Velocity inversion by global optimization using finite-offset common-reflection-surface stacking applied to synthetic and Tacutu Basin seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R165-R174 ◽  
Author(s):  
Marcelo Jorge Luz Mesquita ◽  
João Carlos Ribeiro Cruz ◽  
German Garabito Callapino
Keyword(s):  
Objective Function ◽  
Real Data ◽  
Velocity Model ◽  
Data Sets ◽  
Layer By Layer ◽  
Velocity Inversion ◽  
Very Fast Simulated Annealing ◽  
Target Layer ◽  
Common Reflection Surface ◽  
The Mean

Estimation of an accurate velocity macromodel is an important step in seismic imaging. We have developed an approach based on coherence measurements and finite-offset (FO) beam stacking. The algorithm is an FO common-reflection-surface tomography, which aims to determine the best layered depth-velocity model by finding the model that maximizes a semblance objective function calculated from the amplitudes in common-midpoint (CMP) gathers stacked over a predetermined aperture. We develop the subsurface velocity model with a stack of layers separated by smooth interfaces. The algorithm is applied layer by layer from the top downward in four steps per layer. First, by automatic or manual picking, we estimate the reflection times of events that describe the interfaces in a time-migrated section. Second, we convert these times to depth using the velocity model via application of Dix’s formula and the image rays to the events. Third, by using ray tracing, we calculate kinematic parameters along the central ray and build a paraxial FO traveltime approximation for the FO common-reflection-surface method. Finally, starting from CMP gathers, we calculate the semblance of the selected events using this paraxial traveltime approximation. After repeating this algorithm for all selected CMP gathers, we use the mean semblance values as an objective function for the target layer. When this coherence measure is maximized, the model is accepted and the process is completed. Otherwise, the process restarts from step two with the updated velocity model. Because the inverse problem we are solving is nonlinear, we use very fast simulated annealing to search the velocity parameters in the target layers. We test the method on synthetic and real data sets to study its use and advantages.

Interpolating wide-aperture ground-penetrating radar beyond aliasing

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. H13-H22 ◽  
Author(s):  
Saulo S. Martins ◽  
Jandyr M. Travassos
Keyword(s):  
Ground Penetrating Radar ◽  
Real Data ◽  
Velocity Model ◽  
Data Sets ◽  
Inversion Problem ◽  
Data Set ◽  
Isolated Points ◽  
Antarctic Continent ◽  
Ground Penetrating ◽  
The Antarctic

Most of the data acquisition in ground-penetrating radar is done along fixed-offset profiles, in which velocity is known only at isolated points in the survey area, at the locations of variable offset gathers such as a common midpoint. We have constructed sparse, heavily aliased, variable offset gathers from several fixed-offset, collinear, profiles. We interpolated those gathers to produce properly sampled counterparts, thus pushing data beyond aliasing. The interpolation methodology estimated nonstationary, adaptive, filter coefficients at all trace locations, including at the missing traces’ corresponding positions, filled with zeroed traces. This is followed by an inversion problem that uses the previously estimated filter coefficients to insert the new, interpolated, traces between the original ones. We extended this two-step strategy to data interpolation by employing a device in which we used filter coefficients from a denser variable offset gather to interpolate the missing traces on a few independently constructed gathers. We applied the methodology on synthetic and real data sets, the latter acquired in the interior of the Antarctic continent. The variable-offset interpolated data opened the door to prestack processing, making feasible the production of a prestack time migrated section and a 2D velocity model for the entire profile. Notwithstanding, we have used a data set obtained in Antarctica; there is no reason the same methodology could not be used somewhere else.

From migration to inversion velocity analysis

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S207-S223 ◽  
Author(s):  
Hervé Chauris ◽  
Emmanuel Cocher
Keyword(s):  
Objective Function ◽  
Synthetic Data ◽  
Velocity Model ◽  
Specific Power ◽  
Model Parameters ◽  
Data Sets ◽  
Velocity Analysis ◽  
Low Velocity ◽  
Image Domain ◽  
New Approach

Migration velocity analysis (MVA) is a technique defined in the image domain to determine the background velocity model controlling the kinematics of wave propagation. In the presence of discontinuous interfaces, the velocity gradient used to iteratively update the velocity model exhibits spurious oscillations. For more stable results, we replace the migration part by an inversion scheme. By definition, migration is the adjoint of the Born modeling operator, whereas inversion is its asymptotic inverse. We have developed new expressions in 1D and 2D cases based on two-way wave-equation operators. The objective function measures the quality of the images obtained by inversion in the extended domain depending on the subsurface offset. In terms of implementation, the new approach is very similar to classic MVA. A 1D analysis found that oscillatory terms around the interface positions can be removed by multiplying the inversion result with the velocity at a specific power before evaluating the objective function. Several 2D synthetic data sets are discussed through the computation of the gradient needed to update the model parameters. Even for discontinuous reflectivity models, the new approach provides results without artificial oscillations. The model update corresponds to a gradient of an existing objective function, which was not the case for the horizontal contraction approach proposed as an alternative to deal with gradient artifacts. It also correctly handles low-velocity anomalies, contrary to the horizontal contraction approach. Inversion velocity analysis offers new perspectives for the applicability of image-domain velocity analysis.

