Magnetotelluric Impedance Tensor Research Articles

EMRIDGE: The electromagnetic investigation of the Juan de Fuca Ridge

From July to November 1988, a major electromagnetic (EM) experiment, known as EMRIDGE, took place over the southern end of the Juan de Fuca Ridge in the northeast Pacific. It was designed to complement the previous EMSLAB experiment which covered the entire Juan de Fuca Plate, from the spreading ridge to subduction zone. The principal objective of EMRIDGE was to use natural sources of EM induction to investigate the processes of ridge accretion. Magnetotelluric (MT) sounding and Geomagnetic Depth Sounding (GDS) are well suited to the study of the migration and accumulation of melt, hydrothermal circulation, and the thermal evolution of dry lithosphere. Eleven magnetometers and two electrometers were deployed on the seafloor for a period of three months. Simultaneous land-based data were made available from the Victoria Magnetic Observatory, B.C., Canada and from a magnetometer sited in Oregon, U.S.A. Changes in seafloor bathymetry have a major influence on seafloor EM observations as shown by the orientation of the real GDS induction arrows away from the ridge axis and towards the deep ocean. Three-dimensional (3D) modelling, using a thin-sheet algorithm, shows that the observed EM signature of the Juan de Fuca Ridge and Blanco Fracture Zone is primarily due to nonuniform EM induction within the ocean, associated with changes in ocean depth. Furthermore, if the influence of the bathymetry is removed from the observations, then no significant conductivity anomaly is required at the ridge axis. The lack of a major anomaly is significant in the light of evidence for almost continuous hydrothermal venting along the neo-volcanic zone of the southern Juan de Fuca Ridge: such magmatic activity may be expected to have a distinct electrical conductivity signature, from high temperatures, hydrothermal fluids and possible melt accumulation in the crust. Estimates of seafloor electrical conductivity are made by the MT method, using electric field records at a site 35 km east of the ridge axis, on lithosphere of age 1.2 Ma, and magnetic field records at other seafloor sites. On rotating the MT impedance tensor to the principal axis orientation, significant anisotropy between the major (TE) and minor (TM) apparent resistivities is evident. Phase angles also differ between the principal axis polarisations, and TM phase are greater than 90° at short periods. Thin-sheet modelling suggests that bathymetric changes accounts for some of the observed 3D induction, but two-dimensional (2D) electrical conductivity structure in the crust and upper mantle, aligned with the ridge axis, may also be present. A one-dimensional (1D) inversion of the MT data suggests that the top 50 km of Earth is electrically resistive, and that there is a rise in conductivity at approximately 300 km. A high conductivity layer at 100 km depth is also a feature of the 1D inversion, but its presence is less well constrained.

Strike-angle determination from the magnetotelluric impedance tensor in the presence of noise and local distortion: rotate at your peril!

SUMMARY Determination of the strike of the dominant 2-D geoelectrical structure from magnetotelluric (MT) data is difficult in the presence of both noise and local distortion. This paper illustrates that often the strike angle is the least-stable parameter that can be resolved from the MT data themselves, and that the telluric distortion parameters are usually more robustly estimated. In particular, techniques which rely only on the analytical rotational properties of the MT impedance tensor can yield erroneous results in the presence of even small amounts of noise. The estimation procedure is stabilized once the telluric distortion parameters have been correctly determined and a constrained fit is sought. Also, it is emphasized that even when the true strike angle is known, statistically superior estimates of the regional impedances result when fitting a galvanic distortion model to the data rather than merely rotating the impedance tensor into the determined (or assumed) strike direction.

