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Scaling of the Source Dimensions of Interface and Intraslab Subduction-zone Earthquakes with Moment Magnitude F. O. Strasser, M. C. Arango, and J. J. Bommer

F. O. Strasser,1 M. C. Arango, 2 and J. J. Bommer 2 INTRODUCTION This paper derives source scaling relations between rupture dimensions and moment magnitude for subduction-zone earthquakes, separating between interface events occurring at the contact of the subducting and overriding tectonic plates, and intraslab events, which occur within the subducting slab. These relations are then compared with existing scaling relations, which are predominantly based on data from crustal events. Relations between the dimensions of the rupture zone of earthquakes and the amount of energy released as measured by the seismic moment, M0, or equivalently moment magnitude, Mw, (Hanks and Kanamori 1979), are of great practical use in engineering seismology. Early relations (e.g., Kanamori and Anderson 1975; Wyss 1979) were derived with the purpose of using rupture dimensions to constrain estimates of magnitude. Additionally, the relation between independently determined rupture dimensions and seismic moment also was used to draw inferences in terms of source scaling from comparisons between observed data and predictions of theoretical seismological models (e.g., Kanamori and Anderson 1975; Astiz et al. 1987). Nowadays, moment magnitude is routinely estimated from instrumental recordings, and the scaling relations described above are predominantly used to infer the probable dimensions of an earthquake of given magnitude. Applications include distance calculations using finite-fault distance metrics (e.g., Chiou and Youngs 2006), characterization of seismic sources in seismic hazard analysis, and theoretical studies involving forward-modeling of fault slip and resulting ground motions (e.g., Atkinson and Macias 2009; Somerville et al. 2008). However, the reciprocal relations giving moment magnitude as a function of rupture dimensions may still be useful for estimating the moment magnitude of either historical or hypothetical scenario events for which an estimate of the 1. Seismology Unit, Council for Geoscience, Private Bag X112, Pretoria 0001, South Africa 2. Department of Civil & Environmental Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK doi: 10.1785/gssrl .81.6.941

rupture dimensions is available, for instance on the basis of the dimensions of an observed seismic gap or from fault segmentation models. The most widely used relations for this purpose are the scaling relations developed by Wells and Coppersmith (1994) in a study using a worldwide database of source parameters for 421 crustal earthquakes, from which a subset of 244 events with well-constrained source parameters was selected for regression analysis to derive, among others, relations between the rupture length (L), the rupture width, (W), the rupture area (A), and Mw. A similar study was carried out in terms of surface-magnitude (MS) by Vakov (1996). Both studies were carried out for shallow crustal events, excluding in particular earthquakes associated with subduction zones. The resulting parameters are considered applicable for earthquakes with magnitudes comparable to those in the underlying datasets, i.e. Mw 5.0 to 8.0. The scaling in terms of rupture area of crustal earthquakes at the upper end of this range has recently been investigated by Hanks and Bakun (2002, 2008), building on previous work by Scholz (1982, 1994) and Romanowicz (1992). These studies found that due to limitations on the width of crustal earthquakes, the scaling of area with moment magnitude for large earthquakes beyond a transition magnitude of about Mw 7.0 differed from that observed for smaller events. Mai and Beroza (2000) made use of a collection of finitefault rupture models to investigate source scaling properties. The focus of their study was again the behavior of large crustal earthquakes, hence their database of 31 published slip models of 18 earthquakes included only two events associated with subduction (the 1923 Kanto earthquake and the 1985 Michoacan earthquake). This collection was later expanded into the SRCMOD database of finite-source rupture models (Mai 2004; 2007). The current version of SRCMOD includes a significant number of rupture models of subduction-zone events, which formed the starting point for the present study. A recent study by Somerville et al. (2002) recognized the scaling difference between large crustal and large subductionzone earthquakes. Using a set of seven existing rupture models with heterogeneous slip for large subduction earthquakes, Somerville et al. (2002) looked for systematic features of these slip models and their scaling with seismic moment. These were

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then compared with the characteristics of slip models of crustal earthquakes determined in a previous study (Somerville et al. 1999). Somerville et al. (2002) found that the main differences between the slip models of subduction and crustal earthquakes relate to the rupture area, with rupture areas of subduction earthquakes being larger by a factor of two or more than those of crustal earthquakes having the same seismic moment. The resulting scaling relation for rupture area was subsequently implemented in the simulations of Somerville et al. (2008) to predict ground motions from large earthquakes on the Cascadia subduction zone. With this exception, there are, to the knowledge of the authors, no scaling relations available in the open international literature that have been derived specifically for earthquakes that occur in subduction-zone environments. While several authors have investigated the relations of rupture dimensions of subduction-zone earthquakes, these studies do not derive formal relations comparable to the Wells and Coppersmith (1994) relations for crustal earthquakes. As a result, the latter are sometimes used to estimate the rupture dimensions of subduction-zone earthquakes (e.g., Atkinson and Boore 2003; Atkinson and Macias 2009). The present paper focuses more particularly on the relations between the rupture area (A), rupture length (L), rupture width (W) and moment magnitude of earthquakes that occur in subduction-zone environments.

