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基于有限差分法的射频大地电磁二维正演模拟
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Abstract:
在大多数二维地电模型中，考虑到射频大地电磁响应不存在解析解，本文建立了均匀网格有限差分正演模拟算法。首先，从电磁场满足的变系数亥姆霍兹方程边值问题出发，导出了有限差分法控制方程的离散表达式，并对边界条件近似处理后求解线性方程组得到射频大地电磁场数值解。其次，对均匀半空间模型进行模拟计算，且与解析法计算结果对比，验证了射频大地电磁有限差分正演算法的正确性和稳定性。最后，模拟计算了射频大地电磁典型二维地电模型的响应，总结了异常响应规律，为实测数据的定性解释提供指导。
In the most two-dimensional geo-electric model, there are no analytical solutions for radio-mag- netotelluric responses, so the uniform-meshes finite difference algorithm was developed for numerical results in this paper. Firstly, from the boundary value problem of variable coefficient Helmholtz equation for electric field and magnetic field, the discrete expressions of governing equation are derived from finite difference method. The numerical solutions of electric field and magnetic field are calculated after the approximate treatment on the boundary conditions. Se-condly, through the simulation of homogeneous half-space model and compared with the analytical results, the correctness and stability of the finite difference forward algorithm are verified. Lastly, by the numerical simulation for a two-dimensional model, radio-magnetotelluric responses were summarized, which can provide for qualitative interpretation of field data.
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