ScienceWeek

GEOPHYSICS: TIDAL STRESS, WATER WELLS, AND EARTHQUAKES

The following points are made by Christopher H. Scholz (Nature 2003 425:670):

1) The respective absence and presence of two phenomena associated with earthquakes has been puzzling geophysicists for more than a century. One is the general lack of correlation between earthquakes produced by tectonic forces and the "solid Earth tides" caused by the oscillating stresses created in Earth's crust by the gravitational forces exerted by the Sun and the Moon. The other is that some water wells are extraordinarily sensitive to the seismic waves of distant earthquakes(2).

2) If earthquakes have simple behavior, in which stress on a fault builds up to some threshold at which the fault fails, then one would expect their occurrence to correlate with the daily Earth tides. After many increasingly sophisticated studies, no such general correlation has been found. Yet it has been recently recognized that changes in "static stress" from earthquakes can trigger other earthquakes(3), even when the stress change is as low as 1 kilopascal (4) -- which is roughly the same magnitude of effect associated with Earth tides.

3) Beeler and Lockner(1) conducted rock friction experiments in the laboratory to simulate the situation of a small sinusoidal loading (the Earth tide) being superimposed on linear loading (a fault being loaded tectonically). The laboratory equivalents of the earthquake cycle are "stick–slip" events, in which frictional stress builds up at a "fault" until its adjacent sides begin to slip and a slip instability occurs. Beeler and Lockner mapped the amplitude of the oscillating stress necessary to produce correlation with stick–slip events as a function of the oscillation period. They found two regimes. For oscillations with periods greater than a critical time, the correlation amplitude decreases as 1/f, where f is the frequency of the oscillation. This is just as would be expected from a model -- the Coulomb threshold model -- which assumes that failure occurs at the peak stress. At periods shorter than the critical time, they found that the correlation amplitudes become frequency independent and are orders of magnitude larger than expected from the Coulomb model.

4) The key point is that the stick–slip instability in rock friction is not abrupt. Rather, it follows a nucleation phase, in which the rate of slip increases as an inverse power law of the time to failure, leading to a peak in stress. Fault failure occurs following the peak. The critical time dividing the two correlation regimes corresponds to the duration of nucleation, which is inversely proportional to the linear stressing rate. This nucleation requires that frictional resistance increases with slip velocity and decreases with slip displacement. Beeler and Lockner have constructed a friction law incorporating these properties -- a simple form of rate-state variable friction(5) --and show that it correctly predicts the behavior in the high-frequency regime.

References (abridged):

1. Beeler, N. M. & Lockner, D. A. J. Geophys. Res. B 108, doi:10.1029/2001JB001518 (2003)

2. Brodsky, E. E., Roeloffs, E., Woodcock, D., Gall, I. & Manga, M. J. Geophys. Res. B 108, doi:10.1029/2002JB002321 (2003)

3. Stein, R. S. Nature 402, 605-609 (1999)

4. Ziv, A. & Rubin, A. M. J. Geophys. Res. 105, 13631-13642 (2000)

5. Scholz, C. H. Nature 391, 37-42 (1998)

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