Characterise the non-uniqueness in full-waveform inversion by using the square-root variable metric based null-space shuttle

Q. Liu, Daniel Peter

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Full-waveform inversion is an ill-posed inverse problem, with non-unique solutions. We examine its non-uniqueness by exploring the null-space shuttle, which can generate an ensemble of data-fitting solutions efficiently. We construct this shuttle based on a quasi-Newton method, the square-root variable-metric (SRVM) method. This method enables a retrieval of the inverse data-misfit Hessian after the SRVM-based elastic FWI converges. Combining SRVM with randomised singular value decomposition (SVD), we obtain the eigenvector subspaces of the inverse data-misfit Hessian. The first one among them is considered to determine the null space of the elastic FWI result. Using the SRVM-based null-space shuttle we can modify the inverted result a posteriori in a highly efficient manner without corrupting data misfit. Also, because the SRVM method is embedded through elastic FWI, our method can be extended to multi-parameter problems. We confirm and highlight our methods with the elastic Marmousi example.
Original languageEnglish (US)
Title of host publication81st EAGE Conference and Exhibition 2019
PublisherEAGE Publications BV
ISBN (Print)9789462822894
DOIs
StatePublished - Aug 26 2019

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