Geophys. J. Int. (2001) 147, 272–293 Aftershock zones of large shallow earthquakes: fault dimensions, aftershock area expansion and scaling relations C. Henry and S. Das Department of Earth Sciences, University of Oxford, Parks Road, Oxford, OX1 3PR, UK. E-mail: [email protected] Accepted 2001 May 22. Received 2001 May 5; in original form 2000 August 23 SUMMARY We determine the aftershock areas from relocated hypocentres for 64 dip-slip and eight strike-slip earthquakes in the period 1977–1996 together with those for three recent earthquakes, the 1998 Antarctic plate earthquake, the 1999 Izmit, Turkey earthquake and the 2000 Wharton Basin earthquake. We also include the data for 27 strike-slip earthquakes from Pegler & Das (1996). We find that the location of the hypocentre is essentially random along strike for both strike-slip and dip-slip earthquakes. Subduction zone earthquakes appear to initiate more frequently towards the down-dip edge of the fault, whereas the non-subduction zone dip-slip earthquakes do not have any preferred depth of initiation. The aftershock zones of subduction zone earthquakes often expand substantially along strike and up dip but far less in the down-dip direction, whereas those for non-subduction zone earthquakes do not expand significantly in either the up- or the down-dip direction. Subduction zone thrust earthquakes have larger and more numerous aftershocks than earthquakes in all other tectonic settings. For strike- slip earthquakes, we find that slip increases at least linearly with length. For dip-slip earthquakes, we find that the ratio of length to width increases systematically with length for lengths >40 km, indicating that there is some restriction on fault width; slip is found 17 21 to be proportional to length over the moment range 10 Nm<M0<3r10 Nm, taking our data in conjunction with the data of Wells & Coppersmith (1994). Key words: aftershocks, earthquakes, fault dimensions, scaling relations. the fitting of seismograms. Locating aftershocks is relatively 1 INTRODUCTION reliable and the methods to do this have been well established The 1952 Kern County, California earthquake was the first one for several decades. On the other hand, the inverse problem for for which portable seismometers were set up in the field within the earthquake source is intrinsically very unstable (Kostrov hours of the main shock in order to record the aftershocks, with & Das 1988), and until very recently, sufficiently high-quality Gutenberg, Richter and Benioff all being involved in this project. seismograms and with sufficiently good spatial coverage were Richter (1955) was the first to associate clearly the location of not available for a reliable estimate of the fault dimensions of the aftershocks with the fault rupture area. Richter (1995) demon- the main shock. Even for an Mw=8.0 earthquake as recently as strated the spatial complexity of the aftershock distribution and 1989 (the Macquarie Ridge earthquake), Das (1993) showed noted a slight expansion of the rupture area with time. Since that the teleseismic seismograms were unable to constrain the then, one of the most widely used methods of obtaining the fault area, and aftershocks had to be used to constrain it rupture dimensions is by using aftershocks. The expansion of the a priori. The 1998 Antarctic earthquake is the first one for rupture area with time has been noted for many earthquakes, which the seismograms did constrain the fault rupture area and it is considered that if a short time period after the main (Henry et al. 2000), and hence this is a very promising tool for shock is selected, the aftershock area gives a good estimate of future global studies. Previously, only in land areas with a very the rupture area of the main earthquake. Although the total dense local network had it been possible to constrain rupture moment of the aftershocks is usually only a few per cent of the areas by inverting seismograms. A recent study by Mai & Beroza main shock moment, aftershocks have been disproportionately (2000) using this latter method included mainly Californian well studied due to the possibility of deployment of arrays after earthquakes. the main earthquake. In fact, for several reasons, this method The main purpose of this paper is to obtain the aftershock may be more reliable than trying to find the fault dimensions by areas of many earthquakes worldwide using teleseismic data, 272 # 2001 RAS Aftershock zones of large shallow earthquakes 273 and to discuss the properties of the aftershock areas and the (Ly60), favouring a W model for large events. This was implications of the aftershock dimensions for the problem of disputed by Scholz (1994a) and further discussed by Romanowicz earthquake scaling. (1994) and Scholz (1994b). There is more of a consensus, based on the limited available data, that at least the very largest strike-slip earthquakes (L>200 km) have some restriction on 2 EARTHQUAKE