Crustal Deformation and Fault Mechanics

Strain Measurements and Earthquake Forecasting

A basic tenant of elastic rebound is that elastic strain accumulated between earthquakes is released in seismic slip events. It has long been assumed that measurements of strain accumulation can be used to forecast future earthquakes. One simple model, known as the time predictable model, posits that a future earthquake will occur when the strain relieved in the most recent quake re-accumulates. Another model, known as the slip predictable model, suggests that all of the accumulated strain is released, so that although the time of the earthquake is unpredictable, its magnitude can be forecast.

We test these models using geodetic measurements from the Parkfield segment of the San Andreas Fault. Parkfield is an ideal place to test these and other concepts. It is arguably the best-instrumented fault segment in the world. Magnitude 6 earthquakes have occurred there in 1932, 1966, and most recently in 2004. Based on patterns of previous shocks, the U.S. Geological Survey forecast that a M 6 event would occur in 1988 +/- 5 years. Geodetic measurements have been made in Parkfield since the early 1960’s so that we can invert for the slip distribution in the 1966 quake, as well as the aseismic slip-rate distribution during the interseismic period between 1966 and 2004.

The average velocities of GPS stations in the Parkfield region are shown in the figure below.

Using these measurements and the concepts of linear inverse theory, we are able to estimate the slip-rate distribution as a function of along-strike distance and depth, as shown in the figure below. Parkfield is transitional between the central creeping zone of the San Andreas and the 1857 locked zone. We find that the Parkfield segment is creeping near the earth’s surface but largely locked at seismogenic depths. If the fault slip lags the long-term geologic rate then strain must be accumulating.

We estimate the moment of the 1966 earthquake from the early trilateration measurements. Using a bootstrap procedure we determine the PDF of the moment of the 1966 quake, as shown in (a) in the figure below. From the inversions above we determine the PDF of the moment deficit-rate (b). That is the integrated rate the fault lags the geologic slip-rate.

Finally, from the ratio of these quantities we estimate the time required to accumulate the moment released in the 1966 quake.

As can be seen from the figure above it should have taken at most 27 years for the moment released in 1966 to have re-accumulated. Thus, according to the time predictable model the Parkfield earthquake should have occurred by 1993, at the very latest. Instead it occurred in 2004, 11 years later.

References

Murray, J., P. Segall, P. Cervelli, W. Prescott, J. Svarc, Inversion of GPS data for spatially variable slip-rate on the San Andreas Fault near Parkfield, CA, Geophys. Res. Lett., 28, 359-362, 2001.

Murray, J., P. Segall, Testing time-predictable earthquake recurrence by direct measurement of strain accumulation and release, Nature, 419, 287-291, 2002.