Very long period magnetotellurics at Tucson Observatory: Estimation of impedances

Eleven years (1932–1942) of electric potential and magnetic measurements at the Tucson observatory represent a unique very long period magnetotelluric (MT) data set. We report here on a careful reanalysis of this data using modern processing techniques. We have developed and used novel methods for separating out the quasi‐periodic daily variation fields and for cleaning up outliers and filling in missing data in the time domain. MT impedance tensors, estimated using the cleaned and filled data and using robust frequency domain methods, are well determined and smoothly varying for periods between 4 hours and 10 days. At longer periods the electric field data are swamped by large‐amplitude incoherent noise, particularly after the third year of the experiment. Although we find no evidence for contamination of any field components by oceanic motional induction at tidal periods, the MT impedance estimates do show evidence of small systematic biases due to finite spatial scale geomagnetic sources at harmonies of the daily variation period. These periods are thus removed from the time series and not used in further analysis. We show that the resulting impedance tensor is well modeled by a real, frequency‐independent distortion of a scalar impedance, which is consistent with non‐inductive distortion of the electric fields by local surface geology. To estimate the undetermined static shift of the MT impedance, we compare the long‐period MT results to equivalent MT impedances determined from 46 years of geomagnetic data. Combining the geomagnetic and undistorted MT impedances results in scalar impedance estimates for periods 0.17<T<91 days of unprecedented precision. However, for periods less than one day, the phase and amplitude of this impedance, while individually consistent, are not mutually consistent with any one‐dimensional conductivity distribution. The inconsistency probably results from a combination of subtle multidimensional effects and systematic biases.

Controlled-source tensor magnetotelluric responses of a layered earth with azimuthal anisotropy

SUMMARY We consider a model for fracture-generated anisotropy in the crust represented by a layered earth with azimuthal anisotropy. A theory has been developed to compute electromagnetic fields induced by grounded electric dipoles on such a model. A vector potential is used to derive fields. Reflection coefficients are obtained by matrix recurrence formulae. Comparisons with one-dimensional isotropic models and models of homogeneous half-spaces with azimuthal anisotropy show that our algorithm gives correct results. Results are presented in terms of controlled-source tensor magnetotelluric (CSTMT) impedance tensor and tipper vector. The existence and characteristics of azimuthal anisotropy are revealed by them. We suggest the use of Parkinson’s vectors to delineate anisotropy in practice because magnetic fields are less susceptible to static distortion than electric fields.

Corrections for near surface effects: Decomposition of the magnetotelluric impedance tensor and scaling corrections for regional resistivities: A tutorial

This paper primarily examines the effects of small-scale or near-surface conductivity inhomogeneities on the magnetotelluric (MT) impedance tensor. These effects cause three different types of distortion results. (1) The well-knownstatic shifts of sounding curves. (2) When the underlying regional setting is two-dimensional then the two regional impedances are mixed in an arbitrary coordinate system. Thus the level and shape of each sounding curve is distorted as are the phases. (3) At sufficiently high frequencies these effects generate anomalous magnetic fields that in turn alter the background phases. This tutorial first explores the usefulness of various MT tensor analysis techniques to overcome the problem of phase mixing and to recover regional information in the presence of local geological noise. Synthetic and experimental data are considered. A sequence ofa priori models of increasing complexity are described. The use of appropriate decompositions of the MT tensor each with an increasing number of parameters is emphasised. In a second part, phase mixing and static shifts are examined from a synoptic view. Some static shift removal techniques that can be used in conjunction with the decomposition are discussed. This paper is not a review but rather an investigation of a few methods that the authors have found useful with field data.

A simple technique for analysing and partly removing galvanic distortion from the magnetotelluric impedance tensor: application to Abitibi and Kapuskasing data (Canada)

Galvanic distortion of the regional electrical field by surficial local heterogeneities disturbs the regional inductive response. We present a simple method for (a) detecting the presence of galvanic distortion in the measured impedance tensor, (b) defining the regional dimensionality of the background (1-D or 2-D; 3-D is excluded from the analysis) and (c) recognizing whether or not measurements were taken in the true regional axes (if the regional tensor is 2-D). In the case of distortion of a 1-D regional tensor, a tensor decomposition does not bring more information than that given by the effective impedance (Berdichevsky & Dmitriev 1976). In the case of a 2-D regional tensor, if the measurement axes do not coincide with the regional principal axes, both apparent resistivities and phases will be affected. Whether or not measurement and principal axes coincide will define the form of distortion model to use in the removal technique. A simple inversion method is used for this purpose. The approach, which is a cross between that presented by Bahr (1988) and Groom & Bailey (1989) and does not remove static shift, is tested on synthetic and real data. The results of the application to real data suggest that this type of analysis should be carried out prior to any interpretation of magnetotelluric data collected in regions of complex geology.

