Finite strain and rotation from fault-slip data

doi:10.1016/0191-8141(93)90061-E

Journal of Structural Geology

Volume 15, Issue 6, June 1993, Pages 771-784

https://doi.org/10.1016/0191-8141(93)90061-E Get rights and content

Abstract

The moment tensor summation (MTS) characterizes the infinitesimal strain of a region due to fault rupture during an earthquake. Tectonic strain on a much longer time scale can be found by applying the MTS to fault-slip data, which represent cumulative fault displacement. However, the traditional MTS assumes infinitesimal strain, which may not be appropriate for cumulative displacement on faults. Therefore, it is necessary to examine whether a finite strain treatment is more appropriate. We develop a method to find finite strain from fault-slip data (FSFS) and use it to illuminate two general faulting problems: finite strain and block rotation.

First, the FSFS method is compared to the MTS using both synthetic and real fault data. Strain due to faults must be high (> 60% elongation) before the infinitesimal strain approximation produces errors greater than the variation of typical field data. However, some regions do exhibit very high fault strains and require finite strain analysis.

Second, the FSFS method is used to solve for rotation in regions cut by domino-style faults, a common model for high fault strains and rotation. Given an arbitrary rigid boundary, the method can be used to relate fault strain and block rotation. For example, a paleomagnetic rotation of 40° requires fault strain with a minimum finite elongation of 41%.

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Thus, plasticity theory, which deals with stresses and permanent deformations, provides a clear perspective for the methodology of stress inversion of various geologic structures. The theories of plasticity has inspired structural geologists and seismologists to develop their methods to evaluate tectonic strains (e.g., Conel, 1962; Arthaud, 1969; Arthaud and Mattauer, 1969; Groshong, 1972; Mattauer, 1973; Kostrov, 1974; Hyndman and Weichert, 1983; Molnar, 1983; Gauthier and Angelier, 1985; Jackson and McKenzie, 1988; Marrett and Allmendinger, 1990; Cladouhos and Allmendinger, 1993) and stresses (e.g., Turner, 1953; Rebetsky, 1997, 1999; Fry, 1999, 2001; Sato and Yamaji, 2006a; Axen et al., 2015; Rebetsky et al., 2012; Matsumoto, 2016). A researcher who conducts paleostress analysis expects that paleostress may be different from the present one, the deformation of which may have overprinted the deformation due to the paleostress.
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The Torcal Shear Zone is a 70 km-long, E–W brittle-ductile shear zone that underwent overall dextral transpression during the Late Miocene to Quaternary time. Within the Torcal Shear Zone strain is highly partitioned at multiple scales into shortening, oblique, extensional and strike-slip structures. Moreover, strain partitioning is heterogeneous along-strike giving rise to four distinct structural domains. In the central sector the strain is pure-shear dominated, although narrow sectors parallel to the shear walls are simple-shear dominated. A single N99°E–N109°E trending horizontal velocity vector ( $\vec{V}$ ) could explain the kinematics of the entire central sector of the Torcal Shear Zone. Lateral domains have different strain patterns and are comparable to splay-dominated and thrust-dominated strike-slip fault tips.
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Frictional slip theory and the constraint that slip and shear stress directions be parallel allowed to address reactivation of pre-existing faults. This suggested that stress could also be inverted from reactivated fault and slip data or earthquake focal mechanisms. Early methods relied on geometrical constructions as a substitute for calculations, whereas later methods relied on software as these calculations became tractable with the help of computers. Similar methods were developed for the inversion of stress from crystal twin gliding with non-optimal geometry, with a different criterion that relies on a threshold of the component of shear stress along the gliding line.
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Finite strain and rotation from fault-slip data

Abstract

Tectonophysics

Earth Planet Sci. Lett.

J. Struct. Geol.

Tectonophysics

J. Struct. Geol.

Tectonophysics

Tectonophysics

Tectonophysics

J. Struct. Geol.

Foreland shortening and crustal balancing in the Andes at 30°S latitude

Tectonics

The geometry of the faulting in the Galilee

Israel J. Earth Sci.

Remarks on the paper “The geometry of the faulting in the Galilee” (Freund, 1970)

Israel J. Earth Sci.

Block rotation and deformation by strike-slip faults: 2. The properties of a type of macroscopic discontinuous deformation

J. geophys. Res.

Timing and extent of Neogene tectonic rotation in the western Transverse Ranges, California

Bull geol. Soc. Am.

The relationship between plate motions and seismic moment tensors, and the rates of active deformation in the Mediterranean and Middle East

Geophys. J.

Seismic moment and energy of earthquakes, and seismic flow of rock

Izv. Acad. Sci. USSR Phys. Solid Earth

Plate Tectonics