Elastostatic simulation of dislocation sources in heterogeneous stress fields and multilayered media having irregular interfaces

Abstract

We present an extension of the 2D discontinuity method of Crouch (1976) to simulate dislocation sources in multilayered media having irregular interfaces and surface topography. The magnitudes of dislocations on a given line segment are treated as unknowns that are solved for by satisfying stress or displacement boundary conditions at the center of each line segment. The interaction between dislocation sources within a layer is taken into consideration using analytical kernel functions of homogeneous media. The free surface is simulated by placing dislocation source segments on it and demanding the stress to be zero. Layer interfaces are simulated using dislocation source segments on both sides of the interfaces. The magnitudes of these secondary sources are estimated demanding continuity of stress and displacement on one side of each interface segement. Propagator matrices are introduced to relate the source distributions on neighbouring layers. A simulated vertical dike in a layered medium shows that layering is able to alter the intrusion form and the surface uplift above the intrusion.