Alternative Rupture-Scaling Relationships for Subduction Interface and Other Offshore Environments - PDF Document

Presentation Transcript

  1. Bulletin of the Seismological Society of America, Vol. 107, No. 3, pp. –, June 2017, doi: 10.1785/0120160255 Ⓔ Alternative Rupture-Scaling Relationships for Subduction Interface and Other Offshore Environments by Trevor I. Allen*and Gavin P. Hayes Abstract 9.5subductioninterfaceearthquakesusinga newdatabase ofconsistentlyderivedfinite- fault rupture models from teleseismic inversion. Scaling relationships are derived for rupture area, rupture length, rupture width, maximum slip, and average slip. These re- lationships apply width saturation for large-magnitude interface earthquakes (approx- imately Mw>8:6) for which the physical characteristics of subduction zones limit the depth extent of seismogenic rupture, and consequently, the down-dip limit of strong ground motion generation. On average, the down-dip rupture width for interface earth- quakes saturates near 200 km (196 km on average). Accordingly, the reinterpretation of rupture-area scaling for subduction interface earthquakes through the use of a bilinear scaling model suggests that rupture asperity area is less well correlated with magnitude for earthquakes Mw>8:6. Consequently, the size of great-magnitude earthquakes ap- pears to be more strongly controlled by the average slip across asperities. The sensitivity of the interface scaling relationships is evaluated against geo- graphic region (or subduction zone) and average dip along the rupture interface to assess the need for correction factors. Although regional perturbations in fault-rupture scaling could be identified, statistical significance analyses suggest there is little rationale for implementing regional correction factors based on the limited number of interface rupture models available for each region. Fault-rupture-scaling relationships are also developed for intraslab (within the subducting slab), extensional outer-rise and offshore strike-slip environments. For these environments, the rupturewidth and area scaling properties yield smaller dimen- sions than interface ruptures for the corresponding magnitude. However, average and maximum slip metrics yield larger values than interface events. These observations reflect both the narrower fault widths and higher stress drops in these faulting envi- ronments. Although expressing significantly different rupture-scaling properties from earthquakes in subduction environments, the characteristics of offshore strike-slip earthquake ruptures compare similarly to commonly used rupture-scaling relation- ships for onshore strike-slip earthquakes. Alternative fault-rupture-scaling relationships are developed for Mw7.1– Electronic Supplement: Table of rupture parameters. Introduction Fault-rupture-scaling relationships have numerous ap- plications in both earthquake- and tsunami-hazard analyses. For example, modern event-based probabilistic seismic- hazard analysis (PSHA) codes rely on these relationships to simulate ground-motion fields (GMFs) from randomized pseudoruptures within areal source zones or to scale floating ruptures across a predefined fault surface (e.g., Pagani et al., 2014). If not assuming characteristic earthquake ruptures, the rupture geometries are calculated using fault-scaling rela- tionships (e.g., Wells and Coppersmith, 1994, and others). The GMFs are then determined by these ruptures in concert with ground-motion models that are calibrated to the closest distance to the rupture plane. Rupture-scaling relationships also play a key role in developing GMFs for earthquake im- pact scenarios and probabilistic seismic risk assessments, for paleoseismological studies, and for informing catalog de- clustering algorithms. *Now at Geoscience Australia, GPO Box 378, Canberra, Australian Capital Territory 2601, Australia. BSSA Early Edition / 1

  2. 2 T. I. Allen and G. P. Hayes Table 1 earthquakes that have been developed using a uniform tele- seismic inversion method (Hayes et al., 2015). In both PSHA and PTHA, it is often appropriate to use multiple methods and models to account for the epistemic uncertainty. Herein, we develop alternative fault-rupture- scaling relationships that are appropriate for subduction and other offshore environments that could be used independ- ently, or in concert with alternative scaling relationships in a probabilistic framework. Published Fault-Rupture-Scaling Relationships for Subduction Environments Reference S Sa L W Dmax Dav Intraslab Wells and Coppersmith (1994) Murotani et al. (2008)† Blaser et al. (2010) Leonard (2010)† Strasser et al. (2010) Murotani et al. (2013)† Skarlatoudis et al. (2016)† Present study ✓ ✓ ✓ ✓* ✓* ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Finite-Fault Rupture Models ✓ ✓ Many authors contributed FFRMs for significant global earthquakes (Mai and Thingbaijam, 2014, and references therein). While an excellent resource, many of these contrib- uted models have been developed using disparate approaches and assumptions. Therefore, uncertainties arising from differences in modeling techniques and parameterization can affect the confidence in derivative products when using multiple, different models. Hayes et al. (2015) has developed an FFRM database for most of the Mw≥7:5 global earthquakes since 1990. All rup- ture models in the database use uniform teleseismic inversion- modeling techniques and parameterization. Deep earthquakes (>300 km) are excluded from the dataset, because of their dif- ferent rupture kinematics compared with shallow (<70 km) and intermediate-depth (70–300 km) earthquakes. We use these FFRMs to develop alternative scaling relationships for interface and intraslab subduction zone earthquakes. Addition- ally, scaling relationships based on limited offshore strike-slip and subduction outer-rise events are also provided. In total, 99 FFRMs from the Hayes et al. (2015) databaseareused in these analyses (Ⓔ Table S1, available in the electronic supplement to this article). Because the parameter space used to invert for FFRMs often exceeds the area of primary slip and thus that of strong- motion generation, it is necessary to first trim the FFRMs to an effective rupture area. A consistent two-step process is developedthat trims low-slip subfault areas that are not likely to generate strong ground shaking hazard. First, we attempt to remove noise from each FFRM. The simplification of complexearthquake-rupture processes to a simple planar sur- face (or multiple planar surfaces), rupturing during an ex- panding but finite slip pulse together with complexities in seismic wavepaths, can introduce artifacts into FFRMs. These effects are more commonly observed at the later time- steps in the modeling process. To mitigate noise artifacts from the rupture models, a maximum duration of rupturewas manually assigned to all earthquakes within the Hayes data- set, based on analyses of the more stable earthquake source time functions associated with each FFRM. All slips on FFRM subfaults at time-steps greater than the assigned rup- ture duration were set to zero. The assigned rupture durations for the earthquakes studied are indicated in Ⓔ Table