Global optimization strategies for implementing 3D common-reflection-surface stack using the very fast simulated annealing algorithm: Application to real land data

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. V253-V261 ◽  
Author(s):  
German Garabito
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Computational Cost ◽  
Velocity Model ◽  
Global Search ◽  
Optimization Strategy ◽  
Very Fast Simulated Annealing ◽  
Common Reflection Surface ◽  
Annealing Algorithm

The 3D common-reflection-surface (CRS) stack operator depends on eight kinematic wavefield attributes that must be extracted from the prestack data. These attributes are obtained by an efficient optimization strategy based on the maximization of the coherence measure of the seismic reflection events included by the CRS stacking operator. The main application of these kinematic attributes is to simulate zero-offset stacked data; however, they can also be used for regularization of the prestack data, prestack migration, and velocity model determination. The initial implementations of the 3D CRS stack used grid-search techniques to determine the attributes in several steps with the drawback that accumulated errors can deteriorate the final result. In this work, the global optimization very fast simulated annealing algorithm is used to search for the kinematic attributes by applying three optimization strategies for implementing CRS stacking: (1) simultaneous global search of five kinematic attributes of the 3D common-diffraction-surface stacking operator, (2) two-step global optimization strategy to first search for three attributes and then five attributes of the CRS stacking operator, and (3) simultaneous global search of eight kinematic attributes of the CRS operator. The proposed CRS stacking algorithms are applied to land data of the Potiguar Basin, Brazil. It is demonstrated that the one-step optimization strategy of the eight parameters produces the best results, however, with a higher computational cost.

Using Mahalanobis Clustering Algorithm for College Student Learning Fundamental Mathematics

2012 ◽  
Vol 476-478 ◽  
pp. 2129-2132
Author(s):  
Chin Chun Chen
Keyword(s):  
Objective Function ◽  
Covariance Matrix ◽  
Clustering Algorithm ◽  
Distance Measure ◽  
Real Data ◽  
Threshold Value ◽  
Data Sets ◽  
Multivariate Gaussian Distribution ◽  
Euclidean Distance Function ◽  
College Student Learning

The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In GK-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Mahalanobis Clustering Algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Mahalanobis Clustering Algorithm Based on FCM.

Removing fault shadow distortions from seismic images using depth-velocity modelling and pre-stack depth migration

2012 ◽  
Vol 52 (2) ◽  
pp. 700
Author(s):  
Sergey Birdus ◽  
Alexey Artyomov
Keyword(s):  
Real Data ◽  
Velocity Model ◽  
Velocity Inversion ◽  
Depth Migration ◽  
Velocity Models ◽  
Depth Processing ◽  
Different Types ◽  
Successful Removal ◽  
Velocity Anomalies ◽  
Additional Image

In many areas, fault shadows manifest a serious challenge to seismic imaging. The major part of this problem is caused by different types of velocity variations caused by faults. Pre-stack depth migration with sufficiently accurate velocity model successfully resolves this problem and the high resolution tomographic depth-velocity modelling is the most important component of the solution. During depth processing on a number of real 3D seismic datasets with fault shadows from Australia and other regions, the following were noticed: The appearance of the image distortions below the faults and the convergence speed of the tomographic velocity inversion depend on the acquisition direction. Sometimes, tomographic modelling produces depth-velocity models that closely follow geology, but the models contain non-geological looking anomalies in other areas. In both cases, the depth migration delivers distortion-free images. If anisotropy is present in faulted areas, it creates additional image distortions and can require extra input data and processing efforts. To examine these effects and optimise depth-processing workflow, several 3D synthetic seismic datasets were created for different types of velocity anomalies associated with the faults in isotropic and anisotropic media and different acquisition directions. On synthetic and real data from Australia, different types of fault shadows are illustrated; how they can be solved depending on the acquisition direction are also shown. Some types of the fault shadows are shown to require multi-azimuth illumination to guarantee their successful removal.

Supervised Clustering Algorithm for University Student Learning Algebra

2012 ◽  
Vol 542-543 ◽  
pp. 1376-1379
Author(s):  
Jeng Ming Yih
Keyword(s):  
Objective Function ◽  
Covariance Matrix ◽  
Clustering Algorithm ◽  
Distance Measure ◽  
Real Data ◽  
Threshold Value ◽  
Data Sets ◽  
Multivariate Gaussian Distribution ◽  
Supervised Clustering ◽  
Euclidean Distance Function

The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In GK-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Supervised Clustering Algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Supervised Clustering Algorithm.

scholarly journals Utilizing diffractions in wavefront tomography

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. R65-R73 ◽  
Author(s):  
Alexander Bauer ◽  
Benjamin Schwarz ◽  
Dirk Gajewski
Keyword(s):  
Joint Inversion ◽  
Velocity Model ◽  
Original Data ◽  
Complex Salt ◽  
Reverse Time ◽  
Velocity Inversion ◽  
Velocity Models ◽  
Reflection Data ◽  
Common Reflection Surface ◽  
Zero Offset

