Seismological Research Letters Volume 81, Number 6 November/December 2010 941doi: 10.1785/gssrl.81.6.941

scaling of the source dimensions of interface and intraslab subduction-zone earthquakes with Moment MagnitudeF. O. Strasser, M. C. Arango, and J. J. Bommer

F. O. Strasser,1 M. C. Arango,2 and J. J. Bommer2

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 rela-tions, 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 magni-tude. Additionally, the relation between independently deter-mined 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 seismo-logical 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 met-rics (e.g., Chiou and Youngs 2006), characterization of seis-mic 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 mag-nitude as a function of rupture dimensions may still be use-ful for estimating the moment magnitude of either historical or hypothetical scenario events for which an estimate of the

rupture dimensions is available, for instance on the basis of the dimensions of an observed seismic gap or from fault segmenta-tion models.

The most widely used relations for this purpose are the scal-ing 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-mag-nitude (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 com-parable 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 stud-ies found that due to limitations on the width of crustal earth-quakes, 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 finite-fault rupture models to investigate source scaling proper-ties. 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 subduction-zone earthquakes. Using a set of seven existing rupture mod-els 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

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

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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 lat-ter 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), rup-ture 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 dimen-sions 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 (typi-cally, from depths of 5–10 km to depths of 25–55 km [Llenos and McGuire 2007]) is constrained by transitions from velocity-strengthening behavior to velocity-weakening behavior (Scholz 2002). These transitions have been attributed to changes in sed-iment strength and mineral composition due to changes in tem-perature 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, how-ever, 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 con-strained 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 relation-ship between such structures and the rupture lengths of indi-vidual 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 simi-larly constrain the rupture extent of intraslab events. A compre-hensive 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 earth-quakes from the California Institute of Technology (http://www.tectonics.caltech.edu/slip_history/) as well as finite-fault 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 obser-vational 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 seismo-grams were only included if independent estimates were avail-able 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 < 100 km).

Henry and Das (2001) also point out the need for a uni-form definition of the source dimensions, and calculated the extent of 1-day, 7-day and 30-day aftershock zones for a set of 64 dip-slip earthquakes including 41 interface and 6 intraslab events. They found that aftershock zones of subduction inter-face events tended to expand substantially along strike and up-dip, and that depending on the event considered, the length of the 1-day aftershock zone was likely to under- or overestimate the true rupture length. Tajima and Kanamori (1985) found that the expansion of aftershock zones was dependent on the level of coupling of the subduction zone. The 1-day aftershock dimensions from Henry and Das (2001) were nevertheless added to our dataset, as the set as a whole does not show any systematic bias with respect to the total dimensions derived from slip distributions (Figure 1). For the few earthquakes in common to both sets the difference between models was not more pronounced than the differences observed between rup-ture dimensions assumed in slip inversion studies carried out by different authors.

As in previous studies, values of the source dimensions and moment magnitude were averaged when several studies were available for the same event. Mai and Beroza (2000) defined effective dimensions based on the autocorrelation width of the one-dimensional slip function obtained by summing the slip distribution along strike or down-dip. Given that the full slip distributions required to calculate the effective dimensions thus defined were only available for part of the database consid-ered, the total length, width, and area listed in the individual studies were used. Also, Mai and Beroza (2000) noted that the differences between effective and total dimensions were most pronounced for smaller earthquakes and very long strike-slip events, which are not the focus of the present study. For simi-lar reasons, no attempt was made to derive relations between moment magnitude and the combined area of asperities, Aa, as in the studies by Somerville et al. (1999, 2002) and Ichinose et al. (2006).

The resulting database includes 139 models corresponding to 95 interface events with magnitudes ranging from Mw 6.3 to Mw 9.4, and 21 models corresponding to 20 intraslab events with magnitudes ranging from Mw 5.9 to Mw 7.8. Estimates of the rupture length are available for all events; for a few events, the rupture width could not be constrained, hence the data-bases available for rupture width and rupture area are some-what smaller.

REGRESSION

The average values compiled in the database described above were used as input for regression analyses using ordinary least-

squares regression. For the relations between rupture dimen-sions (L, W, A) and moment magnitude (Mw), the functional form adopted was the same as in previous studies (Wells and Coppersmith 1994; Mai and Beroza 2000):

log10 X( )= a + bMW (1)

and

MW = a + b log10 X( ) (2)

where X is the rupture dimension under consideration (L or W in km, A in km2).

The best estimates of the coefficients a and b are listed in Tables 1 and 2 along with their standard errors and the stan-dard deviation (σ) associated with each equation. The value of the coefficient of multiple determination (R2), which represents the fraction of the total variation of the predicted variable that is explained by the regression, is also listed. The last column of each table shows the number of data points used in each case.

