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ETG 6 - 12 SCHULMANN ET AL.: STRAIN DISTRIBUTIONthe range 1–5 cm yr 1 , the lifetimes of these shear zonesmight be in the range 0.5–4 Myr. These times are too shortfor an assumed duration of orogenic events. If we considerthat the duration of orogenic events is long (over an intervalof several tens of million years), then the computed strainintensities for such given external parameters are unrealisticallyhigh (up to D = 100).9.2. Active Zones[44] Our calculations show that for a transpressional zonewith R vd < 0.2, the strain rate does not exceed a value of 6 10 15 s 1 for any angle of convergence (a). This R vd valuecorresponds to the active zones of Sumatra (d = 300 km, v =70 mm yr 1 , R vd = 0.23) and San Andreas (d = 200 km, v =50 mm yr 1 , R vd = 0.25). For a zone with value R vd = 0.48,corresponding to the Alpine Fault zone in New Zealand,there will be maximum strain rate of 1.58 10 14 s 1distributed over a width of 100 km for a plate velocity of 48mm yr 1 . Zones with R vd >2 (small d, large v) show highstrain rate values of 3.2 10 14 s 1 and will apply fornarrow continental zones (10–20 km) with a mean platevelocity of 5 km yr 1 . Note that all of these values areconsistent with the strain rate estimates suggested by Carterand Tsenn [1987].[45] Assuming that the above mentioned strain valuesdevelop in large zones of homogeneous deformation, inFigure 6b we have plotted recent macroscopic convergenceparameters of well-known active transpressive zones. Wecan take the above listed macroscopic parameters of thesetranspressive zones and ask at what time are the averagestrain intensities developed? Figure 6b shows that theaverage strain of D = 1.2 would be produced in the Sumatrazone after 3.75 Myr, in San Andreas after 4.8 Myr, and inAlpine Fault Zone, New Zealand, after 1.7 Myr.[46] The average strains, characteristic for most of thezones with dispersed deformation are achieved in 5 Myr forzones with R vd = 0.2 and after 10 Myr for zones with R vd =0.1. We note that the New Zealand zone of distributedfaulting would have a strain intensity corresponding to D =13 after 5 Myr, while the San Andreas and Sumatra zoneswould remain within a realistic range of strain intensities (Dof x to y). We note that for the entire lifetime of the SanAndreas system (20 Myr) only the last 5 Myr are attributedto dextral transpression [Walcott, 1993] which is caused byPacific plate rotation [Luyendyk et al., 1985]. Similarfeatures are reported from paleomagnetic investigations ofthe New Zealand system [Walcott, 1987], and therefore anydirect application of the transpressional model to strainaccumulations in time is problematic.9.3. What Effects Could Explain These Discrepancies?[47] We are unable to correlate succinctly the external andinternal parameters of homogeneous transpression. Thisinconsistency, apart from plate rotation, is well explainedby the three concepts of strain partitioning discussed above.Discrete partitioning results in general decrease of finitestrain accumulations and in increase of pure shear componentin deformed zone. The effects of ductile partitioningbecomes important for narrow wrench-dominated zone (lessthan 30% of the width of the whole transpressional zone)and is responsible for decrease of strain accumulation in thepure-shear-dominated zone and increase in the wrenchdominatedzone. We note that the pure-shear-dominatedzone exhibits all structural characteristics of frontal shortening.Viscosity partitioning is marked by different strainrates in domains of different viscosity leading to differentstrain accumulations. In strongly oblique zones (a
SCHULMANN ET AL.: STRAIN DISTRIBUTION ETG 6 - 13logical data allowing estimate of depth changes throughtime exist but so far are related to intrusions of magmas intranspressional regimes [e.g., Melka et al., 1992; Parry etal., 1997]. Future work should certainly concentrate onacquisition of fabric data together with detailed petrologicalinvestigations, to delimit the depth-temperature regime, andwith geochronological investigations, to understand theduration of transpressional orogeny.9.4. Importance of the Switch of Lineation[52] As an additional result of our modeling, we haveobtained information about the switch of lineation thatdeserves to be mentioned in conclusion. Analysis of thelineation produced by the classical transpression modelshows that the switch of lineation during progressive shorteningof the zone is theoretically