Wave‐equation trace interpolation

Geophysics ◽  
1987 ◽  
Vol 52 (7) ◽  
pp. 973-984 ◽  
Author(s):  
Joshua Ronen
Keyword(s):  
Wave Equation ◽  
Conjugate Gradient ◽  
Seismic Data ◽  
Linear Relation ◽  
Field Data ◽  
Iterative Scheme ◽  
Partial Migration ◽  
Spatial Aliasing ◽  
Zero Offset ◽  
Multichannel Seismic Data

Spatial aliasing in multichannel seismic data can be overcome by solving an inversion in which the model is the section that would be recorded in a well sampled zero‐offset experiment, and the data are seismic data after normal moveout (NMO). The formulation of the (linear) relation between the data and the model is based on the wave equation and on Fourier analysis of aliasing. A processing sequence in which one treats missing data as zero data and performs partial migration before stacking is equivalent to application of the transpose of the operator that actually needs to be inverted. The inverse of that operator cannot be uniquely determined, but it can be estimated using spatial spectral balancing in a conjugate‐gradient iterative scheme. The first iteration is conventional processing (including prestack partial migration). As shown in a field data example in which severe spatial aliasing was simulated, a few more iterations are necessary to achieve significantly better results.

Velocity estimation by image-focusing analysis

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. U49-U60 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
New York ◽  
Seismic Data ◽  
Field Data ◽  
Velocity Estimation ◽  
Data Set ◽  
Velocity Function ◽  
Curvature Correction ◽  
Velocity Information ◽  
Zero Offset ◽  
Inherent Ambiguity

Migration velocity can be estimated from seismic data by analyzing, focusing, and defocusing of residual-migrated images. The accuracy of these velocity estimates is limited by the inherent ambiguity between velocity and reflector curvature. However, velocity resolution improves when reflectors with different curvatures are present. Image focusing is measured by evaluating coherency across structural dips, in addition to coherency across aperture/azimuth angles. The inherent ambiguity between velocity and reflector curvature is directly tackled by introducing a curvature correction into the computation of the semblance functional that estimates image coherency. The resulting velocity estimator provides velocity estimates that are (1) unbiased by reflector curvature and (2) consistent with the velocity information that is routinely obtained by measuring coherency over aperture/azimuth angles. Applications to a 2D synthetic prestack data set and a 2D field prestack data set confirm that the proposed method provides consistent and unbiased velocity information. They also suggest that velocity estimates based on the new image-focusing semblance may be more robust and have higher resolution than estimates based on conventional semblance functionals. Applying the proposed method to zero-offset field data recorded in New York Harbor yields a velocity function that is consistent with available geologic information and clearly improves the focusing of the reflectors.

Interpretive evaluation of migrated data

1989 ◽  
Vol 20 (2) ◽  
pp. 17 ◽  
Author(s):  
Ö. Yilmaz
Keyword(s):  
Seismic Data ◽  
Input Data ◽  
Field Data ◽  
Weak Link ◽  
Main Role ◽  
Step Size ◽  
Subsurface Geology ◽  
Spatial Aliasing ◽  
Migration Strategies ◽  
Aperture Width

In practice, migration of seismic data requires decision making with regard to: (1) Different migration strategies ? 2-D/3-D, post-stack/prestack, and time/depth migrations; (2) different migration algorithms for a given strategy ? integral, finite-difference and frequency-wavenumber methods; (3) different parameters for a given algorithm ? aperture width, depth-step size, stretch factor; (4) the input data ? profile length, noise content, spatial aliasing and boundary effects; (5) and finally, migration velocities ? the weak link between the seismic method and the subsurface geology that the former tries to image.The seismic interpreter, whose main role is to infer subsurface geology from the migrated data, normally should not be burdened with the decisions concerning the above factors. Fortunately, migration results often are self-evident; a feature considered geologically implausible on a migrated section can be associated with one or more of the above factors. Based on large number of field data cases, I will discuss each of these factors and provide some generally applicable guidelines for migration that an interpreter can invoke in practice.

