The time-domain magnetotelluric response over three-layer earth models

Magnetotelluric data observed in frequency and time domains are expressed as apparent resistivity. the apparent resistivity is a weighted spatial average of the subsurface resistivity distribution. In this paper, we develop analytical expressions to compute the apparent resistivity in the time domain for various three-layer earth models. the present approach to computing the magnetotelluric response in the time domain is found to overcome the problems encountered by the method of images. the magnetotelluric response in the time domain for various three-level models have been computed and shown graphically. the time-domain responses show a characteristic behaviour with a small change in layered parameters (resistivity and thickness of the layers), whereas frequency-domain responses do not show such behaviour. This characteristic behaviour of time-domain magnetotelluric sounding curves will be useful in the qualitative interpretation of field data.     

Joint Inversion of Geophysical Data

Summary. By jointly inverting several different kinds of geophysical measurements at a site we avoid some of the ambiguity inherent in the individual methods. We show how this can be done for the combination of DC resistivity and magnetotelluric measurements on a layered medium by considering a simple 3-layer model. The combination resolves the resistivity of the thin resistive second layer, even though neither of the two methods can do so alone.
The method is then applied to field data from a shallow sedimentary basin. A blind zone occurs beneath a thick near-surface conductive shale. By a study of the eigenvalue structure of the model it can be seen that resolution in this zone would be slightly enhanced by higher frequency magnetotelluric data, but additional DC data at larger spacing would yield no improvement.     

地球物理方法在地下水污染监测中的应用

目前地球物理方法在水环境保护和治理中得到广泛应用。地球物理方法监测地下水污染是根据污染物与其周围介质在物理、化学性质上的差异,测量污染物理场的分布状态,掌握污染物在地下运移过程和空间分布规律。目前在地下水污染监测中主要的地球物理方法有:大地电磁法、电阻率测井法、自然电位测井法、动态导体充电法探测和地质雷达探测等。地球物理方法在地下水污染监测中有着广泛的应用前景。     

Application of Magnetotelluric (MT) Resistivity to Imaging of Regional Three-Dimensional Geologic Structures and Groundwater Systems

Widespread definition of a groundwater system in three dimensions is necessary for the management and maintenance of groundwater resources. A magnetotelluric (MT) survey can be an effective geophysical prospecting method for imaging regional geological structures by measuring both shallow and deep resistivity. To demonstrate the capability of an MT survey to characterize a groundwater system, the Kumamoto area of central Kyushu in southwestern Japan was selected as a case study site because of its rich groundwater resources. Three-dimensional (3D) MT resistivity structure to a depth of 5?km was modeled by 1D inversion analysis of raw MT data and 3D interpolation of the resultant resistivity column data by the optimization principle method. Consequently, both deep and shallow aquifers were detected. A high-resistivity zone appears at depths between 500 and 2,000?m between the Futagawa?CHinagu faults and the Usuki?CYatsushiro tectonic line, which supports the existence of an aquiclude under the aquifer. The most important characteristic inferred from the 3D resistivity model is that the deep groundwater system below a depth of 1,000?m has two main flow paths. One path is likely to be through porous rocks because the low resistivity zone is regarded as tuff with sand and gravel, and the other flow path is interpreted to be through fractured zones along the Hinagu faults. Hence, the path and direction of the groundwater flows are probably controlled by geologic structures and the configuration of the active faults. These findings support the effectiveness of the MT method for investigating groundwater systems.     

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.     

Joint two-dimensional cross-gradient imaging of magnetotelluric and seismic traveltime data for structural and lithological classification

Collocated magnetotelluric (MT) and seismic profiling is emerging as a necessary combined approach for deep and near-surface imaging but the resulting experimental data are typically interpreted separately since no production programs exist for multidimensional joint inversion of MT and seismic data. We present a joint 2-D inversion approach for imaging collocated MT and seismic refraction data with cross-gradient structural constraints. We describe the main features of the algorithm and first apply it to synthetic data generated for a hypothetical complex geological model. For the synthetic data, we find that the scheme leads to models with remarkable structural resemblance and improved estimates of electrical resistivity and seismic velocity. We apply the scheme to near-surface field data to test the consistency of a previously suggested resistivity–velocity interrelationship and its potential use for subsurface lithofacies discrimination or structural classification. The MT-seismic relationship is found to be in excellent accord with that derived previously for DC resistivity and seismic data set at the test site. Our results suggest that joint MT-seismic cross-gradient imaging leads to improved characterization of heterogeneous geological targets at near-surface to mantle depths.     

