三维地下埋藏点电流源有限差分正演计算

研究了地下埋藏点电流源三维地电介质的有限差分数值方法。首先讨论了三维埋藏直流点电源场方程及边界条件；然后讨论了微分方程的离散化，对于数值求解时电导率应具有一定连续性的要求，采用斯托克斯定理将体积分化为面积分的方法来消除，求解方程利用有限差分技术构成。为了提高计算精度和计算速度以及避免由源奇异性引起的差分计算复杂性，计算时将电位分成二次异常电位和背景电位2部分。在背景场计算中，对地下均匀半空间和水平均匀层状模型的背景场对二次异常场的影响进行讨论。结果发现，将地电模型中各层的电导率和异常体电导率取加权平均，以此作为均匀半空间模型的电导率进行背景场计算时，二次异常场计算结果较差；利用水平层状模型计算背景场，以此为基础计算三维地电场，二次异常场的计算结果有明显的改善。研究表明，利用有限差分数值方法进行复杂地电模型的正演计算，计算速度快，计算结果精度较高。

A new limited difference forwardmethod on 3-D geo-electricalmedium with underground embedding point current source.

In this paper, we transform volume integral into surface integral to remove the requirement of deriving for conductance using Green and Stokes formula, construct the divided equation by limited difference technique. In order to improve the calculating precision and speed avoiding source singularity, we calculate voltage in two parts: abnormity and background. Under calculating background, we research the uniformity half space and multi-layers models, discuss the effect on studied background results to abnormity and overlapping field. The background field is calculated with horizontal layer model, based on which 3-D field is found. The result of quadratic field has more improvement than that of surface symmetrical half space model. The study shows that limited difference forward method has higher precision and computing speed in Geo-electrical forward modeling.