The Research On 3-D Resistivity Forward And Inversion Algorithm On Undulate Topography

The research of geoelectric anomaly on the undulate topography has been a difficult problem in the field of electrical prospecting for a long time. On the one hand, it is the complicated problem itself, on the other hand, a few years ago, the development of science and technology was not advanced. For example, 3-D problem, if the speed and memory of computer do not develop quickly enough, it could not be solved even with the good theory. Nowadays, the development of computer has satisfied the needs about the speed and precision, and it also has provided favorable opportunity for making research on more complicated geophysical problems.The 2-D or 3-D on undulate topography, the problem of resistivity forward mpdeling and inverse imaging has been solved, through more than ten years by the experts home and abroad modeling on level topography and inversion problem also have developed quickly recent years. Such as the intergral equation method, finite-difference method, finite-element method, conjugate gradient algorithm etc. were studied by some scholars. Xu shizhe has solved the 3-D forward problem about the influce of the undulate topography on resistivity with boundary element method. In the first chapter, we introduce the significance and research methods about DC resistivity method, and the new develepment of forward modeling and inversion imaging etc. These research achievements of DC resistivity has established foundation for further studying 3-D resistivity forward modeling and inversion imaging on undulate topography.In the numerical modeling method, finite element method has a lot of advantages: the high precision, the canonical process of solving problem, automatically satisfying the internal boundary condition and adapting to all kinds of distribution of multi-substances etc. So we choose the finite element method, which is belongs to area numerical algorithm. It needs to divide into some cells in the whole area. But for a 3-D problem, the numbers of cells or nodes could be very large, and then we get a huge linear equation. If we solved it out, we can obtain the potential of all nodes.The undulate topography can cause the aberrance of steady electrical field. Stimulating the undulate topography should choose a kind of suitable element, which is tri-prism element. Given the altitude of any three points on the ground, we could fix on a small area. The tri-prism element has no limit on the altitude, that means the tri-prism element could stimulate any landforms. In...