Euler Curvature Can Be a Calculated Success

Contributors: Satinder Chopra, Kurt Marfurt

Several (12, we think) types of seismic-based curvature attributes have been introduced the last few years – and of these, the most-positive and the most-negative curvatures described in last month’s article are the most popular.

Most-positive and most-negative curvatures provide more continuous maps of faults and flexures than do maximum and minimum curvatures, because the latter tend to rapidly change algebraic sign at fault and flexure intersections.

Other attributes, such as mean curvature, Gaussian curvature and shape index, also have been used by a few practitioners.

We describe here a technique called Euler curvature, which has valuable applications.

An attraction of Euler curvature is that it can be calculated in any desired azimuth across a 3-D volume to enhance the definition of specific lineaments. When this apparent curvature (the Euler curvature) is computed in several specific azimuths, the results are quite useful for interpreting azimuth-dependent structure.

The flow diagram in figure 1 explains the method for computing azimuth-dependent Euler curvature.


Mapping the intensities of fracture sets has been a major objective of reflection seismologists. Curvature, acoustic impedance and reflection coherence currently are the most effective attributes used to predict fractures in post-stack seismic data.

We describe here the application of Euler curvature to a 3-D seismic volume from northeast British Columbia, Canada. We use an interactive workflow to utilize Euler curvature much as we do in generating a suite of shaded relief maps.

Figure 2 shows 3-D chair displays through volumes of Euler curvature calculated at azimuths of 0, 45, 90 and 135 degrees from north. The left column shows long-wavelength curvature calculations, and the right column displays short-wavelength calculations.

Notice how east-west lineaments stand out when north-south curvature is estimated (azimuth = 0):

  • When curvature is estimated in an azimuth of 45 degrees, northwest-southeast lineaments are pronounced.
  • When east-west curvature is calculated (azimuth = 90 degrees), north-south features events are emphasized.
  • When northwest-southeast curvature is estimated (azimuth = 135 degrees), events slightly inclined away from north-south are better defined.

The analysis area shown in these figures spans approximately 100 square kilometers.

As emphasized in last month’s article, short-wavelength displays show more lineament detail and resolution than do long-wavelength displays. That principle is illustrated again by the displays in figure 2.

The important concept presented here is that there are obvious advantages in calculating Euler curvature on post-stack seismic volumes, because azimuth directions of curvature can be chosen to highlight lineaments in preferred directions.


Euler curvatures calculated in desired azimuthal directions produce better definitions of targeted lineaments.

Depending on the desired level of detail, either long- wavelength or short-wavelength estimates can be calculated. Short-wavelength Euler curvature would be more beneficial for observing fracture lineaments.

This work is in progress, and we hope to calibrate seismic-based lineaments determined with this technology with lineaments interpreted from image logs.


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

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

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


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Part 2 of 3

This month's column, part two of a three-part series comparing structural and amplitude curvatures, deals with observing fault and fracture lineaments. See: Part 1

See Also: Book

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The presence of hydrocarbon-bearing sandstones within the Eocene of the Forties area was first documented in 1985, when a Forties field (Paleocene) development well discovered the Brimmond field. Further hydrocarbons in the Eocene were discovered in the adjacent Maule field in 2009. Reservoir geometry derived from three-dimensional seismic data has provided evidence for both a depositional and a sand injectite origin for the Eocene sandstones. The Brimmond field is located in a deep-water channel complex that extends to the southeast, whereas the Maule field sandstones have the geometry of an injection sheet on the updip margin of the Brimmond channel system with a cone-shape feature emanating from the top of the Forties Sandstone Member (Paleocene). The geometry of the Eocene sandstones in the Maule field indicates that they are intrusive and originated by the fluidization and injection of sand during burial. From seismic and borehole data, it is unclear whether the sand that was injected to form the Maule reservoir was derived from depositional Eocene sandstones or from the underlying Forties Sandstone Member. These two alternatives are tested by comparing the heavy mineral and garnet geochemical characteristics of the injectite sandstones in the Maule field with the depositional sandstones of the Brimmond field and the Forties sandstones of the Forties field.

The study revealed significant differences between the sandstones in the Forties field and those of the Maule and Brimmond fields), both in terms of heavy mineral and garnet geochemical data. The Brimmond-Maule and Forties sandstones therefore have different provenances and are genetically unrelated, indicating that the sandstones in the Maule field did not originate by the fluidization of Forties sandstones. By contrast, the provenance characteristics of the depositional Brimmond sandstones are closely comparable with sandstone intrusions in the Maule field. We conclude that the injectites in the Maule field formed by the fluidization of depositional Brimmond sandstones but do not exclude the important function of water from the huge underlying Forties Sandstone Member aquifer as the agent for developing the fluid supply and elevating pore pressure to fluidize and inject the Eocene sand. The study has demonstrated that heavy mineral provenance studies are an effective method of tracing the origin of injected sandstones, which are increasingly being recognized as an important hydrocarbon play.

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