Wave‐equation datuming before stack

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 2064-2066 ◽  
Author(s):  
John R. Berryhill
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Arbitrary Shape ◽  
Forward Modeling ◽  
Common Source ◽  
Computationally Efficient ◽  
Seismic Line ◽  
Mathematical Algorithm ◽  
Zero Offset ◽  
Kirchhoff Integral

This note describes the extension to unstacked seismic data of a computationally efficient form of the Kirchhoff integral published several years ago. In the previous paper (Berryhill, 1979), a wave‐equation procedure was developed to change the datum of a collection of zero‐offset seismic traces from one surface of arbitrary shape to another, even when the velocity for wave propagation is not constant. This procedure was designated “wave‐equation datuming,” and its applications to zero‐offset data were shown to include velocity‐replacement datum corrections and multilayer forward modeling. Extending this procedure to unstacked data requires no change in the mathematical algorithm. It is necessary only to recognize that operating on a common‐source group of seismic traces has the effect of extrapolating the receivers from one datum to another, and that, because of reciprocity, operating on a common‐receiver group changes the datum of the sources. Two passes through the data, common‐source computations, then common‐receiver computations, are required to change the datum of an entire seismic line before stack from one surface to another. Common‐source and common‐receiver trace groups must take the form of symmetric split spreads if both directions of dip are to be treated equally; reciprocity allows split spreads to be constructed artificially if the data were not actually recorded in the required form.

Estimation of reflection coefficients from zero‐offset field data

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1634-1645 ◽  
Author(s):  
Børge Arntsen ◽  
Bjørn Ursin
Keyword(s):  
Point Source ◽  
Least Squares ◽  
Seismic Data ◽  
Field Data ◽  
Model Fitting ◽  
Seismic Survey ◽  
Reflection Coefficients ◽  
Data Set ◽  
Seismic Experiment ◽  
Zero Offset

The classical one‐dimensional (1-D) inverse problem consists of estimating reflection coefficients from surface seismic data using the 1-D wave equation. Several authors have found stable solutions to this problem using least‐squares model‐fitting methods. We show that the application of these plane‐wave solutions to seismic data generated with a point source can lead to errors in estimating reflection coefficients. This difficulty is avoided by using a least‐squares model fitting scheme describing vertically traveling waves originating from a point source. It is shown that this method is roughly equivalent to deterministic deconvolution with built‐in multiple removal and compensation for spherical spreading. A true zero‐offset field data set from a specially designed seismic experiment is then used as input to estimate reflection coefficients. Stacking velocities from a conventional seismic survey were used to estimate spherical spreading. The resulting reflection coefficients are shown to correlate well with an available well log.

Three‐dimensional modeling and migration of seismic data using Fourier transforms

Geophysics ◽  
1988 ◽  
Vol 53 (9) ◽  
pp. 1194-1201 ◽  
Author(s):  
Jing Wen ◽  
George A. McMechan ◽  
Michael W. Booth
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Fourier Transforms ◽  
Three Dimensional ◽  
Scale Model ◽  
Model Data ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Zero Offset ◽  
And Migration

Programs for 3-D modeling and migration, using 3-D Fourier transforms to solve the scalar wave equation in frequency‐wavenumber space, are developed, implemented, tested, and applied to synthetic and scale‐model data. With microtasking to fully use four CRAY processors in parallel, we can solve a complete [Formula: see text] modeling problem in about 2.5 minutes (elapsed time); of this time, the two 3-D Fourier transforms take 1 minute and the wave‐equation calculations take 1.5 minutes. The corresponding migration also takes 2.5 minutes. Thus, even iterative 3-D processing is now feasible. The two main assumptions in our algorithm are that the earth has a constant velocity and that the data are zero‐offset (or stacked). Tests with model data verify that the algorithm produces the correct results when these assumptions are satisfied. Tests with scale‐model data show that approximate images may still be obtained when the assumptions are not strictly met; but the images contain a variety of distortions, primarily related to undermigration and overmigration, so caution is required in interpretation.

