Improved amplitude multi-one-way modeling method

Classical paraxial wave equations, also called one-way wave equations, lead to efficient numerical schemes in three-dimensional spaces for computing the wave field. The kinematics is well approximated by these algorithms, however the dynamics is generally not correctly modeled when the medium is inhomogeneous. This prevents from using one-way wave equation scheme for solution of inverse problems. In order to improve estimation of the amplitudes, a new multi-one-way scheme is introduced. This approach is based on an iterative solution of the factorized two-way wave equation with a right-hand side incorporating the information about medium heterogeneities. The numerical scheme is a succession of several classic one-way schemes. The proposed approach takes into account vertical and horizontal velocity variations of the medium and allows modeling reflected waves. Numerical results for several two-dimensional examples with smooth and rough velocity contrasts are compared with finite-difference solutions of the two-way wave equation. It is shown that the multi-one-way scheme significantly reduces the error in the amplitude estimates of the wave field.