Geological noise in magnetotelluric data: a classification of distortion types

Decomposition of the magnetotelluric impedance tensor into parameters relevant to a general Earth model that allows for galvanic distortion and regional induction has become a powerful data evaluation tool. Two similar techniques that incorporate superimposition of local three-dimensional and regional two-dimensional structures are considered. Both techniques have two serious limitations: (1) the conductivity structure might be less complex than assumed in the general model and therefore irrelevant model parameters are derived; (2) the regional conductivity structure may be more complicated than indicated by a two-dimensional model. The first problem is addressed in this paper by considering seven classes of general model of increasing complexity. Procedures are suggested that can be used to assign a particular datum to only one of the model classes. Therefore dimensionality parameters are suggested which include conventional and regional skew as well as local and regional structural dimensionality indicators. To address the second problem, an extension of the decomposition technique is presented that allows for a departure from the purely two-dimensional case for regional structures. An example, together with field data, is provided from the German deep drilling site. It explains how the decomposition technique recovers the two impedance phases belonging to a large regional anomaly although the impedance tensors are influenced by strong local distortion. This example also illustrates how the length scale of inductive structures can be estimated from the frequency dependence of the structural dimensionality parameters.

Near-surface and topographic distortions in electromagnetic induction

The most revealing description of electromagnetic (EM) distortions due to near-surface inhomogeneities and topography is in terms of galvanic and inductive effects. In either case, the distorted electric and magnetic fields can be best visualized as a vectorial sum of primary and secondary fields. Secondary electric fields due to electric charge build-up in the galvanic case persist to the longest periods. In contrast, the secondary electric and magnetic fields due to inductive, vortex currents disappear at long periods. The static shift of magnetotelluric (MT) apparent resistivity sounding curves is a classic example of the galvanic effect. Methods to correct for unwanted distortions such as the static shift can be classified into six categories: use of invariant response parameters, curve shifting, statistical averaging, spatial filtering, use of distortion tensors, and computer modeling. Although invariant impedance calculations are simple to make, they cannot, in general, recover the undistorted impedance. Short period curve shifting is best done with auxiliary soundings such as time domain EM; however, this requires multiple surveys. The shifting of long period MT sounding branches is useful if a standard curve is known and can be matched. Statistical averaging of neighboring MT soundings that are conformal but static shifted has proven very effective at removing random distortions if adaquate data are available. The new EMAP (Electromagnetic Array Profiling) method combats the inherent spatial high pass characteristics of EM distortions by low pass operations in data collection and processing. EMAP proposes the continuous, in-field measurement of electric field dipoles to avoid spatial aliasing. Distortion tensor stripping of topographic distortions is possible since terrain is deterministic but stripping the effects of uncertain subsurface inhomogeneities may be misleading. A new decomposition of the MT impedance tensor under the assumption of surficial three-dimensional (3-D) galvanic effects imposed on a one- or two-dimensional (1-D and 2-D) regional setting promises a way to recover the regional structure. There is a continual need for 3-D computer modeling to test new methods and to calculate topographic and regional effects. Computer modeling has established the value of 2-D modeling of the data identified as transverse magnetic (TM) in some 3-D environments. Ideally, EM distortion correction requires continuous, or at least many, data and the application of more than one correction-modeling scheme.

