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

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 finite-difference 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.