Apparent Resistivity Tensor Research Articles

Subsurface structural trends in Central-Western India: Inferences from magnetotelluric data using the complex MT apparent resistivity tensor

The central-western part of the Indian subcontinent exhibits significant geological diversity and possesses a rich record of different tectonothermal events in the earth's evolutionary history, spanning from the Archean to the present. Precambrian geology in the region is mostly obscured by Cretaceous-Tertiary/Paleocene volcanic eruptions and Proterozoic to Quaternary/recent sedimentary cover. Magnetotelluric (MT) impedance and tipper responses from 146 stations, covering central-western India in a grid fashion with a spacing of ∼55 km, were analyzed to evaluate the subsurface structural trends, dimensionalities, and qualitative characteristics of the electric lithosphere in the region. An advanced Complex Apparent Resistivity Tensor (CART) approach, along with the popular Phase Tensor (PT) approach and induction arrows are utilized to achieve the above goals. The analysis revealed a high degree of 3D induction effects in the data at almost every station and period. The directionality information retrieved from the tensor properties showed that the structural trends in the deep crust and upper mantle of the major geologic domains correlate with the known surface tectonic trend of the respective geologic domain. This study provides vital evidence to support the suspected bifurcation of the Precambrian Aravalli-Delhi Mobile Belt (ADMB) tectonic trend and its extensions into neighboring Kutch, Saurashtra, and Central Indian Tectonic Zone (CITZ) domains. The analysis results indicate a lithospheric scale enhanced conductivity beneath the Malwa plateau, which marks the first major phase of the Reunion mantle plume eruption in India. A critical finding of this study is that the Resistivity Phase Tensor better defines the subsurface resistivity structure and provides much clearer structural information than the conventional Phase Tensor.

Analysis of sensitivity patterns for characteristics of magnetotelluric (MT) response functions in inversion

SUMMARYBecause the magnetotelluric (MT) method uses natural sources, the electric and magnetic fields recorded in the field acquisition are not directly used but usually converted into other MT response functions for interpretation such as inversion. Considering that inversion results are dependent on types of input data, it can be helpful to analyse different characteristics of MT response functions for inversion. In this study, we examine sensitivity patterns of MT response functions used commonly in MT inversion, which are the impedance tensor, apparent resistivity, phase, tipper, effective impedance and phase tensor; and investigate how their sensitivity patterns affect inversion results. We first describe overall tendencies of 3-D sensitivity patterns of the MT response functions, and then classify the MT response functions into six groups based on 2-D sensitivity patterns computed at the surface, which are briefly called ‘surface-sensitivity patterns’ in this study. The ’diagonal components of the impedance’ and ‘off-diagonal components of the phase tensor’, which have four petals-shaped surface-sensitivity patterns along the diagonal directions, belong to Group 1, and contribute to imaging 3-D subsurface structures from receivers installed evenly at the surface. Group 2 contains the ‘xy-components of the impedance, apparent resistivity and phase’ and ‘yy-component of the phase tensor’ whose surface-sensitivity patterns are linear in the y-axis. The ‘yx-components of the impedance, apparent resistivity and phase’ and ‘xx-component of the phase tensor’ that have strong linear surface-sensitivity patterns along the x-axis are classified into Group 3. The MT response functions of Groups 2 and 3 are useful for inversion of structures close to 2-D, whose strike extends along the y- and x-axes, respectively. Groups 4 and 5 include the ‘x- and y-components of tipper’ that possess linearly aligned two petals-shaped surface-sensitivity patterns in the x- and y-axes, respectively. The tipper can be helpful in imaging both 2-D and 3-D structures. The ‘effective impedance’ belongs to Group 6, whose surface-sensitivity patterns appear as a small circle. The surface-sensitivity patterns allow the effective impedance to have an advantage in interpretation of 1-D structures. By using several MT response functions for specific cases of 1-D, 2-D and 3-D interpretation of MT data, we investigate whether characteristics of the sensitivity patterns are reflected in modelling (simulating field data) and inversion results, and then suggest optimal MT response functions for those cases. In doing so, we show how to utilize the characteristics of the sensitivity patterns in inversion, and recommend the input MT response functions for inversion according to MT exploration situations. Our study provides basic information on similarities and differences of major MT response functions for inversion and insights on which MT response functions are suitable to increase the feasibility of MT inversion for different field situations based on the sensitivity patterns.

