Diffraction Traveltime Research Articles

Quantifying anisotropy parameters in weakly anisotropic media through diffraction traveltime parameter clusters

The seismic response datasets obtained from anisotropic media present several challenges for established seismic processing methods. To determine whether wavefront interference stems from anisotropic effects, velocity model heterogeneity, or both remains a key challenge. While reflection signatures may be insufficient for distinguishing these attributes, diffraction information in seismic datasets often provides richer insights into subsurface structures. In response to these challenges, we propose a framework that explores the feasibility of using diffraction traveltime parameters as indicators of anisotropy. By introducing an average measurement velocity derived from a cluster of diffraction traveltime responses, defined as a function of the traveltime slopes estimated from the dataset, we aim to discern the prevalence of anisotropy, heterogeneity, or both within a target region. Experiments conducted with synthetic data designed to simulate realistic scenarios have yielded promising results.

Drone-mounted ground-penetrating radar surveying: Flight-height considerations for diffraction-based velocity analysis

Recent studies highlight the potential of the drone platform for ground-penetrating radar (GPR) surveying. Most guidance for optimizing drone flight heights is based on maximizing the image quality of target responses, but no study yet considers the impact on diffraction traveltimes. Strong GPR velocity contrasts across the air-ground interface introduce significant refraction effects that distort diffraction hyperbolas and introduce errors into diffraction-based velocity analysis. The severity of these errors is explored with synthetic GPR responses, using ray- and finite-difference approaches, and a field GPR data set acquired over a sequence of diffracting features buried up to 1 m depth. Throughout, GPR antennas with 1000 MHz center frequency are raised from the ground to heights <0.9 m (i.e., 0–3 times the wavelength in air). Velocity estimates are within +10% of modeled values (spanning from 0.07 to 0.13 m/ns) if the antenna height is within 1/2 wavelength in air above the ground surface. Greater heights reduce diffraction curvature, damaging velocity precision, and masking diffractions against a background of subhorizontal reflectivity. Field data highlight further problems of the drone-based platform, with data dominated by reverberations in the air gap and reduced spatial resolution of wavelets at target depth. We suggest that a drone-based platform is unsuitable for diffraction-based velocity analysis, and any future drone surveys are benchmarked against ground-coupled data sets.

Detection of subsurface lineaments using edge diffraction

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

Accelerating least-squares Kirchhoff time migration using beam methodology

Least-squares migration is an advanced imaging technique capable of producing images with improved spatial resolution, balanced illumination, and reduced migration artifacts; however, the prohibitive computational cost poses a great challenge for its practical application. We have incorporated the beam methodology into the implementation of Kirchhoff time modeling/migration and developed a fast common-offset least-squares Kirchhoff beam time migration (LSKBTM). Different from conventional Kirchhoff time modeling/migration in which the seismic data are modeled/migrated trace by trace, the mapping operation in Kirchhoff beam time modeling/migration is performed in terms of beam components and is performed only at sparsely sampled beam centers. Therefore, the computational cost of LSKBTM is significantly reduced in comparison with that of least-squares Kirchhoff time migration (LSKTM). In addition, based on the second-order Taylor expansion of the diffraction traveltime, we introduce a quadratic correction term into the inverse/forward local slant stacking, effectively enhancing the computational accuracy of LSKBTM. We used 2D synthetic and 3D field data examples to verify the effectiveness of our method. Our results indicate that LSKBTM can produce images comparable with those of LSKTM, but at considerably reduced computational cost.

Effects of lateral heterogeneity on time-domain processing parameters

SUMMARY Time-domain processing of seismic reflection data has always been an important engine that is routinely utilized to produce seismic images and to expeditiously construct subsurface models. The conventional procedure involves analysing parameters related to the derivatives of reflection traveltime with respect to offset including normal moveout (NMO) velocities (second-order derivatives) and quartic coefficients (fourth-order derivatives). In this study, we propose to go beyond the typical assumption of 1-D laterally homogeneous medium when relating those ‘processing’ parameters to the subsurface medium parameters and take into account the additional influences from lateral heterogeneity including curved interfaces and smoothly variable velocities. We fill in the theoretical gap from previous studies and develop a general framework for such connection in layered anisotropic media. We show that in general, the influences of lateral heterogeneity get accumulated from all layers via a recursive relationship according to the Fermat’s principle and can be approximately quantified in terms of the lateral derivatives of the layer interface surfaces and velocities. Based on the same general principle, we show that our approach can also be used to study the lateral heterogeneity effects on diffraction traveltime and its second-order derivative related to time-migration velocity. In this paper, we explicitly specify expressions for NMO and time-migration velocities with the influences from both types of heterogeneity suitable for 2-D data sets and also discuss possible extensions of the proposed theory to 3-D data sets and to parameters related to higher-order traveltime derivatives. Using numerical examples, we demonstrate that the proposed theory can lead to more accurate reflection and diffraction traveltime predictions in comparison with those obtained based on the 1-D assumption. Both the proposed theoretical framework and its numerical testing for forward traveltime computation presented in this study aid in understanding the effects from lateral heterogeneity on time-processing parameters and also serve as an important basis for designing an efficient technique to separate those influences in important processes such as Dix inversion for a more accurate subsurface model in the future.

