Imaging salt bodies using explicit migration operators offshore Norway

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. S25-S32 ◽  
Author(s):  
Børge Arntsen ◽  
Constantin Gerea ◽  
Tage Røsten
Keyword(s):  
Image Quality ◽  
Computational Cost ◽  
Fourier Method ◽  
Frequency Content ◽  
Data Set ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Velocity Changes ◽  
The Cost ◽  
Better Than

We have tested the performance of 3D shot-profile depth migration using explicit migration operators on a real 3D marine data set. The data were acquired offshore Norway in an area with a complex subsurface containing large salt bodies. We compared shot-profile migration using explicit migration operators with conventional Kirchhoff migration, split-step Fourier migration, and common-azimuth by generalized screen propagator (GSP) migration in terms of quality and computational cost. Image quality produced by the explicit migration operator approach is slightly better than with split-step Fourier migration and clearly better than in common-azimuth by GSP and Kirchhoff migrations. The main differences are fewer artifacts and better-suppressed noise within the salt bodies. Kirchhoff migration shows considerable artifacts (migration smiles) within and close to the salt bodies, which are not present in images produced by the other three wave-equation methods. Expressions for computational cost were developed for all four migration algorithms in terms of frequency content and acquisition parameters. For comparable frequency content, migration cost using explicit operators is four times the cost of the split-step Fourier method, up to 260 times the cost of common-azimuth by GSP migration, and 25 times the cost of Kirchhoff migration. Our results show that in terms of image quality, shot-profile migration using explicit migration operators is well suited for imaging in areas with complex geology and significant velocity changes. However, computational cost of the method is high and makes it less attractive in terms of efficiency.

Optimum split-step Fourier 3D depth migration: Developments and practical aspects

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S167-S175 ◽  
Author(s):  
Jianfeng Zhang ◽  
Linong Liu
Keyword(s):  
Finite Difference ◽  
Heterogeneous Media ◽  
Fourier Transforms ◽  
Computational Cost ◽  
Fourier Method ◽  
Approximate Algorithm ◽  
Wide Angle ◽  
Data Set ◽  
Depth Migration ◽  
Varying Coefficients

We present an efficient scheme for depth extrapolation of wide-angle 3D wavefields in laterally heterogeneous media. The scheme improves the so-called optimum split-step Fourier method by introducing a frequency-independent cascaded operator with spatially varying coefficients. The developments improve the approximation of the optimum split-step Fourier cascaded operator to the exact phase-shift operator of a varying velocity in the presence of strong lateral velocity variations, and they naturally lead to frequency-dependent varying-step depth extrapolations that reduce computational cost significantly. The resulting scheme can be implemented alternatively in spatial and wavenumber domains using fast Fourier transforms (FFTs). The accuracy of the first-order approximate algorithm is similar to that of the second-order optimum split-step Fourier method in modeling wide-angle propagation through strong, laterally varying media. Similar to the optimum split-step Fourier method, the scheme is superior to methods such as the generalized screen and Fourier finite difference. We demonstrate the scheme’s accuracy by comparing it with 3D two-way finite-difference modeling. Comparisons with the 3D prestack Kirchhoff depth migration of a real 3D data set demonstrate the practical application of the proposed method.

Kirchhoff modeling, inversion for reflectivity, and subsurface illumination

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1195-1209 ◽  
Author(s):  
Bertrand Duquet ◽  
Kurt J. Marfurt ◽  
Joe A. Dellinger
Keyword(s):  
Least Squares ◽  
A Priori ◽  
Computational Cost ◽  
Image Point ◽  
Surface Sampling ◽  
Constrained Least Squares ◽  
Amplitude Variation With Offset ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Least Squares Migration

Because of its computational efficiency, prestack Kirchhoff depth migration is currently one of the most popular algorithms used in 2-D and 3-D subsurface depth imaging. Nevertheless, Kirchhoff algorithms in their typical implementation produce less than ideal results in complex terranes where multipathing from the surface to a given image point may occur, and beneath fast carbonates, salt, or volcanics through which ray‐theoretical energy cannot penetrate to illuminate underlying slower‐velocity sediments. To evaluate the likely effectiveness of a proposed seismic‐acquisition program, we could perform a forward‐modeling study, but this can be expensive. We show how Kirchhoff modeling can be defined as the mathematical transpose of Kirchhoff migration. The resulting Kirchhoff modeling algorithm has the same low computational cost as Kirchhoff migration and, unlike expensive full acoustic or elastic wave‐equation methods, only models the events that Kirchhoff migration can image. Kirchhoff modeling is also a necessary element of constrained least‐squares Kirchhoff migration. We show how including a simple a priori constraint during the inversion (that adjacent common‐offset images should be similar) can greatly improve the resulting image by partially compensating for irregularities in surface sampling (including missing data), as well as for irregularities in ray coverage due to strong lateral variations in velocity and our failure to account for multipathing. By allowing unstacked common‐offset gathers to become interpretable, the additional cost of constrained least‐squares migration may be justifiable for velocity analysis and amplitude‐variation‐with‐offset studies. One useful by‐product of least‐squares migration is an image of the subsurface illumination for each offset. If the data are sufficiently well sampled (so that including the constraint term is not necessary), the illumination can instead be calculated directly and used to balance the result of conventional migration, obtaining most of the advantages of least‐squares migration for only about twice the cost of conventional migration.

