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在物探中常常遇到这样一类数学物理问题:给定场的边界条件,求解场域内的场值。例如,大家熟知的磁场向上延拓,就是给定地形上的磁场(边界条件),求解地形上部的磁场值。电阻率法的理论计算也属于这类问题,给定地下电性分布和电源分布,求解电场。当场域的几何特征十分简单(如平面),有可能求得精确的解析解,然而在物探中经常遇到复杂的边界条件(如地形起伏)、复杂的电性分布,精确的解析解根本无法求出,这时必须应用近似的数值方法。
In geophysical exploration, we often encounter such a kind of mathematical physics problem: given the field boundary conditions, solve the field values in the field. For example, the well-known magnetic field extends upward, that is, given the terrain of the magnetic field (boundary conditions), the top of the terrain to solve the magnetic field values. The theoretical calculation of the resistivity method also belongs to this kind of problem. Given the distribution of the subsurface electrical power and the power distribution, the electric field is solved. The geometric characteristics of the field are very simple (such as plane), it is possible to obtain accurate analytical solution, but in geophysical exploration are often encountered complex boundary conditions (such as relief), the complexity of the electrical distribution, the exact analytical solution simply can not Find, then you must apply the approximate numerical method.