Carl Notfors

3D Prestack Beam Migration with Compensation for Frequency Dependent Absorption and Dispersion

Spatial variations in the transmission properties of the overburden cause seismic amplitude attenuation, wavelet phase distortion and seismic resolution reduction on deeper horizons. This poses problems for the seismic interpretation, tying of migration images with well-log data and AVO analysis. We developed an efficient prestack beam Q migration approach to compensate for the frequency dependent dissipation effects in the migration process. A 3D tomographic amplitude inversion approach may be used for the estimation of absorption model. Examples show that the method can mitigate these frequency dependent dissipation effects caused by transmission anomalies and should be considered as one of the processes for amplitude preserving processing that is important for AVO analysis when transmission anomalies are present.

Taking apart beam migration

The years 2000–2001 sparked a flurry of activity on various flavors of beam migration. GEOPHYSICS papers by Yonghe Sun et al. on slant-stack Kirchhoff migration and Ross Hill on Gaussian-beam migration showed the potential of migration methods that combine aspects of Kirchhoff migration with some novel preprocessing. As a result, a number of variant beam-migration methods have arisen in the last few years, some promising great efficiency and some promising great imaging fidelity. On the other hand, because of beam migrations extra preprocessing, a simple interpretation of beam migration, analogous to that of Kirchhoff migration, has been hard to pin down. In this article, we try to add some intuition to the discussion of beam-migration methods. Our task is challenging since, for the most part, we will describe Gaussian-beam migration, which is possibly the most complicated of the slant-stack migrations. Of course, a successful understanding—even a partial understanding—of this important method will make ...

Delayed-shot 3D depth migration, GEOPHYSICS, 70, E21–E28

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3D prestack depth migration with compensation for frequency dependent absorption and dispersion

Spatial variations in the transmission properties of the overburden cause seismic amplitude attenuation, wavelet phase distortion and seismic resolution reduction on deeper horizons. This poses problems for the seismic interpretation, tying of migration images with well-log data and AVO analysis. We developed a prestack depth Q migration approach to compensate for the frequency dependent dissipation effects in the migration process. A 3D tomographic amplitude inversion approach may be used for the estimation of absorption model. Examples show that the method can mitigate these frequency dependent dissipation effects caused by transmission anomalies and should be considered as one of the processes for amplitude preserving processing that is important for AVO analysis when transmission anomalies are present.

Delayed-shot 3-D Prestack Depth Migration

Summary We present a formulation for delayed-shot migration of marine data in 2-D (plane-wave sources) and in 3-D (linear sources and planar sources). We present speedup factors for these delayed- shot migrations over common-shot migration, and we discuss some sampling theory issues associated with the formation of delayed-shot records. On both synthetic and real data examples, delayed-shot migration has produced images comparable to those from common-shot migration. Introduction The increasing demands of imaging complex geologic structures, for example beneath salt bodies, has led the industry to explore wave equation based prestack depth migration methods that do not suffer from the high frequency and multipathing limitations of Kirchhoff migration. However, common- shot migrations based on wavefield extrapolation are typically more computationally intensive, especially when 3-D migrated common image gathers (CIGs) are output. This relative inefficiency has spurred researchers to seek various ways to speed up their wave-equation migration programs. The computational cost of common-shot migration is roughly the cost of migrating a single shot record multiplied by the number of migrated shots. Reducing the number of shots, and consequently the number of migrations, is an obvious way to improve the total migration efficiency, although it is not obvious that simply decimating shots will allow one to maintain the fidelity of the migrated image. A different approach to reducing the number of shots without decimation is based on the linearity of the wave equation: a linear stacking of wavefields initiated at different shotpoints satisfies the same wave equation as each of the individual wavefields. Therefore, migration can be applied to the superposition of different shot records, allowing the total number of migrations to be reduced. This idea has led to the migration of phase-encoded shot records (Romero et al., 2000), in which a subset of all the shot records are linearly combined together by applying some phase functions chosen to reduce the cross-term artifacts. A specialization of this idea, called delayed-shot migration, has also appeared (Whitmore, 1995; Rietveld, 1995; Duquet et al., 2001; Liu, 2002). In this method, a linear time delay, based on the distance from the shotpoints from some reference location, is used to combine different shot records. The surface data are transformed from the response to point sources to the response to linear or planar sources. In this paper, we review our formulation of delayed-shot migration for 3-D prestack imaging of marine data, discuss its realistic cost impact and illustrate its applicability with a synthetic data example. Delayed-shot migration versus common-shot migration Common-shot migration is performed on individual common-shot records, and the individually migrated records are typically stacked to form the final image of the Earths subsurface. Each migration is performed by using the wave equation to downward continue both the wavefield recorded at the receiver locations and the wavefield initiated at the shotpoint, and combining these downward-continued wavefields with an imaging condition. Since the shotpoint is localized in space, it acts (in 3-D) as a point source, emitting waves that are spherical, at least near the shotpoint. Although a localized source distribution near the Earths surface can be considered as a point source, numerical simulation of 2-D wave behavior using finite difference methods typically contains the tacit assumption that the source is a line source in 3-D, with no spreading in the out-of-plane direction. Then it is possible to perform a decomposition of the recorded data into plane-wave components by using some variant of slant stack processing. This involves applying a linear time delay to each shot record (Figure 1). Specifically, each receiver gather is transformed into plane waves as:

