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

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.

Direct and indirect inversion and a new and comprehensive perspective on the role of primaries and multiples in seismic data processing for structure determination and amplitude analysis

“…Inverse methods are either direct or indirect (see, e.g., the definition and examples of direct and indirect inversion in e.g., [2], [3]. Direct methods provide assurance and confidence, that we are solving the problem of interest.…”

“…Among key aspects in effectively designing and managing an industrial or academic research program, are: (1) to be able to identify and select the problems and challenges that need to be addressed and (2) what benefit would derive from a new and effective method that addresses a specific challenge. From our perspective, benefit is measured by an increase in successful exploration drilling and optimizing appraisal and development drill placement.…”

“…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 [2] (see Appendix A). Many methods for parameter estimation, e.g., AVO, are solving a forward problem in an inverse sense and are indirect inversion methods.…”

“…For indirect methods that either: (1) solve a forward problem in an inverse sense, like AVO or (2) are model matching methods like, e.g., FWI, any data can be forward modeled and solved in an inverse sense, or model matched, respectively. In contrast, for direct inverse methods the data required and the algorithms called upon are explicitly and unambiguously defined.…”

Convergence acceleration in scattering series and seismic waveform inversion using nonlinear Shanks transformation

“…depth imaging and velocity inversion (Weglein et al 2009;Luo et al 2011;Weglein et al 2012;Weglein 2013Weglein , 2017Wang & Hung 2014). The subseries approach has been noted by Weglein et al (2003) that it does not suffer the convergence problem in multiple removal.…”