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Chapter 8: AMT Processing with MTPro

MtPro processing software is used to

process acquired MT time series to impedance and phase

data.

A.

Installing and licensing of MTPro

:

Installation of MTPro is easy:  Simply copy the executable file into a designated folder.  This
could be “C:\MTPro” for example.   However , getting the license set up for your computer is a
bit more complicated.   MTPro can be used to process and view the data but without a license it
cannot save or export the data for inversion or contouring.

To get the license do the following:

  1. Click on HELP then ABOUT MTPRO. You will see a menu pop up with the fields “Computer
ID” and “License key”.   There will be a code “Computer ID” field. Copy and Paste this code into
an email message and send it to

[email protected]

and/or

[email protected]

.

2. You will be sent a License Key that you should copy into the “License Key” field. Close the
window and the program then re-start MTPro.  If you now go to “Help”, “About MTPro” you will
get the following screen with the words “This machine is licensed” in the License Key field. You
will now be able to export data for using in other programs such as the Zonge SCS2D  CSAMT-
AMT inversion software.

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Содержание Geode EM3D

Страница 1: ...002 01 REV D Operation Manual For Geode EM3D running GeodEM Ver 3 0 COPYRIGHT 2018 GEOMETRICS INC 2190 Fortune Drive San Jose CA 95131 USA Phone 408 954 0522 Fax 408 954 0902 support mail geometrics com www geometrics com ...

Страница 2: ... 4 Software 18 Chapter 5 SAS System Acquisition Software 31 Chapter 6 Interface to a controlled source transmitter 33 Chapter 7 CSAMT Processing 34 Chapter 8 MT Processing 42 Scalar Processing 52 Chapter 9 Factors determining good versus bad data for Controlled Source Audio Magnetotellurics 58 Chapter 10 General survey principles and typical survey operation 59 Chapter 11 Notes on AMT natural fiel...

Страница 3: ...3 Appendix 2 GPS Setup Software 69 Appendix 3 MT Theory 69 ...

Страница 4: ...ed Ethernet backbone The fundamental theory of MT AMT and CSAMT can be found in a brief review in Appendix 1 Fig 1 shows a four receiver network consisting of four receiver modules with twenty E field channels and four H field channels Fig 1 Network sample setup B System components A typical Geode EM3D will consist of the following components 1 Laptop controller with the acquisition software and p...

Страница 5: ...B operation is given in section below 3 GEM3D Receiver The six channel GEM3D receiver is discussed in more detail in the receiver setup section below Fig 3 GEM3D receiver box 4 Magnetic Induction Coil The Geometrics G20K coils operate on a band width of 0 1 Hz to 20k Hz The operation range of the Geode EM3D CSAMT system is 0 1 Hz to 10 kHz Coils specifications are available at www geometrics com o...

Страница 6: ...ave been tested successfully These can be supplied by the customer or at an additional cost by Geometrics Fig 5 Stainless steel electrode and cable 6 Ethernet Cables The Geode EM3D uses a proprietary Ethernet cable that is specially ruggedized for field use It also has an isolated trigger wire to synchronize all receiver channels on the network without concern for any delay ...

Страница 7: ...rs is through scheduler software using GPS time on the transmitter and PC Controller There is only one GPS unit to control all GEM3D receivers since the GPS connection is to the PC Controller which in turn triggers the acquisition through the dedicated trigger wire in the Ethernet cable described above The GPS used at the writing of this manual is the Global Sat BU 353S4 Receiver but nearly any go...

Страница 8: ...reen shows the number of satellites detected by the GPS receiver In order to function properly you must lock on to at least three satellites The number of satellites detected may vary from GPS receiver to GPS receiver so consult your GPS operator s manual c NIB Network Interface Box The NIB allows the Ethernet interface between the GEM3D receiver network and the Ethernet board on the PC Controller...

Страница 9: ...nds The first GEM3D receiver is the one closest to the acquisition computer in the array Upon starting SAS a start command will be sent to each of these GEM3D which will in turn power up the rest of the GEM3Ds Once the software is up and running and all GEM3Ds are recognized return the switch to the Enable Power Down position This will cause all of the GEM3Ds to shut down when the software is clos...

Страница 10: ...inking link LED on each unit see discussion of blink codes below will indicate that each unit is receiving link pulses from the other d Installation of required software onto Controller All required software should have been pre installed on the PC Controller from the Geometrics factory The following information is only required if the software must be re installed e SAS System Acquisition Softwar...

