One‐pass 3-D seismic extrapolation with the 45° wave equation

Abstract

One‐pass 3-D modeling and migration for poststack seismic data may be implemented by replacing the traditional 45° one‐way wave equation (a third‐order partial differential equation) with a pair of second‐ and first‐order partial differential equations. Except for an extra correction term, the resulting second‐order equation has a form similar to the Claerbout 15° one‐way wave equation, which is known to have a nearly circular impulse response. In this approach, there is no need to compensate for splitting errors. Numerical tests on synthetic data show that this algorithm has the desirable attributes of being second order in accuracy and economical to solve. A modification of the Crank‐Nicholson implementation maintains stability.