An analytical model of hanging-wall and footwall deformation at ramps on normal and thrust faults

We determine stress, strain and structural evolution for an analytical model of moderate angle (10-20 °) ramps developed on both normal faults (normal ramps) and thrust faults (thrust ramps). In the model, a frictionless sliding surface with ramp configuration separates two incompressible, isotropic, viscous half-spaces of different viscosity (η-hanging wall and η′-footwall). Ramps are planar, but ramp-flat corners are locally rounded. Deformation is due solely to translation across the ramp, and regional extension or shortening is ignored. Sliding down a normal ramp causes vertical extension and horizontal shortening in both the hanging wall and the footwall. This conforms with reverse faults seen in experimental models of normal ramps. The stress in the footwall has the same magnitude as that in the hanging wall but the footwall strain rate is reduced in magnitude by the ratio η/η′. Both a hanging-wall syncline and a footwall anticline form. The normal ramp migrates in front of the rising footwall at a rate V_ss = V[η/(η + η′)], where V is the sliding velocity. But the ramp does not change shape. The continuous ramp motion in the model may correspond to the creation of an extensional duplex or chaos zone in brittle rocks. At a normal ramp, mean compressive stress is lowered and deviatoric stress is raised, favoring local faulting and fracture. Sliding up a thrust ramp causes stresses, strain rates and strains of the opposite sign. Horizontal extension and vertical shortening in both walls is consistent with normal faulting. Both a hanging-wall anticline and a footwall syncline form passively. Although the deviatoric stress is raised at the ramp, so is the mean compressive stress, inhibiting fracturing. However, the mean compressive stress is lowered on the adjacent flats, favoring fracturing there.