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.

Conclusions

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.

Comments (0)

 

Geophysical Corner

Geophysical Corner - Satinder Chopra
Satinder Chopra, chief geophysicist (reservoir), at Arcis Seismic Solutions, Calgary, Canada, began serving as the editor of the Geophysical Corner column in 2012.

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

Geophysical Corner - Rob Vestrum

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

Geophysical Corner - Ritesh Kumar Sharma

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

Geophysical Corner

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

VIEW COLUMN ARCHIVES

Image Gallery

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

See Also: Book

Alternative Resources, Structure, Geochemistry and Basin Modeling, Sedimentology and Stratigraphy, Geophysics, Business and Economics, Engineering, Petrophysics and Well Logs, Environmental, Geomechanics and Fracture Analysis, Compressional Systems, Salt Tectonics, Tectonics (General), Extensional Systems, Fold and Thrust Belts, Structural Analysis (Other), Basin Modeling, Source Rock, Migration, Petroleum Systems, Thermal History, Oil Seeps, Oil and Gas Analysis, Maturation, Sequence Stratigraphy, Clastics, Carbonates, Evaporites, Seismic, Gravity, Magnetic, Direct Hydrocarbon Indicators, Resource Estimates, Reserve Estimation, Risk Analysis, Economics, Reservoir Characterization, Development and Operations, Production, Structural Traps, Oil Sands, Oil Shale, Shale Gas, Coalbed Methane, Deep Basin Gas, Diagenetic Traps, Fractured Carbonate Reservoirs, Stratigraphic Traps, Subsalt Traps, Tight Gas Sands, Gas Hydrates, Coal, Uranium (Nuclear), Geothermal, Renewable Energy, Eolian Sandstones, Sheet Sand Deposits, Estuarine Deposits, Fluvial Deltaic Systems, Deep Sea / Deepwater, Lacustrine Deposits, Marine, Regressive Deposits, Transgressive Deposits, Shelf Sand Deposits, Slope, High Stand Deposits, Incised Valley Deposits, Low Stand Deposits, Conventional Sandstones, Deepwater Turbidites, Dolostones, Carbonate Reefs, (Carbonate) Shelf Sand Deposits, Carbonate Platforms, Sebkha, Lacustrine Deposits, Salt, Conventional Drilling, Directional Drilling, Infill Drilling, Coring, Hydraulic Fracturing, Primary Recovery, Secondary Recovery, Water Flooding, Gas Injection, Tertiary Recovery, Chemical Flooding Processes, Thermal Recovery Processes, Miscible Recovery, Microbial Recovery, Drive Mechanisms, Depletion Drive, Water Drive, Ground Water, Hydrology, Reclamation, Remediation, Remote Sensing, Water Resources, Monitoring, Pollution, Natural Resources, Wind Energy, Solar Energy, Hydroelectric Energy, Bioenergy, Hydrogen Energy
Desktop /Portals/0/PackFlashItemImages/WebReady/book-m100-Tectonics-and-Sedimentation-Implications-for-Petroleum-Systems.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 5823 Book

See Also: DL Abstract

It is quite common for reservoir engineers to adjust the geological modelling without recoursing to the geologists by multiplying the porosity, the permeability, the anisotropy (kv/kh), the relative permeabilities, the well factors and many other parameters within their numerical world.

Desktop /Portals/0/images/_site/AAPG-newlogo-vertical-morepadding.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 3100 DL Abstract

Hydrocarbon exploration beneath the shallow allochthonous salt canopy of the ultra-deepwater central Gulf of Mexico has encountered three thick, sand-rich, submarine fan successions that punctuate an otherwise relatively condensed and fine-grained basin center stratigraphy. These sand-rich fans are Late Paleocene, Early Miocene, and Middle Miocene in age and each coincide with periods of very high sediment flux and basin margin instability. They are the primary exploration targets in most ultra-deepwater fields, recent discoveries, and failed exploration tests.

Desktop /Portals/0/images/_site/AAPG-newlogo-vertical-morepadding.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 845 DL Abstract

See Also: Field Seminar

This six-day field seminar is designed to provide participants with an appreciation of the broad range of deep-water reservoir facies, the mechanisms by which they were deposited, their predictive attributes, their reservoir heterogeneity and their stratigraphic architecture.

Desktop /Portals/0/PackFlashItemImages/WebReady/fs-Deep-Water Siliciclastic Reservoirs-California.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 46 Field Seminar

See Also: Short Course

Black Belt Ethics examines the various tenants that define the martial artist’s code of honor. The course reviews each of these tenants and discusses how they can be applied in our personal and professional lives.

Desktop /Portals/0/PackFlashItemImages/WebReady/ace2015-sc05-black-belt-hero.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 14562 Short Course