2.5维直流电法正演中Fourier逆变换离散波数的最优化选取

his article improves the optimization method in terms of both the optimization model and computational method for computing the discrete wavenumbers of inverse Fourier transform, which arise in the 2.5-dimensional direct current resistivity modeling with a point current source. The article is arranged as follows. Firstly, with an analytical solution of electric potential produced by a point source in semi-infinite homogeneous medium, an improved nonlinear optimization problem for computing these wavenumbers based on the method of least squares is presented, followed by its resolution using the differential evolution (DE) algorithm. This DE algorithm does not require imposing initial values on the wavenumbers, which avoids the cumbersome computation when evaluating the matrices from partial derivatives. Additionally, the method enables us to easily determine the discrete wavenumbers and the corresponding weighting coefficients simultaneously. Finally, the computational accuracy against the impact of the number of electrode spacings included in the simulation is discussed. For a number of typical geoelectric models with analytical solutions, the method is justified through comparing the computed results to those in the literature. It is shown that increasing the number of electrode spacings not only dramatically reduces the error of the apparent resistivity near the point source, but also ensures the computational accuracy for models with a large conductivity contrast. It is also noted that the discrete wavenumbers obtained from the proposed method have a higher accuracy and wider range of applications compared with existing ones.