The Boundary Element Method In Geophysics

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 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 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.

The Boundary Element Method in Geophysical Survey

This volume is devoted to the application of the integral equations method (IEM) and boundary elements method (BEM) to problems involving the sounding of geological media using direct current (DC). Adaptive mesh generation algorithms and numerical methods for solving a system of integral equations are discussed. Integral equations for the media, which contains piecewise linear contact boundaries, immersed local inclusions, and subsurface relief, are derived and solved numerically. Both 2.5D and 3D models with ground surface relief are considered. For 2D conductivity distributions, the influence of the relief on the interpretation of results is shown. Search solutions of the direct problem with ground surface relief are compared using the appropriate interpretation of results based on different inversion programs.

Boundary Element Techniques in Geomechanics