Data reconstruction with shot-profile least-squares migration

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB121-WB136 ◽  
Author(s):  
Sam T. Kaplan ◽  
Mostafa Naghizadeh ◽  
Mauricio D. Sacchi
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Approximate Model ◽  
Data Reconstruction ◽  
Profile Least Squares ◽  
The Common ◽  
Least Squares Migration ◽  
Minimal Information

We introduce shot-profile migration data reconstruction (SPDR). SPDR constructs a least-squares migrated shot gather using shot-profile migration and demigration operators. Both operators are constructed with a constant migration velocity model for efficiency and so that SPDR requires minimal information about the underlying geology. Applying the demigration operator to the least-squares migrated shot gather gives the reconstructed data gather. SPDR can reconstruct a shot gather from observed data that are spatially aliased. Given a constraint on the geological dips in an approximate model of the earth’s reflector, signal and aliased energy that interfere in the common shot data gather are disjoint in the migrated shot gather. In the least-squares migration algorithm, we construct weights to take advantage of this separation, suppressing the aliased energy while retaining the signal, and allowing SPDR to reconstruct a shot gather from aliased data. SPDR is illustrated with synthetic data examples and one real data example.

Improving the least-squares image by using angle information to avoid cycle skipping

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S581-S598 ◽  
Author(s):  
Bin He ◽  
Yike Liu ◽  
Yanbao Zhang
Keyword(s):  
Least Squares ◽  
Real Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Propagation Angle ◽  
Time Migration ◽  
The Common

In the past few decades, the least-squares reverse time migration (LSRTM) algorithm has been widely used to enhance images of complex subsurface structures by minimizing the data misfit function between the predicted and observed seismic data. However, this algorithm is sensitive to the accuracy of the migration velocity model, which, in the case of real data applications (generally obtained via tomography), always deviates from the true velocity model. Therefore, conventional LSRTM faces a cycle-skipping problem caused by a smeared image when using an inaccurate migration velocity model. To address the cycle-skipping problem, we have introduced an angle-domain LSRTM algorithm. Unlike the conventional LSRTM algorithm, our method updates the common source-propagation angle image gathers rather than the stacked image. An extended Born modeling operator in the common source-propagation angle domain is was derived, which reproduced kinematically accurate data in the presence of velocity errors. Our method can provide more focused images with high resolution as well as angle-domain common-image gathers (ADCIGs) with enhanced resolution and balanced amplitudes. However, because the velocity model is not updated, the provided image can have errors in depth. Synthetic and field examples are used to verify that our method can robustly improve the quality of the ADCIGs and the finally stacked images with affordable computational costs in the presence of velocity errors.

Least-squares migration with primary- and multiple-guided weighting matrices

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S171-S185 ◽  
Author(s):  
Chuang Li ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Han Yu ◽  
Rongrong Wang
Keyword(s):  
Free Surface ◽  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Multiple Reflections ◽  
Time Migration ◽  
Least Squares Migration

Least-squares migration (LSM) of seismic data is supposed to produce images of subsurface structures with better quality than standard migration if we have an accurate migration velocity model. However, LSM suffers from data mismatch problems and migration artifacts when noise pollutes the recorded profiles. This study has developed a reweighted least-squares reverse time migration (RWLSRTM) method to overcome the problems caused by such noise. We first verify that spiky noise and free-surface multiples lead to the mismatch problems and should be eliminated from the data residual. The primary- and multiple-guided weighting matrices are then derived for RWLSRTM to reduce the noise in the data residual. The weighting matrices impose constraints on the data residual such that spiky noise and free-surface multiple reflections are reduced whereas primary reflections are preserved. The weights for spiky noise and multiple reflections are controlled by a dynamic threshold parameter decreasing with iterations for better results. Finally, we use an iteratively reweighted least-squares algorithm to minimize the weighted data residual. We conduct numerical tests using the synthetic data and compared the results of this method with the results of standard LSRTM. The results suggest that RWLSRTM is more robust than standard LSRTM when the seismic data contain spiky noise and multiple reflections. Moreover, our method not only suppresses the migration artifacts, but it also accelerates the convergence.

Derivation of forward and adjoint operators for least-squares shot-profile split-step migration

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. S225-S235 ◽  
Author(s):  
Sam T. Kaplan ◽  
Partha S. Routh ◽  
Mauricio D. Sacchi
Keyword(s):  
Least Squares ◽  
Born Approximation ◽  
Adjoint Operator ◽  
Velocity Model ◽  
Migration Velocity ◽  
Profile Least Squares ◽  
Measurement Surface ◽  
Adjoint Operators ◽  
Least Squares Migration ◽  
Upper Boundary

The forward and adjoint operators for shot-profile least-squares migration are derived. The forward operator is demigration, and the adjoint operator is migration. The demigration operator is derived from the Born approximation. The process begins with a Green’s function that allows for a laterally varying migration velocity model using the split-step approximation. Next, the earth is divided into horizontal layers, and within each layer the migration velocity model is made to be constant with respect to depth. For a given layer, (1) the source-side wavefield is propagated down to its top using the background wavefield. This gives a background wavefield incident at the layer’s upper boundary. (2) The layer’s contribution to the scattered wavefield is computed using the Born approximation to the scattered wavefield and the background wavefield. (3) Next, its scattered wavefield is propagated back up to the measurement surface using, again, the background wavefield. The measured wavefield is approximated by the sum of scattered wavefields from each layer. In the derivation of the measured wavefield, the shot-profile migration geometry is used. For each shot, the resulting wavefield modeling operator takes the form of a Fredholm integral equation of the first kind, and this is used to write down its adjoint, the shot-profile migration operator. This forward/adjoint pair is used for shot-profile least-squares migration. Shot-profile least-squares migration is illustrated with two synthetic examples. The first uses data collected over a four-layer acoustic model, and the second uses data from the Sigsbee 2a model.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

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.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

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.

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.

scholarly journals Frequency-Domain Common Image Gathers for Quickly Checking the Accuracy of Migration Velocity

2021 ◽  
Vol 9 ◽  
Author(s):  
Haemin Kim ◽  
Yongchae Cho ◽  
Yunseok Choi ◽  
Seungwon Ko ◽  
Changsoo Shin
Keyword(s):  
Frequency Domain ◽  
Deviant Behavior ◽  
Computational Cost ◽  
Real Data ◽  
Velocity Model ◽  
Complex Velocity ◽  
Hybrid Domain ◽  
The Common ◽  
Low Computational Cost ◽  
Complex Velocity Model

The common image gather (CIG) method enables qualitative and quantitative evaluation of the velocity model through the image. The most common such methods are offset-domain common image gather (ODCIG) and angle-domain common image gather (ADCIG). The challenge is that it requires a great deal of additional computation besides migration. We, therefore, introduce a new CIG method that has low computational cost: frequency-domain common image gather (FDCIG). FDCIG simply rearranges data using a gradient (partial image) calculated in the process of obtaining a migration image to represent it in the frequency-depth domain. We apply the FDCIG method to the layered model to show how FDCIGs behave when the velocity model is inaccurate. We also introduced the 3-D SEG/EAGE salt model to show how to apply the FDCIG method in the hybrid domain. Last, we applied 2-D real data. These sample field data also indicate that even in a complex velocity model, deviant behavior by FDCIG appears intuitively if the background velocity is inaccurate.

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