Short- and Middle-Term Earthquake Precursors

Earthquakes are commonly believed to result from slip instability along a fault or from formation of a new fracture that is near the direction of maximum shear stress. The behavior of a geomechanical system as it approaches instability, or catastrophic failure, has been described in earlier work by the author [Dubrovskiy, 1984; Dubrovskiy and Sergeev, 2004] as a "short-term universal precursor" theorem. According to this theorem, if the system has the state of the unstable equilibrium at some set of the critical parameters describing it and this set separates areas of the parameters values relevant to a stable state and unstable state of the system then in stable parameters area external load would cause eigen oscillation of the system with frequencies, which will tend to zero if the system approaches unstable equilibrium at the finite critical wavelengths. Thus prior to an earthquake, one should be able to observe slow oscillations with a frequency that tends to zero as the earthquake approaches. In a system where friction is velocity and displacement dependent, the predicted perturbing oscillations are fault-zone trapped waves. They are propagating along fault (their amplitude attenuates exponentially perpendicular to the fault) and perturbing fault slip speed [Li, Leary, Aki, Malin, 1990]. If trapped waves amplitude is growing with time then the process of the fault slip with uniform speed became unstable and slip instability takes place according to principle of the linear instability. Physically it means that energy is pumping from basic state of the uniform fault slip speed to the trapped waves as the disturbance of this state. The dispersion relation of the trapped waves resembles the well known Rayleigh wave equation; however, the right-hand side of the equation is not zero but a term that depends on friction and wave number [Dubrovskiy and Dieterich, 1990]. At the limit of zero frequency, the trapped waves dispersion equation have solution for some critical wave length only if the friction coefficient has an inverse dependence on displacement, i.e. then the condition of the universal precursor theorem is fulfilled and decreasing of trapped wave frequency (and thereby phase velocity) will be short term precursors of the catastrophic slip instability along fault (earthquake). Such an inverse dependence is known as "friction memory" and means that during slip the opposing fault surfaces become smoother. The value of the inverse dependence on displacement determines some characteristic wave length and consequently the locked and slipping parts of the fault surface will appear. These trapped waves are "short-term" precursors to failure. To look for "middle-term" precursors, we turn to the phenomenon of creep, or plastic behavior, that is observed in the laboratory or in nature prior to failure. Linearizing and solving the linearized equations of ideal plasticity, we find that kx/ky≡ cx/cy=tanα (or -cotα), where kx and ky are x and y components of the wave vector k and cx and cy are x and y components of the phase velocity c, α is the angle between the direction of maximum shear stress (actually fault direction in the case of a new fracture) and x axis. Thus, one could observe the onset of seismic wave anisotropy as a "middle-term" precursor to an earthquake. The time behavior of this "middle-term" precursor can be obtained by solving the full time depended plasticity equations. I am grateful to Gary Fuis (USGS) for useful discussions. This work was supported by Russian Foundation for Basic Research, project no. 03-05-64087.