Curvature Computations Enhance Exploration

Contributors: Satinder Chopra, Kurt Marfurt

Curvature attributes have become popular with seismic interpreters and have found their way into most commercial seismic-interpretation software packages.

Curvature estimates were introduced as computations performed on interpreted 2-D seismic surfaces, and 3-D computations based on volumetric estimates of inline and crossline dip soon followed.

A 3-D volume of curvature values is produced by estimating reflector dip and azimuth at each data sample in a seismic volume.

We denote the output of such calculations as structural curvature because the calculations are performed on time-based or depth-based seismic data that define the geometrical configurations of subsurface structure.

A second type of curvature attribute can be calculated by using seismic reflection amplitudes rather than geometrical shapes of structure. When an interpreter creates a 3-D horizon through a seismic amplitude volume, inline and crossline derivatives of amplitude-magnitude variations can be calculated across this horizon.

Attributes that define the gradient behavior of reflection amplitude in X-Y space across a horizon are called amplitude curvature and are valuable for delineating the edges of bright spots, channels and other stratigraphic features that produce lateral variations in reflection magnitudes.

In figure 1a we show a schematic diagram of the magnitude of a hypothetical seismic amplitude anomaly along image coordinate X. This curve shows an increase in reflection amplitude between image coordinates X1 and X4, with maximum amplitudes occurring between X2 and X3.

Next, we compute the first and second spatial derivatives of this amplitude behavior with respect to X, and show the results in figures 1b and 1c.

Note how the extrema of the second derivative in figure 1c define where the amplitude anomaly undergoes a change in magnitude.

In a 3-D seismic volume, amplitude gradients are computed along structural dip by taking derivatives in inline and crossline directions. Figure 2 shows 3-D chair views of an inline vertical slice through a seismic amplitude volume and the correlation of that profile with energy-weighted amplitude gradients calculated in the inline direction (figure 2a) and in the crossline direction (figure 2b). Both images show independent views of north-south oriented main faults and features related to those faults.

A geological structure has curvature of different spatial wavelengths at various locations across the structure. Thus structural curvature computed at different wavelengths provides different perspectives of the same geology.

Short-wavelength curvature tends to delineate details showing intense, highly localized faulting. In contrast, long-wavelength curvature enhances subtle flexures on a scale of 100, 200 or more image traces that are difficult to see on conventional seismic data.

These long-wavelength features often correlate to fault-generated patterns that are below seismic resolution, shallow bowl-shaped collapse features or modest dome-shaped carbonate buildups.

Figures 3 and 4 compare long-wavelength and short-wavelength computations of most-positive and most-negative amplitude curvatures and structural curvatures.

In figure 3, note that for both long and short wavelengths, most-positive estimates of amplitude-curvature (figures 3a and 3c) provide considerable detail, whereas most-positive structure-curvature displays (figures 3b and 3d) show larger-scale features.

The same physics occurs for estimates of most-negative curvature – amplitude curvature(figures 4a and 4c) depicts fine detail, but structural curvature (figures 4b and 4d) shows larger features.

Amplitude curvature is not a better seismic attribute than structural curvature; it is simply a different attribute. Although structural highs and reflection amplitude anomalies are mathematically independent, they may be coupled by geology.

For example, gas trapped by structure may create a bright spot. In such a case, the second derivatives of structure curvature and reflection amplitude curvature may be related.


When seismic data are processed with amplitude-preserving procedures, amplitude variations can be diagnostic of geologic information – such as changes in porosity, thickness or lithology.

Computing curvature of reflection-amplitude gradients enhances the detection of gas-charged fractures, mineralized cleats in coal seams and other subtle features.

We hope to extend the work shown here to generate rose diagrams of lineaments observed on amplitude-curvature maps and compare these with rose diagrams obtained from image logs.

Acknowledgments: We thank Arcis Corporation for permission to show the data examples, as well as for the permission to publish this work.

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Geophysical Corner - Ritesh Kumar Sharma

Ritesh Kumar Sharma is with Arcis Seismic Solutions, Calgary, Canada.

Geophysical Corner

Geophysical Corner - Satinder Chopra
Satinder Chopra, award-winning chief geophysicist (reservoir), at Arcis Seismic Solutions, Calgary, Canada, and a past AAPG-SEG Joint Distinguished Lecturer began serving as the editor of the Geophysical Corner column in 2012.

Geophysical Corner - Rob Vestrum

Rob Vestrum is chief geophysicist at Thrust Belt Imaging, Calgary, Alberta, Canada.

Geophysical Corner - Kurt Marfurt
AAPG member Kurt J. Marfurt is with the University of Oklahoma, Norman, Okla.

Geophysical Corner

The Geophysical Corner is a regular column in the EXPLORER that features geophysical case studies, techniques and application to the petroleum industry.


Image Gallery

This month’s column deals with a comparison of structural and amplitude curvatures.

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The geometries of clay smears produced in a series of direct shear experiments on composite blocks containing a clay-rich seal layer sandwiched between sandstone reservoir layers have been analyzed in detail. The geometries of the evolving shear zones and volume clay distributions are related back to the monitored hydraulic response, the deformation conditions, and the clay content and strength of the seal rock. The laboratory experiments were conducted under 4 to 24 MPa (580–3481 psi) fault normal effective stress, equivalent to burial depths spanning from less than approximately 0.8 to 4.2 km (0.5 to 2.6 mi) in a sedimentary basin. The sheared blocks were imaged using medical-type x-ray computed tomography (CT) imaging validated with optical photography of sawn blocks. The interpretation of CT scans was used to construct digital geomodels of clay smears and surrounding volumes from which quantitative information was obtained. The distribution patterns and thickness variations of the clay smears were found to vary considerably according to the level of stress applied during shear and to the brittleness of the seal layer. The stiffest seal layers with the lowest clay percentage formed the most segmented clay smears. Segmentation does not necessarily indicate that the fault seal was breached because wear products may maintain the seal between the individual smear segments as they form. In experiments with the seal layer formed of softer clays, a more uniform smear thickness is observed, but the average thickness of the clay smear tends to be lower than in stiffer clays. Fault drag and tapering of the seal layer are limited to a region close to the fault cutoffs. Therefore, the comparative decrease of sealing potential away from the cutoff zones differs from predictions of clay smear potential type models. Instead of showing a power-law decrease away from the cutoffs toward the midpoint of the shear zone, the clay smear thickness is either uniform, segmented, or undulating, reflecting the accumulated effects of kinematic processes other than drag. Increased normal stress improved fault sealing in the experiments mainly by increasing fault zone thickness, which led to more clay involvement in the fault zone per unit of source layer thickness. The average clay fraction of the fault zone conforms to the prediction of the shale gouge ratio (SGR) model because clay volume is essentially preserved during the deformation process. However, the hydraulic seal performance does not correlate to the clay fraction or SGR but does increase as the net clay volume in the fault zone increases. We introduce a scaled form of SGR called SSGR to account for increased clay involvement in the fault zone caused by higher stress and variable obliquity of the seal layer to the fault zone. The scaled SGR gives an improved correlation to seal performance in our samples compared to the other algorithms.
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