Transient electromagnetic inversion: A remedy for magnetotelluric static shifts

Geophysics ◽  
1990 ◽  
Vol 55 (9) ◽  
pp. 1242-1250 ◽  
Author(s):  
Louise Pellerin ◽  
Gerald W. Hohmann
Keyword(s):  
Electric Field ◽  
Apparent Resistivity ◽  
Parametric Representation ◽  
Impedance Tensor ◽  
Static Shift ◽  
Electrode Arrays ◽  
Data Set ◽  
Low Frequencies ◽  
Transient Electromagnetic ◽  
Correction Scheme

Surficial bodies can severely distort magnetotelluric (MT) apparent resistivity data to arbitrarily low frequencies. This distortion, known as the MT static shift, is due to an electric field generated from boundary charges on surficial inhomogeneities, and persists throughout the entire MT recording range. Static shifts are manifested in the data as vertical, parallel shifts of log‐log apparent resistivity sounding curves, the impedance phase being unaffected. Using a three‐dimensional (3-D) numerical modeling algorithm, simulated MT data with finite length electrode arrays are generated. Significant static shifts are produced in this simulation; however, for some geometries they are impossible to identify. Techniques such as spatial averaging and electromagnetic array profiling (EMAP) are effective in removing static shifts, but they are expensive, especially for correcting a previously collected MT data set. Parametric representation and use of a single invariant quantity, such as the impedance tensor determinant, are only useful in limited circumstances and can lead the MT interpreter astray. Transient electromagnetic (TEM) sounding data are relatively inexpensive to collect, do not involve electric field measurements, and are only affected at very early times by surficial bodies. Hence, using TEM data acquired at the same location provides a natural remedy for the MT static shift. We describe a correction scheme to shift distorted MT curves to their correct values based on 1-D inversion of a TEM sounding taken at the same location as the MT site. From this estimated 1-D resistivity structure an MT sounding is computed at frequencies on the order of 1 Hz and higher. The observed MT curves are then shifted to the position of the computed curve, thus eliminating static shifts. This scheme is accurate when the overlap region between the MT and TEM sounding is 1-D, but helpful information can be gleaned even in multidimensional environments. Other advantages of this scheme are that it is straightforward to ascertain if the correction scheme is being accurately applied and it is easy to implement on a personal computer.

Magnetotelluric static shift: Estimation and removal using the cokriging method

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. F25-F34 ◽  
Author(s):  
Benoit Tournerie ◽  
Michel Chouteau ◽  
Denis Marcotte
Keyword(s):  
Apparent Resistivity ◽  
A Priori ◽  
Shift Factor ◽  
Static Shift ◽  
Geostatistical Model ◽  
Data Set ◽  
Resistivity Sounding ◽  
The Difference ◽  
Cross Variogram

We present and test a new method to correct for the static shift affecting magnetotelluric (MT) apparent resistivity sounding curves. We use geostatistical analysis of apparent resistivity and phase data for selected periods. For each period, we first estimate and model the experimental variograms and cross variogram between phase and apparent resistivity. We then use the geostatistical model to estimate, by cokriging, the corrected apparent resistivities using the measured phases and apparent resistivities. The static shift factor is obtained as the difference between the logarithm of the corrected and measured apparent resistivities. We retain as final static shift estimates the ones for the period displaying the best correlation with the estimates at all periods. We present a 3D synthetic case study showing that the static shift is retrieved quite precisely when the static shift factors are uniformly distributed around zero. If the static shift distribution has a nonzero mean, we obtained best results when an apparent resistivity data subset can be identified a priori as unaffected by static shift and cokriging is done using only this subset. The method has been successfully tested on the synthetic COPROD-2S2 2D MT data set and on a 3D-survey data set from Las Cañadas Caldera (Tenerife, Canary Islands) severely affected by static shift.

A method to determine the magnetotelluric static shift from DC resistivity measurements in practice

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. F23-F32 ◽  
Author(s):  
Simona Tripaldi ◽  
Agata Siniscalchi ◽  
Klaus Spitzer
Keyword(s):  
Electrode Spacing ◽  
Impedance Tensor ◽  
Static Shift ◽  
Data Set ◽  
Resistivity Measurements ◽  
Electromagnetic Methods ◽  
Strike Direction ◽  
Distortion Matrix ◽  
Source Electrode

Many efforts have been made to face magnetotelluric (MT) static shift. Impedance tensor analyses give insight to the presence of this feature and allow the determination of some parameters described by the MT distortion matrix. A quantitative determination of the full distortion matrix is, however, still difficult and needs additional measurements. In addition to MT, other electric and electromagnetic methods also are effected by static shift. Using direct current resistivity techniques, e.g., we can determine the static-shift factors in a simpler way because the sources can be controlled. Generally, because the distortion matrix has four entries, four additional quantities have to be determined to describe the static shift completely. They can be achieved, e.g., through measuring two orthogonal electric field components for two orthogonal source configurations. The source electrode spacing, however, has to be sufficiently large to resemble horizontal currents and match the MT plane-wave analog. The procedure at hand extracts the static-shift factors from multielectrode measurements after this condition is met. For the sake of simplicity and demonstration purposes, only inline measurements orthogonal to the strike direction of a 2D model are considered so that the vectorial problem reduces to a scalar one. This procedure is applied to a MT field data set in a regional 2D environment that shows only two additional quantities are necessary to determine the static shift.

