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本文对瞬变电磁法2.5维有限元正演进行了研究.从频率域麦克斯韦方程组出发,经过傅里叶变换推导出了走向y方向频率域电磁场响应的变分问题,然后运用频率域和时间域的转换公式求解出时间域瞬变电磁场的解.在求解频率域电磁场响应时为提高精度采用了基于二次插值的高阶有限元的算法,即单元网格插值为二次函数,同时推导出了经有限元离散后的泛函问题;在求解时间域电磁响应采用了正余弦变换的数字滤波算法.通过基本模型的正演,验证了算法的可行性.同时,也对比了基于G-S变换的线性有限元算法的数值结果,结果表明,本文采用的算法精度更高,层状模型最大延迟采样时间提高到了100 ms以上.
In this paper, the 2.5-D finite element forward modeling of transient electromagnetic method is studied.From Maxwell’s equations of frequency domain, the variational problem of the electromagnetic field response to the y-direction frequency domain is deduced by Fourier transform, and then the frequency domain and time Domain solution to solve the transient electromagnetic field in the time domain solution.In order to improve the accuracy of the electromagnetic field response to the frequency domain, a quadratic interpolation based high-order finite element algorithm is used, that is, the element grid interpolation is a quadratic function, After the discretization of the finite element, the functional problem is solved. The digital filtering algorithm using the sine cosine transform in solving the time domain electromagnetic field is applied. The feasibility of the algorithm is verified by the forward modeling of the basic model. Meanwhile, The numerical results of the linear finite element method show that the proposed algorithm is more accurate and the maximum delay sampling time of the layered model is increased to more than 100 ms.