The relation between rupture initiation and earthquake magnitude

Richard M. Allen
University of California Berkeley

Erik Olson
University of Wisconsin Madison

AGU Fall Meeting 2005

Our 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 lasts only a fraction of the total rupture duration. The observation contradicts conceptual and physical models of fault rupture which typically emphasize the importance of the physical state of a fault plane in control of the final extent of earthquake rupture.

We measure the frequency content of the waveform using the predominant period [Allen and Kanamori, 2003] observed within the first 4 sec of the P-wave trigger. Our dataset consists of 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. If the state is favorable to rupture, the magnitude will be one unit larger than average, while if it is unfavorable the earthquake will be smaller. Understanding the physics of this process may enable us to predict the magnitude of earthquakes without accurate knowledge of the surrounding state of stress across a fault plane.