Invasion Percolation Application to Earthquakes Rupture
In order to apply our model to eathquake rupture we consider the temporal development of a burst as follows:
- • Because a burst is locally connected and temporally well ordered, the burst starts with a single site exactly as in the original model.
- • The bonds connecting this site to adjacent sites are assigned random numbers in the range 0 to 1.
- • If the random number assigned is between 0 and 0.5 (50% of the bonds), the bond opens after a short characteristic time associated with the burst.
- • If the random number assigned is between 0.5 and 1 (50% of the bonds), the bond will open after a characteristic time much longer than that associated with the burst and is effectively eliminated.
- • This process is repeated until the burst terminates and there are no more adjacent sites with random numbers bewteen 0 and 0.5.
These bursts are identical to those previously illustrated, having the same structure and number-area statistics. For a typical large burst, the number of sites added during a given interval of time (several characteristic time steps) is shown.
Moment rate for the Mw 9.0 Tohoku-Oki earthquake of March 11, 2011 [1].
We find excellent agreement between our simulated growth rate of rupture and the observed moment rate for this earthquake.
[1] Lee, S. (2012). Terrestrial Atmospheric and Oceanic Sciences, 23(1), 1–7.