German Höcht

Common‐reflection‐surface stack: Image and attributes

The common‐reflection‐surface stack provides a zero‐offset simulation from seismic multicoverage reflection data. Whereas conventional reflection imaging methods (e.g. the NMO/dip moveout/stack or prestack migration) require a sufficiently accurate macrovelocity model to yield appropriate results, the common‐reflection‐surface (CRS) stack does not depend on a macrovelocity model. We apply the CRS stack to a 2-D synthetic seismic multicoverage dataset. We show that it not only provides a high‐quality simulated zero‐offset section but also three important kinematic wavefield attribute sections, which can be used to derive the 2-D macrovelocity model. We compare the multicoverage‐data‐derived attributes with the model‐derived attributes computed by forward modeling. We thus confirm the validity of the theory and of the data‐derived attributes. For 2-D acquisition, the CRS stack leads to a stacking surface depending on three search parameters. The optimum stacking surface needs to be determined for each point...

Common-reflection-surface stack — a real data example

Abstract The simulation of a zero-offset (ZO) stack section from multi-coverage reflection data is a standard imaging method in seismic processing. It significantly reduces the amount of data and increases the signal-to-noise ratio due to constructive interference of correlated events. Conventional imaging methods, e.g., normal moveout (NMO)/dip moveout (DMO)/stack or pre-stack migration, require a sufficiently accurate macro-velocity model to yield appropriate results, whereas the recently introduced common-reflection-surface stack does not depend on a macro-velocity model. For two-dimensional seismic acquisition, its stacking operator depends on three wavefield attributes and approximates the kinematic multi-coverage reflection response of curved interfaces in laterally inhomogeneous media. The common-reflection-surface stack moveout formula defines a stacking surface for each particular sample in the ZO section to be simulated. The stacking surfaces that fit best to actual events in the multi-coverage data set are determined by means of coherency analysis. In this way, we obtain a coherency section and a section of each of the three wavefield attributes defining the stacking operator. These wavefield attributes characterize the curved interfaces and, thus, can be used for a subsequent inversion. In this paper, we focus on an application to a real land data set acquired over a salt dome. We propose three separate one-parametric search and coherency analyses to determine initial common-reflection-surface stack parameters. Optionally, a subsequent optimization algorithm can be performed to refine these initial parameters. The simulated ZO section obtained by the common-reflection-surface stack is compared to the result of a conventional NMO/DMO/stack processing sequence. We observe an increased signal-to-noise ratio and an improved continuity along the events for our proposed method — without loss of lateral resolution.

Seismics and optics: hyperbolae and curvatures

We rederive and generalize hyperbolic moveout formulae for the common-midpoint (CMP) gather and for the zero-offset (ZO) section that can be efficiently used for macro-model-independent reflection imaging in two-dimensional media. The hyperbolic moveout formulae for the common-midpoint gather are obtained from different Taylor series expansions of a particular parametric moveout surface defined in the multicoverage data space. Such a moveout surface involves three kinematic wave-field attributes of two hypothetical waves, which have to be determined by a coherency analysis. By using hyperbolic moveout curves in the CMP gather and in the ZO section one can determine these attributes in two steps. The relationships between the local shapes of the interfaces and the attributes of the hypothetical wave-fields attributes are considered by means of geometrical optics. The determination of these attributes allows to perform a macro-model-independent ZO simulation and a subsequent inversion.

Seismic constant-velocity remigration

When a seismic common midpoint (CMP) stack or zero‐offset (ZO) section is depth or time migrated with different (constant) migration velocities, different reflector images of the subsurface are obtained. If the migration velocity is changed continuously, the (kinematically) migrated image of a single point on the reflector, constructed for one particular seismic ZO reflection signal, moves along a circle at depth, which we call the Thales circle. It degenerates to a vertical line for a nondipping event. For all other dips, the dislocation as a function of migration velocity depends on the reflector dip. In particular for reflectors with dips larger than 45°, the reflection point moves upward for increasing velocity. The corresponding curves in a Time‐migrated section are parabolas. These formulas will provide the seismic interpreter with a better understanding of where a reflector image might move when the velocity model is changed. Moreover, in that case, the reflector image as a whole behaves to some ex...

Common-Reflection-Surface Stack for Converted Waves

The finite-offset (FO) common-reflection-surface (CRS) stack has been shown to be able to handle not only P-P or S-S but also arbitrarily converted reflections. It can provide different stack sections such as common-offset (CO), common-midpoint (CMP) and common-shot (CS) sections with significantly increased signal-to-noise ratio from the multi-coverage pre-stack seismic data in a data-driven way. It is our purpose in this paper to demonstrate the performance of the FO CRS stack on data involving converted waves in inhomogeneous layered media. In order to do this we apply the FO CRS stack for common-offset to a synthetic seismic data set involving P-P as well as P-S converted primary reflections. We show that the FO CRS stack yields convincing improvement of the image quality in the presence of noisy data and successfully extracts kinematic wavefield attributes useful for further analyses. The extracted emergence angle information is used to achieve a complete separation of the wavefield into its P-P and P-S wave components, given the FO CRS stacked horizontal and vertical component sections.

