General expressions for internal deformation fields due to a dislocation source in a multilayered elastic half-space

Abstract

S U M M A R YWe have obtained general expressions for internal displacement and stress fields due to a point dislocation source in a multilayered elastic half-space under gravity. Most previous expressions for the internal deformation fields were obtained by applying one of two different types of Thomson-Haskell propagator matrix, namely the up-going propagator matrix proposed by Singh (1970) and the down-going propagator matrix proposed by Sato (1971). The solution derived with the up-going propagator matrix is stable below the source, but becomes unstable above the source. In contrast, the solution derived with the down-going propagator matrix is stable above the source, but becomes unstable below the source. We succeeded in unifying the up-going and the down-going propagator matrices into a generalized propagator matrix, and applied it to obtain general expressions that are stable at any depth. By integrating the effects of point sources distributed along an infinitely long horizontal line, we also obtained general expressions for a line dislocation source. We give some examples of internal displacement fields computed with these expressions to examine the effects of layering. Applying the correspondence principle of linear viscoelasticity to the derived elastic solutions, we can obtain the internal viscoelastic displacement and stress fields due to dislocation sources.

Fault slip rates and interseismic deformation in the western Transverse Ranges, California

“…The shear modulus values inferred from seismic velocities [ Kohler et al ., ; Magistrale et al ., ] show that the Ventura Basin near the coast is rather broad, with low‐modulus sediments near the surface down to ~5 km depth, while to the west, the basin has a more localized and irregular shape (Figures ). Numerous existing studies have shown that low‐modulus, near‐surface material can greatly affect resultant surface deformation around slipping faults [e.g., Fay and Humphreys , ; Fialko , ; Fukahata and Matsu'ura , ; Hager et al ., ; Savage , ; Schmalzle et al ., ; Wang et al ., ]. To investigate the first‐order effects of these low‐modulus sediments on interseismic deformation patterns, we present results from kinematic dislocation models that incorporate a layered elastic half‐space using the solutions of Fukahata and Matsu'ura [].…”

“…Numerous existing studies have shown that low‐modulus, near‐surface material can greatly affect resultant surface deformation around slipping faults [e.g., Fay and Humphreys , ; Fialko , ; Fukahata and Matsu'ura , ; Hager et al ., ; Savage , ; Schmalzle et al ., ; Wang et al ., ]. To investigate the first‐order effects of these low‐modulus sediments on interseismic deformation patterns, we present results from kinematic dislocation models that incorporate a layered elastic half‐space using the solutions of Fukahata and Matsu'ura []. In all models presented here, the layered half‐space contains two horizontal layers.…”

3-D Simulation of Tectonic Loading at Convergent Plate Boundary Zones: Internal Stress Fields in Northeast Japan

“…The concrete expressions of the slip-response functions T ij for the gravitating elasticviscoelastic layered structure model are given in MATSU' URA et al (1981) and FUKAHATA and MATSU'URA (2005). Now we decompose the fault slip w into the steady slip at a plate convergence rate v pl and its perturbation Dw as…”

Geometric evolution of a plate interface–branch fault system: Its effects on the tectonic development of the Himalayas

“…The viscoelastic response to a unit step slip q(x,t;x 0 ,s) can be derived from the solution of the associated elastic problem (Sato and Matsu'ura, 1973;Fukahata and Matsu'ura, 2005) by applying the correspondence principle of linear viscoelasticity (Lee, 1955;Radok, 1957). As to the mathematical techniques to derive the concrete expressions for the viscoelastic step-response, refer to the series of papers by Matsu'ura and his co-workers (Matsu'ura et al, 1981;Sato and Matsu'ura, 1988;Matsu'ura and Sato, 1989).…”