Why curvature attribute delineates subtle geologic features? A mathematical approach

Silva, Pedro Mário; Martins, Leonardo de Oliveira; Pampanelli, P.C.; Faustino, G.M.

doi:10.1190/segam2016-13968665.1

Cited by 3 publications

(3 citation statements)

References 18 publications

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“…Hunt et al (2011Hunt et al ( , 2018 used the curvature attributes, in particular, the most positive curvature (with certain parameterization and filtering), to predict the key properties of geologic targets that can potentially yield hazardous natural fractures. Silva et al (2016) demonstrated that the azimuthally-dependent curvature of the seismic data can be understood as a second-order directional derivative and applied as an oriented edge-detection filter. Guo et al (2016) studied the Barnett Shale of the Fort Worth Basin and found that in the survey acquired prior to hydraulic fracturing, AVAz anomalies were stronger and highly correlated with major structural lineaments measured by curvature attributes.…”

Section: Introductionmentioning

confidence: 99%

Hypersurface curvatures of geological features

Ravve

Tertois

Ribet

et al. 2023

Geophysical Journal International

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Summary Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing the orientations and shapes, respectively, of geological reflecting surfaces. Commonly, the input dataset for their computation consists of fine 3D grids of scalar fields representing either the seismic-driven reflectivities (e.g. amplitudes of 3D seismic migrated volumes) or model-driven reflectivities, computed, for example, from the derived elastic impedance parameters. Conventionally, the computation of curvature parameters at each grid point is based on analyzing the local change in the inline/crossline dips, considering the potential existence of a local quadratic reflecting surface in the vicinity of that point. This assumption breaks down for subsurface points in the vicinity of either complex reflecting surfaces (e.g. brittle/rough/tilted synclines/anticlines, ridges/troughs, and saddles) and/or sharp, discontinuous geological features (e.g. fault edges/tips, pinch-outs, fracture systems, channels, and small geobodies), where the values of the computed curvature become extremely high. However, while these high values can indicate the existence of non-reflecting objects, they do not deliver their specific geometric characteristics. In this study we present a novel method that better characterizes the shapes of these complex geological features by extending the assumption of local surfaces (2D surfaces in 3D space) into local hypersurfaces (3D hypersurfaces in 4D space), with their corresponding (three rather than two) principal (and effective) curvature parameters. We demonstrate the advantages of our method by comparing the conventional dip-based surface curvature parameters with the hypersurface curvature parameters, using a synthetic model/image with different types and shapes of geological features and a seismic image of real data containing a complex fault and hidden buried channels.

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Section: Introductionmentioning

confidence: 99%

Hypersurface curvatures of geological features

Ravve

Tertois

Ribet

et al. 2023

Geophysical Journal International

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“…Over the last few decades, a variety of edge detection operators (edge detectors) have been introduced to geophysicists. Most of them are based on the concepts of derivatives [18][19][20][21], gradients [22,23], Laplacian (finding the zero crossings) [24][25][26], and the like. Different from the above standard methods, some alternative edge detectors developed from other approaches are equally effective as the standard methods and are also useful for evaluating new edge detectors.…”

Section: Introductionmentioning

confidence: 99%

Improving GPR Imaging of the Buried Water Utility Infrastructure by Integrating the Multidimensional Nonlinear Data Decomposition Technique into the Edge Detection

Chen

Jeng

2021

Water

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Although ground-penetrating radar (GPR) is effective to detect shallow-buried objects, it still needs more effort for the application to investigate a buried water utility infrastructure. Edge detection is a well-known image processing technique that may improve the resolution of GPR images. In this study, we briefly review the theory of edge detection and discuss several popular edge detectors as examples, and then apply an enhanced edge detecting method to GPR data processing. This method integrates the multidimensional ensemble empirical mode decomposition (MDEEMD) algorithm into standard edge detecting filters. MDEEMD is implemented mainly for data reconstruction to increase the signal-to-noise ratio before edge detecting. A quantitative marginal spectrum analysis is employed to support the data reconstruction and facilitate the final data interpretation. The results of the numerical model study followed by a field example suggest that the MDEEMD edge detector is a competent method for processing and interpreting GPR data of a buried hot spring well, which cannot be efficiently handled by conventional techniques. Moreover, the proposed method should be readily considered a vital tool for processing other kinds of buried water utility infrastructures.

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“…The curvature analysis, as a fundamental tool of signal processing, has been widely used in various industries and disciplines, e.g., medical brain scanners (Joshi et al 1995), optometry (Daniel and Barsky 1997), and terrain analysis (Wood 1996). Since its first introduction to subsurface structure mapping and hydrocarbon reservoir characterization (Lisle 1994), lots of efforts have been devoted to developing and implementing the curvature attribute as well as its variations to structure interpretation from three-dimensional (3D) seismic surveys (e.g., Roberts 2001;Bergler et al 2002;Hart, Pearson and Rawling 2002;Bergbauer, Mukerji and Hennings 2003;Hart and Sagan 2005;Al-Dossary and Marfurt 2006;Blumentritt, Marfurt and Sullivan 2006;Hart 2006;Sullivan et al 2006;Marfurt 2010, 2013;Gao 2014a, 2014b;Silva et al 2016;.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional curvature analysis of seismic waveforms and its interpretational implications

Alfarraj

AlRegib

2018

Geophysical Prospecting

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A B S T R A C TThe idea of curvature analysis has been widely used in subsurface structure interpretation from three-dimensional seismic data (e.g., fault/fracture detection and geomorphology delineation) by measuring the lateral changes in the geometry of seismic events. However, such geometric curvature utilizes only the kinematic information (two-way traveltime) of the available seismic signals. While analysing the dynamic information (waveform), the traditional approaches (e.g., complex trace analysis) are often trace-wise and thereby fail to take into account the seismic reflector continuity and deviate from the true direction of geologic deposition, especially for steeply dipping formations. This study proposes extending the three-dimensional curvature analysis to the waveforms in a seismic profile, here denoted as the waveform curvature, and investigates the associated implications for assisting seismic interpretation. Applications to the F3 seismic dataset over the Netherlands North Sea demonstrate the added values of the proposed waveform curvature analysis in four aspects. First, the capability of the curvature operator in differentiating convex and concave bending allows automatic decomposition of a seismic image by the reflector types (peaks, troughs and zero crossings), which can greatly facilitate computer-aided horizon interpretation and modelling from three-dimensional seismic data. Second, the signed minimum curvature offers a new analytical approach for estimating the fundamental and important reflector dip attribute by searching the orientation associated with least waveform variation. Third, the signed maximum curvature makes it possible to analyse the seismic signals along the normal direction of the reflection events. Finally, the curvature analysis promotes the frequency bands of the seismic signals and thereby enhances the apparent resolution on identifying and interpreting subtle seismic features.

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Why curvature attribute delineates subtle geologic features? A mathematical approach

Cited by 3 publications

References 18 publications

Hypersurface curvatures of geological features

Hypersurface curvatures of geological features

Improving GPR Imaging of the Buried Water Utility Infrastructure by Integrating the Multidimensional Nonlinear Data Decomposition Technique into the Edge Detection

Three‐dimensional curvature analysis of seismic waveforms and its interpretational implications

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