A new approach for calculating the apparent resistivity tensor

A new approach for calculating the apparent resistivity tensor

Magnetotelluric Apparent Resistivity Tensors for Improved Interpretations and 3‐D Inversions

AbstractThe complex magnetotelluric (MT) apparent resistivity tensor can be decomposed into two real tensors, the apparent resistivity and the resistivity phase tensors, which represent relationships between the observed electric field at a point on the Earth's surface and an associated apparent current density. We explain the differences between these tensors and conventional estimates of apparent resistivity and phase for simple resistivity environments and demonstrate, using canonical models in 1‐D and 2‐D environments, that both tensors are more sensitive to vertical and horizontal resistivity gradients than their conventional counterparts. The properties of the new tensors are explained using electromagnetic induction theory and the effects of associated charges at resistivity boundaries. We introduce a new way to plot tensor ellipses, which brings significant improvements to the interpretation of MT data, using appropriate visualization software. The apparent resistivity tensor gives information about the magnitude and direction of apparent resistivity subsurface structures and has a strong response to vertical resistivity contrasts. The resistivity phase tensor is highly sensitive to vertical boundaries and the associated fields in the TM mode. It is also free from static distortions under the same conditions implied for the conventional phase tensor. These findings have prompted a study in the potential of the new tensors for 3‐D inversions. The results from a 3‐D inversion of a canonical oblique conductor straddling two quarter spaces show distinct improvements in resolving the boundaries of the conductor and open a promising field for future studies.

The Effects of 3D Electrical Anisotropy on Magnetotelluric Responses: Synthetic Case Studies

Using the staggered-grid finite difference method, a numerical modeling algorithm for a 3D arbitrary anisotropic Earth is implemented based on magnetotelluric (MT) theory. After the validation of this algorithm and comparison with predecessors, it was applied to several qualitative and quantitative analyses containing electrical anisotropy and a simple 3D prism model. It was found that anisotropic parameters for ρ1 , ρ2 , and ρ3 play almost the same role in affecting 3D MT responses as in 1D and 2D without considering three Euler's angles αS, αD, and αL. Significant differences appear between the off-diagonal components of the apparent resistivity tensor and also between the diagonal components in their values and distributing features under the influence of 3D anisotropy, which in turn help to identify whether the MT data are generated from 3D anisotropic earth. Considering the deflecting effects arising from the inconsistency between the anisotropy axes and the measuring axes, some strategies are also provided to estimate the deflecting angles associated with anisotropy strike αS or dip αD, which may be used as initial values for the 3D anisotropy inversion. [Figure: see text]

The influence of anisotropy on the apparent resistivity tensor: A model study

The investigation of anisotropic structures within the subsurface using direct current resistivity methods (DCR) requires an array set up with measurements in different orientations. Displaying the data by the apparent resistivity tensor provides a powerful tool to easily identify anisotropic structures. In this study we present several characteristics of intrinsic electrical anisotropy and its effect on the apparent resistivity tensor. Above anisotropic anomalies the principle axes of the tensor exhibit a homogeneous pattern with orientation along the anisotropic strike and the aspect ratio related to the anisotropic properties of the medium. Contrary, outside the anomaly the ellipticity of the tensor and its apparent resistivity values are spatially highly variable depending on the location and the orientation of the source current dipole. Some of these features are in clear contrast to the behavior of the tensors above isotropic resistivity anomalies.

Magnetotelluric tensors, electromagnetic field scattering and distortion in three‐dimensional environments

AbstractThis paper describes how subsurface resistivity distributions can be estimated directly from the magnetotelluric (MT) tensor relationship between electric and magnetic fields observed on a three‐dimensional (3‐D) half‐space. It presents an inhomogeneous plane wave analogy where relationships between horizontal electric and magnetic fields, and an apparent current density define an apparent resistivity tensor constructed from a quadratic function of the MT tensor. An extended‐Born relationship allows the electric field to be normalized with respect to an apparent background current density. The model is generalized by including the vertical magnetic field in a 3 by 3 MT response tensor. A complex apparent wave number tensor, constructed from this tensor, has eigenvalues which, using the plane wave analogy, are the vertical wave numbers associated with the eigenpolarizations of propagating waves in the model half space. The elements associated with the vertical magnetic field transfer function define the horizontal wave numbers. An extended 3 by 3 phase tensor contains four elements of the conventional 2 by 2 phase tensor and two elements associated with the vertical magnetic transfer function. The extended phase tensor and a single real distortion tensor with six independent elements can be used to quantify static electric and magnetic field distortions. The approach provides a theoretical basis for visualization and migration of MT data, in comparison with results from other electrical and EM techniques, a starting point for constrained 3‐D inversions, and an assessment of results with other geophysical and geological data.

