球坐标系下三维大地电磁正演研究

大地电磁正演理论研究热点一直以来主要集中在如何提高计算效率和精度，但在剖面足够长、探测深度足够大的情况下，传统的笛卡尔坐标系数值模拟方式难以准确拟合地球曲率形态.本文研究了基于球坐标系的三维大地电磁正演，推导了交错网格有限差分三维正演公式，与一维解析解和三维标准模型测试对比，验证了正演算法的正确性.通过理论模型计算，对比分析球坐标和笛卡尔坐标系正演结果表明：球坐标系模拟更合理，避免了传统笛卡尔坐标拉伸投影所引入的误差，可代替目前的笛卡尔坐标模拟方法.基于球坐标和笛卡尔坐标系的三维大地电磁正演响应值随着频率变低差异越明显.球坐标和笛卡尔坐标计算结果差异度与频率、模型结构和电阻率有关.本文模型计算结果在数万秒周期处已出现接近10%的差异，对于较大尺度的长周期大地电磁，地球曲率的影响不能忽略.

Three-dimensional forward modeling of the magnetotelluric method in spherical coordinates

Theoretical research on forward modeling of the magnetotelluric (MT) method has focused on how to improve the calculation efficiency and precision. When the profile is long enough and detection depth is sufficiently deep, it is difficult to fit the curvature of the earth accurately by numerical simulation in a Cartesian coordinate system. This paper studies three-dimensional MT forward modeling with a staggered grid based in a spherical coordinate system. We deduce the formula for staggered-grid finite difference three-dimensional forward modeling and compare it with of one-dimensional analytical solution and the DTM1 three-dimensional modeling to verify correctness of the algorithm. Calculation on a theoretical model shows that the modeling in the spherical coordinates is more reasonable, which can avoid errors caused by the conventional Cartesian coordinate system, so can replace the Cartesian coordinates modeling method. The differences of 3D MT forward modeling responses in theses two coordinate systems are related with frequency, model structure and resistivity. For example, such differences become more notable with lowering frequency. They are close to 10% at the period of tens of thousands of seconds. It implies that the effect of earth curvature on large-scale long-period MT cannot be ignored, so MT forward modeling on large scales should be conducted in spherical coordinates.