Extended Imaging Condition Research Articles

Deep‐salt: Complete three‐dimensional salt segmentation from inaccurate migrated subsurface offset gathers using deep learning

AbstractDelimiting salt inclusions from migrated images during the velocity model building flow is a time‐consuming activity that depends on highly human‐curated analysis and is subject to interpretation errors or limitations of the images and methods available. We propose a supervised deep learning based method to include three‐dimensional salt geometries in the velocity models. We compare two convolutional networks – based on the U‐Net architecture – which can process three‐dimensional seismic data. One architecture uses three‐dimensional convolutional kernels, and the other has convolutional long short‐term memory units. Each architecture requires specific preprocessing steps which affects their training and predictive performance. Both proposed architectures use subsurface offset gathers obtained from reverse time migration with an extended imaging condition as input and are trained to predict the salt inclusions. The velocity model used in migration is a reasonable approximation of sediment velocity but without salt inclusions. Thus, the migration model and, consequently, the migrated images are inaccurate due to the absence of the salt inclusion in the model using just the sediment velocity information for the segmentation. A similar salt inclusion methodology was previously validated for two‐dimensional approaches; we extend it to the three‐dimensional case. Our approach relies on subsurface common image gathers to focus the sediments' reflections around the zero offset and spread salt reflections' energy over large subsurface offsets. The results show that both proposed network models can accurately delineate the salt bodies in the test models, but when evaluating the trained networks for the three‐dimensional SEG/EAGE salt model, the architecture with convolutional long short‐term memory units has proven to generalize better.

Least-squares reverse time migration in the presence of velocity errors

Least-squares reverse time migration (LSRTM), which aims to match the modeled data with the observed data in an iterative inversion procedure, is very sensitive to the accuracy of the migration velocity model. If the migration velocity model contains errors, the final migration image may be defocused and incoherent. We have used an LSRTM scheme based on the subsurface offset extended imaging condition, least-squares extended reverse time migration (LSERTM), to provide a better solution when large velocity errors exist. By introducing an extra dimension in the image space, LSERTM can fit the observed data even when significant errors are present in the migration velocity model. We further investigate this property and find that after stacking the extended migration images along the subsurface offset axis within the theoretical lateral resolution limit, we can obtain an image with better coherency and fewer migration artifacts. Using multiple numerical examples, we demonstrate that our method provides superior inversion results compared to conventional LSRTM when the bulk velocity errors are as large as 10%.

Direct migration of ambient seismic data

ABSTRACTUtilising ambient seismic energy naturally propagating in the Earth as an alternative approach to active body‐wave seismic investigations has been a topic of interest for a number of decades. However, because ambient surface‐wave arrivals typically are of much greater amplitude than ambient body‐wave energy, significant data signal processing and long recording times are required to mitigate this and other coherent noise sources, and to correlate sufficient reflected body‐wave energy to converge to a stable image. Even for these scenarios, identifying and validating imaged body‐wave reflection events remain challenging. In active‐source investigations, extended imaging condition gathers are used to examine velocity (in)accuracy. Herein, we develop an ambient direct migration approach that uses a novel ambient (deconvolution) extended imaging condition. We simulate synthetic ambient‐wavefield seismic data for two different models and use a field data set from Lalor Lake in Manitoba, Canada, to conduct a series of numerical experiments to demonstrate the velocity sensitivity and long‐term stationarity of ambient‐wavefield seismic data in the migration image domain. Tests with varying global velocity perturbations show a characteristic reflector moveout in deconvolution extended imaging condition gathers that can serve as a diagnostic of reflected ambient body‐wave energy. We illustrate that this imaging formalism, under idealised circumstances, gives comparable results to conventional seismic methods, which extends the use of extended imaging condition gather‐based image validation to ambient‐wavefield seismic data scenarios. We assert that this may be a valuable tool for the validation of ambient migration techniques that to date have yielded largely inconclusive results.