Examples of application of tensorial resistivity probability tomography to architectonic and archaeological targets

We present the results of the application of the tensor resistivity method to the assessment of the state of conservation of some architectonic features of the S.Giovanni a Carbonara monumental monastery (Naples, Italy) and to the recognition of buried remains in the archaeological site of the roman Port of Claudius at Fiumicino (Rome, Italy). The 3D tomographic approach, based on the concept of resistivity anomaly source occurrence probability, has been used for the analysis of the invariant parameter related to the trace of the determinant of the apparent resistivity tensor.

Using tensorial electrical resistivity survey to locate fault systems

This paper deals with the use of the tensorial resistivity method for fault orientation and macroanisotropy characterization. The rotational properties of the apparent resistivity tensor are presented using 3D synthetic models representing structures with a dominant direction of low resistivity and vertical discontinuities. It is demonstrated that polar diagrams of the elements of the tensor are effective in delineating those structures. As the apparent resistivity tensor shows great inefficacy in investigating the depth of the structures, it is advised to accomplish tensorial surveys with the application of other geophysical methods. An experimental example, including tensorial, dipole–dipole and time domain surveys, is presented to illustrate the potentiality of the method. The dipole–dipole model shows high-resistivity contrasts which were interpreted as corresponding to faults crossing the area. The results from the time domain electromagnetic (TEM) sounding show high-resistivity values till depths of 40–60 m at the north part of the area. In the southern part of the survey area the soundings show an upper layer with low-resistivity values (around 30 Ω m) followed by a more resistive bedrock (resistivity >100 Ω m) at a depth ranging from 15 to 30 m. The soundings in the central part of the survey area show more variability. A thin conductive overburden is followed by a more resistive layer with resistivity in the range of 80–1800 Ω m. The north and south limits of the central part of the area as revealed by TEM survey are roughly E–W oriented and coincident with the north fault scarp and the southernmost fault detected by the dipole–dipole survey. The pattern of the polar diagrams calculated from tensorial resistivity data clearly indicates the presence of a contact between two blocks at south of the survey area with the low-resistivity block located southwards. The presence of other two faults is not so clear from the polar diagram patterns, but their location can be afforded combining tensorial, dipole–dipole and TEM results.

Application of tensorial electrical resistivity mapping to archaeological prospection

ABSTRACTAt an archaeological site (Pilisszentkereszt Cistercian Monastery, Hungary) we carried out 3D tensorial geoelectric mapping measurements. We applied the well‐known tensorial form of Ohm’s differential law, where a 2 × 2 resistivity tensor relates to the horizontal current density vector and the corresponding electric field vector. In the DC apparent resistivity tensor there are three independent rotational invariants, and we defined two alternative sets. In the field, the current electrode distance was fixed to 15 m; two perpendicular AB directions were used, and 16×15=240 potential electrodes (with an equidistant space of ) were put in the central (nearly square, 7.5 m × 7 m) area between the current electrodes. Due to a four‐channel measuring system, it was possible to determine both components of a horizontal electric vector at the same time. The time needed to measure all potential differences between the neighbouring potential electrodes (thus to obtain 15×14=210 resistivity tensors), was about 40 minutes. So far, about 239 such maps have been completed, thus we have more than fifty thousand resistivity tensors around the monastery. The tensorial results are shown together with the results of traditional measurements. In field conditions, any resistivity estimation provides reliable information about the subsurface (both the tensor invariants and the traditional mean values). At the same time, the multidimensional (2D and 3D) indicators proved to be informative only in case of significant subsurface inhomogeneities.

RESISTIVITY TENSOR PROBABILITY TOMOGRAPHY

The probability tomography approach developed for the scalar resistivity method is here extended to the 2D tensorial apparent resistivity acquisition mode. The rotational invariant derived from the trace of the apparent resistivity tensor is considered, since it gives on the datum plane anomalies confined above the buried objects. Firstly, a departure function is introduced as the difference between the tensorial invariant measured over the real structure and that computed for a reference uniform structure. Secondly, a resistivity anomaly occurrence probability (RAOP) function is defined as a normalised crosscorrelation involving the experimental departure function and a scanning function derived analytically using the Frechet derivative of the electric potential for the reference uniform structure. The RAOP function can be calculated in each cell of a 3D grid filling the investigated volume, and the resulting values can then be contoured in order to obtain the 3D tomographic image. Each non-vanishing value of the RAOP function is interpreted as the probability which a resistivity departure from the reference resistivity obtain in a cell as responsible of the observed tensorial apparent resistivity dataset on the datum plane. A synthetic case shows that the highest RAOP values correctly indicate the position of the buried objects and a very high spacial resolution can be obtained even for adjacent objects with opposite resistivity contrasts with respect to the resistivity of the hosting matrix. Finally, an experimental field case dedicated to an archaeological application of the resistivity tensor method is presented as a proof of the high resolution power of the probability tomography imaging, even when the data are collected in noisy open field conditions.

