Harmonic encoding for fwi

Abstract

A deterministic method for selecting a set of encoding weights for simultaneous encoded-source inversion of seismic data that will cause the iterative inversion to converge faster than randomly chosen weights. The encoded individual source gathers are summed (), forming a composite gather, and simulated in a single simulation operation. The invention creates multiple realizations of the simulation (), each with its own encoding vector () whose components are the weights for the shots in the composite gather. The encoding vectors of the invention are required to be orthogonal (), which condition cannot be satisfied by random weights, and in various embodiments of the invention are related to eigenvectors of a Laplacian matrix, sine or cosine functions, or Chebyshev nodes as given by the roots of Chebyshev polynomials. For non-fixed receiver geometry, an encoded mask () may be used to approximately account for non-listening receivers.