screen during runtime After exiting the program one can take a look at the FDEMOUT OUT file which contains the results If data has been used in the interpretation the file contains the model parameters the RMS error and the mean of the damping factors the damped 95 confidence limits of the parameters the singular values the damping factors and the parameter eigenvectors The result file also contains the measured and computed response components and the differences If data was not used the file contains just the model parameters some system information and the computed FDEM response Note that normally the result files as well as model
6. files are saved using the File Save results menu item 3 2 GUI widgets Update button needs to be pressed to validate the changes made to any of the text fields defining the system model and inversion parameters Default button resets all layer parameters to their default values 100 Om or 10 Qm and 150 m Loop Fregq text field defines the loop spacing m for frequency sounding or the frequency Hz for geometric sounding Layers text field is used to define the number of layers in the model To update the number of layers one needs to press the Update button When increasing or decreasing the number of layers the unnecessary text widgets get hidden The maximum number of layers is six 6 Single layer can also be removed by giving it a zero thickness and pressing the Update button Increasing or decreasing the number of layers always affects the layers at the bottom There is no possibility to add a new layer in between existing layers The remaining text fields define the resistivity Qm and thickness m of each layer and the resistivity of the basement layer The two text fields Magn susc and S layer at the bottom of the left control panel are used to assign magnetic susceptibility to one of the layers If the model has more than one layer the susceptibility cannot be assigned to the top layer The susceptibility is given in SI units If S layer is equal to zero the magnetic susceptibility is not assigned to any of t
7. 0 10 12500 15 18750 22 78125 34 17188 51 25781 76 88672 115 3301 172 9951 259 4927 389 2390 583 8585 875 7878 1313 682 1 970 522 2955 784 4433 676 6650 514 9975 771 14963 66 The first line is used as a title defining the contents of the file The 3 rd line defines the number of layers NOL the maximum amount of which is 6 Lines 4 and 5 in this case define the resistivity RH Om and the thickness TH m of the two topmost layers The 6 th line defines the resistivity of the bottom layer The 7 th line defines the source type ISYS response type IMOD and sounding type IOPT as they were defined for model files The 8 th line defines the loop spacing or frequency LOOP FREQ and the height of the source receiver system from the ground level The 9 th line defines the magnetic susceptibility and the layer number to which the susceptibility will be assigned The 10 th line defines the number of frequencies NOF or loop spacings in case 13 of geometric sounding The frequency or loop spacing values are then provided at the end of the file Note that the values can be given on multiple lines The results file EDEMINV OUT contains the model parameters and depths the RMS error the mean of the damping factors the damped 95 confidence limits of the parameters the original W and normalized S singular values the damping factors T and the parameter eigenvectors V matrix Some general information concerning the measurement syst
8. FDEMINV 1 D modelling and inversion of frequency domain EM soundings Version 1 5 user s guide Markku Pirttij rvi 2014 University of Oulu e mail markku pirttijarvi at gmail com 1 Introduction FDEMINV is a computer program that can be used to model and to interpret geophysical frequency domain electromagnetic FDEM soundings using a horizontally layered earth model The 1 D model is defined by the resistivity and thickness of the layers and magnetic susceptibility assigned to one of the layers The transmitter is either a vertical or a horizontal magnetic dipole The receiver measures the vertical and horizontal components of the secondary magnetic field The response can defined in different ways as a function of increasing frequency at fixed loop spacing frequency sounding or increasing loop spacing at fixed frequency geometric sounding Parameter optimization which is based on linearized inversion method can be utilized in 1 D interpretations FDEMINV is a 32 bit application that can be run on MS Windows operating system with a graphics display of at least 1024x800 resolution Memory requirements and processor speed and are not critical factors since large data arrays are not used and the EM solution is quite fast to compute even on older computers FDEMINV has a simple graphical user interface GUI that can be used to change the parameter values to handle file input and output and to visualize the EM response and the
9. are included in the inversion To fix some parameter during inversion set the corresponding fix free stays to zero The Sel all button can be used to fix or free all parameters for the inversion 3 3 About the inversion FDEMINV is not an idiot proof interpretation program It requires a proper initial model The Default button provides just one way to define the initial model It is essential that the number of layers is set appropriately before inversion The iterative linearized inversion method can get stuck to a local minimum and therefore the user should pay attention to the validity of the resulting model Due to the well known equivalence condition of conductive layers the conductivity and thickness cannot be interpreted separately To reduce the error estimates of other parameters the resistivity or the thickness of conductive layer should be fixed to some reasonable value before continuing on with the inversion see Fig 3 The RMS error the mean of the damping factors and the width of the error bars can be used to assess the validity of the inversion results Optimally the RMS error should be zero and all damping factors should be equal to one If all parameters are well resolved the error bars which are based on the 95 confidence limits will be very small 11 4 File formats When using the program for interpretation purposes make sure that your input data files DAT are formatted properly before reading in the data Note
