Prestack partial migration

Geophysics ◽  
1980 ◽  
Vol 45 (12) ◽  
pp. 1753-1779 ◽  
Author(s):  
Özdoan Yilmaz ◽  
Jon F. Claerbout
Keyword(s):  
Seismic Data ◽  
Partial Migration ◽  
Velocity Variation ◽  
Square Root ◽  
Seismic Data Processing ◽  
Lateral Velocity ◽  
Data Set ◽  
Significant Term ◽  
Separable Approximation ◽  
Root Operator

Conventional seismic data processing can be improved by modifying wide‐offset data so that dipping events stack coherently. A procedure to achieve this improvement is proposed here, which is basically a “partial” migration of common offset sections prior to stack. It has an advantage over full migration before stack in that, in the case of the latter, the final product is a migrated section. However, the prestack partial migration provides the interpreter with a high‐quality common midpoint (CMP) stacked section which can be subsequently migrated. The theory of prestack partial migration is based on the double square‐root equation, which describes seismic imaging with many shots and receivers. The double square‐root operator in midpoint‐offset space can be separated approximately into two terms, one involving only migration effects and the other involving only moveout correction. This separation provides an analysis of conventional processing. Estimation of errors in the separation yields the equation for prestack partial migration. Extension of the theory for separable approximation to incorporate lateral velocity variation yields a significant term proportional to the product of the first powers of offset, dip, and lateral velocity gradient. This term was used to obtain a rough estimate of lateral velocity variation from a field data set.

Seismic data processing: Current industry practice and new directions

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2452-2457 ◽  
Author(s):  
Philip S. Schultz
Keyword(s):  
Data Processing ◽  
Seismic Data ◽  
Complex Structure ◽  
Seismic Data Processing ◽  
Lateral Velocity ◽  
Data Transformations ◽  
Industry Practice ◽  
Multichannel Filtering ◽  
Ray Bending ◽  
Transform Domains

The last ten years have seen an evolution in the state of the art for seismic data processing on a number of fronts. Data transformations investigated have made some types of analyses much more straightforward. Deconvolution has become a sophisticated process which includes statistical, model‐based, and deterministic methods. Vibroseis® processing has led to a greater understanding of the statistical limitations in recovery of the wave‐field amplitude from sign‐bit recording, and the deconvolution of Vibroseis data has improved. Multichannel filtering and analysis in transform domains have resulted in increasingly effective tools for noise reduction and signal enhancement. In statics analysis, surface consistency as a constraint remains a standard, and refraction analysis has become popular as a means of preconditioning data for residual statics estimation. Advances in stacking methodology have come mainly from addressing three effects: ray bending through lateral velocity variations, complex structure, and source‐receiver azimuth variations. Recently many techniques of interpretation processing have been introduced with the goal of improving the estimate of earth properties, rather than generating a stacked or imaged section of higher fidelity. The interaction among related disciplines has increased and this serves to amplify the effectiveness of each discipline because they are now developing in less isolation.

Concepts of normal and dip moveout

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1637-1647 ◽  
Author(s):  
Christopher L. Liner
Keyword(s):  
Data Processing ◽  
Seismic Data ◽  
Velocity Variation ◽  
Seismic Data Processing ◽  
Prestack Migration ◽  
The Relationship

Both normal moveout and dip moveout are key elements of modern seismic data processing. A nonmathematical discussion of the nature and action of these processes helps to clarify their importance. Special emphasis is given to their history and geometry, as well as the effect of dip, velocity variation, and anisotropy. The relationship between dip moveout and prestack migration is also developed.

scholarly journals Phase and the Hilbert transform

2014 ◽  
Vol 33 (10) ◽  
pp. 1164-1166 ◽  
Author(s):  
Steve Purves
Keyword(s):  
Signal Processing ◽  
Data Processing ◽  
Hilbert Transform ◽  
Seismic Data ◽  
Seismic Attributes ◽  
Seismic Data Processing ◽  
Data Set ◽  
The Hilbert Transform

The concept of phase permeates seismic data processing and signal processing in general, but it can be awkward to understand, and manipulating it directly can lead to surprising results. It doesn't help that the word phase is used to mean a variety of things, depending on whether we refer to the propagating wavelet, the observed wavelet, poststack seismic attributes, or an entire seismic data set. Several publications have discussed the concepts and ambiguities (e.g., Roden and Sepúlveda, 1999 ; Liner, 2002 ; Simm and White, 2002 ).