S1. Next, with FFRM noise removed, we trim subfaults that have slip (Dij) less than a given slip threshold Dlim, in which ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ *Poorly constrained for reverse-faulting events. †Self-similar scaling relationships. In deterministic tsunami assessments, fault-rupture- scaling relationships are an important component for deter- mining the extent of coastline that may be impacted by tsu- nami through the use of both average slip and length scaling of fault rupture along a subduction interface. Probabilistic tsunami-hazard assessments (PTHAs) extend this application by simulating pseudoruptures for a synthetic catalog of pos- sible subduction interface tsunami sources (e.g., Sørensen et al., 2012; Horspool et al., 2014; Thio and Li, 2015). Several fault-rupture-scaling relationships have now been developed specifically for subduction environments (Murotani et al., 2008, 2013; Blaser et al., 2010; Strasser et al., 2010; Somerville et al., 2015; Skarlatoudis et al., 2016). These authors provide a range of equations to re- solve various properties for subduction interface and in-slab ruptures, including rupture area (S), rupture asperity area (Sa), rupture length (L), rupture width (W), maximum slip (Dmax), and average slip (Dav). Some of the aforementioned scaling relations are purely empirical, whereas others in- voke self-similar fault-scaling principles—see Blaser et al. (2010) and Strasser et al. (2010) for further discussion on the comparison of self-similar and non-self-similar scaling. Table 1 indicates scaling relations appropriate for subduc- tion environments and the specific rupture properties that can be resolved. One disadvantage of the previous studies is that they use fault-rupture data from multiple sources, which are often de- rived using disparate methods and assumptions. Therefore, uncertainties arising from differences in modeling techniques and parameterization can affect the confidence in derivative products such as rupture-scaling relationships. These uncer- tainties can be reduced, to a certain extent, by comparing only those models that have been generated using a consis- tent modeling approach. The present study uses a large data- base of finite-fault-rupture models (FFRMs) from recent BSSA Early Edition

  3. Alternative Rupture-Scaling Relationships for Subduction Interface and Other Offshore Environments 3 0 33 30 l l l w w w 27 50 24 FFRM Width (km) 21 Slip (m) 18 100 15 12 9 150 6 3 200 0 0 50 100 150 200 250 300 350 400 FFRM Length (km) Figure 1. subfault of length l and width w. The thick gray line bounds the maximum and minimum subfault indexes for each column i and row j for which the slip Dij≥ Dlim. The thick black line represents the effective rupture dimensions used for L and W. Schematic of fault trimming process. A synthetic finite-fault rupture model (FFRM) is plotted showing the slip for each ?1? EQ-TARGET;temp:intralink-;df1;55;497Dlim? ξ × Dmax: strike subfault (i ? 1;2;…;n) with length l, the effective lengths for each row j are In a recent publication, Ye et al. (2016) recommended a trim- ming threshold of ξ ? 0:15 based on comparisons between static and energy-related stress drops. Although the choice of ξ is still somewhat arbitrary, the chosen value is expected to preserve the areas of significant slip on a fault plane that are likely to generate strong ground shaking. The process for trimming the FFRMs is outlined below and illustrated in Figure 1. To estimate the overall down-dip rupture width W, we first iteratively step though each sub- fault column i along the strike direction and find the effective column width Wi. For each row j in each column i, the upper and lower subfaults with a slip Dijgreater than, or equal to, the minimum slip Dlimare identified. For each down-dip subfault (j ? 1;2;…;n) with width w, the effective down-dip widths for each column i are EQ-TARGET;temp:intralink-;df5;313;473Lj? max?x2;1j;x2;2j;…;x2;nj? − min?x1;1j;x1;2j;…;x1;nj?; ?5? in which x2;ijis the upper row limit, ?i × ljDij≥ Dlim EQ-TARGET;temp:intralink-;df6;313;413 ?6? x2;ij? for i ? 1;2;…;n; 0jDij< Dlim and x1;ijis the lower row limit, ??j − 1? × wjDij≥ Dlim for i ? 1;2;…;n: ?7? EQ-TARGET;temp:intralink-;df7;313;351x1;ij? ∞jDij< Dlim The effective rupture length L is then taken as the 75th per- centile of the distribution ?L1;L2;…;Ln?. The rupture area S for single-segment models is the product of L and W. The maximum slip Dmaxis not dependent on the trimming proc- ess. Given that subfault areas are not equal between models, Dmaxis a function of the rupture model resolution. However, the average slip Davis modified such that the total non- trimmed slip is averaged across the nontrimmed subfaults. Figure 1 shows a schematic diagram of the FFRM trimming process for a single-segment rupture. Although the majority of the dataset used inthis study are single-segment FFRMs, where it is appropriate, multisegment FFRMs have been evaluated (Hayes et al. 2015). For multi- segment models, each segment is individually trimmed using the aforementioned process. The effective rupture width W is then taken as the total down-dip extent of the combined, trimmed segments. The effective rupture length L is taken as the lateral extent of the trimmed rupture segments. The total rupture area S is the summed area of each fault segment k: EQ-TARGET;temp:intralink-;df2;55;295Wi? max?zb;i1;zb;i2;…;zb;in? − min?zu;i1;zu;i2;…;zu;in?; ?2? in which zb;ijis the lower width limit (or bottom of down-dip rupture), ?j × wjDij≥ Dlim EQ-TARGET;temp:intralink-;df3;55;223 ?3? zb;ij? for j ? 1;2;…;n; 0jDij< Dlim and zu;ijis the upper width limit (or top of down-dip rupture), ??j − 1? × wjDij≥ Dlim for j ? 1;2;…;n: ?4? EQ-TARGET;temp:intralink-;df4;55;161zu;ij? ∞jDij< Dlim The effective rupture width is then taken as the 75th percentile of the distribution ?W1;W2;…;Wn?. Similarly, to determine the rupture length L, we iteratively step through each subfault row j along the dip direction. For each along- BSSA Early Edition

  4. 4 T. I. Allen and G. P. Hayes N X ?8? EQ-TARGET;temp:intralink-;df8;55;733S ? Lk× Wk: k?1 Because the FFRM dataset of Hayes et al. (2015) is limited to events occurring since 1990, it lacks many of the largest-mag- nitude subduction events that occurred in instrumental times. To supplement the current dataset, we include fault-rupture models from other studies, including the 1952 Mw8.9 Kam- chatka (Johnson and Satake, 1999), the 1957 Mw8.6 Aleutian Islands (Johnson et al., 1994), the 1960 Mw9.5 Concepción (Moreno et al., 2009), and the 1964 Mw9.3 Prince William Sound (Johnson et al., 1996) earthquakes. Rupture dimensions for these earthquakes were taken from published rupture mod- els (as indicated above). The effective dimensions of strong- motiongenerationforthesehistoricaleventsweretakenas85% ofthemodelextent.Thisvalueisapproximatelycommensurate withtheaveragetrimmingpercentagefromtheanalysisoflarge earthquakes (approximately Mw≥8:0) in the Hayes et al. (2015) FFRM dataset (see Ⓔ Table S1). Hayes et al. (2015) did not attempt to model the great 2004 Mw9.2 Suma- tra earthquake using teleseismic inversion techniques because of the extremely long duration of this event. Consequently, we include the model of Rhie et al. (2007), which uses joint in- version of teleseismic and Ground Positioning System static offset observations. The FFRM of Rhie et al. (2007) was proc- essed in a similar manner to those of Hayes et al. (2015) to obtain the effective rupture parameters. Although every effort was made to use rupture parameters determined from a con- sistently derived teleseismic inversion approach, the historical earthquakes and the 2004 Sumatraevent were considered to be critical for characterizing the rupture-scaling parameters for great (Mw>8:5) earthquakes. Theparametersofrupturearea(S),rupturelength(L),rup- ture width (W), maximum slip (Dmax), and average slip (Dav) were extracted from the trimmed FFRMs for regression analy- sis. These parameters were categorized by event type (e.g., in- terface, intraslab, outer rise, and offshore strike slip) to develop rupture-scaling relationships with earthquake magnitude Mw. Seismic moment M0?