Sparse Inversion for Solving the Coupled Marchenko Equations Including Free-surface Multiples

Myrna Staring, Niels Grobbe, Joost van der Neut, Kees Wapenaar

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientific

8 Citations (Scopus)
28 Downloads (Pure)


We compare the coupled Marchenko equations without free-surface multiples to the coupled Marchenko equations including free-surface multiples. When using the conventional method of iterative substitution to solve these equations, a difference in convergence behaviour is observed, suggesting that there is a fundamental difference in the underlying dynamics. Both an intuitive explanation, based on an interferometric interpretation, as well as a mathematical explanation, confirm this difference, and suggest that iterative substitution might not be the most suitable method for solving the system of equations including free-surface multiples. Therefore, an alternative method is required. We propose a sparse inversion, aimed at solving an under-determined system of equations. Results show that the sparse inversion is indeed capable of correctly solving the coupled Marchenko equations including free-surface multiples, even when the iterative scheme fails. Using sparsity promotion and additional constraints, it is expected to perform better than iterative substitution when working with incomplete data or in the presence of noise. Also, simultaneous estimation of the source wavelet is a potential possibility.
Original languageEnglish
Title of host publication79th EAGE Conference and Exhibition 2017
Subtitle of host publicationParis, France, 12-15 June 2017
Number of pages5
Publication statusPublished - 2017
Event79th EAGE Conference and Exhibition 2017: Energy, Technology, Sustainability - Time to Open a New Chapter - Paris, France
Duration: 12 Jun 201715 Jun 2017
Conference number: 79


Conference79th EAGE Conference and Exhibition 2017


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