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Summary We present a singular spectrum constraint which can be applied to least-squares migration (LSM) to suppress the migration artefacts and crosstalk in the imaging results. The singular spectrum analysis (SSA) is introduced as a preconditioning to the gradient in the offset domain. Since the desired signals in the gradient have better coherence, the artefacts are eliminated by the truncation of dominating singular values. The constraint is tested with least-squares reverse time migration (LSRTM) of incomplete data and plane-wave least-squares reverse time migration (PLSRTM) of encoded plane-waves. The imaging tests to the synthetic data of Marmousi model indicate that LSRTM and PSLRTM with singular spectrum constraint (LSRTM-SSA and PLSRTM-SSA) can produce noise-free images with less iteration compared with the conventional method. Introduction Least-squares migration has been shown to be able to produce high quality migration images (Nemeth et al., 1999; Kuehl and Sacchi, 2003; Dai et al., 2012). The existing LSM is implemented in either data domain or model domain with different misfit functions. The data domain implementation is also called iterative least-squares imaging, because it iteratively updates conventional migration images to the real reflectivity model by local optimization schemes. In addition, the LSM also has the ability to attenuate the migration artefacts introduced by incomplete seismic data (Nemeth et al., 1999), but huge computation is needed. The phase-encoded multisource LSRTM attracts its popularity recently because it has significantly increased computational efficiency compared with conventional LSRTM. Plane-wave encoding is one of the approaches which can suppress crosstalk and enhance coherent signals by stacking images from different planewaves (Dai et al., 2013; Li et al., 2014). However, a considerable number of plane-waves are still necessary although the plane-wave least-squares reverse time migration can suppress crosstalk by optimization. To obtain better suppression of these migration artefacts and crosstalk, some scholars have developed effective constraints (Kuehl and Sacchi, 2001; Fomel, 2007; Xue et al., 2014) to the LSM and improved the computational efficiency.
Summary The multicomponent seismic data processing in areas with complex topography and subsurface geological formation is becoming a challenge. In this paper, an accurate PP and polarity-corrected PS beam migration method withoout slant stack based on surface dip information under complex topography conditions is proposed. Compared to the conventional elastic beam migration with the vector planewave decomposition processing, our method without the following processing can obtain higher imaging quality: (1) elevation statics; (2) phase correction; (3) approximate substitution of velocity and surface dip angle between receivers and the beam center. Numerical results reach our expectation that our method can effectively remedy the imaging energy error caused by the large distance between the beam center and detectors, which usually occurs in the conventional elastic beam migration method. Introduction With the development trends from regular to irregular surface and from acoustic to elastic media, the multicomponent data processing under complex topography condition becomes a challenge. Under complex topography condition, conventional statics processing can’t meet the requirements of imaging quality. Gray (2005) proposed an acoustic Gaussian beam migration (GBM) method based on local statics correction. However, the drawbacks to Gray’s method are that, rapid near-surface velocity variations can compromise the accuracy of a slant stack that has a large spatial extent and rapid elevation variations can make static shifts a poor approximation to wavefields extrapolation. In order to avoid these problems, Yue et al. (2010) presented a relatively amplitudepreserved acoustic GBM method that directly decomposed the records into local plane-wave components on the irregular surface. Yuan et al. (2014) realized an accurate acoustic GBM method without the local plane-wave decomposition for irregular surface and obtained improved image result. Huang et al. (2013) applied local slant stack theory proposed by Hill (1990, 2001) to elastic GBM under complex topography condition. However, this method characterizes backward-continuation vector wavefields by compensating for phase changes from vector beam centers to receivers. When receivers are not in some neighborhood of the beam center, this treatment will lead to amplitude error due to inaccurate Green’s function. Moreover, the differences of near-surface velocity and surface dip angle from the beam center to receivers and the poor spatial sampling of land data lead to inaccuracy and aliasing of the slant stack, respectively.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (0.89)
