scholarly journals Least-squares diffraction imaging using shaping regularization by anisotropic smoothing

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. S313-S325
Author(s):  
Dmitrii Merzlikin ◽  
Sergey Fomel ◽  
Xinming Wu
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Field Data ◽  
Forward Modeling ◽  
Edge Diffraction ◽  
Sparsity Constraints ◽  
Diffraction Imaging ◽  
Least Squares Migration ◽  
Anisotropic Smoothing

We have used least-squares migration to emphasize edge diffractions. The inverted forward-modeling operator is the chain of three operators: Kirchhoff modeling, azimuthal plane-wave destruction, and the path-summation integral filter. Azimuthal plane-wave destruction removes reflected energy without damaging edge-diffraction signatures. The path-summation integral guides the inversion toward probable diffraction locations. We combine sparsity constraints and anisotropic smoothing in the form of shaping regularization to highlight edge diffractions. Anisotropic smoothing enforces continuity along edges. Sparsity constraints emphasize diffractions perpendicular to edges and have a denoising effect. Synthetic and field data examples illustrate the effectiveness of the proposed approach in denoising and highlighting edge diffractions, such as channel edges and faults.

scholarly journals Least-squares path-summation diffraction imaging using sparsity constraints

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S187-S200 ◽  
Author(s):  
Dmitrii Merzlikin ◽  
Sergey Fomel ◽  
Mrinal K. Sen
Keyword(s):  
Plane Wave ◽  
Field Data ◽  
Reservoir Characterization ◽  
Forward Modeling ◽  
Small Scale ◽  
Separation Procedure ◽  
Seismic Reservoir ◽  
Sparsity Constraints ◽  
Diffraction Imaging ◽  
Separation Results

Diffraction imaging aims to emphasize small-scale subsurface heterogeneities, such as faults, pinch-outs, fracture swarms, channels, etc. and can help seismic reservoir characterization. The key step in diffraction imaging workflows is based on the separation procedure suppressing higher energy reflections and emphasizing diffractions, after which diffractions can be imaged independently. Separation results often contain crosstalk between reflections and diffractions and are prone to noise. We have developed an inversion scheme to reduce the crosstalk and denoise diffractions. The scheme decomposes an input full wavefield into three components: reflections, diffractions, and noise. We construct the inverted forward modeling operator as the chain of three operators: Kirchhoff modeling, plane-wave destruction, and path-summation integral filter. Reflections and diffractions have the same modeling operator. Separation of the components is done by shaping regularization. We impose sparsity constraints to extract diffractions, enforce smoothing along dominant local event slopes to restore reflections, and suppress the crosstalk between the components by local signal-and-noise orthogonalization. Synthetic- and field-data examples confirm the effectiveness of the proposed method.

Least-squares migration in the presence of velocity errors

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. S153-S161 ◽  
Author(s):  
Simon Luo ◽  
Dave Hale
Keyword(s):  
Wave Propagation ◽  
Least Squares ◽  
Field Data ◽  
Velocity Model ◽  
Forward Modeling ◽  
Background Model ◽  
Seismic Migration ◽  
Least Squares Migration

Seismic migration requires an accurate background velocity model that correctly predicts the kinematics of wave propagation in the true subsurface. Least-squares migration, which seeks the inverse rather than the adjoint of a forward modeling operator, is especially sensitive to errors in this background model. This can result in traveltime differences between predicted and observed data that lead to incoherent and defocused migration images. We have developed an alternative misfit function for use in least-squares migration that measures amplitude differences between predicted and observed data, i.e., differences after correcting for nonzero traveltime shifts between predicted and observed data. We demonstrated on synthetic and field data that, when the background velocity model is incorrect, the use of this misfit function results in better focused migration images. Results suggest that our method best enhances image focusing when differences between predicted and observed data can be explained by traveltime shifts.

An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. H27-H33 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Least Squares Migration ◽  
Time Extrapolation

To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.

