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... • numerical simulation of seismic wave propagation in three-dimensional inhomogeneous multiscale media; • imaging of small-scale inhomogeneities by focusing the energy of diffracted/scattered waves. For diffraction imaging, we used popular today the so-called dip angle common image gathers (CIG) which are computed in the reference system of the model domain [11]. In this coordinates there is a significant difference in the behavior of reflected and diffracted waves and this difference can be used for their separation [12]. ...

... Strictly speaking, it would be more correct, to associate the second case not with diffraction, but with scattering by the conglomerates of small-scale heterogeneities. For diffraction imaging, we used popular today the so-called dip angle common image gathers (CIG) which are computed in the reference system of the model domain [11]. In this coordinates there is a significant difference in the behavior of reflected and diffracted waves and this difference can be used for their separation [12]. ...

... In this coordinates there is a significant difference in the behavior of reflected and diffracted waves and this difference can be used for their separation [12]. In [11,13] they offered a separation and diffraction imaging method based on separation and migration. For full azimuth observations, azimuthal dependence of diffraction can be used to estimate fracture orientation [1]. ...

Computation of Common Middle Point seismic sections and their subsequent time migration and diffraction imaging provides very important knowledge about the internal structure of 3D heterogeneous geological media and are key elements for successive geological interpretation. Full-scale numerical simulation, that computes all single shot seismograms, provides a full understanding of how the features of the image reflect the properties of the subsurface prototype. Unfortunately, this kind of simulations of 3D seismic surveys for realistic geological media needs huge computer resources, especially for simulation of seismic waves’ propagation through multiscale media like cavernous fractured reservoirs. Really, we need to combine smooth overburden with microstructure of reservoirs, which forces us to use locally refined grids. However, to resolve realistic statements with huge multi-shot/multi-offset acquisitions it is still not enough to provide reasonable needs of computing resources. Therefore, we propose to model 3D Common Middle Point seismic cubes directly, rather than shot-by-shot simulation with subsequent stacking. To do that we modify the well-known "exploding reflectors principle" for 3D heterogeneous multiscale media by use of the finite-difference technique on the base of grids locally refined in time and space. We develop scalable parallel software, which needs reasonable computational costs to simulate realistic models and acquisition. Numerical results for simulation of Common Middle Points sections and their time migration are presented and discussed.

... Yet these objects will provoke the scattering of waves in all directions, a phenomenon called diffraction. Due to their truncated Fresnel zone, diffracted waves contain a higher resolution signal and are valuable for an enhanced interpretation and inversion (Khaidukov et al., 2004;Moser and Howard, 2008;Landa et al., 2008;Huang et al., 2015). However, diffracted signal is not often available to the interpreter because its amplitude can be far weaker than reflected signal and is often lost during processing (Khaidukov et al., 2004). ...

... scattering object, given that the correct velocity model is used, the migration operator will align with the diffraction hyperbola and give rise to a flat response in the dip angle CIG. In contrast, when migrating a point located on a reflector, the operator will respond only at a dip corresponding to the structural inclination angle (Audebert et al., 2005;Landa et al., 2008;Reshef and Landa, 2009;Klokov et al., 2010;Klokov and Fomel, 2012). ...

... All rights reserved. constructive interferences (Landa et al., 2008;Klokov et al., 2010). Figure 2 illustrates the dip angle response of both an horizontal reflector and a scattering point. ...

Diffracted waves carry high resolution information that can help interpreting fine structural details at a scale smaller than the seismic wavelength. However, the diffraction energy tends to be weak compared to the reflected energy and is also sensitive to inaccuracies in the migration velocity, making the identification of its signal challenging. In this work we present an innovative workflow to automatically detect scattering points in the migration dip angle domain using deep learning. By taking advantage of the different kinematic properties of reflected and diffracted waves, we separate the two types of signals by migrating the seismic amplitudes to dip angle gathers using pre‐stack depth imaging in the local angle domain. Convolutional neural networks are a class of deep learning algorithms able to learn to extract spatial information about the data in order to identify its characteristics. They have now become the method of choice to solve supervised pattern recognition problems. In this work, we use wave equation modelling to create a large and diversified dataset of synthetic examples to train a network into identifying the probable position of scattering objects in the subsurface. After giving an intuitive introduction to diffraction imaging and deep learning and discussing some of the pitfalls of the methods, we evaluate the trained network on field data and demonstrate the validity and good generalization performance of our algorithm. We successfully identify with a high accuracy and high resolution diffraction points, including those which have a low signal to noise and reflection ratio. We also show how our method allows us to quickly scan through high dimensional data consisting of several versions of a dataset migrated with a range of velocities to overcome the strong effect of incorrect migration velocity on the diffraction signal. This article is protected by copyright. All rights reserved

... Set of partial reconstruction in a three-dimensional spectral space. (Landa, Fomel and Reshef 2008;Reshef and Landa 2009). In this angle domain, the reflection is always convex upwards, whereas the diffraction is represented as a straight line. ...

... In this angle domain, the reflection is always convex upwards, whereas the diffraction is represented as a straight line. Therefore, the very effective separation procedure here is filtering in the Radon transform domain (Landa et al. 2008;Klokov, Baina and Landa 2010;Klokov and Fomel 2012). ...

The paper presents 3D diffraction imaging based on the spectral decomposition of the different combination of selective or partial images. These images are got by the pre‐stack asymmetric migration procedure which is weighted data summation. Spectral decomposition is done in the Fourier domain with respect to spatial dip and azimuth angles. Numerical examples with the application of different workflows for the synthetic and real data examples demonstrate detailed reliable reconstruction of the fractured zones and reliable reconstruction of fracture orientation on synthetic and real 3D data examples.
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... Expanding on these techniques, coherent subtraction (Schwarz and Gajewski, 2017) was created which uses local coherency measures to suppress reflections. The dip-angle gather domain also saw much success in diffraction imaging (Landa et al., 2008;Klokov and Fomel, 2010), as well as migration separation techniques such as least-squares migration separation methods (Merzlikin and Fomel, 2016;Merzlikin et al., 2020), and double migration with reflection attenuation (Moser and Howard, 2008). However, these methods all leave a volume containing diffractions and noise. ...

... These features are well-suited to diffraction identification as demonstrated in Bauer et al. (2019) and could provide useful inputs to help incentivise the MDDI classification. Additionally, the dip-angle domain has seen much success in diffraction identification, and this can be a powerful domain which may be incorporated into the method (Landa et al., 2008). ...

The seismic wavefield arises from interactions of a source wavefield with subsurface heterogeneities as the wavefield propagates through the earth. In a conventional seismic processing workflow, the reflected portion of the wavefield is enhanced at the expense of the rest of the wavefield. While this is useful, considerable information which is contained outside of the reflections is lost. To alleviate this issue, we propose a deep learning technique which aims to separate the wavefield into three of the wavefield components: reflections, diffractions, and noise. This technique involves first performing several data domain transformations on the input and applying these as input classes on a pixel-by-pixel basis to guide the neural network. A simple separation is performed to remove the reflections and noise, allowing the diffractions to be processed independently. This technique, called Multi-domain diffraction identification, gives a high standard classification of the diffractions in a fraction of the time and computational cost of plane-wave destruction. These diffractions have then been removed from the data and compared with separation results from plane-wave destruction, showing similarities in the diffractions and demonstrating the denoising capability of the method.

... Fang et al. (2017) showed that the fractures with a random spacing can form fracture clusters and the clusters can generate strong multiply-scattered seismic waves which could mislead the reflected P-wave AVOAz results (amplitude variation with offset and azimuth for the reflected waves). On the other hand, people also used diffracted waves by fractures to image fractures (Willis et al., 2006;Landa et al., 2008;Klokov and Fomel, 2012;Fang et al., 2013;Schoepp et al., 2015;Protasov et al., 2016). However, these imaging-based methods have limited capability in distinguishing multiple sets of fractures. ...