Summary Seismic demigration maps reflectivity into data that would be recorded for a defined measurement configuration along the recording surface. Kirchhoff, one-way wave-equation and the full wave-equation based demigration operators have been developed. As an alternative to Kirchhoff operator, Gaussian beam is regular at caustics and shadows due to the complex-value amplitude. In this paper, we present a forward modeling method by Gaussian beam demigration. Based on Born scattering theorem, we derive Gaussian beam demigration operator by expressing Green’s function as a Gaussian-beam summation, and then design a workflow for the algorithm. Numerical application to the point diffractors model and a complex topography model demonstrates that Gaussian beam demigration can map reflectivity into primary reflected or scattered data free from multiples and direct waves. Introduction Demigration is a linearized forward modeling method. Seismic demigration maps the reflectivity or migrated data into data that would be recorded for a defined measurement configuration along the recording surface. Currently, demigration operators can be divided into the following three categories: Kirchhoff demigration, one-wave wave-equation demigration and reverse time demigration. Kirchhoff demigration can be carried out by the isochron stack (Schleicher et al, 1993; Hubral et al, 1996). Later, Santos et al (2000) developed a true amplitude Kirchhoff demigration to compute synthetic seismograms. The second type of demigration is based on one-way wave equation. Claerbout (1985), Stoffa et al (1990) and Popovici (1996) successively proposed and developed the split-step squareroot demigration operator. With regard to the full wave equation, Born approximation based reverse time demigration operator is widely used in least-squares inversion to implement high-quality imaging (Dai and Schuster, 2010). Gaussian beam is the high-frequency asymptotic solution of the wave equation, whose amplitude is regular everywhere due to complex-value dynamic ray tracing parameters. Cervený (1983) used Gaussian beams to compute seismic wavefields and synthetic seismograms. However, in the Gaussian beam forward modeling process, we have to know the true velocity distribution in the subsurface and the position of the interfaces. Demigration generates synthetic seismic data by inputting corresponding reflectivity and background velocity. The implementation of Gaussian beam demigration algorithm can provide theoretical basis for Gaussian-beam based linearized waveform inversion.
Summary Gaussian beam prestack depth migration only produces blurred images with underestimated amplitude caused by sparse receiver sampling, narrow acquisition apertures, and limited wavefields bandwidth. This distortion can be partially corrected by using the model-space least-squares migration approach, where the diagonal Hessian operator is computed explicitly by using Green’s function as a Gaussian-beam summation and then its inverse is applied to migrated images. One important advantage of the modelspace inversion, compared to iterative data-space inversion schemes, is that most of the work, such as computation of the Hessian, is done up front. The proposed algorithm for computing the diagonal Hessian is verified by using a constant velocity model. When Gaussian beam based diagonal Hessian operator is applied to the SEG/EAGE salt synthetic dataset, an improved image with more balanced amplitude especially in areas with low illumination and shadow zones is obtained. Introduction Migration, as an adjoint operator of seismic linearized forward modeling (Claerbout, 1992), produces a blurred image of the subsurface reflectivity resulting from sparse receiver sampling, narrow acquisition apertures, and limited wavefield bandwidth. Although it provides reliable structural information of the subsurface, it makes the subsurface amplitude distorted because of the non-unitary nature of the linearized forward modeling operator. To improve amplitude behaviors, the imaging can be regarded as a least-squares inversion problem. The inversion can be implemented either in the data space (Nemeth et al., 1999; Dai and Schuster, 2013) or in the model space (Guitton, 2004; Valenciano et al., 2006). In the data space, the linearized forward modeling operator and its adjoint are iteratively evaluated to solve the leastsquares inversion problem, where the Hessian is implicitly calculated. However, iterative solver such as conjugate gradients is relatively costly and converges slowly without proper preconditioning. For another, the model-space approach requires explicit calculation of the Hessian matrix and its inverse. Although the Hessian’s main diagonal energy is smeared along its off-diagonals in areas of poor illumination, exact Hessian off-diagonals may be expensive to compute. Linearized Hessian is a diagonally dominant band matrix, whose diagonals are main contribution to the eigenvalue. Under the assumption of the high-frequency approximation and infinite acquisition aperture, diagonal Hessian is widely used to approximate the exact one (Rickett, 2003; Plessix and Mulder, 2004; Symes, 2008).
