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ABSTRACT Least-squares migration is an advanced imaging technique capable of producing images with improved spatial resolution, balanced illumination, and reduced migration artifacts; however, the prohibitive computational cost poses a great challenge for its practical application. We have incorporated the beam methodology into the implementation of Kirchhoff time modeling/migration and developed a fast common-offset least-squares Kirchhoff beam time migration (LSKBTM). Different from conventional Kirchhoff time modeling/migration in which the seismic data are modeled/migrated trace by trace, the mapping operation in Kirchhoff beam time modeling/migration is performed in terms of beam components and is performed only at sparsely sampled beam centers. Therefore, the computational cost of LSKBTM is significantly reduced in comparison with that of least-squares Kirchhoff time migration (LSKTM). In addition, based on the second-order Taylor expansion of the diffraction traveltime, we introduce a quadratic correction term into the inverse/forward local slant stacking, effectively enhancing the computational accuracy of LSKBTM. We used 2D synthetic and 3D field data examples to verify the effectiveness of our method. Our results indicate that LSKBTM can produce images comparable with those of LSKTM, but at considerably reduced computational cost.
- Asia > Middle East > Saudi Arabia (1.00)
- Asia > Middle East > Yemen (0.93)
- Africa > Sudan (0.93)
- (4 more...)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)
Abstract Opportunities and challenges exist for imaging seismic data acquired using conventional marine sources and receivers on the seafloor. Compared with conventional imaging of sea-surface streamer data, seabed acquisition and processing offer some opportunities to provide higher value of information. One of the opportunities is to use P-wave to S-wave converted reflection energy (PS imaging). Challenges include overcoming the effects of current seafloor receiver spacing, which can be large enough to negate the promised resolution gains and complicate the velocity model-building workflow. A synthetic data set illustrates possible imaging improvements that can result from seafloor acquisition as well as image degradation that can result when seafloor receivers are separated by typical current distances.
Summary Seismic imaging (migration) has historically been used to clarify structural targets and to remove diffraction noise from stratigraphic targets. Seismic inversion has taken many forms, including single-trace inversion for impedance contrasts, inverting moveout or waveforms to obtain seismic velocity, and even analyzing amplitudes of unmigrated or migrated data to determine rock properties. In the past, these processes were kept separate from one another. In the present, they are being used more and more in combination. In an ideal future, they will be completely combined into a single process called inversion. I describe how we have arrived where we are, problems with the current state of the art, and what might limit our progress toward the ideal future.
- Europe (0.30)
- North America > United States > Montana > Roosevelt County (0.24)
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.71)
Summary Seismic data acquired over unconventional reservoirs are often analyzed for amplitude-versus-offset (AVO), amplitude-versus-azimuth (AVAZ), or velocity-versus-azimuth (VVAZ) behavior. These analyses, especially the azimuthal analyses, can be useful in determining reservoir properties useful for directional drilling such as fracture orientation or (possibly) stress direction. If the data are not migrated, lateral velocity variations can distort the analysis results; migration can correct the distortions. Migration can produce distortions of its own, however, particularly when the acquisition is (conventionally) sparse; some distortions can be subtle, and it is a challenge to account for all of them. As an example, I show how migration AVAZ distortion can result from conventional acquisition, in the form of azimuthal amplitude modulation due to migration anti-aliasing.
ABSTRACT Seismic migration is a multichannel process, in which some of the properties depend on various grid spacings. First, there is the acquisition grid, which actually consists of two grids: a grid of source locations and, for each source location, a grid of receiver locations. In addition, there is a third grid, the migration grid, whose spacings also affect properties of the migration. Sampling theory imposes restrictions on migration, limiting the frequency content that can be migrated reliably given the grid spacings. The presence of three grids complicates the application of sampling theory except in unusual situations (e.g., the isolated migration of a single shot record). I analyzed the effects of the grids on different types of migration (Kirchhoff, wavefield extrapolation migration, and slant-stack migration), specifically in the context of migration operator antialiasing. I evaluated general antialiasing criteria for the different types of migration; my examples placed particular emphasis on one style of data acquisition, orthogonal source and receiver lines, which is commonly used on land and which presents particular challenges for the analysis. It is known that migration artifacts caused by inadequate antialiasing can interfere with velocity and amplitude analyses. I found, in addition, that even migrations with adequate antialiasing protection can have the side effect of inaccurate amplitudes resulting from a given acquisition, and I tested how this effect can be compensated.
