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Abstract
AAPG Bulletin, V. 84, No. 2 (February 2000), P. 234-249.
Sequential Restoration and Unstraining of Structural Cross
Sections: Applications to Extensional Terranes1S. Gregg Erickson,2 Stuart Hardy,3 and John
Suppe2©Copyright 2000. The American Association of Petroleum Geologists. All rights
reserved.
1Manuscript received August 10, 1998; revised manuscript received May 21, 1999;
final acceptance September 3, 1999.
2Princeton 3D Structure Project, Department of Geosciences, Princeton
University, Princeton, New Jersey 08544. Present address: Department of Geology, P.O. Box
32067, Appalachian State University, Boone, North Carolina 28608-2067; e-mail: [email protected]
3Department of Earth Sciences, The University of Manchester, Manchester M13
9PL, United Kingdom.
This paper benefited from the constructive reviews of William F. Dula and Mark J. Gresko.
Thanks to Ken McClay for permission to use the photograph of the analog sandbox model and
to ARCO and Jebco Seismic, Inc., for permission to use the seismic profiles. The
foundation of the computer code used in this study was written by Delphine Rouby. This
research was funded by the members of the Princeton 3D Structure Project consortium, ARCO,
Amoco, Chevron, Elf, Exxon, Intevep, TPEDB (Tarim), and Texaco. ABSTRACT
We restore cross sections using a strain-minimization strategy that concentrates
displacement on known faults and on slip systems within fault blocks. Growth strata are
used to sequentially restore cross sections, and the misfit of rigidly restored fault
blocks is used to determine the internal strain within each fault block. Texture mapping
allows data (e.g., seismic profile, photograph of an analog model or outcrop) to be imaged
onto the restored state, and the image is translated, rotated, and unstrained during the
restoration. Growth strata are stripped layer by layer to sequentially restore a cross
section. This approach determines the history of deformation, including the activity of
faults and the internal strain accumulated during each growth increment. During each
increment of growth, a cross section is initially restored to a horizontal datum, assuming
that deformation is by rigid-body translations and rotations of fault blocks. Fault blocks
are unstrained by dividing them into smaller triangular elements that accommodate the
internal deformation within each fault block. Translations and rotations of the smaller
rigid elements within each fault block produce a least-squares minimized best fit. After
attaining a best fit of rigid elements, continuity is regained by moving initially
coincident triangle vertices to a common centroid. The change in shape of the triangular
elements in regaining continuity is a measure of strain at that location, assuming
homogeneous strain within each triangular element. Sequential restoration and unstraining
determines the spatial variation and temporal evolution of strain orientations and
magnitudes, calculated at each vertex during each increment of restoration. The method is
tested on an analog sandbox model of deformation in the hanging wall of a listric normal
fault and on two seismic profiles, a listric normal fault system from the Gulf of Mexico,
and a graben developed over salt from the North Sea. The sequential restoration accurately
determines the sequence of faulting in the analog model and provides insights into the
development of the natural examples. The restoration method determines the orientations
and magnitudes of strain, which can be used to predict the orientation, intensity, and
timing of small-scale deformation features.
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