Numerical wavefield simulations with instantaneous time mirror in a 3-D elastic medium

SUMMARY We simulate an instantaneous time mirror (ITM), that is, a rapid short-duration change in elastic material properties, using numerical experiments in time-varying isotropic elastic media. Our implementation in the seismic wave propagation software SeisSol is based on high-order discontinuous Galerkin discretization with ADER time stepping. We develop an eigenvector-based analytical solution for time interfaces for general linear hyperbolic wave systems and apply it to analyse the energy balance at time boundaries and ITMs. The energy increases for all intermittent medium changes for all impedance scaling factors. Our numerical implementation is validated against these analytical solutions and achieves high-order convergence. Its accuracy is further corroborated by estimates of reflection and transmission coefficients and observed frequency shifts across time boundaries, and by acoustic wave speed estimates obtained from focal spots associated with ITM-generated converging P waves that are consistent with theoretical predictions and ground truth values, respectively. We use the ITM implementation to simulate the partitioning of seismic body waves excited by a point source in a spatially homogeneous elastic full space. The response to an intermittent short change in the elastic parameters yields a diverging and converging P and S wavefield. A systematic scaling of the elastic parameters is then used to steer independent ITM reflections of either P or S waves. Numerical ITM solutions as developed here can be used to synthesize converging wavefields in seismic imaging applications, and more generally to analyse the behaviour and manipulation of seismic wavefields in space-time varying media.