Summary As the elastic depth migration can obtain good images of subsurface structures with multi-wave and multicomponent information in seismic record, an effective prestack elastic Gaussian beam migration method is presented in this abstract. Unlike common multicomponent data processing method that separates seismic wave-field into P- and S-wave firstly and migrates them respectively, the proposed method uses the vector Gaussian beam to simultaneously migrate the P- and S-wave for common-shot multi-component seismic data based on the Kirchhoff-Helmholtz type integral for elastic waves. In order to make the imaging results have explicit physical meaning, we refer to the elastic reverse-time migration and present a new imaging principle for ray-based elastic wave migration, in which the decoupled P- and S-wavefileds, instead of multi-component wavefield, are used for crosscorrelation. In addition, an effective polarity correction method is given to handle the polarity changes for PS image, which is critical for converted-waves migration. Numerical experiences with synthetic datasets from Hess and Marmousi-II models not only assure the feasibility of migration scheme of our method, but also demonstrate that complex geological structures are well resolved both in PP and in PS depth images. Introduction With the rapid development of seismic exploration, multiwave and multi-component processing technique plays a more and more important role, and the corresponding migration methods have made great progress over the past decades. In general, there are two basic categories of prestack depth migration for the multi-wave and multicomponent seismic data: scalar migration and elastic migration. The former method first separates the elastic seismic data into P- and S-waves and then migrates them respectively using scalar wave equation (Sun and McMechan, 2001; Hou and Marfurt, 2002), which is easy to implement based on the established acoustic theory but doesn’t make full use of the vector property of elastic wavefield. The latter method directly uses the elastic wave equation to migrate the multi-component seismic records, which is an effective approach for multi-wave and multicomponent exploration. Kirchhoff elastic wave migration was proposed by Kuo and Dai (1984), and then it was extended to anistropic elastic and viscoelastic imaging by Hokstad (2000). This method has high computational efficiency, but is limited by its failure in imaging the multiple arrivals. 2D and 3D elastic reverse-time migration were implemented by Chang and McMechan (1987, 1994) and by Yan and Sava (2008). Later, many authors provide some constructive suggestions about the polarity correction of converted-wave images (Balch and Erdemir, 1994; Rosales and Rickett, 2001; Rosales and Fomel, 2008). Reverse-time migration is based on full wave equation and is the most accurate imaging method so far. However, it is very time-consuming, especially for large exploration areas with fine grids
- Europe (0.29)
- North America > United States (0.15)
Summary Matching pursuit is a technique of signal sparse decomposition, which is often used for time-frequency analysis and denoising processing. Gaussian beam migration (GBM) is an efficient and robust depth imaging method, which not only retains the advantage of ray-based migration, such as flexibility, efficiency and adaptability to the irregular topography, but also has a comparable imaging accuracy to wave equation migration. In this abstract, we applied the matching pursuit algorithm based on the atom library of Ricker wavelet to Gaussian beam migration, and developed a high signal to noise ratio (SNR) depth migration method. Using the matching pursuit, seismic records can be decomposed a series of sparse Ricker atoms with different frequencies and delay times. During the decomposition, through controlling the iteration times properly, lots of random noises are removed. For these decomposed Ricker atoms, we adopt Gaussian beam method to migrate them to the imaging domain, which produces a high SNR depth image. Test results show the proposed method produces depth images superior to those from conventional Gaussian beam migration. It has good noise suppressed effect and defines the steep-dip faults and shallow small-scale geological bodies clearly. Introduction In the seismic data processing, high SNR is one of the most important goals. Common methods used to enhance the SNR include the filtering in frequency domain or F-K domain for suppressing the ground roll, the F-X/F-XY filtering for suppressing the random noise and the radon transformation approaches for suppressing the multiplewave (Linville et al., 1991; Foster et al., 1992). But all the methods above mentioned are all belong to the multiplication denoising category, which destroys the effective seismic signal during suppressing the noise (Zhao et al., 2008). On the other hand, the subtraction denoising methods remove the interfering signal without distorting the effective signal, which has great potentials in the future. Matching-pursuit decomposition may be a good denoising method of subtraction, if we choose the effective atoms to reconstruct original signal or control the iteration times of decomposition properly. In this abstract, we apply this idea to migration processing and developed a high SNR imaging method. Since Gaussian beam migration can image the multiple arrivals accurately and has no steep-dip limitations (Hill, 1990, 2001; Gray et al, 2005, 2009), we use this method to carry out the mapping work from data domain to imaging domain.
