Amplitude-preserved wave-equation migration

We analyze the amplitude variation as a function of reflection angle (AVA) for angle-domain common image gathers (ADCIG) produced via wave-equation migration. Straightforward implementations of the two main ADCIG methods lead to contradictory, thus inaccurate, amplitude responses. The amplitude inaccuracy is related to the fact that downward-continuation migration is the adjoint of upward-continuation modeling, but it is only a poor approximation of its inverse. We derive the frequency-wavenumber domain diagonal weighting operators that make migration a good approximation to the inverse of modeling. With these weights, both ADCIG methods produce consistent results. The main applications that follow from this paper are true-amplitude migration and pseudounitary modeling/migration, usable for iterative inversion. The two most important factors that degrade the accuracy of wave-equation ADCIGs are the limited sampling and offset range, combined with the band-limited nature of seismic data.