The first few seconds of an earthquake

Richard M. Allen
University of California Berkeley

The Kanamori Symposium, Caltech, February 2006

Observations from the first few seconds of P-wave arrivals show a scaling relation between the frequency content of the waveforms and the magnitude of earthquakes. This scaling relation suggests that the magnitude of an earthquake is partially determined by the initiation processes which last only a fraction of the total rupture duration. The observation contradicts the conceptual and physical models of fault rupture which emphasize the importance of the physical state of a fault plane in control of the final extent of earthquake rupture. The P-wave approach to rapid magnitude estimation can also be applied to earthquake warning and alerting systems in order to rapidly assess the hazard posed by an earthquake and issue warning of forthcoming ground shaking.

The frequency content of the waveform is measured using the predominant period observed within the first 4 sec of the P-wave trigger. The measurement has been made on 1842 waveforms from 72 earthquakes with magnitudes ranging from 3.0 to 8.3 from California, Japan, Taiwan and Alaska. The maximum predominant period is found to scale with magnitude, but also the delay of the maximum observations with respect to the trigger scales with magnitude. While up to 4 sec of data is used, the maximum predominant period is observed prior to rupture termination for all earthquakes with magnitude greater than 4. The range of predominant period values for earthquakes of a given size is approximately plus or minus 1 magnitude unit. This variability can be interpreted at the effect of the physical state of the fault plane.

Using the P-wave to estimate the magnitude and the location of an earthquake underway provides the necessary information to generate an "AlertMap" showing the predicted distribution of ground shaking. The AlertMap is available 1 sec after the P-wave arrival at the station closest to the epicenter and can be updated as more data becomes available from additional sensors. Using a set of earthquakes in southern California, we estimate that the AlertMap would be available at the time of the S-wave arrival at the epicenter for 50% of earthquakes and within 5 sec for more than 90% of earthquakes. Using the set of likely future earthquakes in the San Francisco Bay Area identified by the Working Group on California Earthquake Probabilities we find that warning times for damaging earthquakes range from seconds to ~80 sec.

© Richard M Allen