ln this work, we study theoretically and numerically new implementational forms of the image-wave equation for depth remigration This is a partial second-order differential equation similar to the acoustic wave equation. We determine, additionally to consistency and stability, the conditions for dispersion and dissipation of six finite-difference schemes for this equation in different forms, obtained by a change of variables. These conditions cannot be simultaneously satisfied, i.e., a precise result is not easily obtained. Numerical tests confirm the theoretical stability results for three of the investigated schemes but fail for the others. Of the tested schemes, the ones forward in the velocity variable and forward or backward in depth were the most useful ones in the sense that they satisfy the theoretical predictions about their stability and can be utilized to realize the image-wave propagation, the former for increasing velocities and the lalter for decreasing velocities.
image-wave; remigration; finite differences; numerical analysis
