An improved source term for finite-element modelling with the stress-velocity formulation of the wave equation

Abstract

For seismic modelling, imaging and inversion, finite-difference methods are still the workhorse of the industry despite their inability to meet the increasing demand for improved accuracy in subsurface imaging. Finiteelement methods offer better accuracy but at a higher computational cost. A stress-velocity formulation with linear elements and an iterative method, defect correction, for inverting the mass matrix offers fourth-order super-convergence but is susceptible to numerical noise if waves in the wrong part of the dispersion curve are excited. We propose an improved source term that reduces that noise and investigate the accuracy of the method on structured triangular meshes as well as on unstructured rotated meshes. With an optimised source function, it is seen that the dispersive wavelengths can be avoided, giving the defect-correction approach a better performance than the mass-lumped formulation with only a marginal increase in compute effort.