∝ Mw? is related to both the rupture area and average slip according to the standard formulation Figure 2. for earthquakes used in this study. Subplots show the detailed dis- tribution of earthquakes in (b) the southeast Asia and the southwest Pacificregion;(c)SouthAmerica;and(d)theKuril-Aleutianislandarc region. The numbering of epicenters is consistent with the event index in Ⓔ Table S1, available in the electronic supplement to this article. (a) Global distribution of epicenters and rupture types using the trimmed FFRMs for events between Mw7.1 and 9.5. Theorthogonalregressiontechniqueaccountsformeasurement errors in the x and y variables, and the method provides a uni- que solution that is fully reversible. Larger-magnitude earth- quakesweregivenahigherweightintheregressions,owingto their lower frequency of occurrence. Standard deviations, σODR, were assigned to the x and y variables, and these values are converted to regression weights by taking the inverse of their squares (see Data and Resources). For both x and y var- iables, σODRis taken as 0.2 for Mw<7:5 and as 0.1 for Mw>8:0, respectively. Values for σODRare linearly interpo- lated between 0.2 and 0.1 for intermediate magnitudes. A linear relationship is developed between rupture length and moment magnitude (Fig. 3a). The relationship is generally consistent with other published length-scaling re- lationships for larger magnitudes but tends to yield shorter rupture lengths at small magnitudes. The coefficients for the L–Mwrelationship are provided in Table 2. Tajima et al. (2013) and Somerville et al. (2015) sug- gested that the down-diprupturewidth of subduction interface earthquakes may be limited to about 200 km. Although this hypothesis is based on sparse empirical observations from large (approximately Mw>8:4) megathrust earthquakes, ?9? EQ-TARGET;temp:intralink-;df9;55;249M0? μSDav (Aki, 1966), in which μ is the shear modulus (rigidity). The geographic region and average slab dip (where available for interface events) was also determined to explore subduction-zone-specific correction factors. Rupture param- eters for the earthquakes used to develop scaling models herein are presented in Ⓔ Table S1. The earthquakes are mapped in Figure 2, in which the corresponding event in- dexes are consistent with Ⓔ Table S1. Fault-Scaling Relationships for Interface Ruptures Weighted orthogonal regression methods were used to de- velopscalingrelationshipsforinterfacesubductionearthquakes BSSA Early Edition

  5. Alternative Rupture-Scaling Relationships for Subduction Interface and Other Offshore Environments 5 (a) (b) whereas Heuret et al. (2011) suggest the maximum depth of seismogenic rupture is dependent on the velocity and thermal properties of the subducting slab. Many interface subduction fault-rupture-scaling relations fail to consider width saturation in their parameterization. However, models recently proposed by Allen and Hayes (2015) and Somerville et al. (2015) provide alternative scaling relationships that apply rupture width saturation. Somerville et al. (2015), updated in Skarlatoudis et al. (2016), develop a non-self-similar relation that scales with seismic moment M0andappliesa down-diprupturewidthsaturationof200km with a hinge magnitude near Mw8.4, based on the observa- tions of Tajima et al. (2013) and their own data. Preliminary analysis of the empirical data gathered by Allen and Hayes (2015) and updated in this study also suggested saturation of down-dip rupture width (W2) with increasing magnitude for interface earthquakes. We apply a bilinear orthogonal regres- sion of the W2–Mwdata using a fixed gradient of zero above the hinge magnitude Mh. The hinge magnitude was empiri- cally determined to be Mw8.67 with an average saturation width of 196 km (Fig. 3b). However, rupture widths of as much as ∼250 km are possible for shallowly dipping subduc- tion interfaces(e.g., the Alaska subduction zone).There issig- nificant variability among the W-scaling models of other published studies. Although the dataset used in the present study is largely independent of those used in other studies, the preferred bilinear W2-scaling model developed herein appears to be most consistent with the linear model of Strasser et al. (2010) at low magnitudes and the bilinear non-self-similar scalingmodelofSkarlatoudisetal.(2016)atlargemagnitudes (with a similar average upper limit). Although the W2-scaling model is recommended, a linear (W1) relationship between W andMwisprovidedforcomparisonwithotherpublishedmod- els. The linear W1-scaling model was most comparable to the linear model of Strasser et al. (2010). Although down-dip rupturewidth will saturate with mag- nitude, the rupture area (S) will continue to grow as the rupture length increases, albeit at a slower rate. Consequently, we alsoapply an orthogonal bilinear regression to resolve rup- ture area S2to Mwrelationships. Because the trimmed rupture areas of great megathrust earthquakes can be determined from multisegment fault inversions, often with differing rupture widths along the fault strike, we do not enforce the same Mh as was determined from the bilinear W2–Mwrelationship. However, the hinge magnitude at which the gradient of the preferredbilinear S2–Mwrelationship changes issimilar tothe independently determined W2–Mw relationship: Mw 8.63 (Fig. 3c). The use of the bilinear S2model suggests that rup- ture area increases more rapidly than predicted by existing rupture-area-scaling models at magnitudes less than Mhbut more slowly above Mh. A linear S1-scaling model was also developed for completeness. The linear S1-scaling model is most similar to the linear model of Leonard (2010). The advantage of using a consistently derived suite of FFRMs is that the magnitude scaling of rupture slip can be easily determined from the discretized subfaults. Two slip- 103 ) m k ( h t g n e L e r u t p u R ) m k ( h t d i W e r u t p u R 102 WC94 Bea10 L10 Sea10 Mea13 Sea16 AH17 102 Interface Intraslab Outer Rise Strike Slip Other Interface 101 7.0 7.5 8.0 Magnitude 8.5 9.0 9.5 7.0 7.5 8.0 Magnitude 8.5 9.0 9.5 (c) (d) 105 Rupture Area (km2) ) m ( p i l S m u m i x a M 101 104 100 103 7.0 7.5 8.0 Magnitude 8.5 9.0 9.5 7.0 7.5 8.0 Magnitude 8.5 9.0 9.5 (e) (f) 