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IUGG XXIV General Assembly July 2-13, 2007 Perugia, Italy<br />

(S) - <strong>IASPEI</strong> - International Association of Seismology and Physics of the Earth's<br />

Interior<br />

JSS005 Oral Presentation 1913<br />

Empirical and Theoretical Fault Scaling Relations<br />

Dr. Mark Leonard<br />

Geoscience Australia Geohazards <strong>IASPEI</strong><br />

It has been widely observered that the rupture area of small earthquakes (Mo10^21Nm or M>8) have<br />

aspect ratios >4.To account for this I suggest that all earthquakes where the aspect ratio is between<br />

1and 5 follow the power law relation W~L^P (where W=width, L=length). This relation, with P=0.67<br />

(0.6-0.7), applies to both dip slip and strike slip interplate earthquakes and intraplate earthquakes.<br />

Combining this relation with Mo=μDWL (where D= average displacement) gives a series of theoretical<br />

moment-area (log Mo ~ C1 log A ) and moment-length (log Mo ~ C2 log L) relations which depend only<br />

on the relationship between D and L. Relations were developed for four displacement models: (1)<br />

D~W=L^P, (2) D~√A=L^(1+P)/2, (3) D~L, and (4) D~L^(2-P). Model 1 has constant stress drop,<br />

model 2 preserves the C1=3/2 relation and model 4 preserves the C2 =3 relation. By combining<br />

published data sets (e.g.Wells and Coppersmith (1994), Henry and Das (2001) and Romanowicz and<br />

Ruff (2002)) the relative merit of each of these relations is estimated by testing how well C1 and C2 fit<br />

the data. For interplate dip-slip earthquakes the preferred P is 0.67 for fault lengths ranging from 4 km<br />

to 1000 km and for intraplate dip-slip earthquake faults with length ranging from 2 to 40km.Similarly P<br />

= 0.67 for interplate strike-slip earthquakes for fault lengths ranging from 4 to 40km (above which they<br />

become width limited) The log Mo~log L and Mo~log A data are consistent with models 1 & 2 but not<br />

with 3 & 4. The closest fitting model is 1, with C1 = 1.4 & C2 = 2.33, followed closely by 2, with C1=1.5<br />

& C2=2.5. WC94 found C1=1.47(0.045) & C2=2.23(0.06). These theoretically and empirically consistent<br />

models have application to hazard and paleoseismic studies, rupture and ground motion modelling, and<br />

may have application for estimating maximum credible earthquakes in dip-slip tectonics.<br />

Keywords: scaling, relations, faults

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