... The db method uses all signals available in the recorded data, including converted P-to-S/S-to-P waves, internal multiples, and all other possible interactions. This is in sharp contrast with the diffraction imaging (e.g., Landa et al., 2008), whereas these layer reflections should be removed. Figure 3b shows the local average of the compliance field around all 441 targets. ...

... Numerous methods exist for separating diffraction signal from reflection in both the data and image domains [3,4,6,11,12]. Attributes correlated to a diffraction occurring, like focusing [9] or angle-gather flat-ness [13,14], only become available after migration, so these methods typically function by predicting and removing reflections. Recent excitement in applying machine learning techniques to problems related to seismic imaging and interpretation [15][16][17] has extended into the use of pattern recognition [18] and deep learning [19] for diffraction detection. ...

... We illustrate our probabilistic diffraction imaging method on a toy model [13,31,35]. Figure 1 features a chart with the workflow for the imaging process. ...

We propose and demonstrate a probabilistic method for imaging seismic diffractions based on path-integral imaging. Our approach uses oriented velocity continuation to produce a set of slope-decomposed diffraction images over a range of plausible migration velocities. Utilizing the assumption that each partial image in slope is independent enables us to construct an object resembling a probability field from the slope-decomposed images. That field may be used to create weights for each partial image in velocity corresponding to the likelihood of a correctly migrated diffraction occurring at a location within the seismic image for that migration velocity. Stacking these weighted partial images over velocity provides us with a path-integral seismic diffraction image created using probability weights. We illustrate the principles of the method on a simple toy model, show its robustness to noise on a synthetic, and apply it to a 2D field dataset from the Nankai Trough. We find that using the proposed approach creates diffraction images that enhance diffraction signal while suppressing noise, migration artifacts, remnant reflections, and other portions of the wavefield not corresponding to seismic diffraction relative to previously developed diffraction imaging methods, while simultaneously outputting the most likely migration velocity. The method is intended to be used on data which has already had much of the reflection energy removed using a method like plane-wave destruction. Although it suppresses residual reflection energy successfully, this suppression is less effective in the presence of strong reflections typically encountered in complete field data. The approach outlined in this paper is complimentary to existing data domain methods for diffraction extraction, and the probabilistic diffraction images it generates can supplement existing reflection and diffraction imaging methods by highlighting features that have a high likelihood of being diffractions and accentuating the geologically interesting objects in the subsurface that cause those features.

... These methods include singular value decomposition in local image matrices (Zhu and Wu, 2010), pattern recognition along the diffraction traveltime (Figueiredo et al., 2013), the prestack time diffraction imaging method using shot and opening angle gathers (Zhang and Zhang, 2014), the windowed median filter in dip-angle gathers (Liu et al., 2016), and the specularity filter in the prestack domain (Dafni and Symes, 2017). Interestingly, some of the methods in the first and second categories can be extended to the migrated gathers, including the Radon transform (Landa et al., 2008;Reshef and Landa, 2009;Klokov and Fomel, 2012;Silvestrov et al., 2016) and the Mahalanobis-based amplitude damping operation (Li et al., 2020b). In the final category, many methods extract diffraction information based on the different amplitude distribution. ...

... Separating diffractions before the imaging process obtains results in the amplitude distribution and traveltime information of the diffraction event. Furthermore, separated diffraction waves can be used in velocity analysis and migration (Fomel et al., 2007;Landa et al., 2008;Reshef and Landa, 2009;Lin et al., 2018b). Therefore, we propose the common virtual source gather (CVSG) to obtain diffraction events in the prestack domain. ...

Diffractions are the seismic responses of subsurface small-scale geologic discontinuities or inhomogeneities, whose energy is much weaker than that of reflections. To eliminate the masking effect of strong reflections on weak diffractions, a prestack diffraction separation method is proposed based on the common virtual source gather (CVSG) and the median filter. The reflection generated from a reflector can be regarded as originating from a virtual source (or a focused area). According to this behavior, the reflection can be transformed into its corresponding virtual source position to build the CVSG. Unlike the reflection, diffraction cannot be regarded as originating from one virtual source. Therefore, diffractions have a curved shape, whereas reflections are flat in the CVSG. Based on the traveltime moveout method, the reflection traveltime is calculated for describing reflection events and generating CVSG. Theory and a simple synthetic data test demonstrate there is almost no energy lost when transforming between a shot gather and CVSG. Then, for removing the reflection, the median filter is used in the CVSG where the reflection appears as a linear event. Complex synthetic and field examples demonstrate that the proposed method can flatten reflection events and thus can separate diffraction events from strong reflections in the prestack domain.

... For diffraction imaging, we used popular today the so-called dip angle common image gathers (CIG) which are computed in the reference system of the model domain [11]. In this coordinates there is a significant difference in the behavior of reflected and diffracted waves and this difference can be used for their separation [12]. ...

... In this coordinates there is a significant difference in the behavior of reflected and diffracted waves and this difference can be used for their separation [12]. In [11] and [13] they offered a separation and diffraction imaging method based on separation and migration. For full azimuth observations, azimuthal dependence of diffraction can be used to estimate fracture orientation [1]. ...

Computation of Common Middle Point seismic sections and their subsequent time migration and diffraction imaging provides very important knowledge about the internal structure of 3D heterogeneous geological media and are key elements for successive geological interpretation. Full-scale numerical simulation, that computes all single shot seismograms, provides a full understanding of how the features of the image reflect the properties of the subsurface prototype. Unfortunately, this kind of simulations of 3D seismic surveys for realistic geological media needs huge computer resources, especially for simulation of seismic waves’ propagation through multiscale media like cavernous fractured reservoirs. In order to significantly reduce the query of computer resources we propose to model these 3D seismic cubes directly rather than the shot-by-shot simulation with subsequent CMP stacking. To do that we modify the well known "exploding reflectors principle" for 3D heterogeneous multiscale media by use of the finite-difference technique on the base of grids locally refined in time and space. To be able to simulate realistic models and acquisition we develop scalable parallel software, which needs reasonable computational costs. Numerical results for simulation of Common Middle Points sections and their time migration are presented and discussed.

... As a consequence, many small scale structural details such as reflector discontinuities at fault planes, channel edges or boulders may not be well resolved in the image. Yet, those small objects may provoke the scattering of waves in all directions, a phenomenon called diffraction, and diffracted waves may be employed for an enhanced interpretation Khaidukov et al. (2004); Landa et al. (2008); Moser and Howard (2008). Because scattered amplitudes are much weaker than the reflected ones, it is challenging to isolate and interpret the diffraction signal Khaidukov et al. (2004). ...

... The operation is repeated for every lateral and vertical position, yielding data in dependence on x, z and ν that we call dip angle common image gathers (CIGs) Audebert et al. (2002). Because of their different kinematic behaviour, reflected waves and diffracted waves exhibit a distinct response in this domain Landa et al. (2008); Klokov et al. (2010). ...

Diffracted waves carry high resolution information that can help interpreting fine structural details at a scale smaller than the seismic wavelength. Because of the low signal-to-noise ratio of diffracted waves, it is challenging to preserve them during processing and to identify them in the final data. It is, therefore, a traditional approach to pick manually the diffractions. However, such task is tedious and often prohibitive, thus, current attention is given to domain adaptation. Those methods aim to transfer knowledge from a labeled domain to train the model, and then infer on the real unlabeled data. In this regard, it is common practice to create a synthetic labeled training dataset, followed by testing on unlabeled real data. Unfortunately, such procedure may fail due to the existing gap between the synthetic and the real distribution since quite often synthetic data oversimplifies the problem, and consequently the transfer learning becomes a hard and non-trivial procedure. Furthermore, deep neural networks are characterized by their high sensitivity towards cross-domain distribution shift. In this work, we present deep learning model that builds a bridge between both distributions creating a semi-synthetic datatset that fills in the gap between synthetic and real domains. More specifically, our proposal is a feed-forward, fully convolutional neural network for image-to-image translation that allows to insert synthetic diffractions while preserving the original reflection signal. A series of experiments validate that our approach produces convincing seismic data containing the desired synthetic diffractions.

