Improved frequency-domain elastic wave modeling using weighted-averaging difference operators

Abstract

We develop a new finite-difference scheme that reduces the number of grid points per wavelength required in frequency-domain elastic modeling. Our approach computes weighted averages of the spatial second-order derivative and the mass acceleration terms using a 25-point computational stencil. By determining the weighting coefficients to minimize numerical dispersion and numerical anisotropy, we reduce the number of grid points to 3.3 per shear wavelength, with a resulting error in velocities smaller than 1%, Our choice of grid points reduces the computer memory needed to store the complex impedance matrix to 4% of that for a conventional second-order scheme and to 54% of that for a combined second-order scheme. The 25-point weighted averaging scheme of this paper makes it possible to accurately simulate realistic models. Numerical examples show that this technique can achieve the same accurate solutions with fewer grid points than those from previous frequency-domain second-order schemes. Our technique can be extended directly to 3-D elastic modeling; the computational efficiency will be even greater than that realized for 2-D models.