Uniqueness for a seismic inverse source problem modeling a subsonic rupture. Issue 12 (1st December 2016)

• Record Type: Journal Article
• Authors: de Hoop, Maarten V.; Oksanen, Lauri; Tittelfitz, Justin
• Is Part Of: Communications in partial differential equations. Volume 41:Issue 12(2016)
• Page Start: 1895
• Page End: 1917
• Publication Date: 2016-12-01
• Subjects: Geophysics -- inverse problems -- partial differential equations -- wave equation; 35R30 -- 86A22 -- 35L05; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2016.1240183
• Languages: English
• ISSNs: 0360-5302

Abstract

ABSTRACT: We consider an inverse source problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. The inverse source problem, with an arbitrary source term on the right-hand side of the wave equation, is not uniquely solvable. Here we formulate conditions on the source term that allow us to show uniqueness and that provide a reasonable model for the application of interest. We assume that the source term is supported on a finite set of times and that the support in space moves with subsonic velocity. Moreover, we assume that the spatial part of the source is singular on a hypersurface, an application being a seismic rupture along a fault plane. Given data collected over time on a detection surface that encloses the spatial projection of the support of the source, we show how to recover the times and locations of sources microlocally and then reconstruct the smooth part of the source assuming that it is the same at each source location.