Magnetotelluric responses of three‐dimensional bodies in layered earths

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1517-1533 ◽  
Author(s):  
Philip E. Wannamaker ◽  
Gerald W. Hohmann ◽  
Stanley H. Ward
Keyword(s):  
Electric Field ◽  
Apparent Resistivity ◽  
Three Dimensional ◽  
Wave Impedance ◽  
Transverse Magnetic ◽  
Small Scale ◽  
Low Frequencies ◽  
High Frequencies ◽  
Large Structures ◽  
The Earth

The electromagnetic fields scattered by a three‐dimensional (3-D) inhomogeneity in the earth are affected strongly by boundary charges. Boundary charges cause normalized electric field magnitudes, and thus tensor magnetotelluric (MT) apparent resistivities, to remain anomalous as frequency approaches zero. However, these E‐field distortions below certain frequencies are essentially in‐phase with the incident electric field. Moreover, normalized secondary magnetic field amplitudes over a body ultimately decline in proportion to the plane‐wave impedance of the layered host. It follows that tipper element magnitudes and all MT function phases become minimally affected at low frequencies by an inhomogeneity. Resistivity structure in nature is a collection of inhomogeneities of various scales, and the small structures in this collection can have MT responses as strong locally as those of the large structures. Hence, any telluric distortion in overlying small‐scale extraneous structure can be superimposed to arbitrarily low frequencies upon the apparent resistivities of buried targets. On the other hand, the MT responses of small and large bodies have frequency dependencies that are separated approximately as the square of the geometric scale factor distinguishing the different bodies. Therefore, tipper element magnitudes as well as the phases of all MT functions due to small‐scale extraneous structure will be limited to high frequencies, so that one may “see through” such structure with these functions to target responses occurring at lower frequencies. About a 3-D conductive body near the surface, interpretation using 1-D or 2-D TE modeling routines of the apparent resistivity and impedance phase identified as transverse electric (TE) can imply false low resistivities at depth. This is because these routines do not account for the effects of boundary charges. Furthermore, 3-D bodies in typical layered hosts, with layer resistivities that increase with depth in the upper several kilometers, are even less amenable to 2-D TE interpretation than are similar 3-D bodies in uniform half‐spaces. However, centrally located profiles across geometrically regular, elongate 3-D prisms may be modeled accurately with a 2-D transverse magnetic (TM) algorithm, which implicitly includes boundary charges in its formulation. In defining apparent resistivity and impedance phase for TM modeling of such bodies, we recommend a fixed coordinate system derived using tipper‐strike, calculated at the frequency for which tipper magnitude due to the inhomogeneity of interest is large relative to that due to any nearby extraneous structure.

Correction for the static shift in magnetotellurics using transient electromagnetic soundings

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1459-1468 ◽  
Author(s):  
Ben K. Sternberg ◽  
James C. Washburne ◽  
Louise Pellerin
Keyword(s):  
Magnetic Field ◽  
Apparent Resistivity ◽  
Complex Structure ◽  
Transverse Magnetic ◽  
Mountain Range ◽  
Static Shift ◽  
Controlled Source ◽  
Transient Electromagnetic ◽  
Graphical Comparison ◽  
The Magnetic Field

