Time-shift extended imaging for estimating depth errors

The stationary-phase method applied to migration with a time-shift extension in a 2-D constant-velocity model with a dipped reflector produces two solutions in the domain of the extended image: one a straight line and the other a curve. If the velocity differs from the true one, the depth error follows from the depth and apparent dip of the reflector as well as the depth of the amplitude peak at a non-zero time shift, where the two solutions meet and the extended image focuses. The results are compared to finite-frequency results from a finite-difference code. A 2-D synthetic example with a salt diapir illustrates how depth errors can be estimated in an inhomogeneous model after inverting the seismic data for the velocity model.