Survey Sinking Research Articles

Dreamlet source‐receiver survey sinking prestack depth migration

ABSTRACTSurvey sinking migration downward continues the entire surface observed multi‐shot data to the subsurface step by step recursively. Reflected energy from reflectors at current depth appear at zero time and zero offset in the extrapolated wavefield. The data (seismic records) of t > 0 at this depth are equivalent to the data acquired by a survey system deployed at this depth. This is the reason to name the process ‘survey sinking’. The records of negative time need not to be further propagated since they carry no information to image structures beneath the new survey system. In this paper, we combine survey sinking with dreamlet migration. The dreamlet migration method decomposes the seismic wavefield and one‐way wave propagator by complete time‐space localized bases. The localization on time gives flexibility on time‐varying operations during depth extrapolation. In dreamlet survey sinking migration, it only keeps the data for imaging the structures beneath the sunk survey system and gets rid of the data already used to image structures above it. The deeper the depth is, the shorter is the valid time records of the remaining data and less computation is needed for one depth step continuation. For data decomposition, in addition to time axis, dreamlet survey sinking also decomposes the data for source and receiver gathers, which is a fully localized decomposition of prestack seismic data. A three‐scatter model is first used to demonstrate the computational feature and principle of this method. Tests on the two‐dimensional SEG/EAGE salt model show that with reduced data sets the proposed method can still obtain good imaging quality on complex geology structures and a strong velocity contrast environment.

Wave-equation global datuming based on the double square root operator

Current schemes for removing near-surface effects in seismic data processing use either static corrections or wave-equation datuming (WED). In the presence of rough topography and strong lateral velocity variations in the near surface, the WED scheme is the only option available. However, the traditional procedure of WED downward continues the sources and receivers in different domains. A new wave-equation global-datuming method is based on the double-square-root operator, implementing the wavefield continuation in a single domain following the survey sinking concept. This method has fewer approximations and therefore is more robust and convenient than the traditional WED methods. This method is compared with the traditional methods using a synthetic data example.

Full-wave-equation depth extrapolation for migration

Most of the traditional approaches to migration by downward extrapolation suffer from inaccuracies caused by using one-way propagation, both in the construction of such propagators in a variable background and the suppression of propagating waves generated by, e.g., steep reflectors. We present a new mathematical formulation and an algorithm for downward extrapolation that suppress only the evanescent waves. We show that evanescent wave modes are associated with the positive eigenvalues of the spatial operator and introduce spectral projectors to remove these modes, leaving all propagating modes corresponding to nonpositive eigenvalues intact. This approach suppresses evanescent modes in an arbitrary laterally varying background. If the background velocity is only depth dependent, then the spectral projector may be applied by using the fast Fourier transform and a filter in the Fourier domain. In computing spectral projectors, we use an iteration that avoids the explicit construction of the eigensystem. Moreover, we use a representation of matrices leading to fast matrix-matrix multiplication and, as a result, a fast algorithm necessary for practical implementation of spectral projectors. The overall structure of the migration algorithm is similar to survey sinking with an important distinction of using a new method for downward continuation. Using a blurred version of the true velocity as a background, steep reflectors can be imaged in a 2D slice of the SEG-EAGE model.

DSR One‐Way Wave Equation Prestack τ Migration

AbstractBy transforming the classical double‐square‐root (DSR) one‐way wave equation from depth domain to two‐way vertical traveltime (τ) domain, we derive a one‐way DSR wave propagator which can be applied to implement the imaging concept of “survey sinking”. Its algorithm to recursively continue the source and receiver wavefields, which includes a wavenumber domain phase shift in a constant background medium followed by a phase correction in the space domain that accommodates lateral velocity variations, can tackle the effects of lateral velocity variations under complex overburdens. Applying the zero‐offset, zero‐time imaging condition, we develop a DSR equation prestack migration method in which the wavefield continuation and imaging are operated in the τ space. To address the problems that full volume 3‐D DSR equation migration could meet with in practical application, we present a feasible common‐azimuth prestack τ migration approach based on the theory of cross‐line common‐offset migration. Numerical tests show that our prestack τ migration provides a significant improvement over the traditional prestack time migration in laterally varying media.

Equivalence of source‐receiver migration and shot‐profile migration

At first glance, shot-profile migration (Jacobs, 1982) and source-receiver (survey-sinking) migration (Claerbout, 1985) seem to be substantially different algorithms. The basic principles used by the two schemes are different. Shot-profile migration is performed by independently propagating the source wavefield and the receiver wavefield. The image is obtained by crosscorrelating the two wavefields (possibly normalized by the amplitude of the source wavefield). Source-receiver migration is based on the concept of survey sinking, by which we recursively synthesize equivalent data sets at increasing depth. At each depth step, imaging is performed by extracting the wavefield at zero time. Recently, the issue of the relation between shot-profile migration and source-receiver migration has become more relevant because of two important developments: (1) the increase in the practical applications of 3D prestack migration by wavefield continuation for imaging complex structures, and (2) the introduction of methods for computing angle-domain common-image gathers (ADCIG), both for velocity estimation (Biondi and Sava, 1999; Prucha et al., 1999; Clapp and Biondi, 2000) and for amplitude variation with angle (AVA) analysis (de Bruin et al., 1990; Wapenaar et al., 1999; Sava et al., 2001).