LARGE REFLECTION ON AN ARTIFICIAL BOUNDARY CAUSED BY THE COUPLING EFFECT OF DIFFERENT WAVE COMPONENTS

Artificial boundary conditions (ABCs) for elastic waves play a key role in improving the accuracy and computational efficiency of numerical simulations of seismic wave propagation. Extrapolation-type artificial boundary conditions, including Liao’s multi-transmitting formula, Higdon’s one-way wave equations and etc., have been widely used in this field. However, the fundamental characteristics of these ABCs affected by the coupling effect of elastic P- and S-waves have, up to now, not been completely revealed. This work factorizes each of the elastic-wave reflection coefficients of extrapolation-type ABCs into the product of a physical part and a set of control parts. The physical part is a function of the ratio of compressional and shear waves cp/cs, which is the physical property of the elastic wave problem. The control parts are functions of the ABC’s computational velocities caj (j = 1, 2, ···, N) and boundary order N, which are the user-defined control parameters of the ABC. Using this factorization, the characteristics of the boundary reflection coefficients are thoroughly analyzed across the following parameter ranges: cp/cs = 1.5 ~ 4, N = 1, 2, 3, caj = cs + q· (cp−cs), with j = 1, 2, ···, N and q = 0, 0.1, ···, 1.0. The results indicate a key finding that when all computational velocities caj’s approach the value of cp, the S-P reflection mode often exhibits a significant spurious reflection with an amplitude exceeding 1 (corresponding to 100% reflection), and thus causes the boundary reflection error to increase with the boundary order N, rather than decrease. This large spurious reflection, caused by the coupling effect of different wave components, goes against the existing understanding in Liao’s and Higdon’s boundary conditions that increasing the boundary order always makes the solution more accurate. Consequently, this issue must be paid special attention in both theory and application. Using the 85% percentile value of reflection coefficients as an accuracy metric, the applicable ranges of boundary parameters that may cause the above-mentioned large spurious reflection and those can lead to high-precision ABCs are delineated, respectively. Numerical experiments confirm the previously revealed influence of different computational parameters on the accuracy of extrapolation-type ABCs, and present a comparison with the prevalent viscous-spring boundary (a typical stress-type ABC).