Three-dimensional topography corrections of magnetotelluric data

Topographic effects due to irregular surface terrain may prevent accurate interpretation of magnetotelluric (MT) data. Three-dimensional (3-D) topographic effects have been investigated for a trapezoidal hill model using an edge finite-element method. The 3-D topography generates significant MT anomalies, and has both galvanic and inductive effects in any polarization. This paper presents two different correction algorithms, which are applied to the impedance tensor and to both electric and magnetic fields, respectively, to reduce topographic effects on MT data. The correction procedures using a homogeneous background resistivity derived from a simple averaging method effectively decrease distortions caused by surface topography, and improve the quality of subsurface interpretation. Nonlinear least-squares inversion of topography-corrected data successfully recovers most of structures including a conductive or resistive dyke.     

3-D magnetotelluric inversion and model validation with gravity data for the investigation of flood basalts and associated volcanic rifted margins

20 magnetotelluric (MT) soundings were collected on the Isle of Skye, Scotland to provide a high-resolution three-dimensional (3-D) electrical resistivity model of a volcanic province within the framework of a project jointly interpreting gravity, seismic, geological and MT data. The full 3-D inversion of the MT data jointly interpreted with gravity data reveals upper crustal structure. The main features of the model are interpreted in conjunction with previous geological mapping and borehole data. Our model extends to 13 km depth, several kilometres below the top of the Lewisian basement. The top of the Lewisian basement is at approximately 7–8 km depth and the topography of its surface was controlled by Precambrian rifting, during which a 4.5 km thick sequence of Torridonian sediments was deposited. The Mesozoic sediments above, which can reach up to 2.2 km thick, have small-scale depocentres and are covered by up to 600 m of Tertiary lava flows. The interpretation of the resistivity model shows that 3-D MT inversion is an appropriate tool to image sedimentary structures beneath extrusive basalt units, where conventional seismic reflection methods may fail.     

Effects of galvanic distortion on magnetotelluric data over a three-dimensional regional structure

Although the galvanic distortion due to local, near-surface inhomogeneities is frequency-independent, its effect on the magnetotelluric data becomes, in a 3-D structure, frequency-dependent. Therefore, both the apparent resistivity and the phase responses are disturbed, and a correction should be carried out prior to the 3-D interpretation in order to retrieve the 3-D regional impedance tensor. In many cases, the structure is 2-D for depths corresponding to a first range of periods and 3-D for longer periods (called 2-D/3-D). For these cases, a simple method which allows us to retrieve the 3-D regional impedance tensor (except the static shift) is presented. The method proposed uses the Groom & Bailey decomposition of the distortion matrix for the short periods. Three examples are presented: two using synthetic data and one employing real data. These examples show the effect of the galvanic distortion over a regional 2-D/3-D model and the retrieval of the regional transfer functions from the distorted ones.     

Magnetotelluric interpretation of crustal and mantle structure in the Grenville Province

Summary Accurate determinations of depths and conductivities of electrical structures in shield regions are often difficult because of the inhomogeneity of the uppermost crust. A magnetotelluric (MT) station (BAT) in the Grenville Province of the Precambrian Shield in eastern Canada has been in operation since 1975 for time-dependency studies of electrical resistivity changes related to earthquakes. The MT response of the station displays low skew with small to moderate anisotropy. One-dimensional inversion of the apparent resistivity and phase reveals two well-defined conductors in the crust, one at 10 km and the second at the base of the crust. The latter has a resistivity less than 50 Ω m. These results are substantiated by three additional MT stations located up to 40 km distant.
Data from other new MT stations and from stations previously published in the literature are compared with two-dimensional computer model results and with the three-dimensional analogue scale model results of Dosso et al. While additional data for periods less than 100 s would be desirable the results from a number of the MT stations are not inconsistent with a widespread occurrence of a conducting zone at the base of the crust in the Grenville. The inversion analysis also indicates the existence of a conductor at some depth greater than 100 km with a resistivity less than 30 Ω m. This may coincide with a seismic low-velocity zone observed in the mantle under the Canadian Shield.     

