Inversion of seismic reflection data in the acoustic approximation

Abstract

The nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation. The method is based on the generalized least-squares criterion, and it can handle errors in the data set and a priori information on the model. Multiply reflected energy is naturally taken into account, as well as refracted energy or surface waves. The inverse problem can be solved using an iterative algorithm which gives, at each iteration, updated values of bulk modulus, density, and time source function. Each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation (backward in time) of the data residuals. The correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models. This shows, in particular, that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data, and commercially competitive with them.

Estimation of the Subsurface Reflection Coefficient Using the Prestack Reverse-Time Depth Migration.

“…On the other hand, the waveform inversion method for reflected waves is developed by Tarantola (1984), Mora (1987), Bourgeois et al (1989), Pica et al (1990), among others. According to them, the model parameters are iteratively updated using the gradient method for the non-linear inverse problem.…”

“…According to them, the model parameters are iteratively updated using the gradient method for the non-linear inverse problem. For example, taking the impedance 1(x) as a model parameter, the algorithm in the acoustic wavefield is given as below (Tarantola, 1984;Kawasaki, 1992), ƒÂuk(xr,t; xs)=Wd(u0(xr,t; xs)-uk(xr,t; xs)),…”

“…Finally, the present method is compared to the waveform inversion method. The waveform inversion was developed by Tarantola (1984) and others, but since then only a few applications to real data have been reported (Crase et al, 1990(Crase et al, , 1992. This implies that the method still includes some difficulties.…”

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

“…The objective of full-waveform inversion (FWI) is to recover a high-resolution model that is capable of matching the observed seismic data, trace by trace, through repetitive modeling and a local optimization technique (Lailly, 1983;Tarantola, 1984;Virieux and Operto, 2009). Over the past three decades, most FWI techniques have been designed to recover only a P-wave velocity model because of the high computational cost (e.g., Gauthier et al, 1986;Pratt, 1999).…”

Pre-stack full waveform inversion of ultra-high-frequency marine seismic reflection data

“…The quantitative interpretation of pre-stack seismic data is a well-established and widely accepted procedure in industry and basin-scale exploration, in the form of either full waveform inversion (FWI) (Tarantola, 1984) or reflection amplitude versus offset inversion (AVO) (Ruthenford & Williams, 1989). It allows improved imaging of complex structures (Tarantola, 1984;Mora, 1980;Virieux & Operto, 2009), detailed rock physics characterisation of oil and gas reservoir (Ostrander, 1984;Ruthenford & Williams, 1989;Fatti et al, 1994;Mallick & Adhikari, 2015), and enhanced resolution regional geology models (Gulick et al, 2013;Morgan et al, 2013).…”