Abstract: The present invention provides a method of migrating seismic records that retains the information in the seismic records and allows migration with significant reductions in computing cost. The present invention comprises phase encoding seismic records and combining the encoded seismic records before migration. Phase encoding can minimize the effect of unwanted cross terms while still allowing significant reductions in the cost to migrate a number of seismic records.

Abstract: Weighted values of interferometric signals are unwrapped by determining the least squares solution of phase unwrapping for unweighted values of the interferometric signals; and then determining the least squares solution of phase unwrapping for weighted values of the interferometric signals by preconditioned conjugate gradient methods using the unweighted solutions as preconditioning values. An output is provided that is representative of the least squares solution of phase unwrapping for weighted values of the interferometric signals.

Abstract: A phase gradient autofocus system for use in synthetic aperture imaging accurately compensates for arbitrary phase errors in each imaged frame by locating highlighted areas and determining the phase disturbance or image spread associated with each of these highlight areas. An estimate of the image spread for each highlighted area in a line in the case of one dimensional processing or in a sector, in the case of two-dimensional processing, is determined. The phase error is determined using phase gradient processing. The phase error is then removed from the uncorrected image and the process is iteratively performed to substantially eliminate phase errors which can degrade the image.