Migration misfit and reflection tomography: Criteria for prestack migration velocity estimation in laterally varying media

This paper presents a method for velocity analysis in tilted transversely isotropic (TTI) media by combining CDP mapping with a genetic algorithm. CDP mapping is a velocity analysis method for determining anisotropic velocity but has difficulties due to the following factors: (i) it involves a non‐linear and multimodal objective function; (ii) it is prohibitively expensive in the evaluation of candidate solutions, which often involves the calculation of images in the depth domain; (iii) there is often a very large parameter space. Recognizing the global and multimodal nature of the problem, a genetic algorithm is employed to search for the optimal velocity model. The efficiency of the method contributes to two critical processes: rapid model evaluation, achieved by generating CDP mapping only in the neighbourhood of specific reflectors, and fast computation, based on Fermat's principle, of the CDP points and traveltimes in TTI media. The method produces subsurface structure images in the depth domain, and can also solve for Thomsen's anisotropic parameters (ɛ and δ), the vertical velocity and the dip of the symmetry axis in the model space, simultaneously.

Section: The Genetic Algorithmmentioning

confidence: 99%

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

Qin

Zhang

2003

“…where T(k) is the temperature at iteration k, T 0 is the starting acceptance temperature and the parameter C is a decay factor. Some geophysical applications of VFSA are given by Jervis et al (1996), Chunduru, Sen and Stoffa (1996), Varela, Stoffa and Sen (1994) and Sen and Stoffa (1995).…”

Section: The Optimization Algorithmmentioning

confidence: 99%

Background velocity estimation using non‐linear optimization for reflection tomography and migration misfit

Varela

Stoffa

Sen

1998

Self Cite

We show that it is possible to estimate the background velocity for prestack depth migration in 2D laterally varying media using a non‐linear optimization technique called very fast simulated annealing (VFSA). We use cubic splines in the velocity model parametrization and make use of either successive pairs of shot gathers or several constant‐offset sections as input data for the inversion. A Kirchhoff summation scheme based on first‐arrival traveltimes is used to migrate/model the input data during the velocity analysis. We evaluate and compare two different measures of error. The first is defined in the recorded data or (x,t) domain and is based on a reflection‐tomography criterion. The second is defined in the migrated data or (x,z) domain and is based on a migration‐misfit criterion. Depth relaxation is used to improve the convergence and quality of the velocity analysis while simultaneously reducing the computational cost. Further, we show that by coarse sampling in the offset domain the method is still robust. Our non‐linear optimization approach to migration velocity analysis is evaluated for both synthetic and real seismic data. For the velocity‐analysis method based on the reflection‐tomography criterion, traveltimes do not have to be picked. Similarly, the migration‐misfit criterion does not require that depth images be manually compared. Interpreter intervention is required only to restrict the search space used in the velocity‐analysis problem. Extension of the proposed schemes to 3D models is straightforward but practical only for the fastest available computers.

“…Techniques designed to correct image gather moveout by adjusting the velocity model have been widely reported (Deregowski 1990;Stork 1992;Lafond and Levander 1993;Liu and Bleistein 1995). In addition, some authors have taken a global optimization approach: simulated annealing (Varela, Stoffa and Sen 1994); Monte Carlo (Jin and Madariaga 1994); and, as here, GA (Jin and Madariaga 1993;Jervis, Sen and Stoffa 1996). GAs were first introduced by Holland (1975) and are based on a loose analogy with biological systems and the process of natural selection.…”

Section: Introductionmentioning

confidence: 99%

Migration velocity analysis using a genetic algorithm

Docherty

Silva²,

Singh

et al. 1997

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.