Summary Gaussian beams are often used to represent Greenโs functions in three-dimensional Kirchhoff-type true-amplitude migrations because such migrations yield superior images to similar migrations using classical ray-theoretic Greenโs functions. Typically, the integrand of a migration formula consists of two Greenโs functions, each describing propagation to the image pointโone from the source position and the other from the receiver position. The use of Gaussian beams to represent each of these Greenโs functions in 3D introduces two additional double integrals when compared to a Kirchhoff migration using ray-theoretic Greenโs functions, thereby adding a significant computational burden. Hill [2001] proposed a method for reducing those four integrals to two, compromising slightly on the full potential quality of the Gaussian beam representations for the sake of more efficient computation. That approach requires a two-dimensional steepest descent analysis for the asymptotic evaluation of a double integral. The method requires evaluation of the complex traveltimes of the Gaussian beams as well as the amplitudes of the integrands at the determined saddle points. In addition, it is necessary to evaluate the determinant of a certain (Hessian) matrix of second derivatives. Hill [2001] did not report on this last part; thus, his proposed migration formula is kinematically correct but lacks correct amplitude behavior. Here we report on the derivation of a formula for that Hessian matrix in terms of dynamic ray tracing quantities. Introduction True-amplitude Kirchhoff migration requires downward propagation of the source wavefield and downward propagation of the observed data to image points in the subsurface. The downward propagations are accomplished using Greenโs identity, operating on data evaluated along one surface to obtain data at a deeper surface via a convolution-type integral of the data with a Greenโs function. We also also downward propagate the sources other than the point source we assume in this report as a convolution-type integral. This is Kirchhoff migration [Schneider, 1978]. Each of these propagation processes requires evaluation of Greenโs functions at the image point, one from a source, one from a receiver. Then, to obtain the Gaussian beam representation of each Greens function in 3D, it is necessary to carry out a 2D integration of Gaussian beams over all takeoff angles where rays are in the vicinity of the image point. By contrast, the Greens functions for standard Kirchhoff migration, derived from classical asymptotic ray theory, require only a complex function evaluation with no additional integrations. Multiplying the Greenโs functions together, as required by migration theory, results in the need to evaluate four nested integrals for Gaussian beam migration, as opposed to the multiplication of two complex numbers for classical ray-theoretic Greenโs functions. Hill [2001] suggested a method for reducing those four additional integrals to two. Hillโs method first replaces integrals over source and receiver ray parameters with integrals over midpoint and offset ray parameters. He then applies the method of steepest descent for integrals with complex exponents [Bleistein, 1984] to the (innermost) integrals over offset parameters, leaving the (outermost) integrals over midpoint parameters to be computed numerically.
Prestack depth migration is the most glamorous step of seismic processing because it transforms mere data into an image, and that image is considered to be an accurate structural description of the earth. Thus, our expectations of its accuracy, robustness, and reliability are high. Amazingly, seismic migration usually delivers. The past few decades have seen migration move from its heuristic roots to mathematically sound techniques that, using relatively few assumptions, render accurate pictures of the interior of the earth. Interestingly, the earth and the subjects we want to image inside it are varied enough that, so far, no single migration technique has dominated practical application. All techniques continually improve and borrow from each other, so one technique may never dominate. Despite the progress in structural imaging, we have not reached the point where seismic images provide quantitatively accurate descriptions of rocks and fluids. Nor have we attained the goal of using migration as part of a purely computational process to determine subsurface velocity. In areas where images have the highest quality, we might be nearing those goals, collectively called inversion. Where data are more challenging, the goals seem elusive. We describe the progress made in depth migration to the present and the most significant barriers to attaining its inversion goals in the future. We also conjecture on progress likely to be made in the years ahead and on challenges that migration might not be able to meet.
- North America > United States > Alaska > Arctic Ocean > Arctic Basin > Amerasia Basin > Canadian Basin (0.89)
- Europe > United Kingdom > North Sea (0.89)
- Europe > Norway > North Sea (0.89)
- (2 more...)
Taking apart beam migration
Gray, Samuel H., Xie, Yi, Notfors, Carl, Zhu, Tianfei, Wang, Daoliu, Ting, Chu-Ong
The years 2000โ2001 sparked a flurry of activity on various flavors of beam migration. G 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 migration's 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 understandingโeven a partial understandingโof this important method will make it easier to understand the entire family of newly emerging beam-migration techniques.