Страница 11: ...f CH2 are red and black of E field channel 2 Channels 3 4 5 and 6 all have one or more common terminals as follows CH3 red is and yellow is CH4 yellow to right is channel 4 positive and yellow to left is channel 4 negative CH5 yellow to right is channel 5 positive and yellow to left is channel 5 negative CH6 yellow is positive and CH6 black is negative All the yellow terminals share a common conne...

Страница 12: ...12 Fig 11 connecting telluric lines E field B Panel 2 Magnetic field terminals Fig 12 Channel 4 Hz Channel 5 Hx Channel 6 Hy ...

Страница 13: ... channel CH6 is disabled and the H field channel Hy CH6 is enabled If a coils is plugged into Hx the E field channel CH5 is disabled and if a coil is plugged into Hz the E field channel E4 is disabled For example if coils are connected to Hx and Hy the E channels 1 2 3 and 4 are available but channels 5 and 6 are not This is done automatically when a coil is connected to one of the H channels C Pa...

Страница 14: ...Ds flash at a rate of once per second when the Ethernet board is powered up fast flash powered up mode It changes to a rate of once every six seconds when the SAS acquisition software starts up and detects the Ethernet board in the GEM3D receiver slow flash acquisition mode The blue 12V DC power LED flashes at the same rate as the Ethernet LED as an indicator the GEM3D receiver has adequate batter...

Страница 15: ...s are considered to be positive by the software Black terminals are negative and yellow terminals are shared between two adjacent dipoles and can be either negative or positive depend on which dipole When a magnetic sensor is connected to Hy channel 6 the E dipole on channel 6 is disabled When Hx on channel 5 is connected the E field connectors on channel 5 are disabled and when mag Hz is connecte...

Страница 16: ...f the GPS receiver is to synchronize the CSAMT transmitter with the GEM3D receiver acquisition It is also used to set the PC Controller clock The Geode EM3D scheduler software creates a file that sets all the transmission parameters including the start time of the transmission The start time of the transmitter can be synchronized to the acquisition time of the receiver through a GPS on the transmi...

Страница 17: ...17 H Data acquisition See section K 2 Software GEM3D Controller Software I Transmitter See the manufacturer s manual or the make and model of the CSAMT transmitter you are using ...

Страница 18: ...cquisition Suite iii EMmain exe c geometrics Seismic Acquisition Suite Firmware iv EM SAS c GeometricsSurveyAndSettings EM Survey Parameters v EM LOG c GeometricsSurveyAndSettings EM Survey Parameters b Available SAS screens i Noise monitor Described below ii System settings 1 Set Date Time This allows you to set the system time and date 2 Test Tests various performance parameters 3 Sounds Sets au...

Страница 19: ... acquisition sequence Display control as follows 1 Use enter and backspace keys to scroll through the time series 2 Use and keys for zoom control 3 Use left and right arrow keys to show additional channel data if there are more channels than are displayed on the screen iv Save Setup File Saving a setup file will store all the setup parameters created for the survey This can be recalled later as a ...

Страница 20: ...nformation about the survey site 2 Coordinate System Coordinate Parameters General GPS coordinate information 3 Line Frequency Set powerline harmonic filter 50 or 60 Hz 4 Auto Line Freq Detection Automatically sets powerline frequency filters Fig 20 Setup menu General ...

Страница 21: ...ncy schedule for both the CSAMT transmitter operation and the receivers acquisition Fig 21 Setup menu Frequency stepping 1 Maximum frequency Hz 2 Minimum frequency Hz 3 Frequencies per octave 4 Minimum seconds per frequency 5 Minimum cycles per frequency 6 Maximum timing error ...

Страница 22: ... noise notch check box When the box is checked it will look for high amplitude noise leaking into the CSAMT frequency acquisition band and filter out that noise Note this only applies to CSAMT acquisition as it cannot be done in broad band natural field acquisition Setting the parameters in this window then clicking Calc Freq Table will generate the table of acquisition frequencies displayed in th...

Страница 23: ... Roll Backward and Roll Forward rolls the receiver array setup forward or backward along the profile line 5 Transmitter Layout Tx1 indicates one transmitter dipole is used scalar Tx2 indicates two transmitter dipoles are used tensor a Tx1 easting Tx1 northing Tx1 elevation Tx2 easting Tx2 northing Tx2 elevation These fields are the user the defined orientation and elevation of the transmitter dipo...