101 102 ) m ( p i l S e g a r e v A ) m k ( h t d i W 100 1:1 10-1 101 102 103 7.0 7.5 8.0 Magnitude 8.5 9.0 9.5 Length (km) Figure 3. ture parameters from the present study (AH17). Relationships are shown between earthquake magnitude Mwand (a) rupture length L, (b) rupturewidth W, (c) rupture area S, (d) maximum slip Dmax, and (e) average slip Dav, where appropriate, both linear (dashed) and bilinear (solid) fault-scaling relations are provided for width and area scaling. (f) The W–L relationship for interface earthquakes is also shown together with 1:1 L–W scaling (dashed line). The regressions were performed using interface and other interface data classes, and the coefficients for these relationships are given in Table 2. Although not used in the regressions, data points for intraslab, outer-rise, and offshorestrike-slipeventsarealsoshown.Whereapplicable,theAH17 scaling relationships are compared with other published models, in- cluding Wells and Coppersmith (1994; WC94) (a–c) reverse-slip and (d,e) all rupture types; Blaser et al. (2010; Bea10) reverse-slip; Leonard (2010; L10) dip-slip; Strasser et al. (2010; Sea10) interface; Murotani et al. (2013; Mea13); and Skarlatoudis et al. (2016; Sea16) (b) non-self-similar for W and self-similar otherwise. Orthogonal regressions for subduction interface rup- the notion has sound observational and theoretical basis. Hyndman et al. (1997) suggested that the down-dip seismic limit for most subduction zones appears to agree with either a maximum temperature of 350°C or the interface intersection with the fore-arc serpentinized mantle. However, the satura- tion of down-dip rupture widths for large megathrust interface subduction earthquakes most likely varies from one subduc- tion zone to another (Somerville et al., 2015). Indeed, Hayes et al. (2012) quantified seismogenic zone width and observed significant variation between subduction zones, BSSA Early Edition

  6. 6 T. I. Allen and G. P. Hayes Table 2 Interface-Rupture-Scaling Coefficients Determined from Orthogonal Regression Condition† Function A b σx* σy* −2.90 −0.86 −1.91 2.29 −3.63 −5.62 2.23 −4.94 −5.05 0.39 2.29 logL ? a ? b × Mw(km) logW1? a ? b × Mw(km) logW2? a ? b × Mw(km) 0.63 0.35 0.48 0.00 0.96 1.22 0.31 0.71 0.66 0.74 0.00 0.182 0.142 0.137 0.289 0.405 0.294 – – Mw≤8:67 and W2≤ 196 Mw>8:67 – Mw≤8:63 and S2≤ 74;000 Mw>8:63 and 74;000 < S2≤ 137;000 – – W ≤ 196 or L ≤ 369 L > 369 logS1? a ? b × Mw?km2? logS2? a ? b × Mw?km2? 0.255 0.256 0.266 0.267 logDmax? a ? b × Mw(m) logDav? a ? b × Mw(m) logW ? a ? b × logL (km) 0.179 0.209 0.156 0.254 0.315 0.098 All logarithms are to base 10. *σxand σyrefer to the standard deviation of the variables on the left and right side of the equation from the orthogonal regression, respectively. Standard deviations for rupture geometries are in log10 units, whereas magnitudes are linear. †All interface relationships are valid from 7:1 ≤ Mw≤9:5. magnitude models are developed: maximum slip, Dmax (Fig. 3d), and average slip over the trimmed fault area, Dav (Fig. 3e). In addition to L and W scaling, relationships for fault slip are particularly useful for tsunami-hazard modeling and rupture deformation studies. The maximum slip for each earthquake was taken from the FFRM subfault with the larg- est displacement. It should be noted, however, that precise peak displacements are difficult to constrain using teleseis- mic data alone, given the aforementioned trade-off between slip and subfault size and between slip distribution and rup- ture velocity. Consequently, the implied relationships should be considered as representative of the physical process and not an absolute measure of peak slip. Although the Davmodel has a different gradient from other published self-similar scal- ing models for interface earthquakes (Fig 3e), the model lies intermediate between Leonard (2010) and Skarlatoudis et al. (2016) and appears to better represent the average slip for great-magnitude earthquakes (approximately Mw≥9:0). The coefficients for all interface-scaling relationships are provided in Table 2. For completeness, L–W scaling parameters are provided for interface earthquake ruptures. To provide consistency with the bilinear W2–Mwrelationship, the maximum rupture width is limited to 196 km (Fig. 3f). Rupture width scales approximately as three quarters (0.74) of the rupture length for subduction interface earthquakes for ruptures less than the average saturation width (Table 2), with rupture length and width equal near 20–30 km. ence on interface-rupture-scaling properties. The dataset is as- signed a region based on the definition of global subduction zones by Hayes et al. (2012). Figure 4 shows the variability (log10residuals) in subduction interface ruptures, grouped by subduction zone, with respect to the global relations in Figure 3. For length (L), width (W2), and area (S2) rupture scaling, we conduct a Welch’s t-test to determine whether regional differences in the residuals can be considered sta- tistically significant. Although there may be some evidence to support regional differences in rupture-length scaling, the null hypothesis that no regional scaling differences exist can- not be rejected at the 0.05 probability level for any region or rupture metric (Table 3). Based on these analyses (and this dataset), it is difficult to justify the application of regional corrections to the scaling coefficients. Sensitivity of Interface-Scaling Relationships to Slab Dip The sensitivity of the scaling relationships is also evaluated against the average dip across the trimmed rup- ture interface. Trimmed FFRM segments were gridded into a 10 × 10 matrix. The interface dip was estimated at each vertex from the Slab 1.0 models of Hayes et al. (2012) where possible. The average dip for each trimmed FFRM was subsequently calculated. In Figure 5, interface rupture areas are plotted against magnitude and color-coded by the average slab dip. Although no significant bias in rupture scaling could be identified with the dip of the interface, a weak correlation between average dip and the magnitude of interface events was observed. Although only a very small sample over a limited time period, the data suggest that great events (approximately Mw≥8:0) that nucleate on steeply dipping subduction interfaces (approximately ≥ 25°) may occur at lower probabilities than on shallow-dipping inter- faces (approximately ≤ 25°). BSSA Early Edition Regional Dependence of Interface Scaling Different authors identified variations in the physical characteristics of global subduction zones, in parameters such as subductionvelocity, slab age, depth of seismogenic rupture, and maximum magnitude (e.g., Heuret et al., 2011; Hayes etal.,2012;SchellartandRawlinson,2013).Usingthepresent dataset, we investigate whether there is any regional depend-