... The domain shows great potential for diffraction imaging (Audebert et al., 2002;Sava et al., 2005;Reshef and Landa, 2009). In this study, we perform velocity analysis in the time-migrated angle domain and observe that diffraction events appear flat when they are imaged at the diffraction point with accurate migration velocity in the angle gathers constructed with Kirchhoff prestack time migration (PSTM) (Reshef, 2007;Landa et al., 2008;Klokov and Fomel, 2012). Fomel et al. (2007) develop a local varimax measure to optimally choose the migration velocity in the poststack domain. ...

... The incident and scattered rays carry the information of the image points from different directions. Therefore, different incident angles of common-image points can be used to generate the migrated angle gathers using extracted diffractions (Landa et al., 2008). Figure 1 shows the schematic diagram of the angle gathers for an image point, where D is an imaging point in the subsurface. ...

Seismic diffractions contain valuable information regarding small-scale inhomogeneities or discontinuities, and therefore they can be used for seismic interpretation in the exploitation of hydrocarbon reservoirs. Velocity analysis is a necessary step for accurate imaging of these diffractions. A new method for diffraction velocity analysis and imaging is proposed that uses an improved adaptive minimum variance beamforming technique. This method incorporates the minimum variance, coherence factor, and correlation properties to improve the signal-to-noise ratio and enhance correlations. Our method can make seismic diffractions become better focused in semblance panels, allowing for the optimal migration velocity for diffractions to be accurately picked. Synthetic and field examples demonstrate that the migration velocity for the diffractions can differ from that for the reflections. The results suggest that the diffraction velocity analysis and imaging method is feasible for accurately locating and identifying small-scale discontinuities, which leads to the possibility of using this approach for practical application and seismic interpretation.

... Analysis of seismograms in the structural angles coordinate system reveals a significant difference in the reflected and diffracted waves in these coordinates. On this basis, efficient algorithms for separating reflection and diffraction/scattering are proposed and implemented (Landa et al., 2008;Reshef and Landa, 2009). In this angle domain, for many cases, the reflection is convex, whereas the diffraction corresponds to a straight line. ...

... In this angle domain, for many cases, the reflection is convex, whereas the diffraction corresponds to a straight line. Therefore, the effective separation procedure here is filtering in the Radon transform domain (Landa et al., 2008;Klokov, Baina, and Landa 2010;Klokov and Fomel, 2012). Decker, Merzlikin, and Fomel further develop seismic diffraction imaging utilizing the principle of flatness of diffraction events in slope gather together with the plane wave destructor (Decker et al., 2017). ...

We present a 3D diffraction imaging procedure with the subsequent computation of diffraction attributes and their application in field seismic data processing. This procedure consists of a weighted asymmetric summation of 3D seismic data based on Gaussian beams double-focusing. The different mutual geometry of beams produces 3D selective diffraction images concerning scattering azimuth representing the target objects, such as fractures, faults, and caverns. We introduce three diffraction attributes based on 3D selective images: structural diffraction attribute, point diffraction attribute, and the azimuth of structural diffraction. Compared with the conventional diffraction energy, these attributes open the possibility of distinguishing between fractured and cavernous objects and determining the orientations of fractures and faults. Compared with the other diffraction attributes, the proposed attributes result from the analysis of the diffracted wave behavior in 3D media and are not typical image processing algorithms.
We evaluate the approach using synthetic and real data sets containing canonical features like faults, caves, and fracture corridors that generate diffractions.

... Moser and Howard (2008) built the anti-stability phase function to suppress the reflected wave field while enhancing diffracted waves. Landa et al. (2008) and Zhu et al. (2013) used local a dip filter to achieve diffraction and reflection separation in the migration dip domain. Based on the theory of diffraction coherence summation, Berkovitch et al. (2009) proposed using the local time correction formula to parameterize the diffraction travel time curve and then stacked diffraction events while suppressing reflected waves. ...

Diffracted seismic waves may be used to help identify and track geologically heterogeneous bodies or zones. However, the energy of diffracted waves is weaker than that of reflections. Therefore, the extraction of diffracted waves is the basis for the effective utilization of diffracted waves. Based on the difference in travel times between diffracted and reflected waves, we developed a method for separating the diffracted waves via singular value decomposition filters and presented an effective processing flowchart for diffracted wave separation and imaging. The research results show that the horizontally coherent difference between the reflected and diffracted waves can be further improved using normal move-out (NMO) correction. Then, a band-rank or high-rank approximation is used to suppress the reflected waves with better transverse coherence. Following, separation of reflected and diffracted waves is achieved after the filtered data are transformed into the original data domain by inverse NMO. Synthetic and field examples show that our proposed method has the advantages of fewer constraints, fast processing speed and complete extraction of diffracted waves. And the diffracted wave imaging results can effectively improve the identification accuracy of geological heterogeneous bodies or zones.

... Numerous methods exist for separating diffraction signal from reflection, in both the data and image domains (Harlan et al., 1984;Kozlov et al., 2004;Fomel et al., 2007;Moser and Howard, 2008;Berkovitch et al., 2009). Attributes correlated to a diffraction occurring, like focusing (Khaidukov et al., 2004) or angle-gather flatness (Landa et al., 2008;Reshef and Landa, 2009) only become available after migration, so these methods typically function by predicting and removing reflections. Reflection removal leaves the diffractions but also the already present noise. ...

We propose a probabilistic method for imaging seismic diffractions based on path-integral imaging. The method utilizes oriented velocity continuation to generate a suite of slope decomposed diffraction images with different migration velocities. Treating each partial image in slope as independent allows us to construct an object resembling a probability field from the continuation output. That field may be used to construct probability weights for each partial image in velocity that we interpret as the likelihood of a correctly migrated diffraction occurring at a location within the seismic image. Stacking these weighted partial images over velocity provides us with a path-integral seismic diffraction image constructed using probability weights. We apply the method to a 2D field dataset from the Viking Graben. We find that the proposed approach creates diffraction images that better suppress noise, migration artifacts, and remnant reflections than previously developed diffraction imaging methods while simultaneously determining the most likely migration velocity.

... In view of this geometrical characteristics difference between reflections and diffractions, diffractions separation methods are extensively reported in DACIGs. Landa et al. (2008) use plane-wave destruction filter to suppress reflections in DACIGs. Zhang and Zhang (2014) attenuate reflections by muting the Fresnel zones in shot and opening-angle gathers generated by prestack time migration method. ...

... Therefore, if one can separate the diffractions and process them separately, the discontinuities can be directly imaged as opposed to inferred (Fomel et al., 2007). On top of this, separated diffractions have many other uses such as wavefront tomography and velocity analysis (Bauer et al., 2017, Landa et al., 2008. Separating diffractions, however, is not a straightforward task due to the comparatively low amplitude of diffractions, approximately an order of magnitude lower than reflections, as well as the lack of a clear distinction between reflection and diffraction energy (Klokov and Fomel, 2012). ...

Diffraction imaging is a niche imaging technique which aims to directly image discontinuities in the subsurface by separating diffractions from the rest of the wavefield and processing them independently. However, to separate diffractions is a complicated procedure due to their weak amplitudes and the overlap of energies between diffractions and the much stronger reflections. While analytical methods exist to separate diffractions, they require parameterisation, are comparatively computationally expensive, and leave a volume which contains both diffractions and noise. Here, we aim to use a Generative Adversarial Network (GAN) to automatically separate diffractions from reflections on pre-migrated seismic data without the need for parameterisation.
We have applied the GAN to two real datasets, one for validation, which comes from the same dataset used in training, and one which is used solely for prediction. This shows good results for both the validation and prediction data when compared to plane-wave destruction, an analytical separation technique, and is applied in a fraction of the time. The prediction dataset is then added to the overall training data, the network retrained and applied to the same validation data. This further improves the separation on the validation data and suggests that additional data may enhance the separation.

