Title: Modeling Seismic Point-Sources: Multipole Source Inversion
Accurate representation and estimation of seismic sources is crucial to the joint medium-source full waveform inversion (FWI) problem. In the work presented here we focus on the source estimation subproblem, representing seismic sources as truncated series of multipole point-sources. Our main contribution lies in developing a preconditioner for the normal equations related to the source parameter (linear) least squares problem. The proposed preconditioner consists of fractional time derivative/integral operators based on the analytical solutions in unbounded homogeneous media with multipole sources. Numerical results demonstrate better conditioning as dramatic acceleration in convergence of conjugate gradient iterates. As an application we also present some preliminary results for modeling airgun-arrays, one of the most common type of sources used in marine seismic surveying. Results show that 84% of the data can be accounted for with an isotropic point source (monopole term), while an extra 10% can be explained if dipole terms are included.