Pre‐stack Kirchhoff depth migration local space‐shift imaging condition: synthetic and data examples

ABSTRACTExtracting accurate common image angle gathers from pre‐stack depth migrations is important in the generation of any incremental uplift to the amplitude versus angle attributes and seismic inversions that can lead to significant impacts in exploration and development success. The commonly used Kirchhoff migration outputs surface common offset image gathers that require a transformation to angle gathers for amplitude versus angle analysis. The accuracy of this transformation is one of the factors that determine the robustness of the amplitude versus angle measurements. Here, we investigate the possibility of implementing an extended imaging condition, focusing on the space‐lag condition, for generating subsurface reflection angle gathers within a Kirchhoff migration. The objective is to determine if exploiting the spatial local shift imaging condition can provide any increase in angle gather fidelity relative to the common offset image gathers. The same restrictions with a ray‐based approach will apply using the extended imaging condition as both the offset and extended imaging condition method use travel times derived from solutions to an Eikonal equation. The aims are to offer an alternative ray‐based method to generate subsurface angle gathers and to understand the impact on the amplitude versus angle response. To this end, the implementation of the space‐shift imaging condition is discussed and results of three different data sets are presented. A layered three‐dimensional model and a complex two‐dimensional model are used to assess the space shift image gathers output from such a migration scheme and to evaluate the seismic attributes relative to the traditional surface offset common image gathers. The synthetic results show that the extended imaging condition clearly provides an uplift in the measured amplitude versus angle over the surface offset migration. The noise profile post‐migration is also improved for the space‐lag migration due to the double summation inside the migration. Finally, we show an example of a space‐lag gather from deep marine data and compare the resultant angle gathers with those generated from an offset migration and a time‐shift imaging condition Kirchhoff migration. The comparison of the real data with a well log shows that the space‐lag result is a better match to the well compared to the time‐lag extended imaging condition and the common offset Kirchhoff migration. Overall, 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 with an incremental improvement in amplitude versus angle fidelity and lower noise but comes at a higher computational cost.

Increasing resolution of reverse‐time migration using time‐shift gathers

ABSTRACTReverse‐time migration has become an industry standard for imaging in complex geological areas. We present an approach for increasing its imaging resolution by employing time‐shift gathers. The method consists of two steps: (i) migrating seismic data with the extended imaging condition to get time‐shift gathers and (ii) accumulating the information from time‐shift gathers after they are transformed to zero‐lag time‐shift by a post‐stack depth migration on a finer grid. The final image is generated on a grid, which is denser than that of the original image, thus improving the resolution of the migrated images. Our method is based on the observation that non‐zero‐lag time‐shift images recorded on the regular computing grid contain the information of zero‐lag time‐shift image on a denser grid, and such information can be continued to zero‐lag time‐shift and refocused at the correct locations on the denser grid. The extra computational cost of the proposed method amounts to the computational cost of zero‐offset migration and is almost negligible compared with the cost of pre‐stack shot‐record reverse‐time migration. Numerical tests on synthetic models demonstrate that the method can effectively improve reverse‐time migration resolution. It can also be regarded as an approach to improve the efficiency of reverse‐time migration by performing wavefield extrapolation on a coarse grid and by generating the final image on the desired fine grid.

Investigating a time‐shift extended imaging condition in a Kirchhoff pre‐stack depth migration algorithm

ABSTRACTExtracting 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.

Elastic least-squares one-way wave-equation migration

Least-squares migration seeks a reflectivity model that fits the observed data. It is used to compensate for acquisition noise, poor sampling of sources and receivers on the surface, as well as poor illumination of the subsurface. To date, least-squares migration has been mainly restricted to the imaging of acoustic wavefields. We have developed an extension of one-way wave-equation least-squares migration for elastic wavefields in isotropic media. Least-squares migration is an iterative method that requires a forward and an adjoint operator. In elastic least-squares one-way wave-equation migration, the forward operator generates data components from multiparameter images by recursive wavefield decomposition, extrapolation, and recomposition. Conversely, the adjoint operator generates multiparameter images from data components by recursively applying the adjoint of the wavefield recomposition, extrapolation, and wavefield decomposition operators. We use an extended imaging condition and regularize the inversion by applying a smoothing filter on the depth-angle axes of each common image point gather to reduce the effect of source/receiver sampling, noise, and crosstalk artifacts. Elastic least-squares migration is able to compensate for irregular subsurface illumination in elastic imaging and provides an alternative approach to interpolation and wavefield separation of multicomponent seismic data.