  7. Alternative Rupture-Scaling Relationships for Subduction Interface and Other Offshore Environments 7 (a) (b) (c) Length Residuals Width Residuals Area Residuals 0.6 0.6 0.6 0.4 0.4 0.4 log10(Obs / Pred) 0.2 0.2 0.2 0.0 0.0 0.0 −0.2 −0.2 −0.2 −0.4 −0.4 −0.4 −0.6 −0.6 −0.6 3 2 3 2 3 2 1 1 1 6 X E M 6 X E M 6 X E M 4 N A V 8 H T O 4 N A V 8 H T O 4 N A V 8 H T O 4 U L A 4 U L A 4 U L A 9 L O S 9 L O S 9 L O S 1 M A S 1 M U S 1 M A S 1 M U S 1 M A S 1 M U S 1 R U K 1 R U K 1 R U K Figure 4. (using bilinear L2–Mwscaling), (b) rupture width, and (c) rupture area, with respect to the global subduction interface relations in Figure 3. Three-letter codes are consistent with the definition of Hayes et al. (2012): ALU, Aleutian; KUR, Kuril; MEX, Mexico; SAM, South America; SOL, Solomon Islands; SUM, Sumatra; VAN, Vanuatu, and OTH, other regions with undefined slab models. The number of events per region is indicated. Box and whisker plots indicating the residuals of the scaling relationship for different subduction zones for (a) rupture length Fault-Scaling Relationships for Other Rupture Types are statistically different from those of interface earthquakes, we first examine their residuals relative to the coefficients for the interface-scaling relations from Table 2. Figure 6 shows the rupture length, width, and area residuals for each rupture type relative to the bilinear interface coefficients. With the ex- ceptionofrupturelength,differencesbetweentherupturescal- ing of interface and noninterface earthquake types are clearly observed. A subsequent t-test concludes that the datasets for the noninterface event types accept the null hypothesis—that they can be treated as independent datasets—and justifies the development of alternative equations (Table 4). Owing to the sparse data coverage over a limited magnitude range for the other event types, the gradients determined through the orthogonal regression analysis on the interface data are used. The following sections discuss the development of scaling re- lations for each of the other rupture types. The FFRM dataset gathered through this study includes earthquakes for other rupture settings such as intraslab, exten- sional outer-rise, and offshore strike-slip earthquakes. To establishwhetherruptureproperties for theseearthquake types Table 3 Regional-Rupture-Scaling Residual Statistics Region ~ x p-value σ −0.04 −0.03 0.23 0.00 0.02 0.07 −0.12 0.01 0.01 0.13 −0.03 0.07 0.07 −0.01 0.05 −0.02 −0.04 0.02 0.17 −0.01 0.38 0.06 −0.04 0.10 −0.04 −0.05 0.00 Rupture-length residuals ALU KUR MEX SAM SOL SUM VAN OTH ALL ALU KUR MEX SAM SOL SUM VAN OTH ALL ALU KUR MEX SAM SOL SUM VAN OTH ALL 0.25 0.17 0.29 0.17 0.11 0.15 0.08 0.13 0.18 0.15 0.14 0.11 0.09 0.16 0.12 0.07 0.16 0.14 0.13 0.29 0.33 0.25 0.24 0.20 0.09 0.23 0.26 0.821 0.546 0.296 0.524 0.921 0.234 0.069 0.477 – 0.471 0.802 0.330 0.096 0.411 0.683 0.237 0.123 – 0.235 0.840 0.221 0.968 0.472 0.360 0.058 0.215 – Intraslab Rupture Scaling Rupture-width residuals In general, it is observed that intraslab rupture length, width, and area-scaling properties all yield smaller values than interface ruptures for the corresponding magnitude (Fig. 7a–c). However, the average and maximum slip distance is larger than for interface events (Fig. 7d,e). This observation is consistent with the notion that either: (a) the stress drop for intraslab events is higher (e.g., Allmann and Shearer, 2009) or that (b) the shear modulus (rigidity) is larger within downgoing, subducting slabs (e.g., Bilek and Lay, 1999). The coefficients for the intraslab-scaling rela- tionships are provided in Table 5. Although magnitude-dependent intraslab earthquake rupture geometry and slip do appear to vary from those of interface earthquakes, the L–W scaling remains roughly con- sistent between the two earthquake mechanisms when the gradient from the low-magnitude interface model is assumed (i.e., below the saturation width; Fig. 7f). Rupture-area residuals The log10regional-rupture-scaling residuals indicating the median ~ x, standard deviation σ, and p-value based on the null hypothesis that the regional scaling of interface ruptures are significant. BSSA Early Edition

  8. 8 T. I. Allen and G. P. Hayes (∼10 km), some evidence suggests that these earthquakes can extend through the thin oceanic crust into the upper man- tle below (Duputel et al., 2012), generating wider ruptures. The model developed for oceanic strike-slip earthquakes allows rupture width up to ∼40 km for larger events (up to Mw8.6). The maximum and average slip characteristics of offshore strike-slip earthquake ruptures indicate significantly larger values than both interface and in-slab earthquakes (Fig. 7d,e). However, comparing each of the rupture-scaling metrics for offshore strike-slip earthquakes examined herein with the commonly used Wells and Coppersmith (1994) scal- ing relationships suggests that these ruptures behave similarly to onshore strike-slip earthquakes (Fig. 7). In the absence of abundant rupture data from offshore strike-slip earthquakes, these results suggest that rupture-scaling relationships devel- oped for shallow crustal events (e.g., Wells and Coppersmith, 1994,andothers)maybeadequatetouseasaproxyinoceanic environments. The coefficients for the oceanic strike-slip earthquakes are presented in Table 5. Outer-rise earthquakes occur within oceanic crust that is about to be subducted, and their focal planes are typically oriented approximately parallel to the trench axes. In un- coupled subduction zones, extensional (normal faulting) earthquakes are associated with plate bending and/or slab pull forces. In strongly coupled subduction zones, both ten- sional and compressional (reverse faulting) outer-rise events are observed (Christensen and Ruff, 1988). While less common than interface earthquakes, outer-rise earthquakes have the potential to trigger tsunamis, which pose significant hazards to coastal communities (e.g., Satake and Tanioka, 1999). Consequently, it is necessary to understand the rup- ture properties of these events, and their uncertainties, so that they can be modeled in both a probabilistic tsunami- and seismic-hazard framework, as well as for scenario tsunami inundation modeling. Among the FFRMs of Hayes et al. (2015), a small num- ber (four) of outer-rise earthquakes are present. Constraining the gradient of the regression coefficients from the interface relations, initial scaling relationships are derived for outer-rise earthquakes. Both thewidth and area scaling of outer-rise rup- tures tend to yield lower values than for equivalently sized interface events (Fig. 7b,c). In contrast, the slip metrics yield larger values for a given magnitude, which is required to con- serve seismic moment (equation 9). The coefficients for the oceanic outer-rise earthquakes are presented in Table 5. 