Luca De Siena

Seismic imaging necessitates precisely separating P and S waves to mitigate undesirable crosstalk between them. Failure to properly handle this crosstalk can lead to distorted or misinterpreted images. In an elastic anisotropic medium, the polarization of a P wave is not necessarily parallel to its propagating direction, making the separation of P and S waves more difficult than in the case of an elastic isotropic medium. A pure acoustic transversely isotropic (TI) wave equation involves a mixed-domain problem. This usually means the space dependencies and wavenumbers are coupled in the wavefield extrapolator. An efficient solution to the wavefield requires a separation between the space dependencies and wavenumbers in the extrapolator. There are two primary approaches: (1) an analytical separation of the mixed-domain term; and (2) a numerical solution to the mixed-domain term, such as low-rank and Poynting vector methods. In this study, the acoustic approximation is derived by setting the S-wave phase velocity to zero in all phase directions. An analytical separation is developed in this study by employing a Taylor series to linearize the anellipticity term, thereby decoupling the space-dependent and wavenumber-dependent variables within the wavefield extrapolator. The kinematics analysis demonstrates that our method has competitive phase velocity accuracy compared with existing methods. Moreover, the corresponding TI acoustic wave equation can be efficiently solved by the hybrid finite-difference/pseudospectral method. In a 2D case, it only requires one fast Fourier transform, two inverse Fourier transforms, and a few additional spatial differentiations at each time step. Remarkably, our wavefield solution remains independent of the wavefield heterogeneity (as observed in the low-rank approach) and is immune to wavefield interference (as encountered in the Poynting vector method). The developed acoustic approximation ensures the absence of any S-wave artifacts with relatively cheap computation. Numerical examples indicate our acoustic tilted transversely isotropic wave equation is reliable for accurate wavefield modeling and reverse time migration.

SUMMARY Peak delays of acoustic emission (AE) data from rock deformation laboratory experiments are sensitive to both sample heterogeneities and deformation-induced impedance contrasts inside the sample. However, the relative importance of stochastic heterogeneity and discontinuities is uncertain, as is the relationship between peak delays and applied stress and strain. In the companion paper, we presented and analysed peak delay data from AE recorded in a sandstone sample that was triaxially deformed to failure. Here, we simulate P–SV waveforms of dominant frequency 200 kHz in a 2-D isotropic, layered medium using realistic parameters derived from the laboratory experiments previously analysed. Our aim is to provide a physical interpretation of the laboratory findings and constrain the role of a proxy of the evolving fault zone on peak delays. We consider a 2-D fault zone embedded in a host material that simulates the fracture plane as a more compliant layer and allows us to numerically investigate variations in peak delay. Measurements of background parameters, including isotropic velocity and fault thickness were optimized using laboratory data via an evolutionary algorithm. Our simulations clarify that near-source peak delay observations are sensitive to the heterogeneity within zones of intense strain even when far-field approximations are not valid. This sensitivity manifests through the arrival of trapped waves within the layer that is coupled with multiple reflections from the sample boundaries. Substantial uncertainties remain on the possibility of inverting sample parameters with 2-D simulations and such complex physics. Our combined experimental and modelling study suggests that peak delays and coda parameters are sensitive to the heterogeneity caused by faulting and strain variations at different stages of fault-inducing slow deformation.