Surface shear stress, strain, and shear displacement for screw dislocations in a vertical slab with shear modulus contrast

Abstract

Shear stresses, strains, and shear displacements on the free surface of a three-phase half-space (i.e. a half-space containing a vertical slab) produced by screw dislocations within the slab have been determined for shear modulus ratios in the range 0.10 G p slab/p half-space G 10.0 and depths of 1.0-10 km. Normalized quantities were computed using the ratios of stress, strain, or displacement in the three-phase material t o those which would exist in a homogeneous medium. For modulus ratios less than 1.0, increasing the burial depth of the dislocation increases the normalized quantities, and the quantities decrease with increasing dislocation depth for modulus ratios greater than 1 .O. With a modulus contrast of 0.25, which msy be representative of parts of the San Andreas fault zone, and a single dislocation in the slab, increasing the dislocation depth from 1.0 to 10.0 km increases the normalized stress maximum from 0.45 to 0.95 and the normalized strain maximum from 1.7 to 3.8 in the slab. Nomialized displacements are significantly different from 1.0 only within 1-2 fault-zone thicknesses of the dislocation. As the modulus ratio is changed from 1 .O t o 0.25, and with only a single dislocation in the slab, the fraction of the displacement occurring within the fault zone to total displacement nearly doubles. A slip zone in the slab of finite width, modelled using a pair of dislocations with opposing Burger's vectors, causes the normalized quantities to decrease as the distance between the dislocations decreases.

Geodetic Evidence for a Near-Fault Compliant Zone along the San Andreas Fault in the San Francisco Bay Area

“…The difference between the homogeneous and inhomogeneous models will be most pronounced very close to the fault. When compared to a homogeneous elastic half-space model, an elastic model with a compliant zone surrounding the fault predicts very similar (slightly smaller) strains in the far field, but substantially higher strains near the fault (McHugh and Johnston, 1977;Rybicki and Kasahara, 1977).…”

“…Lisowski et al (1991) presented a lateral inhomogeneous model with a narrow zone of compliant material near a fault to explain the abrupt inflection in the velocity profile at Point Reyes. In general, if a fault is embedded in a compliant (lower rigidity) zone, the use of a simple homogeneous elastic half-space model results in an underestimate of the locking depth (McHugh and Johnston, 1977;Rybicki and Kasahara, 1977). The difference between the homogeneous and inhomogeneous models will be most pronounced very close to the fault.…”

Continuous strain measurements during and preceding episodic creep on the San Andreas Fault

“…It is possible that the strains at these locations are of smaller amplitude, owing to a substantially decreased shear modulus in the fault zone. The results of McHugh and Johnston [1977] indicate that the concentration of strain fields near the fault due to about a factor of 4 decrease in fault zone rigidity could result in attenuated strain changes at the measurement points by up to a factor of 8. If this is the case it is possible that the strains expected from Frank's [1973] model would not be clearly distinguishable in these data.…”

Bulk and shear moduli of near-surface geologic units near the San Andreas fault at Parkfield, California

“…Models of weak vertical fault systems have been developed by Kasahara and Rybicki (1977), McHugh and Johnston (1977), Mahrer (1986), and others. The difficulty with these models was the absence of constraints on \ JL and K. The values observed here indicate that the shear modulus, or rigidity, may be as much as 10 times lower in the near-fault regime than in more competent rocks found at greater distances from an active fault system.…”