Numerical Modeling Of Magnetotelluric Fields In Two-dimensional Anisotropic Media

Magnetotelluric sounding (MT) has been widely used since it was introduced by the Soviet Union scholar A. N. Tikhonov and the French scholar Cagniard during1950s. Owing to its own advantages, such as using natural fields, shielding of high resistance and the prospecting depth of several hundreds kilometres, it is widely used in the earth's crust and upper mantle structure research, earthquake prediction, volcanic deep tectonic research, energy and resource exploration, hydrology, engineering and environment, etc. Magnetotelluric sounding is the most important geophysical method to study the earth's crust and upper mantle electrical structure.Over half a century passed, by the means of magnetotelluric method, we have made remarkable achievements in the research of electrical structure in the earth interior at home and abroad, however, most of the research was based on electrical isotropic theory. In general, electrical anisotropy phenomenon also exist in the earth interior, this viewpoint has been accepted by most scholars in the geophysics field. The electrical anisotropy in the crust and the upper mantle is the main link between geoelectric model, underlying structure, and tectonic model. Electrical anisotropy phenomenon is formed by all sorts of causes(it is mainly composed by the earth's tectonic stress field, the earth rupture zone, rock fracture, pore water, geologic sedimentary and so on), it would be beneficial to build electrical model with the practical situation through the systematic and detailed research of the basic theory of electrical anisotropy, as a result, to establish a theoretical basis for analysing and interpreting the electrical structure in the earth interior. As early as in1960s, the one-dimensional electrical anisotropy forward problem had been studied at abroad, while extensive research had been done on three-dimensional electrical anisotropy forward problem till now. Chinese scholars began to study the basic theory of electrical anisotropy from1980s, although they have get some achievements, but the articles systematic and detailed research of the basic theory of electrical anisotropy are less. According to the advantages of electromagnetic method in the research of electrical structures and the research about the basic theory of electrical anisotropy are insufficiency in China, this article is a systematic and detailed research of one-dimensional and two-dimensional magnetotelluric forward problem, as well as one-dimensional magnetotelluric inversion problem for anisotropic layered media on the basis of the electromagnetic method.Firstly, based on the Maxwell's equations, bringing in the conductivity tensor, the analytic expression of one-dimensional electric anisotropic problem is derived, next plenty of one-dimensional electrical anisotropic models are analyzed by the one-dimensional forward procedure which has been programmed, which builds the foundation for the next step of inversion research. Subsequently comes to the research of one-dimensional electrical anisotropic inverse problem, we have made some modifications to the Marquardt's inversion theory according to the characteristics of magnetotelluric sounding curves, the requirement of joint inversion and the nature of electric anisotropic theory, and a new inversion algorithm has been presented on the basis of the Marquardt's inversion theory. Then, the correctness of the mentioned inversion theory is verified by the canned program, Additionally, the processing and interpretation of the measured data of MT in northwest of china not only indicates the practicability of the theory, but also provides a new method for the future research of deep electrical structures. Secondly, based on the Maxwell's equations as well, bringingin the conductivity tensor, a group of second-order differential equations about Ex and Hx are obtained by the features of two-dimensional electrical anisotropic structure, we can use the finite-different method to solve the differential equations and obtain the approximate value for Ex and Hx, the other values of the field components calculated by Ex and Hx; Subsequently, refined bandwidth is modified as variable bandwidth in the finite-difference coefficient matrix by the introduction of topography, which requires a slight modification to the Gaussian elimination, and similarly, we get the values of all field components in the usage of finite-difference equation. We conduct the forward calculation for plenty of general and particular two-dimensional electrical anisotropic models (two circumstances including topography or not) by the programmed two-dimensional forward procedure, studying its influences on the observing magnetotelluric electromagnetic field and recognizing the characteristics of electromagnetic propagation in particular geological settings, as a result, laying the foundation for the interpretation of magnetotelluric data in the future. At last, we have brought in the electrical anisotropic theory into the interpreting of magnetotelluric field data based on this article's achievement, by means of one-dimensional inversion interpretation and two-dimensional forward fitting interpretation of magnetotelluric field data measured in different places, on the one hand, demonstrate that the electrical anisotropic phenomena is generally in the Earth's crust and upper mantle, on the other hand, proving the correctness of the mentioned theory and the practicability of the procedure. Additionally, the proposed theory and procedure are not only capable of providing theoretical foundation and technical direction for interpretation the electrical anisotropy phenomenon in magnetotelluric field data, but also providing a new method for the research of Earth's electrical structures in the future.