Strain partitioning
{{Short description|Distribution of strain experienced by a geological mass by type and intensity}}
In structural geology, strain partitioning is the distribution of the total strain experienced on a rock, area, or region, in terms of different strain intensity and strain type (i.e. pure shear, simple shear, dilatation).{{cite journal|last1=Jones|first1=Richard|last2=Tanner|first2=P.W. Geoff|title=Strain partitioning in transpression zones|journal=Journal of Structural Geology|date=1995|volume=17|issue=6|pages=793–802|bibcode=1995JSG....17..793J|doi=10.1016/0191-8141(94)00102-6}}{{cite journal|last1=Carreras|first1=Jordi|last2=Cosgrove|first2=John|last3=Druguet|first3=Elena|title=Strain partitioning in banded and/or anisotropic rocks: Implications for inferring tectonic regimes|journal=Journal of Structural Geology|date=2013|volume=50|pages=7–21|doi=10.1016/j.jsg.2012.12.003|bibcode=2013JSG....50....7C}}{{cite book|last1=Fossen|first1=Haakon|title=Structural Geology|date=2012|publisher=Cambridge University Press|location=New York, USA|isbn=978-0-521-51664-8}} This process is observed on a range of scales spanning from the grain – crystal scale to the plate – lithospheric scale, and occurs in both the brittle and plastic deformation regimes. The manner and intensity by which strain is distributed are controlled by a number of factors listed below.
Influencing factors
All four of these factors below may individually or in combination contribute toward the distribution of strain. Therefore, each of these factors must be taken into consideration when analyzing how and why strain is partitioned:
: anisotropy such as preexisting structures, compositional layering, or cleavage planes. Isotropic lines "separate mutually orthogonal principle trajectories on each side. In a plane-strain field, the strain is zero at isotropic points and lines, and they can be termed neutral points and neutral lines."Jean-Pierre Brun (1983) "Isotropic points and lines in strain fields", Journal of Structural Geology 5(3):321–7
: rheology
: boundary conditions – the geometrical and mechanical properties and
: stress orientation – critical angles by which stress is applied.
Subdivisions
Strain partitioning across the literature is diverse and has been divided into three subdivisions according to the American Geological Institute:
: superposition of individual strain components that produce the finite strain
: the accumulation of strain influenced by constituent rock materials and
: individual deformation mechanisms that contribute toward producing the finite strain.
Superposition of individual strain components
= Oblique convergent margins =
File:Strain partitioning at an oblique convergent margin.jpg. The obliquity of plate convergence (blue arrows) induces stress components that are normal to the margin (yellow arrow) and parallel to the margin (green arrow). Elevated magnitudes of the arc parallel component induces horizontal translation (red arrows) between the wedge and the backstop. Adapted and modified from Platt, 1993.]]
Convergent margins where the angle of subduction is oblique will often result in the partitioning of strain into an arc parallel component (accommodated by strike slip faults or shear zones) and an arc normal component (accommodated through thrust faults).{{cite journal|last1=Platt|first1=J.P.|title=Mechanics of Oblique Convergence|journal=Journal of Geophysical Research|date=1993|volume=98|issue=B9|pages=16,239–16,256|bibcode=1993JGR....9816239P|doi=10.1029/93JB00888}}{{cite journal|last1=McCaffrey|first1=Robert|title=Oblique Plate Convergence, Slip Vectors, and Forearc Deformation|journal=Journal of Geophysical Research|date=1992|volume=97|issue=B6|pages=8905–8915|bibcode=1992JGR....97.8905M|doi=10.1029/92JB00483}} This occurs as a response to shear stress exerted at the base of the overriding plate that is not perpendicular to the plate margin.{{cite journal|last1=Syron|first1=Richard|last2=Taylor|first2=Michaeal|last3=Murphy|first3=Michael|title=Oblique convergence, arc-parallel extension, and the role of strike-slip faulting in the High Himalaya|journal=Geosphere|date=2011|volume=7|issue=2|pages=582–596|doi=10.1130/GES00606.1|bibcode=2011Geosp...7..582S|doi-access=free}}
== Fundamental factors which control strain partitioning within oblique orogens ==
- Stress orientation: Increased subduction angle increases the arc parallel component.
- Rheology and anisotropy: Mechanical properties of the wedge: (coulomb vs plastic) influence the wedge geometry.
- Boundary conditions: The friction and geometry between the backstop and the wedge constitute the boundary conditions.
== Example: Himalayan Orogen ==
The Himalaya is a strain partitioned orogen which resulted from the oblique convergence between India and Asia.{{cite journal|last1=Murphy|first1=M.A.|last2=Taylor|first2=M.H.|last3=Gosse|first3=J.|last4=Silver|first4=R.P.|last5=Whipp|first5=D.M.|last6=Beaumont|first6=C.|title=Limit of strain partitioning in the Himalaya marked by large earthquakes in western Nepal|journal=Nature Geoscience|date=2014|volume=7|issue=1|pages=38–42|doi=10.1038/NGEO2017|bibcode=2014NatGe...7...38M}} Convergence between the two landmasses persists today at a rate of 2 cm/yr. The obliquity of plate convergence increases toward the western portion of the orogen, thus inducing a greater magnitude of strain partitioning within the western Himalaya than in the central.