Tilted transverse isotropic reverse time migration with angle gathers: Implementation and efficiency

We have developed a 3D reverse time migration (RTM) implementation, with an extended imaging condition, in the presence of tilted transverse isotropy (TTI), using finite-difference time-domain solvers on the rotated staggered grid (RSG) and the Lebedev grid. We have evaluated dispersion analysis of both schemes for a sample TTI medium. Using synthetic and real seismic data in realistic execution configurations, we found surprising inconsistency with quantitative cost estimates in the literature. For fixed accuracy, the RSG scheme proved most efficient in our tests, and not two to three times less efficient, as had been posited. Of course, variability may arise with particular medium properties, computer architectures, or software implementations. Having analyzed wavefield modeling performance in detail, we then quantified the realistic costs associated with the imaging condition in RTM, especially extended imaging conditions. For large extensions of the imaging condition, the associated cost dominates the total execution time and adds very significantly to the total cost of the migration. Our implementation targets both shared and distributed memory parallelism, making it suitable for general CPU clusters, nonuniform memory access architectures, and Intel Xeon-Phi. We have also discussed other aspects of our implementation in detail. In particular, we have explored an alternative method to achieve concurrent communication and computation in RTM.

Extended imaging conditions for passive seismic data

Seismic monitoring at injection sites (e.g., CO2 sequestration, hydraulic fracturing) has become an increasingly common tool amongst oil and gas producers. The information obtained from these data is often limited to seismic event properties (e.g., location, initiation time, moment tensor), the accuracy of which greatly depends on the assumed or estimated elastic velocity models. However, estimating accurate 3D velocity models from passive array data remains a challenging problem. Extended imaging conditions (eICs) for passive wave-equation imaging algorithms represent a key step towards generating – and verifying – elastic velocity models. By extending imaging conditions away from zero-lag in time and space we can better evaluate the focusing of a given event based on the principle that waves focus at zero lag only when the velocity models are correct. We demonstrate that given an elastic medium and multi-component recordings, we can propagate and correlate microseismic P- and S-wavefield modes to compute eICs for P- and S- velocity perturbations. We observe that the maximum correlation deviates from the zero-lag in time and space for a P/S cross-correlation imaging condition when using an incorrect P- and/or S-wave velocity, and thus there is sensitivity to velocity error not observable when using individual wavefield components.

Extended wave-equation imaging conditions for passive seismic data

The information obtained from seismic monitoring at injection sites is often limited to seismic event properties (e.g., location, origin time, moment tensor), the accuracy of which greatly depends on the assumed or estimated elastic velocity models. Current traveltime-based methods to calibrate velocity models rely on having distinct arrivals. In surface seismic monitoring, however, the signal-to-noise ratio of arrivals is often too poor for pick-based methods, and migration techniques are needed. Wave-equation migration can image microseismic sources without the need for picking or knowledge of the onset time by reconstructing the wavefield through the model space and applying an imaging condition. We have devised extended imaging conditions for passive seismic wave-equation imaging algorithms, and we have found that they represent a key step toward verifying and updating elastic velocity models. By extending imaging conditions away from zero lag in time and space, we can better evaluate the focusing of a given event based on a self-consistency principle that direct arrival waves focus at zero lag only when the velocity models were correct. We have determined that given an elastic medium and multicomponent recordings, we can propagate and correlate microseismic P- and S-wavefield modes to compute extended imaging conditions that are sensitive to P- and S-wave velocity perturbations. The extended image volume is robust to sparsely sampled data and high levels of noise and is sensitive to velocity model errors. The extended image volume can be used to determine relative P- and S-wave velocity updates to improve focusing.

Reverse-time demigration using the extended-imaging condition

The forward and inverse process of seismic migration and demigration or remodeling has many useful applications in seismic data processing. We evaluated a method to reobtain the seismic reflection data after migration, by inverting the common image point gathers produced by reverse-time migration (RTM) with an extended-imaging condition. This provided a transformation of the results of seismic data processing in the image domain back to the data domain. To be able to reconstruct the data with high fidelity, we set up demigration as a least-squares inverse problem and we solved it iteratively using a steepest-descent method. Because we used an extended-imaging condition, the method is not dependent on an accurate estimate of the migration-velocity field, and it is able to accurately reconstruct both primaries and multiples. At the same time, because the method is based on RTM, it can accurately handle seismic reflection data acquired over complex geologic media. Numerical results showed the feasibility of the method and highlighted some of its applications on 2D synthetic and field data sets.

