A WNAD method for seismic stress-field modeling in heterogeneous media

In this article, we first present the weighted nearly analytic discrete (WNAD) method for acoustic and elastic wave equations. Then we compute numerical error of the stress-field for the 2-D acoustic initial value problem using the WNAD method, the conventional finite-difference method and the fourth-order Lax-Wendroff correction (LWC) scheme. Numerical calculations of the relative errors show that WNAD method has the highest accuracy among these methods. Finally, we present the stress-field snapshots generated and compare the numerical results computed by the WNAD method with those of the fourth-order LWC scheme and the fourth-order staggered-grid FDM for the 2-D inhomogeneous medium case. Promising numerical results illustrate that the results of the WNAD method have no visible numerical dispersion or sourcenoises even though too coarse grids are used. What's more, the WNAD method computes not only the values of the displacement U, but also the gradients of 17, which makes it more convenient and accurate for computing the stress fields. The continuity of the stress is satisfied automatically even when the models have large velocity contrast between adjacent layers because of using local connection relations of the displacement U and its gradients.