... The third type of method performs separation of diffraction in the migrated domain. It includes muting reflections by focusing-defocusing (Khaidukov, Landa & Moser 2004), the radon transformation in the migrated dip-angle domain (Landa, Fomel & Reshef 2008;Reshef & Landa 2009;Klokov & Fomel 2012), diffraction imaging in shot and opening-angle gathers (Zhang & Zhang 2014), taper function in specular gathers, a windowed median filer in the migrated dip-angle gathers (Liu et al. 2016), a high-resolution radon-based procedure in the poststack RTM (reverse-time migration) domain (Silvestrov et al. 2016) and the specularity filter in the prestack RTM (Dafni & Symes 2017) dipangle domain. ...

Separating weak diffractions in the prestack domain plays a vital role in high-resolution imaging small-scale discontinuities or inhomogeneities, which are associated with the migration paths and storage spaces for carbonate fracture-cave reservoirs. A shot-domain diffraction separation method is proposed with a SVMF (space-varying media filter) in the flattened shot domain. The diffractions with fast dynamic changings, including damping amplitudes and phase reversal, are filtered out by the spacing-varying median filter along the prediction-step directions of the flattened shot domain. The proposed method opens a possibility for separating diffractions in the shot domain and has an advantage in the traditional common-offset diffraction separation method. A numerical experiment illustrates the good performance of the proposed method in eliminating reflections and separating diffractions in the shot domain, and the field application further verifies its potential value in resolving the hidden small-scale cavities and tiny faults in carbonate reservoirs.

... The kinematic differences between reflection and diffraction are studied and used in the above methods. Based on the differences, these methods can also be extended to suppress reflection and enhance diffraction energy in the migrated gathers (Audebert et al. 2002;Qin et al. 2005;Landa, Fomel and Reshef 2008;Reshef and Landa 2009;Klokov and Fomel 2012;Zhang and Zhang 2014). ...

As an ideal carrier of high‐resolution information, seismic diffractions can be used to clarify and locate small‐scale discontinuities or inhomogeneities in the subsurface. However, a diffraction is weak and thus be suppressed by the specular reflection. Furthermore, a diffraction would be destroyed by the conventional imaging method due to the polarity reversal of diffraction. In this paper, we analyze the behavior of diffractions and reflections. For the image point on a horizontal or oblique reflector, the zone on both sides of the stationary point have same energy after using a cosine weight function. Based on the behavior, we propose the adaptive phase filter to adjust the polarity of the energy on both sides, and calculate it through the illumination angle and the reflector dip angle. This method avoids the calculation of the Fresnel zones and can further suppress residual reflections that disturb the diffraction images. Synthetic and field data applications show that the desired imaging results can be obtained by the proposed method. The test results demonstrate that the method is efficient in detecting small‐scale discontinuities or inhomogeneities in the subsurface and can provide high‐resolution information for seismic interpretation. This article is protected by copyright. All rights reserved

... As migration collapses diffractions to a point on the seismic image, a separate domain is used for separation generated during the migration process (Reshef and Landa, 2009). The dip-angle gather domain is commonly used for this form of separation (Landa et al., 2008), and many methods exist within this domain for separation, including radon filtering (Klokov and Fomel, 2012) and apex destruction (Kozlov et al., 2004). Additionally, there exist machine learning methods for separation including pioneering work from Serfaty et al. (2018) who were the first to demonstrate diffraction separation using deep learning and used the directional image gather domain, separation in the dip-angle gather domain (Tschannen et al., 2020) and diffraction point detection (Maciel and Biloti, 2014). ...

Diffraction imaging is the process of separating diffractions from the seismic wavefield and imaging them independently, highlighting subsurface discontinuities. While there are many analytic‐based methods for diffraction imaging which use kinematic, dynamic, or both, properties of the diffracted wavefield, they can be slow and require parameterisation. Here, we propose a training an image‐to‐image Generative Adversarial Network to automatically separate diffractions on pre‐migrated seismic data in a fraction of the time of conventional methods. To train the Generative Adversarial Network, plane‐wave destruction was applied to a range of synthetic and real images from field data to create training data. This training data was screened and any areas where the plane‐wave destruction did not perform well, such as synclines and areas of complex dip, were removed to prevent bias in the neural network. A total of 14132 screened images were used to train the final Generative Adversarial Network.
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... The seismic coda represents a train of seismic events that are multiply scattered by fractures. Another important contribution in the fracture characterization includes seismic imaging/ migration of singly diffracted waves by fractures (e.g., Landa et al., 2008;Klokov and Fomel, 2012;Schoepp et al., 2015;Protasov et al., 2016;Silvestrov et al., 2016). The kinematic behavior of singly scattered waves (also called diffractions) was proposed to image the subsurface fractures (e.g., Landa et al., 2011Landa et al., , 2013Landa, 2012). ...

Obtaining information on the spatial distribution of subsurface natural and induced fractures is critical in the production of geothermal or hydrocarbon fluids. Traditional seismic characterization methods for subsurface fractures are based on the assumption of effective anisotropy medium theory, which may not be true in reality when the fracture distribution is random. We have tested the recently proposed double-beam method to characterize nonuniformly distributed fractures. We built a 3D layered reservoir model; the reservoir layer was geometrically irregular, and it contained a set of randomly spaced fractures with spatially varying fracture compliances. We used an elastic full-wave finite-difference method to model the wavefield, where we treat the fractures as linear-slip boundaries and the data include all elastic multiple scattering. Taking the surface seismic data as input, the double-beam method forms a focusing source beam and a focusing receiver beam toward the fracture target. The fracture information is derived from the interference pattern of these two beams, which includes fracture orientation, fracture spacing, and fracture compliance as a function of spatial location. The fracture orientation parameter is the most readily determined parameter even for multiple nonorthogonal coexistent fracture sets. The beam-interference amplitude depends on the fracture spacing and compliance in a local average sense for random fractures. The beam-interference amplitude is large when there are many fractures or the compliance value is large, which is important in the interpretation of the fluid-transport properties of a reservoir.

... To accurately estimate the local slopes, Lin et al. (2018a) propose an improved PWD method using the L 1 -norm and wavelet transform to separate diffractions. Landa et al. (2008) exploit the sensitivity of diffraction events to the migration velocity error in the dip-angle domain and design a local-dip filter to achieve diffraction separation. Khaidukov et al. (2004) focus and mute the reflection energy at imaginary source points to separate diffractions in their focusing-defocusing method. ...

Seismic diffractions are the responses of small-scale discontinuous structures. They contain subwavelength geologic information. Thus, diffractions can be utilized for high-resolution imaging. The energy of the diffractions is generally much weaker than that of reflections. Therefore, diffracted energy is typically masked by specular reflected energy. Diffraction/reflection separation is a crucial pre-processing step for diffraction imaging. To resolve the diffraction-separation problem, we propose a method based on multichannel singular-spectrum analysis (MSSA) algorithm for diffraction separation by reflection suppression. The MSSA algorithm utilizes the differences in the kinematic and dynamic properties between reflections and diffractions to suppress time-linear signals (reflections) and separate weaker time-nonlinear signals (diffractions) in the common-offset or poststack domain. For the time-linear signals, the magnitudes of the singular values are proportional to the energy strength of the signals. The stronger the energy of a component of the linear signals, the larger the corresponding singular values. The singular values of reflections and diffractions have dissimilar spatial distributions in the singular-value spectrum, because of the differences in their linear properties and energy. Only the singular values representing diffractions are selected to reconstruct seismic signals. Synthetic data and field data are used to test the proposed method. The results demonstrate a good performance of the MSSA algorithm in enhancing diffractions and suppressing reflections.

... Diffraction image is critical for seismic interpretation as it provides significant indication of localized geological heterogeneities that is generally beyond normal resolution obtained by traditional seismic images. Many methods have been proposed to generate the diffraction-only images (Landa et al., 2008;Schoepp et al., 2014;Zhang et al., 2014). One popular method is based on dip-angle gather (Liu et al., 2016) where the reflection energy is converted to one focused point and the diffraction energy is a flat event for accurate velocity model. ...

