Quantitative structural analyses and numerical modelling of ...

SCHULMANN ET AL.: STRAIN DISTRIBUTION ETG 6 - 7Figure 4. (a) Diagram showing the development of strain symmetry (K ) in time (parameter k t )forvarious convergence angles (a). (b) Diagram showing the relationship between strain symmetry (K ) andangle of convergence (a) through three time sections (5, 10, and 15 Myr). The curves show only slightdependence of K on the R vd values and on time.[31] However, the RFD is not easily defined in ancienttranspressional zones, and we can make only rough estimatesbased on petrological data and observed depth ofMoho. Such analysis shows that in the case of shear zonesof southern Madagascar the depth in which the rocks wereoriginally located was around 60–70 km [Martelat et al.,1997; Pili et al., 1997]. Martelat et al. and Pili et al. alsosuggested that the lithospheric shear zones are coupled withunderlying mantle so that the RFD may be located evendeeper in the mantle lithosphere [Teyssier and Tikoff, 1997;Vauchez et al., 1998].6. Superposition of Strain Parameters inTranspressive Belts[32] The preceding considerations and results enable us tocreate a type of map of strain parameters registered in rockselevated to the surface. Figure 6 shows such a map whereisolines of strain intensities D and isolines of strain symmetryK are superposed on a diagram of convergence angleagainst time parameter (a - k t space). We have addedcontours of RFD/z 0 to this (dashed curves in Figure 6).These shows the times when the samples are elevated closeto the surface. The ratio RFD/z 0 also expresses the acrosswidthshortening of the zone. The shaded area in a -] k tspace shows the range of naturally observed strain intensities.For these D values (strain intensities) the strainsymmetry parameter K corresponds well with high or lowa (angle of convergence), respectively, for vertical andhorizontal orientation of lineation. On the other hand theintensity of strain (D) is not very sensitive to the angle ofconvergence greater than 20° (pure-shear-dominated transpression)but is strongly dependent on time. For the case ofvery obliquely convergent zones (low a) the time needed toaccumulate observed strain intensities are almost twice aslong as for high convergence angles. The maximum strainsat the right side of the shaded area in Figure 6 may beattributed to rock samples elevated from thickened midcrustaldepths (40 km) of transpressional zones. However,this is only valid for zones with convergence angles >50°.For more oblique zones, only very shallow samples (uppermost25% of the zone) can be exhumed. This also meansthat horizontal stretching lineations may be exhumed fromvery shallow depths in soft transpressional zones.7. Effects of Strain Partitioning on TemporalStrain Parameter Development[33] Next we examine the effects of three different typesof strain partitioning on the temporal development of finitestrain parameters.[34] Discrete displacement partitioning is modeled usingan approach of Teyssier et al. [1995]. In their model,variable amounts of total lateral displacement can be consideredto be consumed by discrete faulting. This isexpressed by a ratio p 1 between fault-accommodated lateraldisplacement and total lateral displacement. The evolutionof strain parameters in the viscous domain of homogeneous75