The table below shows relative velocities of India's convergence with Asia. The lateral variability in velocity between the central and marginal regions of the orogen suggest strain is partitioned due to oblique convergence.
| class="wikitable" | ||
| Location | Arc Normal | Arc Parallel |
|---|---|---|
| Western | ~10 mm/yr Northward | ~20 mm/yr Westward |
| Central | ~30 mm/yr Northward | ~0 mm/yr |
| Eastern | ~15 mm/yr Northward | ~20 mm/yr Eastward |
= Transpression and transtension =
Strain partitioning is common within transpressive and transtensive tectonic domains.{{cite journal|last1=Fossen|first1=Haakon|last2=Tikoff|first2=Basil|last3=Teyssier|first3=Christian|title=Strain modeling of transpressional and transtensional deformation|journal=Norsk Geologisk Tidsskrift|date=1994|volume=74|pages=134–145|url=http://folk.uib.no/nglhe/Papers/NGT%201994%20Transpression.pdf}} Both regimes involve a component of pure shear (transpression – compressive, transtension – extensive) and a component of simple shear. Strain may be partitioned by the development of a strike slip fault or shear zone across the actively deforming region.
== Example: Coast Mountains British Columbia ==
The Coast Mountains of British Columbia are interpreted as a transpressive orogen which formed during the Cretaceous.{{cite journal|last1=Chardon|first1=Dominique|last2=Andronicos|first2=Christopher|last3=Hollister|first3=Lincoln|title=Large-scale transpressive shear zone patterns and displacements within magmatic arcs: The Coast Plutonic Complex, British Columbia|journal=Tectonics|date=1999|volume=18|issue=2|pages=278–292|bibcode=1999Tecto..18..278C|doi=10.1029/1998TC900035|doi-access=free}} Oblique subduction induced the development of several shear zones which strike parallel to the orogen. The presence of these shear zones suggest that strain is partitioned within the Coast Orogen which resulted in horizontal translation of terranes for several hundred kilometers parallel to the orogen.
File:Homogeneous and partitioned strain within transpressive and transtensive tectonic regimes.jpg
= Strain factorization =
Strain factorization is a mathematical approach to quantify and characterize the variation of strain components in terms of the intensity and distribution that produces the finite strain throughout a deformed region.{{cite journal|last1=Sanderson|first1=David|last2=Marchini|first2=W.R.D.|title=Transpression|journal=Journal of Structural Geology|date=1984|volume=6|issue=5|pages=449–458|doi=10.1016/0191-8141(84)90058-0|bibcode=1984JSG.....6..449S}}{{cite journal|last1=Evans|first1=Mark|last2=Dunne|first2=William|title=Strain factorization and partitioning in the North Mountain thrust sheet, central Appalachians, U.S.A|journal=Journal of Structural Geology|date=1991|volume=13|issue=1|pages=21–35|bibcode=1991JSG....13...21E|doi=10.1016/0191-8141(91)90098-4}} This effort is achieved through matrix multiplication.{{cite book|last1=Ramsay|first1=John|last2=Huber|first2=Martin|title=The Techniques of Modern Structural Geology Volume 1: Strain Analysis|date=1983|publisher=Academic Press|location=London|isbn=978-0-12-576901-3}}{{cite book|last1=Ramsay|first1=John|last2=Huber|first2=Martin|title=The Techniques of Modern Structural Geology Volume 2: Folds and Fractures|date=1987|publisher=Academic Press|location=London|isbn=978-0-12-576902-0}} Refer to the figure below to conceptually visualize what is obtained through strain factorization.
Influence of rock material rheology
At the grain and crystal scale, strain partitioning may occur between minerals (or clasts and matrix) governed by their rheological contrasts.{{cite book|last1=Neuendorf|first1=Kaus|last2=Mehl|first2=James|last3=Jackson|first3=Julia|title=Glossary of Geology|date=2005|publisher=American Geological Institute|location=Alexandria, VA, United States|edition=5|isbn=978-0-922152-76-6}}{{cite journal|last1=Goodwin|first1=Laurel|last2=Tikoff|first2=Basil|title=Competency contrast, kinematics, and the development of foliations and lineations in the crust|journal=Journal of Structural Geology|date=2002|volume=24|issue=6–7|pages=1065–1085|bibcode=2002JSG....24.1065G|doi=10.1016/S0191-8141(01)00092-X}}{{cite journal|last1=Michibayashi|first1=Katsuyoshi|last2=Murakami|first2=Masami|title=Development of a shear band cleavage as a result of strain partitioning|journal=Journal of Structural Geology|date=2007|volume=29|issue=6|pages=1070–1082|doi=10.1016/j.jsg.2007.02.003|bibcode=2007JSG....29.1070M|hdl=10297/508|hdl-access=free}} Constituent minerals of differing rheological properties in a rock will accumulate strain differently, thus inducing mechanically preferable structures and fabrics.
= Example =
File:Deformation mechanisms (Passchier and Trouw).jpeg
Rocks that contain incompetent (mechanically weak) minerals such as micas and more competent (mechanically stronger) minerals such as quartz or feldspars, may develop a shear band fabric. The incompetent minerals will preferentially form the C-surfaces and competent minerals will form along the S-surfaces.
Individual deformation mechanisms
Strain partitioning is also known as a procedure for decomposing the overall strain into individual deformation mechanisms which allowed for strain to be accommodated. This approach is performed from geometrical analysis of rocks on the grain – crystal scale. Strain partitioning of deformation mechanisms incorporates those mechanisms which occur both simultaneously and/or subsequently as tectonic conditions evolve, as deformation mechanisms are a function of strain rate and pressure-temperature conditions. Performing such a procedure is important for structural and tectonic analysis as it provides parameters and constraints for constructing deformation models.{{cite journal|last1=Mitra|first1=Shankar|title=A Quantitative Study of Deformation Mechanisms and Finite Strain in Quartzites|journal=Contributions to Mineralogy and Petrology|date=1976|volume=59|issue=2|pages=203–226|bibcode=1976CoMP...59..203M|doi=10.1007/BF00371309}}