VELOCITY-ESTIMATION IMPROVEMENTS AND MIGRATION/DEMIGRATION USING CRS WITH CONTINUING DECONVOLUTION IN THE TIME DOMAIN

To obtain an image of the earth’s subsurface, time-imaging methods can be applied, as they are reasonably fast, less sensitive to velocity model errors than depth-imaging methods and, usually, easy to parallelize. A powerful tool for time-imaging consists of a series of prestack time-migrations and demigrations. We apply multi-parameter stacking techniques to obtain an initial time-migration velocity model. The velocity model building proposed here is based on the kinematic wavefield attributes of the common-reflection surface method. A subsequent refinement of the velocities uses a coherence filter which is based on a predetermined threshold, and followed by an interpolation and smoothing. Then, we perform a migration deconvolution to obtain the final time-migrated image. The migration deconvolution consists of one iteration of least-squares migration with an estimated Hessian. We estimate the Hessian by non-stationary matching filters, i.e., in a data-driven fashion. The model building uses the framework of the common-reflection-surface , and the migration deconvolution is fully automated. Therefore, minimal user interaction is required to carry out both the velocity model refinement and the image update. We apply the suggested approaches of velocity refinement and migration deconvolution to complex synthetic and field data. INTRODUCTION Time migration is an attractive tool to produce subsurface images because it is reasonably fast, less sensitive to the model errors than depth migration and, usually, a massively parallelized technique. A highly focused time image is, however, achievable only with sufficiently well-determined migration velocities. Thus, a refinement of the initial time-migration velocities is often applied to obtain an improved final image. Also, time migration is derived by considering many assumptions, among others a straight ray propagation, regularly sampled seismic data and an infinite migration aperture. However, these assumptions are violated when sufficiently complex subsurface structures and field data are considered. Thus, time-migrated images usually suffer from imperfections of the operator, exhibiting artifacts (Hertweck et al., 2003), such as the commonly observed migration swings. Conventionally, a residual moveout (RMO) analysis is used to reduce the impact of the model errors on the image, (e.g., Yilmaz (2001). The RMO analysis is an iterative approach to update velocities based on the analysis of the flattening of events in the common-image gathers (CIG) after time migration. Another approach to perform the velocity update after prestack time-migration is common-offset migration followed by application of inverse normal moveout (NMO) and subsequent velocity analysis on the newly generated gathers. The obtained gathers contain time-migrated reflections with approximately hyperbolic moveout and are therefore suitable for classical one-dimensional or multidimensional velocity analysis (Dell et al., 2012). To reduce migration artifacts, several image-enhancement techniques, e.g., dipor structure-oriented filters, are usually applied after time migration. These methods, however, can introduce a certain smoothing into the migrated images, which may increase uncertainties in 52 Annual WIT report 2018 fault interpretation. A comprehensive imaging theory based on migration and demigration in the depth domain is presented by Hubral et al. (1996) and Tygel et al. (1996). In their work, Huygens surfaces and isochrons form the central ingredients, and are combined with proper amplitude weighting to preserve amplitudes. Similar to the works mentioned above, Iversen et al. (2012) presented a time-based approach. They used reflection times, slopes, and curvatures as parameters to perform migration and demigration. Here, we propose a technique to solve both time-migration problems mentioned earlier, i.e., migration artifacts and velocity analysis. Our method is based on the duality of modeling/imaging operators (see Claerbout et al., 1996). For one thing, time migration can be achieved by summation over traces (amplitude stacking) which aims to focus events, correct dips, unfold triplications, and collapse diffractions. Following Yilmaz (2001), a corresponding migration operator can be described by a double-square-root equation. While for the other thing, time demigration can be carried out by performing a semicircle superposition (amplitude spreading) which aims to restore (model) seismic data based on provided reflectivity models. The smearing (demigration) of the amplitudes can be described by a single-square-root equation. In this case, we use the same traveltimes for both steps. The advantage of the cascaded forward and backward transformation is data enhancement and regularization due to the incorporated summation of the migration, which reduces noise. Furthermore, a general conflicting dip handling is naturally incorporated in the migration process. On the one hand, a correctly migrated image should not contain conflicting dips with the exception of multiples. On the other hand, the demigration reconstructs the dips in the original unmigrated domain. A condition to perform these steps is a suitable velocity model, which can be automatically generated via, e.g., the common-reflection-surface (CRS) method (Jäger et al., 2001). In the first part of the paper, we suggest an efficient strategy to calculate an original starting velocity model and introduce a refinement of the migration velocities. The method utilizes kinematic wavefield attributes of the CRS method, i.e., angles and curvatures of wavefronts (Hubral, 1983) and also uses a coherence filtering of the velocities, which further conditions the final velocity model for migration. In the second part, we describe the migration and demigration in terms of traveltimes. Furthermore, we briefly review the theory of least-squares migration and show that our time-migration/demigration approach can also be used for migration deconvolution. To do this, we estimate matching filters, which are convolved with the migrated image to enhance image quality. Finally, we demonstrate the applicability of the suggested fully automated workflow for complex synthetic and field-data examples. CONCEPTUAL FRAMEWORK Automatic velocity model building using CRS We perform a multidimensional coherence analysis using the implicit CRS method (Vanelle et al., 2010) to extract kinematic wavefield attributes (Hubral, 1983). In principle, any double-square-root (DSR) expression (e.g., Walda et al., 2017) can be used instead of implicit CRS. An automated local coherence analysis employing the normalized semblance coefficient (Neidell and Taner, 1971) picks at every data point a subset of CRS attributes, and determines by optimization the best set consistent with the data (Nelder and Mead, 1965). The obtained kinematic wavefield attributes are described as different order terms of a Taylor series expansion of the squared hyperbolic traveltime (Müller, 1999): t(∆x,∆h) = (t0 + p∆x) 2 + 2t0(N∆x 2 +M∆h) . (1a) p = ∂t ∂x ∣∣∣∣ x0,h0 , N = ∂t ∂x2 ∣∣∣∣ x0,h0 , M = ∂t ∂h2 ∣∣∣∣ x0,h0 (1b) p = 2 sinα v0 , , M = cos α v0RNIP , N = cos α v0RN (1c) The displacement between the point under consideration (xm, h) ,denoting midpoint and half-offset, and a central point (x0, h0) is ∆x = xm − x0,∆h = h − h0. The traveltime at the expansion point x0, h0 is denoted by t0 and the derivatives are p,M, and N . The near-surface velocity v0 has to be provided. An exploding-reflector experiment can be used to illustrate the physical meaning of the CRS attributes (see Figure 1). The angle α denotes the incidence angle of the emerging ray from a fictitous source at Annual WIT report 2018 53 the normal-incident-point (NIP). RNIP is the radius of curvature of the emerging wavefront at the surface from a point source at NIP. RN is the radius of curvature of the emerging wavefront at the surface of an exploding-reflector segment around NIP. Then, α,RNIP and RN , extracted by local coherence analysis