10. d fast Hankel transform filters Geoph Prospecting 38 545 568 Frischknecht F C Labson V F Spies B R and Anderson W L 1991 Profiling methods using small sources In Nabighian M N ed Electromagnetic methods in applied geophysics Volume 2 Applications SEG p 105 270 Keller G V Frischknecht F C 1966 Electrical methods in geophysical prospecting Pergamon Press Pirttij rvi M 2003 Numerical modeling and inversion of geophysical electromagnetic measurements using a thin plate model PhD thesis Acta Univ Oul A403 Univ of Oulu 8 Terms of use and disclaimer You can use the FDEMINV program free of charge The program can be downloaded from a website at the University of Oulu https wiki oulu fi x MoU7AQ The program is provided as is The author MP and the University of Oulu disclaim all warranties expressed or implied with regard to this software In no event shall the author or the University of Oulu be liable for any indirect or consequential damages or any damages whatsoever resulting from loss of use data or profits arising out of or in connection with the use or performance of this software 17
11. de the name of the file Model and result files are saved in standard ASCH text format The graphs are saved as they appear on the screen in landscape A4 size 7 FDEM soundings soundings 1 File Settings Exit Update Channels Linear FDEM sounding Default Logia Sampo Gefinex 4008S Loop m Freq Hz 600 00 i i Frequency sounding VMD coplanar Elevation m oo lters 10 600 0 m amp h 0 0 m Thres 1 0000 System and model description Response App resistivity and phase Model parameters Layers 4 Sel all i Resist Ohmm Thickness m 1 Res Ohmm 245934 Fee 1 1 1245 9 252 6 129 3 2 Res Ohmm T 00 0 g ate i 0 1 Layer 3 Susc 1 000000 RMS error 0 056996 Damp mean 0 668157 2 Thick m 4 62 3 Res Ohmm 1786 39 3 Thick m 129 29 4 Res Ohmm 0 10 Frequency Hz Magn suse SI S layer 3 w yidaq 10 101 103 104 107 107 10 10 107 107 104 comp Resist Ohmm comp lt 0 Response 1 Response 2 meas meas lt 0 FDEM sounding over 1 D layered earth by M Pirttij rvi 2014 Figure 3 Screenshot of FDEM application where Sampo Gefinex apparent resistivity and phase data has been interpreted using a 4 layer model The resistivity of the conductive second layer has been fixed and strong susceptibility k 1 SI has been assigned for the third layer The Settings menu co
12. em is also given source and sounding types loop spacing and height The results file also contains the measured and computed response components and the difference between the measured and the computed data It also contains the weights if they were used in the inversion The FDEMINV OUT file contains also the computed magnetic field components H01 H02 Re Im H1 Re Im H2 Re Im H1 H01 Re Im H2 H01 and Re Im H1 H01 H2 H02 Here HO1 and H02 are free space magnetic fields HO1 and H1 are the vertical or horizontal magnetic fields of a VMD or HMD H02 and H2 are the horizontal or vertical magnetic fields of a VMD or HMD Note that for historical reasons the character is used to comment out lines for the Gnuplot plotting program At the bottom the FDEMINV OUT file are given the data values required to create the model curve and the error bars using a third party plotting program If data were not read in the output file would just contain the model parameters and the computed FDEM response 14 5 Graph options Several graph parameters can be adjusted by editing the FDEMINV DIS file Note that the format of the DIS file must be preserved If the file format becomes corrupted the program crashes while initializing the GUI In this case one should delete the file and a new one with default parameter values will be generated automatically the next time the program is started The file format and default parameter values
13. he layers Channels button at the top of the right control panel is used to show either both response components or just one of the response components To select desired component the button needs to be pressed multiple times The scaling of the graph changes according to the selected component If data has been read in for interpretation only the currently visible data component s 10 is are used in the inversion The radio buttons below the Channels button are used to set the scaling of the horizontal axis of the response graph linear or logarithmic logio The remaining widgets become active only after some data has been read in using the File Read data item Optimize button is used to start the inversion ters text field defines the number of successive iterations Thres text field defines the minimum singular value threshold used in the optimization This parameter actually multiplied by 1000 controls the strength of the damping Decreasing its value will loosen the damping and make the inversion method work more like a steepest descent algorithm Increasing its value might be advantageous if the inversion gets unstable The default values for the number of iterations and the threshold are 10 and 1 0 actually 1 e 3 respectively The remaining text fields Free on the right side of each resistivity and thickness value are used to exclude 0 or to include 1 that parameter from or to the inversion By default all parameters