An algebraic formulation of geophysical inverse problems

Many geophysical inverse problems derive from governing partial differential equations with unknown coefficients. Alternatively, inverse problems often arise from integral equations associated with a Green's function solution to a governing differential equation. In their discrete form such equations reduce to systems of polynomial equations, known as algebraic equations. Using techniques from computational algebra one can address questions of the existence of solutions to such equations as well as the uniqueness of the solutions. The techniques are enumerative and exhaustive, requiring a finite number of computer operations. For example, calculating a bound to the total number of solutions reduces to computing the dimension of a linear vector space. The solution set itself may be constructed through the solution of an eigenvalue problem. The techniques are applied to a set of synthetic magnetotelluric values generated by conductivity variations within a layer. We find that the estimation of the conductivity and the electric field in the subsurface, based upon single-frequency magnetotelluric field values, is equivalent to a linear inverse problem. The techniques are also illustrated by an application to a magnetotelluric data set gathered at Battle Mountain, Nevada. Surface observations of the electric ( E _y ) and magnetic ( H _x ) fields are used to construct a model of subsurface electrical structure. Using techniques for algebraic equations it is shown that solutions exist, and that the set of solutions is finite. The total number of solutions is bounded above at 134 217 728. A numerical solution of the algebraic equations generates a conductivity structure in accordance with the current geological model for the area.     

The Backus–Gilbert theory for piecewise continuous structures with variable discontinuity levels and its application to the magnetotelluric inverse problem

Summary. The Backus–Gilbert theory is extended to the case when the models are piecewise continuous vector functions of depth with variable discontinuity locations. In addition, some of the layers may be represented by linear combinations of known functions. For such layers only a finite number of discrete parameters is to be determined. The iterative process for obtaining a model satisfying the data is convergent, the numerical procedure by which the iterations are performed being equivalent to the method of spectral decomposition for continuous structures. The method of obtaining the Fréchet kernels by using the first perturbation of the differential system satisfied by the corresponding functionals is shown to be valid.
The theory is applied to the magnetotelluric problem, Fréchet kernels being calculated for isotropic and non-isotropic structures.
A few numerical examples are described.     

A search for the ratio between gravity variation and vertical displacement due to a surface load

A data space approach to magnetotelluric (MT) inversion reduces the size of the system of equations that must be solved from M × M , as required for a model space approach, to only N × N , where M is the number of model parameter and N is the number of data. This reduction makes 3-D MT inversion on a personal computer possible for modest values of M and N . However, the need to store the N × M sensitivity matrix J remains a serious limitation. Here, we consider application of conjugate gradient (CG) methods to solve the system of data space Gauss–Newton equations. With this approach J is not explicitly formed and stored, but instead the product of J with an arbitrary vector is computed by solving one forward problem. As a test of this data space conjugate gradient (DCG) algorithm, we consider the 2-D MT inverse problem. Computational efficiency is assessed and compared to the data space Occam's (DASOCC) inversion by counting the number of forward modelling calls. Experiments with synthetic data show that although DCG requires significantly less memory, it generally requires more forward problem solutions than a scheme such as DASOCC, which is based on a full computation of J .     

Generalized thin sheet analysis in magnetotellurics: an extension of Price's analysis

Summary. Price's thin sheet analysis for electromagnetic fields has been extended in order to model the effects of crustal resistivity and conductivity variations on magnetotelluric fields. These extensions allow for a general layered medium below the crust and also account for the vertical resistance of the crust as well as its horizontal conductance. An important parameter emerges from the analysis which determines the distance it takes for the crustal current levels to readjust to changes in the crustal conductance. This adjustment distance is given by the square root of the conductivity thickness product multiplied by the resistivity thickness product. Approximate analytical solutions were developed for two-dimensional geometries in order to demonstrate these effects as well as the modifications produced by finite source wavelengths.     

Magnetotelluric response of a uniformly stratified earth containing a magnetized layer

Summary The magnetotelluric (MT) response is studied of a uniformly stratified earth which contains a magnetized layer. The impedance as a function of the layer parameters (resistivity, ρ permeability, μ and thickness h ) is discussed. The MT response from a layer (μ, ρ, h ) is equivalent to that from a layer (μ/μ_r=μ₀, μ_rρ, μ_r h ) where μ_r is the relative permeability of the layer. Thus the effect of a magnetized layer is to make it apppear μ_r times more resistive and μ_r times thicker than an unmagnetized equivalent layer. Master curves of apparent resistivity and phase are computed for three-layer models with varying permeability associated with varying resistivity in each layer. An example of MT field data is presented in which the most reasonable interpretation is that a magnetized layer exists beneath the observatory site.     