Страница 24: ...tact resistance for each channel 10 Data Folder and Calibration Folder creates and points to the location of the data and calibration files respectively 11 Import Layout and Export Layout reads or saves the patch setup as a template for future surveys iv GPS This screen sets up parameters for GPS synchronization with the transmitter and provides information about the status of the GPS The Com Port...

Страница 25: ... corner of the window Clicking on the System will display the SAS software version number and allow the operator to change the system time and date set receiver test parameters and turn on or off various system sounds vi Stop SAS Closes the background acquisition software vii Set Default Triggering Parameters This sets a default trigger sensitivity at 50 and trigger hold off time at 0 2 seconds vi...

Страница 26: ...ies acquired Each time series is acquired as a SEG2 file which is converted into a common GTS file for the survey 5 Skip Checking a skip box allows the operator to not acquire data in the designated frequency band 6 Cycling Acquisition The acquisition will automatically continue to cycle through the frequency bands until acquisition is manually stopped 7 Note that you can change the time scale dis...

Страница 27: ...activated time series In the example above there is a 1 second delay between each record acquisition to allow for settling of the system between acquisitions as defined in Delay Between Bands x Stop Recording Ends data acquisition sequence xi Measure contact resistance The contact resistance measurement determines the contract resistance on each E field channels The measurement is done simultaneou...

Страница 28: ...ecord length is 375 samples The acquired frequency is 2 667 Hz The bottom field boxes show that CSAMT is being recorded there is one receiver box COM5 is used for the GPS with 9 satellites detected a 60 Hz harmonics comb filter is active the display is of an acquisition of 2 667 Hz and it is the first time through the acquisition cycle Note that you can change the time scale displayed on the scree...

Страница 29: ...s Per Screen setting For example if there are 36 channels six receiver boxes and the Channels Per Screen is set to 6 you can view each receiver box six channels individually by using the left right arrow keys 3 Remove DC Offset centers the time series display by removing any DC voltage offset 4 Gain settings a Fixed gain allows the operator to set a predetermined gain in dB for the E field channel...

Страница 30: ...p simulated acquisition This feature is disabled in the current software version Note The Geo2010 software creates a setup file with all the system parameters recorded This is an XML file which requires an XML reader such as XML Notepad XML Notepad can be download for free from the Microsoft website The XML setup file is located in the same older as the SEG2 dat files for the survey An example of ...

Страница 31: ... Also refer to section Chapter 4 Software 2 GEM3D Controller setup b Setup IV Start SAS Fig 32 SAS noise monitor Clicking on System will display the following Set Date Time This allows you to change the clock in the controller PC Test The test mode Sounds You can change the sounds Version Number This shows the version number of the SAS software being used ...

Страница 32: ...lay a set of time series indicating background signal on each channel Click on System to see the following 5 Set Date Time to set of system clock of the PC Controller Test described below Sounds to set the beep indicators Version number to view the version number of the SAS software being used 6 Details of SAS System Test functions Update acquisition board BIOS Loader Network performance tuning Ge...

Страница 33: ...he GEM3D Scheduler file is created under the Setup Frequency Stepping menu in GeodEM 2010 software The details of the frequency stepping menu is discussed in section K 2 b ii of this manual Once the schedule file is created it must be transferred to the transmitter controller See you transmitter manual for transmitter operation details ...

Страница 34: ... Installing GeoCSAMT Fig 34 CSAMT processing software menu Processing Steps After acquisition of either scalar or tensor CSAMT data the results can be processed to create impedance phase and other parameters Do the following 1 Open the program GeoCsamt 2 Click on File and select Add GTS Files 3 The window below will pop up Click on Add GTS Files ...

Страница 35: ... Open The following window will be displayed Fig35 Adding file for processing menu NOTE In order for the GeoCSAMT or MTPro processing software to create a continuous line when the stations are rolled to a new position the Patch Name must be different for each setup If the Patch Name is the same the processing software will average them together To do tensor processing the transmitter parameters mu...

Страница 36: ...ty impedance phase and a number of other processed displays can be chosen by clicking on the Plot Type arrow 9 Edit CSAMT data To edit out specific frequencies a Read in the GST file s to see the impedance curves b Left click the edit icon at the far left of the top icon bar c Left click on the data point you want to mask out of the exported data The clicked point will be grayed out as shown below...

