Effects of rigidity layering, gravity and stress relaxation on 3‐D subsurface fault displacement fields

SUMMARY Elastic dislocation theory has been modified to determine 3‐D subsurface displacements for faults in a three‐layer elastic‐gravitational medium. A new set of kernel functions for Fourier‐Bessel integrals describing subsurface displacements have been derived, using the Thomson‐Haskell propagator matrix technique, and has been used to investigate the effect of layering and gravity on subsurface displacement fields. Within our three‐layer model, layer 1 may be used to represent the seismogenic upper crust, layer 2 the ductile lower crust and layer 3 the ductile mantle. For a point source within the upper layer, lower layer rigidity moduli control the amplitude and wavelength of displacements within the upper layer and the relative distribution of uplift and subsidence within foot and hanging wall. Displacement variations, due to lower layer rigidity moduli changes, increase with depth and are profound at the base of the upper layer and within the lower layers. High‐rigidity‐moduli lower layers attenuate the upper layer displacement field, while a decrease gives amplification. The effect of gravity on the subsurface displacement field is more pronounced when the rigidity of the lower layers is small. The elastic‐gravitational dislocation model has been used to examine co‐seismic and post‐seismic components of surface and subsurface displacement during extension of continental lithosphere. The model predicts surface co‐seismic footwall uplift and hanging‐wall subsidence; the co‐seismic subsidence being greater than the uplift. Post‐seismic relaxation of stress within the lower crust and mantle by post‐seismic ductile deformation, gives an increase in footwall uplift and a decrease in maximum hanging‐wall subsidence within the upper layer. A decrease in upper layer rigidity due to post‐seismic brittle or plastic deformation within the upper crust leads to a decrease in the wavelength of surface footwall uplift and hanging‐wall subsidence. The elastic‐gravitational dislocation model has also been used to investigate the development of Moho topography during continental extension. Co‐seismically Moho under footwall is predicted to uplift, while that under hanging wall subsides but by a smaller magnitude. During post‐seismic relaxation Moho topography is predicted at first to increase in magnitude and then to decay. The existence of preserved Moho topography uplift associated with old continental rifts implies a finite long‐term ductile strength within the lower crust and mantle.