scholarly journals A competitive comparison of multiparameter stacking operators

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. V275-V283 ◽  
Author(s):  
Jan Walda ◽  
Benjamin Schwarz ◽  
Dirk Gajewski
Keyword(s):  
Optimization Technique ◽  
Computational Cost ◽  
Initial Guess ◽  
Time Shift ◽  
Data Set ◽  
Velocity Shift ◽  
Common Reflection Surface ◽  
The One ◽  
Better Than ◽  
Good Agreement

The classic common-midpoint (CMP) stack, which sums along offsets, suffers in challenging environments in which the acquisition is sparse. In the past, several multiparameter stacking techniques were introduced that incorporate many neighboring CMPs during summation. This increases data redundancy and reduces noise. Multiparameter methods that can be parameterized by the same wavefront attributes are multifocusing (MF), the common-reflection-surface (CRS), implicit CRS, and nonhyperbolic CRS (nCRS). The CRS-type operators use a velocity-shift mechanism to account for heterogeneity by changing the slope of the asymptote. On the other hand, MF uses a different mechanism: a shift of reference time while preserving the slope of the asymptote. We have formulated MF such that it uses the same mechanism as the CRS-type operators and compare them on a marine data set. In turn, we investigate the behavior of time-shifted versions of the CRS-type approximations. To provide a fair comparison, we use a global optimization technique, differential evolution, which allows to accurately estimate a solution without an initial guess solution. Our results indicate that the velocity-shift mechanism performs, in general, better than the one incorporating a time shift. The double-square-root operators are also less sensitive to the choice of aperture. They perform better in the case of diffractions than conventional hyperbolic CRS, and this fact is in good agreement with previous works. In our work the nCRS is of almost the same computational cost as that of conventional hyperbolic CRS, but it generally leads to a superior fit; therefore, we recommend its use in the future.

Case Study: Improving the quality of the seismic reflection image for a Fujian mineral exploration data set with offset-domain common-image gathers

Geophysics ◽  
2021 ◽  
pp. 1-45
Author(s):  
Guofeng Liu ◽  
Xiaohong Meng ◽  
Johanes Gedo Sea
Keyword(s):  
Wave Equation ◽  
Image Quality ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Mineral Exploration ◽  
Velocity Model ◽  
Image Point ◽  
Single Shot ◽  
Data Set ◽  
Depth Migration

Seismic reflection is a proven and effective method commonly used during the exploration of deep mineral deposits in Fujian, China. In seismic data processing, rugged depth migration based on wave-equation migration can play a key role in handling surface fluctuations and complex underground structures. Because wave-equation migration in the shot domain cannot output offset-domain common-image gathers in a straightforward way, the use of traditional tools for updating the velocity model and improving image quality can be quite challenging. To overcome this problem, we employed the attribute migration method. This worked by sorting the migrated stack results for every single-shot gather into the offset gathers. The value of the offset that corresponded to each image point was obtained from the ratio of the original migration results to the offset-modulated shot-data migration results. A Gaussian function was proposed to map every image point to a certain range of offsets. This helped improve the signal-to-noise ratio, which was especially important in handing low quality seismic data obtained during mineral exploration. Residual velocity analysis was applied to these gathers to update the velocity model and improve image quality. The offset-domain common-image gathers were also used directly for real mineral exploration seismic data with rugged depth migration. After several iterations of migration and updating the velocity, the proposed procedure achieved an image quality better than the one obtained with the initial velocity model. The results can help with the interpretation of thrust faults and deep deposit exploration.