Anisotropic migration velocity analysis using reverse-time migration

Seismic anisotropy, if not accounted for, can cause significant mispositioning of the reflectors in depth-migrated images. Accounting for anisotropy in depth migration requires velocity analysis tools that can estimate the anisotropic background velocity field. We extended wave equation migration velocity analysis to deal with 2D tilted transverse isotropic media. The velocities were obtained automatically by nonlinear optimization of the focusing and stack power of common-image point gathers constructed using an extended imaging condition. We used the elastic two-way wave equation to reconstruct the wavefields needed for the image and gradient computations. This led to an anisotropic migration velocity analysis algorithm based on reverse-time migration. We illustrated the method with synthetic and field data examples based on marine surface seismic acquisition. The results showed that the method significantly improves the quality of the depth-migrated image. However, as is common in the case of velocity analysis using surface seismic data, the estimation of anisotropic parameters seems to be strongly nonunique.

Multicomponent joint migration velocity analysis in the angle domain for PP-waves and PS-waves

Employing the vector processing of multicomponent seismic data, elastic Kirchhoff migration is used to conduct a multicomponent joint migration velocity analysis (MVA) of PP- and PS-waves in the angle domain. In vector-wavefield imaging, the elastic imaging condition has been extended to nonzero time and space shifts. We apply the extended imaging condition to elastic Kirchhoff migration to extract angle-domain common-image gathers (ADCIGs) of PP- and PS-waves. This method, which is derived from 3D wave propagation theory, directly operates on the vector wavefields and automatically resolves the problem of PS-wave polarity reversal in the migration sections. Based on the kinematic characteristics of PP- and PS-waves in the incident-angle domain, the velocity updating functions for P- and S-waves are derived. By combining the ADCIGs flatness criterion and the PP- and PS-wave image-depth consistency principle, the accuracy of P- and S-wave velocities can be assessed. The method was tested on a 2D thin-interbed model and the 2D Marmousi2 model. We found that the proposed method extracts the PP- and PS-wave ADCIGs effectively and produces appropriate P- and S-wave velocity fields. This method can be applied to time-delay gathers and to vertical or inline gathers in the 3D case.

Wide-azimuth angle gathers for wave-equation migration

Extended common-image-point (CIP) gathers contain all of the necessary information for decomposition of reflectivity as a function of the reflection and azimuth angles at selected locations in the subsurface. This decomposition operates after the imaging condition applied to wavefields reconstructed by any type of wide-azimuth migration method, e.g., using downward continuation or time reversal. The reflection and azimuth angles are derived from the extended images using analytic relations between the space-lag and time-lag extensions. The transformation amounts to a linear Radon transform applied to the CIPs obtained after applying the extended imaging condition. If information about the reflector dip is available at the CIP locations, then only two components of the space-lag vectors are required, thus reducing computational cost and increasing the affordability of the method. Applications of this method include the study of subsurface illumination in areas of complex geology where ray-based methods are not usable and the study of amplitude variation with reflection and azimuth angles if the subsurface illumination is sufficiently dense. Migration velocity analysis could also be implemented in the angle domain, although an equivalent implementation in the extended domain is less costly and more effective.

Extended imaging conditions for wave-equation migration

Wavefield-based migration velocity analysis using the semblance principle requires computation of images in an extended space in which we can evaluate the imaging consistency as a function of overlapping experiments. Usual industry practice is to assemble those seismic images in common-image gathers that represent reflectivity as a function of depth and extensions, e.g., reflection angles. We introduce extended common-image point (CIP) gathers constructed only as a function of the spaceand time-lag extensions at sparse and irregularly distributed points in the image. Semblance analysis using CIP’s constructed by this procedure is advantageous because we do not need to compute gathers at regular surface locations and we do not need to compute extensions at all depth levels. The CIP’s also give us the flexibility to distribute them in the image at irregular locations aligned with the geologic structure. Furthermore, the CIP’s remove the depth bias of common-image gathers constructed as a function of the depth axis. An interpretation of the CIP’s using the scattering theory shows that they are scattered wavefields associated with sources and receivers inside the subsurface. Thus, when the surface wavefields are correctly reconstructed, the extended CIP’s are characterized by focused energy at the origin of the spaceand time-lag axes. Otherwise, the energy defocuses from the origin of the lag axes proportionally with the cumulative velocity error in the overburden. This information can be used for wavefield-based tomographic updates of the velocity model, and if the velocity used for imaging is correct, the coordinate-independent CIP’s can be a decomposed as a function of the angles of incidence.