Seismic trace interpolation using the pyramid transform

We present a new method called the pyramid transform for seismic trace interpolation. The pyramid transform is a resampling of data in the f-x-y domain that gives rise to frequency dependent spatial grids with a relationship that the sampling interval is inversely proportional to the frequency. Such transformation is reversible for wavefields. Using prediction filter, we demonstrate that seismic trace interpolation in the pyramid domain is more robust in the presence of noise and conflicting dips than interpolation in the conventional f-x-y domain.

Imaging using multi‐arrivals: Gaussian beams or multi‐arrival Kirchhoff?

Single-arrival Kirchhoff migration is an accurate and reliable depth migration method except in cases of extreme geologic complexity, where it is not as accurate as most wavefield continuation methods. Also, where geology is extremely complex and multipathing occurs, its reliance on migrated image gathers indexed by offset (while more convenient than image gathers indexed by shot number) causes problems for both amplitude analysis and velocity analysis. On the other hand, most wavefield continuation methods are relatively expensive, and problems with amplitudes and migrated image gathers remain. Multiarrival Kirchhoff migration can, to a large degree, overcome the problems associated with both single-arrival Kirchhoff and wavefield continuation methods, but the data flow problems can be serious in a production environment. Gaussian beams can be used to provide accurate Green’s functions for multi-arrival Kirchhoff migration, and in the limiting case, kinematically accurate Gaussian beam migration can be modified to provide accurate amplitudes and migrated gathers indexed by angle.

Subsalt imaging in Walker Ridge, Gulf of Mexico

Summary 3D seismic data from a 40-block area in Walker Ridge was processed through 3D velocity model building. Targeted 3D prestack-depth-migrated lines and slab were generated. The 3D depth-migrated target lines show continuous subsalt horizons extending from salt-free to subsalt locations. Detailed seismic stratigraphy and faults in the Tertiary subsalt section are clearly imaged. These features appear to be genetically influenced by a deeper structural high in the Cretaceous section. Images from a depthmigrated slab further reveal that the faults identified on the target lines are part of a regional normal fault system. The resulting high-quality subsalt images motivated us to conduct a series of tests to study the sensitivity of subsalt images to traveltime computation and migration parameters. Migration examples using different parameters will be shown during the presentation.

Accurate And Efficient Explicit 3-D Migration

This paper describes an approach to the design of accurate filter coefficients for 3D post-stack migration using a modified McClellan transformation matrix and a standard filter synthesis algorithm. With this technique very efficient migration operators with near perfect circularly symmetry and very steep dip capability are constructed. Some practical aspects of explicit migraion are discussed and the high fidelity of the proposed algorithm s demonstrated.

Multi-Azimuth Seismic Data Imaging in the Presence of Orthorhombic Anisotropy

SUMMARY The presence of orthorhombic anisotropy can severely affect the imaging of multi-and wide-azimuth data. Analysis of multi-azimuth (MAZ) data often reveals noticeable fluctuations in moveout between different acquisition directions, preventing constructive summation of MAZ images. Vertical transverse isotropy (VTI) effects can also cause well misties and higher order moveout. We have developed an approach for imaging in the presence of orthorhombic anisotropy. Both synthetic and real data from offshore Australia show that our approach can take into account the co-existing HTI/VTI effects of orthorhombic anisotropic media, reduce the structural discrepancies between seismic images built for different azimuths, producing a constructive summation of MAZ dataset, resolving well misties, and delivering a step-change in the final seismic image quality.