Improved Integral Equation Method for Rapid 3-D Forward Modeling of Magnetotelluric

Abstract

Computational cost tremendously restricts the wide application of conventional integral equation (IE) method in large-scale magnetotelluric (MT) modeling. A couple of obstacles limit the developments of traditional MT modeling based on the IE method. They are: O (N2) space complexity of memory requirements for storing coefficients of dense matrix; singularity of Dyadic Green’s function; low efficiency of using digital filtering, such as Hankel transform, to calculate the Bessel function integral within the dyadic Green’s function, as well as inefficiency of accumulative calculation of 3-D discrete convolution. To solve these problems, we use an analytical formula instead of the Hankel transform to compute the integral of the Bessel function and replace a block cell by a spherical cell with the same volume to integrate through the singularity. Because the coefficient matrices are symmetric and antisymmetric three-level block-Toeplitz (BT) and Toeplitz + Hankel matrices, only non-redundant entities of the matrix are computed and stored. Afterwards, 3-D fast Fourier transform (FFT) is used to expedite matrix–vector multiplication at each successive iteration when using the contraction iterative method to solve the system of equations, which decreases memory and time consumption sharply compared with the traditional IE method.