30 Rupture Area (km2) 105 25 Average Dip (°) 20 104 15 10 103 7.0 7.5 8.0 Magnitude 8.5 9.0 9.5 Figure 5. color-coded by the average dip of the rupture interface. Interface rupture area versus magnitude. Data are A comparison of these intraslab-scaling relations with those of Strasser et al. (2010) reveals both relations demon- strate similar characteristics relative to the interface-scaling relations; that is, they both show smaller intraslab rupture di- mensions for a given magnitude (Fig. 7a–c). However, our scaling relations yield systematically shorter rupture lengths for a given magnitude than the model of Strasseret al. (2010). Other Offshore Earthquake Types Although the focus of the present study has been on the more commonly observed subduction interface and intraslab earthquakes, a small data sample was also compiled to pro- vide information on the rupture behavior of offshore strike- slip and extensional outer-rise earthquakes. In the recent seis- mological record, we witnessed several examples of each rupture type, including the Mw8.6 2012 Indian Ocean earth- quake (e.g., Duputel et al., 2012; Yue et al., 2012) and the Mw8.1 2007 Kuril Islands earthquake (Ammon et al., 2008), respectively. However, to our knowledge, no information on the appropriate source scaling for these two faulting types exists in the context of their oceanic settings. Using the fixed gradients obtained from the interface regression analyses, visual examination of the length and width scaling for offshore strike-slip ruptures suggests that these earthquakes generate longer rupture lengths relative to interface earthquakes and significantly narrower ruptures (Figs. 7a,b). The latter observation is likely a consequence of thinner oceanic crust (e.g., Mooney et al., 1998) that is avail- able to rupture (though some recent oceanic strike-slip earth- quakes seem to have ruptured into the oceanic mantle; e.g., Duputel et al., 2012). Thus, in order for magnitude to in- crease, the earthquake ruptures appear to have much larger slip, both Davand Dmax(e.g., equation 9). Although it may typically be expected that oceanic strike-slip earthquakes should not have vertically dipping ruptures any thicker than typical oceanic crustal settings Evaluation of Finite-Fault Trimming Method With the exception of the relationship for Dmax, the scal- ing relationships presented herein are necessarily dependent on the FFRM trimming method chosen. The trimming proc- ess is necessary because rupture-model-inversion space must be chosen a priori to exceed the expected rupture area; thus there should be significant portions of the model that have low (or zero) slip. We investigate the performance of the previously described trimming method using crustal earth- BSSA Early Edition

  9. Alternative Rupture-Scaling Relationships for Subduction Interface and Other Offshore Environments 9 (a) (b) (c) 1.0 1.0 1.0 Length Residuals Width Residuals Area Residuals 0.5 0.5 0.5 log10(Obs / Pred) 0.0 0.0 0.0 −0.5 −0.5 −0.5 −1.0 −1.0 −1.0 1 1 1 4 e s i R r e t u O 4 e s i R r e t u O 4 e s i R r e t u O 8 8 1 8 1 1 1 1 1 6 e c a f r e t n I 6 e c a f r e t n I 6 e c a f r e t n I 2 b 2 b 2 b p i l S e k i r t S p i l S e k i r t S p i l S e k i r t S a l s a r t n I a l s a r t n I a l s a r t n I Figure 6. types relative to the bilinear interface-scaling coefficients in Table 2. Rupture-scaling residuals for interface events (enclosed in solid boxes) are compared with the other rupture types. The number of events for each rupture type is indicated. Box and whisker plots indicating model residuals in (a) rupture length, (b) rupturewidth, and (c) rupture area for different event quakes, for which coseismic rupture lengths can be more re- liably determined from postevent reconnaissance or through interferometric methods (e.g., interferometric synthetic aper- ture radar). A listing of earthquakes used for this purpose is provided in Table 6. Figure 8 shows the comparison of ob- served coseismic rupture lengths against those determined from the FFRMs. Figure 8 reveals an excellent correspon- dence between the observed and modeled rupture lengths with a standard deviation of the residuals of 0.04 log units. Relative to the standard deviation of the scaling models themselves (e.g., Table 2), the uncertainty of determining rupture dimensions from FFRMs is a minor contribution rel- ative to the aleatory variability between earthquakes. not possible. Consequently, resolving the effective area that generates large displacements and strong ground motions is a challenging task. Prior to the advent of FFRM techniques, rupture geometries for large offshore earthquakes were largely inferred from the distribution of aftershock epicenters in the days following the mainshock (e.g., Wells and Copper- smith, 1994). Although this method still provides a rapid and useful validation of FFRMs, the distribution of aftershocks may not accurately represent the true rupture area or the region of strong-motion generation from the mainshock. Exploration of the scatter between alternative subduc- tion interface-length-scaling linear (L) relationships from various authors suggests that most of the models broadly agree (Fig. 3a). However, there is significant scatter among published width- and area-scaling models (Fig. 3b,c). A key factor driving the difference in rupture scaling is the assumption of either linear (e.g., Blaseret al., 2010; Leonard, 2010; Strasser et al., 2010) or width-limited bilinear scaling (e.g., Skarlatoudis et al., 2016; this study). Those models that assume a linear W–Mwgenerally predict narrower rupture widths for interface events at lower magnitudes and larger rupture widths for great-sized earthquakes (approximately Mw≥8:7). Despite the independent nature of the datasets used to derive their relationships, there is good agreement between the rupture-width saturation of subduction interface earthquakes between the Skarlatoudis et al. (2016) bilinear rupture-width scaling model and the model proposed herein. In contrast to other published relationships, the model herein proposes bilinear interface magnitude-area rupture scaling. The bilinear parameterization yields larger areas of significant ground-motion generation for smaller magnitude events than predicted by alternative relationships (approxi- mately Mw8.0–8.8) but generally suggests smaller rupture areas for great-sized earthquakes (Fig. 3c). Notably, the bilinear area-scaling model suggests that the area of strong ground motion generation is less well correlated to mag- nitude above Mh. This suggests that fault segments with Discussion The characterization of earthquake rupture models in subduction and oceanic environments carries a higher degree of uncertainty than for shallow crustal earthquakes because direct observation of surface displacement surrounding the source and of the extent of the coseismic rupture is generally Table 4 Rupture-Scaling Residual Statistics by Event Type Relative to the Preferred Interface-Type Coefficients ~Δ Event Type p-value σ −0.17 0.04 0.00 −0.14 −0.33 −0.55 −0.26 −0.26 −0.44 Rupture-length residuals Intraslab Outer rise Strike slip Intraslab Outer rise Strike slip Intraslab Outer rise Strike slip 0.16 0.08 0.17 0.14 0.09 0.19 0.26 0.19 0.30 0.001 0.797 0.218 0.000 0.005 0.000 0.000 0.057 0.000 Rupture-width residuals Rupture-area residuals The median (~ x), standard deviation (σ), and p-value of the log10 rupture-scaling residuals by event type relative to interface event type scaling coefficients in Table 2. BSSA Early Edition

