Solving the 3D Acoustic Wave Equation with Higher-order Mass-lumped Tetrahedral Finite Elements

Abstract

SUMMARY Present-day computers allow for realistic 3D simulations of seismic wave propagation, as well as migration and inversion of seismic data with numerical solutions of the full wave equation. The finitedifference method is popular because of its simplicity but suffers from accuracy degradation for complex models with sharp interfaces between large impedance contrasts and for models with rough topography. A tetrahedral mesh offers more flexibility and maintains its accuracy if element boundaries are aligned with sharp interfaces. Higher-order finite elements with mass lumping provide a fully explicit time-stepping scheme. We have implemented elements of degree one, two, and three for the 3D acoustic wave equation. Numerical tests confirm the accuracy of the mass-lumped elements. There are two different third-degree elements that have almost the same accuracy, but one has a more favourable stability limit than the other. Convergence analysis shows that the higher the order of the element, the better the computational performance is. A low-storage implementation with OpenMP shows good scaling on 4-and 8-node platforms.