Wave-propagation modeling using the distributional finite difference method.

In the last decade, the Spectral Element Method (SEM) has become a popular alternative to the Finite Difference method (FD) for modeling wave propagation through the Earth. Though this can be debated, SEM is often considered to be more accurate and flexible than FD. This is because SEM has exponential convergence, it allows to accurately model material discontinuities, and complex structures can be meshed using multiple elements. In the mean time, FD is often thought to be simpler and more computationally efficient, in particular because it relies on structured meshed that are well adapted to computational architectures. In this work, we present a numerical scheme called the Distributional Finite Difference method (DFD), which combines the efficiency and the relative simplicity of the finite difference method together with an accuracy that compares to that of the finite/spectral element method. Similarly to SEM, the DFD method divides the computational domain in multiple elements but their size can be arbitrarily large. Within each element, the computational operations needed to model wave propagation closely resemble that of FD which makes the method very efficient, in particular when large elements are employed. Further, large elements may be combined with smaller ones to accurately mesh certain regions of space having complex geometry and material discontinuities, thus ensuring higher flexibility. We present numerical examples showing the accuracy and the interest of the DFD method for modeling wave propagation through the Earth.