Zeitschriftenartikel: „Diffraction“

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Kanasewich, Ernest R., and Suhas M. Phadke. "Imaging discontinuities on seismic sections." GEOPHYSICS 53, no. 3 (March 1988): 334–45. http://dx.doi.org/10.1190/1.1442467.

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In routine seismic processing, normal moveout (NMO) corrections are performed to enhance the reflected signals on common‐depth‐point or common‐midpoint stacked sections. However, when faults are present, reflection interference from the two blocks and the diffractions from their edges hinder fault location determination. Destruction of diffraction patterns by poststack migration further inhibits proper imaging of diffracting centers. This paper 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. Also, because the diffracted signals are present on all traces, one can use all of them to obtain a stacked trace for one possible diffractor location. Repetition of this procedure for diffractors assumed to be located beneath each surface point results in the common‐fault‐ point (CFP) stacked section, which shows diffractor locations by high amplitudes. 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.

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Khaidukov, V., E. Landa, and T. J. Moser. "Diffraction imaging by focusing‐defocusing: An outlook on seismic superresolution." GEOPHYSICS 69, no. 6 (November 2004): 1478–90. http://dx.doi.org/10.1190/1.1836821.

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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.

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Grasmueck, Mark, Tijmen Jan Moser, Michael A. Pelissier, Jan Pajchel, and Kenri Pomar. "Diffraction signatures of fracture intersections." Interpretation 3, no. 1 (February 1, 2015): SF55—SF68. http://dx.doi.org/10.1190/int-2014-0086.1.

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Fractured rock causes diffractions, which are often discarded as noise in ground-penetrating radar (GPR) and seismic data. Most fractures are too thin, too steep, and their displacement is too small to be imaged by reflections, and diffractions are the only detectable signal. To decipher the information about fracture geometry and distribution contained in diffractions, we compare 3D synthetic ray-Born modeling with high-density 3D GPR data and outcrop observations from the Cassis Quarry in Southern France. Our results reveal how the intersection between two fractures is the basic geologic element producing a recordable diffraction. In this new model, two intersecting fractures are represented by one finite-length line diffractor. The intersection of three fractures is a 3D cross composed of three line diffractors. Fractures extending over several meters in the outcrop display linear clusters of diffraction circles in unmigrated GPR time slices. Such large-scale fracture intersections are composed of many aligned short subwavelength line diffractors due to fracture roughness and variations of fracture opening. The shape irregularities and amplitude variations of composite diffraction signatures are a consequence of the geometry and spacing of the intersecting fractures generating them. With three simple base-type intersecting fracture models (horizontal dip, gentle dip, and steep dip), the fracture network geometry can be directly deciphered from the composite diffraction signatures visible on unmigrated time slices. The nonrandom distribution of diffractions is caused by fracture trends and patterns providing information about fracture dip, spacing, and continuity of fractured domains. With the similarity law, the diffraction phenomena observed in GPR data are very similar in character to those seen on the seismic scale with the wavelength as the scaling link. GPR data serve as a proxy to decipher seismic diffractions.

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Xingchen Pan, Xingchen Pan, Suhas P. Veetil Suhas P. Veetil, Cheng Liu Cheng Liu, Qiang Lin Qiang Lin, and Jianqiang Zhu Jianqiang Zhu. "High-contrast imaging for weakly diffracting specimens in coherent diffraction imaging." Chinese Optics Letters 11, no. 2 (2013): 021103–21105. http://dx.doi.org/10.3788/col201311.021103.

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Ruoqiu Wang, Ruoqiu Wang, Zhiyu Zhang Zhiyu Zhang, Chengli Guo Chengli Guo, Donglin Xue Donglin Xue, and and Xuejun Zhang and Xuejun Zhang. "Effects of fabrication errors on diffraction efficiency for a diffractive membrane." Chinese Optics Letters 14, no. 12 (2016): 120501–6. http://dx.doi.org/10.3788/col201614.120501.

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6

Barad, Karen. "Diffracting Diffraction: Cutting Together-Apart." Parallax 20, no. 3 (July 3, 2014): 168–87. http://dx.doi.org/10.1080/13534645.2014.927623.

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Dell, Sergius, Anna Pronevich, Boris Kashtan, and Dirk Gajewski. "Diffraction traveltime approximation for general anisotropic media." GEOPHYSICS 78, no. 5 (September 1, 2013): WC15—WC23. http://dx.doi.org/10.1190/geo2012-0346.1.

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Diffractions play an important role in seismic processing because they can be used for high-resolution imaging and the analysis of subsurface properties like the velocity distribution. Until now, however, only isotropic media have been considered in diffraction imaging. We have developed a method wherein we derive an approximation for the diffraction response for a general 2D anisotropic medium. Our traveltime expression is formulated as a double-square-root equation that allows us to accurately and reliably describe diffraction traveltimes. The diffraction response depends on the ray velocity, which varies with angle and thus offset. To eliminate the angle dependency, we expand the ray velocity in a Taylor series around a reference ray. We choose the fastest ray of the diffraction response, i.e., the ray corresponding to the diffraction apex as the reference ray. Moreover, in an anisotropic medium, the location of the diffraction apex may be shifted with respect to the surface projection of the diffractor location. To properly approximate the diffraction response, we consider this shift. The proposed approximation depends on four independent parameters: the emergence angle of the fastest ray, the ray velocity along this ray, and the first- and second-order derivatives of the ray velocity with respect to the ray angle. These attributes can be determined from the data by a coherence analysis. For the special case of homogeneous media with polar anisotropy, we establish relations between anisotropy parameters and the parameters of the diffraction operator. Therefore, the stacking attributes of the new diffraction operator are suitable to determine anisotropy parameters from the data. Moreover, because diffractions provide a better illumination than reflections, they are particularly suited to analyze seismic anisotropy at the near offsets.