... Separating diffractions before the imaging process can obtain the diffracted wavefields to further analyze the energy distribution or traveltime of the diffraction (Fomel et al., 2007;Landa et al., 2008;Reshef and Landa, 2009;Lin et al., 2018). Plane-wave destruction (PWD) is an effective method that can remove linear events (reflections) in the common-offset domain with an accurate slope field. ...

Diffracted waves provide the opportunity to detect small-scale subsurface structures because they give wide illumination direction of geological discontinuities such as faults, pinch-outs, and collapsed columns. However, separating diffracted waves is challenging because diffracted waves have greater geometrical amplitude losses and are generally weaker than reflections. To retain more diffracted waves, a pre-stack diffraction separation method is proposed based on the local slope pattern and plane-wave destruction method. Generally, it is difficult to distinguish between the hyperbolic reflections and hyperbolic diffractions using the data-driven local slope estimation in the shot domain. Therefore, we transfer the slope estimation in the shot domain to the velocity analysis in the common midpoint domain and the ray parameter calculation in the stack domain. The connection between the local slope and the normal move-out velocity and the surface-ray parameter is known, which provides a novel approach for estimating the local slope of the hyperbolic reflected waves in the shot domain. The estimated slope can provide an exact slope-based operator for the plane-wave destruction (PWD) method, thus allowing the PWD to separate diffracted waves from reflected waves in the shot domain. Synthetic and field data tests demonstrate the feasibility and effectiveness of the proposed pre-stack diffraction separation method.

... Therefore, if one can separate the diffractions and process them separately, the discontinuities can be directly imaged as opposed to inferred (Fomel et al., 2007). On top of this, separated diffractions have many other uses such as wavefront tomography and velocity analysis (Bauer et al., 2017, Landa et al., 2008. Separating diffractions, however, is not a straightforward task due to the comparatively low amplitude of diffractions, approximately an order of magnitude lower than reflections, as well as the lack of a clear distinction between reflection and diffraction energy (Klokov and Fomel, 2012). ...

... Fang et al. (2017) showed that fractures with a random spacing can form fracture clusters and the clusters can generate strong multiply-scattered seismic waves that could mislead the interpretation of reflected P-wave AVOAz results (amplitude variation with offset and azimuth for the reflected waves). On the other hand, waves that are diffracted from fractures can also be used to image fracture characteristics (e.g., Willis et al. 2006, Landa et al. 2008, Klokov and Fomel 2012, Fang et al. 2013, Schoepp et al. 2015, Protasov et al. 2016, Silvestrov et al. 2016). However, these imaging-based methods have limited capability in distinguishing multiple sets of fractures. ...

... These fracture detection method related to the anisotropy of medium are based on the effective medium theory (EMT) that assumes the fractures are uniformly distributed in the space (e.g., Cook 1989, Tod 2003, Zhang et al. 2009). Another alternative seismic fracture detections use scattered waves to image the fracture features via imaging algorithms (e.g., Lerche 1985, Lerche and Petroy 1986, Willis et al. 2006, Landa et al. 2008, Klokov and Fomel 2012, Fang et al. 2014, Schoepp et al. 2015, Zhu et al. 2015, Protasov et al. 2016, Silvestrov et al. 2016). These imaging-based methods are able to indicate the fracture distribution and relative compliances for single fracture sets but have limited capability in detecting multiple coexistent fracture sets. ...

... It is a challenging task to determine a proper Fresnel zones. The dip-angle common image gather (Audebert et al., 2002;Landa et al., 2008;Klokov and Fomel, 2013;Li et al., 2020) facilitates the estimation of fresnel zone. For conventional migration methods, many authors have introduced the Fresnel zone (i.e. ...

... Fomel (2002) presented the plane-wave destruction (PWD) filter, which separates diffractions from reflections in the time domain. The PWD method applies the local slopes of reflections to construct a prediction-error filter based on the local plane-wave theory, thereby removing strong reflections (Claerbout, 1992;Landa et al., 2008;Lin et al., 2018a;Liu et al., 2010;Lowney et al., 2020;Yu et al., 2017). The common reflection surface (CRS) method is a commonly used approach for separating and imaging diffractions (e.g., Dell & Gajewski, 2011;Rad et al., 2018;Schwarz et al., 2014). ...

Diffractions with good illumination carry valuable subwavelength information below the Rayleigh limit and can be used for high-resolution imaging of small-scale discontinuous features. As diffractions are characterized by weak energy, diffracted wavefield separation is a key step before imaging of discontinuities. The traditional multichannel singular-spectrum analysis (MSSA) for diffraction separation considers the constant rank strategy. It is challenging to estimate the appropriate rank for various data. In this study, we propose a robust adaptive rank-reduction method for 3D diffraction separation and imaging. It utilizes the low-rank characteristics of reflections in the common-offset or poststack domain based on the MSSA algorithm. The method considers the kinematic and dynamic differences of reflections and diffractions, and combines the energy intensity and smoothed curvature to accurately estimate the rank thresholds as well as the ranks of the reflections and diffractions. Three-dimensional multilayer and complex synthetic examples are used to demonstrate the feasibility of the proposed method in removing reflections and separating diffractions and achieving high-resolution imaging with diffractions, which is helpful for seismic data interpretation.

We have developed an efficient and practical wave-equation-based technique to image subsurface geologic features such as isolated scatterers, reflector edges, fault, fracture zones, and erosion whose information is mainly contained in diffracted waves. This technique has the ability to directly reveal and differentiate important geologic features compared with results obtained using reflected seismic waves. This new technique comprises three steps. First, the source and receiver wavefields are decomposed into left- and right-downgoing propagating waves, respectively. Second, applying the imaging condition to the right-downgoing source and receiver wavefields to generate the so-called right-right image. Similarly, a left-left image is generated. Third, the left-left and right-right images are multiplied sample-by-sample to form the final diffraction-based image. The key idea of this method is based on the fact that any dipping reflector exhibits a particular dip direction, so its subsurface image can exist either in the left-left or the right-right image, but not in both. As a result, the sample-by-sample multiplication of the two images eliminates the reflector images. Alternatively, because diffractions are generated by subsurface geologic features, which act as secondary sources and radiate in all directions, ranging from [Formula: see text] to 90°, their energy can exist in both images. After multiplication of both images, only the diffractors remain, whereas the reflectors are suppressed. Our method is applicable only for diffracting objects that radiate in all directions. An exception occurs when reflectors exhibit zero dip. In such a case, zero-dip reflectors could be present in both images and leak into the final diffractor image. We mitigate this problem in several ways, such as omitting near zero-offset input data, muting vertical-propagation components, or applying an [Formula: see text]-[Formula: see text] filter on the final diffraction image.

We have built a vertical traveltime difference gather to image diffractions in the 3D time domain. This significantly improves detection of small-scale faults and heterogeneities in 3D seismic data. The vertical traveltime difference gather is obtained using 3D Kirchhoff prestack time migration based on the traveltime-related inline and crossline dip anlges, which is closely related to the 2D dip-angle gather. In vertical traveltime difference gathers, diffraction events exhibit flattening, while reflection events have convex upward sloping shapes. Different from 2D dip-angle gather, Fresnel zone related specular reflections are precisely focused on the given regions over all offsets and azimuths, thus leaving more diffraction energy after muting. To image linear diffractors, such as faults in 3D, the vertical traveltime difference gather can be extended into 2D by adding a dip-azimuth dimension. This makes it possible to correct phases of edge diffractions and detect the orientations of the linear diffractors. The memory requirement of the vertical traveltime difference or vertical traveltime difference plus azimuth gathers is much less than that of the 2D dip-angle gathers. We can store the gathers at each lateral position and then correct the phase and enhance the weak diffractions in 3D cases. Synthetic and field data tests demonstrate the effectiveness of the proposed 3D diffraction imaging method.