3-D seismic imaging in crystalline rock environments: An approach based on diffraction focusing

Diffracted waves are seismic waves that backscatter from localized discontinuities in the earth. They describe backscattering from interfaces with either a curvature locally approaching infinity or occur if medium properties change on a scale smaller than the predominant seimic wavelength. Both types of diffracted events are of great importance in seismic processing as they allow to identify the presence of small inhomogeneities, truncations, faults, or pinch-out layers. However, to reliable interpret such subsurface features, diffractions should be properly imaged. An inherent part of the imaging is therefore a velocity model building tuned to diffractions. We present a method for 3-D velocity analysis based on the medium's diffraction response. We propose to evaluate a focusing norm along diffraction traveltimes in the time domain. The focusing analysis considers both amplitude and phase of the diffracted events which results in several output volumes: three migration velocities for point diffractions, and one migration velocity and azimuth for edge diffractions. As additional information, the focusing analysis provides two coherence volumes which can be used to classify the back-scattering geology. Application of the proposed imaging strategy to 3-D seismic field data, acquired in the context of geothermal exploration in eastern Germany, reveals that crystalline rocks cause a rich diffraction response whose focusing can provide complementary insight into structures that are notoriously hard to image conventionally.

Enhancement of diffractions in prestack domain by means of a finite-offset double-square-root traveltime

Exploration of redundancy contained in the seismic data set assures enhancement of images that are based on stacking results. This enhancement is the goal of developing multiparametric traveltime equations that are able to approximate reflection and diffraction events in general source-receiver configurations. The main challenge of using these equations is to estimate a large number of parameters in a computationally feasible, reliable, and fast way. To obtain a better fit for diffraction traveltime events than the ones in the literature, we have derived a finite-offset (FO) double-square-root (DSR) diffraction traveltime equation (which depends on 10 parameters in three dimensions and four parameters in two dimensions). Moreover, to reduce the number of parameters, we have developed another version called simplified FO-DSR diffraction traveltime equation (which depends on five parameters in three dimensions and two parameters in two dimensions), which delivers a similar performance. We have developed operators that make use of the simplified FO-DSR traveltime equation to construct the so-called diffraction-only data set volumes (or, more simply, D-volumes) assuring enhancement in the diffraction extraction process. The D-volume construction has two steps: first, a stacking procedure to separate the diffraction events from the input data set and second, a spreading procedure to enhance the quality of these diffractions. As proof of concept, our approach has been tested on 2D/3D synthetic and 2D field data sets with successful results.

Post‐stack diffraction imaging in vertical transverse isotropy media using non‐hyperbolic moveout approximations

ABSTRACTDiffractions carry valuable information about local discontinuities and small‐scale objects in the subsurface. They are still not commonly used in the process of geological interpretation. Many diffraction imaging techniques have been developed and applied for isotropic media, whereas relatively few techniques have been developed for anisotropic media. Ignoring anisotropy can result in low‐resolution images with wrongly positioned or spurious diffractors. In this article, we suggest taking anisotropy into account in two‐dimensional post‐stack domain by considering P‐wave non‐hyperbolic diffraction traveltime approximations for vertical transverse isotropy media, previously developed for reflection seismology. The accuracy of the final images is directly connected to the accuracy of the diffraction traveltime approximations. We quantified the accuracy of six different approximations, including hyperbolic moveout approximation, by the application of a post‐stack diffraction imaging technique on two‐dimensional synthetic data examples.

Interpretation of hard rock seismic data using 3D prestack diffraction imaging

Mineral deposits are associated with geological settings characterized by discontinuities and complex structural heterogeneities such as fracture zones, small-scale objects, intrusive and steeply dipping structures. Therefore, detecting such heterogeneities is of primary interest in mineral exploration. Usually, the scale and shape of such heterogeneities cause the seismic energy to diffract rather than reflect. Despite the natural lack of reflectors and potentially abundant number of diffractors, there are only few case studies of diffraction imaging in hard rock environments with almost no examples of diffraction imaging in prestack domain. Herein, we fill this gap by implementing a 3D prestack diffraction imaging technique to detect point diffractors in hard rock environment. The technique includes computation of diffraction traveltime curves followed by semblance analysis along the curves, with high value of semblance corresponding to high diffractivity. The performance of the method is demonstrated on a 3D synthetic seismic data and applied to a 3D field seismic data set recorded over Kevitsa mineral deposit in the northern Finland. The results of the 3D prestack diffraction imaging method suggest that diffractivity is a powerful attribute that can be used with other seismic attributes for the interpretation of seismic data in hard rock environments.