  10. 10 T. I. Allen and G. P. Hayes (a) (b) candidate models by comparing the overall fit, as well as the complexity, of any given model. Here, weexamine therelative qualityofthelinearW1andbilinearW2width-scaling models. Using the full dataset, the W1width-scaling model was deter- mined to have a marginally better AIC value than the W2 model(−68:4relativeto−67:7),withthebilinearmodelbeing 71% as likely as the linear fit to model the rupture-width data. However, if we only consider earthquakes of magnitude Mw≥8:0, which are less abundant in the dataset but more im- portant (see Fig. 2b), the four-coefficient bilinear parameter- ization is 92% as likely as the two-coefficient linear parame- terization to model the rupture-width data. Although these tests suggest there may be limited ben- efit in using a more complex model, statistical measures of likelihood can only be so effective in assessing the quality of a model and often cannot capture real-world complexities in earthquake source physics. These likelihood metrics must be placed in the context of the physical world, in which down- dip rupture widths, continuing to grow with increasing mag- nitude, become less likely owing to the thermal properties of subduction interfaces (e.g., Hyndman et al., 1997). Conse- quently, given the similar AIC assessments, we continue to recommend the bilinear rupture-width model as the preferred scaling relationship with earthquake magnitude. There are few magnitude–slip scaling relationships for interface earthquakes. The empirical model proposed herein suggests larger average (Dav) and maximum (Dmax) slips for large-magnitude earthquakes than the self-similar models of Murotani et al. (2013) and Skarlatoudis et al. (2016) (Fig. 3d,e). This appears to be consistent with FFRMs from recent megathrust earthquakes (e.g., the great- sized 2004 Mw9.2 Sumatra–Andaman Islands and 2011 Mw9.0 Tohoku earthquakes). The most-commonly applied intraslab-specific rupture- scaling model is that of Strasser et al. (2010). Their model and those proposed herein generally show similar character- istics relative to interface scaling relationships (Fig. 7a–c). That is, they both show smaller rupture dimensions for a given magnitude for intraslab events. The relationships pro- posed herein also provide rupture-slip scaling, which shows greater maximum and average slip for intraslab events (Fig. 7d–f), which is required to conserve seismic moment given the smaller rupture geometries (equation 9). This is consistent with the notion that intraslab earthquakes gener- ally have higher stress drops than interface events. Because intraslab earthquakes are generally not expected to grow much beyond Mw8.0 (because they are typically limited to the thickness of the subducting slab, with the exception of rare, multifault ruptures like the 2013 Mw8.3 Okhotsk earth- quake), only linear scaling models are proposed. Based on the sparse dataset of offshore strike-slip- faulting earthquake rupture models gathered herein, we observesimilar rupture scaling to that observed from onshore strike-slip earthquakes from other studies (Fig. 7). Because of the small sample dataset of 11 earthquakes, and their apparent similar behavior to the rupture scaling observed for 103 ) m k ( h t g n e L e r u t p u R ) m k ( h t d i W e r u t p u R 102 102 101 7.0 7.5 8.0 8.5 9.0 7.0 7.5 8.0 8.5 9.0 Magnitude Magnitude (c) (d) 105 Rupture Area (km2) ) m ( p i l S m u m i x a M 101 104 Interface Intraslab Outer Rise Strike Slip WC94 SS S10 Intraslab Interface Intraslab Outer Rise Strike Slip Other Interface 100 103 7.0 7.5 8.0 8.5 9.0 7.0 7.5 8.0 8.5 9.0 Magnitude Magnitude (e) (f) 101 102 ) m ( p i l S e g a r e v A ) m k ( h t d i W 100 101 1:1 10-1 102 Length (km) 103 7.0 7.5 8.0 8.5 9.0 Magnitude Figure 7. Relationships are shown between earthquake magnitude Mw and (a) rupture length L, (b) rupture width W, (c) rupture area S, (d) maxi- mum slip Dmax, and (e) average slip Dav. (f) Length–width scaling is also shown together with 1:1 L–W scaling (gray dashed line). Where applicable, the Strasseret al. (2010; S10 intraslab) scaling relations are shownforin-slabearthquakeruptures,aswellastheWellsandCopper- smith (1994; WC94 SS) relationship for crustal strike-slip ruptures. Orthogonal regressions for other offshore rupture types. relativelysmaller asperity areas have the potential to generate great-magnitude earthquakes (Mw>9:0) than might be pre- dicted by existing area-magnitude scaling relationships. The occurrence of these great-magnitude events assumes that the average slip across the rupture surface continues to grow with magnitude. This effect was recently demonstrated through the 2011 Mw9.0 Tohoku earthquake, which had sig- nificantly smaller rupture dimensions than had previously been observed for an earthquake of its magnitude. There is clearly a trade-off between the complexity of the model and its ability to predict real-world observations. Con- sequently, one must weigh the improved predictive power of our four-coefficient bilinear model against the simpler two- coefficientmodelusedforbothrupturewidthandrupturearea. Akaike information criterion (AIC; Akaike, 1973) is a mea- sure of the relative quality of one or more statistical models to a given dataset. The method is often used to determine the relative likelihood (e.g., Wagenmakers and Farrell, 2004) of BSSA Early Edition

  11. Alternative Rupture-Scaling Relationships for Subduction Interface and Other Offshore Environments 11 500 relative to interface-rupturing events, suggesting that the off- shore strike-slip events possess significantly higher stress drops. Similarly, while also derived from a small dataset, the rupture scaling indicated for outer-rise earthquakes suggests narrower rupture widths than do interface earthquakes of the same size, but larger average slips (Fig. 7). As previously discussed, the scaling relationships pre- sented herein are necessarily dependent on theFFRM and the trimming method chosen (with the exception of the relation- ship for Dmax). The aforementioned method used in this study was designed to be both repeatable and to preserve the area of fault rupture capable of strong ground motion and tsunami-wave generation. Mai and Beroza (2000) derive effective rupture dimensions from the autocorrelation of the slip function as an alternative trimming procedure. The change in length following the trimming process in the present study is generally consistent with Mai and Beroza (2000). Other studies developed alternative logic to capture fault parameters. The Next Generation Attenuation project used a preferential logic based on: (1) field observations of coseismic surface ruptures; (2) FFRMs; and (3) observations of aftershock distributions (Chiou et al., 2008). When FFRMs are used, Chiou et al. (2008) recommends that regions of more than 50 cm of coseismic slip should not be trimmed. In this study, we do not follow this convention be- cause the resolution of the FFRMs for offshore earthquakes is generally not as accurate as for the crustal earthquakes considered by Chiou et al. (2008). In another study exploring the recorded ground-motion field from the 2011 Tohoku earthquake (Stewart et al., 2013), the distance to seismic rup- ture is calculated by trimming regions of the preferred FFRM for which slip is less than 3 m. Finally, it is worth noting that 2001-11-14 2002-11-03 ) m k ( h t g n e L c i m s i e s o C d e v r e s b O 2008-05-12 2013-09-24 200 2015-04-25 2006-04-20 100 2001-01-26 2005-10-08 50 50 100 Trimmed Rupture Length (km) 200 500 Figure 8. against those determined from the FFRMs. For reference, the dashed lines indicate the