Velocity analysis based on the analysis of the focusing conditions of a downward continuation operator for a velocity field, has been redefined by different authors Audebert (1996); Berkhout (1996); Clapp and Biondi (1997). These papers explore new ideas in migration velocity estimation based on kinematic and dynamic focusing conditions, addressing complex lateral velocity gradients. In his last papers in 1997, Clapp combined the ideas presented by Berkhout (1996) and Audeberd (1996) and presented methodology for estimation of the focusing operator through homothetic perturbations of the traveltime field. In this paper we work with a more standard depth focusing methodology to estimate migration velocities for 3-D data sets, based on a fast and accurate 3-D prestack depth migration algorithm in common-azimuth domain Biondi and Palacharla (1996).
In our last paper Malcotti and Biondi (1997), we showed some preliminary results of the 2-D and 3-D depth focusing analysis methodology for the migrations velocity, using constant velocities and seismic diffractors. Those results were based on a 2-D phase shift migration in the CMP domain and constant velocity Claerbout (1985). In contrast, in this paper, we change the downward continuation operator to a 3-D prestack depth migration along common-azimuth sections(Biondi et al, 1996). We present some results using two different data sets, a 2-D synthetic data set and a real 3-D seismic data set. Both geologic models are characterized by complex shallow velocities that makes the imaging of deeper flat horizon difficult.
In addition, we show by applying this methodology 3-D real data set, one of the most important characteristics of depth focusing analysis is its independence from the dimensionality of the data. A depth-focus error-gather does not change for 2-D or 3-D prestack data. Moreover, a depth error gather is a 2-D gather of zero-offset traces extracted in every step of the downward continuation process. Therefore, it allows the evaluation of the migration velocity on a 2-D gather (i.e., depth error gather) which is built from 3-D downward continuation of the data.