Optimized Chebyshev Fourier migration: A wide-angle dual-domain method for media with strong velocity contrasts

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. S23-S34 ◽  
Author(s):  
Jin-Hai Zhang ◽  
Wei-Min Wang ◽  
Shu-Qin Wang ◽  
Zhen-Xing Yao
Keyword(s):  
Fourier Transform ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Taylor Expansion ◽  
Wide Angle ◽  
Square Root ◽  
Lateral Velocity ◽  
Dual Domain ◽  
Root Operator

A wide-angle propagator is essential when imaging complex media with strong lateral velocity contrasts in one-way wave-equation migration. We have developed a dual-domain one-way propagator using truncated Chebyshev polynomials and a globally optimized scheme. Our method increases the accuracy of the expanded square-root operator by adding two high-order terms to the traditional split-step Fourier propagator. First, we approximate the square-root operator using Taylor expansion around the reference background velocity. Then, we apply the first-kind Chebyshev polynomials to economize the results of the Taylor expansion. Finally, we optimize the constant coefficients using the globally optimized scheme, which are fixed and feasible for arbitrary velocity models. Theoretical analysis and nu-merical experiments have demonstrated that the method has veryhigh accuracy and exceeds the unoptimized Fourier finite-difference propagator for the entire range of practical velocity contrasts. The accurate propagation angle of the method is always about 60° under the relative error of 1% for complex media with weak, moderate, and even strong lateral velocity contrasts. The method allows us to handle wide-angle propagations and strong lateral velocity contrast simultaneously by using Fourier transform alone. Only four 2D Fourier transforms are required for each step of 3D wavefield extrapolation, and the computing cost is similar to that of the Fourier finite-difference method. Compared with the finite-difference method, our method has no two-way splitting error (i.e., azimuthal-anisotropy error) for 3D cases and almost no numerical dispersion for coarse grids. In addition, it has strong potential to be accelerated when an enhanced fast Fourier transform algorithm emerges.

ADVANCES IN 3-D SEISMIC DATA PROCESSING TECHNIQUES

1992 ◽  
Vol 32 (1) ◽  
pp. 276
Author(s):  
T.J. Allen ◽  
P. Whiting
Keyword(s):  
Data Processing ◽  
Seismic Data ◽  
Three Dimensional ◽  
Velocity Model ◽  
Migration Velocity ◽  
Seismic Data Processing ◽  
Data Set ◽  
Migration Velocity Analysis ◽  
Processing Techniques ◽  
Made In

Several recent advances made in 3-D seismic data processing are discussed in this paper.Development of a time-variant FK dip-moveout algorithm allows application of the correct three-dimensional operator. Coupled with a high-dip one-pass 3-D migration algorithm, this provides improved resolution and response at all azimuths. The use of dilation operators extends the capability of the process to include an economical and accurate (within well-defined limits) 3-D depth migration.Accuracy of the migration velocity model may be improved by the use of migration velocity analysis: of the two approaches considered, the data-subsetting technique gives more reliable and interpretable results.Conflicts in recording azimuth and bin dimensions of overlapping 3-D surveys may be resolved by the use of a 3-D interpolation algorithm applied post 3-D stack and which allows the combined surveys to be 3-D migrated as one data set.

3-D moveout inversion in azimuthally anisotropic media with lateral velocity variation: Theory and a case study

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1202-1218 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Correction Term ◽  
Anisotropic Media ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Velocity Variation ◽  
Variation Theory ◽  
Fractured Reservoir ◽  
Lateral Velocity ◽  
Data Set ◽  
Zero Offset

Reflection moveout recorded over an azimuthally anisotropic medium (e.g., caused by vertical or dipping fractures) varies with the azimuth of the source‐receiver line. Normal‐moveout (NMO) velocity, responsible for the reflection traveltimes on conventional‐length spreads, forms an elliptical curve in the horizontal plane. While this result remains valid in the presence of arbitrary anisotropy and heterogeneity, the inversion of the NMO ellipse for the medium parameters has been discussed so far only for horizontally homogeneous models above a horizontal or dipping reflector. Here, we develop an analytic moveout correction for weak lateral velocity variation in horizontally layered azimuthally anisotropic media. The correction term is proportional to the curvature of the zero‐offset traveltime surface at the common midpoint and, therefore, can be estimated from surface seismic data. After the influence of lateral velocity variation on the effective NMO ellipses has been stripped, the generalized Dix equation can be used to compute the interval ellipses and evaluate the magnitude of azimuthal anisotropy (measured by P-wave NMO velocity) within the layer of interest. This methodology was applied to a 3-D “wide‐azimuth” data set acquired over a fractured reservoir in the Powder River Basin, Wyoming. The processing sequence included 3-D semblance analysis (based on the elliptical NMO equation) for a grid of common‐midpoint “supergathers,” spatial smoothing of the effective NMO ellipses and zero‐offset traveltimes, correction for lateral velocity variation, and generalized Dix differentiation. Our estimates of depth‐varying fracture trends in the survey area, based on the interval P-wave NMO ellipses, are in good agreement with the results of outcrop and borehole measurements and the rotational analysis of four‐ component S-wave data.