Geomagnetic induction in the Tasman Sea and electrical conductivity structure beneath the Tasman Seafloor

SUMMARY During the Tasman Project of Seafloor Magnetotelluric Exploration recordings were made of the natural magnetic and electric field variations along a line of seafloor sites crossing the Tasman Sea. Using these data and additional magnetic field recordings made on the Australian continent the pattern of geomagnetic induction in the Tasman Sea Region is examined. An investigation of the seafloor magnetotelluric impedance tensor indicates the geomagnetic induction is influenced by the large-scale 3-D conductivity structure of the region. This result is confirmed by a study of impedance estimates obtained using the vertical gradient sounding method (in which the seafloor impedance is determined from the attenuation of the horizontal magnetic field variations through the ocean). Inversion of the E-polarization impedance component from sites in the central Tasman Sea indicates the conductivity structure at depths greater than about 100 km is laterally homogeneous in this region. It is probable that the conductivity structure at these sites includes a high-conducting layer similar to one observed in the Pacific Ocean. One seafloor site, lying on the Tasmantid Seamount Chain, exhibits an increased conductivity at depths of less than 100 km. The increased conductivity may be due to heating of the lithosphere by a hotspot, one proposed source of the seamount chain.

Comments On ‘Concerning dispersion relations for the magnetotelluric impedance tensor’ By E. Yee and K. V. Paulson

SUMMARY Yee & Paulson (1988) derive an integral representation and some dispersion relations for a general magnetotelluric impedance tensor measured at a single point on the surface of the 3-D Earth. These results derive from the assumption that the impedance tensor defines a linear system which is causal and passive. We give a more careful discussion of the justification for causality and passivity and show that they do not follow from simple physical arguments; at the very least, there is a substantial gap in the mathematical derivation given by Yee & Paulson (1988). In fact, both conditions can almost certainly fail for physically realizable 3-D conductivities. We present a qualitative analysis of some simple examples which illustrate how this could occur, and give examples of estimated impedance tensors which are clearly not consistent with the passivity condition. We thus conclude that the relevance to real data of many of the results derived by Yee & Paulson must be seriously questioned. Key word: magnetotellurics.

Reply to the ‘Comments on: Concerning dispersion relations for the magnetotelluric impedance tensor’ By G. D. Egbert

Reply to the ‘Comments on: Concerning dispersion relations for the magnetotelluric impedance tensor’ By G. D. Egbert

Structure of the Atlantic margin of Mauritania (western Africa) based on geoelectrical and drilling data

Magnetotelluric data have been used in southern Mauritania to study crustal structures related to the Senegal-Mauritania basin. Observations were made at 10 sites along a 225 km northwest-southeast profile, beginning near the Atlantic shoreline and ending near the western border of the Mauritanides orogenic belt. The determinant parameters of the magnetotelluric impedance tensor were interpreted to obtain layered models beneath each of the sites. For sites near the coast, one-dimensional modeling of the data was followed by two-dimensional modeling. The models produced indicate three important layers in the electrical stratigraphy. In the western part of the traverse, unexpectedly low resistivities of about 3 ohm ⋅ metres (Ω⋅m) occur in the Mesozoic formations, which rapidly thicken seaward. Beneath the sedimentary sequences, the basement rocks have fairly uniform resistivities (1000-1500 Ω⋅m). Conductive layers were detected within the crustal section in the eastern part of the basin. In the depth range of 13 to 17 km, resistivities decrease to less than 20 Ω⋅m. This 2-5-km-thick zone dips gently eastward, suggesting the presence of a free fluid phase. By combining the information derived from the onshore geoelectrical model and the offshore seismic and deep-well data, a schematic geologic cross section through the Mauritania continental margin is proposed.

Quantitative interpretation of rotationally invariant parameters in magnetotellurics

Use of rotationally invariant parameters derived from the magnetotelluric impedance tensor avoids problems with identification of electrical strike. However, quantitative analysis of an invariant must be used with caution. Layered models from inversion of invariant sounding curves accurately estimate the structure, as does one‐dimensional inversion of an invariant parameter, if the site is away from conductive three‐dimensional (3‐D) heterogeneities. Inversions at sites both above and away from a resistive heterogeneity and above a conductive heterogeneity result in errors. The errors are most serious at sites above a finite conductor. A section created by interpolation of layered models derived from invariants should always be modeled with multidimensional programs to verify the section’s accuracy. The above conclusions hold regardless of the type of invariant parameter used. We found no advantage to using the determinant over the arithmetic mean of the impedance tensor, or vice versa.

