  In this paper we consider the one dimensional spring-block model describing
earthquake faulting. By using geometric singular perturbation theory and the
blow-up method we provide a detailed description of the periodicity of the
earthquake episodes. In particular, the limit cycles arise from a degenerate
Hopf bifurcation whose degeneracy is due to an underlying Hamiltonian structure
that leads to large amplitude oscillations. We use a Poincar\'e
compactification to study the system near infinity. At infinity the critical
manifold loses hyperbolicity with an exponential rate. We use an adaptation of
the blow-up method to recover the hyperbolicity. This enables the
identification of a new attracting manifold that organises the dynamics at
infinity. This in turn leads to the formulation of a conjecture on the
behaviour of the limit cycles as the time-scale separation increases. We
illustrate our findings with numerics and suggest an outline of the proof of
this conjecture.