Summary We adopt the time-space Gaussian beam for seismic data prestack depth migration in this abstract. This method belongs to the category of ray-based beam methods. It decomposes source wavelet into a set of Gaussian functions and propagates these Gaussian functions along appropriate central ray paths to construct the forward seismic wavefield, which is comparable to that produced by finite difference method. For the backward propagation of recorded wave-filed, the Kirchhoff integral equation is used, in which the Green function is represented approximately by time-space Gaussian beam summation. The subsurface image is obtained by calculating the coherence between the direct and back-propagated wave-fields. Unlike Kirchhoff migration and conventional Gaussian beam migration, we perform the ray tracing from subsurface imaging points to the receiver surface to compute the backward Green function, which adhering strictly to the mathematical basis of the Gaussian beam summation method. In addition, our method is carried out in the time-space domain, which could reveal the local time features of seismic wave-field that can be used to reduce the coherence noise of depth images. Two typical numerical examples confirm the validity and adaptibility of the time-space Gaussian beam migration. Introduction Because of the regularity and high accuracy in description of seismic wave-filed, the Gaussian beam method has been generally applied in seismic migration over the past decades (Hill 1990, 2001; Gray et al, 2005, 2009; Yue et al, 2010), which is achieved by correlating the direct and backpropagated beam waves of frequency domain in the intersection area. From the point of reverse-time extrapolation of recorded wave-filed, Popov et al (2010) proposed the Gaussian beam summation migration method, which is carried out by correlating the forward and backward wave-filed of time domain at every imaging point. Because this method uses frequent Fourier transformation, the computational efficiency is very low. Based the sparse representation and decomposition of shot gather with frame function, Gaussian packet migration also make great progress (Zacek et al, 2006; Geng et al, 2011; Li and Wang, 2013), but it needs complex mathematics transformation and is difficult to implement.
Viscoacoustic Reverse Time Migration by Adding a Regularization Term
Tian, Kun (Shengli Geophysical Research Institute of Sinopec) | Huang, Jianping (China University of Petroleum, Huadong) | Bu, Changcheng (SGRI, SINOPEC) | Li, Guolei (SGRI, SINOPEC) | Yan, Xinhua (SGRI, SINOPEC) | Lu, Jinfeng (SGRI, SINOPEC)
Summary The real geological medium is close to viscoelastic media in which seismic wave propagate with dispersion and attenuation. It is important to compensate the unwanted viscous effects in seismic processing. It is more accurate and physically more consistent to mitigate these effects in a wave-equation-based prestack depth migration. Historically, reverse time migration (RTM) based on directly solving the two-way wave equation has provided a superior way to image complex geologic regions. However, instability usually arises when considering compensation for absorption. Most researchers conduct high frequency filtering in wavenumber domain before or during wavefield extrapolate in RTM to ensure stability. In this paper, we use viscoacoustic wave equation derived by Bai et al. (2013) to do Q-RTM and stabilize extrapolate by adding a regularization term. Compared with direct filtering, the regularization parameter can be space-varying. So this is suitable for severely variational regions. And we also find that source normalized cross-correlation imaging condition is more suitable in Q-RTM. Introduction It has been broadly observed that real earth media attenuate and disperse seismic waves, which indicates earth is not an ideal elastic body. Large anelastic effects are found for instance in shallow sediments, fractured rocks, saturated rocks. In migrating such data sets, we usually obtain poor seismic images of the structure within and below such high-attenuation area. So it is important to correct these unwanted effects in seismic processing and make the final image more interpretable. Early efforts to compensate for the seismic attenuation were performed in the unmigrated data domain with an inverse Q-filter (Wang, 2006). These method were based on a one-dimensional backward propagation and cannot correctly handle real geological complexity. Because anelastic attenuation and phase dispersion effects on wavefields occur during the wave propagation, it is more accurate and physically more consistent to mitigate these effects in a wave-equation-based prestack depth migration (Zhu et al., 2014). Much effort has been put forth in developing an inverse Qmigration using one-way wave equation migration (Yu et al., 2002). One-way wave equation migration is implemented in the frequency domain, so it is natural to incorporate attenuation in imaging. Historically, reverse time migration (RTM) based on directly solving the twoway wave equation has provided a superior way to image complex geologic regions. And some researchers have tried to compensate viscoacoustic effects in RTM, and obtained better results (Zhang et al., 2010, Suh et al., 2012, Bai et al., 2013, Zhu et al., 2014).