Standardized volume-rendering of contrast-enhanced renal magnetic resonance angiography

2005 ◽  
Vol 46 (5) ◽  
pp. 497-504 ◽  
Author(s):  
Ö. Smedby ◽  
R. Öberg ◽  
B. Åsberg ◽  
H. Stenström ◽  
P. Eriksson
Keyword(s):  
Magnetic Resonance ◽  
Image Quality ◽  
Magnetic Resonance Angiography ◽  
Volume Rendering ◽  
Maximum Intensity Projection ◽  
Data Set ◽  
3D Data ◽  
Contrast Enhanced ◽  
Better Than ◽  
Good Agreement

Purpose: To propose a technique for standardizing volume-rendering technique (VRT) protocols and to compare this with maximum intensity projection (MIP) in regard to image quality and diagnostic confidence in stenosis diagnosis with magnetic resonance angiography (MRA). Material and Methods: Twenty patients were examined with MRA under suspicion of renal artery stenosis. Using the histogram function in the volume-rendering software, the 95th and 99th percentiles of the 3D data set were identified and used to define the VRT transfer function. Two radiologists assessed the stenosis pathology and image quality from rotational sequences of MIP and VRT images. Results: Good overall agreement (mean κ = 0.72) was found between MIP and VRT diagnoses. The agreement between MIP and VRT was considerably better than that between observers (mean κ = 0.43). One of the observers judged VRT images as having higher image quality than MIP images. Conclusion: Presenting renal MRA images with VRT gave results in good agreement with MIP. With VRT protocols defined from the histogram of the image, the lack of an absolute gray scale in MRI need not be a major problem.

Azimuth moveout for 3-D prestack imaging

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 574-588 ◽  
Author(s):  
Biondo Biondi ◽  
Sergey Fomel ◽  
Nizar Chemingui
Keyword(s):  
Integral Operator ◽  
Impulse Response ◽  
Constant Velocity ◽  
Computational Cost ◽  
Data Set ◽  
Depth Migration ◽  
Prestack Migration ◽  
Migration Operator ◽  
Time Space ◽  
Strong Curvature

We introduce a new partial prestack‐migration operator called “azimuth moveout” (AMO) that rotates the azimuth and modifies the offset of 3-D prestack data. Followed by partial stacking, AMO can reduce the computational cost of 3-D prestack imaging. We have successfully applied AMO to the partial stacking of a 3-D marine data set over a range of offsets and azimuths. When AMO is included in the partial‐stacking procedure, high‐frequency steeply dipping energy is better preserved than when conventional partial‐stacking methodologies are used. Because the test data set requires 3-D prestack depth migration to handle strong lateral variations in velocity, the results of our tests support the applicability of AMO to prestack depth‐imaging problems. AMO is a partial prestack‐migration operator defined by chaining a 3-D prestack imaging operator with a 3-D prestack modeling operator. The analytical expression for the AMO impulse response is derived by chaining constant‐velocity DMO with its inverse. Equivalently, it can be derived by chaining constant‐velocity prestack migration and modeling. Because 3-D prestack data are typically irregularly sampled in the surface coordinates, AMO is naturally applied as an integral operator in the time‐space domain. The AMO impulse response is a skewed saddle surface in the time‐midpoint space. Its shape depends on the amount of azimuth rotation and offset continuation to be applied to the data. The shape of the AMO saddle is velocity independent, whereas its spatial aperture is dependent on the minimum velocity. When the azimuth rotation is small (⩽20°), the AMO impulse response is compact, and its application as an integral operator is inexpensive. Implementing AMO as an integral operator is not straightforward because the AMO saddle may have a strong curvature when it is expressed in the midpoint coordinates. An appropriate transformation of the midpoint axes to regularize the AMO saddle leads to an effective implementation.

Three‐dimensional depth imaging with generalized screens: A salt body case study

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1132-1139 ◽  
Author(s):  
Jérôme H. Le Rousseau ◽  
Henry Calandra ◽  
Maarten V. de Hoop
Keyword(s):  
Three Dimensional ◽  
Fourier Method ◽  
Seismic Survey ◽  
Tectonic Deformation ◽  
Data Set ◽  
Depth Imaging ◽  
Depth Migration ◽  
Velocity Models ◽  
The North ◽  
Zero Offset

We illustrate the performance of the generalized screen propagator on real seismic data for 3D zero‐offset and prestack depth imaging. We use TotalFinaElf's L7D data set from the North Sea, a 3D marine seismic survey that contained limited azimuthal coverage. The subsurface shows significant tectonic deformation, including an intrusive salt body in sedimentary sequences. A transformation to common azimuth is applied prior to the 3D prestack depth imaging procedure. We compare the performance of the generalized screen propagator with that of a hybrid phase shift plus interpolation (PSPI)/split‐step Fourier method. Three‐dimensional prestack results confirm the generalized screen method handles multipathing more accurately. Comparisons are also made with Kirchhoff migration results. The results differ mainly in the fine‐scale irregularities of the image and not in the wavefront set of the image. Using synthetic models of similar structure (the SEG/EAGE salt model), we further illustrate the importance of multipathing and multiple scattering. Overall, our results show that our wave‐equation approach produces better images than the Kirchhoff approach to prestack depth migration; we attribute this mainly to a more complete handling of wave diffraction in the generalized screen expansion, which becomes important in strongly heterogeneous and irregular velocity models such as the ones containing salt bodies.

