Phase‐shift time‐stepping for reverse‐time migration

Author(s):  
Ben D. Wards ◽  
Gary F. Margrave ◽  
Michael P. Lamoureux
Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. S165-S177 ◽  
Author(s):  
Wei Dai ◽  
Gerard T. Schuster

A plane-wave least-squares reverse-time migration (LSRTM) is formulated with a new parameterization, where the migration image of each shot gather is updated separately and an ensemble of prestack images is produced along with common image gathers. The merits of plane-wave prestack LSRTM are the following: (1) plane-wave prestack LSRTM can sometimes offer stable convergence even when the migration velocity has bulk errors of up to 5%; (2) to significantly reduce computation cost, linear phase-shift encoding is applied to hundreds of shot gathers to produce dozens of plane waves. Unlike phase-shift encoding with random time shifts applied to each shot gather, plane-wave encoding can be effectively applied to data with a marine streamer geometry. (3) Plane-wave prestack LSRTM can provide higher-quality images than standard reverse-time migration. Numerical tests on the Marmousi2 model and a marine field data set are performed to illustrate the benefits of plane-wave LSRTM. Empirical results show that LSRTM in the plane-wave domain, compared to standard reverse-time migration, produces images efficiently with fewer artifacts and better spatial resolution. Moreover, the prestack image ensemble accommodates more unknowns to makes it more robust than conventional least-squares migration in the presence of migration velocity errors.


2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Anitha Koduru ◽  
P. R Mohanty

AbstractIn hydrocarbon exploration, wave-equation migration techniques play an important role in imaging the complex geological structures. Usually, post-stack migration scheme is applied to the seismic data to improve the resolution with restoration of dipping reflectors to their true position. As a result, the migrated time sections are interpretable in terms of subsurface features. As a numerical study, three fault models are considered for the present study. First of all, synthetic time sections are generated corresponding to three models. Later, post stack migration schemes such as Gazdag(PS), Phase-shift with turning rays and reverse time migration (T-K) domain techniques are applied in order to judge the imaging accuracy, preservation of true amplitude and computational speed. All the three post stack time migrated sections delineate the structure with their throw.However, the reverse time migrations (T-K) clearly delineate the reflectors in restoring the throw properly with minimum computational time. In order to test the validity the numerical results, similar exercise has been undertaken using field seismic data of KG basin, India. The results indicates that the field migrated sections are imaged. But, the reverse time migration (T-K ) provides the best subsurface image with restoration of reflectors and collapse of diffracted events with least computational time. Gazdag (PS) and Phase-Shift with turning migrated section shows the reduction of amplitude whereas, the reverse time migration preserved the amplitude fully.


Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. S177-S185 ◽  
Author(s):  
Ekkehart Tessmer

Reverse-time migration is based on seismic forward modeling algorithms, where spatial derivatives usually are calculated by finite differences or by the Fourier method. Time integration in general is done by finite-difference time stepping of low orders. If the spatial derivatives are calculated by high-order methods and time stepping is based on low-order methods, there is an imbalance that might require that the time-step size needs to be very small to avoid numerical dispersion. As a result, computing times increase. Using the rapid expansion method (REM) avoids numerical dispersion if the number of expansion terms is chosen properly. Comparisons with analytical solutions show that the REM is preferable, especially at larger propagation times. For reverse-time migration, the REM needs to be applied in a time-stepping manner. This is necessary because the original implementation based on very large time spans requires that the source term is separable in space and time. This is not appropriate for reverse-time migration where the sources have different time histories. In reverse-time migration, it might be desirable to use the Poynting vector information to estimate opening angles to improve the quality of the image. In the solution of the wave equation, this requires that one calculates not only the pressure wavefield but also its time derivative. The rapid expansion method can be extended easily to provide this time derivative with negligible extra cost.


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