SCALING slip and tend towards M0 3 L scaling (Scholz 1994b; Bodin & How earthquakes scale with size is a problem of great Brune 1996; Fujii & Matsu’ura 2000). Most empirical studies of importance. Without knowing the relationship between fault earthquake scaling, including all of those cited above, have size and other source parameters, it would be impossible to been based on compilations of earthquake parameters from the make ground motion predictions, essential for the construction literature, in some cases using measurements made using very of earthquake-resistant structures, for large, infrequent earth- different methodologies. Pegler & Das (1996) have argued that in quakes based on the recordings from smaller, more frequent the observational study of scaling relationships it is important ones in the same region. Scaling relations are also often used to to analyse all earthquakes in a uniform manner. They com- estimate seismic moment from length or vice versa, a very recent pared Harvard CMT (centroid moment tensor) moments to example being Parsons et al. (2000). Finally, scaling relations fault lengths measured from relocated aftershock distributions provide insight into the mechanics of earthquake rupture. The for large crustal strike-slip earthquakes from 1977–1992. They 2 17 problem was first considered by Aki (1967), and has been a found that M0 3 L over the moment range 5r10 Nm 21 subject of vigorous research since. The seismic moment M0 is to 1.4r10 N m, with no indication of a break in slope mu¯A, where m is the rigidity, u¯ is the mean slip and A is the fault at y7r1019 N m as observed by Romanowicz (1992), and area. The rupture area on any planar fault can be approxi- thereby supporting the original finding of Scholz (1982). mated either by a rectangle or by an ellipse (a circle being a No study comparable to Pegler & Das (1996) has been special case of this). For a rectangular fault of length L and carried out for dip-slip earthquakes. The recent compilation of width W, M0=mu¯LW. For an elliptical fault, M0=(p/4)mu¯LW, earthquake data by Wells & Coppersmith (1994) uses sub- where L and W are now the lengths of the axes of the ellipse. surface length (primarily determined from aftershocks occur- Thus, in general, M0=Cmu¯LW, where C is a geometrical factor ring from a few hours to a few days after the main shock) and lying between about 0.75 and 1. Empirical scaling relations the seismically determined scalar moment for 50 thrust and found between M0 and fault dimensions can be used to make 24 normal earthquakes from 1952–1993 in the moment range 16 20 inferences regarding the factors that control mean slip. For 2r10 Nm<M0<3r10 N m. For this magnitude range they 2.2 2.3 small earthquakes, which may be defined as those with rupture found that M0 3 L for thrust earthquakes and M0 3 L for dimensions smaller than the down-dip width of the seismogenic normal earthquakes. The study by Wells & Coppersmith (1994) layer, LyW. Hanks (1977) compiled seismic moments and fault includes both intraplate and interplate earthquakes, but of the radii, r, for 390 earthquakes, mostly from southern California, thrust earthquakes only two were clearly interplate subduction 11 20 3 in the range 10 Nm<M0<10 N m, and found that M0 3 r , zone earthquakes. Many large dip-slip earthquakes have occurred 21 indicating that u¯ 3 r. The scaling for large earthquakes is since 1977, several of which have M0<10 N m, and which expected to be different. to our knowledge have not been included in any similar In a seminal paper, Scholz (1982) discussed scaling relation- compilation. The combination of the Harvard CMT catalogue ships for large earthquakes. If the base of the fault is clamped and International Seismological Centre (ISC) hypocentre and during the rupture, then slip is limited by the rupture width. phase data is a rich resource for studies of earthquake scaling Scholz (1982) called this the ‘W model’. It implies mean slip that has not yet been fully utilized. is constant for large earthquakes as long as the stress drop is constant, so that M 3 L. In any such model, rupture takes the 0 3 DATA SELECTION AND form of a travelling pulse of slip (Archuleta & Day 1980; Das METHODOLOGY 1981; Day 1982). If the base of the fault is free, then rupture width places no limit on fault slip. Scholz (1982) called such a We carry out an analysis similar to Pegler & Das (1996) to model the ‘L model’ because slip in this case is controlled by study 64 shallow dip-slip earthquakes from 1977–1996. We fault length. Theoretical calculations (Das 1982) show that if extend the data range for the dip-slip earthquakes covered by the base of the fault is free, slip continues in the interior of an the Wells & Coppersmith (1994) study to earthquakes an order expanding rectangular earthquake fault until a healing phase of magnitude greater in moment, using a uniform method arrives from the longer ends of the fault.