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Moment-Length Scaling of Large Strike-Slip Earthquakes and the Strength of Faults

Barbara Romanowicz and Larry Ruff (University of Michigan)


There has been a long lasting controversy in the literature as to whether earthquake moment ($M_0$) scales with $L^2$ or $L$ for large earthquakes, where $L$ is the length of the fault. In simple terms, the issue hinges on whether the average slip $d$ during an earthquake grows with $L$ or the width $W$ 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 $\Delta\sigma$ is proportional to $d/W$, hence slip scales with $W$ for constant $\Delta\sigma$. This implies scaling of $M_0$ with $L^n$, where $n=3$ for small earthquakes and $n=1$ for large earthquakes with $W=W_0$. Scholz (1982) proposed an alternative model, in which the slip scales with $L$. This model was motivated by inspection of slip versus length data that were available at that time. It implied that $n=2$ 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 $n=3$ for moments smaller than $\sim 0.6-0.8 \times 10^{20} Nm$, as known previously, while for larger moments, the data favored a scaling with $n=1$, compatible with dislocation theory. Romanowicz and Rundle (1993) then showed, based on scale invariance arguments (e.g. Rundle, 1989), that the $n=1$ and $n=2$ 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 $L$ tapers off at large $L$ (e.g. Bodin and Brune, 1996). This view has recently received further support from numerical modelling (Shaw and Scholz, 2001).

Dataset used

We considered the catalog of Pegler and Das (1996) (PD96 in what follows), who have combined $M_0$ estimates from the Harvard CMT catalog, with $L$ for large earthquakes from 1977 to 1992 based on relocated 30-day aftershock zones. We add to this dataset the standard collection of reliable $M_0$/$L$ 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 $M_o > 0.05 \times 10^{20} Nm$ 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 $M > 4$ 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.

Figure 18.1: Moment-length plot for the dataset described. Lines corresponding to $n=3$ bracketing most of the data have been drawn for reference. Circles correspond to recent data for which length was estimated from the NEIC catalog.

Results and Conclusions

Most of the data follow the $n=3$ trend, albeit with significant dispersion, except for the largest events (Figure 18.1). We separated our dataset into two subsets: subset $A$ comprises mostly events that occurred in a continental setting, and/or which, if their moment is larger than $1 \times 10^{20}Nm$, follow the trend of events on the San Andreas and Anatolian faults, on which the analysis of Romanowicz (1992) was based. The second subset ($''B''$) 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 $M_0$/$L$ plots are shown in Figure 18.2.

Figure 18.2: Moment-length plots for $A$ (bottom) and $B$ (top) events. Best fitting $n=1$ trends are indicated for each subset of data. Circles as in Figure 1, diamonds from other sources. Triangle is Luzon'90 event. Vertical lines point to the length estimates of PD96 for Aegean Sea events

We infer that each data subset can be fit rather tightly with an $n=1$ trend for the largest events. The change of scaling simply corresponds to a larger moment for events in subset $B$ ( $M_o \sim 5\times 10^{20} Nm$) than for those in subset $A$ ( $M_0 \sim 0.8-1\times 10^{20} Nm$). For both subsets, the change in scaling occurs for $L \sim 80 km$. For smaller events, the dispersion is large, but, on average, the best fitting $n=3$ trend plots lower for subset $B$.

This difference in the position of the break in scaling in each subset can originate either from a difference in $W_o$, or from a difference in $\Delta\sigma$. If we assume that $W_o$ 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 $B$ has larger $\Delta\sigma$ than subset $A$. 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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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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