Diffraction Events Research Articles

Precision physics with the proton spectrometer and diffractive physics measurements from CMS

We describe recent results from CMS and TOTEM on hard diffraction, diffractive jets and jet gap jet events. We also give the first sensitivities and limits on quartic anomalous couplings and axion-like particles at high mass using the LHC as a \gamma \gammaγγ collider. The predicted sensitivities with 300 fb^{-1}−1 are better by two or three orders of magnitude compared to the more standard methods at the LHC without measuring intact protons after collision.

DiffraPy: An open-source Python software for seismic diffraction imaging

Seismic diffraction events, often overlooked as noise in conventional seismic imaging methods, contain valuable high-resolution information about subsurface structures and heterogeneities. Furthermore, the diffractive component of the wavefield is masked by the stronger reflection events. Although the literature presents innovative methods for separating diffracted events from the total wavefield, there are currently limited options of open-source alternatives in seismic diffraction processing and imaging. In this study, we introduce DiffraPy, an open-source Python package specifically designed for performing both conventional and diffraction-oriented migrations. The main workflow involves implementing an anti-stationary phase filter in the Kirchhoff migration for enhancing energy outside the Fresnel zone. Additionally, we propose using the semblance matrix obtained from the dip field calculation as an additional weight in conventional migration. The code provides functionality for forward modeling seismic data, allowing for new testing and experimentation. We demonstrate the general workflow of the code using a toy model and evaluate its capabilities on a synthetic salt model. In both cases, the program successfully suppressed the majority of reflected energy in the diffraction-oriented image. The final image highlights the responses of small lenses, discontinuities, and faults, providing valuable insights into the subsurface for interpretation. Despite the method sensitivity to variations in the correct velocity model, we demonstrate that our code is capable of imaging diffractors even when utilizing incorrect migration velocities of up to 5%. Our wavenumber analysis reveals the diffraction image preservation of smaller wavelengths, indicating higher resolution compared to conventional products. Future implementations may include extension to 3D datasets and improve the computational efficiency of our code. We expect our code to offer the geosciences community the first freely accessible and well-documented Python alternative for testing, reproducing, and exploring diffraction imaging examples.

High‐frequency wide‐angle reflection and refraction method for structural engineering ground‐penetrating radar surveys

AbstractElectromagnetic wave velocity in ground‐penetrating radar (GPR) constant offset data can be estimated via the diffraction hyperbola fitting method. This method is applicable when radargrams contain diffraction events (hyperbolic patterns) caused by scatters in the host smaller or equal to the dominant wavelength. An alternative method for velocity estimation, if no intrusive information is available for a direct correlation, requires the collection of multi‐offset data. The method is quite common for broad geophysical applications; however, it seems not to be fully utilized for engineering applications, such as slabs/walls where thickness estimation and depth of the embedded features are critical requirements for structural assessments. This method would also overcome the limitations in velocity calibration in environments with no hyperbolic signal signatures. The aim of this study is to explore multi‐offset high‐frequency GPR applications, specifically the wide‐angle reflection and refraction method, for structural engineering, to understand whether it is feasible, possible limitations, and advantages. Numerical models reproducing reinforced concrete elements and a cavity wall were analysed to understand the wave behaviour and predict the response prior to testing on real cases. The main purpose is to explore how reinforcing bars can affect the velocity spectra derived from semblance analysis and what the response would be in a case of multi‐layered structure with increasing velocity with depth (cavity wall). The comparison with real cases showed that, despite some intrinsic limitations, high‐frequency multi‐offset approach could be part of standard workflow for all those surveys where no other velocity estimation method is feasible.

Plane-wave UTD-PO formulation for multiple-plateau diffraction analysis assuming negative incidence angles

We present a detailed methodology for investigating radiowave multiple diffraction events over rectangular barriers (here termed plateaus) when exposed to a plane wave originating from a low-lying source. Based on Babinet’s principle, our approach uses the combined uniform theory of diffraction-physical optics (UTD-PO), and is validated via 60 GHz measurements performed on a scaled replica of the setting under investigation. As an additional validation, theoretical results at 2 GHz of the corresponding spherical-wave solution converge with those of the presented plane-wave formulation with expanding distance between the source and the first obstacle. The proposed method has a crucial advantage in that it solely considers single diffractions via recursion, thus precluding the need for the diffraction coefficients to include higher order diffraction terms. The work’s findings and insights are salient for mobile communication system design in settings where the adjacent rectangular structures are higher than the transmitting antenna.

