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 16534 Book

See Also: Bulletin Article

Sequence stratigraphy and coal cycles based on accommodation trends were investigated in the coal-bearing Lower Cretaceous Mannville Group in the Lloydminster heavy oil field, eastern Alberta. The study area is in a low accommodation setting on the cratonic margin of the Western Canada sedimentary basin. Geophysical log correlation of coal seams, shoreface facies, and the identification of incised valleys has produced a sequence-stratigraphic framework for petrographic data from 3 cored and 115 geophysical-logged wells. Maceral analysis, telovitrinite reflectance, and fluorescence measurements were taken from a total of 206 samples. Three terrestrial depositional environments were interpreted from the petrographic data: ombrotrophic mire coal, limnotelmatic mire coal, and carbonaceous shale horizons. Accommodation-based coal (wetting- and drying-upward) cycles represent trends in depositional environment shifts, and these cycles were used to investigate the development and preservation of the coal seams across the study area.

The low-accommodation strata are characterized by a high-frequency occurrence of significant surfaces, coal seam splitting, paleosol, and incised-valley development. Three sequence boundary unconformities are identified in only 20 m (66 ft) of strata. Coal cycle correlations illustrate that each coal seam in this study area was not produced by a single peat-accumulation episode but as an amalgamation of a series of depositional events. Complex relations between the Cummings and Lloydminster coal seams are caused by the lateral fragmentation of strata resulting from the removal of sediment by subaerial erosion or periods of nondeposition. Syndepositional faulting of the underlying basement rock changed local accommodation space and increased the complexity of the coal cycle development.

This study represents a low-accommodation example from a spectrum of stratigraphic studies that have been used to establish a terrestrial sequence-stratigraphic model. The frequency of changes in coal seam quality is an important control on methane distribution within coalbed methane reservoirs and resource calculations in coal mining. A depositional model based on the coal cycle correlations, as shown by this study, can provide coal quality prediction for coalbed methane exploration, reservoir completions, and coal mining.

Desktop /Portals/0/PackFlashItemImages/WebReady/accommodation-based-coal-cycles-and-significant.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 5686 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 4462 CD-DVD

See Also: Learn! Blog

With the recent surge in new techniques and technology, as well as new plays put into production, a tremendous opportunity exists in both U.S. and international reservoirs to apply lessons learned to existing reservoirs in order to economically increase production and recoverable reserves.

Desktop /Portals/0/PackFlashItemImages/WebReady/revitalizing-reservoirs-key-questions-to-address-hero.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 20935 Learn! Blog

See Also: Map

Desktop /Portals/0/images/_site/AAPG-newlogo-vertical-morepadding.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 4303 Map