TRANSIENT CREEP OF A COMPOSITE LOWER CRUST .1. CONSTITUTIVE THEORY

A composite model is proposed to describe the time-dependent response of the Earth's lower crust. The motivation for such a model is twofold : First, new observations of widespread postseismic deformation indica te that the deep continental crust responds viscoelastically, having b oth long- and short-term decay times. Second, by any number of observa tionally based rationales, the lower crust is compositionally and stru cturally heterogeneous over many length scales. For heterogeneities th at have much smaller characteristic lengths than the minimum deformati on wavelength of interest, the aggregate rheology can be described by composite media theory. For wavelengths of the order of the thickness of the lower crust (approximate to 25-40 km) and larger, composite the ory may be applied to heterogeneities that are smaller than about seve ral hundred meters, or equivalent to the vertical extent of a thick lo wer crustal mylonitic shear zone. The composite media theory developed here is constructed using both Eshelby-Mori-Tanaka theory for aligned generalized spheroidal inclusions and a generalized self-consistent m ethod. The inclusions and matrix are considered to be Maxwellian visco elastic: a rheology that is consistent with past homogeneous models of postseismic stress relaxation. The composite theory presented here in troduces a transient response to a suddenly imposed stress held which does not appear in homogeneous Maxwell models. Analytic expressions fo r the amplitude and duration of the transient and for the effective lo ng- and short-term viscosities of the composite are given which descri be the sensitivity to inclusion concentration (phi), to shape, and to ratio of inclusion-to-matrix viscosity (R).