Nonlinear extended images via image-domain interferometry

Wave-equation, finite-frequency imaging and inversion still face many challenges in addressing the inversion of highly complex velocity models as well as in dealing with nonlinear imaging (e.g., migration of multiples, amplitude-preserving migration). Extended images (EIs) are particularly important for designing image-domain objective functions aimed at addressing standing issues in seismic imaging, such as two-way migration velocity inversion or imaging/inversion using multiples. General one- and two-way representations for scattered wavefields can describe and analyze EIs obtained in wave-equation imaging. We have developed a formulation that explicitly connects the wavefield correlations done in seismic imaging with the theory and practice of seismic interferometry. In light of this connection, we define EIs as locally scattered fields reconstructed by model-dependent, image-domain interferometry. Because they incorporate the same one- and two-way scattering representations usedfor seismic interferometry, the reciprocity-based EIs can in principle account for all possible nonlinear effects in the imaging process, i.e., migration of multiples and amplitude corrections. In this case, the practice of two-way imaging departs considerably from the one-way approach. We have studied the differences between these approaches in the context of nonlinear imaging, analyzing the differences in the wavefield extrapolation steps as well as in imposing the extended imaging conditions. When invoking single-scattering effects and ignoring amplitude effects in generating EIs, the one- and two-way approaches become essentially the same as those used in today’s migration practice, with the straightforward addition of space and time lags in the correlation-based imaging condition. Our formal description of the EIs and the insight that they are scattered fields in the image domain may be useful in further development of imaging and inversion methods in the context of linear, migration-based velocity inversion or in more sophisticated image-domain nonlinear inverse scattering approaches.

Moveout analysis of wave-equation extended images

Conventional velocity analysis applied to images produced by wave-equation migration with a crosscorrelation imaging condition uses moveout information from space lags or focusing information from time lag. However, more robust velocity-estimation methods can be designed to simultaneously take advantage of the semblance and focusing information provided by migrated images. Such a velocity estimation requires characterization of the moveout surfaces defined jointly for space- and time-lags extended images. The analytic solutions to the moveout surfaces can be derived by solving the system of equations representing the shifted source and receiver wavefields. The superposition of the surfaces from many experiments (shots) is equivalent to the envelope for the family of the individual surface. The envelopeforms a shape that can be characterized as a cone in the extended space of depth, space lag, and time lag. When imaged with the correct velocity, the apex of the cone is located at the correct reflection depth and at zero space and time lags. When imaged with the incorrect velocity, the apex of the cone shifts in the depth direction and along the time-lag axis. The characteristics of the cones are directly related to the quality of the velocity model. Thus, their analysis provides a rich source of information for velocity model-building. Synthetic examples verify the derived formulas characterizing the moveout surfaces. The analytic formulas match the numeric experiments well, demonstrating the accuracy of the formulas. Based on information provided by the extended imaging condition, future application for velocity updates can benefit from the robustness of the depth-focusing analysis and of the high resolution of the semblance analysis.

Isotropic angle-domain elastic reverse-time migration

Multicomponent data usually are not processed with specifically designed procedures but with procedures analogous to those used for single-component data. In isotropic media, the vertical and horizontal components of the data commonly are taken as proxies for the P- and S-wave modes, which are imaged independently with the acoustic wave equations. This procedure works only if the vertical and horizontal components accurately represent P- and S-wave modes, which generally is not true. Therefore, multicomponent images constructed with this procedure exhibit artifacts caused by incorrect wave-mode separation at the surface. An alternative procedure for elastic imaging uses the full vector fields for wavefield reconstruction and imaging. The wavefields are reconstructed using the multicomponent data as a boundary condition for a numerical solution to the elastic wave equation. The key component for wavefield migration is the imaging condition, which evaluates the match between wave-fields reconstructed from sources and receivers. For vector wave fields, a simple component-by-component crosscorrelation between two wavefields leads to artifacts caused by crosstalk between the unseparated wave modes. We can separate elastic wavefields after reconstruction in the subsurface and implement the imaging condition as crosscorrelation of pure wave modes instead of the Cartesian components of the displacement wavefield. This approach leads to images that are easier to interpret because they describe reflectivity of specified wave modes at interfaces of physical properties. As for imaging with acoustic wavefields, the elastic imaging condition can be formulated conventionally (crosscorrelation with zero lag in space and time) and extended to nonzero space and time lags. The elastic images produced by an extended imaging condition can be used for angle decomposition of primary (PP or SS) and converted (PS or SP) reflectivity. Angle gathers constructed with this procedure have applications for migration velocity analysis and amplitude-variation-with-angle analysis.