Shallow inhomogeneities can lead to severe problems in the interpretation of magnetotelluric (MT) data by shifting the MT apparent resistivity sounding curve by a scale factor, which is independent of frequency on the standard log‐apparent‐resistivity versus log‐frequency display. The amount of parallel shift, commonly referred to as the MT static shift, can not be determined directly from conventionally recorded MT data at a single site. One method for measuring the static shift is a controlled‐source measurement of the magnetic field. Unlike the electric field, the magnetic field is relatively unaffected by surface inhomogeneities. The controlled‐source sounding (which may be a relatively shallow sounding made with lightweight equipment) can be combined with a deep MT sounding to obtain a complete, undistorted model of the earth. Inversions of the static shift‐corrected MT data provide a much closer match to well‐log resistivities than do inversions of the uncorrected data. The particular controlled‐source magnetic‐field sounding which we used was a central‐induction Transient ElectroMagnetic (TEM) sounding. Correction for the static shift in the MT data was made by jointly inverting the MT data and the TEM data. A parameter which allowed vertical shifts in the MT apparent resistivity curves was included in the computer inversion to account for static shifts. A simple graphical comparison between the MT apparent resistivities and the TEM apparent resistivities produced essentially the same estimate of the static shift (within 0.1 decade) as the joint computer inversion. Central‐induction TEM measurements were made adjacent to over 100 MT sites in central Oregon. The complete data base of over 100 sites showed an average static shift between 0 and 0.2 decade. However, in the rougher topography and more complex structure of the Cascade Mountain Range, the majority of the sites had static shifts of the order of 0.3 to 0.4 decade. The static shifts in this area are probably due to a combination of topography and surficial inhomogeneities. The TEM apparent resistivity (which is used to estimate the unshifted MT apparent resistivity) does not necessarily agree with either the transverse electric (TE) or the transverse magnetic (TM) MT polarization. TEM apparent resistivity may occur between the two, or may agree with one of the two polarizations, or may lie outside the MT polarizations.

3D marine magnetotelluric inversion: A hybrid impedance and direct-field approach

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. E335-E346
Author(s):  
Lutz Mütschard ◽  
Ketil Hokstad ◽  
Torgeir Wiik ◽  
Bjørn Ursin
Keyword(s):  
Electric Field ◽  
Real Data ◽  
Source Distribution ◽  
Impedance Tensor ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Source ◽  
Field Approach ◽  
Impedance Inversion ◽  
Field Inversion

The measured electromagnetic field in magnetotellurics (MT) is composed of the natural source field and its subsurface response. Commonly, the data are represented as impedances, the complex ratio between the horizontal electric and magnetic fields. This measure is independent of the source distribution because the impedance-tensor estimation contains a deconvolution operator. We have used a Gauss-Newton-type 3D MT inversion scheme to compare impedance-data inversion with an inversion using the recorded electric field directly. The use of the observed electric field is beneficial to the inversion algorithm because it simplifies the estimation of the sensitivities. The direct-field approach permits the use of the observed data without processing, but it presumes knowledge of the source distribution. A method to estimate the time-variable strength and polarization of the incoming plane-wave source is presented and tested on synthetic and real-data examples. The direct-field inversion is successfully applied to a synthetic and a real data set within marine settings. A comparison with the conventional impedance inversion is conducted. The results of the synthetic data example are very similar, with a slightly more accurate reconstruction of the model in the impedance case, whereas the direct-field inversion produces a smoother inversion result when compared with the impedance case. The mapping of a resistive salt structure in the real-data example indicates deviations in the final conductivity models. The impedance inversion suggests a deeper rooted resistive structure, whereas the direct-field inversion predicts a more compact structure limited to the overburden. We have evaluated the advantages of the new approach like the simplification of the sensitivity calculation, limitations, and disadvantages like knowledge of the source distribution.

scholarly journals Inverting magnetotelluric data with distortion correction—stability, uniqueness and trade-off with model structure

2020 ◽  
Vol 222 (3) ◽  
pp. 1620-1638 ◽  
Author(s):  
M Moorkamp ◽  
A Avdeeva ◽  
Ahmet T Basokur ◽  
Erhan Erdogan
Keyword(s):  
Real Data ◽  
Distortion Correction ◽  
Impedance Tensor ◽  
Strong Impact ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Near Surface ◽  
Transient Electromagnetic ◽  
Electromagnetic Measurements ◽  
Galvanic Distortion

SUMMARY Galvanic distortion of magnetotelluric (MT) data is a common effect that can impede the reliable imaging of subsurface structures. Recently, we presented an inversion approach that includes a mathematical description of the effect of galvanic distortion as inversion parameters and demonstrated its efficiency with real data. We now systematically investigate the stability of this inversion approach with respect to different inversion strategies, starting models and model parametrizations. We utilize a data set of 310 MT sites that were acquired for geothermal exploration. In addition to impedance tensor estimates over a broad frequency range, the data set also comprises transient electromagnetic measurements to determine near surface conductivity and estimates of distortion at each site. We therefore can compare our inversion approach to these distortion estimates and the resulting inversion models. Our experiments show that inversion with distortion correction produces stable results for various inversion strategies and for different starting models. Compared to inversions without distortion correction, we can reproduce the observed data better and reduce subsurface artefacts. In contrast, shifting the impedance curves at high frequencies to match the transient electromagnetic measurements reduces the misfit of the starting model, but does not have a strong impact on the final results. Thus our results suggest that including a description of distortion in the inversion is more efficient and should become a standard approach for MT inversion.