Seismic wavefield information extraction method based on adaptive local singular value decomposition

The key to seismic data processing is to extract the wavefield information related to the subsurface geological targets. In this paper, we first introduce the low-rank signal priority and the strong energy signal priority characteristics of the Singular Value Decomposition (SVD) method. By analyzing the characteristics of the second-order difference spectrum of typical seismic data, we find two indicative parameters to adaptively select the singular value threshold for extracting reflection and diffraction events. Our proposed Adaptive Local Singular Value Decomposition (ALSVD) method takes advantage of the local analysis, and can effectively extract the weak signals in the seismic data. It is a robust method with good resolution and separation integrity, which is beneficial to seismic migration, seismic imaging, and evaluation of Oil and gas traps. Synthetic examples and field examples demonstrate the effectiveness of this method.

Common‐offset domain reflection–diffraction separation with deep learning

AbstractSeparation of diffracted from reflected events in seismic data is still challenging due to the relatively low amplitude of the diffracted wavefield compared to the reflected wavefield as well as the overlap in the kinematics of reflection and diffraction events. A workflow based on deep learning can be a simple and fast alternative, but using training data made by physics‐based modelling is expensive and lacks diversity in terms of noise, amplitude, frequency content and wavelet. This results in poor generalization beyond the training data without retraining and transfer learning. In this paper, we demonstrate successful applications of reflection–diffraction separation using a conventional U‐net architecture. The novelty of our approach is that we do not use synthetic data created from physics‐based modelling, but instead use only synthetic data built from basic geometric shapes. Our domain of application is the pre‐migration common‐offset domain where reflected events resemble local geology and the diffracted wavefield consists of downward convex hyperbolic diffraction patterns. Both patterns were randomly perturbed in many ways while maintaining their intrinsic features. This approach is inspired by the common practice of data augmentation in deep learning for machine vision applications. Since many of the standard data augmentation techniques lack a geophysical motivation, we have instead perturbed our synthetic training data in ways to make more sense from a signal processing perspective or given our ‘domain knowledge’ of the problem at hand. We did not have to retrain the network to show good results on the field data set. The large variety and diversity in examples enabled to trained neural networks to show encouraging results on synthetic and field data sets that were not used in training.

Diffraction imaging of discontinuities using migrated dip-angle gathers

Diffractions produced by subsurface geological features are an effective means of imaging small-scale discontinuities at high resolution. We developed a novel diffraction imaging approach that combines the geometric mode decomposition (GMD) algorithm and least-squares Gaussian distribution fitting (LSGDF) technique. In the dip-angle domain, reflections tend to look like smiles and are mainly focused in areas related to Fresnel zones, whereas diffractions spread over a wide illumination area due to their uniform radiation propagation. The GMD algorithm can effectively and simultaneously extract line-like components consisting of reflected energy in the Fresnel zone and diffracted energy in dip-angle gathers. The energy discrepancies between the reflection and diffraction events in the extracted line-like components allow for the separation of diffractions and suppression of reflections in dip-angle gathers using LSGDF. Numerical applications illustrate that the proposed method can eliminate large continuous reflectors and reveal discontinuous subsurface features. A real data example demonstrates the capability of the diffraction-imaging workflow in enhancing the resolving power of the imaging of subsurface geologic structures.