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Kim, Sooyoon, Soon Jee Seol, Joongmoo Byun, and Seokmin Oh. "Extraction of diffractions from seismic data using convolutional U-net and transfer learning." GEOPHYSICS 87, no. 2 (January 27, 2022): V117—V129. http://dx.doi.org/10.1190/geo2020-0847.1.

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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 have developed a DL-based diffraction extraction method that preserves the amplitude and phase characteristics of diffractions. Through the systematic generation of a training data set using synthetic modeling based on t-distributed stochastic neighbor embedding analysis, this technique extracts not only faint diffractions but also diffraction tails overlapped by strong reflection events. We also determine that the DL model pretrained with a basic synthetic data set 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.

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Bakhtiari Rad, Parsa, and Craig J. Hickey. "Seismic diffraction separation in the near surface: Detection of high-contrast voids in unconsolidated soils." GEOPHYSICS 86, no. 3 (March 11, 2021): WA13—WA23. http://dx.doi.org/10.1190/geo2020-0366.1.

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Seismic diffractions carry the signature of near-surface high-contrast anomalies and need to be extracted from the data to complement the reflection processing and other geophysical techniques. Because diffractions are often masked by reflections, surface waves, and noise, careful diffraction separation is required as a first step for diffraction imaging. A multiparameter time-imaging method is used to separate near-surface diffractions. The implemented scheme makes use of the wavefront attributes that are reliable fully data-derived processing parameters. To mitigate the effect of strong noise and wavefield interference in near-surface data, our workflow incorporates two wavefront-based parameters, dip angle and coherence, as additional constraints. The output of the diffraction separation is a time trace-based stacked section that provides the basis for further analysis and applications such as time migration. To evaluate the performance of the proposed wavefront-based workflow, it is applied to two challenging field data sets that were collected over small culverts in very near-surface soft soil environments. The results of the proposed constrained workflow and the existing unconstrained approach are presented and compared. The proposed workflow demonstrates superiority over the existing method by attenuating more reflection and noise, leading to improved diffraction separation. The abundance of unmasked diffractions reveals that the very near surface is highly scattering. Time migration is carried out to enhance anomaly detection by focusing the isolated diffractions. Although strong diffractivity is observed at the approximate location of the targets, there are other diffracting zones observed in the final sections that might bring uncertainties for interpretation.

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Zhang, Jianfeng, and Jiangjie Zhang. "Diffraction imaging using shot and opening-angle gathers: A prestack time migration approach." GEOPHYSICS 79, no. 2 (March 1, 2014): S23—S33. http://dx.doi.org/10.1190/geo2013-0016.1.

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We have developed a migration scheme that can image weak diffractions in time. This significantly contributes to conventional interpretation in detecting small-scale faults and heterogeneities. The proposed scheme images diffractions using the shot and opening-angle gathers generated by prestack time migration (PSTM). Here, the shot and opening-angle gather represents a 2D migrated gather in terms of shot locations and opening angles between the incident- and scattered-rays. We muted the Fresnel zones related to reflections, corrected phases of diffractions, and enhanced diffractions in the migrated gathers. As a result, the proposed diffraction PSTM can image diffractions with and without phase-reversal. Moreover, the weak diffractions tangent to reflections can be clearly imaged. Diffraction PSTM can update migration velocities according to behaviors of reflection and diffraction events in the migrated gathers by scanning, thus overcoming a crucial problem in diffraction imaging. The reflector dips used in diffraction PSTM are obtained by picking the angles related to reflections in the shot and opening-angle gathers for a partial migration. Synthetic and field data tests demonstrate the validity of diffraction PSTM.

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Peterie, Shelby L., and Richard D. Miller. "Near-surface scattering phenomena and implications for tunnel detection." Interpretation 3, no. 1 (February 1, 2015): SF43—SF54. http://dx.doi.org/10.1190/int-2014-0088.1.

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Tunnel locations are accurately interpreted from diffraction sections of focused mode converted P- to S-wave diffractions from a perpendicular tunnel and P-wave diffractions from a nonperpendicular (oblique) tunnel. Near-surface tunnels are ideal candidates for diffraction imaging due to their small size relative to the seismic wavelength and large acoustic impedance contrast at the tunnel interface. Diffraction imaging algorithms generally assume that the velocities of the primary wave and the diffracted wave are approximately equal, and that the diffraction apex is recorded directly above the scatterpoint. Scattering phenomena from shallow tunnels with kinematic properties that violate these assumptions were observed in one field data set and one synthetic data set. We developed the traveltime equations for mode-converted and oblique diffractions and demonstrated a diffraction imaging algorithm designed for the roll-along style of acquisition. Potential processing and interpretation pitfalls specific to these diffraction types were identified. Based on our observations, recommendations were made to recognize and image mode-converted and oblique diffractions and accurately interpret tunnel depth, horizontal location, and azimuth with respect to the seismic line.

