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A direct inverse method for subsurface properties; the conceptual and practical benefit and added value in comparison with all current indirect methods, for example, amplitude-variation-with-offset and full-waveform inversion

Arthur B. Weglein
A direct inverse method for subsurface properties; the conceptual and practical benefit and added value in comparison with all current indirect methods, for example, amplitude-variation-with-offset and full-waveform inversion
Interpretation (Tulsa) (May 2017) 5 (3): SL103-SL121

Abstract

Direct inverse methods solve the problem of interest; in addition, they communicate whether the problem of interest is the problem that we (the seismic industry) need to be interested in. When a direct solution does not result in an improved drill success rate, we know that the problem we have chosen to solve is not the right problem - because the solution is direct and cannot be the issue. On the other hand, with an indirect method, if the result is not an improved drill success rate, then the issue can be either the chosen problem, or the particular choice within the plethora of indirect solution methods, or both. The inverse scattering series (ISS) is the only direct inversion method for a multidimensional subsurface. Solving a forward problem in an inverse sense is not equivalent to a direct inverse solution. All current methods for parameter estimation, e.g., amplitude-variation-with-offset and full-waveform inversion, are solving a forward problem in an inverse sense and are indirect inversion methods. The direct ISS method for determining earth material properties defines the precise data required and the algorithms that directly output earth mechanical properties. For an elastic model of the subsurface, the required data are a matrix of multicomponent data, and a complete set of shot records, with only primaries. With indirect methods, any data can be matched: one trace, one or several shot records, one component, multicomponent, with primaries only or primaries and multiples. Added to that are the innumerable choices of cost functions, generalized inverses, and local and global search engines. Direct and indirect parameter inversion are compared. The direct ISS method has more rapid convergence and a broader region of convergence. The difference in effectiveness increases as subsurface circumstances become more realistic and complex, in particular with band-limited noisy data.


ISSN: 2324-8858
EISSN: 2324-8866
Serial Title: Interpretation (Tulsa)
Serial Volume: 5
Serial Issue: 3
Title: A direct inverse method for subsurface properties; the conceptual and practical benefit and added value in comparison with all current indirect methods, for example, amplitude-variation-with-offset and full-waveform inversion
Author(s): Weglein, Arthur B.
Affiliation: University of Houston, Mission-Oriented Seismic Research Program, Department of Physics, Houston, TX, United States
Pages: SL103-SL121
Published: 201705
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 89
Accession Number: 2017-085782
Categories: Economic geology, geology of energy sourcesApplied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Reference includes data from GeoScienceWorld, Alexandria, VA, United States. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 201745
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