2-D full-wavefield inversion for wide-aperture, elastic, seismic data

Abstract

S U M M A R YFull-wavefield inversion of two-component (elastic), wide-aperture, seismic data from surface sources and receivers simultaneously provides 2-D estimates of both P and SV velocity distributions. T h e algorithm operates on common-source gathers; it involves cross-correlation of propagating source and residual wavefields to define the steepest descent direction used to update t h e velocities at each point in a 2-D finite-difference grid. The solution is stable even in t h e presence of random noise and when the input traces are unequally spaced. Examples include a stack of flat layers and a folded and faulted structure.

Waveform inversion using a logarithmic wavefield

“…Because Lailly ͑1983͒ and Tarantola ͑1984͒ suggested that the back-propagation algorithm of reverse-time migration can be used in seismic inversion, their ideas have commonly been used in time-domain traveltime tomography inversion and waveform inversion ͑Bamberger et al, 1982; Kolb et al, 1986;Gauthier et al, 1986;Tarantola, 1986Tarantola, , 1987Tarantola et al, 1988;Mora, 1987Mora, , 1989Sun and McMechan, 1992;Cao et al, 1990;Pica et al, 1990;Xu et al, 1995;Zhou et al, 1995͒. After Pratt et al ͑1998͒ applied the same idea to frequency-domain waveform inversion and showed that the back-propagation algorithm could be used efficiently for waveform inversion of largescale geologic models, the technique began to be used frequently ͑Pratt, 1999; Pratt and Shipp, 1999;Hicks and Pratt, 2001͒.…”

Crust and Lithospheric Structure - Active Source Studies of Crust and Lithospheric Structure

“…Sun and McMechan (1992) and Pratt et al (1996) applied 2-D elastic and acoustic full-waveform inversion to synthetic wide-angle data. Full-waveform inversion of real wide-angle data for 2-D models is just beginning to be applied (e.g., Chironi et al, 2006;Operto et al, 2006;Ravaut et al, 2004;Shipp and Singh, 2002).…”

A new optimization approach for source-encoding full-waveform inversion

“…The minimization method for randomized inversion is called stochastic optimization and is based on machine learning methods (Goldberg, 1989;Spall, 1992Spall, , 2003Hoos and Stutzle, 2004;Yu et al, 2010). In the stochastic optimization framework, the search direction in each iteration of the inverse problem is considered to be a random but educated guess that should lead toward the true solution.…”

“…We will not address this important subject but instead assume that a reasonably accurate initial velocity model is available and that computational cost is the main problem, especially in 3D. In conventional FWI (Tarantola, 1984(Tarantola, , 1986Mora, 1987;Crase et al, 1990;Pratt and Worthington, 1990;Sun and McMechan, 1992;Bunks et al, 1995;Pratt et al, 1996Pratt et al, , 1998Pratt et al, , 2001Djikpéssé and Tarantola, 1999;Shipp and Singh, 2002;Causse, 2002;Mulder and Plessix, 2004;Sirgue and Pratt, 2004;Sourbier et al, 2008;Symes, 2008;Virieux and Operto, 2009), the seismic simulations are performed for each individual seismic source separately. Therefore, the cost of conventional FWI is proportional to the number of sources.…”

“…They correct for the fact that the steps are random. This is done by either (1) averaging over all the past updated models, (2) averaging over past gradients, or (3) averaging the Hessian operator (Goldberg, 1989;Spall, 1992Spall, , 2003Hoos and Stutzle, 2004). In this paper, we borrow some ideas from the area of stochastic optimization and propose our own method for the solution of the source-encoding FWI problem.…”