Convergence analyses of different modeling schemes for piecewise heterogeneous media

摘要

Several flexible approximate solutions to the generalized Lippmann-Schwinger integral equation are compared for wave-propagation simulation in piecewise heterogeneous media, with a great saving of computing time and memory. To handle, the prohibitively expensive boundary-volume integral equation system, a Born series is applied to both the boundary-scattering and volume-scattering waves, leading to the Born-series approximation (BSA) scheme and the improved Born-series approximation (IBSA) scheme. An alternative approach to solve the boundary-volume integral equation matrix is the generalized minimal residual method (GMRES). These iteration schemes are' validated by dimensionless frequency responses to a heterogeneous semicircular alluvial valley. Numerical experiments, compared with the full-waveform numerical solution, indicate that the convergence rates of these methods decrease gradually with increasing velocity perturbations. The comparison also shows that the IBSA scheme gives a superior performance over the other methods, with the least iterations to achieve the necessary convergence. The BSA scheme has a faster convergence than the GMRES method when the velocity perturbation less than 10 percent. For the velocity perturbation larger than 15 percent, it converges slower and even hardly achieves convergence by comparison with other methods.