The effect of neotectonic movements on the gradients and curvatures of theNorthern Eurasian lithosphere surface

The data on neotectonic vertical crustal movements (VCM) incorporated in th e neotectonic map of North Eurasia on the scale 1 : 5000000 [Grachev, 1997] are used to study the geometric characteristics of surface deformations of the North Eurasia lithosphere and to map the modulus of the VCM amplitude gradient Grad, mean curvature K-mean, Gaussian curvature H, and curvature i ntensity K-int. Kinematic VCM patterns in main geostructural zones and in i ndividual regions within these zones are analyzed. Multivariate statistical methods are used to reveal correlations between various geometric characte ristics in both the geostructural zones distinguished on the map and indivi dual regions. Factors influencing the variability of the study characterist ics are determined. Analysis of the correlations and geometric interpretati on of the results art: based on the classification of surfaces accepted in differential geometry and, in particular, on our study of gradients and cur vatures of some model surfaces. It is suggested that the results obtained i n this work make it possible to classify neotectonic structural forms not o nly according to the activity of vertical movements but also on the basis o f a complex of much more subtle features (the values of specific curvature characteristics and correlations between them). It is shown that the surfac e-averaged curvature intensity K-int, which is introduced as the modulus of half-difference between principal curvatures, is determined most reliably as compared with other curvature characteristics. Along with the kinematic meaning of the K-int value, this leads to the conclusion that the surface-a veraged curvature intensities can be regarded as a scalar parameter that mo st reliably and adequately characterizes the deformation patterns in most r egions. The applicability of the results obtained in this work to the deter mination of tectonic stress fields and crustal shortening are discussed. Th is paper is supplemented by appendixes that define the quantities used and their main quantitative relationships.