The common reflecting element (CRE) method revisited

The common reflecting element (CRE) method is an interesting alternative to the familiar methods of common midpoint (CMP) stack or migration to zero offset (MZO). Like these two methods, the CRE method aims at constructing a stacked zero-offset section from a set of constant-offset sections. However, it requires no more knowledge about the generally laterally inhomogeneous subsurface model than the near-surface values of the velocity field. In addition to being a tool to construct a stacked zero-offset section, the CRE method simultaneously obtains information about the laterally inhomogeneous macrovelocity model. An important feature of the CRE method is that it does not suffer from pulse stretch. Moreover, it gives an alternative solution for conflicting dip problems. In the 1-D case, CRE is closely related to the optical stack. For the price of having to search for two data-derived parameters instead of one, the CRE method provides important advantages over the conventional CMP stack. Its results are similar to those of the MZO process, which is commonly implemented as an NMO correction followed by a dip moveout (DMO) correction applied to the original constant-offset section. The CRE method is based on 2-D kinematic considerations only and is not an amplitude-preserving process.

Seismic and Optics - Hyperbolae and Curvatures

An important part of macro-velocity-independent seismic imaging is the analytic description of the kinematic reflection response of curved reflectors below inhomogeneous media.

Applications of the common‐reflection‐surface stack

The simulation of a zero-offset stack section from multicoverage seismic reflection data for 2-D media is a widely used seismic reflection imaging method that reduces the amount of data and enhances the signal-to-noise ratio. The aim of the common-reflection-surface stack is not only to provide a well-simulated zero-offset stack section but also to determine certain attributes of hypothetical wavefronts at the surface useful for a subsequent inversion.

A new look at subsurface illumination in seismic imaging

To improve the illumination of the subsurface is the purpose of every seismic acquisition and imaging method. The success of standard seismic/stack imaging routines, such as Kirchhoff-type Pre-stack Depth Migration or NMO/DMO/stack depends on the required macro-velocity model. From kinematic point of view they also implicitly assume with respect to the illumination a fixed shape of the reflector. In contrast a common-reflection surface stack is a selective stack depending only on the near-surface velocity. It accounts for different reflector shapes and enables us to establish the macro velocity model after the zero-offset simulation. INTRODUCTION In this paper we give an insight into different stacking routines from a kinematic point of view. As representative for standard imaging methods we have chosen the NMO/DMO/stack and the pre-stack depth migration (PreSDM). The latter two processes are for comparison implemented in the form of unweighted Kirchhoff-type (target-oriented) procedures. With the objective to improve images and the macro-model determination we introduce the so-called common-reflection-surface (CRS) stack, which is closely related to “multifocusing” proposed by (Berkovitch et al., 1994). The CRS stack provides in our opinion a new powerful approach to construct simulated zero-offset (ZO) sections from multicoverage reflection data. In addition to the simulated ZO section we obtain important wavefield attributes that enable us to construct the macro-velocity model ((Hubral, 1983), (de Bazelaire and Viallix, 1994)). MACRO-VELOCITY-MODEL BASED IMAGING To explain in simple terms the ”standard illumination” of a subsurface reflector point R involved in all standard reflection imaging methods, we have constructed Fig. 1. This 1email: ghoecht@gpiwap4.physik.uni-karlsruhe.de 55 56 shows a dome-like subsurface reflector in the lower constant-velocity half space and traveltime curves from the reflector in the midpoint(x)-half-offset(h) and time(t) domain. All common-offset (CO) reflection-time curves define the so-called CO-reflection-time surface of the subsurface reflector in the (x-h-t) space. The reflections from the subsurface reflector pointR are found in the (x-h-t) space along the so-called common-reflectionpoint (CRP) trajectory, which is confined to the CO-reflection-time surface.There exists a simple analytic formula in the constant-velocity case for the CRP trajectory. NMO/DMO/Stack In NMO/DMO/stack the reflections from point R along the CRP trajectory are transported into pointP0 by summing the seismic data in the (x-h-t) space along the Kirchhofftype MZO-stacking surface. This corresponds to the following traveltime surface: First, construct the zero-offset (ZO) depth-migrated image of point P0, which is the lower halfcircle isochrone of P0 centered at X0 in Fig. 1. Then demigrate this isochrone back into the (x-h-t) domain for the respective offset 2h. PreSDM In pre-stack depth migration the reflections from point R distributed along the CRP trajectory (bold curve in the (x-h-t) space in Fig. 1 and 2) are transported into point R. This is achieved by summing all seismic data in the (x-h-t) space along the Kirchhoff-type CO migration pre-stack surface. This surface corresponds to the traveltime surface in the (x-h-t) space constructed for a ”diffractor point” at R. CRS Stacking In Fig. 2, we have placed into point R an arc pertaining to the reflector circle CR. This arc becomes in 3D a surface, which justifies the terminology CRS. The arc is assumed to have the same orientation and radius of curvature as the searched-for reflector at R. The trajectories define a travel-time surface in (x-h-t) space, which we call the CRS surface for pointR. Our purpose is to find this surface and then use it as a stacking surface for pointP0. This is implemented in the following way. Select an arbitrary point P0 in the (x-t) plane, for which one wants to find the amplitude value of the CRS stack. Affix at the resulting ZO isochrone in the depth domain different circular reflector arcs (”test mirrors”) and perform for each of them a coherency analysis along the corresponding CRS surface in the time domain. For the CRS surfaces of those test mirrors, which lead to large coherency values, we subsequently perform the CRS stack. These surfaces will obviously pertain to actual reflector mirrors that locally approximate the searched-for reflectors. As search parameters we use, at X0, the incidence angle and the radius of a hypothetical wavefront RN that results if the cho-