- Transportation (1.00)
- Energy > Oil & Gas > Upstream (1.00)
Gaussian-beam depth migration and related beam migration methods can image multiple arrivals, so they provide an accurate, flexible alternative to conventional single-arrival Kirchhoff migration. Also, they are not subject to the steep-dip limitations of many (so-called wave-equation) methods that use a one-way wave equation in depth to downward-continue wavefields. Previous presentations of Gaussian-beam migration have emphasized its kinematic imaging capabilities without addressing its amplitude fidelity. We offer two true-amplitude versions of Gaussian-beam migration. The first version combines aspects of the classic derivation of prestack Gaussian-beam migration with recent results on true-amplitude wave-equation migration, yields an expression involving a crosscorrelation imaging condition. To provide amplitude-versus-angle (AVA) information, true-amplitude wave-equation migration requires postmigration mapping from lateral distance (between image location and source location) to subsurface opening angle. However, Gaussian-beam migration does not require postmigration mapping to provide AVA data. Instead, the amplitudes and directions of the Gaussian beams provide information that the migration can use to produce AVA gathers as part of the migration process. The second version of true-amplitude Gaussian-beam migration is an expression involving a deconvolution imaging condition, yielding amplitude-variation-with-offset (AVO) information on migrated shot-domain common-image gathers.
- North America > United States > Colorado (0.28)
- North America > Canada (0.28)
TTI Wave-equation Migration
Bale, Richard A. (Stanford University) | Gray, Samuel H. (Stanford University) | Graziella, M. (Stanford University)
INTRODUCTION Summary We describe a phase-shift plus interpolation (PSPI) method for wave-equation migration in TTI media. To apply the PSPI methodology for anisotropy, we generate reference operators based upon phase error criteria with respect to the symmetry axis direction, and exploit correlations between parameters. The method is demonstrated on an elastic synthetic dataset generated over a thrust-belt setting, as found in the Canadian Foothills. Many hydrocarbon reservoirs, such as those in the Rocky Mountain Foothills of western Canada, lie below dipping clastic sequences characterized by tilted transverse isotropy (TTI) (Isaac and Lawton, 2004). Several authors (e.g. Vestrum et al., 1999) have shown the importance of accounting for the tilt of the symmetry axis when imaging such reservoirs using anisotropic migration, in order to correctly locate structures laterally. To realize this goal, typically Kirchhoff algorithms have been upgraded to handle TTI. Improved results can be obtained using Gaussian beam TTI migration (Zhu et al., 2005). As for isotropic migration, superior results for significantly greater effort are expected from the use of wave-equation migration methods on TTI data. In contrast to ray-tracing based methods, wave-equation migration is able to handle multi-pathing in a natural way, and is not based upon a high-frequency approximation to the wave equation. Shan and Biondi (2005) have demonstrated both 2-D and 3-D implementations of TTI wave-equation migration, using an implicit operator with explicit correction, applied in the space-frequency (x-y-f) domain. For isotropic migration, the Hale-McLellan transform (Hale, 1991) offers an efficient method to produce accurate 3-D responses (without numerical anisotropy) using an x-y-f domain operator. However, since Hale-McLellan is based on circular symmetry, this luxury is not obviously available for TTI, which lacks such symmetry. An alternative approach to wave-equation migration is based upon applying phase-shift operators in the wavenumber-frequency (k-f) domain. This choice has advantages of operator stability and accurate steep dip behavior. The main drawback, compared to x-f migration, is that lateral variations in the medium are not naturally accommodated by k-f domain operators. For isotropic migration, a number of methods have been proposed to address this issue, including: phase-shift plus interpolation (PSPI), split-step and Fourier finite difference. Generally, all of these are based upon the idea of migrating with a number of reference velocities, and then applying some form of correction to improve the fidelity for lateral velocity variations. We first outline the basic phase-shift operator, and then describe how PSPI and split-step methods can be adapted for the TTI algorithm. Split-step correction for TTI The accuracy of the operators may be enhanced by application of a split-step correction. The standard splitstep correction (Stoffa et al., 1990) can be thought of as a vertical shift to account for the difference between the reference velocity and the actual (x-dependent) velocity. The result is that near-horizontal reflectors are accurately imaged, while dipping reflectors have residual errors. In the presence of TTI, it is often assumed that the symmetry axis is normal to bedding (in fact, this assumption may beneeded to determine the axis direction
- Geology > Structural Geology > Tectonics > Compressional Tectonics > Fold and Thrust Belt (0.55)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock (0.37)