Revisiting Multiple-Scattering Principles in a Crustal Waveguide: Equipartition, Depolarization and Coda Normalization

Abstract

Listen

Translate article

Seismic waves radiated by small crustal earthquakes are prone to multiple mode conversions caused by reflection and transmission at interfaces, and scattering by small-scale heterogeneities in the bulk of the medium. The goal of this study is to clarify the complex interplay between volume scattering and interface reflections in crustal waveguides and how it will impact the crustal energy propagation. To carry out this task, we have incorporated a rigorous description of wave polarization in the context of Monte–Carlo simulations of the multiple-scattering process by introducing a five-dimensional Stokes vector. To shed light on the wave content of the regional short-period seismic wavefield, we investigate the asymptotic partitioning of seismic energy onto P, SV and SH polarizations in the coda, as well as the angular distribution of energy flux in the waveguide. In full elastic space, equipartition theory predicts that (1) the energy ratio between P- and S-wave energies tends to $$\beta ^3/(2\alpha ^3)$$ , (2) an equal distribution of energy among SV- and SH-waves and (3) that energy fluxes are isotropic. In the presence of interfaces, we find that the isotropy of the wavefield is systematically broken and that energy ratios are shifted to the detriment of P-waves and in favor of SV-waves in a non-absorbing medium. This implies that a residual polarization is preserved in the waveguide. Through an extensive parametric study, we illustrate in detail how the anisotropy of the wavefield, the partitioning ratios and the shear wave polarization depend on the crustal attenuation parameters. The role of the initial polarization at the source has also been examined. In the case of an explosion and a shear dislocation with equal magnitude, we find that the energy level in the coda can differ by more than one order of magnitude when the effect of crustal scattering becomes very weak compared to reflections or transmissions at interfaces. When comparing different shear dislocation mechanisms, we find that the energy level in the coda can differ by up to 60%. While equipartition, depolarization and coda normalization remain fundamental guides to our understanding of the coda, their application requires a good a priori knowledge of the attenuation properties of the crust.