There has been a long lasting controversy in the literature as to whether earthquake moment () scales with or for large earthquakes, where is the length of the fault. In simple terms, the issue hinges on whether the average slip during an earthquake grows with or the width of the fault. The issue of scaling is particularly important for seismic hazard estimation based on lengths of fault segments, since significantly different estimates of maximum possible earthquake size can be obtained for a given region, depending on the scaling law.

Several large strike
slip earthquakes have occurred in various tectonic settings in the past 5 years, adding well documented data to the global collection of
moment and length estimates for such earthquakes. Based on this augmented dataset, we have reexamined the controversial issue of scaling of
seismic moment with length of rupture (*Romanowicz and Ruff*, 2002).

Dislocation theory predicts that stress drop is proportional to , hence slip scales with for constant
. This implies scaling of with , where for small earthquakes and for large earthquakes with
.
*Scholz* (1982) proposed an alternative model, in which the slip
scales with . This model was motivated by inspection of
slip versus length data that were available at that time. It implied that for
large earthquakes. On the other hand, *Romanowicz* (1992) compiled
the existing dataset for large strike-slip earthquakes on quasi-vertical
transcurrent faults. She concluded that moment scales with for moments
smaller than
, as known previously, while for larger moments, the data favored
a scaling with , compatible with dislocation theory. *Romanowicz and Rundle* (1993) then showed, based on
scale invariance arguments (e.g. *Rundle*, 1989), that the and scalings could also be
differentiated on the basis of frequency-moment statistics, favoring of the
"W-model".

Since then, the controversy has continued, using theoretical (e.g. *Sornette and Sornette*, 1994) as well as observational arguments (e.g. *Pegler and Das*, 1996; *Mai and Beroza*, 2000). On the other hand, new compilations of slip versus length data indicate that the increase of slip with
tapers off at large (e.g. *Bodin and Brune*, 1996). This view has recently
received further support from numerical modelling (*Shaw and Scholz*, 2001).

We considered the catalog of *Pegler and Das* (1996) (PD96 in what follows), who have combined estimates from the Harvard CMT catalog, with for large earthquakes from 1977 to 1992 based on relocated
30-day aftershock zones. We add to this dataset the standard collection of reliable / data for large strike-slip earthquakes since 1900 (e.g. *Romanowicz,* 1992), data for great central Asian events since the 1920's (*Molnar and Denq*, 1984), as well as
data for recent large strike-slip events (e.g Balleny Islands '98; Izmit, Turkey '99 and Hector
Mines, CA, '99) that have been studied using
a combination of modern techniques (i.e. field observations, waveform modelling, aftershock relocation).

We also considered 15 other strike-slip events of moment
that occurred in the period 1993-2001. Three of these events were
recently studied by *Henry and Das* (2001), and we used their length estimates.
For the other 12, we obtained estimates of length based on the distribution of
aftershocks of in the month following the event, as given in the NEIC contribution to the
Council of National Seismic Systems (CNSS) catalog.
We only kept those events with a clearly delineated aftershock zone.

Most of the data follow the trend, albeit with significant
dispersion, except for the largest events (Figure 18.1).
We separated our dataset into two subsets:
subset comprises mostly events that occurred in a continental setting, and/or which, if their
moment is larger than
, follow the trend of events on the
San Andreas and Anatolian faults, on which the analysis of *Romanowicz * (1992) was based. The
second subset () comprises the 12 large "anomalous" events mentioned above, four great earthquakes in central Asia, as well as smaller
events occurring in an oceanic setting. The resulting separate / plots are shown in
Figure 18.2.

We infer that each data subset can be fit rather tightly with an trend for the largest events. The change of scaling simply corresponds to a larger moment for events in subset ( ) than for those in subset ( ). For both subsets, the change in scaling occurs for . For smaller events, the dispersion is large, but, on average, the best fitting trend plots lower for subset .

This difference in the position of the break in scaling in each subset can originate either from
a difference in , or from a difference in .
If we assume that cannot be much larger for events that occur in oceanic versus
continental crust (at most a factor of 2 difference), Figure 18.2 implies that subset has larger than subset . In other words, in the latter case, the
corresponding faults are weaker. This result is consistent with
studies that have compared intra-plate and
inter-plate events (e.g. *Kanamori and Anderson,* 1975; *Scholz et al.*, 1986),
or determined that a continental
inter-plate fault such as the San Andreas Fault in California is "weak" (e.g. *Zoback and Zoback*, 1987).

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for shallow strike-slip earthquakes: Quasi-static models and dynamic
rupture propagation,*Bull. Seismol. Soc. Am.*, **86**, 1292-1299, 1996.

Henry, C. and S. Das, Aftershock zones of large shallow earthquakes: fault dimensions,
aftershock area expansion and scaling relations, *Geophys. J. Int*, **147**, 272-293.

Kanamori, H. and D. L. Anderson, Theoretical basis of some empirical
relations in seismology, *Bull. Seism. Soc. Am.*, **65**, 1073-1095, 1975.

Mai, P. and C. Beroza, Source scaling properties from finite fault
rupture models, *Bull. Seism. Soc. Am.*, **90**, 605-615, 2000.

Molnar, P. and Q. Denq, Faulting associated with large earthquakes and the average
rate of deformation in central and eastern Asia, *J. Geophys. Res.*, **89**, 6203-6227, 1984.

Pegler, G. and S. Das, Analysis of the relationship between seismic moment
and fault length for large crustal strike-slip earthquakes between 1977-92,
*Geophys. Res. Lett.*, **23**, 905-908, 1996.

Romanowicz, B. Strike-slip earthquakes on quasi-vertical transcurrent
faults: inferences for general scaling relations, *Geophys. Res. Lett.*, **19**, 481-484, 1992.

Romanowicz, B.; Ruff, L. J., On moment-length scaling of large strike slip earthquakes and the strength of faults, 10.1029/2001GL014479, 2002.

Romanowicz, B. and J. B. Rundle, On scaling relations for large earthquakes,
*Bull. Seism. Soc. Am.*, **83**, 1294-1297, 1993.

Scholz, C. H., C. A. Aviles and S. G. Wesnousky, Scaling differences between
large interplate and large intraplate earthquakes, *Bull. Seism. Soc. Am.*, **76**, 65-70, 1986.

Shaw, B. E. and C. H. Scholz, Slip-length scaling in large earthquakes: observations and theory and implications for earthquake physics, *Geophys. Res.
Lett.*, **28**, 2995-2998, 2001.

Sornette, D. and A. Sornette, Theoretical implications of a recent non-linear
diffusion equation linking short-time deformation to long-time tectonics,
*Bull. Seism. Soc. Am.*, **84**, 1679-1983, 1994.

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