14. m then computes the FDEM response of the initial model and builds up the user interface shown in Fig 3 The FDEM response is plotted in the graph area along with a resistivity depth curve of the model and a description of the model and system parameters If measured data has been read in for interpretation the data are plotted using symbols circles and triangles Red and blue colors are used to display positive and negative response values respectively 3 1 Menus As shown in Appendix the main window of the FDEMINV application contains two menus The File menu has the following nine options Read model Open an existing model file INP Save model Save the model into a file INP Read in measured data for interpretation DAT Read data Save the results into a file OUT Save results Read dis Read in new graph parameters from a file DIS Save the graph in Adobe s Postscript format PS Save Graph as PS Save the graph in Adobe s Encapsulated Postscript format EPS Save Graph as EPS Save the graph in Adobe s Acrobat PDF format PDF Save Graph as PDF F Save the graph in portable network graphics format PNG Save Graph as PNG Save Graph as WMF Save the graph in Windows metafile format WMF Save Graph as GIF Save the graph in Windows metafile format GIF Selecting any of these menu options brings up a typical Windows file selection Open Save dialog that can be used to provi
15. model The user interface and the data visualization are based on the DISLIN graphics library http www dislin de Despite its inversion capabilities FDEMINV is intended primarily for forward modeling and testing One of the main objectives was to develop a general purpose method to transform FDEM responses into apparent resistivity So far such method has not been found particularly if the source and receiver are above the surface of the earth 1 1 Installing the program The FDEMINV program requires only the 32 bit executable file FDEMINV EXE The distribution file FDEMINV ZIP also contains a short description file IREADME TXT this user s manual FDEMINV_MANU PDF and an example data file EXAMPLE DAT To install the program simply unzip the distribution files on your hard disk or USB stick and a new folder appears 2 The EM measurement systems Fig 1 illustrates the three measurement systems considered in FDEMINV The transmitter Tx is either a vertical VMD or a horizontal HMD magnetic dipole that is to say a horizontal or a vertical loop on or above the ground surface The receiver Rx is located at the same height level at some distance L away from the source FDEMINV computes two magnetic field components The first component solid black arrow is always parallel to the source dipole and the second one dashed gray arrow is perpendicular to that In case of VMD the second component is the horizontal axial compo
16. nent directed away from the source In case of a HMD source the second component is the vertical one Please note that in coaxial HMD configuration no vertical primary field is generated which prevents computation of Hx Hz Hz Hx ratios and apparent resistivity and phase Figure 1 Schematic view of the three VMD and HMD system configurations FDEMINV can be used to model both frequency and geometric soundings In frequency soundings the distance between the source and the receiver is kept fixed and the measurements are made using varying frequencies The attenuation of EM fields depends on the conductivity or its reciprocal the resistivity and the frequency Therefore high frequencies give information about the upper parts of the earth whereas low frequency data contains information from greater depths In geometric soundings the frequency is kept fixed and the loop spacing is varied When the loop spacing is short the data contains information near the surface When the loop spacing increases more and more information will be obtained from the deeper parts of the earth For more detailed information about the geophysical EM measurement systems please be referred to common geophysical literature e g Frischknecht et al 1991 FDEMINV computes the apparent resistivity and phase using the ratio of the vertical and horizontal magnetic field components Although similar method has been used in the French BRGM Melis frequency soundi
17. ng system for example the method is not widely used and therefore a short description is provided in the following The 10 base logarithm of the imaginary quadrature part of the ratio of vertical and horizontal magnetic field components F Logio Im Hz Hx is first computed and tabulated using the homogeneous half space model over a wide range of dimensionless induction parameter a kr where r is the loop spacing and k OLoOn 27f is angular frequency 4o is magnetic permeability of the free space and oj is the conductivity of the lower half space In practice the computation is made using a fixed loop spacing and frequency and varying the host conductivity or resistivity values Fig 2 illustrates the F ratio fora VMD system on the surface of homogeneous half space Since the F ratio is a continuously decreasing function of the induction parameter the apparent resistivity of the VMD or HMD system above layered earth can be obtained using reverse interpolation Let us assume that at some frequency the computed or measured values of vertical and horizontal magnetic field are Hx and Hz which gives rise to ratio F Reverse interpolation from y to x axis of the curve shown in Fig 2 gives an induction parameter value qj In practice the interpolation is made using the logio values of the induction parameter and linear extrapolation is used beyond the computed range if necessary By its definition the apparent resistivity is such a
