Delayed-shot 3D depth migration

For 3D seismic imaging in structurally complex areas, the use of migration by wavefield extrapolation has become widespread. By its very nature, this family of migration methods operates on data sets that satisfy a wave equation in the context of a single, physically realizable field experiment, such as a common-shot record. However, common-shot migration of data recorded over dipping structures requires a migration aperture much larger than the recording aperture, resulting in extra computations. A different type of wave-equation record, the response to a linear or planar source, can be synthesized from all the common-shot records. Synthesizing these records from common-shot records involves slant-stack processing, or applying delays to the various shots; we call these records delayed-shot records. Delayed-shot records don't suffer from the aperture problems of common-shot records since their recording aperture is the length of the seismic survey. Consequently, delayed-shot records hold potential for efficient, accurate imaging by wavefield extrapolation. We present a formulation of delayed-shot migration in 2D and 3D (linear sources) and its application to 3D marine streamer data. This formulation includes a discussion of sampling theory issues associated with the formation of delayed-shot records. For typical marine data, 2D and 3D delayed-shot migration can be significantly more efficient than common-shot migration. Synthetic and real data examples show that delayed-shot migration produces images comparable to those from common-shot migration.

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Simulation of complete seismic surveys for evaluation of experiment design and processing

Geophysics ◽

10.1190/1.1443976 ◽

1996 ◽

Vol 61 (2) ◽

pp. 496-508 ◽

Cited By ~ 7

Author(s):

Turgut Özdenvar ◽

George A. McMechan ◽

Preston Chaney

Keyword(s):

Composite System ◽

Real Data ◽

Seismic Survey ◽

Data Sets ◽

Seismic Surveys ◽

Depth Migration ◽

Data Line ◽

Processing Algorithms ◽

The Cost ◽

Survey Designs

Synthesis of complete seismic survey data sets allows analysis and optimization of all stages in an acquisition/processing sequence. The characteristics of available survey designs, parameter choices, and processing algorithms may be evaluated prior to field acquisition to produce a composite system in which all stages have compatible performance; this maximizes the cost effectiveness for a given level of accuracy, or for targets with specific characteristics. Data sets synthesized for three salt structures provide representative comparisons of time and depth migration, post‐stack and prestack processing, and illustrate effects of varying recording aperture and shot spacing, iterative focusing analysis, and the interaction of migration algorithms with recording aperture. A final example demonstrates successful simulation of both 2-D acquisition and processing of a real data line over a salt pod in the Gulf of Mexico.

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An explicit, unconditionally stable, 15‐degree depth migration and modeling algorithm implemented in poststack, directional, and prestack modes

Geophysics ◽

10.1190/1.1443161 ◽

1991 ◽

Vol 56 (9) ◽

pp. 1412-1422

Author(s):

Alvin K. Benson

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Three Dimensional ◽

Inhomogeneous Media ◽

Unconditional Stability ◽

Data Sets ◽

Unconditionally Stable ◽

Depth Migration ◽

Implicit Schemes ◽

Modeling Algorithm

An explicit, unconditionally stable, finite‐difference depth migration and modeling algorithm is formulated and implemented for the fifteen‐degree wave equation in poststack, directional (rotational), and prestack modes for inhomogeneous media. It is about two times faster than implicit schemes. The simplicity, unconditional stability, and speed of the algorithm are appealing for numerous applications, especially prestack and three‐dimensional data sets.

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3‐D imaging using higher order fast marching traveltimes

Geophysics ◽

10.1190/1.1468621 ◽

2002 ◽

Vol 67 (2) ◽

pp. 604-609 ◽

Cited By ~ 56

Author(s):

Alexander Mihai Popovici ◽

James A. Sethian

Keyword(s):

Real Data ◽

Second Order ◽

Data Sets ◽

Velocity Analysis ◽

Fast Marching ◽

First Order ◽

Interval Velocity ◽

Migration Velocity Analysis ◽

Imaging Results ◽

The Common

Recently, fast marching methods (FMM) beyond first order have been developed for producing rapid solutions to the eikonal equation. In this paper, we present imaging results for 3‐D prestack Kirchhoff migration using traveltimes computed using the first‐order and second‐order FMM on several 3‐D prestack synthetic and real data sets. The second order traveltimes produce a much better image of the structure. Moreover, insufficiently sampled first order traveltimes can introduce consistent errors in the common reflection point gathers that affect velocity analysis. First‐order traveltimes tend to be smaller than analytic traveltimes, which in turn affects the migration velocity analysis, falsely indicating that the interval velocity was too low.

