Efficient simultaneous wave-equation statics and trace regularization by series approximation

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. U19-U28 ◽  
Author(s):  
Robert J. Ferguson

To address the problems of irregular trace spacing and statics correction, simultaneous regularization and wave-equation statics (WE statics) are implemented by least-squares inversion. In general, inversion is found to be intractable in three dimensions, so series approximation is made to reduce significantly the number of required integrals. The resulting operator is suitable for direct inversion or for use with gradient methods. Real and synthetic data are used to determine the viability of the inversion. For synthetic data, even for severe velocity variation and topography, inversion converges to an acceptable solution, and aliasing is reduced significantly. Similarly, for real data, inversion is found to return an antialiased, regularized result with WE statics applied.

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
João Lobo ◽  
Rui Henriques ◽  
Sara C. Madeira

Abstract Background Three-way data started to gain popularity due to their increasing capacity to describe inherently multivariate and temporal events, such as biological responses, social interactions along time, urban dynamics, or complex geophysical phenomena. Triclustering, subspace clustering of three-way data, enables the discovery of patterns corresponding to data subspaces (triclusters) with values correlated across the three dimensions (observations $$\times$$ × features $$\times$$ × contexts). With increasing number of algorithms being proposed, effectively comparing them with state-of-the-art algorithms is paramount. These comparisons are usually performed using real data, without a known ground-truth, thus limiting the assessments. In this context, we propose a synthetic data generator, G-Tric, allowing the creation of synthetic datasets with configurable properties and the possibility to plant triclusters. The generator is prepared to create datasets resembling real 3-way data from biomedical and social data domains, with the additional advantage of further providing the ground truth (triclustering solution) as output. Results G-Tric can replicate real-world datasets and create new ones that match researchers needs across several properties, including data type (numeric or symbolic), dimensions, and background distribution. Users can tune the patterns and structure that characterize the planted triclusters (subspaces) and how they interact (overlapping). Data quality can also be controlled, by defining the amount of missing, noise or errors. Furthermore, a benchmark of datasets resembling real data is made available, together with the corresponding triclustering solutions (planted triclusters) and generating parameters. Conclusions Triclustering evaluation using G-Tric provides the possibility to combine both intrinsic and extrinsic metrics to compare solutions that produce more reliable analyses. A set of predefined datasets, mimicking widely used three-way data and exploring crucial properties was generated and made available, highlighting G-Tric’s potential to advance triclustering state-of-the-art by easing the process of evaluating the quality of new triclustering approaches.


Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 786-799 ◽  
Author(s):  
P. B. Dillon

Wave‐equation migration can form an accurate image of the subsurface from suitable VSP data. The image’s extent and resolution are determined by the receiver array dimensions and the source location(s). Experiments with synthetic and real data show that the region of reliable image extent is defined by the specular “zone of illumination.” Migration is achieved through wave‐field extrapolation, subject to an imaging procedure. Wave‐field extrapolation is based upon the scalar wave equation and, for VSP data, is conveniently handled by the Kirchhoff integral. The migration of VSP data calls for imaging very close to the borehole, as well as imaging in the far field. This dual requirement is met by retaining the near‐field term of the integral. The complete integral solution is readily controlled by various weighting devices and processing strategies, whose worth is demonstrated on real and synthetic data.


Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. B153-B165 ◽  
Author(s):  
Kai Yang ◽  
Hong-Ming Zheng ◽  
Li Wang ◽  
Yu-Zhu Liu ◽  
Fan Jiang ◽  
...  

An integrated wave-equation datuming scheme improves the imaging quality of seismic data from overthrust areas. It can be regarded as integrated because upward-layer replacement is included. In this scheme, data are downward continued to a nonplanar datum (such as the base of the weathering layer), followed by upward continuation from the nonplanar datum to a final planar datum using a one-way extrapolator. When compared with a Kirchhoff integral, this method can deal better with the strong lateral velocity variation within the near surface. After a test on synthetic data, the scheme is applied successfully to real 2D overthrust data acquired in the Qi-Lian foothills, western China. Compared with results using static corrections, integrated wave-equation datuming results lead to better reconstruction of the diffractions and reflections, more reliable migration-velocity analyses, and stronger stack and final depth images.


Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. U1-U8 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah

Macro-velocity model building is important for subsequent prestack depth migration and full-waveform inversion. Wave-equation migration velocity analysis uses the band-limited waveform to invert for velocity. Normally, inversion would be implemented by focusing the subsurface offset common-image gathers. We reexamine this concept with a different perspective: In the subsurface offset domain, using extended Born modeling, the recorded data can be considered as invariant with respect to the perturbation of the position of the virtual sources and velocity at the same time. A linear system connecting the perturbation of the position of those virtual sources and velocity is derived and solved subsequently by the conjugate gradient method. In theory, the perturbation of the position of the virtual sources is given by the Rytov approximation. Thus, compared with the Born approximation, it relaxes the dependency on amplitude and makes the proposed method more applicable for real data. We determined the effectiveness of the approach by applying the proposed method on isotropic and anisotropic vertical transverse isotropic synthetic data. A real data set example verifies the robustness of the proposed method.


Geophysics ◽  
1988 ◽  
Vol 53 (10) ◽  
pp. 1311-1322 ◽  
Author(s):  
V. Shtivelman ◽  
A. Canning

Seismic sections are usually datum corrected by static shifting. For small differences in elevation and slow velocity variations between the input datum and the output datum, static shifting is a sufficiently accurate datum correction procedure. However, for significant differences in elevations and a more complicated velocity model, the accuracy of the static solution may prove to be insufficient; and a more exact method should be used. In this paper, we study the limitations of the static method of datum correction and develop simple and effective extrapolation schemes based on the wave equation, schemes which lead to more accurate datum correction. The distortions of seismic events caused by static correction are illustrated by a number of simple examples. To reduce the distortions, we propose a number of extrapolation schemes based on the asymptories of the Kirchhoff integral solution of the 2-D scalar wave equation. Application of the extrapolation algorithms to synthetic data shows that they provide accurate datum corrections even for a nonplanar input datum and vertical and lateral velocity variations. The algorithms have been successfully applied to real data.


Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. S95-S101 ◽  
Author(s):  
Tariq Alkhalifah

Using the stationary-phase method, prestack phase-shift migration is implemented one offset at a time. This separate-offset implementation allows for a Fourier (reasonably fast) wave-equation-type migration on data with irregular offset sampling. However, the separate-offset phase-shift migration, like its zero-offset counterpart, handles only vertically inhomogeneous media. Using the combination of the split-step and phase-shift-plus-interpolation (PSPI) approaches, the separate-offset phase-shift migration is extended to handle laterally inhomogeneous media. The cost of the separate-offset implementation is practically equivalent to that of the conventional zero-offset version. However, due to the lack of exact source and receiver ray-trajectory information in the separate-offset implementation, the combined split-step and PSPI handles only smooth lateral inhomogeneity. Specifically, it produces images equivalent to those resulting from smoothing the velocity model laterally over a window equal to the half offset. Thus, for zero-offset or laterally homogeneous media, the separate-offset migration is equivalent to any wave-equation-based migration. Errors might occur for finite-offset data in laterally inhomogeneous media. Such errors depend primarily on the strength of lateral inhomogeneity. Using this separate-offset phase-shift migration, accurate images of synthetic data of a model with large reflector dips and good images from real data from offshore Trinidad are obtained.


