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1.
Reverse‐time migration gives high‐quality, complete images by using full‐wave extrapolations. It is thus not subject to important limitations of other migrations that are based on high‐frequency or one‐way approximations. The cross‐correlation imaging condition in two‐dimensional pre‐stack reverse‐time migration of common‐source data explicitly sums the product of the (forward‐propagating) source and (backward‐propagating) receiver wavefields over all image times. The primary contribution at any image point travels a minimum‐time path that has only one (specular) reflection, and it usually corresponds to a local maximum amplitude. All other contributions at the same image point are various types of multipaths, including prismatic multi‐arrivals, free‐surface and internal multiples, converted waves, and all crosstalk noise, which are imaged at later times, and potentially create migration artefacts. A solution that facilitates inclusion of correctly imaged, non‐primary arrivals and removal of the related artefacts, is to save the depth versus incident angle slice at each image time (rather than automatically summing them). This results in a three‐parameter (incident angle, depth, and image time) common‐image volume that integrates, into a single unified representation, attributes that were previously computed by separate processes. The volume can be post‐processed by selecting any desired combination of primary and/or multipath data before stacking over image time. Separate images (with or without artifacts) and various projections can then be produced without having to remigrate the data, providing an efficient tool for optimization of migration images. A numerical example for a simple model shows how primary and prismatic multipath contributions merge into a single incident angle versus image time trajectory. A second example, using synthetic data from the Sigsbee2 model, shows that the contributions to subsalt images of primary and multipath (in this case, turning wave) reflections are different. The primary reflections contain most of the information in regions away from the salt, but both primary and multipath data contribute in the subsalt region.  相似文献   

2.
It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution.  相似文献   

3.
This paper describes least‐squares reverse‐time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient‐based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high‐wavenumber artefacts. It is also shown that least‐squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse‐time migration. The methodology is currently feasible in 2‐D and can naturally be extended to 3‐D when computational resources become more powerful.  相似文献   

4.
Seismic time‐lapse surveys are susceptible to repeatability errors due to varying environmental conditions. To mitigate this problem, we propose the use of interferometric least‐squares migration to estimate the migration images for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for interferometric least‐squares migration, and the data are approximately redatumed to this reference reflector before imaging. This virtual redatuming mitigates the repeatability errors in the time‐lapse migration image. Results with synthetic and field data show that interferometric least‐squares migration can sometimes reduce or eliminate artifacts caused by non‐repeatability in time‐lapse surveys and provide a high‐resolution estimate of the time‐lapse change in the reservoir.  相似文献   

5.
In the application of a conventional common‐reflection‐surface (CRS) stack, it is well‐known that only one optimum stacking operator is determined for each zero‐offset sample to be simulated. As a result, the conflicting dip situations are not taken into account and only the most prominent event contributes to any a particular stack sample. In this paper, we name this phenomenon caused by conflicting dip problems as ‘dip discrimination phenomenon’. This phenomenon is not welcome because it not only leads to the loss of weak reflections and tips of diffractions in the final zero‐offset‐CRS stacked section but also to a deteriorated quality in subsequent migration. The common‐reflection‐surface stack with the output imaging scheme (CRS‐OIS) is a novel technique to implement a CRS stack based on a unified Kirchhoff imaging approach. As far as dealing with conflicting dip problems is concerned, the CRS‐OIS is a better option than a conventional CRS stack. However, we think the CRS‐OIS can do more in this aspect. In this paper, we propose a workflow to handle the dip discrimination phenomenon based on a cascaded implementation of prestack time migration, CRS‐OIS and prestack time demigration. Firstly, a common offset prestack time migration is implemented. Then, a CRS‐OIS is applied to the time‐migrated common offset gather. Afterwards, a prestack time demigration is performed to reconstruct each unmigrated common offset gather with its reflections being greatly enhanced and diffractions being well preserved. Compared with existing techniques dealing with conflicting dip problems, the technique presented in this paper preserves most of the diffractions and accounts for reflections from all possible dips properly. More importantly, both the post‐stacked data set and prestacked data set can be of much better quality after the implementation of the presented scheme. It serves as a promising alternative to other techniques except that it cannot provide the typical CRS wavefield attributes. The numerical tests on a synthetic Marmousi data set and a real 2D marine data set demonstrated its effectiveness and robustness.  相似文献   