Wavefront tomography is known to be an efficient and stable approach for velocity inversion that does not require accurate starting models and does not interact directly with the prestack data. Instead, the original data are transformed to physically meaningful wavefront attribute fields. These can be automatically estimated using local-coherence analysis by means of the common-reflection-surface (CRS) stack, which has been shown to be a powerful tool for data analysis and enhancement. In addition, the zero-offset wavefront attributes acquired during the CRS stack can be used for sophisticated subsequent processes such as wavefield characterization and separation. Whereas in previous works, wavefront tomography has been applied mainly to reflection data, resulting in smooth velocity models suitable for migration of targets with moderately complex overburden, we have emphasized using the diffracted contributions in the data for velocity inversion. By means of simple synthetic examples, we reveal the potential of diffractions for velocity inversion. On industrial field data, we suggest a joint inversion based on reflected and diffracted contributions of the measured wavefield, which confirms the general finding that diffraction-based wavefront tomography can help to increase the resolution of the velocity models. Concluding our work, we compare the quality of a reverse time migrated result using the estimated velocity model with the result based on the inversion of reflections, which reveals an improved imaging potential for a complex salt geometry.

Coupling direct inversion to common-shot image-domain velocity analysis

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R497-R514 ◽  
Author(s):  
Yubing Li ◽  
Hervé Chauris
Keyword(s):  
Objective Function ◽  
Velocity Gradient ◽  
Large Scale ◽  
Synthetic Data ◽  
Essential Element ◽  
Velocity Model ◽  
Data Sets ◽  
Velocity Analysis ◽  
Image Domain ◽  
Direct Inversion

Migration velocity analysis is a technique used to estimate the large-scale structure of the subsurface velocity model controlling the kinematics of wave propagation. For more stable results, recent studies have proposed to replace migration, adjoint of Born modeling, by the direct inverse of the modeling operator in the context of extended subsurface-offset domain. Following the same strategy, we have developed a two-way-wave-equation-based inversion velocity analysis (IVA) approach for the original surface-oriented shot gathers. We use the differential semblance optimization (DSO) objective function to evaluate the quality of inverted images depending on shot positions and to derive the associated gradient, an essential element to update the macromodel. We evaluate the advantages and limitations through applications of 2D synthetic data sets, first on simple models with a single-reflector embedded in various background velocities and then on the Marmousi model. The direct inverse attenuates migration smiles by compensating for geometric spreading and uneven illuminations. We slightly modified the original DSO objective function to remove spurious oscillations around interface positions in the velocity gradient. These oscillations are related to the fact that the locations of events in the image domain depend on the macromodel. We pay attention to the presence of triplicated wavefields. It appears that IVA is robust even if artifacts are observed in the seismic migrated section. The velocity gradient leads to a stable update, especially after a Gaussian smoothing over a wavelength distance. Coupling common-shot direct inversion to velocity analysis offers new possibilities for the extension to 3D in the future.

scholarly journals A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3003
Author(s):  
Jurgita Arnastauskaitė ◽  
Tomas Ruzgas ◽  
Mindaugas Bražėnas
Keyword(s):  
Goodness Of Fit ◽  
Distribution Density ◽  
Empirical Distribution ◽  
Real Data ◽  
Multivariate Normality ◽  
Data Sets ◽  
Goodness Of Fit Test ◽  
Absolute Deviation ◽  
Test For Multivariate Normality ◽  
The Mean

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

Prestack migration velocity estimation using nonlinear methods

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 138-150 ◽  
Author(s):  
Michael Jervis ◽  
Mrinal K. Sen ◽  
Paul L. Stoffa
Keyword(s):  
Objective Function ◽  
Real Data ◽  
Velocity Model ◽  
Optimization Methods ◽  
Velocity Estimation ◽  
Model Parameters ◽  
Waveform Data ◽  
Nonlinear Methods ◽  
Depth Migration ◽  
Computationally Intensive

We describe here methods of estimating interval velocities based on two nonlinear optimization methods; very fast simulated annealing (VFSA) and a genetic algorithm (GA). The objective function is defined using prestack seismic data after depth migration. This inverse problem involves optimizing the lateral consistency of reflectors between adjacent migrated shot records. In effect, the normal moveout correction in velocity analysis is replaced by prestack depth migration. When the least‐squared difference between each pair of migrated shots is at a minimum, the true velocity model has been found. Our model is parameterized using cubic‐B splines distributed on a rectangular grid. The main advantages of using migrated data are that they do not require traveltime picking, knowledge of the source wavelet, and expensive computation of synthetic waveform data to assess the degree of data‐model fit. Nonlinear methods allow automated determination of the global minimum without relying on estimates of the gradient of the objective function, the starting model, or making assumptions about the nature of the objective function itself. For the velocity estimation problem, the VFSA converges 4 to 5 times faster than the GA for both a 2-D synthetic example and a structurally complex real data example from the Gulf of Mexico. Though computationally intensive, this problem requires few model parameters, and use of a fast traveltime code for Kirchhoff migration makes the algorithm tractable for real earth problems.

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