2015 ◽  
Vol 12 (13) ◽  
pp. 10137-10166
Author(s):  
R. N. C. Latimer ◽  
D. A. Risk

Abstract. Physical soil properties create lags between temperature change and corresponding soil responses, which obscure true Q10 values and other biophysical parameters such as depth of production. This study examines an inversion approach for estimating Q10 and depth of production (Zp) using physically based soil models, constrained by observed high-frequency surface fluxes and/or concentrations. Our inversion strategy uses a 1-D multi-layered soil model that simulates realistic temperature and gas diffusion. We tested inversion scenarios on synthetic data using a range of constraining parameters, time averaging techniques, mechanisms to improve computational efficiency, and various methods of incorporating real data into the model. Overall, we have found that with carefully constrained data, inversion was possible. While inversions using exclusively surface flux measurements could succeed, constraining the inversion using multiple shallow subsurface CO2 measurements proved to be most successful. Inversions constrained by these shallow measurements returned Q10 and Zp values with average errors of 1.85 and 0.16 % respectively. This work is a first step toward building a reliable framework for removing physical effects from high frequency soil CO2 data. Ultimately, we hope that this process will lead to better estimates of biophysical soil parameters and their variability on short timescales.


Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 627-636 ◽  
Author(s):  
Pantelis M. Soupios ◽  
Constantinos B. Papazachos ◽  
Christopher Juhlin ◽  
Gregory N. Tsokas

This paper deals with the problem of nonlinear seismic velocity estimation from first‐arrival traveltimes obtained from crosshole and downhole experiments in three dimensions. A standard tomographic procedure is applied, based on the representation of the crosshole area into a number of cells which have an initial slowness assigned. For the forward modeling, the raypath matrix is computed using the revisited ray bending method, supplemented by an approximate computation of the first Fresnel zone at each point of the ray, hence using physical and not only mathematical rays. Since 3-D ray tracing is incorporated, the inversion technique is nonlinear. Velocity images are obtained by a constrained least‐squares inversion scheme using both “damping” and “smoothing” factors. The appropriate choice of these factors is defined by the use of appropriate criteria such as the L-curve. The tomographic approach is improved by incorporating a priori information about the media to be imaged into our inversion scheme. This improvement in imaging is achieved by projecting a desirable solution onto the null space of the inversion, and including this null‐space contribution with the standard non‐null‐space inversion solution. The efficiency of the inversion scheme is tested through a series of tests with synthetic data. Moreover, application in the area of the Ural Mountains using real data demonstrates that the proposed technique produces more realistic velocity models than those obtained by other standard approaches.


Author(s):  
P.L. Nikolaev

This article deals with method of binary classification of images with small text on them Classification is based on the fact that the text can have 2 directions – it can be positioned horizontally and read from left to right or it can be turned 180 degrees so the image must be rotated to read the sign. This type of text can be found on the covers of a variety of books, so in case of recognizing the covers, it is necessary first to determine the direction of the text before we will directly recognize it. The article suggests the development of a deep neural network for determination of the text position in the context of book covers recognizing. The results of training and testing of a convolutional neural network on synthetic data as well as the examples of the network functioning on the real data are presented.


2021 ◽  
Vol 40 (3) ◽  
pp. 1-12
Author(s):  
Hao Zhang ◽  
Yuxiao Zhou ◽  
Yifei Tian ◽  
Jun-Hai Yong ◽  
Feng Xu

Reconstructing hand-object interactions is a challenging task due to strong occlusions and complex motions. This article proposes a real-time system that uses a single depth stream to simultaneously reconstruct hand poses, object shape, and rigid/non-rigid motions. To achieve this, we first train a joint learning network to segment the hand and object in a depth image, and to predict the 3D keypoints of the hand. With most layers shared by the two tasks, computation cost is saved for the real-time performance. A hybrid dataset is constructed here to train the network with real data (to learn real-world distributions) and synthetic data (to cover variations of objects, motions, and viewpoints). Next, the depth of the two targets and the keypoints are used in a uniform optimization to reconstruct the interacting motions. Benefitting from a novel tangential contact constraint, the system not only solves the remaining ambiguities but also keeps the real-time performance. Experiments show that our system handles different hand and object shapes, various interactive motions, and moving cameras.


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