2.5-D frequency-domain seismic wave modeling in heterogeneous, anisotropic media using a Gaussian quadrature grid technique

We present an extension of the spectral element method (SEM), called the Gaussian quadrature grid technique, for 2.5-D frequency-domain seismic wave modeling in heterogeneous, anisotropic media having arbitrary free-surface topography. The technique has two new features. First, it employs a point-gridded model sampled by irregular Gaussian quadrature abscissa rather than a hexahedral-element mesh so as to simplify the procedures of matching the free-surface topography and the subsurface interface geometry. Furthermore, it offers flexibilities in the subdomain sizes, the Gaussian quadrature scheme and orders employed, and the number of subdomain abscissae in terms of the model geological characteristics. Second, we have incorporated a simple implementation of the 2.5-D perfectly matched layer (PML) technique to suppress the reflections from the artificial boundaries. We show that removing the artificial reflections in arbitrary anisotropic media can be achieved by simply employing the so-called "PML model parameters," which are specified complex density and elastic moduli obtained by the PML theory. The two features do not compromise the main advantages of the SEM, such as the high accuracy, the sparse system matrix, and wide applicability for arbitrary geological models. We numerically show the excellent effects of the PML model parameters and the capability of the presented method by means of homogeneous, isotropic, and anisotropic models that have analytic solutions for verification. In addition, we demonstrate performance on homogeneous and heterogeneous, anisotropic models, both having an undulating free-surface topography. The model results yield global views of the vectorial wavefields in the frequency domain.