Multi‐component separation of PP and SS by a least‐squares migration method: Synthetic and field data tests

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.

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Least-squares Gaussian beam migration

Geophysics ◽

10.1190/geo2015-0328.1 ◽

2016 ◽

Vol 81 (3) ◽

pp. S87-S100 ◽

Cited By ~ 22

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.

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

Geophysics ◽

10.1190/geo2015-0637.1 ◽

2016 ◽

Vol 81 (4) ◽

pp. S195-S206 ◽

Cited By ~ 5

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.

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

Journal of Geophysics and Engineering ◽

10.1093/jge/gxz098 ◽

2019 ◽

Vol 17 (1) ◽

pp. 148-159 ◽

Cited By ~ 2

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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Least‐squares migration of incomplete reflection data

Geophysics ◽

10.1190/1.1444517 ◽

1999 ◽

Vol 64 (1) ◽

pp. 208-221 ◽

Cited By ~ 463

Author(s):

Tamas Nemeth ◽

Chengjun Wu ◽

Gerard T. Schuster

Keyword(s):

Least Squares ◽

Frequency Distribution ◽

Field Data ◽

Radar Data ◽

Data Set ◽

Frequency Distributions ◽

Vertical Seismic Profiling ◽

Reflection Data ◽

Ground Penetrating ◽

Least Squares Migration

A least‐squares migration algorithm is presented that reduces the migration artifacts (i.e., recording footprint noise) arising from incomplete data. Instead of migrating data with the adjoint of the forward modeling operator, the normal equations are inverted by using a preconditioned linear conjugate gradient scheme that employs regularization. The modeling operator is constructed from an asymptotic acoustic integral equation, and its adjoint is the Kirchhoff migration operator. We tested the performance of the least‐squares migration on synthetic and field data in the cases of limited recording aperture, coarse sampling, and acquisition gaps in the data. Numerical results show that the least‐squares migrated sections are typically more focused than are the corresponding Kirchhoff migrated sections and their reflectivity frequency distributions are closer to those of the true model frequency distribution. Regularization helps attenuate migration artifacts and provides a sharper, better frequency distribution of estimated reflectivity. The least‐squares migrated sections can be used to predict the missing data traces and interpolate and extrapolate them according to the governing modeling equations. Several field data examples are presented. A ground‐penetrating radar data example demonstrates the suppression of the recording footprint noise due to a limited aperture, a large gap, and an undersampled receiver line. In addition, better fault resolution was achieved after applying least‐squares migration to a poststack marine data set. And a reverse vertical seismic profiling example shows that the recording footprint noise due to a coarse receiver interval can be suppressed by least‐squares migration.

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Least-squares migration in the presence of velocity errors

Geophysics ◽

10.1190/geo2013-0374.1 ◽

2014 ◽

Vol 79 (4) ◽

pp. S153-S161 ◽

Cited By ~ 33

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.

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Least-squares diffraction imaging using shaping regularization by anisotropic smoothing

Geophysics ◽

10.1190/geo2019-0741.1 ◽

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.

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Viscoacoustic least-squares migration with a blockwise Hessian matrix: an effective Q approach

Journal of Geophysics and Engineering ◽

10.1093/jge/gxaa017 ◽

2020 ◽

Author(s):

Mingpeng Song ◽

Jianfeng Zhang ◽

Jiangjie Zhang

Keyword(s):

Least Squares ◽

Field Data ◽

Hessian Matrix ◽

Data Sets ◽

Matrix Approach ◽

Inverse Approach ◽

Time Migration ◽

Q Model ◽

Prestack Time Migration ◽

Least Squares Migration

Abstract We present an explicit inverse approach using a Hessian matrix for least-squares migration (LSM) with Q compensation. The scheme is developed by incorporating an effective Q-based solution of the viscoacoustic wave equation into a blockwise approximation to the Hessian in LSM, which is implemented after the so-called deabsorption prestack time migration (PSTM). The effective Q model used fully accounts for frequency-dependent traveltime and amplitude at the same imaging location. We can extract the effective Q parameters by scanning during previous deabsorption PSTM. This avoids the challenging task of building the Q model. The blockwise Hessian matrix approach decomposes the full Hessian matrix into a series of computationally tractable small-sized matrices using a localised approach. We derive the explicit formula of the offset-dependent Hessian matrix using an analytical Green's function obtained from deabsorption PSTM. In this way, we can approximate a reflectivity imaging for the targeted zone by a spatial deconvolution of the migrated result with an explicit inverse. The resulting scheme broadens the frequency-band of imaging by deabsorption, and improves the subsurface illumination and spatial resolution through the inverse Hessian. A high-resolution, true-amplitude migrated gather can then be obtained. Synthetic and field data sets demonstrate the proposed blockwise LS-QPSTM.

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Fast least-squares migration with a deblurring filter

Geophysics ◽

10.1190/1.3155162 ◽

2009 ◽

Vol 74 (6) ◽

pp. WCA83-WCA93 ◽

Cited By ~ 71

Author(s):

Naoshi Aoki ◽

Gerard T. Schuster

Keyword(s):

Least Squares ◽

Model Test ◽

Field Data ◽

Waveform Inversion ◽

Synthetic Data ◽

Regularization Scheme ◽

Practical Tool ◽

Marine Data ◽

The Cost ◽

Least Squares Migration

Least-squares migration (LSM) is a linearized waveform inversion for estimating a subsurface reflectivity model that, relative to conventional migration, improves spatial resolution of migration images. The cost, however, is high because LSM typically requires 10 or more iterations, which is at least 20 times more than the CPU cost of conventional migration. To alleviate this expense, we offer a deblurring filter that can be used in a regularization scheme or a preconditioning scheme to give acceptable LSM images with less than one-third the cost of the standard LSM method. Our results in applying deblurred LSM to synthetic data and field data support this claim. In particular, a Marmousi2 model test shows that the data residual for preconditioned deblurred LSM decreases rapidly in the first iteration, which is equivalent to 10 or more iterations of LSM. Empirical results suggest that regularized deblurred LSM after three iterations is equivalent to about 10 iterations of LSM. Applying deblurred LSM to 2D marine data gives a higher-resolution image compared to those from migration or LSM with three iterations. These results suggest that LSM combined with a deblurring filter allows LSM to be a fast, practical tool for improved imaging of complicated structures.

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