We develop an unconditionally stable, explicit depth migration method. The downward continuation operator derived by a finite-difference approximation of the one-way equation is given by the exponential of a banded matrix. We approximate this exponential by decomposing the banded matrix into block diagonal matrices, of which the exponential can be computed analytically. The derived downward continuation operator is explicit and unconditionally stable, and thus it may be efficiently implemented on either vector or parallel computers.
First, we apply this algorithm to a 15-degree migration. To increase the accuracy at steep dip, we add more leading terms to the Taylor-series expansion of the square-root operator. However, the improvement in accuracy gained by adding more terms to the Taylor series is at the expense of higher computational cost.