A High-Precision Elastic Reverse-Time Migration for Complex Geologic Structure Imaging in Applied Geophysics

High-precision elastic reverse-time migration (ERTM) imaging has always been one of the trends in the development of geophysics. However, current wavefield simulations using time-domain finite-difference (FD) approaches in ERTM have second-order temporal accuracy, resulting in travel time changes and waveform distortion in wavefield propagation with large time steps, i.e., temporal dispersion. Errors caused by the temporal dispersion can lead to erroneous imaging locations and out-of-focus diffraction events. A new ERTM and its workflow are established here using temporal and spatial high-order FD accuracy wavefields and the vector-based imaging condition. Our method computes elastic vector-based wavefields by solving a P- and S-wave decomposition form of a quasi-stress–velocity equation. An advanced finite-difference scheme is employed in the wavefield solution to achieve simulation with temporal fourth-order accuracy and spatial arbitrary even-order accuracy. The normalized dot-product imaging condition of the source and receiver P/S wavefields is then applied to generate high-quality images. The elastic wavefield simulation and ERTM numerical examples presented here reveal that the anti-dispersion workflow can improve modeling and imaging accuracy. In addition, the field data application shows that our method can achieve reasonable and reliable ERTM images. This method can integrate the most advanced imaging techniques into this computational framework to improve imaging accuracy.

New insights in glaciers characterization by differential diagnosis integrating GPR and remote sensing techniques: A case study for the Eastern Gran Zebrù glacier (Central Alps)

In GPR profiles, ice is usually imaged as a mostly electromagnetic transparent facies. However, diffraction events, as well as internal layering, can be also observed. In some cases, the bedrock below glaciers is masked by dense diffractions usually interpreted as the effect of liquid water pockets inside the so-called warm ice. However, the actual physical meaning of such GPR facies is not always obvious, because it can be related also to mixed debris and ice deposits.We adopted a strategy well known in medical sciences and referred as “differential diagnosis” in order to infer which is the actual meaning of a high scattering facies imaged within the Eastern Gran Zebrù glacier (Central Italian Alps) and, more generally, of all the internal glacier features. In fact, in many cases, there is no direct information to limit the subjectivity of geophysical interpretation; therefore, we provide all the discriminative hypotheses based on both independent and integrated criteria including GPR attribute analysis, imaging effects, reflection analysis, GPR frequency evaluations combined with geomorphological and remote sensing data obtained by two photogrammetric UAV and thermal infrared surveys.On the basis of the differential diagnosis, we concluded that the high scattering zone embedded within the studied glacier is most likely related to a mixture of ice and debris probably formed during a past shrinking phase. Beside this case study, this approach could be helpful in other GPR glaciological surveys, in which the target is related not only to the bedrock detection, but also to a detailed analysis of the internal facies of a glacier.

Generative models for the transfer of knowledge in seismic interpretation with deep learning

Interpreting seismic data requires the characterization of a number of key elements such as the position of faults and main reflections, presence of structural bodies, and clustering of areas exhibiting a similar amplitude versus angle response. Manual interpretation of geophysical data is often a difficult and time-consuming task, complicated by lack of resolution and presence of noise. In recent years, approaches based on convolutional neural networks have shown remarkable results in automating certain interpretative tasks. However, these state-of-the-art systems usually need to be trained in a supervised manner, and they suffer from a generalization problem. Hence, it is highly challenging to train a model that can yield accurate results on new real data obtained with different acquisition, processing, and geology than the data used for training. In this work, we introduce a novel method that combines generative neural networks with a segmentation task in order to decrease the gap between annotated training data and uninterpreted target data. We validate our approach on two applications: the detection of diffraction events and the picking of faults. We show that when transitioning from synthetic training data to real validation data, our workflow yields superior results compared to its counterpart without the generative network.

Prestack seismic data interpolation and enhancement with common‐reflection‐surface–based migration and demigration

ABSTRACTThe standard common‐reflection‐surface stacking method simulates high‐quality zero‐offset stacked data from multi‐coverage prestack data and, as by‐products, provides three kinematic wavefield attributes in two dimensions that can be applied to solve reflection seismic problems. One of the most significant applications of those attributes is for interpolation and enhancement of prestack data through the partial common‐reflection‐surface stack approach. Because this interpolation method is based on the stacking process, it usually introduces spurious noises that can create artefacts in the migration results. In order to overcome these limitations, a new prestack data interpolation and enhancement method is presented by applying the attributes and the common‐reflection‐surface operator based on two fundamental seismic imaging operations: the Kirchhoff‐type time migration and demigration. The diffraction curves required to apply these two fundamental operations are particular cases of the common‐reflection‐surface stack operator, which better fits the diffraction events and, consequently, is the best approximation for the Kirchhoff migration operator. From synthetic and real data, impulse responses of the migration and demigration operations are shown to demonstrate how this new approach regularizes and interpolates prestack data. A simple synthetic example shows good accuracy for reconstructed reflection events and well‐resolved conflicting dip events. The application example in real data reveals that the proposed approach provides cleaner regularized sections with better reconstructed events than the results of the well‐known partial common‐reflection‐surface stack approach. It has been successfully shown that the proposed approach is a well‐founded alternative for interpolation and denoising of seismic data and produces better preconditioned data for prestack migration.

