Preconditioner for estimation of multipole sources via full waveform inversion

Accurate representation and estimation of seismic sources is crucial to the joint medium-source full waveform inversion problem. We focus on the source estimation subproblem and its difficulties, where seismic sources are modeled by truncated series of multipoles. The source full waveform inversion formulation results in a highly ill-conditioned (potentially ill-posed) linear least squares problem which we attempt to solve iteratively via conjugate gradient. Our main contribution lies in developing a preconditioner to accelerate the performance of conjugate gradient on multipole source inversion. The proposed preconditioner consists of (fractional) time derivative/integral operators based on analytical solutions to the wave equation with multipole sources in an unbounded, homogeneous medium. Numerical results in 2D demonstrate that the conjugate gradient iterations are accelerated when incorporating the proposed preconditioning scheme. •Anisotropic seismic sources are represented as truncated series of multipoles point sources.•Multipole source estimation problem via full waveform inversion is a highly ill-conditioned, potentially ill-posed, linear inversion problem.•Multipole source inversion solved iteratively via conjugate gradient.•We develop preconditioners based on analytical solutions to the wave equation with multipole sources.•Numerical experiments demonstrate an acceleration of conjugate gradient when our preconditioning scheme is used.