  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.