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MAZ depth-velocity modelling and imaging with azimuthal anisotropy

The APPEA Journal ◽

10.1071/aj09087 ◽

2010 ◽

Vol 50 (2) ◽

pp. 723

Author(s):

Sergey Birdus ◽

Erika Angerer ◽

Iftikhar Abassi

Keyword(s):

Seismic Data ◽

Real Data ◽

Azimuthal Velocity ◽

Velocity Model ◽

Azimuthal Anisotropy ◽

Lessons Learned ◽

Seismic Survey ◽

Depth Migration ◽

Velocity Anisotropy ◽

Interval Velocity

Processing of multi and wide-azimuth seismic data faces some new challenges, and one of them is depth-velocity modelling and imaging with azimuthal velocity anisotropy. Analysis of multi-azimuth data very often reveals noticeable fluctuations in moveout between different acquisition directions. They can be caused by several factors: real azimuthal interval velocity anisotropy associated with quasi-vertical fractures or present day stress field within the sediments; short-wavelength velocity heterogeneities in the overburden; TTI (or VTI) anisotropy in the overburden; or, random distortions due to noise, multiples, irregularities in the acquisition geometry, etcetera. In order to build a velocity model for multi-azimuth pre-stack depth migration (MAZ PSDM) taking into account observed azimuthal anisotropy, we need to recognise, separate and estimate all the effects listed above during iterative depth-velocity modelling. Analysis of seismic data from a full azimuth 3D seismic land survey revealed the presence of strong spatially variable azimuthal velocity anisotropy that had to be taken into consideration. Using real data examples we discuss major steps in depth processing workflow that took such anisotropy into account: residual moveout estimation in azimuth sectors; separation of different effects causing apparent azimuthal anisotropy (see A–D above); iterative depth-velocity modelling with azimuthal anisotropy; and, subsequent MAZ anisotropic PSDM. The presented workflow solved problems with azimuthal anisotropy in our multi-azimuth dataset. Some of the lessons learned during this MAZ project are relevant to every standard narrow azimuth seismic survey recorded in complex geological settings.

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The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis

Geophysics ◽

10.1190/1.2993536 ◽

2008 ◽

Vol 73 (6) ◽

pp. S241-S249 ◽

Cited By ~ 47

Author(s):

Xiao-Bi Xie ◽

Hui Yang

Keyword(s):

Wave Equation ◽

Synthetic Data ◽

Velocity Model ◽

Migration Velocity ◽

Data Sets ◽

Velocity Analysis ◽

Depth Migration ◽

Sensitivity Kernel ◽

Migration Velocity Analysis ◽

Tomography Method

We have derived a broadband sensitivity kernel that relates the residual moveout (RMO) in prestack depth migration (PSDM) to velocity perturbations in the migration-velocity model. We have compared the kernel with the RMO directly measured from the migration image. The consistency between the sensitivity kernel and the measured sensitivity map validates the theory and the numerical implementation. Based on this broadband sensitivity kernel, we propose a new tomography method for migration-velocity analysis and updating — specifically, for the shot-record PSDM and shot-index common-image gather. As a result, time-consuming angle-domain analysis is not required. We use a fast one-way propagator and multiple forward scattering and single backscattering approximations to calculate the sensitivity kernel. Using synthetic data sets, we can successfully invert velocity perturbations from the migration RMO. This wave-equation-based method naturally incorporates the wave phenomena and is best teamed with the wave-equation migration method for velocity analysis. In addition, the new method maintains the simplicity of the ray-based velocity analysis method, with the more accurate sensitivity kernels replacing the rays.

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Seismic imaging using lateral adaptive windows

Geophysics ◽

10.1190/1.3359799 ◽

2010 ◽

Vol 75 (2) ◽

pp. S73-S79

Author(s):

Ørjan Pedersen ◽

Sverre Brandsberg-Dahl ◽

Bjørn Ursin

Keyword(s):

Seismic Data ◽

Seismic Imaging ◽

Synthetic Data ◽

Real Data ◽

Extrapolation Methods ◽

Depth Migration ◽

Large Velocity ◽

Migration Method ◽

Wavefield Extrapolation ◽

The Impact

One-way wavefield extrapolation methods are used routinely in 3D depth migration algorithms for seismic data. Due to their efficient computer implementations, such one-way methods have become increasingly popular and a wide variety of methods have been introduced. In salt provinces, the migration algorithms must be able to handle large velocity contrasts because the velocities in salt are generally much higher than in the surrounding sediments. This can be a challenge for one-way wavefield extrapolation methods. We present a depth migration method using one-way propagators within lateral windows for handling the large velocity contrasts associated with salt-sediment interfaces. Using adaptive windowing, we can handle large perturbations locally in a similar manner as the beamlet propagator, thus limiting the impact of the errors on the global wavefield. We demonstrate the performance of our method by applying it to synthetic data from the 2D SEG/EAGE [Formula: see text] salt model and an offshore real data example.

