Scattered wave and coda reliability in 3D elastic seismic simulation: new insights for the advancement of inversion studies.

In this study we investigate the behavior of seismic waves in a high-scattering medium using numerical simulations of the full wavefied based on the Spectral Element Method solutions of the wave equation. The simulated 3D elastic medium was designed to have Laplacian correlated heterogeneity, creating a realistic representation of the complexities present in natural seismic environments. We conducted analyses on three distinct cases, each characterized by increasing levels of heterogeneity fluctuation, ranging from 10% to 25% standard deviation.We checked the consistency between theoretical results and simulations with regard to the value of the mean free path, the asymptotic behavior at long times and the partitioning of energy between compressional and shear modes. Excellent agreements were obtained, indicating the reliability of the numerical models of coda waves used here.  Our analyses are made both at depth and at the free surface, allowing us to compare the behavior of seismic waves under varying conditions. Additionally, we validated our findings by conducting independent numerical simulations of wave energy densities that used Monte Carlo methods to solve the Radiative Transfer Equation, thus corroborating the robustness and accuracy of our results for long lapse times.We show that under specific conditions, existing simulation codes can effectively replicate wave propagation in a highly scattered medium. This implies that a greater part of the waveform, namely the late envelops, could be employed in inversion processes, thus opening up new possibilities in the realm of inversion studies. Furthermore, we used these simulations to investigate the behavior of the wavefield and its gradient, exploring the information that can be extracted from their evolution over time to improve characterization of environmental heterogeneity.