Earthquake scaling and statistics. The scaling of slip with length Stress drop Seismic moment Earthquake magnitude Magnitude statistics Fault statistics. The scaling of fault length and slip. Normalized slip profiles of normal faults of different length. From Dawers et al., 1993.
Normalized slip profiles of normal faults of different length.
From Dawers et al., 1993
Displacement versus fault length
What emerges from this data set is a linear scaling between displacement and fault length.
Figure from: Schlische et al, 1996
The seismic moment is a physical quantity (as opposed to earthquake magnitude) that measures the strength of an earthquake. It is equal to:
G is the shear modulus
A = LxW is the rupture area
D is the average co-seismic slip
(It may be calculated from the
amplitude spectra of the seismic
Figure from: Schlische et al, 1996
Richter noticed that the vertical offset between every two curves is independent of the distance. Thus, one can measure the magnitude of a given event with respect to the magnitude of a reference event as:
where A0 is the amplitude of the reference event and is the epicentral distance.
The diagrams to the right show slip distribution inferred for several well studied quakes. It is interesting to compare the rupture area of a magnitude 7.3 (top) with that of a magnitude 5.6 (smallest one near the bottom).
Magnitude classification (from the USGS):
0.0-3.0 : micro
3.0-3.9 : minor
4.0-4.9 : light
5.0-5.9 : moderate
6.0-6.9 : strong
7.0-7.9 : major
8.0 and greater : great
The intensity scale, often referred to as the Mercalli scale, quantifies the effects of an earthquake on the Earth’s surface, humans, objects of nature, and man-made structures on a scale of 1 through 12. (from Wikipedia)
I shaking is felt by a few people
V shaking is felt by almost everyone
VIII cause great damage to poorly built structures
XII total destruction
Fortunately, there are many more small quakes than large ones. The figure below shows the frequency of earthquakes as a function of their magnitude for a world-wide catalog during the year of 1995.
This distribution may be fitted with:
where n is the number of earthquakes whose magnitude is greater than M. This result is known as the Gutenberg-Richter relation.
Figure from simscience.org
Cumulative length distribution of subfaults of the San Andreas fault.
Question: what gives rise to the drop-off in the small magnitude with respect to the G-R distribution?
Seismological observations show that:
Co-seismic slip is very heterogeneous.
Slip duration (rise time) at any given point is much shorter than the total rupture duration
Example from the 2004 Northern Sumatra giant earthquake
Preliminary result by Yagi.
Uploaded from: www.ineter.gob.ni/geofisica/tsunami/com/20041226-indonesia/rupture.htm
The origin and behavior with time of barriers and asperities:
Fault geometry - fixed in time and space?
Stress heterogeneities - variable in time and space?
According to the barrier model (Aki, 1984) maximum slip scales with barrier interval.
If this was true, fault maps could be used to predict maximum earthquake magnitude in a given region.
But quite often barriers fail to stop the rupture…
The 1992 Mw7.3 Landers (CA):
The 2002 Mw7.9 Denali (Alaska):
Figure from: pubs.usgs.gov
Figure from: www.cisn.org
While in the barrier model ruptures stop on barriers and the bigger the rupture gets the bigger the barrier that is needed in order for it to stop, according to the asperity model (Kanamori and Steawart, 1978) earthquakes nucleate on asperities and big ruptures are those that nucleate on strong big asperities.
That many ruptures nucleate far from areas of maximum slip is somewhat inconsistent with the asperity model.