3D wavefield extrapolation with optimum split-step Fourier method

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. T95-T108 ◽  
Author(s):  
Linong Liu ◽  
Jianfeng Zhang
Keyword(s):  
Finite Difference ◽  
Fourier Transforms ◽  
Computational Cost ◽  
Fourier Method ◽  
Detailed Comparison ◽  
Higher Order ◽  
Order Correction ◽  
Data Sets ◽  
Wide Angle ◽  
Depth Migration

A one-way propagator is proposed for more accurately modeling wide-angle wavefields in the presence of severe lateral variations of the velocity. The method adds a higher-order correction to improve the split-step Fourier method by directly designing a cascaded operator that matches the exact phase-shift operator of a varying velocity. Using an optimization scheme, the coefficients in the cascaded operator are determined according to the local velocity distribution and the prescribed angular range of wavefield propagation. The proposed algorithm is implemented alternately in spatial and wavenumber domains using fast Fourier transforms, as in the split-step Fourier and generalized-screen methods. This algorithm can achieve higher accuracy than the generalized-screen method for wide-angle wavefields, although the same numerical scheme is used with comparable computational cost. No extra error arises for the proposed algorithm when used for 3D wave propagation, in contrast to methods that introduce an implicit finite–difference higher-order correction to the split-step Fourier method, such as the Fourier finite difference (FFD) and wide-angle screen methods. A detailed comparison of the proposed one-way propagator with the split-step Fourier, generalized-screen, and FFD methods is presented. The 2D Marmousi and 3D SEG/EAEG overthrust data sets are used to test the prestack depth-migration schemes developed based on the proposed one-way propagators.

Prestack Gaussian‐beam depth migration

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1240-1250 ◽  
Author(s):  
N. Ross Hill
Keyword(s):  
Gaussian Beam ◽  
Velocity Structure ◽  
Saddle Points ◽  
Three Dimensional ◽  
Seismic Energy ◽  
Data Set ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Beam Depth ◽  
Gaussian Beam Migration

Kirchhoff migration is the most popular method of three‐dimensional prestack depth migration because of its flexibility and efficiency. Its effectiveness can become limited, however, when complex velocity structure causes multipathing of seismic energy. An alternative is Gaussian beam migration, which is an extension of Kirchhoff migration that overcomes many of the problems caused by multipathing. Unlike first‐arrival and most‐energetic‐arrival methods, which retain only one traveltime, this alternative method retains most arrivals by the superposition of Gaussian beams. This paper presents a prestack Gaussian beam migration method that operates on common‐offset gathers. The method is efficient because the computation of beam superposition isolates summations that do not depend on the seismic data and evaluates these integrals by considering their saddle points. Gaussian beam migration of the two‐dimensional Marmousi test data set demonstrates the method’s effectiveness for structural imaging in a case where there is multipathing of seismic energy.

Imaging complex structures with semirecursive Kirchhoff migration

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 577-588 ◽  
Author(s):  
Dimitri Bevc
Keyword(s):  
Wave Equation ◽  
Adverse Effects ◽  
Velocity Structure ◽  
Computational Cost ◽  
Downward Continuation ◽  
Complex Structures ◽  
Complex Velocity ◽  
Data Set ◽  
Kirchhoff Migration ◽  
Small Depth

I present a semirecursive Kirchhoff migration algorithm that is capable of obtaining accurate images of complex structures by combining wave‐equation datuming and Kirchhoff migration. The method is successful because breaking up the complex velocity structure into small depth regions allows traveltimes to be calculated in regions where the computation is well‐behaved and where the computation corresponds to energetic arrivals. The traveltimes computed in such a region are used first for imaging and second for downward continuation of the entire survey (shots and receivers) to the boundary of the next region. This process results in images comparable to those obtained by shot‐profile migration, but at reduced computational cost. Because traveltimes are computed for small depth domains, the adverse effects of caustics, headwaves, and multiple arrivals do not develop. In principle, this method requires only the same number of traveltime calculations as a standard migration. Tests on the Marmousi data set produce excellent results.

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