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Sheng, Tongjie, and Jingtao Zhao. "Separation and imaging of diffractions using a dilated convolutional neural network." GEOPHYSICS 87, no. 3 (March 28, 2022): S117—S127. http://dx.doi.org/10.1190/geo2021-0260.1.

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Seismic diffractions provide high-resolution details of small-scale geologic discontinuities, and diffraction imaging can be an important contribution to the exploration of faults, fractures, and cavities. However, reflections with strong energy generally mask the existence of weak diffractions in seismic records, and separating diffractions is necessary to see the full benefit of diffraction imaging. Here, a modified convolutional neural network (CNN) is used for separating diffractions. The input wavefields are modeled as the summation of individual diffractions and reflections, the network parameters are learned from multiple input data instances by minimizing the distance between the output of the network and the diffractions, and reflections are implicitly removed. To enhance the diffraction separation performance, we have used dilated convolutions to aggregate diffraction information, then combined batch normalization and residual learning to speed up the training process. The modified CNN can realize adaptive diffraction separation and avoid setting parameters in the subsequent application process. The synthetic Sigsbee2A model demonstrates the performance of the proposed method in removing high-slope reflections and imaging small-scale scatterers. The application to the Nankai field data further illustrates the ability of the methods to extract weak diffractions beneath the interference of other waves, revealing potential reservoir-related geologic features.

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Maciel, Susanne, and Ricardo Biloti. "A statistics-based descriptor for automatic classification of scatterers in seismic sections." GEOPHYSICS 85, no. 5 (September 1, 2020): O83—O96. http://dx.doi.org/10.1190/geo2018-0673.1.

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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.

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Peterie, Shelby L., Richard D. Miller, Julian Ivanov, and Steven D. Sloan. "Shallow tunnel detection using SH-wave diffraction imaging." GEOPHYSICS 85, no. 2 (January 30, 2020): EN29—EN37. http://dx.doi.org/10.1190/geo2018-0731.1.

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Clandestine tunnels, used for drug or human trafficking and tactical operations, pose a security threat worldwide and remain elusive targets for detection with geophysical methods. P-wave diffraction imaging is an increasingly common technique for detecting subsurface discontinuities that are smaller than the seismic wavelength (such as faults, pinch outs, and small voids) and has been successfully used to detect shallow tunnels. P-wave diffractions from tunnels typically have very low signal-to-noise ratios and are therefore challenging wavefield components for imaging. Mode-specific amplitude characteristics of theoretical diffractions from a shallow tunnel were evaluated using 9C seismic modeling. Results indicate that SH-wave diffraction has the largest amplitude and coherent phase characteristics along the traveltime hyperbola, making it ideal for diffraction imaging. In real data acquired over a 9.2 m deep tunnel, amplitudes of SH-wave diffractions are 20 dB greater than P-wave diffractions. The tunnel signature on the P-wave diffraction section is of low amplitude relative to the background. The SH-wave diffraction section has a high-amplitude signal focused at the horizontal location and a traveltime consistent with the tunnel location, indicating that the SH-wave may be optimal for diffraction imaging to detect shallow tunnels.

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Hassan, Safaa, Yan Jiang, Khadijah Alnasser, Noah Hurley, Hualiang Zhang, Usha Philipose, and Yuankun Lin. "Generation of over 1000 Diffraction Spots from 2D Graded Photonic Super-Crystals." Photonics 7, no. 2 (April 10, 2020): 27. http://dx.doi.org/10.3390/photonics7020027.

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For the first time, we are able to generate over 1000 diffraction spots from a graded photonic super-crystal with a unit super-cell size of 12a × 12a where a is the lattice constant and hole radii are gradually changed in dual directions. The diffraction pattern from the graded photonic super-crystal reveals unique diffraction properties. The first order diffractions of (±1,0) or (0,±1) disappear. Fractional diffraction orders are observed in the diffraction pattern inside a square with vertices of (1,1), (1,−1), (−1,−1) and (−1,−1). The fractional diffraction can be understood from lattices with a period of a. However, a dual-lattice model is considered in order to explain higher-order diffractions. E-field intensity simulations show a coupling and re-distribution among fractional orders of Bloch waves. There are a total of 12 × 12 spots in E-field intensity in the unit supercell corresponding to 12 × 12 fractional diffraction orders in the diffraction pattern and 12 × 12 fractional orders of momentum in the first Brillouin zone in k-space.

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Berkovitch, Alex, Igor Belfer, Yehuda Hassin, and Evgeny Landa. "Diffraction imaging by multifocusing." GEOPHYSICS 74, no. 6 (November 2009): WCA75—WCA81. http://dx.doi.org/10.1190/1.3198210.

