Computing and efficiently visualizing 3D strain or stress tensors

JL Rudkiewicz and J. -F. Lecomte. ( 2016 )
in: 2016 RING Meeting, ASGA

Abstract

Restoring 3D geological structures with geomechanical or geometrical methods generates large data sets of tensor data. When performing successive restoration steps, the tensor data becomes 4D as it varies trough time. Strain or stress data might be a proxy for fracture orientation or density. Strain data can also be used to quality control the structural interpretation. The question then arises on how to efficiently analyze the data in an evolving 3D world. Whereas the traditional representation of the individual tensor components  xx ,  yy ,  zz etc is still very used, more sophisticated ways exist and some have been tested. Based upon the eigenvalue decomposition of the tensors, several ways of representing the data will be shown. The most simple graphic displays lines along the eigenvectors. The most unusual being superquadric glyphs. It turns out that simple arrow glyphs are the most appropriate in real life cases when trying to quality control data. However, the size, diameter and length of the arrows are important. This will be illustrated on a real example from the well-known Sheep Mountain anticline. On this example, we will show how to select either the most or the least deformed areas. Finally, the comparison of tensor data with fracture orientations is solved through the classical Wulff or Schmidt stereonet, provided the data can be sampled along well path and filtered out in an efficient way. Care should however be taken to correctly account for reorientations during the geological history. The orientation of minimum stress or stain in the past is the same at present day only if its supporting rock has not been rotated since then. The reorientation due to past rotations must therefore be taken into account.

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BibTeX Reference

@INPROCEEDINGS{,
    author = { Rudkiewicz, JL and Lecomte, J. -F. },
     title = { Computing and efficiently visualizing 3D strain or stress tensors },
 booktitle = { 2016 RING Meeting },
      year = { 2016 },
 publisher = { ASGA },
  abstract = { Restoring 3D geological structures with geomechanical or geometrical methods generates large data
sets of tensor data. When performing successive restoration steps, the tensor data becomes 4D as it varies
trough time. Strain or stress data might be a proxy for fracture orientation or density. Strain data can also
be used to quality control the structural interpretation.
The question then arises on how to efficiently analyze the data in an evolving 3D world. Whereas the
traditional representation of the individual tensor components  xx ,  yy ,  zz etc is still very used, more
sophisticated ways exist and some have been tested. Based upon the eigenvalue decomposition of the
tensors, several ways of representing the data will be shown. The most simple graphic displays lines
along the eigenvectors. The most unusual being superquadric glyphs.
It turns out that simple arrow glyphs are the most appropriate in real life cases when trying to quality
control data. However, the size, diameter and length of the arrows are important. This will be illustrated
on a real example from the well-known Sheep Mountain anticline. On this example, we will show how to
select either the most or the least deformed areas.
Finally, the comparison of tensor data with fracture orientations is solved through the classical Wulff
or Schmidt stereonet, provided the data can be sampled along well path and filtered out in an efficient
way. Care should however be taken to correctly account for reorientations during the geological history.
The orientation of minimum stress or stain in the past is the same at present day only if its supporting
rock has not been rotated since then. The reorientation due to past rotations must therefore be taken into
account. }
}