An overview of reproducible 3D seismic data processing and imaging using Madagascar

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. F9-F20 ◽  
Author(s):  
Can Oren ◽  
Robert L. Nowack
Keyword(s):  
Data Processing ◽  
Open Source ◽  
Open Source Software ◽  
Seismic Data ◽  
Software Package ◽  
3D Seismic ◽  
Seismic Data Processing ◽  
Data Set ◽  
Open Source Software Package ◽  
3D Seismic Data

We present an overview of reproducible 3D seismic data processing and imaging using the Madagascar open-source software package. So far, there has been a limited number of studies on the processing of real 3D data sets using open-source software packages. Madagascar with its wide range of individual programs and tools available provides the capability to fully process 3D seismic data sets. The goal is to provide a streamlined illustration of the approach for the implementation of 3D seismic data processing and imaging using the Madagascar open-source software package. A brief introduction is first given to the Madagascar open-source software package and the publicly available 3D Teapot Dome seismic data set. Several processing steps are applied to the data set, including amplitude gaining, ground roll attenuation, muting, deconvolution, static corrections, spike-like random noise elimination, normal moveout (NMO) velocity analysis, NMO correction, stacking, and band-pass filtering. A 3D velocity model in depth is created using Dix conversion and time-to-depth scaling. Three-dimensional poststack depth migration is then performed followed by [Formula: see text]-[Formula: see text] deconvolution and structure-enhancing filtering of the migrated image to suppress random noise and enhance the useful signal. We show that Madagascar, as a powerful open-source environment, can be used to construct a basic workflow to process and image 3D seismic data in a reproducible manner.

Prestack migration by split‐step DSR

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1412-1416 ◽  
Author(s):  
Alexander Mihai Popovici
Keyword(s):  
Phase Shift ◽  
Square Root ◽  
Variable Velocity ◽  
Step Method ◽  
Lateral Velocity ◽  
Data Set ◽  
Prestack Migration ◽  
Imaging Results ◽  
Velocity Variations ◽  
Migration Equation

The double‐square‐root (DSR) prestack migration equation, though defined for depth variable velocity, can be used to image media with strong velocity variations using a phase‐shift plus interpolation (PSPI) or split‐step correction. The split‐step method is based on applying a phase‐shift correction to the extrapolated wavefield—a correction that attempts to compensate for the lateral velocity variations. I show how to extend DSR prestack migration to lateral velocity media and exemplify the method by applying the new algorithm to the Marmousi data set. The split‐step DSR migration is very fast and offers excellent imaging results.

Wave-equation global datuming based on the double square root operator

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. U35-U43 ◽  
Author(s):  
Wenge Liu ◽  
Bo Zhao ◽  
Hua-wei Zhou ◽  
Zhenhua He ◽  
Hui Liu ◽  
...  
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Square Root ◽  
New Wave ◽  
Lateral Velocity ◽  
Near Surface ◽  
Traditional Procedure ◽  
Wavefield Continuation ◽  
Static Corrections ◽  
Root Operator

Current schemes for removing near-surface effects in seismic data processing use either static corrections or wave-equation datuming (WED). In the presence of rough topography and strong lateral velocity variations in the near surface, the WED scheme is the only option available. However, the traditional procedure of WED downward continues the sources and receivers in different domains. A new wave-equation global-datuming method is based on the double-square-root operator, implementing the wavefield continuation in a single domain following the survey sinking concept. This method has fewer approximations and therefore is more robust and convenient than the traditional WED methods. This method is compared with the traditional methods using a synthetic data example.

Evaluation of two‐pass three‐dimensional migration

Geophysics ◽  
1988 ◽  
Vol 53 (1) ◽  
pp. 32-49 ◽  
Author(s):  
John A. Dickinson
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Three Dimensional ◽  
Velocity Variation ◽  
Lateral Velocity ◽  
Data Manipulation ◽  
Depth Migration ◽  
Data Comparison ◽  
Time Migration ◽  
Order Of Magnitude

The theoretically correct way to perform a three‐dimensional (3-D) migration of seismic data requires large amounts of data manipulation on the computer. In order to alleviate this problem, a true, one‐pass 3-D migration is commonly replaced with an approximate technique in which a series of two‐dimensional (2-D) migrations is performed in orthogonal directions. This two‐pass algorithm produces the correct answer when the velocity is constant, both horizontally and vertically. Here I analyze the error due to this algorithm when the velocities vary vertically. The analysis has two parts: first, a theoretical analysis is performed in which a formula for the error is derived; and second, a field data comparison between one‐pass and two‐pass migrations is shown. My conclusion is that two‐pass 3-D migration is, in general, a very good approximation. Its errors are usually small, the exceptions being when both the reflector dip is large (in practice this typically means greater than about 25 to 40 degrees) and the orientation of the reflector is in neither the inline nor the crossline direction. Even then the error is the same order of magnitude as that due to the uncertainty in the migration velocities. These conclusions are still valid when there is lateral velocity variation, as long as this variation is accounted for by trace stretching. The analysis presented here deals with time migration; no claims are made regarding depth migration.

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