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Correct identification of geologic discontinuities, such as faults, pinch-outs, and small-size scattering objects, is a primary challenge of the seismic method. Seismic response from these objects is encoded in diffractions. Our method images local heterogeneities of the subsurface using diffracted seismic events. The method is based on coherent summation of diffracted waves arising in media that include interface discontinuities and local velocity heterogeneities. This is done using a correlation procedure that coherently focuses diffraction energy on a seismic section by flattening diffraction events using a new local-time-correction formula to parameterize diffraction traveltime curves. This time correction, which is based on the multifocusing method, depends on two parameters: the emergent angle and the radius of curvature of the diffracted wavefront. These parameters are estimated directly from prestack seismic traces. The diffraction multifocusing stack (DMFS) can separate diffracted and reflected energy on a stacked section by focusing diffractions to the diffraction location and defocusing the reflection energy over a large area.

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Zhang, Dongliang, Tong W. Fei, Constantine Tsingas, and Yi Luo. "Efficient wave-equation-based diffraction imaging." GEOPHYSICS 84, no. 5 (September 1, 2019): S389—S399. http://dx.doi.org/10.1190/geo2018-0568.1.

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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.

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Zhao, Jingtao, Caixia Yu, Suping Peng, and Jingjie Cao. "Least-squares imaging of diffractions by solving a hybrid L1-L2 norm minimization problem." GEOPHYSICS 86, no. 1 (January 1, 2021): S59—S72. http://dx.doi.org/10.1190/geo2019-0720.1.

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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. Because 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 and L1 regularizations for penalizing the amplitudes of the reflection and diffraction images, respectively. A classic Kirchhoff diffraction demigration operator is implemented on an initial diffraction image model to synthesize diffracted/scattered waves. A Kirchhoff reflection demigration operator, formulated by considering the local reflection slopes and a cosine attenuation weighting function, is implemented on an initial reflection image to synthesize the 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. Our method can remove steep-slope reflections, increase the focusing power of the diffractions, and eliminate noise. Two numerical experiments demonstrate its capability of separating and imaging small-scale discontinuities and inhomogeneities. The exposed geologic 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 geologic disasters because an emergency of water bursting or gas leakage may happen.

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Weidong Qu, Weidong Qu, Huarong Gu Huarong Gu, and and Qiaofeng Tan and Qiaofeng Tan. "Design of refractive/diffractive hybrid optical elements for beam shaping with large diffraction pattern." Chinese Optics Letters 14, no. 3 (2016): 031404–31407. http://dx.doi.org/10.3788/col201614.031404.

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Coimbra, Tiago A., J. Jadsom S. de Figueiredo, Jörg Schleicher, Amélia Novais, and Jessé C. Costa. "Migration velocity analysis using residual diffraction moveout in the poststack depth domain." GEOPHYSICS 78, no. 3 (May 1, 2013): S125—S135. http://dx.doi.org/10.1190/geo2012-0340.1.

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Diffraction events contain more direct information on the medium velocity than reflection events. We have developed a method for migration velocity improvement and diffraction localization based on a moveout analysis of over- or undermigrated diffraction events in the depth domain. The method uses an initial velocity model as input. It provides an update to the velocity model and diffraction locations in the depth domain as a result. The algorithm is based on the focusing of remigration trajectories from incorrectly migrated diffraction curves. These trajectories are constructed by applying a ray-tracing-like approach to the image-wave equation for velocity continuation. The starting points of the trajectories are obtained from fitting an ellipse or hyperbola to the picked uncollapsed diffraction events in the depth-migrated domain. Focusing of the remigration trajectories points out the approximate location of the associated diffractor, as well as local velocity attributes. Apart from the migration needed at each iteration, the method has a very low computational cost, but relies on the identification and picking of uncollapsed diffractions. We tested the feasibility of the method using synthetic data examples from three simple constant-gradient models and the Sigsbee2B data. Although we were able to build a complete velocity model in this example, we think of our technique as one for local velocity updating of a slightly incorrect model. Our tests showed that, within regions where the assumptions are satisfied, the method can be a powerful tool.

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N/A, N/A. "Holographic Diffraction Gratings." Laser & Optoelectronics Progress 45, no. 8 (2008): 81. http://dx.doi.org/10.3788/lop20084508.0081.

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Bošnjaković, Dejan, Marko Gregorc, Hui Li, Martin Čopič, Valentina Domenici, and Irena Drevenšek-Olenik. "Mechanical Manipulation of Diffractive Properties of Optical Holographic Gratings from Liquid Crystalline Elastomers." Applied Sciences 8, no. 8 (August 9, 2018): 1330. http://dx.doi.org/10.3390/app8081330.

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An appealing property of optical diffractive structures from elastomeric materials is a possibility to regulate their optical patterns and consequently also their diffractive features with mechanical straining. We investigated the effect of strain on diffraction characteristics of holographic gratings recorded in a monodomain side-chain liquid crystalline elastomer. The strain was imposed either parallel or perpendicular to the initial alignment direction of the material. At temperatures far below the nematic–paranematic phase transition, straining along the initial alignment affects mainly the diffraction pattern, while the diffraction efficiency remains almost constant. In contrast, at temperatures close to the nematic–paranematic phase transition, the diffraction efficiency is also significantly affected. Straining in the direction perpendicular to the initial alignment strongly and diversely influences both the diffraction pattern and the diffraction efficiency. The difference between the two cases is attributed to shear–stripe domains, which form only during straining perpendicular to the initial alignment and cause optical diffraction that competes with the diffraction from the holographic grating structure.

