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1 Acta Geophysica Polonica

1 1999

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Splitting stress motion equation into seismic wave and fault-related fields

Teisseyre R., Yamashita T.

Acta Geophysica Polonica

1999

Vol. 47, nr 2

135-137

Considering elastic continuum with defects (strictly speaking: continuum with a continuous distribution of the self-strain nuclei, like in thermo-elastic or elasto-plastic bodies), we have to consider the elastic and self parts of the total strain and stress fields. Accordingly, we can split the motion equations (as expressed for stresses) into a wave field and a fault-related field, assuming that the self stresses play a decisive role on a fault. We show that the fault constitutive equation is a special case of the motion equation. The fault-related equation can be transformed into equation for dislocation density, identical with the 1D equation for evolution of dislocation field equivalent to the commonly considered fault slip constitutive equation. We discuss the fault equation as expressed in terms of dislocation field and we consider the static and dynamic approximations. Static approximation relates to the early phases: the infaltion phase from dislocation stress resistance to friction (phase characterized by an exponential decrease of stress resistance which corresponds to dislocation velocity increase in the expotential creep) and the fracture slip nucleation phase (governedby slip weakening law). Dynamic approximation relates to the slip propagation phase (governed by slipp velocity weakening law). Instead of the instability source introduced by the friction weakening laws for all these phases, we might introduce the source/sink function; such a function should first of all describe the coalescence processes between the dislocations of opposite sings (such an elementary process preserves material continuity) and also between the dislocation arrays of opposite sings (such a coalescence of the arrays can well describe a nucleation process of a crack-material fracturing, or/and a coalescence of two cracs).When the put this function proportional to a stress surface curvature, or equivalently a gradient of dislocation density on a fault, it will represent an inverse of a mean distance between the opposite dislocation groups; we image, in this way, and ability to create a coalescence process - and instability. Atraction forces between the opposite dislocations can effectively produce a weaking effect, making it easier for a dislocation (or crack) to propagate. Some exaples of the numerical solutions for stresses on a fault with the spontaneously simulated seismic events are discussed. From the fault solution we obtain an evolution pattern of a dislocation field; the respective values on a fault plane may then serve as the boundary conditions to slove the wave part equation for stresses in the 2D space and time domain.