2D acoustic wavefield simulation by improved stiffness and mass matrices of bilinear square element

Abstract

In the frequency domain, we optimize the entries of the element stiffness matrix computed on a square element with the purpose of approximating the 2D acoustic wave equation with the second spatial order. The optimized matrices are computed from the minimization of the normalized phase velocity as a function of propagation angle and the number of grid points per wavelength, leading to a remarkable reduction in the numerical error. The optimized number of 4.1 sample points in a wavelength, with a maximum error in velocities <0.3%, offering the simulation of large-scale realistic models. The superior performance of the optimized matrices to those from the lumped, consistent and eclectic matrices, is evident from the numerical examples presented, with consequent reduction not only in the numerical dispersion/anisotropy but also in an improved resolution. It is noteworthy that optimized matrices give modeling results with better accuracy than models from the high-order spectral element method. Our methodology is easily extendable to the accurate discretizing of the general 3D elastic wave equation that optimizes the bandwidth of the impedance matrix, availing computational resources for accurately modeling the compressional and shear wave velocities, density, as well as multi-parameter inversion.