Past Event: Oden Institute Seminar

Acoustic Imaging and Multiple Removal via Model Order Reduction

Alexander Mamonov, Department of Mathematics, University of Houston

Abstract

We introduce a novel framework for imaging and removal of multiples from waveform data based on model order reduction. The reduced order model (ROM) is an orthogonal projection of the wave equation propagator (Green's function) on the subspace of discretely sampled time domain wavefield snapshots. The projection can be computed just from the knowledge of the boundary waveform data using the block Cholesky factorization. Once the ROM is found, its use is twofold. First, given a rough knowledge of kinematics, the projected propagator can be backprojected to obtain an image of reflectors in the medium. ROM computation implicitly orthogonalizes the wavefield snapshots. This highly nonlinear procedure differentiates our approach from the conventional linear migration methods (Kirchhoff, RTM). It allows to resolve the reflectors independently of the knowledge of the kinematics and to untangle the nonlinear interactions between the reflectors. As a consequence, the resulting images are almost completely free from the multiple reflection artifacts. Second, the ROM computed from the original, multiply scattered waveform data can be used to generate the Born data set, i.e. the data that the measurements would produce if the propagation of waves in the unknown medium obeyed Born approximation instead of the full wave equation. Obviously, such data only contains primary reflections and the multiples are removed. Moreover, the multiply scattered energy is mapped back to primaries. Consecutively, existing linear imaging and inversion techniques can be applied to Born data to obtain reconstructions in a direct, non-iterative manner.