The regression results for the relations predicting rupture dimensions as a function of Mw (Equation 1) are shown in Figure 2, along with the data used in the regression, and 95% confidence intervals on the mean. These results show a good agreement of the data with a log-linear model, also reflected in the high R2 values, most of which are greater than 0.8. The somewhat poorer fit observed for the log10(W) – Mw relation for interface events may be a consequence of the dependence of W on the dip angle of the interface. The values of σ range for these equations are comparable to, if on average somewhat larger than, the values found for relations for crustal earth-quakes. The very small value of σ for the log10(W) – Mw for the intraslab dataset is likely to reflect undersampling due to the small size of the dataset available, and is not recommended for use in applications where the uncertainty associated with the scaling relation is considered explicitly.

Figure 2 also shows the best-fit line that would be obtained by assuming self-similar scaling (i.e., force the coefficient b in Equation 1 to 0.5 for L and W, and to 1.0 for A, to reflect direct proportionality between seismic moment and rupture area. Comparison of these lines with the 95% confidence intervals show that the hypothesis of self-similar scaling can be rejected at the 95% confidence level for both the log10(L)  –  Mw and log10(W) – Mw relations for interface events; although it cannot be rejected for the log10(A) – Mw relation for interface events, it would appear that this is due to a compensating effect between the deviations of the log10(L) – Mw and log10(W) – Mw from self-similar scaling, with the former having a steeper slope than expected for self-similar scaling (b = 0.585) and the lat-ter having a gentler slope (b = 0.351). For intraslab events, self-similarity can be rejected at the 95% confidence level only for the log10(W) – Mw relation, although it is noteworthy that the slopes for all three relations are very similar to their interface counterparts. The observed departure from self-similarity may

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TABLE 1Regression results for relations between rupture dimensions, rupture area, and moment magnitude, for interface events.

s.e. denotes the standard error of the coefficient under consideration, r 2 the coefficient of multiple determination, and n the total number of points used in the regression.

a s.e. (a) b s.e. (b) σ r 2 n

log10(L) = a + b × Mw –2.477 0.222 0.585 0.029 0.180 0.814 95log10(W ) = a + b × Mw –0.882 0.226 0.351 0.029 0.173 0.634 85log10(A) = a + b × Mw –3.476 0.397 0.952 0.051 0.304 0.805 85Mw = a + b × log10(L) 4.868 0.141 1.392 0.069 0.277 0.814 95Mw = a + b × log10(W ) 4.410 0.277 1.805 0.151 0.392 0.634 85Mw = a + b × log10(A) 4.441 0.179 0.846 0.046 0.286 0.805 85

▲ Figure 1. Datasets from which the average values of rupture dimensions and moment magnitude used in the regression analysis were derived.

6 7 8 9 10101

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103

MW

L(k

m)

SRCMOD (Mai, 2004; 2007) Henry & Das (2001)

Fujii & Matsu'ura (2000) Individual studies

Interface

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W(k

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Interface

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Intraslab

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TABLE 2Regression results for relations between rupture dimensions, rupture area, and moment magnitude, for intraslab events.

s.e. denotes the standard error of the coefficient under consideration, r 2 the coefficient of multiple determination, and n the total number of points used in the regression.

a s.e. (a) b s.e. (b) σ r 2 n

log10(L) = a + b × Mw –2.350 0.453 0.562 0.064 0.146 0.813 20log10(W ) = a + b × Mw –1.058 0.217 0.356 0.031 0.067 0.893 18log10(A) = a + b × Mw –3.225 0.598 0.890 0.085 0.184 0.874 18Mw = a + b × log10(L) 4.725 0.274 1.445 0.164 0.234 0.813 20Mw = a + b × log10(W ) 3.407 0.317 2.511 0.217 0.178 0.893 18Mw = a + b × log10(A) 4.054 0.288 0.981 0.093 0.193 0.874 18

▲ Figure 2. Regression results for the prediction of rupture dimensions as a function of moment magnitude. The dashed lines indicate the ±95% confidence intervals for the mean, and the heavy gray line indicates the best fit when self-similar scaling is assumed. The values shown for the individual data points are averaged over all models in the database in the case of multiple models being available for the same event.

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have implications for source scaling studies, where the use of a self-similar model will lead to linear dimensions for interface events that are in disagreement with observations, even though the rupture area would be consistent.

Figures 3, 4, and 5 compare the relations derived in this study with the equivalent relations of Wells and Coppersmith (1994), Mai and Beroza (2000), and Somerville et al. (1999, 2002), which are predominantly derived from crustal earth-quake data, with the exception of Somerville et al. (2002).