possible. However, thecorresponding strain intensities are very high and the degreeof oblateness does not permit meaningful measurement of thechange in the linear fabric. An interesting observation is thatoblate fabrics are measured only exceptionally, more oftenwe have to deal with lineation (vertical or horizontal andclose to plain strain symmetries). In contrast to the model, innature horizontal and vertical lineations are often observedsimultaneously in transpressional zones [Hudleston et al.,1988; Schultz-Ela and Hudleston, 1991; Melka et al., 1992;Tikoff and Greene, 1997]. This fact underlines the ideas ofpartitioning of the strain in transpressional zones [Tikoff andGreene, 1997] or perhaps to later superposition of simpleshear zones on already existing fabrics [Jones and Tanner,1995].Appendix A: Strain Parameters[53] In the transpressional model, computation of thethree-dimensional motion path of rock samples and strainparameters in the transpressive belt are based on thevelocity gradient tensor:0 10 _g 0L ¼ @ 0 _e 0 A: ðA1Þ0 0 _eThe pure shear strain rate component _e (corresponding tovertical extrusion and horizontal shortening) and simpleshear rate component _g (corresponding to lateral horizontaldisplacement) are calculated using the respective equations:_e ¼ n d sin a_g ¼ n cos a;d ðA3ÞðA2Þwhere v is the relative plate velocity, d is zone width, and ais the angle of convergence (Figure 1). In our model we willconsider an example of constant strain rate during temporaldevelopment of a transpressional zone, so for given periodfinite strain parameters can be obtained from followingfinite strain tensor:0_g1_ecos a ½ 1 exp ð _et ÞŠ01F ¼ @ 0 exp ð _et Þ 0 A: ðA4Þ0 0 exp ð_etÞDuring deformation we trace rock samples moving in thetranspressive zone (Figure 1b). At each position of a rocksample we calculate finite strain geometry, i.e., the principaldirections and the principal stretches by taking theeigenvectors and square roots of eigenvalues, respectively,of ‘‘Cauchy-Green tensor’’ FF T [Truesdell and Toupin,1960], which are further used to calculate the parameters Kand D [Ramsay and Huber, 1983, pp. 201–202].[54] Strain intensity is expressed by the D value:qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD ¼ R xy 1 2þ Ryz 1 2: ðA5ÞThe strain symmetry K value is calculated asK ¼ R xy 1R yz 1 ; ðA6Þwhere R xy = S 1 /S 2 and R yz = S 2 /S 3 represent elongationaspect ratios measured on orthogonal axes. Furthermore,when K = 0 a (S) planar fabric is indicated, and for K =1(LS) a plane strain fabric in which foliation is equally strongas lineation, and K = 1 for a linear fabric without foliation.[55] Vertical displacement produced by the pure shearcomponent can be expressed by a valuezt ðÞ¼z 0 exp ð_etÞ;ðA7Þwhere z 0 = z(t 0 ) is the initial vertical distance of a rocksample above a reference level (rigid floor depth) of zeroelevation.Appendix B: Discrete Partitioning[56] To evaluate strain parameters in a domain wherediscrete partitioning operate, we can use above definedapproach using following recalculated values of angle ofconvergence a and R vdtan a 0 ¼tan að1 p 1 ÞðB1ÞqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR 0 vd ¼ R vd ð1 p 1 Þ 2 cos 2 a þ sin 2 a; ðB2Þwhere p 1 is ratio between fault-accommodated lateraldisplacement and total lateral displacement.Appendix C: Ductile Partitioning[57] Ductile partitioning in transpression zone results indecomposition of velocity gradient tensor into two componentsfor pure shear zone (L PSD ) and wrench-dominatedzone (L WDZ ) as follows:010 0 0L PSD ¼ @ 0 _e ð1 p 2 Þ 0 A0 0 _e ð1 p 2 ÞðC1Þ010 _g 0L WDZ ¼ @ 0 _ep 2 0 A; ðC2Þ0 0 _ep 281
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Contentsviii4.7 Schulmann, Konopás
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Dedicated to my wife Markéta, daug
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Foreword 2First topic “Quantitati
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1. Quantitative analysis of deforma
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Chapter 2Mechanisms of lower crusta
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2. Mechanisms of lower crustal flow
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EXHUMATION IN LARGE HOT OROGEN 275m
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Probabi l irequencyProbabi l ireque
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ORIGIN OF FELSIC MIGMATITES 45Fig.
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