Analytical and experimental study of simple geologic structures

An analytical method is derived which gives the elastic response of a homogeneous rock layer to two-dimensional distributions of vertical displacement applied along its lower boundary. Displacement field, stress distribution, and distortional strain-energy density diagrams are presented for three types of displacement applied at the lower boundary of 5-km thick layers possessing average sedimentary rock properties. These three types of displacement are: (1) sinusoidal vertical displacement and no horizontal displacement; (2) an approximate step in vertical displacement and no horizontal displacement; and (3) sinusoidal vertical and horizontal displacement (horizontal displacement 90 degrees out of phase with the vertical). Displacement fields and stress distributions for each type of applied displacement are nearly independent of the elastic characteristics of the layers. The magnitudes of displacement necessary to initiate fracture at some point in the layer are small (3.7-8.2 m) for the three types of applied displacement. For applied displacement (1) and (3), the initial fracture is a vertical tensile crack at the crest of the fold. For applied displacement (2), the initial fracture is either a vertical crack at the upper surface or a shear fracture at the lower surface.