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Wang, Hang, Xingye Liu, and Yangkang Chen. "Separation and imaging of seismic diffractions using a localized rank-reduction method with adaptively selected ranks." GEOPHYSICS 85, no. 6 (November 1, 2020): V497—V506. http://dx.doi.org/10.1190/geo2020-0215.1.

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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.

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Burnett, William A., Alexander Klokov, Sergey Fomel, Rishidev Bansal, Enru Liu, and Tim Jenkinson. "Seismic diffraction interpretation at Piceance Creek." Interpretation 3, no. 1 (February 1, 2015): SF1—SF14. http://dx.doi.org/10.1190/int-2014-0091.1.

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We applied time-domain seismic diffraction imaging to a 3D data set from the Piceance Creek Field, Piceance Basin, northwest Colorado. The work was motivated by the need for insight into natural fracture distribution, thought to influence production. We used a novel chain of two previously developed processing steps to separate diffractions from the recorded wavefield — One step is applied to the conventional stack volume, and the other was applied to migrated dip-angle gathers. The diffractions were then imaged independently for interpretation. Comparison of seismic attributes, commonly used for fracture characterization, found that the resulting diffraction image had lateral resolution comparable to or greater than the discontinuity-type attributes and provided information complementary to azimuthal anisotropy measurements. The diffraction image from Piceance Creek had advantages over attributes in interpretation confidence because diffractions were a direct seismic response to subsurface features of intermediate size. Although these features were larger than the fractures thought to influence production, knowledge of intermediate-scale features can improve fracture prediction in the context of geologic scaling relationships or rock physics models. Qualitative interpretation of the diffraction amplitudes distinguished edge-type and line-type diffractions, indicative of fault versus channel-fill features, respectively. Even the largest faults at Piceance Creek only generated diffractions where contrasting lithologies were juxtaposed. Where there was lateral contrast, diffractions appeared to delineate small faults and channels with vertical resolution limited to the same order as the conventional seismic image.

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Zhao, Jingtao, Caixia Yu, Suping Peng, and Chuangjian Li. "3D diffraction imaging method using low-rank matrix decomposition." GEOPHYSICS 85, no. 1 (January 1, 2020): S1—S10. http://dx.doi.org/10.1190/geo2018-0417.1.

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Seismic weak responses from subsurface small-scale geologic discontinuities or inhomogeneities are encoded in 3D diffractions. Separating weak diffractions from a strong reflection background is a difficult problem for diffraction imaging, especially for the 3D case when they are tangent to or interfering with each other. Most conventional diffraction separation methods ignore the azimuth discrepancy between reflections and diffractions when suppressing reflections. In fact, the reflections associated with a specific pair of azimuth-dip angle possess sparse characteristics, and the diffractions adhering to Huygens’ principle behave as low-rank components. Therefore, we have developed a 3D low-rank diffraction imaging method that uses the Mahalanobis-based low-rank and sparse matrix decomposition method for separating and imaging 3D diffractions in the azimuth-dip angle image matrix. The advantages of our 3D diffraction imaging method not only includes the handling of interfering events but also includes ensuring a better protection of weak diffractions. The numerical experiment illustrates the good performance of our method in imaging small-scale discontinuities and inhomogeneities. The field data application of carbonate reservoirs further confirms its potential value in resolving the masked small-scale cavities that can provide storage spaces and a migration pathway for petroleum.

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Santos, Luiz Alberto, Eloise Helena Policarpo Neves, Antônio Fernando Menezes Freire, Marco Antônio Cetale Santos, Ryo Matsumoto, and Claudia M. I. Ajus. "Diffraction velocity analysis in a single-channel seismic survey in the Joetsu Basin." GEOPHYSICS 85, no. 2 (February 12, 2020): U47—U53. http://dx.doi.org/10.1190/geo2019-0011.1.

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Historically, marine research has been using single-channel seismic (SCS) devices for scientific projects. Despite SCS’s abundant data availability and the contribution it has brought for subsurface comprehension, few efforts have been dedicated to improve the SCS processing flow to extract more information carried by seismic signals and for better imaging. Diffractions present the necessary means to estimate sediment acoustic properties useful for imaging, stability studies, and geohazard prevention. The root-mean-square (rms) velocity is estimated from diffractions using a diffraction velocity analysis workflow composed of the following main steps: separation of diffractions from specular events using stationary phase properties and plane-wave destruction filtering, determination of diffractor locations in time, velocity scanning using constant rms velocity time migration, automatic picking of rms velocity at the diffractor location in the scan volume, and quality control to avoid spurious rms velocity. The method circumvents the sparsity and nonuniform distribution of diffractions for smooth lateral velocity change conditions. Application in a SCS line acquired in the Joetsu Basin, Japan Sea, indicates improvement in the focusing of deeper events compared to the previous processing flow, and it adds consistent information about the acoustic properties of the subsurface.

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Bolotovskiĭ, Boris M., and Evgenii A. Galst'yan. "Diffraction and diffraction radiation." Physics-Uspekhi 43, no. 8 (August 31, 2000): 755–75. http://dx.doi.org/10.1070/pu2000v043n08abeh000683.

