起伏地形下可控源音频大地电磁三维数值模拟

Three-dimensional Modeling of Controlled Source Audio Magnetotelluric Data with Topography

起伏地形对可控源音频大地电磁(CSAMT)响应具有强烈的影响,因此在CSAMT数据处理解释时需要考虑地形。同时,实际的地下地质情况和地表的地形情况通常比较复杂,地质结构和地形大部分情况下都是三维的。在水平地表三维有限差分CSAMT数值模拟算法的基础上,推导了利用地下交错网格采样点处的总磁场计算起伏地形下空气-地下介质分界面处的总电场和总磁场的表达式,从而实现了起伏地形下三维CSAMT数值模拟算法。在算法实现过程中,采用伪δ函数代替麦克斯韦方程中的场源项和直接计算总场的策略,避免了原有的将总场分离成背景场和二次场的策略在复杂地质条件下难以选择合适背景电阻率的问题。为了直接模拟总场,起伏地形下三维CSAMT数值模拟算法给出了新的三维正演方程的边界条件。将模拟水平地表三维异常体和三维山峰地形两个理论模型得到的响应结果与前人算法的计算结果进行对比,验证了所实现算法的正确性和有效性。

The topography has a strong effect on the controlled source audio magnetotelluric（ CSAMT） data,therefore,the topography should be considered when interpreting the CSAMT data. The real subsurface geological structure and the topography of the surface are usually more complex and are three-dimensional spaces in most cases. Based on the three-dimensional finite-difference CSAMT modeling algorithm for flat surface,this paper presents a new method to calculate the total electric field at the air-earth interface with topography from the total magnetic fields at subsurface staggered sampling points,modeling the three-dimensional CSAMT responses on topography. In the new algorithm,the pseudo-delta function is used to replace the source to directlycalculate the total field,avoiding the limitation of selecting the appropriate background resistivity structure under complex geological structure conditions when the total field is separated into the background field and the secondary field. In order to simulate the total field directly,this study used the new boundary condition of the three-dimensional forward equation in the three-dimensional CSAMT modeling algorithm with topography. The correctness and validity of the algorithm are verified by comparing the response results obtained from the two models（ the flat surface model with 3 D anomaly and the three-dimensional trapezoidal-hill model） with the results of the previous algorithms.