Pre‐migration diffraction separation using generative adversarial networks

ABSTRACTDiffraction imaging is the process of separating diffraction events 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 parameterization. Here, we propose an image‐to‐image generative adversarial network to automatically separate diffraction events 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. These training data were 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 14,132 screened images were used to train the final generative adversarial network. The trained network has been applied across several geologically distinct field datasets, including a 3D example. Here, generative adversarial network separation is shown to be comparable to a benchmark separation created with plane‐wave destruction, and up to 12 times faster. This demonstrates the clear potential in generative adversarial networks for fast and accurate diffraction separation.

Prestack diffraction separation in the common virtual source gather

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 that 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.

Improving the resolution of impedance inversion in karst systems by incorporating diffraction information: A case study of Tarim Basin, China

Different scales of voids and cavities in karst systems demonstrate considerable potential as exploration targets in the Tarim Basin, northwest China. Numerous diffraction events exist in the seismic data above the karst reservoir in this area because of the strong impedance contrast and irregular shape of voids. The conventional impedance inversion method using migrated data as an input cannot easily estimate the location of voids and the impedance inside the voids. In this case, an alternative approach to impedance inversion that considers the diffractive component of the total wavefield and uses the unmigrated data as an input should be used. The inversion consists of a least-squares minimization of the misfit function between the observed and modeled data. Forward modeling incorporates a combination of reflection and diffraction wavefield components. The adopted method is applied to physical modeling and field data recorded above the karst reservoir. This study’s physical modeling test simulates observed field data and is performed using a high-resolution and high-fidelity 3D modeling system. Inversion results obtained by the proposed and conventional methods are compared. Physical modeling and a field data application show that the adopted impedance inversion method improves the karst location estimation and the acoustic impedance within the voids.

Separation and imaging of seismic diffractions using a localized rank-reduction method with adaptively selected ranks

Seismic diffractions are weak seismic events hidden within the more dominant reflection events in a seismic profile. Separating diffraction energy from the poststack seismic profiles can help infer the subsurface discontinuities that generate the diffraction events. The separated seismic diffractions can be migrated with a traditional seismic imaging method or a specifically designed migration method to highlight the diffractors, that is, the diffraction image. Traditional diffraction separation methods based on the underlying plane-wave assumption are limited by either the inaccurate slope estimation or the plane-wave assumption of the plane-wave destruction filter and thus will cause reflection leakage into the separated diffraction profile. The leaked reflection energy will deteriorate the resolution of the subsequent diffraction imaging result. We have adopted a new diffraction separation method based on a localized rank-reduction (LRR) method. The LRR method assumes the reflection events to be locally low-rank and the diffraction energy can be separated by a rank-reduction operation. Compared to the global rank-reduction method, the LRR method is more constrained in selecting the rank and is free of separation artifacts. We use a carefully designed synthetic example to demonstrate that the LRR method can help separate the diffraction energy from a poststack seismic profile with kinematically and dynamically accurate performance.

Detection of Underground Anomalies Using Analysis of Ground Penetrating Radar Attribute

