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# Introduction

Velocity is the link between time and depth; therefore, velocity estimation is the most fundamental and important problem in seismic imaging. In the literature, different migration velocity estimation methods can be found; one method is depth focusing analysis. This method is based on the fact that the wave-propagation enegy is best focused when migration velocity is correct. The focusing analysis ideas was introduced by Doherty and Claerbout (1974), and presented the fundamental equation for focusing analysis:

 Vr Zr = Vm Zf , (1)

where Vr is the real wave propagation velocity, Zr is the real reflect or depth, Vm is the migration velocity and Zf is the the focusing depth. Therefore, the wave-field downward continued with the real propagation velocity Vr to reach the real depth is equivalent to the wave-field downward continued with an erroneous velocity Vm to reach the focusing depth.

Yilmaz and Chambers (1984) presented the time version of equation (1) and applied the focusing analysis method with a time migration operator. Later, working with a depth migration operator the focus panel was modified into a depth error focusing panel and depth focusing analysis Faye and Jeannot (1986). The depth error panel provided a direct relationship between the real reflector depth (Zr), the focusing depth (Zf) and the reflector migrated depth (Zm) obtained at the imaging condition (t=0 s) with the wrong migration velocity Vm. Therefore the real velocity is estimated assuming flat horizons and small velocity errors. MacKay and Abma (1992) discussed the details of this technique and presented a modified version of equation (1) for the case of dipping reflectors, assuming a constant velocity.

Depth error panels in complex areas have interpretation problems. The depth error panels are made of traces downward continued with the wrong velocity; therefore the focusing energy has an erroneous positioning in depth and space. Consequently, there is energy partially migrated, considered a spurious event that complicates the depth error panel interpretation. MacKay and Abma (1993) proposed the use of the residual curvature like a weighting function on the focus panels. Audebert and Diet (1993) and Jeannot and Berranger (1994) proposed and a residual zero-offset migration of the depth error panels, where the energy is mapped to the migrated CMP coordinates.

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; it is a 2-D gather of zero-offset traces extracted in every step of the downward continuation process. This feature of the depth error panels make possible evaluate migration velocity by a 2-D gather built from 3-D downward continuation data.

The goal of this paper is to present a depth migration velocity estimation tool based on a 3-D downward continuation operator in common-azimuth domain as well as to present depth focusing ideas. Partial results of the 3-D depth focusing velocity analysis analysis based on a 2-D and 3-D prestack downward continuation operator and the 2-D and 3-D kinematic bases of 3D focusing analysis are discuss.

Next: Building and interpreting the Up: Malcotti and Biondi: Depth Previous: Malcotti and Biondi: Depth
Stanford Exploration Project
11/11/1997