Imaging and velocity estimation with depth‐focusing analysis

Abstract

Prestack depth migration uses two imaging conditions, zero time and zero offset, during downward continuation to form a migrated depth section. When the migration velocities are exact, the two imaging conditions act in a complementary fashion to yield a focused image. When the migration velocities are in error, reflected energy collapses to zero offset at depths that are inconsistent with the zero‐time imaging condition. The result is a deteriorated seismic image. However, by interpreting the nonzero times at which focusing actually occurs, the migration velocities can be updated iteratively in a process called depth‐focusing analysis. To produce a well‐focused seismic image, the goal of depth‐focusing analysis must be the elimination of focusing errors; however, practical considerations can prevent this goal from being achieved. Therefore, to relax the sensitivity of the migrated image to focusing errors, we introduce a nonzero‐time imaging condition by extracting the data along the interpreted surface of focusing from the depth‐focusing analysis volume. This method, called focal‐surface imaging, estimates the results of prestack depth migration using the updated velocities. Depth‐focusing analysis is shown to be a robust approach to velocity estimation and imaging. Limitations arising from constant‐velocity and low‐dip approximations are reduced in the presence of increasing velocities with depth. Lateral velocity errors, sources of exaggerated focusing errors and diverging velocity solutions, can also be addressed by applying a damping factor to the interpreted depth errors. Velocity estimation and focal‐surface imgaging, using iterative prestack depth migration, were applied to a southern North Sea data set. Starting with a regional velocity function, the first iteration provided an updated velocity field that more accurately conformed to the known lithologies. The focal‐surface image, formed from the same iteration, contained significantly more focused energy than the conventional section formed by prestack depth migration. However, structural differences between the two sections indicated the need for another iteration of migration using the updated velocities. The second iteration indicated smaller velocity errors and enough similarity between the migrated section and the new focal‐surface image to indicate that further iterations were unnecessary.

Correlation-based seismic velocity inversion

“…The generalized imaging condition (Doherty & Claerbout, 1974;Yilmaz & Chambers, 1984;MacKay & Abma, 1992;Rickett & Sava, 2002;Sava & Fomel, 2006) allows a finite spatial and temporal shift between the wavefields. The correct velocity model will focus energy in the correlation at zero shift.…”

“…The underlying principle of MVA has not changed, but the precise way in which way the amount of focusing of the image is measured and the migration algorithms themselves have evolved. A few well-known methods found in this class are Differential Semblance Optimization (DSO), proposed by Symes & Carazzone (1991), which uses flatness of image gathers as a measure, and methods based on a generalized imaging condition, proposed by Doherty & Claerbout (1974) and elaborated on by many others (Yilmaz & Chambers, 1984;Stork, 1992;MacKay & Abma, 1992;Rickett & Sava, 2002;Sava & Biondi, 2004;Sava & Fomel, 2006). These methods have been proven successful on data in which multiples are not too strong (Mulder & ten Kroode, 2002;Shen et al, 2003;Dussaud & Symes, 2005;Li & Symes, 2007).…”

Velocity Analysis by Perturbation

“…In DFA. all three assumptions are used (MacKay and Abma, in 1992). In RCA, the assumptions vary with migration types.…”

Probing the extended image volume

“…The traditional RTM image is obtained by extracting the zerolag section from the extended image volume according to the traditional imaging condition. The idea of introducing redundant coordinates in the image domain goes back to the 'survey-sinking' concept of Claerbout (1985), and many variants have been considered over the years (MacKay and Abma, 1992;Berkhout, 1997;Rickett and Sava, 2002;Sava and Fomel, 2006;de Hoop et al, 2006;Yang and Sava, 2010). Stolk and de Hoop (2006) showed that such extended image volumes -in contrast to image volumes obtained by data-binning procedures-are essentially artifactfree, even for complex models.…”