6.
Scattered ground roll is a type of noise observed in land seismic data that can be particularly difficult to suppress. Typically, this type of noise cannot be removed using conventional velocity‐based filters. In this paper, we discuss a model‐driven form of seismic interferometry that allows suppression of scattered ground‐roll noise in land seismic data. The conventional cross‐correlate and stack interferometry approach results in scattered noise estimates between two receiver locations (i.e. as if one of the receivers had been replaced by a source). For noise suppression, this requires that each source we wish to attenuate the noise from is co‐located with a receiver. The model‐driven form differs, as the use of a simple model in place of one of the inputs for interferometry allows the scattered noise estimate to be made between a source and a receiver. This allows the method to be more flexible, as co‐location of sources and receivers is not required, and the method can be applied to data sets with a variety of different acquisition geometries. A simple plane‐wave model is used, allowing the method to remain relatively data driven, with weighting factors for the plane waves determined using a least‐squares solution. Using a number of both synthetic and real two‐dimensional (2D) and three‐dimensional (3D) land seismic data sets, we show that this model‐driven approach provides effective results, allowing suppression of scattered ground‐roll noise without having an adverse effect on the underlying signal.  相似文献   

7.
We present a Gaussian packet migration method based on Gabor frame decomposition and asymptotic propagation of Gaussian packets. A Gaussian packet has both Gaussian‐shaped time–frequency localization and space–direction localization. Its evolution can be obtained by ray tracing and dynamic ray tracing. In this paper, we first briefly review the concept of Gaussian packets. After discussing how initial parameters affect the shape of a Gaussian packet, we then propose two Gabor‐frame‐based Gaussian packet decomposition methods that can sparsely and accurately represent seismic data. One method is the dreamlet–Gaussian packet method. Dreamlets are physical wavelets defined on an observation plane and can represent seismic data efficiently in the local time–frequency space–wavenumber domain. After decomposition, dreamlet coefficients can be easily converted to the corresponding Gaussian packet coefficients. The other method is the Gabor‐frame Gaussian beam method. In this method, a local slant stack, which is widely used in Gaussian beam migration, is combined with the Gabor frame decomposition to obtain uniform sampled horizontal slowness for each local frequency. Based on these decomposition methods, we derive a poststack depth migration method through the summation of the backpropagated Gaussian packets and the application of the imaging condition. To demonstrate the Gaussian packet evolution and migration/imaging in complex models, we show several numerical examples. We first use the evolution of a single Gaussian packet in media with different complexities to show the accuracy of Gaussian packet propagation. Then we test the point source responses in smoothed varying velocity models to show the accuracy of Gaussian packet summation. Finally, using poststack synthetic data sets of a four‐layer model and the two‐dimensional SEG/EAGE model, we demonstrate the validity and accuracy of the migration method. Compared with the more accurate but more time‐consuming one‐way wave‐equation‐based migration, such as beamlet migration, the Gaussian packet method proposed in this paper can correctly image the major structures of the complex model, especially in subsalt areas, with much higher efficiency. This shows the application potential of Gaussian packet migration in complicated areas.  相似文献   

8.
Survey sinking migration downward continues the entire surface observed multi‐shot data to the subsurface step by step recursively. Reflected energy from reflectors at current depth appear at zero time and zero offset in the extrapolated wavefield. The data (seismic records) of t > 0 at this depth are equivalent to the data acquired by a survey system deployed at this depth. This is the reason to name the process ‘survey sinking’. The records of negative time need not to be further propagated since they carry no information to image structures beneath the new survey system. In this paper, we combine survey sinking with dreamlet migration. The dreamlet migration method decomposes the seismic wavefield and one‐way wave propagator by complete time‐space localized bases. The localization on time gives flexibility on time‐varying operations during depth extrapolation. In dreamlet survey sinking migration, it only keeps the data for imaging the structures beneath the sunk survey system and gets rid of the data already used to image structures above it. The deeper the depth is, the shorter is the valid time records of the remaining data and less computation is needed for one depth step continuation. For data decomposition, in addition to time axis, dreamlet survey sinking also decomposes the data for source and receiver gathers, which is a fully localized decomposition of prestack seismic data. A three‐scatter model is first used to demonstrate the computational feature and principle of this method. Tests on the two‐dimensional SEG/EAGE salt model show that with reduced data sets the proposed method can still obtain good imaging quality on complex geology structures and a strong velocity contrast environment.  相似文献   