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28

Bolotovskii, Boris M., and Evgenii A. Galst'yan. "Diffraction and diffraction radiation." Uspekhi Fizicheskih Nauk 170, no. 8 (2000): 809. http://dx.doi.org/10.3367/ufnr.0170.200008a.0809.

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29

Hu, Wen, Xiaojing Huang, and Hanfei Yan. "Dynamic diffraction artefacts in Bragg coherent diffractive imaging." Journal of Applied Crystallography 51, no. 1 (February 1, 2018): 167–74. http://dx.doi.org/10.1107/s1600576718000274.

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This article reports a theoretical study on the reconstruction artefacts in Bragg coherent diffractive imaging caused by dynamical diffraction effects. It is shown that, unlike the absorption and refraction effects that can be corrected after reconstruction, dynamical diffraction effects have profound impacts on both the amplitude and the phase of the reconstructed complex object, causing strong artefacts. At the dynamical diffraction limit, the reconstructed shape is no longer correct, as a result of the strong extinction effect. Simulations for hemispherical particles of different sizes show the type, magnitude and extent of the dynamical diffraction artefacts, as well as the conditions under which they are negligible.

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Huang, Shuan-Yu, Bing-Yau Huang, Chi-Chung Kang, and Chie-Tong Kuo. "Diffraction and Polarization Properties of Electrically–Tunable Nematic Liquid Crystal Grating." Polymers 12, no. 9 (August 26, 2020): 1929. http://dx.doi.org/10.3390/polym12091929.

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This work demonstrates an electrically-tunable nematic liquid crystal (NLC) diffraction grating with a periodic electrode structure, and discusses the polarization properties of its diffraction. The efficiency of the first-order diffraction can be gradually controlled by applying external electric fields cross the NLC, and the maximum diffraction efficiency of the first-order diffraction that can be obtained is around 12.5% under the applied voltage of 5.0 V. In addition to the applied electric field, the efficiency of the first-order diffraction can also vary by changing the polarized state of the incident beam. Antisymmetric polarization states with symmetrical intensities in the diffractions corresponding to the +1 and −1 order diffraction signals are also demonstrated.

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Lin, Peng, Suping Peng, Jingtao Zhao, and Xiaoqin Cui. "Diffraction separation and imaging using multichannel singular-spectrum analysis." GEOPHYSICS 85, no. 1 (January 1, 2020): V11—V24. http://dx.doi.org/10.1190/geo2019-0201.1.

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Seismic diffractions are the responses of small-scale discontinuous structures. They contain subwavelength geologic information. Thus, diffractions can be used for high-resolution imaging. The energy of 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 preprocessing step for diffraction imaging. To resolve the diffraction-separation problem, we have developed a method based on the multichannel singular-spectrum analysis (MSSA) algorithm for diffraction separation by reflection suppression. The MSSA algorithm uses 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 is, the larger the corresponding singular values will be. 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 our method. The results reveal the good performance of the MSSA algorithm in enhancing diffractions and suppressing reflections.

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Huang, Yunsong, Dongliang Zhang, and Gerard T. Schuster. "Tomographic resolution limits for diffraction imaging." Interpretation 3, no. 1 (February 1, 2015): SF15—SF20. http://dx.doi.org/10.1190/int-2014-0079.1.

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We derived formulas for the tomographic resolution limits [Formula: see text] of diffraction data. Resolution limits exhibited that diffractions can provide twice or more the tomographic resolution of specular reflections and therefore led to more accurate reconstructions of velocities between layers. Numerical simulations supported this claim in which the tomogram inverted from diffraction data was noticeably more resolved compared to that inverted from specular data. The specular synthetics were generated by sources on the surface, and the diffraction data were generated by buried diffractors. However, this advantage is nullified if the intensity and signal-to-noise ratio of the diffractions are much less than those of the pervasive specular reflections.

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Bansal, Reeshidev, and Matthias G. Imhof. "Diffraction enhancement in prestack seismic data." GEOPHYSICS 70, no. 3 (May 2005): V73—V79. http://dx.doi.org/10.1190/1.1926577.

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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 moveout 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.

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Steinberg, Shlomi, Ravi Ramamoorthi, Benedikt Bitterli, Arshiya Mollazainali, Eugene D'Eon, and Matt Pharr. "A Free-Space Diffraction BSDF." ACM Transactions on Graphics 43, no. 4 (July 19, 2024): 1–15. http://dx.doi.org/10.1145/3658166.

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Free-space diffractions are an optical phenomenon where light appears to "bend" around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.

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GOULIANOS, KONSTANTIN. "QCD ASPECTS OF HADRONIC DIFFRACTION." International Journal of Modern Physics A 20, no. 19 (July 30, 2005): 4442–49. http://dx.doi.org/10.1142/s0217751x05028041.

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Experimental results on soft and hard diffractive processes obtained by the CDF Collaboration in [Formula: see text] interactions are examined with emphasis on regularities that point to QCD aspects of hadronic diffraction. Data are interpreted in a phenomenological approach in which diffractive cross sections are related to the underlying inclusive parton distribution functions of the nucleon. In this approach, diffraction appears to be mediated by the exchange of low-x partons subject to color constraints.