Images of the magnetotelluric apparent resistivity tensor

We present a method for converting the magnetotelluric (MT) impedance tensor into an apparent resistivity tensor. The inclusion of anisotropic permittivity and conductivity into Maxwell’s equations leads to a tensor expression for the propagation constant. To solve Maxwell’s equations we assume exponentially decreasing electric fields in the vertical direction, which implies that the subsurface is regarded as homogeneous but anisotropic. This approach effectively makes use of an anisotropic substitute model, in which contrasts and strike directions of conductivity anomalies are transformed into equivalent amounts and directions of anisotropy. We call this method propagation number analysis (PNA). Rotationally invariant parameters calculated from the resistivity tensor are physically meaningful quantities that are directly applicable to imaging methods. Imaging results of PNA are compared with Egger’s eigenstate analysis and LaTorraca’s singular-value decomposition method using synthetic data from 3-D MT modelling. With PNA, we obtain a comprehensive image of the subsurface that uniquely images structural details of the anomalies. Contrary to other methods, the results of PNA are stable and significant under extreme 3-D conditions. Application of PNA to MT data from the Waterberg Fault in Namibia unravels a complicated 3-D impedance and reveals a clear correlation between the resistivity tensor and the surface geology.

Controlled source apparent resistivity tensors and their relationship to the magnetotelluric impedance tensor

SUMMARY The time-domain surface electric fields produced by a step current in collocated grounded sources can be represented by an apparent resistivity tensor defined by the relationship between the measured (time-varying) electric field and a reference field equal to the steady-state current density in a uniform half-space. A magnetic field response tensor is similarly defined for the horizontal components of the magnetic field. The ‘magnetic field apparent resistivity tensor’ is derived from a linear combination of the contractions of the outer product of the magnetic field response tensor. Frequency-domain apparent resistivity tensors are derived from the Laplace transforms of the corresponding time-domain electric and magnetic field response tensors. Both the frequency and time-domain tensors are independent of the source orientation where the sources can be approximated as (infinitesimal) dipoles. A simple combination of the frequencydomain (impulse response) tensors can be used to derive the controlled source magnetotelluric (CSMT) impedance tensor. The magnetic field apparent resistivity tensor is a useful representation of the conductivity structure only where the source‐receiver offset is much less than the diffusion or skin depth and behaves in a similar way to the ‘early-time’ apparent resistivity traditionally used to represent time-domain electromagnetic data. Numerical modelling results demonstrate that the (horizontal) magnetic field apparent resistivity is insensitive to the localized 3-D conductivity structures that are typically the target of exploration surveys. In contrast, the electric field apparent resistivity tensor depends sensitively upon the conductivity structure and is well behaved over the entire time or frequency range used in long-offset transient electromagnetic or CSMT measurements. By using the electric field apparent resistivity tensor, ‘source effects’ that hinder a conventional impedance tensor analysis of CSMT data can be avoided. Images of simple 3-D structures created from the invariants of the electric field apparent resistivity tensor (in either the time or frequency domain) provide a useful representation of the subsurface conductivity structure despite the simplicity of this imaging procedure. These images are independent of the coordinate system used to express the data and are, to a good approximation, independent of the current source orientations.

Electric field polarization around Ioannina VAN station, Greece, inferred from a resistivity mapping

In the summer of 1997, we made a bipole–dipole mapping survey around Ioannina station of VAN (Varotsos, Alexopoulos, and Nomicos), where detection of the pre-seismic electric signal (SES) has been repeatedly reported. Since we had found the characteristic directional properties of the electric field in the previous study, the present study was aimed to examine it by investigating the shallow electric structure around the station. The apparent resistivity tensor was derived from two sets of measured voltages at each receiver position. From a rough sketch of the resistivity tensor distribution, we found that the electric field was enhanced along the direction parallel to the trend of the basin at receivers located in the conductive basin, and perpendicular to it at receivers in the resistive mountainside. Conductance distribution models with thin plates were constructed by using the measured voltages. The results showed that the VAN station is located on the resistive portion near the contact between the conductive and the resistive part. Furthermore, we simulated the apparent resistivity tensor near the VAN station on the inferred conductance distribution model. Although the directional property similar to those of magnetotelluric (MT) and lightning electric field was not reproduced there, we found that the electric field polarization is affected by heterogeneous structure not only around receivers but also around the source.

