Inverse Schrödinger Scattering for Seismic Imaging
Summary
The use of inverse scattering methods in seismic exploration is rapidly expanding. This generally involves classical wave equations which describe the traversion of waves through acoustic media. In particular, one may recover data of an inhomogeneous penetrable medium in the subsurface of the Earth by first probing it with an incident field and then measuring the reflected waves from some observation position. The data, however, is scattered and the objective of inverse scattering methods is thus to reconstruct the scattering potential of waves traversing the aforementioned scattering medium.
In my thesis, I treat the inverse Schrödinger scattering problem whereby we attempt to reconstruct the scattering potential of a medium from measurements of the medium response to a harmonic exitation which can be formulated by the Schrödinger equation. In quantum physics, this problem has been well treated and I draw parallels between the Schrödinger equation, for which there exist exact inversion methods, and the classical wave equation for which, in three dimensions at least, no exact inversion methods exist. Moreover, the inverse Schrödinger scattering problem is configured and thus generalised to the setting of seismic imaging.
In particular, I compare fast layer stripping algorithms which recursively reconstruct the scattering potential under the assumption of weak scattering and otherwise alongside integral equation based methods and also sampling schemes for reconstructing the potential in the frequency domain.