High-precision Fourier forward modeling of potential fields

Abstract

We analyzed the numerical forward methods in the Fourier domain for potential fields. Existing Fourier-domain forward methods applied the standard fast Fourier transform (FFT) algorithm to inverse transform a conjugate symmetrical spectrum into a real field. It had significant speed advantages over space-domain forward methods but suffered from problems including aliasing, imposed periodicity, and edge effect. Usually, grid expansion was needed to reduce these errors, which was equivalent to the numerical evaluation of the oscillatory Fourier integral using the trapezoidal rule with smaller steps. We tested a high-precision Fourier-domain forward method based on a combined use of shift-sampling technique and Gaussian quadrature theory. The trapezoidal rule applied by the standard FFT algorithm to evaluate the continuous Fourier transform was modified by introducing a shift parameter [Formula: see text]. By choosing optimum values of [Formula: see text] as Gaussian quadrature nodes, we developed a Gauss-FFT method for Fourier forward modeling of potential fields. No grid expansion was needed, the sources can be set near the boundary of the fields or even go beyond the boundary. The Gauss-FFT method converged to the space-domain solution much faster than the standard FFT method with grid expansion. Forward modeling results almost identical to space-domain ones can be obtained in less time. Numerical examples, of both simple and complex 2D and 3D source forward modeling, revealed the reliability and adaptability of the method.