基于非均一场源的球坐标大地电磁模拟方法

Spherical magnetotelluric modeling based on non-uniform source

大地电磁测深理论与数据处理解释均假定平面电磁波垂直入射地下空间,但随着研究尺度的逐渐扩大,使得因地球弧度产生的影响难以忽略.此时,传统笛卡尔坐标体系及平面波场源不再适用于大尺度的大地电磁数据正反演解释.本文提出并实现了一种基于球坐标系的大地电磁交错网格有限差分三维正演算法,并对电场进行极向-环向分解,结合球谐函数和贝塞尔函数构建了可取代平面波的场源模型.首先利用经纬度信息构建三维地电模型,将场源设置于模型空间正上方,然后通过直接求解球坐标系下麦克斯韦方程来获得大地电磁响应.在此基础上,本文设计了球坐标下具有不同分辨率的多个三维地电模型,阐述了由球体模型到笛卡尔模型的转换方法,详细对比了两种坐标体系在计算效率、所求得的电场和视电阻率方面的差异.结果表明二者差异度主要与电性横向分布和地图投影方法有关,与周期并不存在明显的单调递增关系.

Traditionally,magnetotellurics(MT)rests on an assumption that plane wave is incident vertically into flat Earth.With more and more magnetotellurics data coming in and the expansion of research area,Cartesian approximation and plane wave assumption may no longer be suitable for the large-scale modeling due to the inevitable Earth curve.We have developed a kind of magnetotellurics forwarding code in spherical coordinates based on staggered grid finite difference method.In addition,the electric fields are represented by poloidal-toroidal decomposition,then solved based on spherical harmonic and Bessel function to construct the source model that can be used to replace plane wave.The spherical model is built directly through geographic information like latitude and longitude,and the forward response will be obtained by solving the Maxwell’s equations in terms of spherical format.Electric field components defined on curving cell edges are the primary EM field that is computed iteratively utilizing a quasi-minimum residual scheme,with a divergence correction applied periodically.Taking into account the versatility and convenience,this spherical forward code is developed on the open source ModEM which provides a ready framework for rapid implementation of new application or algorithms.Large scale three-dimensional conductive models with different resolution are built and transformed to their corresponding Cartesian models by Lambert Conformal Conic map projection which can maintain the shape of original spherical model.We compare their forward response such as electric fields and apparent resistivity computed from spherical and Cartesian coordinates respectively.Under the combined effect of conductivity distribution and the unavoidable deformation,electric fields and apparent resistivities show stronger difference at the place where conductivity contrasts.All the forward calculations are implemented on the blade server in the form of frequency parallel scheme,spherical model usually takes twice time than Cartesian.According to real bathometry data,we make the China continent and its adjacent sea model to research the forward difference between spherical and Cartesian coordinates.