Least-Squares Reverse-Time Migration

Yao, Gang; Jakubowicz, H.

doi:10.1190/segam2012-1425.1

Cited by 31 publications

(12 citation statements)

References 33 publications

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“…This is because the imaging condition for RTM is based on cross-correlation, and therefore retains (actually amplifies) the imprint of the source signature. Unlike RTM, by fitting the image to recorded data, LSRTM compensates for the source signature using a deconvolution imaging condition (Yao et al, 2012a). Consequently, the LSRTM image has weaker sidelobes and higher resolution.…”

Section: Gradient Descent With Bb Schemementioning

confidence: 99%

“…Thereby, the amplitudes of the later arrivals in the modeled data of LSRTM (Figure 2(f)) are closer to those in the recorded data ( Figure 2(d)) than in the case of RTM (Figure 2(e)). These advantages of LSRTM are intrinsic to the combination of least-squares inversion and reverse-time migration, and can be obtained with other implementations of LSRTM, such as that of Yao et al, (2012a). However, LSRTM is not immune to the effect of migration velocity errors.…”

Section: Gradient Descent With Bb Schemementioning

confidence: 99%

“…In this example, the source wavelet used for migration is the processed air gun signature provided by PGS. Weighting regularization is applied to boost the convergence speed of the middle and low parts of the model (For more details please see Section 5.2 of the PhD thesis of Yao (2013)). By comparison of the two images in Figure 6, the three advantages of LSRTM shown in the previous examples can also be seen in this example.…”

Section: A Field Datasetmentioning

confidence: 99%

“…This will remove high-wavenumber artifacts and mitigate the effect of spatial aliasing to generate better images. Unlike the matrix formulation of least-squares reverse-time migration (Yao et al, 2012a), this scheme does not formulate the Jacobian matrix explicitly thus reducing the memory cost down to the same level as conventional RTM. Consequently, this scheme is ready for 3D implementation.…”

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Least-squares reverse-time migration for reflectivity imaging

Yao

2015

Sci. China Earth Sci.

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A least-squares reverse-time migration scheme is presented for reflectivity imaging. Based on an accurate reflection modeling formula, this scheme produces amplitude-preserved stacked reflectivity images with zero phase. Spatial preconditioning, weighting and the Barzilai-Borwein method are applied to speed up the convergence of the least-squares inversion. In addition, this scheme compensates the effect of ghost waves to broaden the bandwidth of the reflectivity images. Furthermore, roughness penalty constraint is used to regularize the inversion, which in turn stabilizes inversion and removes high-wavenumber artifacts and mitigates spatial aliasing. The examples of synthetic and field datasets demonstrate the scheme can generate zerophase reflectivity images with broader bandwidth, higher resolution, fewer artifacts and more reliable amplitudes than conventional reverse-time migration. Migration is a key technique for subsurface seismic imaging by repositioning the recorded data to the location where reflection occurs. Although in principle this requires the inverse of a modeling operator, in practice the adjoint of the modeling operator is used instead. There are two main reasons for such use of adjoint migration operators. Firstly, applying adjoint operator requires significantly less calculation than inverse operators, as it is much cheaper to compute the adjoint operator than the inverse operator. Secondly, adjoint operators are unconditionally stable, since only multiplication and addition are involved in their production, whereas division is required to compute an inverse operator. Adjoint operators therefore apply to nearly all migration methods, including reverse-time migration (RTM). In cases where the data is subject to significant aliasing, truncation, noise, or are incomplete, the adjoint operator is not a good approximation to the inverse operator, and will therefore degrade the resolution of the final migrated image. Moreover, even with perfect data, an adjoint operator still produces imperfect images (Claerbout, 1992). Hence, it is desirable to use the inverse operator to migrate seismic data. A generalized inverse operator can be obtained by using a least-squares approach. Nemeth et al. (1999) implemented Kirchhoff migration in the least-squares inversion frame to form a least-squares migration method. The examples demonstrate improved resolution and amplitudes of the images. In addition, the least-squares migration is able to mitigate the side effects of limited aperture, gaps and coarse spatial sampling of the recorded data. To reduce the computational cost of least-squares Kirchhoff migration (Nemeth et al., 1999), Liu et al. (2005) combined leastsquares inversion with wave-path migration, which is faster than Kirchhoff migration, to give a more efficient method

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Section: Gradient Descent With Bb Schemementioning

confidence: 99%

Section: Gradient Descent With Bb Schemementioning

confidence: 99%

Section: A Field Datasetmentioning

confidence: 99%

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confidence: 99%

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Least-squares reverse-time migration for reflectivity imaging

Yao

2015

Sci. China Earth Sci.

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“…Dai et al (2010) developed 3D LSRTM and reduced the computation cost by introducing phase encoding technology. Yao et al (2012aYao et al ( , 2012b gave the theory and synthetical examples of linear and non-linear LSRTM. Dong et al (2012) proved that LSRTM can preserve amplitude and has higher resolution by tests on synthetic and real data.…”

Section: Introductionmentioning

confidence: 99%

Least‐Squares Reverse Time Migration in Visco‐Acoustic Media

Guo

Tian

2014

Chinese J of Geophysics

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As the subsurface medium is widely viscous, it is necessary to compensate absorption and to correct dispersion of seismic waves in true‐amplitude pre‐stack imaging. The instability problem encountered in conventional inverse‐Q migration hinders the application of the method. In this work, imaging was treated as a linear inverse problem named least‐squares reverse time migration (LSRTM). Firstly, we linearized the wave equation and defined the cost function. Then based on the derived equations of the adjoint wave propagation operator, iterative solution was derived using the adjoint‐state method. At last dynamical phase encoding technology was used to reduce computation cost. This method breaks a new way for imaging in visco‐acoustic media while avoiding the instability problem. The true‐amplitude imaging results can be obtained while compensating absorption and correcting dispersion automatically. It is also a good way to suppress the imaging noise and correct amplitude unbalance caused by geometrical spreading or weak illumination. Compared with conventional reverse time migration (RTM), this method can yield results with higher resolution and lower imaging noise. The validity of the method was demonstrated by the numerical test on synthetic seismic data.

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Re‐Exploration into Migration of Seismic Data

Chen

Hua‐Ming

2016

Chinese J of Geophysics

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The formula of migration of seismic data is re‐derived by using the forward propagation equations of seismic waves, in which the migration of seismic data is viewed as an approximate solution to the linear waveform inverse problem, a scattering migration method suitable for scattering seismic data and a reflection migration method suitable for reflection seismic data are proposed. Based on the scattering theory of seismic wave propagation, firstly we study and establish the migration theory for scattering seismic data through the linear equation describing the forward propagation of primary scattering wave. A subsurface reflectivity function is derived by applying the high frequency approximation to the spatial variation of velocity perturbation function generating the scattering field, and a forward propagation equation of reflection wave using the reflectivity function is derived from the propagation equation of scattering wave, then we study and establish the migration theory for reflection seismic data through the linear equation describing the forward propagation of primary reflection wave. We pointed out and corrected the shortcomings in Claerbout's migration method. The migration method of seismic data introduced in this paper is an improvement to current migration technique and theory, and establishes a solid theoretical base of mathematical physics for the migration of reflection seismic data. The migration results from the new methods have correct phase, accurate position and improved resolution.

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Least-Squares Reverse-Time Migration

Cited by 31 publications

References 33 publications

Least-squares reverse-time migration for reflectivity imaging

Least-squares reverse-time migration for reflectivity imaging

Least‐Squares Reverse Time Migration in Visco‐Acoustic Media

Re‐Exploration into Migration of Seismic Data

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