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Kapitonov, Yu V., P. Yu Shapochkin, Yu V. Petrov, V. A. Lovtcius, S. A. Eliseev, and Yu P. Efimov. "Diffraction from excitonic diffraction grating." Journal of Physics: Conference Series 1368 (November 2019): 022013. http://dx.doi.org/10.1088/1742-6596/1368/2/022013.

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37

Bauman, Robert P. "Diffraction and Non‐Diffraction Fringes." Physics Teacher 34, no. 6 (September 1996): 339. http://dx.doi.org/10.1119/1.2344471.

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38

Yang Liangliang, 杨亮亮, 崔庆丰 Cui Qingfeng, 刘涛 Liu Tao, and 薛常喜 Xue Changxi. "Measurement of Diffraction Efficiency for Diffractive Optical Elements." Acta Optica Sinica 32, no. 4 (2012): 0412007. http://dx.doi.org/10.3788/aos201232.0412007.

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39

Rhodes, William T., and M. Sue McMeekin. "Diffraction efficiency of random binary-amplitude diffracting screens." Applied Optics 33, no. 32 (November 10, 1994): 7569. http://dx.doi.org/10.1364/ao.33.007569.

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40

Garfagnini, A. "Inclusive Diffraction and Diffractive Final States at HERA." Nuclear Physics B - Proceedings Supplements 174 (December 2007): 59–62. http://dx.doi.org/10.1016/j.nuclphysbps.2007.08.089.

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41

Hermerschmidt, Andreas, Sven Krüger, and Günther Wernicke. "Binary diffractive beam splitters with arbitrary diffraction angles." Optics Letters 32, no. 5 (February 2, 2007): 448. http://dx.doi.org/10.1364/ol.32.000448.

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42

Klokov, Alexander, Damir Irkabaev, Osareni C. Ogiesoba, and Nail Munasypov. "Correlation between seismic diffractions extracted from vertical seismic profiling data and borehole logging in a carbonate environment." Interpretation 3, no. 2 (May 1, 2015): T121—T129. http://dx.doi.org/10.1190/int-2014-0156.1.

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Seismic diffractions may play an important role in seismic interpretation because they characterize geologic objects that might not be visible for conventional seismic attribute analysis. Diffractivity may be caused by, and consequently may define, tectonic dislocations (faults and fractures), lithologic variations, and fluid saturation within rocks. We have tied seismic diffractions extracted from vertical seismic profiling (VSP) data and borehole logging, from which we recognized the reasons that were responsible for diffractivity of the strata. First, we processed a multisource multicomponent VSP data set to extract seismic diffractions and constructed diffraction images of the strata for all three of the VSP data components. Then, we performed joint analysis of well logs and diffractions to obtain petrophysical attributes associated with diffraction images. We divided the rock succession into several units, which have different diffraction properties. We identified compacted rock, alternating intervals, isolated fractured zones, and fluid-saturated layers.

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Dell, Sergius, and Dirk Gajewski. "Common-reflection-surface-based workflow for diffraction imaging." GEOPHYSICS 76, no. 5 (September 2011): S187—S195. http://dx.doi.org/10.1190/geo2010-0229.1.

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Imaging of diffractions is a challenge in seismic processing. Standard seismic processing is tuned to enhance reflections. Separation of diffracted from reflected events is frequently used to achieve an optimized image of diffractions. We present a method to effectively separate and image diffracted events in the time domain. The method is based on the common-reflection-surface-based diffraction stacking and the application of a diffraction-filter. The diffraction-filter uses kinematic wavefield attributes determined by the common-reflection-surface approach. After the separation of seismic events, poststack time-migration velocity analysis is applied to obtain migration velocities. The velocity analysis uses a semblance based method of diffraction traveltimes. The procedure is incorporated into the conventional common-reflection-surface workflow. We apply the procedure to 2D synthetic data. The application of the method to simple and complex synthetic data shows promising results.

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Badawi, F., and P. Villain. "Stress and elastic-constant analysis by X-ray diffraction in thin films." Journal of Applied Crystallography 36, no. 3 (May 20, 2003): 869–79. http://dx.doi.org/10.1107/s0021889803002486.

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Residual stresses influence most physical properties of thin films and are closely related to their microstructure. Among the most widely used methods, X-ray diffraction is the only one allowing the determination of both the mechanical and microstructural state of each diffracting phase. Diffracting planes are used as a strain gauge to measure elastic strains in one or several directions of the diffraction vector. Important information on the thin-film microstructure may also be extracted from the width of the diffraction peaks: in particular, the deconvolution of these peaks allows values of coherently diffracting domain size and microdistortions to be obtained. The genesis of residual stresses in thin films results from multiple mechanisms. Stresses may be divided into three major types: epitaxic stresses, thermal stresses and intrinsic stresses. Diffraction methods require the knowledge of the thin-film elastic constants, which may differ from the bulk-material values as a result of the particular microstructure. Combining an X-ray diffractometer with a tensile tester, it is possible to determine X-ray elastic constants of each diffracting phase in a thin-film/substrate system, in particular the Poisson ratio and the Young modulus. It is important to notice that numerous difficulties relative to the application of diffraction methods may arise in the case of thin films.