The importance of seismic diffractions has been recognized in subsurface imaging. Diffractions might contain useful information about small-scale geological structures and heterogeneities, e.g. faults, pinch-outs, thin lenses, fractures etc and can be very helpful for prospecting and development of fractured reservoirs. One of the most challenging task in diffraction imaging is the separation of diffractions from reflections. In this work, we present a new diffraction filter based on the projected (first) Fresnel zone (PFZ) to enhance diffraction separation and imaging. We found that the difference in the width of the PFZ appears to be a very consistent parameter for diffraction separation and thus, can be used as a robust diffraction filter. We derived the width of the PFZ from wavefront attributes, which are determined using the common-reflection-surface method. Applications to a simple gradient model as well as a complex synthetic data set validate our approach.

Diffractions comprise the seismic response of subsurface geological discontinuities and thus can provide detailed geological information during 3-D seismic exploration. The separation of weak diffractions from specular reflections is challenging, especially when the diffractions and reflections have similar kinematical characteristics in the 3-D pre-stack case. Conventional separation methods often estimate the local slope based on optimization or the Hilbert transform, which directly depends on the distribution behaviour of seismic events and may lead to the aliasing effects of the hyperbolic reflected and diffracted slopes in the shot domain. In this study, a different method is employed: local slopes are parametrized and constrained to the normal moveout velocity and ray parameter, which can distinguish reflections and diffractions in the shot domain and enhance the stability and accuracy of local slopes. Interestingly, when the receiver line and the geological edge are coplanar, the corresponding edge diffractions and reflections exhibit extremely similar behaviour, rendering them indistinguishable. Considering this phenomenon, a 3-D pre-stack diffraction separation strategy is proposed based on the estimation of the local slopes in two orthogonal directions. Thus, the accurate local slope can be used for plane-wave destruction when separating diffractions in the 3-D pre-stack domain. Synthetic and field data applications demonstrate that the proposed separation strategy is effective and can obtain high-quality diffraction wavefields for detecting the subsurface discontinuous structure.

Accurate identification of the locations and orientations of small-scale faults plays an important role in seismic interpretation. We have developed a 3-D migration scheme that can image small-scale faults using diffractions in time. This provides a resolution beyond the classical Rayleigh limit of half a wavelength in detecting faults. The scheme images weak diffractions by building a modified dip-angle gather, which is obtained by replacing the two dip angles dimensions of the conventional 2-D dip-angle gather with tangents of the dip angles. We build the modified 2-D dip-angle gathers by calculating the tangents of dip angles following 3-D prestack time migration (PSTM). In the resulting modified 2-D dip-angle gathers, the Fresnel zone related to the specular reflection exhibits an ellipse. Comparing with the conventional 2-D dip-angle gather, diffraction event related a fault exhibits a straight cylinder shape with phase-reversal across a line related the orientation of the fault. As a result, we can not only mute the Fresnel zones related to reflections, correct phase for edge diffractions and obtain the image of faults, but also detect the orientations of 3-D faults using the modified dip-angle gathers. Like the conventional dip-angle gathers, the modified dip-angle gathers can also be used to image diffractions resulting from other sources. 3-D Field data tests demonstrate the validity of the proposed diffraction imaging scheme.

Amplitude versus offset analysis is a fundamental tool for determining the physical properties of reservoirs but generally hampered by the blurred common image gathers (CIGs). The blurring can be optimally corrected using the blockwise least-squares prestack time migration (BLS-PSTM), where common-offset migrated sections are divided into a series of blocks related to the explicit offset-dependent Hessian matrix and the following inverse filtering is iteratively applied to invert the corresponding reflectivity. However, calculating the Hessian matrix is slow. We present a fast BLS-PSTM via accelerating Hessian calculation with dip-angle Fresnel zone (DFZ). DFZ is closely related to optimal migration aperture, which significantly attenuates migration swings and reduces the computational cost of PSTM. Specifically, our fast BLS-PSTM is implemented as a two-stage process. First, we limit the aperture for any imaging point with an approximated the projected Fresnel zone before calculating the Hessian matrix. Then, we determine whether a seismic trace contributes to the imaging point via DFZ during calculating the Hessian matrix. Numerical tests on synthetic and field data validate the distinct speedup with higher-quality CIGs compared to BLS-PSTM.

Interpretation of sand injectite reservoirs from conventional reflection seismic data is a complicated exercise. The complex geometries of injectites are challenging to detect and resolve by using conventional seismic processing due to their lateral and vertical variability in thickness and dip. Steeply dipping injection dikes tend to appear blurred or distorted on reflection images, and interpretation of their positioning and thickness carries an important level of uncertainty. Structural attributes derived from reflection images are used to support interpretation, but they suffer from a lack of spatial resolution and vertical continuity. We introduce a novel interpretation workflow that includes a diffraction image in addition to the conventional reflection image to improve the detectability and resolution of steep injection dikes and small-scale features. The diffraction image is generated in a migrated dip-angle domain where diffracted and reflected energy can be separated. A case study from a large injection complex in the Norwegian North Sea illustrates the superiority of the diffraction image over conventional structural attributes to support the interpretation and characterization of thin and steeply dipping injectites. The complementarity of the reflection and diffraction images is exploited by visualization techniques (e.g., corendering) or by combining interpretations from separate images, providing a complete picture of the injection complex geometries. Diffraction imaging proved to be a valuable tool to improve the level of detail and confidence in the interpreted injectites, both for modeling and well-planning purposes.

Diffraction images can directly indicate local heterogeneities such as faults, fracture zones, and erosional surfaces that are of high interest in seismic interpretation and unconventional reservoir development. We propose a new tool called pseudo dip-angle gather (PDAG) for imaging diffractors using the wave equation. PDAG has significantly lower computational cost compared with the classical dip-angle gather (DAG) due to using plane-wave gathers, a fast local Radon transform algorithm, and one-side decomposition assumption. Pseudo dip angle is measured from the vertical axis to the bisector of the plane-wave surface incident angle and scattered wave-propagation angle. PDAG is generated by choosing the zero lag of the correlation of the plane-wave source wavefields and the decomposed receiver wavefields. It reveals similar diffraction and reflection patterns to DAG, i.e. diffractions spreading as a flat event and reflections focused at a spectacular angle, while they may have dissimilar coverage for diffraction and different focused locations for reflection compared with that of DAG. A windowed median filter is then applied to each PDAG for extracting the diffraction energy and suppressing the focused reflection energy. Besides, the stacked PDAG can be used to evaluate the migration accuracy by measuring the flatness of the image gathers. Numerical tests on both synthetic and field data sets demonstrate that our method can efficiently produce accurate results for diffraction images.

Diffractions in the seismic data are associated with the small-scale subsurface structures, thus their separation and imaging are helpful in characterizing the underground discontinuities with a high resolution that cannot be reached by traditional reflection imaging methods. Traditional seismic slope-based diffraction separation methods are strongly affected by the accuracy and stability of the slope estimation methods, e.g., the plane-wave destruction (PWD) method. When the local seismic slope is not properly estimated, the separated seismic diffraction waves suffer from the mixture between the reflection and diffraction energy due to their coupling in the slope map. We propose an automatic local rank-reduction (LRR) method to separate 3D diffraction waves from zero-offset seismic data, based on which we conduct 3D migration to output the diffraction images. Due to the difficulty in choosing the rank in each local 3D window, we apply an adaptive strategy to obtain the optimal rank. The proposed LRR method with adaptively selected ranks (LRRA) is applied to several 3D synthetic and field data examples and demonstrated to perform better than the traditional PWD, the LRR, and the global rank-reduction (GRR) methods.