Current channelling and three-dimensional effects detected from magnetotelluric data from a sedimentary basin in Sierras Pampeanas, Argentina

Aquifer-bearing intermontane sedimentary basins of the Sierras Pampeanas in the northwest of Argentina are in general very deep and narrow and contain economically important deposits of Tertiary sediments. This paper presents the results of a study to characterize the sedimentary basin bounded to the west by Sierra de Famatina and to the east by Sierra de Velasco, where an electromagnetic sensing technique, the magnetotelluric (MT) method, was applied. 12 MT sites were deployed along a 30  km E–W transect. Some of the data collected were used to derive a 2-D resistivity model of the basin. The model shows a subsurface trough with a thick (approximately 8  km) sedimentary sequence above it. Anomalous behaviour of the E–W electric-field component ( E _y ) was detected in the period range 1–100  s, where the amplitude of this component was below the instrumental noise level. The cause of this anomaly is not known, but it might be due to the presence of an embedded conducting body between 8 and 10  km, which would give rise to N–S current channelling.     

The statistical distribution of magnetotelluric apparent resistivity and phase

The marginal distributions for the magnetotelluric (MT) magnitude squared response function (and hence apparent resistivity) and phase are derived from the bivariate complex normal distribution that describes the distribution of response function estimates when the Gauss–Markov theorem is satisfied and the regression random errors are normally distributed. The distribution of the magnitude squared response function is shown to be non-central chi-squared with 2 degrees of freedom, with the non-centrality parameter given by the squared magnitude of the true MT response. The standard estimate for the magnitude squared response function is biased, with the bias proportional to the variance and hence important when the uncertainty is large. The distribution reduces to the exponential when the expected value of the MT response function is zero. The distribution for the phase is also obtained in closed form. It reduces to the uniform distribution when the squared magnitude of the true MT response function is zero or its variance is very large. The phase distribution is symmetric and becomes increasingly concentrated as the variance decreases, although it is shorter-tailed than the Gaussian. The standard estimate for phase is unbiased. Confidence limits are derived from the distributions for magnitude squared response function and phase. Using a data set taken from the 2003 Kaapvaal transect, it is shown that the bias in the apparent resistivity is small and that confidence intervals obtained using the non-parametric delta method are very close to the true values obtained from the distributions. Thus, it appears that the computationally simple delta approximation provides accurate estimates for the confidence intervals, provided that the MT response function is obtained using an estimator that bounds the influence of extreme data.     

Three-dimensional magnetotelluric inversion using non-linear conjugate gradients

We have formulated a 3-D inverse solution for the magnetotelluric (MT) problem using the non-linear conjugate gradient method. Finite difference methods are used to compute predicted data efficiently and objective functional gradients. Only six forward modelling applications per frequency are typically required to produce the model update at each iteration. This efficiency is achieved by incorporating a simple line search procedure that calls for a sufficient reduction in the objective functional, instead of an exact determination of its minimum along a given descent direction. Additional efficiencies in the scheme are sought by incorporating preconditioning to accelerate solution convergence. Even with these efficiencies, the solution's realism and complexity are still limited by the speed and memory of serial processors. To overcome this barrier, the scheme has been implemented on a parallel computing platform where tens to thousands of processors operate on the problem simultaneously. The inversion scheme is tested by inverting data produced with a forward modelling code algorithmically different from that employed in the inversion algorithm. This check provides independent verification of the scheme since the two forward modelling algorithms are prone to different types of numerical error.     

Very high electrical conductivity beneath the Münchberg Gneiss area in Southern Germany: implications for horizontal transport along shear planes

New magnetotelluric data from the Münchberg Gneiss complex in Southern Germany reveal a zone of extremely high electrical conductivity. 1-D modelling of the data is justified in the period range 0.01 to 10  s. At least three layers are required to explain the steepness of the apparent resistivity curves, and the best-fitting models comprise four layers with successively higher conductivities. The layers of highest conductivity at depths between 2.2 and 3.6  km correlate with pronounced bands of high seismic reflectivity (profile DEKORP 85-4N). The Münchberg complex is today widely recognized as a tectonic klippe, consisting of rocks whose metamorphic and stratigraphic order is inverted rather than overturned. The material was transported into its present position by predominantly horizontal tectonic forces along shear zones. We interpret the high conductivity and high reflectivity as remnants of this transport process.     

Natural electromagnetism in the Rhine Graben

Summary. Together with experiments by differential geomagnetic soundings, magnetotelluric soundings have been performed in the Rhine Graben. The results of the former have been presented and discussed before. We try to show that it is not necessary to call upon the notion of induction in surrounding areas to justify the characteristics of the observed anomalous magnetic fields. Theoretical calculations of these fields on structures defined by the interpretation of magnetotelluric sounds, or by geological and other geophysical data, agree very well with experimental data. We conclude that magnetotelluric experiments and interpretations are valid as the Rhine Graben is a well-known region allowing us to verify our interpretation.