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.

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