Summary We present the weighted least-squares reverse time migration (WLSRTM) method to deal with noisy seismic data from rugged topography condition. The conventional least-squares optimization will suffer a mismatch problem with noisy observed data because the noise can’t be modelled by the Born modelling factor. This mismatch will encourage the ill-posedness of the inversion problem. We smooth the ill-posedness by a weighted misfit function which minimizes the contribution of noise to the gradient. And the noise in seismic data is suppressed by Born modelling of the final imaging results. To test the validity of the proposed method, an imaging test is applied to the SEG rugged topography model. The imaging results proved the ability of WLSRTM to improve the signal-to-noise ratio (SNR) of images and smooth the robustness of leastsquares reverse time migration (LSRTM). Moreover, the predicted shot data by Born modelling is noisy-free with little loss of desired signals. Introduction The seismic acquisition environment is extremely tough in the west exploration area of China. On one hand, the topographic undulation is acute so that the geophones can’t be placed regularly on a horizontal surface. On the other hand, the noise in common shot record is abundant because of the interference of environment, human factors and instrumental error, etc. To overcome these problems, the imaging method should be properly modified to fit with the irregular seismic data. In general, migration methods of seismic data from rugged topography are mainly two ways. One is to modify the wave field before migration which adopts the elevation static moveout method to adjust the rugged data to a floating or fixed datum. Berryhill et al. (1979) firstly advanced the concept of wave equation datum correction and then he extended this method to the pre-stack domain (1984). The other kind of way is to directly perform depth migration from rugged topography. Wiggins et al. (1984) proved that the Kirchhoff migration can perfectly adapt to the irregular surface without datum correction. In order to fit with strong velocity variation, Shragge et al. (2014) proposed the direct reverse time migration (RTM) method by altering the computational geometry from Cartesian to a topographic coordinate.
- Asia > China (0.25)
- North America > United States (0.16)
Summary Velocity estimation technique has always been the core issue of seismic exploration. Full waveform inversion (FWI) (Tarantola, 1984) is an effective method for reconstructing highly resolved models of the earth's velocity distribution. It can be implemented in either the space-frequency (Pratt et al., 1998) or the space time domains (Zhou et al., 1995). It more accurately estimates subsurface velocity estimation than conventional techniques do, especially in geologically complex areas. As for areas with a rugged surface, we proposed a velocity inversion method based on coordinate transform forward modeling and reverse-time migration method. The effect largely depends on the modeling techniques during inversion. In seismic inversion theory, migration imaging can be thought as one step of the process of inversion iteration. One step of FWI equals to the migration. In this paper, we first introduce coordinate transform finite difference forward modeling method, then we perform rugged surface reverse-time migration and velocity inversion. Tests with model and field data prove the correctness and effectiveness of our method. Introduction The theory of Seismic Imaging by Inversion researches the nature of seismic wave propagation. Currently, there are two hot points in the area of Seismic Exploration: FWI and Least Squares Migration. Both of them can be defined by the framework of inversion. Full waveform seismic inversion can potentially extract the maximum amount of information from geophysical data in a manner consistent with geological and geophysical constraints. FWI attempts to find an earth model( density, P-wave velocity, S-wave velocity, etc.)that best explains the measured seismic data and also satisfies known constraints. This leads us to FWI, where full-wave equation modeling is performed at each iteration of the optimization in the final model of the previous iteration. All types of waves are involved in the optimization, including diving waves, super critical reflections, and multi-scattered waves such as multiples. The techniques used for the forward modeling vary and include volumetric methods such as finite-element methods(Marfurt, 1984; Min et al., 2003), finite-difference methods(Virieux, 1986), finite-volume methods(Brossier et al.,2008),boundary integral methods such as reflectivity methods (Kennett, 1983); generalized screen methods (Wu, 2003);
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)