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.

Comments (0)


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 - 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

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

Desktop /Portals/0/images/_site/AAPG-newlogo-vertical-morepadding.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 4481 Book

See Also: Bulletin Article

The Marcellus Shale is considered to be the largest unconventional shale-gas resource in the United States. Two critical factors for unconventional shale reservoirs are the response of a unit to hydraulic fracture stimulation and gas content. The fracture attributes reflect the geomechanical properties of the rocks, which are partly related to rock mineralogy. The natural gas content of a shale reservoir rock is strongly linked to organic matter content, measured by total organic carbon (TOC). A mudstone lithofacies is a vertically and laterally continuous zone with similar mineral composition, rock geomechanical properties, and TOC content. Core, log, and seismic data were used to build a three-dimensional (3-D) mudrock lithofacies model from core to wells and, finally, to regional scale. An artificial neural network was used for lithofacies prediction. Eight petrophysical parameters derived from conventional logs were determined as critical inputs. Advanced logs, such as pulsed neutron spectroscopy, with log-determined mineral composition and TOC data were used to improve and confirm the quantitative relationship between conventional logs and lithofacies. Sequential indicator simulation performed well for 3-D modeling of Marcellus Shale lithofacies. The interplay of dilution by terrigenous detritus, organic matter productivity, and organic matter preservation and decomposition affected the distribution of Marcellus Shale lithofacies distribution, which may be attributed to water depth and the distance to shoreline. The trend of normalized average gas production rate from horizontal wells supported our approach to modeling Marcellus Shale lithofacies. The proposed 3-D modeling approach may be helpful for optimizing the design of horizontal well trajectories and hydraulic fracture stimulation strategies.

Desktop /Portals/0/PackFlashItemImages/WebReady/organic-rich-marcellus-shale-lithofacies-modeling.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 5725 Bulletin Article

See Also: CD DVD

Desktop /Portals/0/images/_site/AAPG-newlogo-vertical-morepadding.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 4086 CD-DVD

See Also: DL Abstract

In his classic 1965 GSA Bulletin paper “Origin of ‘Reverse Drag’ on the Downthrown Side of Normal Faults” Hamblin presented a conceptual model linking the formation of reverse drag (the down-warping of hanging wall strata toward a normal fault) to slip on faults with listric (curved, concave up) cross-sectional profiles. Although this model has been widely accepted, some authors have noted that reverse drag may also form in response to slip on planar faults that terminate at depth. A universal explanation for the origin of reverse drag, a common element of extensional terranes, thus remains elusive almost 50 years after Hamblin’s seminal paper on the subject.

Desktop /Portals/0/images/_site/AAPG-newlogo-vertical-morepadding.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 10303 DL Abstract

See Also: Online e Symposium

This seminar focuses on the role geoscience leaders and mentors play in retaining top talent.

Desktop /Portals/0/PackFlashItemImages/WebReady/oc-es-retention-tools-for-leaders-and-mentors.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 1485 Online e-Symposium