WAVE EQUATION VELOCITY ANALYSIS
, by Alfonso Gonzalez-Serrano and Jon F. Claerbout
The retarded Snell midpoint coordinate frame enables us to interpret velocity analysis from the wave equation
point of view. The imaging conditions applied to the coordinate transformation equations provide an exact way
of estimating velocities in CMP gathers. Transforming the wave equation from physical variables to the new
variagles and putting the data into the new reference coordinates permits a migration, collapsing the energy
toward the stationary part of skewed hyperboloids, where we can measure velocities as functions of event
coordinates. Alternatively, we can project the data onto the t'-T plane, where the energy will focus almost
independently of the migration velocity and departures of the focused events from the expected coordinates
give the true material velocities. This plane can be more appropriate for seafloor multiple removal. Both
synthetic and real data examples of the first procedure are shown for the exact and 15-degree
frequency-wavenumber domain operators.
STANFORD