18. ntains following items Comp gt Meas Remove Meas Sounding type Source type Field component Normalized field Ratio Apparent resistivity Free space field Normalization Define freq dist Phase rad deg Grid show hide Weights in out Error bars Make the computed response synthetic measured data Remove information about measured data Choose frequency or geometric sounding type Choose coplanar VMD coplanar HMD or coaxial HMD system Response is one of the field component Re Im or Mod Pha Response is one of the normalized field components Response is the ratio between the two components Response is the apparent resistivity and phase Include or exclude the free space field from the total magnetic field Choose response normalization plain percent parts per million Set frequencies or loop spacings for frequency or geometric sounding Computed phase will be either in degrees or radians Show or grid lines in response graph and model view Data weights read from file can be excluded from inversion Choose how the error bars are drawn in the model view In case of the VMD source the first field component H1 is vertical magnetic field and the second H2 is horizontal axial magnetic field In case of HMD the first field component H1 is horizontal parallel or coaxial horizontal magnetic field and the second H2 is the vertical magnetic field which cannot be computed in case of coplanar HMD configuration Consequentl
19. on algorithm and the filter coefficients used to compute the Hankel transforms are based on Christensen s 1990 optimized filter coefficients The inversion method which is based on the singular value decomposition and adaptive damping method is described in my PhD thesis Pirttijarvi 2003 The FDEMINV program is written in Fortran90 and compiled with Intel Visual Fortran 15 The graphical user interface is based on the DISLIN graphics library version 10 4 by Helmut Michels http www dislin de Because DISLIN is available for other operating systems FDEMINV could be compiled on Mac OS and Linux without major modifications At the moment however the source code is not made available and I do not intend to provide active support for the program If 16 you find the computed results erroneous or if you have suggestions for improvements please inform me Please note that FDEMINV has not been tested thoroughly and that its usability in data interpretation is quite modest For example data weights cannot be edited manually Interpretation of frequency domain soundings is going to be implemented in future versions of Jointem software for combined a k a joint interpretation of TEM VES VLF R and AMT MT soundings For more information about the current status of Jointem and other software please visit my home page of free geophysical software at https wiki oulu fi x EoU7AQ 7 References Christensen N B 1990 Optimize
20. value of the resistivity or conductivity of the homogeneous half space that produces the same EM response as the layered earth Since the loop spacing and frequency are known the host conductivity which now represents the apparent resistivity can be solved simply as p 2mu f 1 la Qm The phase response related to the apparent resistivity is computed as tan Im Hz Hx Re Hz Hx rad or deg Note that the method used to compute apparent resistivity could be used to transform measured data as well This requires however that both the vertical and the horizontal magnetic field have been measured The transformation method does not work with HMD systems The magnetic field used to compute the F ratio is the sum of free space and homogeneous half space magnetic fields and for some dipole dipole systems the vertical magnetic field is zero Therefore the interpolation of the F ratio cannot be used to compute the apparent resistivity for the coplanar HMD system for example Logio Im H2 Hx T T T logoak Figure 2 The F ratio used to interpolate the apparent resistivity for a VMD source on the surface of homogeneous half space 3 Using the program On startup FDEMINV reads model parameters from the FDEMINV INP file and graphics parameters from the FDEMINV DIS file If these files can not be found when the program is started new ones with default parameter values are automatically created The progra
21. y the normalizing free space magnetic field HO is the vertical for VMD source and horizontal for HMD source The computed response is one of the thirteen possibilities Re real in phase component Im imaginary quadrature or out of phase component Mod modulus amp Pha phase of the response Apparent resisitivity and phase between vertical and horizontal field IMOD 1 Normalized field 2 Re Im H1 H0O 3 Re Im H2 HO 4 Mod Pha H1 HO 5 Mod Pha H2 HO Ratio 6 Re Im H1 H2 7 Re Im H2 H1 8 Mod Pha H1 H2 9 Mod Pha H2 H1 Field component 10 Re Im H1 11 Re Im H2 12 Mod Pha H1 13 Mod Pha H2 Except for apparent resistivity the response depends on the choice of Free space field menu item because normally the free space field HO is added to the total magnetic field eg H1 H0 Hs1 Excluding the free space field thus allows inspecting the secondary magnetic field alone Normalization percents or parts per million is possible for the following four response types Re Im H1 H0 Re Im H2 H0 Re Im H1 H2 Re Im H2 H1 IMOD 2 3 6 or 7 Define freq dist item can be used to set the minimum and maximum frequency values and number of frequencies in case of frequency soundings or the minimum and maximum loop spacing and the number of loop spacings in case of geometric sounding The values are provided using an input dialog and the frequencies or loop spacings are automatically computed so that they are
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