Modeling seismic wave propagation in the earth using the distributional finite difference method

We present the theory and applications of the Distributional Finite Difference Method (DFD). The DFD method is an efficient tool for modeling the propagation of elastic waves in heterogeneous media in the time domain. It decomposes the modeling domain into multiple elements that can have arbitrary sizes. When using large elements, the DFD algorithm resembles the finite difference method because the wavefield is updated using operations involving band diagonal matrices only. This makes the DFD method computationally efficient. When small elements are employed, the DFD method permits to mesh complicated structures as in the finite element or the spectral element methods. We present numerical examples showing that the proposed algorithm accurately accounts for free surfaces, solid-fluid interfaces and accommodates non-conformal meshes. Seismograms obtained using the proposed method are compared to those computed using analytical solutions and the spectral element method. The DFD method requires fewer points per wavelength (down to 3) than the spectral element method (5 points per wavelength) to achieve comparable accuracy. We present examples demonstrating the advantages of the DFD method for modeling wave propagation in the Earth at the global and regional scales.