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Yang, Bo, Luwen Xu, Ni Qiu, Jiaxi Yang, and Guangming Wang. "Simulation of Multiple Acoustic Diffraction Based on An Iterative Ray Tracing Method." Journal of Physics: Conference Series 2450, no. 1 (March 1, 2023): 012001. http://dx.doi.org/10.1088/1742-6596/2450/1/012001.

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Abstract The classical geometrical theory of diffraction is not available for simulating multiple diffractions in wave propagation. To improve the simulating accuracy for multiple diffractions, a multiple acoustic diffraction simulating method based on ray iteration tracing is proposed in this paper. In this method, the ray occurring at the edge of the wall is split into multiple sub-rays. Then, these sub-rays are continually traced based on the classical ray-tracing theory. The numerical verification demonstrates that this method is valid for simulating multiple diffractions.

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Artioli, Gilberto. "Single-crystal neutron diffraction." European Journal of Mineralogy 14, no. 2 (March 22, 2002): 233–39. http://dx.doi.org/10.1127/0935-1221/2002/0014-0233.

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47

Hurley, Noah, Steve Kamau, Khadijah Alnasser, Usha Philipose, Jingbiao Cui, and Yuankun Lin. "Laser Diffraction Zones and Spots from Three-Dimensional Graded Photonic Super-Crystals and Moiré Photonic Crystals." Photonics 9, no. 6 (June 3, 2022): 395. http://dx.doi.org/10.3390/photonics9060395.

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The laser diffraction from periodic structures typically shows isolated and sharp point patterns at zeroth and ±nth orders. Diffraction from 2D graded photonic super-crystals (GPSCs) has demonstrated over 1000 spots due to the fractional diffractions. Here, we report the holographic fabrication of three types of 3D GPSCs through nine beam interferences and their characteristic diffraction patterns. The diffraction spots due to the fractional orders are merged into large-area diffraction zones for these three types of GPSCs. Three distinguishable diffraction patterns have been observed: (a) 3 × 3 Diffraction zones for GPSCs with a weak gradient in unit super-cell, (b) 5 × 5 non-uniform diffraction zones for GPSCs with a strong modulation in long period and a strong gradient in unit super-cell, (c) more than 5 × 5 uniform diffraction zones for GPSCs with a medium gradient in unit super-cell and a medium modulation in long period. The GPSCs with a strong modulation appear as moiré photonic crystals. The diffraction zone pattern not only demonstrates a characterization method for the fabricated 3D GPSCs, but also proves their unique optical properties of the coupling of light from zones with 360° azimuthal angles and broad zenith angles.

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Butt, Muhammad A., and Svetlana N. Khonina. "Non-Diffractive Beams for State-of-the-Art Applications." Micromachines 15, no. 6 (June 9, 2024): 771. http://dx.doi.org/10.3390/mi15060771.

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Gupta, Vipul K., and Sean R. Agnew. "Indexation and misorientation analysis of low-quality Laue diffraction patterns." Journal of Applied Crystallography 42, no. 1 (January 9, 2009): 116–24. http://dx.doi.org/10.1107/s0021889808042349.

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A Laue X-ray diffraction pattern indexing scheme, similar to a method previously proposed for convergent beam and backscattered electron diffraction patterns, was implemented. Experimental diffraction patterns are compared with simulated templates corresponding to crystals of prescribed orientations. The orientation of a diffracting volume is determined by maximizing a normalized cross correlation index between experimental and theoretical patterns. The advantages of template matching include (i) elimination of the requirement for extensive peak search/fitting analysis; (ii) the ability to index overlapped diffraction patterns obtained from neighboring grains or second phase particles; and (iii) the ability to confidently index patterns of low quality. A best fit orientation can then be determined by a least-squares fitting approach based on singular value decomposition. The misorientation within a diffracting volume is calculated from `smeared' and/or `split' Laue patterns. The methodologies developed are illustrated using micro-Laue diffraction data obtained from the wake of a fatigue crack.

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Bakhtiari Rad, Parsa, Benjamin Schwarz, Dirk Gajewski, and Claudia Vanelle. "Common-reflection-surface-based prestack diffraction separation and imaging." GEOPHYSICS 83, no. 1 (January 1, 2018): S47—S55. http://dx.doi.org/10.1190/geo2016-0445.1.

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Diffraction imaging can lead to high-resolution characterization of small-scale subsurface structures. A key step of diffraction imaging and tomography is diffraction separation and enhancement, especially in the full prestack data volume. We have considered point diffractors and developed a robust and fully data-driven workflow for prestack diffraction separation based on wavefront attributes, which are determined using the common-reflection-surface (CRS) method. In the first of two steps, we apply a zero-offset-based extrapolation operator for prestack diffraction separation, which combines the robustness and stability of the zero-offset CRS processing with enhanced resolution and improved illumination of the finite-offset CRS processing. In the second step, when the finite-offset diffracted events are separated, we apply a diffraction-based time migration velocity model building that provides high-quality diffraction velocity spectra. Applications of the new workflow to 2D/3D complex synthetic data confirm the superiority of prestack diffraction separation over the poststack method as well as the high potential of diffractions for improved time imaging.

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