9.
With ill‐posed inverse problems such as Full‐Waveform Inversion, regularization schemes are needed to constrain the solution. Whereas many regularization schemes end up smoothing the model, an undesirable effect with FWI where high‐resolution maps are sought, blocky regularization does not: it identifies and preserves strong velocity contrasts leading to step‐like functions. These models might be needed for imaging with wave‐equation based techniques such as Reverse Time Migration or for reservoir characterization. Enforcing blockiness in the model space amounts to enforcing a sparse representation of discontinuities in the model. Sparseness can be obtained using the ?1 norm or Cauchy function which are related to long‐tailed probability density functions. Detecting these discontinuities with vertical and horizontal gradient operators helps constraining the model in both directions. Blocky regularization can also help recovering higher wavenumbers that the data used for inversion would allow, thus helping controlling the cost of FWI. While the Cauchy function yields blockier models, both ?1 and Cauchy attenuate illumination and inversion artifacts.  相似文献   

10.
In order to account for the effects of elastic wave propagation in marine seismic data, we develop a waveform inversion algorithm for acoustic‐elastic media based on a frequency‐domain finite‐element modelling technique. In our algorithm we minimize residuals using the conjugate gradient method, which back‐propagates the errors using reverse time migration without directly computing the partial derivative wavefields. Unlike a purely acoustic or purely elastic inversion algorithm, the Green's function matrix for our acoustic‐elastic algorithm is asymmetric. We are nonetheless able to achieve computational efficiency using modern numerical methods. Numerical examples show that our coupled inversion algorithm produces better velocity models than a purely acoustic inversion algorithm in a wide variety of cases, including both single‐ and multi‐component data and low‐cut filtered data. We also show that our algorithm performs at least equally well on real field data gathered in the Korean continental shelf.  相似文献   

11.
Gaussian beam depth migration overcomes the single‐wavefront limitation of most implementations of Kirchhoff migration and provides a cost‐effective alternative to full‐wavefield imaging methods such as reverse‐time migration. Common‐offset beam migration was originally derived to exploit symmetries available in marine towed‐streamer acquisition. However, sparse acquisition geometries, such as cross‐spread and ocean bottom, do not easily accommodate requirements for common‐offset, common‐azimuth (or common‐offset‐vector) migration. Seismic data interpolation or regularization can be used to mitigate this problem by forming well‐populated common‐offset‐vector volumes. This procedure is computationally intensive and can, in the case of converted‐wave imaging with sparse receivers, compromise the final image resolution. As an alternative, we introduce a common‐shot (or common‐receiver) beam migration implementation, which allows migration of datasets rich in azimuth, without any regularization pre‐processing required. Using analytic, synthetic, and field data examples, we demonstrate that converted‐wave imaging of ocean‐bottom‐node data benefits from this formulation, particularly in the shallow subsurface where regularization for common‐offset‐vector migration is both necessary and difficult.  相似文献   

12.
Extracting true amplitude versus angle common image gathers is one of the key objectives in seismic processing and imaging. This is achievable to different degrees using different migration techniques (e.g., Kirchhoff, wavefield extrapolation, and reverse time migration techniques) and is a common tool in exploration, but the costs can vary depending on the selected migration algorithm and the desired accuracy. Here, we investigate the possibility of combining the local‐shift imaging condition, specifically the time‐shift extended imaging condition, for angle gathers with a Kirchhoff migration. The aims are not to replace the more accurate full‐wavefield migration but to offer a cheaper alternative where ray‐based methods are applicable and to use Kirchhoff time‐lag common image gathers to help bridge the gap between the traditional offset common image gathers and reverse time migration angle gathers; finally, given the higher level of summation inside the extended imaging migration, we wish to understand the impact on the amplitude versus angle response. The implementation of the time‐shift imaging condition along with the computational cost is discussed, and results of four different datasets are presented. The four example datasets, two synthetic, one land acquisition, and a marine dataset, have been migrated using a Kirchhoff offset method, a Kirchhoff time‐shift method, and, for comparison, a reverse time migration algorithm. The results show that the time‐shift imaging condition at zero time lag is equivalent to the full offset stack as expected. The output gathers are cleaner and more consistent in the time‐lag‐derived angle gathers, but the conversion from time lag to angle can be considered a post‐processing step. The main difference arises in the amplitude versus offset/angle distribution where the responses are different and dramatically so for the land data. The results from the synthetics and real data show that a Kirchhoff migration with an extended imaging condition is capable of generating subsurface angle gathers. The same disadvantages with a ray‐based approach will apply using the extended imaging condition relative to a wave equation angle gather solution. Nevertheless, using this approach allows one to explore the relationship between the velocity model and focusing of the reflected energy, to use the Radon transformation to remove noise and multiples, and to generate consistent products from a ray‐based migration and a full‐wave equation migration, which can then be interchanged depending on the process under study.  相似文献   

