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.

Can we image complex structures with first‐arrival traveltime?

Geophysics ◽  
1993 ◽  
Vol 58 (4) ◽  
pp. 564-575 ◽  
Author(s):  
Sébastien Geoltrain ◽  
Jean Brac
Keyword(s):  
Eikonal Equation ◽  
Geological Structure ◽  
Complex Structures ◽  
Complex Velocity ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Finite Differencing ◽  
Explicit Reference ◽  
First Arrival ◽  
Kirchhoff Depth Migration

We experienced difficulties when attempting to perform seismic imaging in complex velocity fields using prestack Kirchhoff depth migration in conjunction with traveltimes computed by finite‐differencing the eikonal equation. The problem arose not because of intrinsic limitations of Kirchhoff migration, but rather from the failure of finite‐differencing to compute traveltimes representative of the energetic part of the wavefield. Further analysis showed that the first arrival is most often associated with a marginally energetic event wherever subsequent arrivals exist. The consequence is that energetic seismic events are imaged with a kinematically incorrect operator and turn out mispositioned at depth. We therefore recommend that first‐arrival traveltime fields, such as those computed by finite‐differencing the eikonal equation, be used in Kirchhoff migration only with great care when the velocity field hosts multiple transmitted arrivals; such a situation is typically met where geological structure creates strong and localized velocity heterogeneities, which partition the incident and reflected wavefields into multiple arrivals; in such an instance, imaging cannot be strictly considered a kinematic process, as it must be performed with explicit reference to the relative amplitudes of multiple arrivals.

Optimization of the parameters in complex Padé Fourier finite-difference migration

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S259-S269 ◽  
Author(s):  
Marco Salcedo ◽  
Amélia Novais ◽  
Jörg Schleicher ◽  
Jessé C. Costa
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Rotation Angle ◽  
Computational Cost ◽  
Wide Angle ◽  
Model Data ◽  
Data Set ◽  
Dependent Parameter ◽  
The One

Complex Padé Fourier finite-difference migration is a stable one-way wave-equation technique that allows for better treatment of evanescent modes than its real counterpart, in this way producing fewer artifacts. As for real Fourier finite-difference (FFD) migration, its parameters can be optimized to improve the imaging of steeply dipping reflectors. The dip limitation of the FFD operator depends on the variation of the velocity field. We have developed a wide-angle approximation for the one-way continuation operator by means of optimization of the Padé coefficients and the most important velocity-dependent parameter. We have evaluated the achieved quality of the approximate dispersion relation in dependence on the chosen function of the ratio between the model and reference velocities under consideration of the number of terms in the Padé approximation and the branch-cut rotation angle. The optimized parameters are chosen based on the migration results and the computational cost. We found that by using the optimized parameters, a one-term expansion achieves the highest dip angles. The implementations were validated on the Marmousi data set and SEG/EAGE salt model data.

scholarly journals Wave-equation migration velocity analysis using plane-wave common-image gathers

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. S327-S340 ◽  
Author(s):  
Bowen Guo ◽  
Gerard T. Schuster
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Computational Cost ◽  
Migration Velocity ◽  
Memory Storage ◽  
Velocity Analysis ◽  
Data Set ◽  
Image Domain ◽  
Migration Velocity Analysis ◽  
Wave Migration

Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain, or time-lag common-image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, we have developed a WEMVA method using plane-wave CIGs. Plane-wave CIGs reduce computational cost and memory storage because they are directly calculated from prestack plane-wave migration and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic data sets and a field data set validate the efficiency and effectiveness of this method.

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.

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.

Green’s function implementation of common‐offset, wave‐equation migration

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1813-1821 ◽  
Author(s):  
Andreas Ehinger ◽  
Patrick Lailly ◽  
Kurt J. Marfurt
Keyword(s):  
Wave Equation ◽  
Green's Functions ◽  
Wave Equations ◽  
Green’S Functions ◽  
Data Set ◽  
Kirchhoff Migration ◽  
Migration Velocity Analysis ◽  
Standard Wave ◽  
The Cost ◽  
Wavefield Extrapolation

Common‐offset migration is extremely important in the context of migration velocity analysis (MVA) since it generates geologically interpretable migrated images. However, only a wave‐equation‐based migration handles multipathing of energy in contrast to the popular Kirchhoff migration with first‐arrival traveltimes. We have combined the superior treatment of multipathing of energy by wave‐equation‐based migration with the advantages of the common‐offset domain for MVA by implementing wave‐equation migration algorithms via the use of finite‐difference Green’s functions. With this technique, we are able to apply wave‐equation migration in measurement configurations that are usually considered to be of the realm of Kirchhoff migration. In particular, wave‐equation migration of common offset sections becomes feasible. The application of our wave‐equation, common‐offset migration algorithm to the Marmousi data set confirms the large increase in interpretability of individual migrated sections, for about twice the cost of standard wave‐equation common‐shot migration. Our implementation of wave‐equation migration via the Green’s functions is based on wavefield extrapolation via paraxial one‐way wave equations. For these equations, theoretical results allow us to perform exact inverse extrapolation of wavefields.

