Shot-domain deblending using least-squares inversion

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. V241-V256 ◽  
Author(s):  
Shaohuan Zu ◽  
Hui Zhou ◽  
Qingqing Li ◽  
Hanming Chen ◽  
Qingchen Zhang ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Conjugate Gradient ◽  
Acquisition Cost ◽  
Field Data ◽  
Gradient Algorithm ◽  
Convolution Operators ◽  
Excellent Performance ◽  
Simultaneous Source ◽  
Temporal Overlap

Simultaneous source acquisition, which allows a temporal overlap between shot records, has significant advantages to improve data quality (e.g., denser shooting) and reduce acquisition cost (e.g., efficient wide-azimuth shooting). We have developed a novel shot-domain deblending approach for a wide-azimuth simultaneous shooting survey based on an inversion scheme. The inverse problem is formulated by introducing two convolution operators that can respectively destruct the signal and interference and is solved by a conjugate-gradient algorithm in the least-squares sense. Our approach breaks down the limit that source separation can only be implemented in some domains other than the shot domain based on the incoherency principle. Our shot-domain approach does not require the random dithering time; thus, it is very flexible to use in a wide-azimuth simultaneous shooting survey. Three numerically blended synthetic examples were developed to demonstrate the excellent performance of our method. The feasibility has been further validated via a field-data example that is numerically blended from two realistic marine towed streamers.

Accelerating extended least-squares migration with weighted conjugate gradient iteration

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S165-S179 ◽  
Author(s):  
Jie Hou ◽  
William W. Symes
Keyword(s):  
Least Squares ◽  
Conjugate Gradient ◽  
Degrees Of Freedom ◽  
Velocity Model ◽  
Domain Model ◽  
Gradient Algorithm ◽  
Range Data ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Least Squares Migration

Least-squares migration (LSM) iteratively achieves a mean-square best fit to seismic reflection data, provided that a kinematically accurate velocity model is available. The subsurface offset extension adds extra degrees of freedom to the model, thereby allowing LSM to fit the data even in the event of significant velocity error. This type of extension also implies additional computational expense per iteration from crosscorrelating source and receiver wavefields over the subsurface offset, and therefore places a premium on rapid convergence. We have accelerated the convergence of extended least-squares migration by combining the conjugate gradient algorithm with weighted norms in range (data) and domain (model) spaces that render the extended Born modeling operator approximately unitary. We have developed numerical examples that demonstrate that the proposed algorithm dramatically reduces the number of iterations required to achieve a given level of fit or gradient reduction compared with conjugate gradient iteration with Euclidean (unweighted) norms.

The use of the conjugate‐gradient algorithm in the computation of predictive deconvolution operators

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2752-2758 ◽  
Author(s):  
Fulton Koehler ◽  
M. Turhan Taner
Keyword(s):  
Least Squares ◽  
Conjugate Gradient ◽  
Single Channel ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Time Varying ◽  
Simple Formulation ◽  
Deconvolution Problem ◽  
Levinson Algorithm ◽  
Multichannel Deconvolution

A number of excellent papers have been published since the introduction of deconvolution by Robinson in the middle 1950s. The application of the Wiener‐Levinson algorithm makes deconvolution a practical and vital part of today’s digital seismic data processing. We review the original formulation of deconvolution, develop the solution from another perspective, and demonstrate a general and rigorous solution that could be implemented. By “general” we mean a deterministic time‐varying and multichannel operator design, and by “rigorous” we mean the straightforward least‐squares error solution without simplifying to a Toeplitz matrix. Also we show that the conjugate‐gradient algorithm used in conjunction with the least‐squares problem leads to a satisfactory simplification; that in the computation of the operators, the square matrix involved in the normal equations need not be computed. Furthermore, the product of this matrix with a column matrix can be obtained directly from the data as a result of two cascaded simple convolutions. The time‐varying deconvolution problem is shown to be equivalent to the multichannel deconvolution problem. Hence, with one simple formulation and associated programming, the procedure can be utilized for time‐constant single‐channel and multichannel deconvolution and time‐varying single‐channel and multichannel deconvolution.

Substituting smoothing with low-rank decomposition — Applications to least-squares reverse time migration of simultaneous source and incomplete seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S267-S283 ◽  
Author(s):  
Yangkang Chen ◽  
Min Bai ◽  
Yatong Zhou ◽  
Qingchen Zhang ◽  
Yufeng Wang ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Low Rank ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Decomposition Operator ◽  
Rank Decomposition ◽  
Simultaneous Source ◽  
Low Rank Decomposition

Seismic migration can be formulated as an inverse problem, the model of which can be iteratively inverted via the least-squares migration framework instead of approximated by applying the adjoint operator to the observed data. Least-squares reverse time migration (LSRTM) has attracted more and more attention in modern seismic imaging workflows because of its exceptional performance in obtaining high-resolution true-amplitude seismic images and the fast development of the computational capability of modern computing architecture. However, due to a variety of reasons, e.g., insufficient shot coverage and data sampling, the image from least-squares inversion still contains a large amount of artifacts. This phenomenon results from the ill-posed nature of the inverse problem. In traditional LSRTM, the minimum least-squares energy of the model is used as a constraint to regularize the inverse problem. Considering the residual noise caused by the smoothing operator in traditional LSRTM, we regularize the model using a powerful low-rank decomposition operator, which can better suppress the migration artifacts in the image during iterative inversion. We evaluate in detail the low-rank decomposition operator and the way to apply it along the geologic structure of seismic reflectors. We comprehensively analyze the performance of our algorithm in attenuating crosstalk noise caused by simultaneous source acquisition and migration artifacts caused by insufficient space sampling via two synthetic examples and one field data example. Our results indicate that compared to the conventional smoothing operator, our low-rank decomposition operator can help obtain a cleaner LSRTM image and obtain a slightly better edge-preserving performance.

scholarly journals Seismic imaging of incomplete data and simultaneous-source data using least-squares reverse time migration with shaping regularization

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. S11-S20 ◽  
Author(s):  
Zhiguang Xue ◽  
Yangkang Chen ◽  
Sergey Fomel ◽  
Junzhe Sun
Keyword(s):  
Least Squares ◽  
Incomplete Data ◽  
Gradient Algorithm ◽  
Reverse Time ◽  
Crosstalk Noise ◽  
Reverse Time Migration ◽  
Direct Imaging ◽  
Time Migration ◽  
Source Data ◽  
Simultaneous Source

Simultaneous-source acquisition improves the efficiency of the seismic data acquisition process. However, direct imaging of simultaneous-source data may introduce crosstalk artifacts in the final image. Likewise, direct imaging of incomplete data avoids the step of data reconstruction, but it can suffer from migration artifacts. We have proposed to incorporate shaping regularization into least-squares reverse time migration (LSRTM) and use it for suppressing interference noise caused by simultaneous-source data or migration artifacts caused by incomplete data. To implement LSRTM, we have applied lowrank one-step reverse time migration and its adjoint iteratively in the conjugate-gradient algorithm to minimize the data misfit. A shaping operator imposing structure constraints on the estimated model was applied at each iteration. We constructed the shaping operator as a structure-enhancing filtering to attenuate migration artifacts and crosstalk noise while preserving structural information. We have carried out numerical tests on synthetic models in which the proposed method exhibited a fast convergence rate and was effective in attenuating migration artifacts and crosstalk noise.

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

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