A comparison of techniques for magnetotelluric response function estimation

Spectral analysis of the time‐varying horizontal magnetic and electric field components yields the magnetotelluric (MT) impedance tensor. This frequency dependent 2×2 complex tensor can be examined for details which are diagnostic of the electrical conductivity distribution in the Earth within the relevant (frequency dependent) inductive scale length of the surface observation point. As such, precise and accurate determination of this tensor from the electromagnetic time series is fundamental to successful interpretation of the derived responses. In this paper, several analysis techniques are applied to the same data set from one of the EMSLAB Lincoln Line sites. Two subsets of the complete data set were selected, on the basis of geomagnetic activity, to test the methods in the presence of differing signal‐to‐noise ratios for varying signals and noises. Illustrated by this comparison are the effects of both statistical and bias errors on the estimates from the diverse methods. It is concluded that robust processing methods should become adopted for the analysis of MT data, and that whenever possible remote reference fields should be used to avoid bias due to uncorrelated noise contributions.

Interpretation of synthetic three‐dimensional magnetotelluric data

The magnetotelluric (MT) method is an electromagnetic sounding technique used in geophysical exploration that is based on the measurement of surface electric and magnetic fields. The presence of three‐dimensional conducting heterogeneities near the surface of the Earth obscures conducting regions buried deeper in the Earth and leads to interpretational errors. In this paper a procedure referred to as “wave number filtering” is developed that dramatically reduces the undesirable effects of three‐dimensional heterogeneities on the Zxy and Zxx components of the MT impedance tensor, where the x axis is arbitrarily determined by the line of the MT survey. The Zyx and Zyy components of the MT impedance tensor are improved to some extent by wave number filtering, but the amount of improvement depends on the location with respect to the anomalous region and does not, in general, result in a correct interpretation. The wave number filtering process is evaluated by comparing the filtered and the unfiltered apparent resistivities derived from the MT impedance tensor for a particular three‐dimensional model consisting of a heterogeneous region on the surface of an otherwise homogeneous Earth.

The use of data-adaptive filtering for noise removal on magnetotelluric data

A new method is described which can be used to reduce the bias error as well as the random error of the magnetotelluric impedance tensor. This reduction in noise can be done in a single stack, thus making averaging unnecessary or keeping it to a minimum. This can speed up a magnetotelluric sounding considerably. The method is based on a data-adaptive filtering technique. A unique feature of the method is that no a priori information of the signal or noise characteristic is necessary for its operation. Another advantage is that the method adapts itself to changing signal and/or noise characteristics. It is shown how random noise, spikes and steps can be removed by this method. A description of the noise problems in MT is given. The data-adaptive method is described and its properties are illustrated by applying it to severely distorted synthetic signals. Its effectiveness in reducing MT tensor bias and random noise is shown through the use of the unit impedance tensor.

Application of the magnetotelluric impedance tensor to earthquake prediction research in Greece : Chouliaris, G; Rasmussen, T M Tectonophysics V152, N1/2, 10 Sept 1988, P119–135

Application of the magnetotelluric impedance tensor to earthquake prediction research in Greece : Chouliaris, G; Rasmussen, T M Tectonophysics V152, N1/2, 10 Sept 1988, P119–135

Decomposition of magnetotelluric impedance tensors in the presence of local three‐dimensional galvanic distortion

