Wave‐front Charts and Three Dimensional Migrations

Abstract

A computer is required to calculate the complex wave‐front charts which are needed in many areas. On a medium size computer wave‐front charts can be constructed using up to 40 layers. Each layer can be a constant velocity or can start with any velocity and have an increase in velocity with vertical time. These wave‐front charts may be automatically plotted for use in migration in a vertical plane. At the same time that the wave‐front chart is being obtained, a list may be made which shows the depth and offset for each reflection time and stepout value. This migration list may be used to migrate values from time maps in three dimensions. Before migrating, these time maps should have contours of all time values even though overlapping occurs as on buried foci of sharp synclines. Thus, it is a simple matter to make a migrated depth map from any time map regardless of the crookedness and discontinuity of the profiles or the lack of cross‐line control.

On crustal structure deduced from seismic time-distance curves

“…Mort -Smith (1939 discussed the simplifications tha t result, in a few cases, when velocity is considered as a function of vertical travel-time. Musgrave (1961) recently used this type of function . A review of these types of analytical calculations was made by Kaufman (1953), who produced two detailed and extensive tables.…”

MIGRATION TO ZERO OFFSET (DMO) FOR A CONSTANT VELOCITY GRADIENT: AN ANALYTICAL FORMULATION1

“…The shape of the constant traveltime surfaces can be computed numerically for arbitrarily complex velocity models (Musgrave 1961), but can also be derived analytically in some simple situations. The constant velocity case is trivial and corresponds to the well-known ellipsoid whose foci coincide with the source and receiver locations.…”

“…The zerooffset mapping is then characterized by a perfectly elliptical impulse response that intersects the source and the receiver at zero time. Furthermore, this process is less sensitive to velocity than either normal moveout or migration and can be implemented efficiently using integral (Kirchhoff-like) methods (Deregowski and Rocca 1981;Hale 1991) or Fourier transform methods (Biondi and Ronen 1987;Notfors and Godfrey 1987). In spite of these advantages, constant-velocity MZO can lead to unacceptable errors in the imaging of steeply dipping reflectors, when the seismic wave velocity varies rapidly in the subsurface.…”

3D ACOUSTIC PRESTACK REVERSE‐TIME MIGRATION1

“…Examples of integral solutions include French (1974) and Schneider (1978); multistep solutions include Berkhout and de Jong (1981), Gibson, Larner and Levin (1983) and Dickinson (1988); f-k domain solutions include Herman et al (1982), Stolt (1978) and Wen, McMechan and Booth (1988). Papers presenting a variety of other perspectives and algorithms are Musgrave (1961), Sattlegger (1964), Jakubowicz and Levin (1983), Wen and McMechan (1987), Blacquière et al (1988), Karrenbach and Gardner (1988), Kitchenside (1988) and Chang and McMechan (1989a).…”

“…We know of no other attempts to develop prestack migration software in 3D, but the principles are widely applied in 2D. For 2D acoustic data, prestack algorithms have been presented by Jain and Wren (1980), Chang and McMechan (1986), Hu and McMechan (1986), Reshef and Kosloff (1986), among others. For 2D elastic data, prestack algorithms have been presented by Kuo and Dai (1984), Sun and McMechan (1986), Chang and McMechan (1987) and Wapenaar, Kinneging and Berkhout (1987).…”