Elastic time-reverse modeling imaging conditions

Abstract

Abstract Since the Earth is elastic, it is worth the computational burden to process multicomponent data for elastic phenomena with fully coupled time-domain wave-equation propagators. At every time sample in the back-propagated model domain, the complete wave field is decomposed exactly into compressional and shear wave components by simple spatial derivatives. Then, physically significant images are extracted from extrapolated hyper-cubes by applying appropriate imaging conditions. To locate subsurface sources (or diffractors) with the time-reverse modeling algorithm, the imaging condition required is the correlation of P and S energy since only at the source location are the two events collocated. The impulse response of the algorithm is anti-symmetric in physical space and can be enhanced through post-processing with a spatial derivative or integral. Source Focusing The time-reverse modeling (TRM) algorithm was developed for locating sources within a model domain (Fink, 1999; Gajewski and Tessmer, 2005). The method is suited for locating earthquakes, microseismic events, or tremor sources. The difference between TRM and reverse-time migration (RTM) (Levin, 1984) is the lack of a known source wave field for TRM. Otherwise, data are treated in the same manner: reversed in time and used as source functions at the acquisition locations. The difference between a specular reflection and a stimulated heterogeneity, or diffractor, is that data contain only a direct arrival ray path: The "from-path". This contrasts to reflection seismic whose time delays are the sum of the "to-path" and the "from-path." Without some knowledge of the to-path, imaging algorithms based on delays between a reference event and a scattering event, including RTM and interferometry, are incapable of finding sources within a domain. In contrast, the TRM algorithm exploits the ability to collapse travel-time surfaces (hyperbolic cones) using wave-equation propagators.