Diffraction imaging method by Mahalanobis-based amplitude damping

Clarifying and locating small-scale discontinuities or inhomogeneities in the subsurface, such as faults and collapsed columns, plays a vital role in safe coal mining because these discontinuities or inhomogeneities may destroy the continuity of layers and result in dangerous mining accidents. Diffractions carry key information from these objects and therefore can be used for high-resolution imaging. However, diffracted/scattered waves are much weaker than reflected waves and consequently require separation before being imaged. We have developed a Mahalanobis-based diffraction imaging method by modifying the classic Kirchhoff formula with an exponential function to account for the dynamic differences between reflections and diffractions in the shot domain. The imaging method can automatically account for destroying of reflected waves, constructive stacking of diffracted waves, and strengthening of scattered waves. The method can overcome the difficulties in handling Fresnel apertures, and it is suitable for high-resolution imaging because of the consistency of the waveforms in the shot domain. Although the proposed method in principle requires a good migration velocity model for calculating elementary diffraction traveltimes, it is robust to an inaccurate migration velocity model. Two numerical experiments demonstrate the feasibility of the proposed method in removing reflections and highlighting diffractions, and one field application further confirms its efficiency in resolving masked faults and collapsed columns.

Diffractivity — Another attribute for the interpretation of seismic data in hard rock environment, a case study

The primary objective of seismic exploration in a hard rock environment is the detection of heterogeneities such as fracture zones, small-scale geobodies, intrusions, and steeply dipping structures that are often associated with mineral deposits. Prospecting in such environments using seismic-reflection methods is more challenging than in sedimentary settings due to lack of continuous reflector beds and predominance of steeply dipping hard rock formations. The heterogeneities and “fractal” aspect of hard rock geologic environment produce considerable scattering of the seismic energy in the form of diffracted waves. These scatterers can be traced back to irregular and often “sharp-shaped” mineral bodies, magmatic intrusions, faults, and complex and heterogeneous shear zones. Due to the natural lack of reflectors and abundant number of diffractors, there are only a few case studies of diffraction imaging in hard rock environments. There are almost no theoretical models or field examples of diffraction imaging in prestack domain. We have filled this gap by applying a 3D prestack diffraction imaging method to image point diffractors. We calculated the diffractivity by computing the semblance of seismic data along diffraction traveltime curves in the prestack domain. The performance of the method is evaluated on a synthetic case and a field seismic data set collected over the Kevitsa mineral deposit in northern Finland. The high-resolution results obtained by the application of prestack diffraction imaging suggest that diffractivity is a robust attribute that can be used in addition to other seismic attributes for the interpretation of seismic data in hard rock environment.

The offset-midpoint traveltime pyramid of P-waves in homogeneous orthorhombic media

The offset-midpoint traveltime pyramid describes the diffraction traveltime of a point diffractor in homogeneous media. We have developed an analytic approximation for the P-wave offset-midpoint traveltime pyramid for homogeneous orthorhombic media. In this approximation, a perturbation method and the Shanks transform were implemented to derive the analytic expressions for the horizontal slowness components of P-waves in orthorhombic media. Numerical examples were shown to analyze the proposed traveltime pyramid formula and determined its accuracy and the application in calculating migration isochrones and reflection traveltime. The proposed offset-midpoint traveltime formula is useful for Kirchhoff prestack time migration and migration velocity analysis for orthorhombic media.

Enhancement of prestack diffraction data and attributes using a traveltime decomposition approach

Diffractions not only carry important information about small-scale subsurface structures, they also possess unique properties, which make them a powerful tool for seismic processing and imaging. Since a point diffractor scatters an incoming wave to all directions, a diffraction event implies better illumination than a reflection, because the rays travel through larger parts of the subsurface. Furthermore, unlike the reflection case, in which the emergence location of the reflected wave depends on the source position, in the case of non-Snell scattering, up-going and down-going raypaths are decoupled. Based on this decoupling, we introduce a diffraction traveltime decomposition principle, which establishes a direct connection between zero-offset and finite-offset diffraction wavefield attributes. By making use of this approach, we are able to enhance diffractions and obtain high-quality diffraction wavefield attributes at arbitrary offsets in the prestack domain solely based on zero-offset processing without any further optimization of attributes. We show the accuracy of the method by fitting diffraction traveltimes, and on simple waveform data. Application to complex synthetic data shows the ability of the proposed approach to enhance diffractions and provide high-quality wavefield attributes even in sparsely illuminated regions such as subsalt areas. The promising results reveal a high potential for improved prestack data enhancement and further applications such as efficient diffraction-based finite-offset tomography.