Страница 37: ...xport the data file to be read by Zonge Engineering s SCS2D CSAMT inversion software you need to click File then select either the EDI or AVG format If the EDI format has been chosen start the program edi2avg exe Read the EDI file and convert it to the AVG format The Zonge SCS2D program can read the AVG file and do a 1 D and 2 D inversion No additional conversion is required for SCS2D to read the ...

Страница 38: ...version software The files will have the same name but with an MDE and STN extension instead of an AVE extension 1 CSAMT Pro can do CSAMT tensor processing In order to do Tensor CSAMT two perpendicular transmitter dipoles which are called Tx1 and Tx2 respectively are needed to set up in the field Assume we first connect transmitter to Tx2 we need set Array Type as Tensor CSAMT and Current Tx as Tx...

Страница 39: ... CSAMTPro program and select Add GTS files menu Fig2 Make sure the Patch Names are identical for same setup array type is CSAMT Tensor and the Tx No is correct for each GTS file Click OK button and we will get CSAMT tensor data Figure 3 As MTPro program the red curve is Zxy and blue one is Zyx ...

Страница 40: ...ection are the blue diamonds Note that X direction resistivites are the red squares and Y direction resistivities are the blue diamonds Bostic transformation The Bostic transformation of CSAMT data is a point by point conversion of apparent resistivity and depth to true resistivity and depth ...

Страница 41: ...41 2 Similar to MTPro database save and open features are added to CSAMT program Figure 4 ...

Страница 42: ... or contouring To get the license do the following 1 Click on HELP then ABOUT MTPRO You will see a menu pop up with the fields Computer ID and License key There will be a code Computer ID field Copy and Paste this code into an email message and send it to support geometrics com and or wfei geometrics com 2 You will be sent a License Key that you should copy into the License Key field Close the win...

Страница 43: ...s Do the following 1 Click on File Add GTS Files 2 A new window will pop up Click on Add GTS Files 3 Navigate to the date files previous set up in the Data Folder field in the Geode EM2010 program under Patch Setup 4 Select anywhere from 1 to multiple MT data files by doing a Ctrl click on each one Then click Open The following window will be displayed ...

Страница 44: ...tation X dipole Ey1 sounding station y dipole Hx1 station Hx Hy1 station Hy Ex1 if this station used Hz it would be shown here Since no Hz exists the position is filled with Ex1 and is not used Hx4 local reference for in X direction Hy4 local reference for y direction The reference sensors may be changed For example if the user prefers to use E field measurements as the local reference the last tw...

Страница 45: ...tation is the angle of the measured station 1 The plot layout button second from the right allows you to choose how many soundings are displayed 2 The station arrow third from the left shows what channels are used in the sounding 3 The patch arrow second from the left shows the data folder name 4 The plot type display arrow at the left shows the various graphics that can be displayed as follows be...

Страница 46: ...the processed GTS or MT file as an AVG file for inversion processing Zonge Geophysics SCS2D AMT CSAMT inversion software 9 You can mask out the use of a sounding by doing a Ctrl right click on the sounding you do not want to use or export For example the image below shows the soundings for stations Ex2 and Ex5 have been disables The sounding labels for Ex2 and Ex5 are greyed out to show they are m...

Страница 47: ...rection resistivities are the blue diamonds Parallel Test Noise Calculation The parallel test noise calculation allows the user to do a basic field test of the noise level comparing any two pairs similar parallel sensors For example Ex1 and Ex2 or Ey1 and Ey2 or Hy1 and Hy2 The results of the test show a similar curve to below ...

Страница 48: ... Coherence Tipper Skew and Tipper Beta It is beyond the scope of this manual to explain the geophysical uses of these functions However the most commonly viewed tipper functions are the magnitude and phase as shown below For the Geode EM3D the vertical magnetic field Hz is generally measured by the G100K high frequency coil The lowest practical frequency of the G100K coils is 10 Hz Therefore the p...

Страница 49: ... one of the files to they both match For example in the image below there are two files with an array name of Laurel 44 AMT field3 and two files with the array name of Laurel 44 AMT field4 If the names are not changed then field4 soundings and field3 soundings will be processed separately in MTPro However if you change the names to match the two files will be processing as the same soundings You m...

