Structure Independent Velocity Estimation

Abstract

Many commonly used velocity estimation procedures assume that the reflectors are horizontal. Because of this, their performance tends to degrade as the reflectors become curved or discontinuous. Much of this degradation can be traced to the fact that data recorded over nonhorizontal reflectors need not resemble in detail the subsurface in the area where they were recorded. Diffraction and scattering are the major complicating factors. Beginning with the scalar wave equation and using a small dip assumption, approximate wave equations which quite accurately model both near‐ and wide‐angle reflections generated by one or more sources can be found. Finite difference formulations of these equations can be used to demonstrate that surface recorded seismic reflections which have been downward continued to the depth of their source reflectors must resemble those reflectors in detail. This property of downward continuation can be exploited to improve velocity estimates by using downward continuation as a preprocessor for velocity estimation techniques. Both synthetic and field data examples show that estimates based on downward continued data do not exhibit diffraction effects and are not dependent upon reflector dip. Synthetic data examples also illustrate that the use of downward continuation allows accurate velocity estimates to be made from no record data recorded over an earth in which the reflectors are random functions of the horizontal and vertical coordinates. For reasonable data parameters, theoretical considerations indicate that the coherence of properly downward continued random reflector data measured along the true velocity hyperbolic should be greater than a similar measure on the corresponding surface data. This coherence increase should make velocity estimates based on downward continued random reflector data less susceptible to noise than estimates based on surface recorded data.

Velocity analysis based on minimum entropy

“…This was also mentioned by Taner et al (1970) and later by Blackburn (1980). Arguing that downward wave field extrapolation focusses diffraction energy and thus diminishes its smearing effect, Doherty and Claerbout (1976) Gardner et al (1974) and Sattlegger (1975), and applied in practice by Dohr and Stiller (1975) and Sattlegger et al (1976). Owusu et al (1983) extend the application of this method to three-dimensional data using a fast migration algorithm.…”

“…We saw (subsection 1.4.2) that this approach was discussed by Gardner et al (1974), Sattlegger (1975, Doherty and Claerbout (1976), Owusu et al (1983). In the philosophy behind velocity analysis techniques as considered by the above authors diffraction energy is 'tolerated' as an inevitable part of the input data to be coped with, and certainly not as a source of velocity information.…”

7. Migration Velocity Analysis

“…Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ Historically, vertical velocity updating for prestack depth migration was defined for the wavefield-continuation methods, particularly for source-receiver migration (Doherty and Claerbout, 1976;Yilmaz and Chambers, 1984;MacKay and Abma, 1993), prior to being defined for Kirchhoff-migration methods (Deregowski, 1990). Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ Historically, vertical velocity updating for prestack depth migration was defined for the wavefield-continuation methods, particularly for source-receiver migration (Doherty and Claerbout, 1976;Yilmaz and Chambers, 1984;MacKay and Abma, 1993), prior to being defined for Kirchhoff-migration methods (Deregowski, 1990).…”

Structure of the East Pacific Rise crest from multichannel seismic reflection data

“…First, the rough topography clearly violates the usual assumption of flat horizontal layering. The diffractions present in the data require that for any velocity analysis to be accurate the data should be migrated as constant offset sections, before they are combined into common depth points [Doherty, 1975].…”