Imaging conditions for prestack reverse-time migration

Abstract

Numerical implementations of six imaging conditions for prestack reverse-time migration show widely differing ability to provide accurate, angle-dependent estimates of reflection coefficients. Evaluation is in the context of a simple, one-interface acoustic model. Only reflection coefficients estimated by normalization of a crosscorrelation image by source illumination or by receiver-/source-wavefield amplitude ratio have the correct angle dependence, scale factor, and sign and the required (dimensionless) units; thus, these are the preferred imaging-condition algorithms. To obtain accurate image amplitudes, source- and receiver-wavefield extrapolations must be able to accurately reconstruct their respective wavefields at the target reflector.

Common-image gathers using the excitation amplitude imaging condition

“…In some cases, mutipathing must be addressed accurately. However, the excitation imaging condition also offers the opportunity to apply the deconvolution imaging condition without the worry of dividing over zero, a common limitation in the conventional U∕D (Claerbout, 1971;Chattopadhyay and McMechan, 2008) approach that requires a stabilization step. In extended images, because of the involvement of multiple lags, such features prove to be even more helpful.…”

“…which is an image with correct phase and amplitude under the assumption of a dispersion-free medium (Chattopadhyay and McMechan, 2008). The final image is then given by a summation of Iðx; s j Þ over all shots to obtain IðxÞ.…”

Prestack reverse-time depth migration of arbitrarily wide-angle wave equations

“…Imaging conditions is one of the main content in prestack reverse-time migration, via a simple, one-interface acoustic model, Chattopadhyay et al (2008) studied the migration result of excitation-time imaging conditions, cross-correlation imaging conditions and amplitude-ratio imaging conditions, which imply that in the same computational parameters the amplitude-ratio imaging conditions can provide the best resolution. But in practical computation, applying cross-correlation imaging conditions and amplitude-ratio imaging conditions need to do a forward modeling of given interval velocity model, which increase the calculation amount to two times of reverse-time propagation, moreover the application of these two imaging conditions also needs extensive computer time, when dealing with the huge velocity model problem, the time used to applying the imaging condition can be even longer than that used in migration.…”

Converted-wave seismic imaging: Amplitude-balancing source-independent imaging conditions

“…The incident wavefield in the denominator of equations 1 and 2 can be zero. Many studies have investigated how to avoid the division by zero and suggest different solutions (Valenciano and Biondi, 2003;Kaelin and Guitton, 2006;Chattopadhyay and McMechan, 2008;Schleicher et al, 2008). One solution is to multiply the numerator and denominator by the denominator and to add a small number to the denominator (Valenciano and Biondi, 2003).…”