There are many occasions on which the magnetotelluric impedance tensor is affected by local galvanic distortion (channelling) of electric currents arising from induction in a conductive structure which is approximately two‐dimensional (2‐D) on a regional scale. Even though the inductive behavior is 2‐D, the resulting impedance tensor can be shown to have three‐dimensional (3‐D) behavior. Conventional procedures for rotating the impedance tensor such as minimizing the mean square modulus of the diagonal elements do not in general recover the principal axes of induction and thus do not recover the correct principal impedances but rather linear combinations of them. This paper presents a decomposition of the impedance tensor which separates the effects of 3‐D channeling from those of 2‐D induction. Where the impedance tensor is actually the result of regional 1‐D or 2‐D induction coupled with local frequency independent telluric distortion, the method correctly recovers the principal axes of induction and, except for a static shift (multiplication by a frequency independent real constant), the two principal impedances. Also obtained are two parameters (twist and shear), which partially describe the effects of telluric distortion. It is shown that the tensor operator which describes the telluric distortions can always be factored into the product of three tensor sub‐operators (twist, shear, local anisotropy) and a scalar. This product factorization allows assimilation of local anisotropy, if present, into the regional anisotropy. The method of decomposition is given in the paper along with a discussion of the improvements obtained over the conventional method and an example with real data.

Concerning dispersion relations for the magnetotelluric impedance tensor

SUMMARY Adopting a purely systems-theoretic viewpoint, it is shown how a small set of well-established general physical principles such as causality, stability, and passivity, applied to the earth system, determines the analytical properties of the associated impedance tensor in the complex frequency plane. These physical principles and their consequences are utilized to obtain an integral representation for the impedance tensor based upon the Cauer representation for positive functions. This representation is developed primarily by the imposition of the passivity and symmetry requirement on the impedance tensor. As an application, the representation is employed to develop a set of inequality constraints (necessary conditions) that must be verified by the impedance tensor. Since linearity and passivity imply causality, the Cauer integral representation for the impedance tensor is then utilized to derive a subtracted dispersion relation that connects the real and imaginary Hermitian parts of the tensor on the real frequency axis. Furthermore, it is shown how subtracted dispersion relations for the impedance tensor may be developed directly from the causality principle without recourse to the Cauer representation. In this fashion, the dispersion relations for the scalar response function, developed by Weidelt and Fischer & Schnegg in the context of 1-D and 2-D earth systems, respectively, have been extended to the tensor response function corresponding to general 3-D earth systems. Although the focus in this paper is limited to the explicit development of dispersion relations for the impedance tensor, the applicability and scope of the methods utilized are of a more general nature and can be employed to develop integral relationships for other Earth response functions (e.g. tipper responses). For the general 3-D earth, the dispersion relations have direct applications in the formulation of consistency tests, the construction of consistent estimates of the impedance tensor, and the identification of non-linearities.

The application of the magnetotelluric impedance tensor to earthquake prediction research in Greece

Continuous short period (0.1–3600 s) measurements of the magnetotelluric field components were conducted simultaneously at two sites in Greece for a period of 5 weeks. The estimation of the impedance tensor elements from 8-hr windows of recorded data, at each station, is found to describe the local electromagnetic induction with great accuracy. The computation of the residual electric field, obtained as the difference between the observed and estimated inductive part of the electric fields, clearly improves the detection of any local electric field anomaly. This method was used in an attempt to detect precursory Sci smic electrical signals (SES) that have been reported to precede earthquakes in Greece. The results indicate the success of this method in resolving ambiguities about the nature of the reported SES, i.e. whether it has an external or internal source. Although during the recording period no large earthquake occurred, five with a magnitude of between M L = 4.0 and M L = 4.3 occurred within a radius of 150 km from one of the stations. The magnetotelluric recordings and the computed residual electric fields for the time intervals reported to contain the SES precursors to these events were analysed in some detail. In two of the cases it was found that the sources could not be related to earthquake processes. In the other three cases the nature of the source of the suspected SES, although electric, could not be established with certainty. These results indicate that for earthquakes of small magnitude ( M L ≤ 4.3) or of large epicentral distance ( r ≥ 100 km), the detection of a SES is extremely difficult.