Periodic plane-wave least-squares reverse time migration for diffractions

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. S185-S198
Author(s):  
Chuang Li ◽  
Jinghuai Gao ◽  
Zhaoqi Gao ◽  
Rongrong Wang ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Image Quality ◽  
Plane Wave ◽  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Diffraction Imaging ◽  
Periodic Plane

Diffraction imaging is important for high-resolution characterization of small subsurface heterogeneities. However, due to geometry limitations and noise distortion, conventional diffraction imaging methods may produce low-quality images. We have adopted a periodic plane-wave least-squares reverse time migration method for diffractions to improve the image quality of heterogeneities. The method reformulates diffraction imaging as an inverse problem using the Born modeling operator and its adjoint operator derived in the periodic plane-wave domain. The inverse problem is implemented for diffractions separated by a plane-wave destruction filter from the periodic plane-wave sections. Because the plane-wave destruction filter may fail to eliminate hyperbolic reflections and noise, we adopt a hyperbolic misfit function to minimize a weighted residual using an iteratively reweighted least-squares algorithm and thereby reduce residual reflections and noise. Synthetic and field data tests show that the adopted method can significantly improve the image quality of subsalt and deep heterogeneities. Compared with reverse time migration, it produces better images with fewer artifacts, higher resolution, and more balanced amplitude. Therefore, the adopted method can accurately characterize small heterogeneities and provide a reliable input for seismic interpretation in the prediction of hydrocarbon reservoirs.

Least-squares migration with a blockwise Hessian matrix: A prestack time-migration approach

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R625-R640 ◽  
Author(s):  
Bowu Jiang ◽  
Jianfeng Zhang
Keyword(s):  
Least Squares ◽  
Field Data ◽  
Hessian Matrix ◽  
Total Variation Regularization ◽  
Data Sets ◽  
Reflection Point ◽  
Inverse Approach ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Least Squares Migration

We have developed an explicit inverse approach with a Hessian matrix for the least-squares (LS) implementation of prestack time migration (PSTM). A full Hessian matrix is divided into a series of computationally tractable small-sized matrices using a localized approach, thus significantly reducing the size of the inversion. The scheme is implemented by dividing the imaging volume into a series of subvolumes related to the blockwise Hessian matrices that govern the mapping relationship between the migrated result and corresponding reflectivity. The proposed blockwise LS-PSTM can be implemented in a target-oriented fashion. The localized approach that we use to modify the Hessian matrix can eliminate the boundary effects originating from the blockwise implementation. We derive the explicit formula of the offset-dependent Hessian matrix using the deconvolution imaging condition with an analytical Green’s function of PSTM. This avoids the challenging task of estimating the source wavelet. Moreover, migrated gathers can be generated with the proposed scheme. The smaller size of the blockwise Hessian matrix makes it possible to incorporate the total-variation regularization into the inversion, thus attenuating noises significantly. We revealed the proposed blockwise LS-PSTM with synthetic and field data sets. Higher quality common-reflection-point gathers of the field data are obtained.

Modified imaging principle: An alternative to preserved-amplitude least-squares wave-equation migration

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. S221-S230 ◽  
Author(s):  
Denis Kiyashchenko ◽  
René-Edouard Plessix ◽  
Boris Kashtan
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Least Squares ◽  
Forward Modeling ◽  
Acoustic Wave Equation ◽  
Impedance Contrast ◽  
Least Squares Migration

Impedance contrast images can result from a least-squares migration or from a modified imaging principle. Theoretically, the two approaches should give similar results, but in practice they lead to different estimates of the impedance contrasts because of limited acquisition geometry, difficulty in computing exact weights for least-squares migration, and small contrast approximation. To analyze those differences, we compare the two approaches based on 2D synthetics. Forward modeling is either a finite-difference solver of the full acoustic wave equation or a one-way wave-equation solver that correctly models the amplitudes. The modified imaging principle provides better amplitude estimates of the impedance contrasts and does not suffer from the artifacts at-tributable to diving waves, which can be seen in two-way, least-squares migrated sections. However, because of the shot-based formulation, artifacts appear in the modified imaging principle results in shadow zones where energy is defocused. Those artifacts do not exist with the least-squares migration algorithm because all shots are processed simultane-ously.

