Quantitative structural analyses and numerical modelling of ...

ETG 6 - 4 SCHULMANN ET AL.: STRAIN DISTRIBUTIONFigure 2. (a) Diagram showing relation between strain intensity (D) and time (expressed by timeparameter, k t , where t = k t /R vd ). The dot-dashed curves show time evolution of D for different angle ofconvergence (a). The distribution curve at the left shows the envelope of natural strains summarized byPfiffner and Ramsay [1982], Hrouda [1993], and others. The horizontal line through the maximum (at D =1.2) shows the strain observable by field measurements. (b) The relationship between strain intensity (D)and angle of convergence (a) through three time sections (5, 10, and 15 Myr). The contours show variationsof R vd values, which distinguish narrow and fast converging transpressive orogens (R vd > 0.5) from wideand slowly converging ones (R vd < 0.5). Vertical lines at convergence angles 30° and 50° show strainaccumulations for R vd values of active transpressive zones in New Zealand and Sumatra, respectively.suggests that the base of lithospheric transpressional zonesis not always present as a rigid floor. In such a case, verticalmovements within the system are controlled by isostaticalresponse and can thus lead also to downward motion ofmaterial early in the shortening history.4. Modeling of Internal Parameters ofTranspressional Systems[16] We calculate the internal strain parameters of transpressionalsystems (strain rate, finite strain intensity, andsymmetry and orientation of finite strain axes) in terms ofexternal parameters defined above. The description ofmethod of calculations and derivation of equations are givenin Appendices A–D.4.1. Strain Rates and Finite Strain Intensities[17] The first result of our model is that in the range ofassumed R vd , a strain rate interval from 10 14 s 1 to 10 16s 1 is obtained. This is within the range of generallyassumed strain rates extrapolated from experimental laboratorydata [Carter and Tsenn, 1987] and corresponds wellto that deduced for natural orogens by Pfiffner and Ramsay[1982]. Theoretical curves of finite strain accumulation fordifferent obliquities are presented in Figure 2b. In Figure 2bthe strain intensity parameter D (see Appendix A) is plottedon the vertical axis against the time parameter, k t , whichrelates the time of deformation with R vd , the ratio ofconvergence velocity and initial zone widthk t ¼ tR vd :The introduction of such a time parameter follows from thedefinition of the transpression model and allows us to graphthe temporal developments corresponding to zones ofdifferent width and convergence velocities (Figure 2a). Ifthe ratio R vd = 1, the scale of the k t axis represents timedirectly in million years. For other R vd values we obtain thecorresponding time from equation (1).[18] In order to compare Figure 2a with those on Figure 7of Pfiffner and Ramsay [1982] each of the curves calculatedfor convergence angles varying from a =0° to 90° is labeledwith its strain rate value. Because of the triaxial character ofthe deformation in transpressive zones we use a strain ratecalculated as rate of change of the square root of theminimum eigenvalue corresponding to short axis of instantaneousstrain tensor, and instead of R = X/Z, which is a goodcharacteristic for plane strain we use the D parameter.ð1Þ72