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首先使用最优化方法计算在点源二维傅氏反变换问题中使用的波数,得到了两组波数,分别包含7个和9个.在极距范围为0.1 m到1000 m时,这两组波数傅氏反变换的误差在0.1%以内.然后使用有限单元法,结合文章中给出的波数,分别模拟了均匀大地,K型和H型地电结构的测深曲线,结果与解析解对比,相对误差在3%以内,而使用前人学者提出的波数在极距大于200 m时出现与解析解分离的情况.最后使用不同波数计算两个二维模型,与三维有限元模拟结果对比,验证了该组波数的正确性.同时发现,使用7个波数与9个波数计算精度相似,建议使用7个波教进行模拟.
First, we use the optimization method to calculate the wavenumber used in the point-source 2D inverse Fourier Transform, and obtain two groups of wavenumbers, which respectively contain 7 and 9. When the polar distance is in the range of 0.1 m to 1000 m, The error of wavenumber inverse Fourier transform is less than 0.1%. Then, the finite element method and the wavenumber given in the article are used to simulate the sounding curve of the geoelectric structure with uniform earth, K-type and H-type respectively. The results are compared with the analytic solution , The relative error is less than 3%, while the wave numbers proposed by the predecessors are separated from the analytic solution when the polar distance is more than 200 m. Finally, two 2D models are calculated by using different wave numbers. Compared with the 3D finite element simulation results, The correctness of wave numbers in this group is verified.It is also found that using 7 wave numbers and 9 wave numbers have similar calculation accuracy, it is suggested to use 7 waves to simulate.