The comparison highlights a clear pattern of comparable lengths to crustal events but greater widths, leading to greater rupture areas, consistent with the finding of Somerville et al. (2002). The scaling of rupture length with magnitude is very similar for interface and intraslab events. An important result, in the opinion of the authors, is the finding that average rupture widths for intraslab events are smaller by about 30% than those of interface events, but the rate of increase with magnitude (slope of the relation) is similar for both types of events and broadly in agreement with that of the Wells and Coppersmith (1994) relation for all data. Smaller rupture widths for intra-slab events compared to interface events would be expected from the geometry of the subducting slab, whose thickness will limit the width of intraslab events. Furthermore, high values of stress drop have been observed for several intraslab events (e.g., Choy and Boatwright 1995; Choy and Kirby 2004; Morikawa and Sasatani 2004). However, it remains unclear whether these high values of stress drop are a cause or a consequence of the

small rupture extent, and even whether a causal relation exists between these two physical phenomena.

In terms of rupture area, the intraslab events have a similar scaling to crustal events according to the Wells and Coppersmith (1994) relations, while interface events tend to have larger areas by a factor of up to 2 which increases with magnitude. The predicted areas found in the present study are, however, smaller than those predicted by the relations of Somerville et al. (2002) and Mai and Beroza (2000) for dip-slip events, which appear to converge at large magnitudes. Since both these studies are based on a limited number of events (seven to eight events), this could reflect a sampling effect. Note that for events with Mw ≤ 7.0, the relation for interface events derived in the present study gives similar results to the Mai and Beroza (2000) relation for dip-slip events.

The scaling of the aspect ratio L:W has also been inves-tigated. For crustal events, a power-law relation has been pro-posed by Chiou and Youngs (2006) based on the database used in the Next Generation Attenuation (NGA) project (Power et al. 2008). The relatively high value of the exponent in the power-law (b = 3.097) for the Chiou and Youngs (2006) rela-tions leads to very large values when these relations are extended beyond Mw 8.0. Closer examination of the data used by Chiou and Youngs (2006) reveals that this behavior is controlled by large strike-slip earthquakes (particularly the largest three with aspect ratios ranging from 6 to 20). Fitting a similar power-law relation to the dataset compiled in the present study reveals that the aspect ratios of subduction earthquakes also appear to

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ture

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th(k

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Wells and Coppersmith (1994) - Crustal, all dataWells and Coppersmith (1994) - Crustal, reverseWells and Coppersmith (1994) - Crustal, normalMai and Beroza (2000) - Mainly crustal, all dataMai and Beroza (2000) - Mainly crustal, dip-slip eventsMai and Beroza (2000) - Mainly crustal, all data, effective lengthMai and Beroza (2000) - Mainly crustal, dip-slip events, effective lengthThis study - Subduction interfaceThis study - Subduction intraslab

▲ Figure 3. Comparison of the log10(L)-Mw relation with existing relations derived predominantly from data from crustal earthquakes (dashed when extended beyond the limits of the underlying dataset).

Seismological Research Letters Volume 81, Number 6 November/December 2010 947

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Wid

th(k

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Wells and Coppersmith (1994) - Crustal, all dataWells and Coppersmith (1994) - Crustal, reverseWells and Coppersmith (1994) - Crustal, normalMai and Beroza (2000) - Mainly crustal, all dataMai and Beroza (2000) - Mainly crustal, dip-slip eventsMai and Beroza (2000) - Mainly crustal, all data, effective widthMai and Beroza (2000) - Mainly crustal, dip-slip events, effective widthThis study - Subduction interfaceThis study - Subduction intraslab

▲ Figure 4. Comparison of the log10(W )-Mw relation with existing relations derived predominantly from data from crustal earthquakes (dashed when extended beyond the limits of the underlying dataset).

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a(k

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Wells and Coppersmith (1994) - Crustal, all dataWells and Coppersmith (1994) - Crustal, reverseWells and Coppersmith (1994) - Crustal, normalMai and Beroza (2000) - Mainly crustal, all dataMai and Beroza (2000) - Mainly crustal, dip-slip eventsMai and Beroza (2000) - Mainly crustal, all data, effective areaMai and Beroza (2000) - Mainly crustal, dip-slip events, effective areaSomerville et al. (2002) - SubductionSomerville et al. (1999) - CrustalThis study - Subduction interfaceThis study - Subduction intraslab

▲ Figure 5. Comparison of the log10(A)-Mw relation with existing relations derived predominantly from data from crustal earthquakes, and the relation derived for subduction earthquakes by Somerville et al. (2002). The relations are shown using a dashed line when they are extended beyond the limits of the underlying dataset.

