{{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).<ref name=Jones&Tanner>{{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}}</ref><ref name=Carreras>{{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}}</ref><ref name=Fossen>{{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}}</ref> 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.<ref name=Jones&Tanner /><ref name=Carreras /> The manner and intensity by which strain is distributed are controlled by a number of factors listed below.<ref name=Carreras />
== 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:<ref name=Carreras /> : 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."<ref>Jean-Pierre Brun (1983) "Isotropic points and lines in strain fields", Journal of Structural Geology 5(3):321–7</ref> : rheology : boundary conditions – the geometrical and mechanical properties and : stress orientation – critical angles by which stress is applied.<ref name=Jones&Tanner /><ref name=Carreras /><ref name=Fossen />
== 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.<ref name=AGI />
== Superposition of individual strain components == The superposition of individual strain components can be expressed at the tectonic scale involving oblique convergent margins and transpression / transtension tectonic regimes.<ref name=Jones&Tanner />
=== Oblique convergent margins === [[File:Strain partitioning at an oblique convergent margin.jpg|upright=2|thumb|Block diagram illustrating strain partitioning at an oblique convergent margin. 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.<ref name=Platt93 />]] 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).<ref name=Platt93>{{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}}</ref><ref name=McCaffery92>{{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}}</ref> This occurs as a response to shear stress exerted at the base of the overriding plate that is not perpendicular to the plate margin.<ref name=Platt93 /><ref name=McCaffery92 /><ref name=Styron>{{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}}</ref>
==== Fundamental factors which control strain partitioning within oblique orogens ==== *'''Stress orientation''': Increased subduction angle increases the arc parallel component.<ref name=Platt93 /><ref name=McCaffery92 /> *'''Rheology and anisotropy''': Mechanical properties of the wedge: (coulomb vs plastic) influence the wedge geometry.<ref name=Platt93 /><ref name=McCaffery92 /> *'''Boundary conditions''': The friction and geometry between the backstop and the wedge constitute the boundary conditions.<ref name=Platt93 /><ref name=McCaffery92 />
==== Example: Himalayan Orogen ==== The Himalaya is a strain partitioned orogen which resulted from the oblique convergence between India and Asia.<ref name=Murphy2014>{{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}}</ref> Convergence between the two landmasses persists today at a rate of 2 cm/yr.<ref name=Murphy2014 /> 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.<ref name=Murphy2014 />
The table below<ref name=Styron /> 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.<ref name=Styron /><ref name=Murphy2014 /> {| 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.<ref name=TyesTik /><ref name=FossenNorsk>{{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=https://folk.uib.no/nglhe/Papers/NGT%201994%20Transpression.pdf}}</ref> Both regimes involve a component of pure shear (transpression – compressive, transtension – extensive) and a component of simple shear.<ref name=Fossen /><ref name=TyesTik /><ref name=FossenNorsk /> Strain may be partitioned by the development of a strike slip fault or shear zone across the actively deforming region.<ref name=TyesTik /><ref name=FossenNorsk />
==== Example: Coast Mountains British Columbia ====
The Coast Mountains of British Columbia are interpreted as a transpressive orogen which formed during the Cretaceous.<ref name=CPCTect>{{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}}</ref> Oblique subduction induced the development of several shear zones which strike parallel to the orogen.<ref name=CPCTect /> 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.<ref name=CPCTect />
600px|thumbnail|center|Block diagram illustrating the difference between homogeneous and partitioned strain within transpressive and transtensive tectonic regimes. The partitioning of strain occurs through the development of a strike slip or shear zone (shown with red arrows) across the actively deforming region (brown). Adaptation and modification from (Teyssier et al., 1995;<ref name=TyesTik>{{cite journal|last1=Teyssier|first1=Christian|last2=Tikoff|first2=Basil|last3=Markley|first3=Michelle|title=Oblique plate motion and continental tectonics|journal=Geology|date=1995|volume=23|issue=5|pages=447|doi=10.1130/0091-7613(1995)023<0447:OPMACT>2.3.CO;2|bibcode=1995Geo....23..447T}}</ref> Fossen, 2012;<ref name=Fossen /> Jones and Tanner, 1995;<ref name=Jones&Tanner /> Sanderson and Marchini, 1984<ref name=Transpression />)
=== 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.<ref name=Transpression>{{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}}</ref><ref name=RamsayHuber1 /><ref name=RamsayHuber2 /><ref name=Evans&Dunne>{{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}}</ref> This effort is achieved through matrix multiplication.<ref name=RamsayHuber1>{{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}}</ref><ref name=RamsayHuber2>{{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}}</ref> Refer to the figure below to conceptually visualize what is obtained through strain factorization.
600px|thumbnail|center|Conceptual illustration of strain factorization. This highlights how the order of superposition of pure and simple shear components produce differing geometries, as matrix multiplication is non-commutative. Adaptation and modifications from Ramsay and Huber, 1983;<ref name=RamsayHuber1 /> Ramsay and Huber, 1987<ref name=RamsayHuber2 />
== 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.<ref name=Carreras /><ref name=AGI>{{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}}</ref><ref name=GoodwinTikoff>{{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}}</ref><ref name=Japan>{{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}}</ref> Constituent minerals of differing rheological properties in a rock will accumulate strain differently, thus inducing mechanically preferable structures and fabrics.<ref name=GoodwinTikoff /><ref name=Japan />
=== Example === 300px|thumbnail|right|Simplistic illustration of different deformation mechanisms which produce the finite strain. Citation for different types of deformation mechanisms acquired from (Passchier and Trouw, 2005)<ref name=Micro-tectonics>{{cite book|last1=Passchier|first1=Cees|last2=Trouw|first2=Rudolph|title=Micro-tectonics|date=2005|publisher=Springer|location=New York|isbn=978-3-540-64003-5|edition=5th}}</ref>
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.<ref name=GoodwinTikoff /><ref name=Japan /> The incompetent minerals will preferentially form the C-surfaces and competent minerals will form along the S-surfaces.<ref name=GoodwinTikoff /><ref name=Japan />
== 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.<ref name=RamsayHuber1 /> This approach is performed from geometrical analysis of rocks on the grain – crystal scale.<ref name=RamsayHuber1 /> 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.<ref name=RamsayHuber1 /><ref name=Evans&Dunne /> Performing such a procedure is important for structural and tectonic analysis as it provides parameters and constraints for constructing deformation models.<ref name=Evans&Dunne /><ref name=Mitra76>{{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}}</ref>
== See also == *Compatibility (mechanics) *Convergent boundary *Finite strain theory *Strike-slip tectonics {{clear}}
== References == {{reflist}}
{{Structural geology}}
Category:Structural geology