The instantaneous apparent resistivity tensor: a visualization scheme for LOTEM electric field measurements

Long-offset transient electromagnetic (LOTEM) data have traditionally been represented as early- and late-time apparent resistivities. Time-varying electric field data recorded in a LOTEM survey made with multiple sources can be represented by an ‘instantaneous apparent resistivity tensor’. Three independent, coordinate-invariant, time-varying apparent resistivities can be derived from this tensor. For dipolar sources, the invariants are also independent of source orientation. In a uniform-resistivity half-space, the invariant given by the square root of the tensor determinant remains almost constant with time, deviating from the half-space resistivity by a maximum of 6 per cent. For a layered half-space, a distance-time pseudo-section of the determinant apparent resistivity produces an image of the layering beneath the measurement profile. As time increases, the instantaneous apparent resistivity tensor approaches the direct current apparent resistivity tensor. An approximate time-to-depth conversion can be achieved by integrating the diffusion depth formula with time, using the determinant apparent resistivity at each instant to represent the resistivity of the conductive medium. Localized near-surface inhomogeneities produce shifts in the time-domain apparent resistivity sounding curves that preserve the gradient, analogous to static shifts seen in magnetotelluric soundings. Instantaneous apparent resistivity tensors calculated for 3-D resistivity models suggest that profiles of LOTEM measurements across a simple 3-D structure can be used to create an image that reproduces the main features of the subsurface resistivity. Where measurements are distributed over an area, maps of the tensor invariants can be made into a sequence of images, which provides a way of ‘time slicing’ down through the target structure.

Examples of ac resistivity prospecting in archaeological research

In this paper we present the results of an alternating current resistivity survey, with a view to future tomographic processing. Two examples are given to evaluate the validity and the resolution of the method. The first in the Sabine Necropolis of Colle del Forno (Montelibretti, Rome), the second in the Etruscan settlement of Poggio Colla (Vicchio, Florence). All the measurements were carried out utilising current up to 512 Hz and a mobile dipole MN along straight lines, having two fixed current probes A and B. It was found that skin effect is uninfluential in the frequency range adopted. Given the absence of natural or artificial disturbances in the signal (e.g. electrode polarization and self potential), it was possible to perform very fast measurements with two operators only. Moreover, the use of a multiple dipole source configuration allows the calculation of the determinant of the apparent resistivity tensor. In the examples shown, this parameter detects the actual position of buried structures independently of the direction of the electric sources.

Reply to Comment on 'Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor' by X. Li and L. B. Pedersen1

Geophysical ProspectingVolume 42, Issue 5 p. 527-529 Reply to Comment on ‘Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor’ by X. Li and L. B. Pedersen1 H.M. Bibby, H.M. Bibby Institute of Geological and Nuclear Science, PO Box 1320, Wellington, New Zealand.Search for more papers by this author H.M. Bibby, H.M. Bibby Institute of Geological and Nuclear Science, PO Box 1320, Wellington, New Zealand.Search for more papers by this author First published: July 1994 https://doi.org/10.1111/j.1365-2478.1994.tb00227.xCitations: 3 1 Received November 1993, accepted December 1993. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume42, Issue5July 1994Pages 527-529 RelatedInformation

Comment on 'Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor' by H.M. Bibby and G.W. Hohmann1

Geophysical ProspectingVolume 42, Issue 5 p. 525-526 Comment on ‘Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor’ by H.M. Bibby and G.W. Hohmann1 Xiaobo Li, Xiaobo Li Department of Geophysics, Villavaegen 16, S-752 36 Uppsala, Sweden.Search for more papers by this authorLaust B. Pedersen, Laust B. Pedersen Department of Geophysics, Villavaegen 16, S-752 36 Uppsala, Sweden.Search for more papers by this author Xiaobo Li, Xiaobo Li Department of Geophysics, Villavaegen 16, S-752 36 Uppsala, Sweden.Search for more papers by this authorLaust B. Pedersen, Laust B. Pedersen Department of Geophysics, Villavaegen 16, S-752 36 Uppsala, Sweden.Search for more papers by this author First published: July 1994 https://doi.org/10.1111/j.1365-2478.1994.tb00226.xCitations: 4 1 Received October 1993, accepted December 1993. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume42, Issue5July 1994Pages 525-526 RelatedInformation

Reply to Comment on 'Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor'by D. Doicin1

Reply to Comment on 'Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor'by D. Doicin1

Comment on 'Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor'by H.M. Bibby and G.W. Hohmann1

Comment on 'Three-dimensional interpretation of multiple-source bipole-dipole resistivity data using the apparent resistivity tensor'by H.M. Bibby and G.W. Hohmann1