Least-squares Gaussian beam migration

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. S87-S100 ◽  
Author(s):  
Hao Hu ◽  
Yike Liu ◽  
Yingcai Zheng ◽  
Xuejian Liu ◽  
Huiyi Lu
Keyword(s):  
Least Squares ◽  
Gaussian Beam ◽  
Spatial Resolution ◽  
Field Data ◽  
Synthetic Data ◽  
Data Sets ◽  
Data Set ◽  
Seismic Acquisition ◽  
Gaussian Beam Migration ◽  
Least Squares Migration

Least-squares migration (LSM) can be effective to mitigate the limitation of finite-seismic acquisition, balance the subsurface illumination, and improve the spatial resolution of the image, but it requires iterations of migration and demigration to obtain the desired subsurface reflectivity model. The computational efficiency and accuracy of migration and demigration operators are crucial for applying the algorithm. We have developed a test of the feasibility of using the Gaussian beam as the wavefield extrapolating operator for the LSM, denoted as least-squares Gaussian beam migration. Our method combines the advantages of the LSM and the efficiency of the Gaussian beam propagator. Our numerical evaluations, including two synthetic data sets and one marine field data set, illustrate that the proposed approach could be used to obtain amplitude-balanced images and to broaden the bandwidth of the migrated images in particular for the low-wavenumber components.

scholarly journals Mitigation of defocusing by statics and near-surface velocity errors by interferometric least-squares migration with a reference datum

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S195-S206 ◽  
Author(s):  
Mrinal Sinha ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Prior Knowledge ◽  
Seismic Data ◽  
Field Data ◽  
Velocity Model ◽  
Well Logs ◽  
Surface Velocity ◽  
Near Surface ◽  
Reference Layer ◽  
Least Squares Migration

Imaging seismic data with an erroneous migration velocity can lead to defocused migration images. To mitigate this problem, we first choose a reference reflector whose topography is well-known from the well logs, for example. Reflections from this reference layer are correlated with the traces associated with reflections from deeper interfaces to get crosscorrelograms. Interferometric least-squares migration (ILSM) is then used to get the migration image that maximizes the crosscorrelation between the observed and the predicted crosscorrelograms. Deeper reference reflectors are used to image deeper parts of the subsurface with a greater accuracy. Results on synthetic and field data show that defocusing caused by velocity errors is largely suppressed by ILSM. We have also determined that ILSM can be used for 4D surveys in which environmental conditions and acquisition parameters are significantly different from one survey to the next. The limitations of ILSM are that it requires prior knowledge of a reference reflector in the subsurface and the velocity model below the reference reflector should be accurate.

scholarly journals Image domain least-squares migration with a Hessian matrix estimated by non-stationary matching filters

2019 ◽  
Vol 17 (1) ◽  
pp. 148-159 ◽  
Author(s):  
Song Guo ◽  
Huazhong Wang
Keyword(s):  
Least Squares ◽  
Numerical Experiments ◽  
Field Data ◽  
Hessian Matrix ◽  
Computational Cost ◽  
Image Deblurring ◽  
Data Set ◽  
Image Domain ◽  
Slow Convergence ◽  
Least Squares Migration

Abstract Assuming that an accurate background velocity is obtained, least-squares migration (LSM) can be used to estimate underground reflectivity. LSM can be implemented in either the data domain or image domain. The data domain LSM (DDLSM) is not very practical because of its huge computational cost and slow convergence rate. The image domain LSM (IDLSM) might be a flexible alternative if estimating the Hessian matrix using a cheap and accurate approach. It has practical potential to analyse convenient Hessian approximation methods because the Hessian matrix is too huge to compute and save. In this paper, the Hessian matrix is approximated with non-stationary matching filters. The filters are calculated to match the conventional migration image to the demigration/remigration image. The two images are linked by the Hessian matrix. An image deblurring problem is solved with the estimated filters for the IDLSM result. The combined sparse and total variation regularisations are used to produce accurate and reasonable inversion results. The numerical experiments based on part of Sigsbee model, Marmousi model and a 2D field data set illustrate that the non-stationary matching filters can give a good approximation for the Hessian matrix, and the results of the image deblurring problem with combined regularisations can provide high-resolution and true-amplitude reflectivity estimations.

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