V. I. Dmitriev

Models and Methods of Magnetotellurics

Magnetotelluric methods are finding increasing applications for imaging electrically conductive structures below the Earths surface in both industrial and academic research. In Models and Methods of Magnetotellurics, the authors provide a systematic approach to understanding the modern theory of ill-posed problems which is essential to making confident meaningful interpretation of magnetotelluric and magnetovariational soundings. The interpretation is conducted out in an interactive way, including the hypotheses tests and successive partial inversions with priority of the tippers, magnetic tensors and impedance-phases, which keep out the destructive static effects of near-surface inhomogeneities. The efficiency of the interpretation is exemplified by new geoelectric models of the Baikal rift /one and the Cascadian subduction /one.

Quasi-analytical approximations and series in electromagnetic modeling

The quasi‐linear approximation for electromagnetic forward modeling is based on the assumption that the anomalous electrical field within an inhomogeneous domain is linearly proportional to the background (normal) field through an electrical reflectivity tensor λ⁁. In the original formulation of the quasi‐linear approximation, λ⁁ was determined by solving a minimization problem based on an integral equation for the scattering currents. This approach is much less time‐consuming than the full integral equation method; however, it still requires solution of the corresponding system of linear equations. In this paper, we present a new approach to the approximate solution of the integral equation using λ⁁ through construction of quasi‐analytical expressions for the anomalous electromagnetic field for 3-D and 2-D models. Quasi‐analytical solutions reduce dramatically the computational effort related to forward electromagnetic modeling of inhomogeneous geoelectrical structures. In the last sections of this paper...

The fundamental model of magnetotelluric sounding

It is widely believed that the Tikhonov-Cagniard model can be applied in the magnetotelluric method of exploration geophysics if the horizontal field changes are sufficiently slow. Actually, this is overly restrictive and may give rise to unjustified doubts about the validity of the Tikhonov-Cagniard model. This paper shows that the condition determining the applicability of the model is the linearity of the horizontal field changes, rather than the slowness of these changes. This considerably extends the sphere of practical applications of the Tikhonov-Cagniard model.

Magnetotellurics in the context of the theory of ill-posed problems

This volume serves as an introduction to modern magnetotellurics originating with the pioneering work of Tikhonov and Cagniard. It presents a comprehensive summary of theoretical and methodological aspects of magnetotellurics. It provides a bridge between textbooks on electrical prospecting and numerous papers on magnetotelluric methods scattered among various geophysical journals and collections. The book has been written in the terms of the theory of ill-posed problems and contains a special chapter encouraging readers to master the elements of this theory that defines the philosophy of the physical experiment. The book thus offers the connected and consistent account of the principles of magnetotellurics from that single viewpoint. The book also brings together developments from many sources and involves some little-known results developed in Russia in Tikhonovs magnetotellurics school. Of particular interest are concluding chapters of the book that demonstrate the potential of magnetotellurics in oil and gas surveys, including discovery of the Urengoy gas field in Western Siberia, one of the largest gas fields in the world. This potential also is revealed in studies of the earths crust and upper mantle.

Integral Electric Current Method in 3-D Electromagnetic Modeling for Large Conductivity Contrast

We introduce a new approach to 3-D electromagnetic (EM) modeling for models with large conductivity contrast. It is based on the equations for integral current within the cells of the discretization grid, instead of the electric field or electric current themselves, which are used in the conventional integral-equation method. We obtain these integral currents by integrating the current density over each cell. The integral currents can be found accurately for the bodies with any conductivity. As a result, the method can be applied, in principle, for the models with high-conductivity contrast. At the same time, knowing the integral currents inside the anomalous domain allows us to compute the EM field components in the receivers using the standard integral representations of the Maxwells equations. We call this technique an integral-electric-current method. The method is carefully tested by comparison with an analytical solution for a model of a sphere with large conductivity embedded in the homogenous whole space

TENSOR GREEN FUNCTION FOR THE SYSTEM OF MAXWELL'S EQUATIONS IN A LAYERED MEDIUM

A general method is considered for the construction of the tensor Green function for Maxwells equations in a layered medium. An efficient algorithm for the evaluation of the tensor Green function is proposed. The properties of various components of the Green tensor are investigated.

Solving an Integral Equation of the First Kind by Spline Approximation

A method based on a special minimum-derivative spline is proposed for solving a Fredholm integral equation of the first kind.

Joint three-dimensional inversion of magnetotelluric and magnetovariational data

The problem of quantitative three-dimensional interpretation of the magnetotelluric (MT) data ranks among the most difficult problems in electromagnetic (EM) geophysics. Our paper presents a new rigorous numerical method for MT inversion, based on the integral equations technique. An important feature of the proposed method is the calculation of the Frechet derivative with the aid of a quasi-analytical approximation with an inhomogeneous background. This approach simplifies the algorithm of inversion and requires only a single forward modeling on each iteration. We have also developed a method for a joint inversion of MT and magnetovariational (MV) data. We show in the present paper that the joint inversion of MT impedances and the Wiese-Parkinson vectors can automatically allow for the static shift in the observed data, which is caused by the geoelectric inhomogeneities contained in the near-surface layer.

Anisotropy of Induced Polarization In the Context of the Generalized Effective-medium Theory

In this paper, we study the anisotropy effect in IP data in the context of the generalized effective-medium theory of induced polarization (GEMTIP). The effective-medium conductivity defined by the GEMTIP model, in a general case, is represented by a tensor function. This tensorial property of the effective-medium conductivity provides a new insight on the anisotropy phenomenon in the IP effect. As an example, we consider a multiphase composite polarized model of a rock formation with ellipsoidal inclusions. We demonstrate that the effective conductivity of this formation may be anisotropic, even if the host rock and all the grains are electrically isotropic.

Integral Characteristic Method in the Inverse Problem of Optical Coating Design

The article describes and analyzes an optical coating synthesis algorithm that uses the integral refraction coefficient method.