Boundary shape waveform inversion for two-dimensional basin structure using three-component array data of plane incident wave with an arbitrary azimuth

Abstract

We extend a new waveform inversion scheme (Aoi et al., 1995) for estimating underground structure with an irregular-shaped basement as a target to cases where plane waves with an arbitrary azimuth impinge on the structure, i.e., from a direction not necessarily perpendicular to the major axis of the structure. We proved the validity of this scheme by numerical experiments. We had already achieved the formulation and numerical experiments for the cases where an SH wave impinges on a 2D basin structure and had shown that we could estimate the entire basin structure with seismic waveforms from only a few surface stations by using whole waveforms that include the surface waves. However, when the epicenter is located out of the plane including the observation stations, even the cases of 2D structure cannot be treated as a simple 2D (SH or P-SV) problem because of the wave with an azimuth that is not 0°. Therefore, by dealing with 3D wave fields in the present study, we extend the inversion scheme in order to apply it to incident waves with an arbitrary azimuth. The differential seismograms, which represent the sensitivity of change in the waveform, show different patterns in three components, and we demonstrate that inversion with three components, compared with the inversion with only one of them, leads to a linearized equation system with a smaller condition number and a more stable computation. Furthermore, we detect certain parts that are estimated with much less difficulty than others, depending on the direction from which the incident wave impinged. In the latter case, we can estimate the entire structure by employing simultaneously several data from incident waves arriving from different directions. We thus demonstrate by numerical experiments that the extension of our inversion method to cases where the incident wave with an arbitrary azimuth impinges on the structure enables us to estimate with increased accuracy an underground structure under more general conditions of the epicenter locations.