The use and misuse of apparent resistivity in electromagnetic methods

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1462-1471 ◽  
Author(s):  
Brian R. Spies ◽  
Dwight E. Eggers
Keyword(s):  
Apparent Resistivity ◽  
Early Time ◽  
Asymptotic Formulas ◽  
Voltage Response ◽  
Late Time ◽  
Induced Voltage ◽  
Resistivity Curve ◽  
Transient Electromagnetic ◽  
Electromagnetic Methods ◽  
Tem Method

Problems and misunderstandings arise with the concept of apparent resistivity when the analogy between an apparent resistivity computed from geophysical observations and the true resistivity structure of the subsurface is drawn too tightly. Several definitions of apparent resistivity are available for use in electromagnetic methods; however, those most commonly used do not always exhibit the best behavior. Many of the features of the apparent resistivity curve which have been interpreted as physically significant with one definition disappear when alternative definitions are used. It is misleading to compare the detection or resolution capabilities of different field systems or configurations solely on the basis of the apparent resistivity curve. For the in‐loop transient electromagnetic (TEM) method, apparent resistivity computed from the magnetic field response displays much better behavior than that computed from the induced voltage response. A comparison of “exact” and “asymptotic” formulas for the TEM method reveals that automated schemes for distinguishing early‐time and late‐time branches are at best tenuous, and those schemes are doomed to failure for a certain class of resistivity structures (e.g., the loop size is large compared to the layer thickness). For the magnetotelluric (MT) method, apparent resistivity curves defined from the real part of the impedance exhibit much better behavior than curves based on the conventional definition that uses the magnitude of the impedance. Results of using this new definition have characteristics similar to apparent resistivity obtained from time‐domain processing.

The use of wavelet transforms for improved interpretation of airborne transient electromagnetic data

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. E117-E123 ◽  
Author(s):  
Vanessa Nenna ◽  
Adam Pidlisecky
Keyword(s):  
Wavelet Transforms ◽  
Oil And Gas ◽  
Spatial Scales ◽  
Data Sets ◽  
Data Set ◽  
Topographic Features ◽  
Transient Electromagnetic ◽  
Power Maps ◽  
Southern Alberta ◽  
Cultural Noise

The continuous wavelet transform (CWT) is used to create maps of dominant spatial scales in airborne transient electromagnetic (ATEM) data sets to identify cultural noise and topographic features. The introduced approach is applied directly to ATEM data, and does not require the measurements be inverted, though it can easily be applied to an inverted model. For this survey, we apply the CWT spatially to B-field and dB/dt ATEM data collected in the Edmonton-Calgary Corridor of southern Alberta. The average wavelet power is binned over four ranges of spatial scale and converted to 2D maps of normalized power within each bin. The analysis of approximately 2 million soundings that make up the survey can be run on the order of minutes on a 2.4 GHz Intel processor. We perform the same CWT analysis on maps of surface and bedrock topography and also compare ATEM results to maps of infrastructure in the region. We find that linear features identified on power maps that differ significantly between B-field and dB/dt data are well correlated with a high density of infrastructure. Features that are well correlated with topography tend to be consistent in power maps for both types of data. For this data set, use of the CWT reveals that topographic features and cultural noise from high-pressure oil and gas pipelines affect a significant portion of the survey region. The identification of cultural noise and surface features in the raw ATEM data through CWT analysis provides a means of focusing and speeding processing prior to inversion, though the magnitude of this affect on ATEM signals is not assessed.

scholarly journals A parallel finite‐difference approach for 3D transient electromagnetic modeling with galvanic sources

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1192-1202 ◽  
Author(s):  
Michael Commer ◽  
Gregory Newman
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Electric Field ◽  
Electric Fields ◽  
Time Derivative ◽  
Stable Solution ◽  
Parallel Computer ◽  
Staggered Grid ◽  
Electromagnetic Modeling ◽  
Transient Electromagnetic

A parallel finite‐difference algorithm for the solution of diffusive, three‐dimensional (3D) transient electromagnetic field simulations is presented. The purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources (grounded wires) over arbitrarily complicated distributions of conductivity and magnetic permeability. Using a staggered grid and a modified DuFort‐Frankel method, the scheme steps Maxwell's equations in time. Electric field initialization is done by a conjugate‐gradient solution of a 3D Poisson problem, as is common in 3D resistivity modeling. Instead of calculating the initial magnetic field directly, its time derivative and curl are employed in order to advance the electric field in time. A divergence‐free condition is enforced for both the magnetic‐field time derivative and the total conduction‐current density, providing accurate results at late times. In order to simulate large realistic earth models, the algorithm has been designed to run on parallel computer platforms. The upward continuation boundary condition for a stable solution in the infinitely resistive air layer involves a two‐dimensional parallel fast Fourier transform. Example simulations are compared with analytical, integral‐equation and spectral Lanczos decomposition solutions and demonstrate the accuracy of the scheme.

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