Diffraction images can be used for modeling reservoir heterogeneities at or below the seismic wavelength scale. However, the extraction of diffractions is challenging because their amplitude is weaker than that of overlapping reflections. Recently, deep learning (DL) approaches have been used as a powerful tool for diffraction extraction. Most DL approaches use a classification algorithm that classifies pixels in the seismic data as diffraction, reflection, noise, or diffraction with reflection, and takes whole values for the classified diffraction pixels. Thus, these DL methods cannot extract diffraction energy from pixels for which diffractions are masked by reflections. We proposed a DL-based diffraction extraction method that preserves the amplitude and phase characteristics of diffractions. Through the systematic generation of a training dataset using synthetic modeling based on t-distributed stochastic neighbor embedding (t-SNE) analysis, this technique extracts not only faint diffractions, but also diffraction tails overlapped by strong reflection events. We also demonstrated that the DL model pre-trained with basic synthetic dataset can be applied to seismic field data through transfer learning. Because the diffractions extracted by our method preserve the amplitude and phase, they can be used for velocity model building and high-resolution diffraction imaging.

Diffraction imaging can increase the spatial resolution of seismic images beyond conventional means to provide interpreters with high-resolution structural and stratigraphic sections. The reflection image of a specular reflector only exists in either the positive- or negative-dip structure image; however, the image of a diffractor appears in both positive- and negative-dip image. By applying sample-by-sample multiplication imaging condition to the opposite dip images, the diffraction energy is retained while the reflection energy is significantly attenuated. The two dip images are generated by separating the source and receiver wavefields into different propagation directions. Two challenges are faced when we use the left-down-going source and receiver wavefields to calculate the positive-dip structure image and the right-down-going source and receiver wavefields to generate the negative-dip structure image. First, we need to compute the up- and down-going wavefields by Hilbert transform with respect to time and depth for both source and receiver wavefields. This operation requires two additional forward modeling calculations with the Hilbert-transformed source and receiver wavefields. Second, the information provided by the up-going wave is missing if we only employ the down-going wave to generate two opposite dip structure images. To overcome the limitations of the one-way imaging condition, we propose using the two-way imaging condition of positive- and negative-dip structure images. Impulse response analysis demonstrates that the two-way imaging condition has the ability to image the positive- and negative-dip structure images separately. Without up- and down-going wavefield separation, the up-going source and receiver wavefields can generate the same structure dip as using the down-going source and receiver wavefields. Results show that using the two-way imaging condition can provide broader illumination and enhance the diffraction image because of additional contribution from the up-going wavefield. In addition, it saves almost half the computation cost compared to using the one-way imaging condition.

Knowledge of the spatial distribution of subsurface fractures is critical for improving the production of geothermal and oil/gas. The double-beam (DB) method using acoustic waves has been shown to be capable of characterizing the irregularly distributed fractures, including multiple coexisting fracture sets. We propose to extend the DB method to elastic waves, in particular for P-to-S waves scattered by fractures, using 3-component seismic data. This elastic double-beam (EDB) method can add additional information to cross-validate the DB images of P-P waves and increase our confidence in final fracture characterization results. To test the EDB method, we used a 3D layered reservoir model with multiple non-orthogonal coexisting fracture sets, which captures a wide range of geological scenarios. Based on this model, we modeled 3-component data using an elastic full-wave finite-difference method. For each subsurface target, the EDB method outputs DB images of P-P, P-Sin and P-Santi waves, where Sin and Santi represent the in-plane (polarized perpendicular to the fracture plane strike) and antiplane (polarized parallel to the fracture plane strike) scattered vector S waves. Numerical results show that EDB is a reliable tool to detect the fracture distribution using the self-verification feature, namely, P-P, P-Sin, and P-Santi should all give the same fracture parameters for truly existing fractures. Using EDB, the existence and orientation of fractures are more reliably estimated than fracture compliance for irregular fracture sets. EDB is not sensitive to random noise in data up to high noise levels. EDB can work properly when velocity models have mild deviations from the true models. The EDB amplitude is large where fractures are dense or the compliance value is large, or both; these can be important in the interpretation of the fluid transport properties of a reservoir.

Both the singly and multiply scattered waves generated from interfaces of a fractured medium have strong energy and their propagation directions contain information of fracture parameters. To exploit the useful information in the scattered waves, a fracture scattering imaging method is developed based on the reverse time migration and angle decomposition. In this method, a fracture-parameter-related local image matrix is constructed in the angle domain based on the relation between the fracture parameters and the propagation angle of the scattered waves. The distribution of the scattered waves in the proposed image matrix can be used to invert for fracture parameters and identify the energy of scattered waves. The image of fractures can be obtained by summing up the energy of the scattered waves from the proposed image matrix. Synthetic and field examples are followed to demonstrate the new method is effective to migrate the fracture scattered waves at the correct spatial position and accurately extract fracture parameters.

Detection and imaging of sub-wavelength features in the subsurface using diffracted waves are rapidly gaining momentum in the oil and gas industry as well as in the fields of engineering, archeology, and homeland security. Most of the proposed methods include coherent summation of the recorded wavefield along diffraction traveltime surfaces from point scatterers. The summation focuses energy onto point-like diffractors which appear at the resulting images as prominent anomalies. However, in cases when the target is an elongated object such as a fault plane, fracture, tunnel, or elongated cave, a more efficient imaging method can be constructed. We present an algorithm for detecting and characterizing linear subsurface elements using a linear diffractor operator. The proposed algorithm is based on the coherent summation of the edge diffraction generated by the entire lineament and on the analysis of the calculated coherence measure (semblance). The advantages and limitations of the proposed method are demonstrated, and the results are compared to the conventional point-diffractor-based techniques. Synthetic and real data examples demonstrate that using a linear-diffractor-based algorithm can dramatically improve the detection of linear objects.

Traditional diffraction images without a specific migration kernel for promoting focusing abilities may cause confusion to seismic interpretation, because diffraction images may show a finite array response of diffracted/scattered waves. Since diffractors are discontinuous and sparsely distributed, a least-squares diffraction-imaging method is formulated by solving a hybrid L1-L2 norm minimization problem that imposes a sparsity constraint on diffraction images. It uses two different forward modeling operators for reflections and diffractions, and L2, L1 regularizations for penalizing the amplitudes of reflection and diffraction images, respectively. A classic Kirchhoff diffraction de-migration operator is implemented on an initial diffraction image model to synthesize diffracted/scattered waves. A Kirchhoff reflection de-migration operator formulated by considering local reflection slopes and a cosine attenuation weighting function, is implemented on an initial reflection image to synthesize reflected waves. A modified alternating direction approach of multipliers is developed for iteratively solving this minimization problem to create diffraction images and their separated diffractions. The depths and local reflection slopes of the reflection images are fixed during this iteration. To alleviate the energy leakage between diffractions and reflections, after performing the plane-wave destruction method on the conventional migration data, its estimated reflection image and residual image are provided as the initial reflection and diffraction images, respectively. The proposed method can remove steep-slope reflections, increase the focusing power of diffractions, and eliminate noise. Two numerical experiments demonstrate its capability of separating and imaging small-scale discontinuities and inhomogeneities. The exposed geological structures in the tunnel of field coal mining further illustrate this method’s potential in ascertaining hidden faults, edges, and collapsed columns. A safety warning should be definitely required if a mining working surface is advancing these hidden geological disasters, because an emergency of water bursting or gas leakage may happen.

Fracture-cave reservoirs in carbonate rocks are characterized by a large difference in fracture and cavity size, and a sharp variation in lithology and velocity, thereby resulting in complex diffraction responses. Some small-scale fractures and caves cause weak diffraction energy and would be obscured by the continuous reflection layer in the imaging section, thereby making them difficult to identify. This paper develops a diffraction wave imaging method in the dip domain, which can improve the resolution of small-scale diffractors in the imaging section. Common imaging gathers (CIGs) in the dip domain are extracted by Gaussian beam migration. In accordance with the geometric differences of the diffraction being quasilinear and the reflection being quasiparabolic in the dip-domain CIGs, we use slope analysis technique to filter waves and use Hanning window function to improve the diffraction wave separation level. The diffraction dip-domain CIGs are stacked horizontally to obtain diffraction imaging results. Wavefield separation analysis and numerical modeling results show that the slope analysis method, together with Hanning window filtering, can better suppress noise to obtain the diffraction dip-domain CIGs, thereby improving the clarity of the diffractors in the diffraction imaging section.