Страница 50: ...50 Selected files After editing array names ...

Страница 51: ...and the electrodes parallel Since E channels 3 4 5 and 6 have shared terminals to test all E channels and the H channels will require three acquisitions As follows Set channels 1 2 3 and 5 as E dipoles parallel to one another This will provide four E field parallel measurements without any shared electrodes Do an MT acquisition Set channels 4 and 6 as parallel E dipole channels Do an MT acquisitio...

Страница 52: ...y high low frequency noise in the graph above is the result of using metal stakes in the ground instead of porous pot electrodes At low frequencies below 1 Hz porous pot electrodes are preferable for noise measurements ...

Страница 53: ...he data as scalar data when adding GTS files change the click the Array Type menu arrow and select Scalar MT This will allow MTPro to process the data as scalar only Example above of processed scalar data Exporting EDI files from MTPro ...

Страница 54: ...TS files or saved MT files The export of the EDI files is done as follows 1 Read in the GTS files or an MT file into MTPro version 3 00 or greater Build date of May 11 or later 2 Click File Export EDI file It will show you the EDI export menu as follows 3 Make sure each EDI Data ID is unique for each station and the name length is 10 characters or less In the example above the EDI Data ID s are no...

Страница 55: ... file names 4 Enter a latitude and longitude reading for one of the stations Use the negative singe for latitudes in the southern hemisphere and longitudes in the western hemisphere For example 5 Click on Calc Lat Lngg Coord to have the program calculate all the Lat Long positions for the other soundings See below ...

Страница 56: ...ng stations Ex are off line then the GPS coordinates can be entered manually for those individual stations 2 If incorrect GPS measurements were entered you can re enter the correct values in then re calculate all values by clicking on the Cal Lat Long Coord while the changed value is still highlighted 3 Any field sounding can be disabled by toggling the Enable field from Yes to No Export of Google...

Страница 57: ...57 ...

Страница 58: ...degrees For tensor CSAMT one transmitter dipole should be parallel to Ex and the other parallel to Ey C Transmitter signal amplitude The GEM3D receiver has detected a 20 kW transmitter at a distance of 25 kilometers from the survey site At that distance the transmitter signal amplitude is in the low microvolt range As the distance increases and the ground resistivity between the transmitter dipole...

Страница 59: ... telluric E field channels Caution should be taken in the proper preparation and maintenance of the porous pots For example if copper copper sulfate non polarizing electrodes are used the solution must be kept saturated meaning there should be undissolved CuSO4 crystals in the solution b Electrode dipole cables If electrode cables are left out overnight they may be eaten by rodents causing shortin...

Страница 60: ...spheric signals That means it does not require the processing software to included transmitter terms i e any information about the transmitter can be ignored other than the assumption it is far field and un polarized 3 Because there are natural field signals from as low as 0 0001 Hz to over 50 000 Hz a great depth can be mapped using natural field MT and relatively shallow features detected in the...

Страница 61: ...an 5 km generally cannot be done using CSAMT 3 A CSAMT transmitter generally can transmit up to 1 000 Volts at anywhere from 2 to 30 Amps into the ground This requires health and safety precautions to be strictly observed 4 Often when lower frequencies are acquired they enter into the near field This is mostly seen in high resistivity sites when the transmitter is too close for far field measureme...

Страница 62: ... segment The segment concept comes from 3D seismic layout It is normally 1 and a maximum 2 without an LTU in Geode EM3D Byte 7 Unsigned Integer Number of Boxes in the layout Byte 8 Unsigned Integer Number of channels in the layout Byte 9 Unsigned Integer Number of coils in the layout Byte 10 Unsigned Integer line frequency either 50 or 60 Hz Byte 11 Unsigned Integer 0 if using GPS time 1 if using ...

Страница 63: ... mentioned in this memo Byte 85 86 87 88 89 90 91 92 8 bytes IEEE Float sign bit 11 bit exponent 52 bit mantissa Tx1 dipole length in meters Byte 93 94 95 96 97 98 99 100 8 bytes IEEE Float sign bit 11 bit exponent 52 bit mantissa The easting coordinate of Tx1 dipole center Byte 101 102 103 104 105 106 107 108 8 bytes IEEE Float sign bit 11 bit exponent 52 bit mantissa The elevation of Tx1 dipole ...

