Modeling Resistivity and IP Methods
The resistivity method is a classical geophysical exploration technique that plays important roles in mineral exploration, hydrogeological and geological engineering exploration, and, to a lesser extent, earthquake prediction Analytical methods can be used to generate synthetic results for a few simple forward problems. However, for most forward problems we must use numerical methods. Alfano (1959). Dieter et al. (1969), Lee (1975), Snyder (1976), Oppliger (1984). Eskola et al. (1984), and Kostyanev (1994) use the integral equation method for modeling resistivity and IP responses. Spiegel et al. (1980) simulate the terrain effect on 2-D resistivity surveys using a conformai transformation The use of the finite-element method (FEM) has led to significant improvement in accuracy (Coggon 1971; Rijo 1977; Fox et al 1980 Pridmore et al 1981 Holcombe etal 1984) But for some “problems with complex boundaries such as the 1984 Xu et al., 1988)
This chapter presents the application of the BEM to calculate the electric potential-field due to a point source over 2-D and 3-D geometrical sections.
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The Boundary Element Method in Geophysics
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.