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Multicomponent prestack depth migration by scalar wavefield extrapolation

Geophysics ◽

10.1190/1.1527088 ◽

2002 ◽

Vol 67 (6) ◽

pp. 1886-1894 ◽

Cited By ~ 21

Author(s):

Anning Hou ◽

Kurt J. Marfurt

Keyword(s):

Wave Equation ◽

Single Shot ◽

Complex Structures ◽

Scalar Wave ◽

Prestack Depth Migration ◽

Depth Migration ◽

Polarization Filtering ◽

Polarity Reversals ◽

Wavefield Extrapolation ◽

Propagation Velocities

We present a new multicomponent prestack depth migration methodology based on successive application of conventional scalar wave equation migration. We do not separate the data into PP‐ and PS‐waves; rather, we migrate each x‐, y‐, and z‐component of the data using both P and S propagation velocities, followed by polarization filtering in the depth domain. By generating intermediate images in the depth domain, we can account for polarity reversals of the PS reflection for all dips. Since the polarization angles are calculated from the data, it is straightforward to accommodate anisotropic effects (quasi‐P and quasi‐S) into multicomponent migration. The multicomponent migration results in our synthetic examples demonstrate that even for a single shot gather, we can obtain clean PP‐ and PS‐wave images over complex structures and resolve the problem of PS‐wave polarity reversals.

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Modified Hybrid Discriminant Analysis Methods and Their Applications in Machine Learning

Discrete Dynamics in Nature and Society ◽

10.1155/2020/1512391 ◽

2020 ◽

Vol 2020 ◽

pp. 1-5

Author(s):

Liwen Huang

Keyword(s):

Discriminant Analysis ◽

Real Data ◽

Classification Algorithms ◽

Data Sets ◽

Analysis Method ◽

Linear Discriminant ◽

Discriminant Model ◽

Discriminant Models ◽

The Common ◽

Better Than

This paper presents a new hybrid discriminant analysis method, and this method combines the ideas of linearity and nonlinearity to establish a two-layer discriminant model. The first layer is a linear discriminant model, which is mainly used to determine the distinguishable samples and subsample; the second layer is a nonlinear discriminant model, which is used to determine the subsample type. Numerical experiments on real data sets show that this method performs well compared to other classification algorithms, and its stability is better than the common discriminant models.

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Wave-equation-based image warping

Geophysics ◽

10.1190/geo2015-0117.1 ◽

2016 ◽

Vol 81 (1) ◽

pp. V1-V6 ◽

Cited By ~ 4

Author(s):

Adel Khalil ◽

Henning Hoeber

Keyword(s):

Image Processing ◽

Wave Propagation ◽

Wave Equation ◽

Reservoir Characterization ◽

Real Data ◽

Image Warping ◽

Data Sets ◽

Physical Context ◽

Seismic Image ◽

Effective Signal

In seismic processing and reservoir characterization, we often need to measure relative displacements between different realizations of data. Over the years, many methods have been developed using different measures of similarity. Such alignment or warping methods are often effective signal or image processing tools. However, none of the available methods are directly driven by the physics of seismic imaging. We have found that a seismic image can be considered as a field governed by the wave equation. We visualized different image realizations as snapshots of the wavefield at different times, and these conveyed the required displacements or time shifts. By formulating the problem in a physical context, we obtained displacements that honored the directionality of the wave propagation. For example, 4D time shifts on migrated stacks were obtained in a direction normal to the reflectors. We have computed these shifts in an inverted finite-difference scheme. To overcome limitations of the two-way wave equation in this application, we factorized it to its one-way counterparts. The method was demonstrated on synthetic and real data sets.

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Fast and robust common-reflection-surface parameter estimation

Geophysics ◽

10.1190/geo2017-0113.1 ◽

2018 ◽

Vol 83 (1) ◽

pp. O1-O13 ◽

Cited By ~ 5

Author(s):

Anders U. Waldeland ◽

Hao Zhao ◽

Jorge H. Faccipieri ◽

Anne H. Schistad Solberg ◽

Leiv-J. Gelius

Keyword(s):

Signal To Noise Ratio ◽

Synthetic Data ◽

Real Data ◽

Structure Tensor ◽

Data Sets ◽

Fast Method ◽

Surface Parameter ◽

Common Reflection Surface ◽

The Common ◽

The Cost

The common-reflection-surface (CRS) method offers a stack with higher signal-to-noise ratio at the cost of a time-consuming semblance search to obtain the stacking parameters. We have developed a fast method for extracting the CRS parameters using local slope and curvature. We estimate the slope and curvature with the gradient structure tensor and quadratic structure tensor on stacked data. This is done under the assumption that a stacking velocity is already available. Our method was compared with an existing slope-based method, in which the slope is extracted from prestack data. An experiment on synthetic data shows that our method has increased robustness against noise compared with the existing method. When applied to two real data sets, our method achieves accuracy comparable with the pragmatic and full semblance searches. Our method has the advantage of being approximately two and four orders of magnitude faster than the semblance searches.

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