Quantitative structural analyses and numerical modelling of ...

LEXA ET AL.: COLLISION IN WEST CARPATHIANS 5 - 15Thus2 @_e 11þ @_e 12þ @_e 22¼ 0@x 1 @x 2 @x 1@_e 11þ @_e 21þ 2 @_e 22¼ 0@x 2 @x 1 @x 2ðA9Þ[52] Although we compute the horizontal velocity field,the vertical strain rate can be estimated by equation (8) thatallows us to assess at every step the tensors of instantaneousand finite deformation and related parameters of deformation,such as intensity[50] We replace the strain rate tensor by horizontalcomponents of velocity u 1 , u 2_e ij ¼ 1 @u iþ @u jðA10Þ2 @x j @x iand finally obtain a system of elliptic partial differentialequationssymmetryqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD ¼ R xy 1 2þ Ryz 1 2ðA12ÞK ¼ R xy 1 R yz 1 ðA13Þ4 @2 u 1@x 2 1@ 2 u 2@x 2 1þ @2 u 1@x 2 þ 3 @2 u 2¼ 02@x 1 @x 2þ 4 @2 u 2@x 2 þ 3 @2 u 1¼ 02@x 1 @x 2ðA11Þand orientations of lineations and foliations. Because of theassumed form of the strain rate tensor, equation (A4), themodel can produce only horizontal or vertical lineations andfoliations and can be regarded as generalized (locallyvariable) transpression.[51] The system can be solved by the finite elementmethod. Dirichlet and Neumann boundary conditions maybe applied to segments of the domain boundaries so thatthey correspond to geological settings (rigid indenter, freeinflow or outflow of material).[53] Acknowledgments. We are grateful to the Geological Survey ofthe Slovak Republic for significant financial support during the initialstages of our research. This work has been also supported by the CharlesUniversity Agency grant 216/1999/B-GEO. The salaries of K. Schulmannand O. Lexa were covered by Ministry of Education grant 24313005.ReferencesAllemand, P., and J. M. 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