Distributional finite-difference modelling of seismic waves

This study introduces a distributional finite-difference method (DFDM) for modelling the propagation of elastic waves in heterogeneous media in the time domain. DFDM decomposes the modelling domain into multiple elements that can have arbitrary sizes. When large elements are used, the proposed method closely resembles the finite-difference method because the wavefield is updated using operations involving band diagonal matrices only. Thus DFDM is computationally efficient. When smaller elements are used, DFDM looks closer to the finite-element or the spectral element methods and permits to mesh complicated structures. A complete multidomain algorithm for modelling elastic wave propagation in arbitrarily heterogeneous media is presented. The algorithm's stability is discussed, and the usual Courant condition governs the stability of the proposed scheme. Numerical examples show that the proposed algorithm accurately accounts for free surfaces, solid-fluid interfaces and accommodates non-conformal meshes in their basic form. Seismograms obtained using the proposed method are compared to those computed using analytical solutions and the spectral element method. To achieve comparable accuracy, DFDM requires fewer points per wavelength than the spectral element method, for example.