13.
We reformulate the equation of reverse‐time migration so that it can be interpreted as summing data along a series of hyperbola‐like curves, each one representing a different type of event such as a reflection or multiple. This is a generalization of the familiar diffraction‐stack migration algorithm where the migration image at a point is computed by the sum of trace amplitudes along an appropriate hyperbola‐like curve. Instead of summing along the curve associated with the primary reflection, the sum is over all scattering events and so this method is named generalized diffraction‐stack migration. This formulation leads to filters that can be applied to the generalized diffraction‐stack migration operator to mitigate coherent migration artefacts due to, e.g., crosstalk and aliasing. Results with both synthetic and field data show that generalized diffraction‐stack migration images have fewer artefacts than those computed by the standard reverse‐time migration algorithm. The main drawback is that generalized diffraction‐stack migration is much more memory intensive and I/O limited than the standard reverse‐time migration method.  相似文献   

14.
Hydrological studies focused on Hortonian rainfall–run‐off scaling have found that the run‐off depth generally declines with the plot length in power‐law scaling. Both the power‐law proportional coefficient and the scaling exponent show great variability for specific conditions, but why and how they vary remain unclear. In the present study, the scaling of hillslope Hortonian rainfall–run‐off processes is investigated for different rainfall, soil infiltration, and hillslope surface characteristics using the physically based cell‐based rainfall‐infiltration‐run‐off model. The results show that both temporally intermittent and steady rainfalls can result in prominent power‐law scaling at the initial stage of run‐off generation. Then, the magnitude of the power‐law scaling decreases gradually due to the decreasing run‐on effect. The power‐law scaling is most sensitive to the rainfall and soil infiltration parameters. When the ratio of rainfall to infiltration exceeds a critical value, the magnitude of the power‐law scaling tends to decrease notably. For different intermittent rainfall patterns, the power‐law exponent varies in the range of ?1.0 to ?0.113, which shows an approximately logarithmic increasing trend for the proportional coefficient as a function of the run‐off coefficient. The scaling is also sensitive to the surface roughness, soil sealing, slope angle, and hillslope geometry because these factors control the run‐off routing and run‐on infiltration processes. These results provide insights into the variable scaling of the Hortonian rainfall–run‐off process, which are expected to benefit modelling of large‐scale hydrological and ecological processes.  相似文献   

15.
Potential, potential field and potential‐field gradient data are supplemental to each other for resolving sources of interest in both exploration and solid Earth studies. We propose flexible high‐accuracy practical techniques to perform 3D and 2D integral transformations from potential field components to potential and from potential‐field gradient components to potential field components in the space domain using cubic B‐splines. The spline techniques are applicable to either uniform or non‐uniform rectangular grids for the 3D case, and applicable to either regular or irregular grids for the 2D case. The spline‐based indefinite integrations can be computed at any point in the computational domain. In our synthetic 3D gravity and magnetic transformation examples, we show that the spline techniques are substantially more accurate than the Fourier transform techniques, and demonstrate that harmonicity is confirmed substantially better for the spline method than the Fourier transform method and that spline‐based integration and differentiation are invertible. The cost of the increase in accuracy is an increase in computing time. Our real data examples of 3D transformations show that the spline‐based results agree substantially better or better with the observed data than do the Fourier‐based results. The spline techniques would therefore be very useful for data quality control through comparisons of the computed and observed components. If certain desired components of the potential field or gradient data are not measured, they can be obtained using the spline‐based transformations as alternatives to the Fourier transform techniques.  相似文献   

16.
The conditions under which the Saint Venant equations system for unsteady open channel flow, as an initial–boundary value problem, becomes self‐similar are investigated by utilizing one‐parameter Lie group of point scaling transformations. One of the advantages of this methodology is that the self‐similarity conditions due to the initial and boundary conditions can also be investigated thoroughly in addition to the conditions due to the governing equation. The obtained self‐similarity conditions are compared with the scaling relationships that are derived through the Froude similitude. It is shown that the initial–boundary value problem of a one‐dimensional unsteady open channel flow process in a prototype domain can be self‐similar with that of several different scaled domains. However, the values of all the flow variables (at specified time and space) under different scaled domains can be upscaled to the same values in the prototype domain (at the corresponding time and space), as shown in this study. Distortion in scales of different space dimensions has been implemented extensively in physical hydraulic modelling, mainly because of cost, space and time limitations. Unlike the traditional approach, the distinction is made between the longitudinal–horizontal and transverse–horizontal length scales in this study. The scaled domain obtained by the proposed approach, when scaling ratios of channel width and water depth are equal, is particularly important for the similarity of flow characteristics in a cross‐section because the width‐to‐depth ratio and the inclination angles of the banks are conserved in a cross‐section. It is also shown that the scaling ratio of the roughness coefficient under distorted channel conditions depends on that of hydraulic radius and longitudinal length. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal and economical flexibility in setting up physical hydraulic models. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

