True Amplitude One-Way Waves

In homogeneous media, the two-way wave operator (or just wave operator) can be substituted by the product of two one-way wave operators that form the standard factoring of the wave equation. These one-way operators generate two one-way wave equations, which are fast tools for modeling and migration since they allow us to separate the two-way wave (or full wave), which is the solution of the full wave equation, into two one-way waves, a downgoing and an upgoing one. Since these one-way waves are solutions<br>of the wave equation in homogeneous media, they satisfy the same approximate (ray-theory) differential equations, eikonal and transport equations, as does the full wave, that is, their traveltime and amplitudes agree in first order approximation with those of the full wave. Since these oneway wave equations produce correct traveltimes even in inhomogeneous media, they have been used in wave equation migration WEM (Claerbout, 1971; 1985). However, in this case, they do not correctly treat reflection amplitudes.<br>Therefore, using them, only kinematically correct migrated images are obtained. In this paper, we study how the oneway wave operators need to be changed to make the oneway waves produce the same amplitudes of the full wave and keep the traveltime agreement.