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increase with magnitude, but with a gentler slope. Observed values (averaged over alternative models) are in general less than 3, and less than 4 for great (Mw > 8.0) earthquakes. While inslab strike-slip earthquakes sometimes occur, they are gener-ally smaller in magnitude than the crustal events included in the dataset used by Chiou and Youngs (2006). This difference in styles-of-faulting is likely to contribute to the observed dif-ferences in the scaling of the aspect ratio for crustal and sub-duction events. The fitted power-law relations are, however, less well-constrained than the previously derived equations for L, W, and A, particularly for the intraslab dataset. It therefore appears preferable to use the well-constrained relations for L and W as a function of Mw to define the extent of the rupture area when only magnitude information is available. In cases where independent estimates of both Mw and A are available, it is recommended to use the better-constrained relation for L and infer W from the ratio A:L.

In order to illustrate the differences between the relations derived herein and previously derived relations, Tables 3 and 4 present the values predicted using various relations for two scenario applications. In Table 3, the values of L, W, and A calculated for an Mw 8.0 event are presented. The results show that the difference in rupture dimensions can be up to a factor of the order of 2.4. Conversely, Table 4 presents the estimates of moment magnitude that would be obtained from rupture lengths of 50 km, 100 km, and 200 km. Only the Wells and Coppersmith (1994) relations are used in this comparison because the other studies do not provide coefficients for Mw

as a function of rupture dimensions. Differences of up to 0.5 Mw units are observed, and the discrepancy between the val-ues predicted by the relations derived in the present study and the Wells and Coppersmith (1994) relations increases with increasing rupture length (and hence magnitude). These results illustrate that using the Wells and Coppersmith (1994) rela-tions to estimate the magnitude corresponding to a given rup-ture length will result in underestimation of the moment mag-nitude for large subduction interface events.

CONCLUSIONS

Source scaling relations to estimate the dimensions of the rupture of interface and intraslab earthquakes at subduction zones based on their moment magnitude have been derived. The results show significant differences in scaling compared to relations for crustal relations, in particular in terms of rupture width and hence rupture area and aspect ratio.

Rupture lengths, on the other hand, are broadly compara-ble to the subsurface rupture lengths of crustal events of similar magnitude. Rupture widths of intraslab events have also been found to be on average 30% smaller for intraslab events than for interface events of the same magnitude. These relations reveal a departure from self-similar scaling, particularly notice-able for interface events. In combination with the differences in scaling coefficients, this indicates that the use of equations derived from crustal events is probably not appropriate for use to predict the rupture dimensions of subduction-zone events.

TABLE 3Comparison of the rupture dimensions predicted for an Mw 8.0 interface event by various scaling relations. The number in

brackets indicates the ratio between the value predicted by the relation derived in the present study, and that estimated by the relation under consideration.

l (km) w (km) a (km2)

This study—Interface 160 [1.00]

85[1.00]

13734[1.00]

Wells and Coppersmith (1994)—All 191[0.84]

35[2.38]

6166[2.23]

Wells and Coppersmith (1994)—Reverse 166[0.96]

47[1.81]

7079[1.94]

Mai and Beroza (2000)—All 147[1.09]

67[1.27]

10765[1.28]

Mai and Beroza (2000)—Dip-slip 195[0.82]

104[0.81]

20207[0.68]

Somerville et al. (2002) — — 26062[0.53]

TABLE 4Comparison of the Mw values predicted for a given rupture lengths by various scaling relations.

l = 50 km l = 100 km l = 200 km

This study—Interface 7.23 7.65 8.07Wells and Coppersmith (1994)—All 7.05 7.40 7.75Wells and Coppersmith (1994)—Reverse 6.90 7.24 7.58

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The scaling relations herein should hopefully prove useful tools for studies concerned specifically with the source charac-teristics and ground motions of subduction-zone events.

POSTSCRIPT

At the stage of proof checking of this paper, it came to our attention that another set of scaling relationships for subduc-tion earthquakes has been produced by a team at the University of Potsdam (Blaser et al. 2010), and we would like to alert the reader to that model as well since this alternative provides a means of addressing epistemic uncertainty in such empirical relationships between magnitude and rupture dimensions.

ACKNOWLEDGMENTS

The work presented here was considerably facilitated by the efforts of Martin Mai and co-workers in collating a database of uniformly determined parameters of slip models, and by the willingness of the authors of these and other such models to making digital versions of their slip models openly available. The second author was funded by the Alβan program of the European Union, as well as the Colfuturo program; this finan-cial support is gratefully acknowledged. The authors further wish to thank Martin Mai, two anonymous reviewers, as well as Seismological Research Letters Editor Luciana Astiz, whose insightful comments on the manuscript led to considerable improvements.

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Astiz, L., H. Kanamori, and H. Eisler (1987). Source characteristics of earthquakes in the Michoacan seismic gap in Mexico. Bulletin of the Seismological Society of America 77 (4), 1,326–1,346.

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