Страница 64: ... white space in the keyword but values do have this restriction A white space is used as a separator between the keyword and value strings Keyword and value string pairs are separated by a NULL character Below are free string keywords at this moment 5 18 2016 But it could be modified in future if necessary SURVEY Survey name of the field work COMPANY Company doing the survey CLIENT The client of t...

Страница 65: ...egment description is 49 bytes It contains following 6 fields Byte0 15 unused it was assigned as the survey line the segment but is disabled at this moment May of 2016 Byte 16 unsigned integer Number of receiver boxes in the segment Byte 17 24 8 bytes IEEE Float sign bit 11 bit exponent 52 bit mantissa planned telluric dipole length in the segment The actual E channel dipole length can be changed ...

Страница 66: ...II character string Channel definition Byte 16 Byte 31 ASCII character string Calibration file name for H channel Byte 32 unsigned integer Channel number in seg2 file created by SAS program Byte 33 unsigned integer Shared pots 0 no shared pots 1 share one pot 2 share two pots Byte 34 unsigned integer High pass filter settings 0 DC coupling 1 0 1 Hz cut off frequency 2 0 01 Hz cut off frequency Byt...

Страница 67: ...t 8 bit exponent 23 bit mantissa Signal frequency in Hz Byte 37 40 unsigned integer Number of stacks in the record Byte 41 44 unsigned integer Transmitter divisor based Tx clock frequency of 4 980 736 Hz To make file flexible to add new parameters during development I use free format strings to store some parameters after each record tag The string size in bytes is specified in Byte 9 12 as mentio...

Страница 68: ... data is stored in 4 bytes IEEE floating point sign bit 8 bit exponent and 23 bit mantissa The record data is stored channel by channel The bytes of each channel are 4 X number samples bytes 29 32 in record tag ...

Страница 69: ...he MT practitioner are described by Maxwell s equations In differential form they are Faraday s Law 1 Ampere s Law 2 3 Coulomb s Law 4 where E is the electric field H is the magnetic field is conductivity is permitivity and is free electric charge Here the notation E and H indicates vector harmonic time dependency so that the peak instantaneous vector value E of E is given by E Re ei t E where is ...

Страница 70: ...rm earth where the z direction is positive downward we need only consider the field components and and can set the other components of the E and H fields to zero With equation 5 becomes 6 because the plane wave does not vary in the x and y directions This differential equation has a general solution where the coefficients E0 and E0 are constants which can be found by applying boundary conditions B...

Страница 71: ...istance This distance is called a skin depth One wavelength is 2 radians so one skin depth is a bit less than one sixth of a wavelength Wavelength is given by 2 so one skin depth is given by 1 where the wave number is 2 so 2 1 4 10 503 2 7 f f meters At the earth s surface z 0 and from equation 6 Ex 0 At the skin depth the amplitude of the down going wave has deceased to E E e x 0 1 which is 1 e o...

Страница 72: ...ch we can measure them Impedance In the air above a uniform earth we expect to find an electromagnetic field composed of electromagnetic waves propagating downward and reflected waves propagating upward This situation is described for an electric field component by 7 The coefficient subscripts 0 indicate that this expression applies to layer 0 the air and the superscripts indicate the direction of...

Страница 73: ...dance Z For the case of a homogeneous earth Z This is the basis for defining the apparent resistivity a it is the resistivity of a homogeneous earth which would yield the same surface impedance as measured over an inhomogeneous earth at a particular location and frequency Because 1 4 0 E H e x y i we can write a x y i E H 0 2 In general apparent resistivity is complex e g the IP phenomena but we r...

Страница 74: ...ulation because when the source fields are nearly plane waves the impedance elements Zij are time invariant The scalar surface impedance Z E H ij i j is easier to calculate but can vary as the direction of the source fields vary The tensor impedance can be calculated from a number of records N using the least squares method where the difference between a measured electric field component is minimi...

Страница 75: ...and Zyy are obtained in a similar way The surface impedance is usually expressed as apparent resistivity and impedance phase and they are calculated from the surface impedance components as ij ij ij Z f Z 1 2 0 2 2 and ij ij ij Z Z tan Im Re 1 whether they are based on scalar or tensor calculations Z E H H H E H H H H H H H H X H H xx x y y x x x y y x y y x x x y y Z E H H H E H H H H H H H H X H...

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