Stacking apertures and estimation strategies for reflection and diffraction enhancement

It is well known that the quality of stacking results (e.g., noise reduction, event enhancement, and continuity) can be greatly influenced not only by the traveltime operator chosen but also by the apertures used. We have considered two so-called diffraction-stack traveltimes, together with the corresponding apertures, designed to enhance reflections and diffractions, respectively. The first one is the common-reflection-surface (CRS) diffraction traveltime that is obtained from the general CRS traveltime upon the condition that the target reflector reduced to a point, which we refer to as the diffraction CRS (DCRS) traveltime. The second one is the double-square-root (DSR) traveltime, well established in time migration. We have observed that the DCRS and DSR traveltimes depend on fewer parameters (two in 2D and five in 3D) than the full CRS traveltime (three in 2D and eight in 3D). For the DCRS and DSR traveltimes, we have proposed specific apertures based on the projected Fresnel zone, which are able to produce high-quality stacked sections using less parameters to be estimated. The key factor in that approach lies in the choice of traveltime operators together with careful selection of stacking apertures. In particular, suitable choices of operators and apertures lead to stacking volumes in which reflections are enhanced (and the diffractions are attenuated) or the corresponding ones in which diffractions are enhanced (and reflections are attenuated). Synthetic and field data confirm the proposed approach has good potential for image-quality improvement.

Diffraction traveltime approximation for TI media with an inhomogeneous background

Diffractions in seismic data contain valuable information that can help improve our modeling capability for better imaging of the subsurface. They are especially useful for anisotropic media because they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. We develop a scheme for diffraction traveltime computations based on perturbation of the anellipticity anisotropy parameter for transversely isotropic media with tilted axis of symmetry (TTI). The expansion, therefore, uses an elliptically anisotropic medium with tilt as the background model. This formulation has advantages on two fronts: first, it alleviates the computational complexity associated with solving the TTI eikonal equation, and second, it provides a mechanism to scan for the best-fitting anellipticity parameter [Formula: see text] without the need for repetitive modeling of traveltimes, because the traveltime coefficients of the expansion are independent of the perturbed parameter [Formula: see text]. The accuracy of such an expansion is further enhanced by the use of Shanks transform. We established the effectiveness of the proposed formulation with tests on a homogeneous TTI model and complex media such as the Marmousi and BP models.

Diffraction traveltime approximation for general anisotropic media

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.

2D common‐offset traveltime based diffraction enhancement and imaging

ABSTRACTThe diffracted energy in a seismic recording contains key information about small‐scale inhomogeneities or discontinuities of the subsurface. Diffractions can therefore lead to high‐resolution imaging of subsurface structures associated with hydrocarbon traps. However, seismic diffracted signals are often much weaker than specular reflections and consequently require enhancement before they can be utilized. In this paper diffractions are enhanced relative to reflections based on two traveltime techniques, namely the modified common‐reflection‐surface approach, which uses the common‐reflection‐surface technique with some modification to tailor it for diffractions and the replacement‐media approach derived here for the purpose of a simplified parametrization of diffraction traveltimes. Both approaches are implemented in the common‐offset domain with the use of a finite‐offset central ray unlike the zero‐ or small‐offset diffraction enhancement techniques that use a zero‐offset central ray. The validity of the two moveout expressions is tested using velocity data taken from a smooth isotropic Marmousi model. A feasibility test was also carried out with respect to the new replacement‐media traveltime approximation addressing the various effects of signal‐to‐noise ratio, depth and lateral displacement of the diffractor location. Finally, diffraction enhancement and imaging was performed on 2D seismic data from the Jequitinhonha basin offshore Brazil. Diffractions were significantly enhanced and a high‐resolution image of the discontinuities of the subsurface was obtained.

Automatic detection and imaging of diffraction points using pattern recognition

ABSTRACTHydrocarbon reservoirs are generally located beneath complex geological structures. Frequently, such areas contain seismic diffractors that carry detailed structure information in the order of the seismic wavelength. Therefore, the development of computational facilities capable of detecting diffractor points with a good resolution is desirable but has been a challenge in the area of seismic processing. In this work, we present a method for the detection of diffraction points in the common‐offset‐gather domain. The method applies a two‐class k nearest neighbours (kNN) pattern recognition technique to amplitudes along diffraction traveltime curves to distinguish between diffractions and reflections or noise. While the method, in principle, requires knowledge of the migration velocity field, it is very robust with respect to an erroneous model. Numerical examples using synthetic seismic and field ground‐penetrating‐radar (GPR) data demonstrate the feasibility of the technique and show its usefulness for automatically mapping diffraction points in a seismic section. In our applications, the method was able to detect all diffractions present in the data and did not produce any false positives.

Common-reflection-surface-based workflow for diffraction imaging

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.

Diffraction imaging by multifocusing

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.