Dr. Mario Bencomo (Dept. of Mathematics, CSU-Fresno)

10/12/2023  3:10pm

Abstract:

Inverse problems are a classification of mathematical problems in engineering and science that involve estimating model parameters/inputs relative to a “forward/direct” problem. In this talk I will present several examples of inverse problems to elucidate the definition and highlight typical mathematical challenges. I will also discuss in depth an application in the field of seismic imaging: estimation of complex seismic sources. Accurate representation and estimation of seismic sources is crucial to the accuracy of imaging algorithms in exploration seismology. In order to account for source anisotropy, seismic sources of point-support are modeled as multipoles, i.e., a finite series of derivatives of the spatial delta function. The multipole source inverse problem results in a highly ill-conditioned linear least squares problem which presents a challenge for iterative solvers such as conjugate gradient (CG). A preconditioner consisting of time differo-integral operators based on analytical solutions to the wave equation is proposed to accelerate CG iterations.