A possible new hydrocarbon play, offshore central West Greenland

1998 ◽  
pp. 28-30
Author(s):  
Nina Skaarup ◽  
James A. Chalmers
Keyword(s):  
Seismic Data ◽  
Mineral Resources ◽  
Source Rocks ◽  
Bright Spot ◽  
Offshore Area ◽  
West Greenland ◽  
The Government ◽  
Structural Closure ◽  
Multichannel Seismic Data ◽  
Seismic Lines

NOTE: This article was published in a former series of GEUS Bulletin. Please use the original series name when citing this article, for example: Skaarup, N., & Chalmers, J. A. (1998). A possible new hydrocarbon play, offshore central West Greenland. Geology of Greenland Survey Bulletin, 180, 28-30. https://doi.org/10.34194/ggub.v180.5082 _______________ The discovery of extensive seeps of crude oil onshore central West Greenland (Christiansen et al. 1992, 1994, 1995, 1996, 1997, 1998, this volume; Christiansen 1993) means that the central West Greenland area is now prospective for hydrocarbons in its own right. Analysis of the oils (Bojesen-Koefoed et al. in press) shows that their source rocks are probably nearby and, because the oils are found within the Lower Tertiary basalts, the source rocks must be below the basalts. It is therefore possible that in the offshore area oil could have migrated through the basalts and be trapped in overlying sediments. In the offshore area to the west of Disko and Nuussuaq (Fig. 1), Whittaker (1995, 1996) interpreted a few multichannel seismic lines acquired in 1990, together with some seismic data acquired by industry in the 1970s. He described a number of large rotated fault-blocks containing structural closures at top basalt level that could indicate leads capable of trapping hydrocarbons. In order to investigate Whittaker’s (1995, 1996) interpretation, in 1995 the Geological Survey of Greenland acquired 1960 km new multichannel seismic data (Fig. 1) using funds provided by the Government of Greenland, Minerals Office (now Bureau of Minerals and Petroleum) and the Danish State through the Mineral Resources Administration for Greenland. The data were acquired using the Danish Naval vessel Thetis which had been adapted to accommodate seismic equipment. The data acquired in 1995 have been integrated with the older data and an interpretation has been carried out of the structure of the top basalt reflection. This work shows a fault pattern in general agreement with that of Whittaker (1995, 1996), although there are differences in detail. In particular the largest structural closure reported by Whittaker (1995) has not been confirmed. Furthermore, one of Whittaker’s (1995) smaller leads seems to be larger than he had interpreted and may be associated with a DHI (direct hydrocarbon indicator) in the form of a ‘bright spot’.

SeismicWaveTool: Continuous and discrete wavelet analysis and filtering for multichannel seismic data

2013 ◽  
Vol 184 (1) ◽  
pp. 162-171 ◽  
Author(s):  
J.J. Galiana-Merino ◽  
J.L. Rosa-Herranz ◽  
S. Rosa-Cintas ◽  
J.J. Martinez-Espla
Keyword(s):  
Wavelet Analysis ◽  
Seismic Data ◽  
Discrete Wavelet ◽  
Discrete Wavelet Analysis ◽  
Multichannel Seismic Data

scholarly journals Wave Equation Datuming Applied to Seismic Data in Shallow Water Environment and Post-Critical Water Bottom Reflection

Energies ◽  
2017 ◽  
Vol 10 (9) ◽  
pp. 1414 ◽  
Author(s):  
Umberta Tinivella ◽  
Michela Giustiniani ◽  
Ivan Vargas-Cordero
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Seismic Data ◽  
Water Environment ◽  
Shallow Water Environment ◽  
Water Bottom
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