Need of specifying underground construction works for supporting further tasks as maintenance, repairing, or setting up new underground structures. For these needs, ground penetrating radar, one of the efficient geophysical methods, can bring high-resolution and quick underground image revealing existence of both natural and artificial anomalies. Its fixed receiver-transmitter antennas setting as constant offset is commonly used in urban areas. Conventionally, hyperbolae events are crucial indicator for scattering objects as kinds of pipes, water drainage system, and concrete building structures as well as sink holes. Calculation of their depths and sizes requires migration analysis with the environment velocity. Migrated sections with different velocity show different chaos degrees of transformation from a hyperbola diffraction curve to its focused area. We have researched diagrams of different Ground Penetrating Radar attributes as energy, entropy, and varimax dependent on two variables, velocity and window zone covering diffraction events from a set of synthetic data and real data, in specifying the environment velocity. We have developed a novel technique for evaluation of the ground velocity and object’s size by combination of the new varimax diagram and the Kirchhoff migration method. The technique can define contribution of diffracted ground penetrating radar waves for building the diagram after removing the reflection contribution. The synthetic datasets consist of different random background noise levels and expressions of different-sized circular and rectangular pipes. The real data is measured for detecting two underground gas pipes in Ba Ria – Vung Tau province, Vietnam.

A statistics-based descriptor for automatic classification of scatterers in seismic sections

Discontinuities and small structures induce diffractions on seismic or ground-penetrating radar (GPR) acquisitions. Therefore, diffraction images can be used as a tool to access valuable information concerning subsurface scattering features, such as pinch outs, fractures, and edges. Usually, diffraction-imaging methods operate on diffraction events previously detected. Pattern-recognition methods are efficient to detect, image, and characterize diffractions. The use of this kind of approach, though, requires a numerical description of image points on a seismic section or radargram. We have investigated a new descriptor for seismic/GPR data that distinguishes diffractions from reflections. The descriptor consists of a set of statistical measures from diffraction operators sensitive to kinematic and dynamic aspects of an event. We develop experiments in which the proposed descriptor was incorporated into a pattern-recognition routine for diffraction imaging. The obtained method is useful for performing the automatic classification of image points using supervised and unsupervised algorithms, as a complementary step to Kirchhoff imaging. We also develop a new type of filtering, designed to address anomalies on the diffraction operators caused by interfering events. We evaluate the method using synthetic seismic data and real GPR data. Our results indicate that the descriptor correctly discriminates diffractions and shows promising results for low signal-to-noise-ratio situations.

High-Resolution Coherency Functionals for Improving the Velocity Analysis of Ground-Penetrating Radar Data

We aim at verifying whether the use of high-resolution coherency functionals could improve the signal-to-noise ratio (S/N) of Ground-Penetrating Radar data by introducing a variable and precisely picked velocity field in the migration process. After carrying out tests on synthetic data to schematically simulate the problem, assessing the types of functionals most suitable for GPR data analysis, we estimated a varying velocity field relative to a real dataset. This dataset was acquired in an archaeological area where an excavation after a GPR survey made it possible to define the position, type, and composition of the detected targets. Two functionals, the Complex Matched Coherency Measure and the Complex Matched Analysis, turned out to be effective in computing coherency maps characterized by high-resolution and strong noise rejection, where velocity picking can be done with high precision. By using the 2D velocity field thus obtained, migration algorithms performed better than in the case of constant or 1D velocity field, with satisfactory collapsing of the diffracted events and moving of the reflected energy in the correct position. The varying velocity field was estimated on different lines and used to migrate all the GPR profiles composing the survey covering the entire archaeological area. The time slices built with the migrated profiles resulted in a higher S/N than those obtained from non-migrated or migrated at constant velocity GPR profiles. The improvements are inherent to the resolution, continuity, and energy content of linear reflective areas. On the basis of our experience, we can state that the use of high-resolution coherency functionals leads to migrated GPR profiles with a high-grade of hyperbolas focusing. These profiles favor better imaging of the targets of interest, thereby allowing for a more reliable interpretation.

Imaging 3-D faults using diffractions with modified dip-angle gathers

SUMMARY 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.

3D diffraction imaging with Kirchhoff time migration using vertical traveltime difference gathers

We have built a vertical traveltime difference (VTD) gather to image diffractions in the 3D time domain. This significantly improves detection of small-scale faults and heterogeneities in 3D seismic data. The VTD gather is obtained using 3D Kirchhoff prestack time migration based on the traveltime-related inline and crossline dip angles, which is closely related to the 2D dip-angle gather. In VTD gathers, diffraction events exhibit flattening, whereas reflection events have convex upward-sloping shapes. Different from the 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 three dimensions, the VTD gather can be extended into two dimensions 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 VTD or VTD 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 our 3D diffraction imaging method.