CURVAZa program to calculate magnitude and direction of maximum structural curvature and fracture-flow index ?
The total aperture of fold-related extensional fractures within a unit distance is proportional to the structural curvature, which is approximately equal to the second derivative. Eigenvalues and vectors of a Jacobian matrix of a structural surface correspond to magnitude and direction of the maximum and minimum second derivatives. The Jacobian matrix can be determined from structural grid data and used to evaluate both direction and magnitude of principal curvatures and total fracture aperture per unit distance. Two orthogonal sets of extensional fractures are associated with a dome-shaped fold. The main set of extensional fractures strikes perpendicular to the maximum structural curvature. A secondary set of extensional fractures may also be present perpendicular to the minimum curvature. Knowing the direction of extensional fractures also allows the calculation of the aperture reduction as a function of the in-situ stress ratio and angle between fractures and maximum in-situ stress orientation. A computer program, CURVAZ, is introduced to find the direction and the aperture of extensional fractures from second derivatives of a structural surface. The program modifies apertures using in-situ stress information and calculates a fracture-flow index (FFI). The results are presented as stick plot maps, which show both the direction and the magnitude of principal curvatures or FFI.
fracture-flow index eigenvalues jacobian direction and magnitude in-situ stress principal structural curvatures