Seismic Hazard <strong>in</strong> <strong>Sydney</strong>Proceed<strong>in</strong>gs of <strong>the</strong> one day workshopA)B)Figure 5 Fault data from tunnels logs. a) Frequency histogram of fault strikes and b)Plot of fault displacement versus distance to closest adjacent fault.DERIVATION OF FAULT SCALING RELATIONS FOR THE SYDNEY REGIONIn general, <strong>the</strong> parameters of earthquake rupture length, width, displacement, and seismic momentscale <strong>in</strong> quite predictable ways. These parameters can be related by scal<strong>in</strong>g relations. Scal<strong>in</strong>grelations enable <strong>the</strong> prediction of, for example, <strong>the</strong> length and magnitude of an earthquake rupturegiven its displacement. The observed field data <strong>in</strong> <strong>Sydney</strong> is fault offset and we have <strong>in</strong>terpreted this<strong>in</strong> terms of a number of dist<strong>in</strong>ct earthquakes by us<strong>in</strong>g a displacement-length scal<strong>in</strong>g relationship. Adisplacement-magnitude relationship is used to predict <strong>the</strong> range of mean magnitudes associatedwith our range of mean SED valuesMany different earthquake scal<strong>in</strong>g relationships have been developed over <strong>the</strong> past several decades,<strong>the</strong> most well-known of which are those derived by Wells and Coppersmith (1994). Theirrelationships are now recognised as hav<strong>in</strong>g some limitations (e.g. Stirl<strong>in</strong>g et al., 2002), <strong>the</strong> mostsignificant for this study be<strong>in</strong>g that <strong>the</strong>y are based on l<strong>in</strong>ear, ra<strong>the</strong>r than bil<strong>in</strong>ear regressions. It has67
Seismic Hazard <strong>in</strong> <strong>Sydney</strong>Proceed<strong>in</strong>gs of <strong>the</strong> one day workshopbeen recognised for some time that large shallow earthquakes rupture <strong>the</strong> entire crustal thickness andare thus width-limited. Such earthquakes scale differently to smaller events (e.g. Scholz, 1982,Shimazaki, 1986). In this study, where displacements are relatively small and associated rupturewidths and lengths are also modest, scal<strong>in</strong>g relations that are self-similar, i.e. length, width, anddisplacement all <strong>in</strong>crease <strong>in</strong> proportion to seismic moment, are appropriate. Seismologically basedrelations, ra<strong>the</strong>r than geological ones, are best <strong>in</strong> this situation as surface geological data are sparsefor small earthquakes as few rupture to <strong>the</strong> surface.The parameter that controls a self-similar displacement-length relationship is static stress drop(Mohammadioun & Serva, 2001). Stress drops, although certa<strong>in</strong>ly not a measure of absolute stresslevels <strong>in</strong> <strong>the</strong> crust, are often used as a guide. A simple division between high stress drops for<strong>in</strong>traplate earthquakes compared with lower stress drops for <strong>in</strong>terplate earthquakes has beenrecognised (Scholz et al., 1986). Kanamori and Allen (1986) noted an almost equivalent differencebetween high stress drops for earthquakes occurr<strong>in</strong>g on crustal faults with long recurrence <strong>in</strong>tervalsversus low stress drops on short recurrence <strong>in</strong>terval faults. These values have been determ<strong>in</strong>ed fromgeological observations of large earthquakes world-wide.For cont<strong>in</strong>ental <strong>Australia</strong> we would expect high stress drops, it be<strong>in</strong>g a typical <strong>in</strong>traplateenvironment with relatively low rates of seismicity and long recurrence <strong>in</strong>tervals. Earlydeterm<strong>in</strong>ations of stress drops for cont<strong>in</strong>ental <strong>Australia</strong>n earthquakes by Denham et al. (1981) andMumme (1984) found very low values of 10 bars or less. In <strong>the</strong>se studies, rupture lengths werederived from aftershock distributions. In a follow<strong>in</strong>g section we discuss how aftershockdistributions systematically overestimate rupture lengths for world-wide data. It seems that forcont<strong>in</strong>ental <strong>Australia</strong>n earthquakes this effect is particularly pronounced. For example, <strong>in</strong> <strong>the</strong>Mecker<strong>in</strong>g earthquake, <strong>the</strong> secondary fault<strong>in</strong>g, accompanied by aftershocks, was seen to developover a period of weeks after <strong>the</strong> ma<strong>in</strong>shock and, <strong>in</strong> one case, over 22 months (Gordon & Lewis,1980). Seismological studies of <strong>the</strong> Mecker<strong>in</strong>g earthquake show that it was, <strong>in</strong> fact, a high stressdrop event. Teleseismic body wave modell<strong>in</strong>g by Vogfjord and Langston (1987) determ<strong>in</strong>ed asource duration of 3–5 s, correspond<strong>in</strong>g to a stress drop of ~100 bars. In <strong>the</strong>ir elastic dislocationmodell<strong>in</strong>g <strong>the</strong> subsurface fault length was assumed to be 20 km, significantly shorter than <strong>the</strong> curved37 km length of <strong>the</strong> surface fault scarp. A detailed study of aftershock depths by Langston (1987)also concluded that <strong>the</strong> crust was very strong <strong>in</strong> cont<strong>in</strong>ental <strong>Australia</strong> and that associated crustalstresses were high.The Tennant Creek earthquake comprised three ma<strong>in</strong> events with each be<strong>in</strong>g associated withseparate episodes of surface fault<strong>in</strong>g (Crone et al., 1992). Such an expansion of fault<strong>in</strong>g with timewould also be expected to be accompanied by an expansion of <strong>the</strong> aftershock distribution asobserved <strong>in</strong> <strong>the</strong> Mecker<strong>in</strong>g earthquake. Such expansion is now understood <strong>in</strong> terms of stresstrigger<strong>in</strong>g (e.g. K<strong>in</strong>g et al., 1994) whereby <strong>the</strong> <strong>in</strong>itial dislocation triggers slip on adjacent faults. Theprevalence of such expansion or trigger<strong>in</strong>g is more an <strong>in</strong>dication of high stresses with<strong>in</strong> <strong>the</strong> crustra<strong>the</strong>r than low stresses.O<strong>the</strong>r evidence that <strong>the</strong> crust <strong>in</strong> cont<strong>in</strong>ental regions is <strong>in</strong> a critical state of stress comes from deepborehole data (Townend & Zoback, 2000, Zoback & Townend, 2001), which show that hydrostatic,ra<strong>the</strong>r than lithostatic, pore pressures exist <strong>in</strong> <strong>the</strong> brittle crust. The lower pore pressures mean that<strong>the</strong> crust is much stronger than it o<strong>the</strong>rwise would be, and thus capable of withstand<strong>in</strong>g high stresslevels from tectonic driv<strong>in</strong>g forces. Areas of cont<strong>in</strong>ental crust can thus behave as rigid plates overtime scales of tens to hundreds of millions of years.68