CONSTRAINTS ON RUPTURE DIMENSIONS OF SUBDUCTION EARTHQUAKES There are obvious physical constraints on the rupture dimensions of subduction-zone earthquakes, which need to be acknowledged prior to any purely statistical interpretation of observational data. Subduction-zone earthquakes are generally classified into interface earthquakes occurring at the contact between the subducting and the overriding plate, and intraslab events occurring within the subducting slab. The occurrence of seismic events at the interface is restricted to a seismogenic zone whose up-dip and down-dip extent (typically, from depths of 5–10 km to depths of 25–55 km [Llenos and McGuire 2007]) is constrained by transitions from velocitystrengthening behavior to velocity-weakening behavior (Scholz 2002). These transitions have been attributed to changes in sediment strength and mineral composition due to changes in temperature and pressure (e.g., Byrne et al. 1988; Hyndman and Wang 1993; Oleskevich et al. 1999). The width and dip of the seismogenic zone vary from one subduction zone to another, depending on the level of coupling between the plates in contact (Pacheco et al. 1993). These parameters provide a constraint on the down-dip width of interface earthquakes. It should, however, be noted that in some instances, coseismic rupture has been observed to extend beyond the locked zone into regions of aseismic slip (e.g., Kanamori and McNally 1982), thus the down-dip width of great interface earthquakes may exceed the width of the locked zone. Along strike, the length of interface events may be constrained by the presence of lateral structures such as oceanic

ridges or seamounts. However these structures can act as either barriers or asperities (e.g., Kanamori 1986), hence the relationship between such structures and the rupture lengths of individual earthquakes remains somewhat unclear (Llenos and McGuire 2007). Fore-arc rheology, basin size, and subducting seafloor roughness have also been linked to constraints on the size of great interface earthquakes (Llenos and McGuire 2007; Morgan et al. 2008). The geometry and brittleness of the subducting slab similarly constrain the rupture extent of intraslab events. A comprehensive review of the geometry of the various subduction zones is beyond the scope of this study; global compilations of down-dip widths and dip angles of the seismogenic portions of subduction zones can be found in Pacheco et al. (1993) and Tichelaar and Ruff (1993). Furthermore, values for a particular subduction zone are generally well-documented in regional studies. These local constraints should be borne in mind when applying the scaling relations derived in the present study based on a global dataset of source parameters of subduction-zone earthquakes.

DATABASE The database used here is primarily based on the SRCMOD database compiled by Martin Mai and co-workers (Mai 2004; 2007), from which subduction-type events have been extracted. These data have been supplemented by a number of recent studies describing the rupture process of individual events. In addition to published articles (Barrientos 1988; Choy and Dewey 1988; Satake 1995; Delouis et al. 1997; Courboulex et al. 1997; Kikuchi and Yamanaka 2001; Pritchard et al. 2007; Ichinose et al. 2004; 2006; Takeo et al. 1993; Morikawa and Sasatani 2004; Quintanar et al. 1999;Yamamoto et al. 2002; Aoi et al. 2005; Delouis and Legrand 2007; Vallée et al. 2003), these individual studies included the slip models posted on the Web sites of the database of slip maps of recent large earthquakes from the California Institute of Technology (http:// www.tectonics.caltech.edu/slip_history/) as well as finitefault model inversions by the US Geological Survey (USGS) (http://earthquake.usgs.gov/regional/world/historical.php) and GeoAzur (http://geoazur.oca.eu/spip.php?rubrique57). The rupture dimensions derived from re-evaluated 1-day aftershock distributions by Henry and Das (2001) were also included. The interface dataset was furthermore supplemented by the subduction events in the dataset compiled by Fujii and Matsu’ura (2000), which consists of a reappraised selection of events from previous compilations by Wells and Coppersmith (1994), Purcaru and Berckhemer (1982), and Sato (1989). In order to derive a meaningful scaling relation from observational data, it is important to ensure that the parameters used in the regression have been derived in a consistent manner. This is particularly an issue for the rupture dimensions, which can be estimated using various methods. Wells and Coppersmith (1994) favored the extent of the best-defined aftershock zone to define the source dimensions, although they acknowledged that the ruptures defined by early aftershocks may be slightly larger than the actual co-seismic rupture zone, following Mendoza

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and Hartzell (1988). Estimates of rupture length calculated from geodetic modelling or from corner frequencies of seismograms were only included if independent estimates were available for corroboration. Darragh and Bolt (1987) note that the discrepancy between the extent of the aftershock zone and the rupture length estimated through other means is particularly a problem for the estimation of shorter ruptures (L