Quantitative structural analyses and numerical modelling of ...

5 - 14 LEXA ET AL.: COLLISION IN WEST CARPATHIANSthe structural evolution in the weak domain represented by theGemer Unit. Such a type of modeling could be used tovalidate chosen boundary conditions, i.e., the role of rigidpromontories for complex structural evolutions in terrainswith polyphase deformation.5.2. Timescales of the Proposed Model[44] The timescale of the model is controlled by velocity ofthe indenting block. We have chosen the arbitrary velocity of1 cm/yr for the sake of simplicity. However, in the caseof Vepor and Gemer Units, we can define the velocity ofmovement of our kinematically fixed system. On the basis ofthe knowledge of approximate initial width and stratigraphicrecord of the Mesozoic (Fatric) basin in front of theVepor basement [Plašienka, 1997], the rate of shortening isestimated to be about 1 cm/yr, and the duration of theshortening process is estimated at about 20 Myr. Plašienka[1997] also demonstrated that the original frontal closure ofthe Fatric Basin passed to transpressive movements after20 Myr. This means that the differential movement of rigidindenter, which moves together with the whole kinematicsystem, has to generate a defined finite strain at the sameperiod of time. Moreover, the initiation of TGSZ activity maycorrespond to a transition from frontal to transpressionalmovements recorded in the northern edge of the wholekinematic system. Once this rough timescale is established,then the absolute velocity of our indenter should be four timesslower than suggested in the model to generate the observedstrain pattern.5.3. Development of Topography, Exhumation, andAsymmetry of GCF[45] The model allows estimation of average verticalstrains and, because of a fixed lower boundary condition,also the vertical elevation. We can expect that the surfaceelevation represent local topography generated by shorteningof the viscous sheet. The lateral distribution of topographyfollows the exponential distribution of finite strain inareas of pure shear-dominated deformation. Figure 8dshows the distribution of topography in front of an indentingblock after 7 Myr of shortening. It is to be noted that thedomain of highest topography follows the axial zone of theGCF, where the degree of metamorphism associated withthe development of cleavage is most important.[46] Although our model predicts vertical cleavage in theentire domain, we observe that the cleavage forms a positivefan-like structure. We interpret this pattern as a result ofdifferent amount of vertical shortening due to differentgravitational potential across the GCF. This mechanism ismanifested by the development of late kink bands with kinkplanes perpendicular or oblique to strongly developed verticalcleavage.Appendix A[47] The equations governing the deformation of a thinviscous sheet were published by England and McKenzie[1982]. We provide here the derivation of equations for thesimplest case of Newtonian rheology as they have beenused for our modeling. The model assumes a relatively thinviscous plate with no tractions at top and bottom surfaceand negligible vertical gradients of horizontal velocitycomponents. Creep equation reads@t ij@x j¼ @p@x iðA1Þwhere T is the deviatoric stress tensor and p is the pressure,and repeated index means summation. Assuming a linearconstitutive relationt ij ¼ 2h_e ijequation (1) can be written as2h @_e ij@x j¼ @p@x i[48] The strain rate tensor of the form01_e 11 _e 12 0_E ¼_e 21 _e 22 0BC@A0 0 _e 33ðA2ÞðA3ÞðA4Þis assumed. Then the equation containing the vertical strainrate _e 33 reduces to2h @_e 33@x 3¼ @p@x 3ðA5Þ[49] Integrating the equation over the vertical dimensionx 3 , we obtain2h_e 33 ¼ p þ fðx 1 ; x 2 Þ ðA6Þwhere the upper strike means vertical average. Because ofthe model assumptions we can put f (x 1 ,x 2 ) = 0 everywhere.We substitute from equation (A6) in the first equation (A3)integrated over the vertical dimension and obtain2h @ _e 1j@x j¼ @p@x 1¼ 2h @ _e 33@x 1and similarly for the second equation. The resulting equationscan be written as@_e ij@x j@_e 33@x i¼ 0 i ¼ 1; 2; j ¼ 1; 2 ðA7Þwhere we omit the signs of vertical averaging. Massconservation for incompressible flow requires that_e 33 ¼ ð_e 11 þ _e 22 Þ ðA8Þ98