Migration velocity analysis using a genetic algorithm

Abstract

Migration velocity analysis, a method for determining long wavelength velocity structure, is a critical step in prestack imaging. Solution of this inverse problem is made difficult by a multimodal objective function; a parameter space often vast in extent; and an evaluation procedure for candidate solutions, involving the calculation of depth-migrated image gathers, that can be prohibitively expensive. Recognizing the global nature of the problem, we employ a genetic algorithm (GA) in the search for the optimum velocity model. In order to describe a model efficiently, regions of smooth variation are identified and sparsely parametrized. Region boundaries are obtained via map migration of events picked on the zero-offset time section. Within a region, which may contain several reflectors, separate components describe long and short wavelength variations, eliminating from the parameter space, models with large velocity fluctuations. Vital to the success of the method is rapid model evaluation, achieved by generating image gathers only in the neighbourhood of specific reflectors. Probability of a model, which we seek to maximize, is derived from the flatness of imaged events. Except for an initial interpretation of the zero-offset time section, our method is automatic in that it requires no picking of residual moveout on migrated gathers. Using an example data set from the North Sea, we show that it is feasible to solve for all velocity parameters in the model simultaneously: the method is global in this respect also.

Monte Carlo Methods in Geophysical Inverse Problems

“…[27] Within a few years of their introduction, genetic algorithms became quite popular within the Earth sciences and were applied in a wide range of areas. Some examples include earthquake hypocenter location [Kennett and Sambridge, 1992;Sambridge and Gallagher, 1993;Billings et al, 1994;Wan et al, 1997;Muramatsu and Nakanishi, 1997]; estimation of focal mechanisms and seismic source characteristics [Kobayashi and Nakanishi, 1994;Zhou et al, 1995a;Sileny, 1998;Yu et al, 1998]; mantle viscosity estimation [King, 1995;Kido et al, 1998]; groundwater monitoring and management problems [McKinney and Lin, 1994;Ritzel et al, 1994;Cieniawski et al, 1995;Rogers et al, 1995;Tang and Mays, 1998]; meteorite classification [Conway and Bland, 1998]; seismic anisotropy estimation [Horne and Macbeth, 1994;Levin and Park, 1997]; near-source seismic structure [Zhou et al, 1995b]; regional, crustal seismic structure and surface wave studies [Lomax and Snieder, 1994Drijkoningen and White, 1995;Yamanaka and Ishida, 1996;Neves et al, 1996]; design of microseismic networks [Jones et al, 1994]; fission track dating [Gallagher, 1995]; seismic profiling and migration [Jervis et al, 1993;Jin and Madariaga, 1993;Nolte and Frazer, 1994;Horne and Macbeth, 1994;Boschetti et al, 1996;Docherty et al, 1997]; seismic receiver functions studies [Shibutani...…”

Two-dimensional velocity macro model estimation from seismic reflection data by local differential semblance optimization: applications to synthetic and real data sets

“…Most existing methods are based on the maximization of a semblance criterion measured on the CIGs. Examples tested on real data have been shown by Jin & Madariaga (1993), Jin & Madariaga (1994), Docherty et al (1997), Jervis et al (1996) and Varela et al (1998). The choice of the mis®t criterion varies slightly from one author to another, but all cost functions are multimodal (with secondary minima).…”

“…In practice, the use of global optimization requires such a sparse parametrization of the velocity ®eld that bias is unavoidable and can lead to important unresolved details. To overcome this dif®culty, a layer-stripping approach (Jin & Madariaga 1994) and a multigrid parametrization (with primary and secondary velocity nodes) (Docherty et al 1997) have been proposed.…”

“…DSO has been extensively tested for 1-D cases (Symes 1993;Symes & Kern 1994;Gockenback & Symes 1995). The differential semblance cost function exhibits much better properties in terms of convexity and unimodality than classical semblance as de®ned for example by Docherty et al (1997).…”

CDP mapping in tilted transversely isotropic (TTI) media. Part II: Velocity analysis by combining CDP mapping with a genetic algorithm

“…There are two schemes for recon- * E-mail: zhangzj@mail.igcas.ac.cn structing velocities or elastic parameters in anisotropic media from surface data: anisotropic velocity analysis (Alkhalifah and Tsvankin 1995;Sayers 1995;Alkhalifah et al 1996;Tsvankin 1997;Grechka and Tsvankin 2000;Grechka et al 2001;Zhang 2002) and traveltime inversion (Tsvankin and Thomsen 1995;Grechka and McMechan 1997;Sayers and Ebrom 1997;Grechka 1998;Zhang et al 2003). We propose a method for mapping the CDP velocity that is similar to the migration velocity analysis in isotropic media (Liu and Bleistein 1995;Tieman 1995;Docherty et al 1997;Liu 1997).…”