Straight-rays redatuming: A fast and robust alternative to wave-equation-based datuming

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. U37-U46 ◽  
Author(s):  
Tariq Alkhalifah ◽  
Claudio Bagaini
Keyword(s):  
Wave Equation ◽  
Computational Cost ◽  
Synthetic Data ◽  
Velocity Model ◽  
Common Source ◽  
Detailed Knowledge ◽  
Surface Integral ◽  
Data Set ◽  
Interval Velocity ◽  
Static Correction

Wave-equation-based redatuming is expensive and requires a detailed knowledge of the shallow velocity field. We derive the analytical expression of a new prestack wavefield extrapolation operator, the Topographic Datuming Operator (TDO), which applies redatuming based on straight-rays approximation above and below a chosen datum. This redatuming operator is directly applied to common-source gathers to downward continue the source and the receivers, simultaneously, to the datum level without resorting to common-receiver gathers. As a result, the method is far more efficient and robust than the conventional wave-equation-based redatuming and does not require an accurate depth-domain interval velocity model. In addition, TDO, unlike wave-equation-based redatuming, requires effective velocities above datum, and thus can be applied using attributes valid for static correction methods. Effective velocities beneath the datum permit us to replace the surface integral, which is needed for wave-equation redatuming with a line integral. In the particular case of infinite (in practice, very high with respect to the shallow layers) velocity beneath the datum, the TDO impulse response collapses to a point, and TDO redatuming is equivalent to conventional static correction, which may, therefore, be regarded as a special case of the newly derived operator. The computational cost of applying TDO is slightly larger than static corrections, yet provides higher quality results partially attributable to the ability of TDO to suppress diffractions emanating from anomalies above datum. Since TDO is an operation based on geometrical optics approximation, velocity after TDO is not biased by the vertical shift correction associated with conventional static correction. Application to a synthetic data set demonstrates the features of the method.

Frequency-domain wave-equation traveltime inversion with a monofrequency component

Geophysics ◽  
2021 ◽  
Vol 86 (6) ◽  
pp. R913-R926
Author(s):  
Jianhua Wang ◽  
Jizhong Yang ◽  
Liangguo Dong ◽  
Yuzhu Liu
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Time Domain ◽  
Computational Cost ◽  
Velocity Model ◽  
Receiver Side ◽  
Data Set ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
The Time Domain

Wave-equation traveltime inversion (WTI) is a useful tool for background velocity model building. It is generally formulated and implemented in the time domain, in which the gradient is calculated by temporally crosscorrelating the source- and receiver-side wavefields. The time-domain source-side snapshots are either stored in memory or are reconstructed through back propagation. The memory requirements and computational cost of WTI are thus prohibitively expensive, especially for 3D applications. To partially alleviate this problem, we provide an implementation of WTI in the frequency domain with a monofrequency component. Because only one frequency is used, it is affordable to directly store the source- and receiver-side wavefields in memory. There is no need for wavefield reconstruction during gradient calculation. In such a way, we have dramatically reduced the memory requirements and computational cost compared with the traditional time-domain WTI realization. For practical implementation, the frequency-domain wavefield is calculated by time-domain finite-difference forward modeling and is transformed to the frequency domain by an on-the-fly discrete Fourier transform. Numerical examples on a simple lateral periodic velocity model and the Marmousi model demonstrate that our method can obtain accurate background velocity models comparable with those from time-domain WTI and frequency-domain WTI with multiple frequencies. A field data set test indicates that our method obtains a background velocity model that well predicts the seismic wave traveltime.

scholarly journals A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3978
Author(s):  
Rocco Peter Fornari ◽  
Piotr de Silva
Keyword(s):  
Organic Molecules ◽  
Ph Value ◽  
Computational Cost ◽  
Legendre Transform ◽  
Good Prediction ◽  
Redox Potentials ◽  
Free Energies ◽  
Hybrid Functional ◽  
Data Set ◽  
State Changes

Discovering new materials for energy storage requires reliable and efficient protocols for predicting key properties of unknown compounds. In the context of the search for new organic electrolytes for redox flow batteries, we present and validate a robust procedure to calculate the redox potentials of organic molecules at any pH value, using widely available quantum chemistry and cheminformatics methods. Using a consistent experimental data set for validation, we explore and compare a few different methods for calculating reaction free energies, the treatment of solvation, and the effect of pH on redox potentials. We find that the B3LYP hybrid functional with the COSMO solvation method, in conjunction with thermal contributions evaluated from BLYP gas-phase harmonic frequencies, yields a good prediction of pH = 0 redox potentials at a moderate computational cost. To predict how the potentials are affected by pH, we propose an improved version of the Alberty-Legendre transform that allows the construction of a more realistic Pourbaix diagram by taking into account how the protonation state changes with pH.

Adaptive sampling of potential-field data: A direct approach to compressive inversion

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. IM1-IM9 ◽  
Author(s):  
Nathan Leon Foks ◽  
Richard Krahenbuhl ◽  
Yaoguo Li
Keyword(s):  
Potential Field ◽  
Adaptive Sampling ◽  
Field Data ◽  
Computational Cost ◽  
Large Field ◽  
Magnetic Data ◽  
Data Sampling ◽  
Data Types ◽  
Data Set ◽  
Potential Field Data

Compressive inversion uses computational algorithms that decrease the time and storage needs of a traditional inverse problem. Most compression approaches focus on the model domain, and very few, other than traditional downsampling focus on the data domain for potential-field applications. To further the compression in the data domain, a direct and practical approach to the adaptive downsampling of potential-field data for large inversion problems has been developed. The approach is formulated to significantly reduce the quantity of data in relatively smooth or quiet regions of the data set, while preserving the signal anomalies that contain the relevant target information. Two major benefits arise from this form of compressive inversion. First, because the approach compresses the problem in the data domain, it can be applied immediately without the addition of, or modification to, existing inversion software. Second, as most industry software use some form of model or sensitivity compression, the addition of this adaptive data sampling creates a complete compressive inversion methodology whereby the reduction of computational cost is achieved simultaneously in the model and data domains. We applied the method to a synthetic magnetic data set and two large field magnetic data sets; however, the method is also applicable to other data types. Our results showed that the relevant model information is maintained after inversion despite using 1%–5% of the data.

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