Seeing the Earth crust as crisscrossed by faults filled with fluid at close to lithostatic pressures, we develop a model in which its elastic modulii are different in net tension versus compression. In constrast with standard nonlinear effects, this ``threshold nonlinearity is non-perturbative and occurs for infinitesimal perturbations around the lithostatic pressure taken as the reference. For a given earthquake source, such nonlinear elasticity is shown to (i) rotate, widen or narrow the different lobes of stress transfer, (ii) to modify the $1/r^2$ 2D-decay of elastic stress Green functions into the generalized power law $1/r^{gamma}$ where $gamma$ depends on the azimuth and on the amplitude of the modulii asymmetry. Using reasonable estimates, this implies an enhancement of the range of interaction between earthquakes by a factor up to 5-10 at distances of several tens of rupture length. This may explain certain long-range earthquake triggering and hydrological anomalies in wells and suggest to revisit the standard stress transfer calculations which use linear elasticity. We also show that the standard double-couple of forces representing an earthquake source leads to an opening of the corresponding fault plane, which suggests a mechanism for the non-zero isotropic component of the seismic moment tensor observed for some events.
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