Displacement Field due to Nonuniform Slip along a Long Dip-Slip Fault in Two Welded Half-Spaces

The solution of static deformation of two homogeneous, isotropic, and perfectly elastic half-spaces in welded contact due to a long dip-slip fault with uniform slip is well known. The aim of the present article is to obtain the static deformation of two homogeneous, isotropic, and perfectly elastic half-spaces in welded contact due to nonuniform slip along a long dip-slip fault. The fault is vertical and lies entirely in the lower half-space, extending up to the interface. Four slip profiles are considered: linear, parabolic, elliptic, and cubic. Closed-form expressions for the elastic residual field have been obtained for the different slip profiles. The displacement field due to four nonuniform slip profiles is compared with the displacement field due to uniform slip. For comparison, we have assumed the source potency for different slip profiles to be the same, which is achieved by taking the fault slip at the interface constant and varying the fault width. It is found that the displacement field varies significantly at the fault width rather than at the interface. Moreover, uniform slip along the fault makes the edges singular. This singularity at the lower edge is not present in the case of nonuniform slip along a long dip-slip fault.