17.
Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two‐way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation‐based reflection waveform inversion using one‐way wave equations to retrieve the background velocity. In this method, one‐way wave equations are used for the seismic wave forward modelling, migration/de‐migration and the gradient computation of objective function in frequency domain. Compared with the method using two‐way wave equation, the proposed method benefits from the lower computational cost of one‐way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two‐way wave equation both for two‐ and three‐dimensional situations. Through numerical analysis, we also find that one‐way wave equations can better construct the low wavenumber reflection wavepath without producing high‐amplitude short‐wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.  相似文献   

18.
不依赖子波、基于包络的FWI初始模型建立方法研究   总被引：3，自引：3，他引：0       下载免费PDF全文
地震全波形反演(FWI)从理论走向实际面临着诸多难题,其中之一就是需要一个较高精度的初始模型,另一个难题就是需要一个较为精确的震源子波,初始模型和震源子波的准确程度严重影响着全波形反演的最终结果.为此,本文提出了不依赖子波、基于包络的FWI初始模型建立的方法,建立了相应的目标函数,推导出了反演的梯度,给出了伴随震源的表达式,理论上分析了不依赖子波FWI的可行性.在数值试验中,讨论了参考道的选取方式,通过分析归一化目标函数收敛速率,认为近偏移距参考道优于远偏移距参考道,在地震数据含干扰噪音时,平均道作为参考道要优于最小偏移距参考道.通过包络、包络对数、包络平方三种目标函数反演结果的比较,发现包络对数目标函数对深层的反演效果最好.通过不同子波的试验进一步验证了本方法的正确性.  相似文献   

19.
We develop a new time‐domain reverse‐time migration method called double plane‐wave reverse‐time migration that uses plane‐wave transformed gathers. Original shot gathers with appropriate data acquisition geometry are double slant stacked into the double plane‐wave domain with minimal slant stacking artefacts. The range of plane‐wave components needed for migration can be determined by estimating the maximum time dips present in shot gathers. This reduces the total number of input traces for migration and increases migration efficiency. Unlike the pre‐stack shot‐profile reverse‐time migration where the number of forward propagations is proportional to the number of shots, the number of forward propagations needed for the proposed method remains constant and is relatively small even for large seismic datasets. Therefore, the proposed method can improve the efficiency of the migration and be suitable for migrating large datasets. Double plane‐wave reverse‐time migration can be performed for selected plane‐wave components to obtain subsurface interfaces with different dips, which makes the migration method target oriented. This feature also makes the method a useful tool for migration velocity analysis. For example, we are able to promptly obtain trial images with nearly horizontal interfaces and adjust velocity models according to common image gathers. Seismic signal coming from steeply dipping interfaces can be included into the migration to build images with more detailed structures and higher spatial resolution as better velocity models become available. Illumination compensation imaging conditions for the proposed method are also introduced to obtain images with balanced amplitudes.  相似文献   

20.
In conventional seismic exploration, especially in marine seismic exploration, shot gathers with missing near‐offset traces are common. Interferometric interpolation methods are one of a range of different methods that have been developed to solve this problem. Interferometric interpolation methods differ from conventional interpolation methods as they utilise information from multiples in the interpolation process. In this study, we apply both conventional interferometric interpolation (shot domain) and multi‐domain interferometric interpolation (shot and receiver domain) to a synthetic and a real‐towed marine dataset from the Baltic Sea with the primary aim of improving the image of the seabed by extrapolation of a near‐offset gap. We utilise a matching filter after interferometric interpolation to partially mitigate artefacts and coherent noise associated with the far‐field approximation and a limited recording aperture size. The results show that an improved image of the seabed is obtained after performing interferometric interpolation. In most cases, the results from multi‐domain interferometric interpolation are similar to those from conventional interferometric interpolation. However, when the source–receiver aperture is limited, the multi‐domain method performs better. A quantitative analysis for assessing the performance of interferometric interpolation shows that multi‐domain interferometric interpolation typically performs better than conventional interferometric interpolation. We also benchmark the interpolated results generated by interferometric interpolation against those obtained using sparse recovery interpolation.  相似文献   

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