A 2.5D finite-difference algorithm for elastic wave modeling using near-optimal quadratures

We have developed a 2.5D finite-difference algorithm to model the elastic wave propagation in heterogeneous media. In 2.5D problems, it is assumed that the elastic properties of models are invariant along a certain direction. Therefore, we can convert the 3D problem into a set of 2D problems in the spectral domain. The 3D solutions are then obtained by applying a numerical integration in the spectral domain. Usually, the quadrature points used in the numerical integration scheme are sampled from the real axis in the spectral domain. The convergence of this quadrature can be very slow especially at high frequencies. We have applied the optimal quadrature scheme for the spectral integration. This is equivalent to transforming the contour of integration from the real axis into a path in the complex plane. Our numerical studies have indicated more than 10 times of reduction in the number of quadrature points compared with sampling along the real axis in the spectral domain. This scheme alleviates the bottleneck of computing speed in the 2.5D elastic wave modeling. Furthermore, it can improve the computational efficiency of 2.5D elastic full-waveform inversion algorithms.