Summary We use the simulated plane wave section method to separate specular reflections and diffraction events. We show that plane wave sections naturally separate specular and diffracted events and allow us to use plane-wave distruction filters to suppress specular events resulting in plane-wave sections of diffractions. A synthetic example demonstrates the effectiveness of our method in imaging faults and small-scale discontinuities.

The authors describe a method of modeling seismic waves interacting with single liquid-filled large cracks based on the Kirchhoff approximation and then apply it to field data in an attempt to estimate the size of a hydraulic fracture. They first present the theory of diffraction of seismic waves by fractures using a Green`s function representation and then compute the scattered radiation patterns and synthetic seismograms for fractures with elliptical and rectangular shapes of various dimensions. It is shown that the characteristics of the diffracted wavefield from single cracks are sensitive to both crack size and crack shape. Finally, they compare synthetic waveforms to observed waveforms recorded during a hydraulic fracturing experiment and are able to predict successfully the size of a hydraulically induced fracture (length and height). In contrast to previously published work based on the Born approximation, the authors model both phases and amplitudes of observed diffracted waves. The modeling has resulted in an estimation of a crack length 1.1 to 1.5 times larger than previously predicted, whereas the height remains essentially the same as that derived using other techniques. This example demonstrates that it is possible to estimate fracture dimensions by analyzing diffracted waves.

Plane-wave destruction filters originate from a local plane-wave model for characterizing seismic data. These filters can be thought of as a time–distance (T -X) ana-log of frequency-distance (F-X) prediction-error filters and as an alternative to T -X prediction-error filters. The filters are constructed with the help of an implicit finite-difference scheme for the local plane-wave equation. Several synthetic and real data examples show that finite-difference plane-wave destruction filters perform well in applications such as fault detection, data interpolation, and noise attenuation.

Diffractions always need more advertising. It is true that conventional seismic processing and migration are usually successful in using specular reflections to estimate subsurface velocities and reconstruct the geometry and strength of continuous and pronounced reflectors. However, correct identification of geological discontinuities, such as faults, pinch‐outs, and small‐size scattering objects, is one of the main objectives of seismic interpretation. The seismic response from these structural elements is encoded in diffractions, and diffractions are essentially lost during the conventional processing/migration sequence. Hence, we advocate a diffraction‐based, data‐oriented approach to enhance image resolution—as opposed to the traditional image‐oriented techniques, which operate on the image after processing and migration. Even more: it can be shown that, at least in principle, processing of diffractions can lead to superresolution and the recovery of details smaller than the seismic wavelength.
The so‐called reflection stack is capable of effectively separating diffracted and reflected energy on a prestack shot gather by focusing the reflection to a point while the diffraction remains unfocused over a large area. Muting the reflection focus and defocusing the residual wavefield result in a shot gather that contains mostly diffractions. Diffraction imaging applies the classical (isotropic) diffraction stack to these diffraction shot gathers. This focusing‐muting‐defocusing approach can successfully image faults, small‐size scattering objects, and diffracting edges. It can be implemented both in model‐independent and model‐dependent contexts. The resulting diffraction images can greatly assist the interpreter when used as a standard supplement to full‐wave images.

We propose a method for estimating interval velocity using the kinematic information in defocused diffractions and reflections. We extract velocity information from de-focused migrated events by analyzing their residual focus-ing in physical space (depth and midpoint) using prestack residual migration. The results of this residual-focusing analysis are fed to a linearized inversion procedure that produces interval velocity updates. Our inversion proce-dure uses a wavefield-continuation operator linking pertur-bations of interval velocities to perturbations of migrated images, based on the principles of wave-equation migration velocity analysis introduced in recent years. We measure the accuracy of the migration velocity using a diffraction-focusing criterion instead of the criterion of flatness of migrated common-image gathers that is commonly used in migration velocity analysis. This new criterion enables us to extract velocity information from events that would be challenging to use with conventional velocity analysis methods; thus, our method is a powerful complement to those conventional techniques. We demonstrate the effectiveness of the proposed methodology using two examples. In the first example, we estimate interval velocity above a rugose salt top inter-face by using only the information contained in defocused diffracted and reflected events present in zero-offset data. By comparing the results of full prestack depth migration before and after the velocity updating, we confirm that our analysis of the diffracted events improves the velocity model. In the second example, we estimate the migration velocity function for a 2D, zero-offset, ground-penetrating radar data set. Depth migration after the velocity estima-tion improves the continuity of reflectors while focusing the diffracted energy.

Seismic diffractions are often considered noise and are intentionally or implicitly suppressed during processing. Diffraction-like events include true diffractions, wave conversions, or fracture waves which may contain valuable information about the subsurface and could be used for interpretation or imaging. Using synthetic and field data, we examine workflows to separate diffractions from reflections that allow enhancement of diffraction-like signals and suppression of reflections. The workflows consist of combinations of standard processing modules. Most workflows apply normal move-out corrections to flatten reflection hyperbolas, which eases their removal. We observe that the most effective techniques are the decomposition of seismic gathers into eigensections and flows based on Radon transformations. © 2005 Society of Exploration Geophysicists. All rights reserved.

Summary We examine some aspects of the Kirchhoff migration in the angle domains. The angle domains we refer to are the scattering angle domain (both opening and azimuth of scattering), which replaces the surface related offset and azimuth of acquisition, and the illumination dip angle domain (having two components in 3D). We examine the insight given to the Kirchhoff summation and to the stationary phase approximation, by virtue of the decomposition of the migration in the illumination dip angle domain. Additionally we point out some differences between angle domain and offset domain migration.

Diffracted waves contain valuable information regarding both the structure and composition of the media they are in. In seismic data processing, however, these waves are usually regarded as noise. In this paper, we present an attempt to use scattered/diffracted waves for the detection of local heterogeneities. The method is based on the detection of diffracted waves by concentrating the signal amplitudes from diffracting points on the seismic section. This is done using a correlation procedure that enhances the amplitude of the seismic signal at the location of the diffractors on the common-diffraction-point section (D-section), The new local time correction for diffraction traveltime curve parameterization is based on the radius of curvature of the diffracted wavefront and near-surface velocity. We use the idea of seismic monitoring for detection and delineating local objects which may occur within the subsurface resulting from human activity or fast geological processes. The method consists of continuous repetition of seismic experiments above an investigated area, constructing D-sections, and comparing the images obtained.

Presents a new technique which helps in the interpretation of diffracting edges by concentrating the signal amplitudes from discontinuous diffracting points on seismic sections. It involves application to the data of moveout and amplitude corrections appropriate to an assumed diffractor location. The maximum diffraction amplitude occurs at the location of the receiver for which the diffracting discontinuity is beneath the source-receiver midpoint. Since the amplitudes of these diffracted signals drop very rapidly on either side of the midpoint, an appropriate amplitude correction must be applied. The method was tested for synthetic data with and without noise. It proves to be quite effective, but is sensitive to the velocity model used for moveout corrections. Therefore, the velocity model obtained from NMO stacking is generally used for enhancing diffractor locations by stacking. Finally, the technique was applied to a field reflection data set from an area south of Princess well in Alberta. -from Authors

ABSTRACTA method of detection of diffracted waves on common-offset sections is proposed. The method utilizes the main kinematic and dynamic properties of the diffracted waves. The detection algorithm is defined by an automatic procedure including phase correlation of the diffracted waves and the application of certain statistical criteria. This procedure enables us to make decisions with regard to the presence of the diffracted waves and also to estimate parameters of the scattering objects. The method is applied to synthetic and field data and, even for a relatively low signal-to-noise ratio, it gives reliable results.

Velocity analysis in the dip-angle domain: Presented at the 69th Annual International Conference and Exhibition

- M Reshef