Modeling the Magnetotelluric Field
In recent decades, the magnetotelluric (MT) method has been applied widely to geotectonics, oil and gas surveys, geothermal investigations, and earthquake prediction. Forward modeling for the 1-D MT problem is analytical. However, for the 2-D case one must use numerical methods. Presently, the most commonly used numerical method is the FEM (Silvester and Haslam, 1972; Reddy and Rakin, 1975; Xu and Zhao, 1985; Wannamaker et al., 1986, 1987; and Chouteau and Bouchard, 1988).
This chapter presents the application of the BEM to 2-D MT forward modeling. The BEM is most useful if there exists a single in-homogeneous body underground (Xu and Zhao, 1987) and, more importantly, for the study of 2-D and 3-D terrain effects on the MT field (Xu and Zhou, 1997; Xu et al., 1997). When the geological structure is complex, the FEM is obviously superior to the BEM
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The boundary element method (BEM) divides only the boundaries of the region under investigation into elements, so it diminishes the dimensionality of the problem, e.g., the 3D problem becomes a 2D problem, and the 2D problem becomes a 1D problem. This simplifies inputting the model into a computer and greatly reduces the number of algebraic equations. The advantage of this is even more evident for some 3D and infinite regional problems that often are encountered in geophysics. Originally published in China, this well-organized book is likely the most comprehensive work on the subject of solving applied geophysical problems. Basic mathematical principles are introduced in Chapter 1, followed by a general yet thorough discussion of the BEM in Chapter 2. Chapters 3 through 7 introduce the applications of BEM to solve problems of potential-field continuation and transformation, gravity and magnetic anomalies modeling, electric resistivity and induced polarization field modeling, magnetotelluric modeling, and various seismic modeling problems. Finally, in Chapter 8, a brief discussion is provided on how to incorporate the BEM and the finite-element method (FEM) together. In each chapter, detailed practical examples are given, and comparisons to both analytic and other numerical solutions are presented. This is an excellent book for numerically oriented geophysicists and for use as a textbook in numerical-analysis classes.