standard deviation from the Mw–L scaling model for subduction earthquakes (Table 2). Each data point is an- notated with the earthquake’s date. Comparison of observed coseismic rupture lengths onshore strike-slip events, it may be prudent to assume rup- ture-scaling properties of those existing relationships that are defined based on much larger datasets of onshore coseismic ruptures (e.g., Wells and Coppersmith, 1994; Hanks and Bakun, 2002; and others). Although from only a small sam- ple size, it is interesting to note the large differences in rup- ture area and slip for our offshore strike-slip earthquakes Table 5 Rupture-Scaling Coefficients for Other Offshore Earthquake Rupture Styles Type a SEa b* MwRange σx −3.03 −2.87 −2.81 −1.01 −1.18 −1.39 −3.89 −3.89 −4.04 −4.73 −4.58 −4.39 −4.81 −4.70 −4.52 0.35 0.04 −0.22 Length: logL ? a ? b × Mw(km) Inslab Outer rise Strike slip Inslab Outer rise Strike slip Inslab Outer rise Strike slip Inslab Outer rise Strike slip Inslab Outer rise Strike slip Inslab Outer rise Strike slip 0.04 0.04 0.05 0.03 0.04 0.06 0.06 0.08 0.08 0.05 0.08 0.08 0.06 0.08 0.10 0.03 0.02 0.06 0.63 0.14 0.08 0.15 0.15 0.08 0.17 0.19 0.11 0.2 0.21 0.14 0.21 0.22 0.14 0.26 0.13 0.09 0.18 7.3–8.3 7.4–8.2 7.2–8.7 7.3–8.3 7.4–8.2 7.2–8.7 7.3–8.3 7.4–8.2 7.2–8.7 7.3–8.3 7.4–8.2 7.2–8.7 7.3–8.3 7.4–8.2 7.2–8.7 7.3–8.3 7.5–8.2 7.5–8.7 Width: log W ? a ? b × Mw(km) 0.35 Area: logS ? a ? b × Mw?km2? 0.96 Maximum slip: logDmax? a ? b × Mw(m) 0.71 Average slip: logDav? a ? b × Mw(m) 0.66 Width–length: logW ? a ? b × logL (km) 0.74 All logarithms are base 10. SEais the standard error on the variable a. *Gradients b determined from linear regression of interface-rupture-scaling coefficients (Table 2). The constant a is determined from orthogonal regression in all cases. BSSA Early Edition

  12. 12 T. I. Allen and G. P. Hayes Table 6 Crustal Earthquakes Used to Evaluate the Determination of Rupture Length from the FFRMs Date Trimmed Length (km) Minimum Coseismic Length (km) Maximum Coseismic Length (km) (yyyy/mm/dd) Place Mw References 2001/01/26 2001/11/14 2002/11/03 Bhuj, India Central Kunlun, China Denali, Alaska 7.61 7.84 7.97 75 414 264 80 400 340 80 400 340 Jade et al. (2002) Lin et al. (2002) Eberhart-Phillips et al. (2003) and Haeussler et al. (2004) Jayangondaperumal and Thakur (2008) and Chini et al. (2011) Rogozhin et al. (2009) Dong et al. (2008) and Liu-Zeng et al. (2009) Zinke et al. (2014) and Zhou et al. (2015) Diao et al. (2015) and Wang and Fialko (2015) 2005/10/08 Kashmir, Pakistan 7.57 75 65 75 2006/04/20 2008/05/12 Koryakia, Russia Wenchuan, China 7.58 7.88 132 259 140 200 140 300 2013/09/24 Balochistan, Pakistan 7.72 198 205 225 2015/04/25 Gorkha, Nepal 7.86 160 150 185 FFRM, finite-fault rupture model. thereare also trade-offs between Dmaxand the resolution of the subfault area chosen by the FFRM modeler. Thus the maxi- mumslippredictedbytheequationshereinshouldonlybecon- sidered as representative of the physical rupture process. in which the assumed maximum earthquake magnitude may be basedsolelyontheassumedasperity(orfault)area.Specifically, subduction interface earthquakes with larger average slip for a given asperity area would yield larger ground-motion ampli- tudes and would likely generate larger coseismic displacements on the ocean floor, leading to more severe tsunami waves. The regional variability in interface-rupture-scaling char- acteristics, which may arise from factors such as varying slab dip, velocity, or temperature, was also investigated (Fig. 4). However, hypothesis testing currently does not support re- gion-specific adjustment factors (Table 3). Although no sig- nificant bias in rupture scaling could be identified with the dip of the interface, a potential link between dip and the likely maximum magnitude of interface events was observed in the present FFRM dataset (which is typically limited to post-1990 events). The data suggest that great events (approximately Mw≥8:0) that nucleate on steeply dipping subduction inter- faces (approximately ≥ 25°) may occur at much lower prob- abilities than on shallow-dipping interfaces, particularly for regions characterized by continental subduction. Not included in our dataset is the 1985 Mw7.96 Michoacán, Mexico, earth- quake (e.g., Ekström et al., 2012), which occurred in the more steeply dipping Mexico subduction zone (slab dip ∼26°; Hayesetal.,2012).Theoccurrenceofthe1985eventsuggests that Mw8.0 may not be the upper magnitude limit in steeply dipping subduction environments. However, the likelihood of the occurrence of these great-sized earthquakes may be lower than in more shallowly dipping subduction zone settings. Rupture-scaling relationships are also provided for intraslab earthquakes, as well as for offshore strike-slip and tensional outer-rise events. Because these faulting types represent a smaller population of the FFRM database, their associated models are constrained by the magnitude-scaling rates for interface events. In all cases, rupture areas tend to be smaller than for interface events of the same magnitude, with larger maximum and average slip. These observations reflect both the narrower fault widths that have the potential to rup- ture and likely higher stress drops. Conclusions Using a new database of consistently derived FFRMs from teleseismic inversion, alternative rupture-scaling rela- tionships have been developed for earthquakes in subduction (interface and intraslab) and other offshore environments. The magnitude limits and conditions of use for the equations are provided in Tables 2 and 5. Interface-rupture-scaling re- lationships are provided for rupture area (S), rupture length (L), rupture width (W), maximum slip (Dmax), and average slip (Dav) for earthquakes between Mw7.1 and 9.5. Based on the observations of Hyndman et al. (1997), the down-dip seismogenic limit for most subduction zones ap- pears to agree with either a maximum temperature of 350°C or the thrust intersection with the fore-arc serpentinized man- tle. This suggests that there should be some lower limit to down-dip rupture extent, which appears to be consistent with the empirical data from this and other studies (e.g., Tajima et al., 2013). We observe that the down-dip rupture width appears to saturate for larger-magnitude earthquakes near 200 km (196 km on average). A bilinear Mw–W scaling model is developed that reflects this magnitude saturation of rupture width (Fig. 3b). Unlike other existing subduction interface-rupture-scaling relations, we also assume bilinear Mw–S scaling. This relationship yields larger rupture areas for magnitudes between approximately Mw8.0 and 8.8, but smaller areas at large magnitudes (Fig. 3c). Furthermore, this bilinear area-scaling model suggests that fault asperity area is less well correlated with magnitude for earthquakes of Mw>8:6. Consequently, the magnitude for great earth- quakes appears to be more strongly controlled by the average slip across the rupture asperity. This observation may have consequences for earthquake- and tsunami-hazard assessments BSSA Early Edition

  13. Alternative Rupture-Scaling Relationships for Subduction Interface and Other Offshore Environments 13 Bilek, S. L., and T. Lay (1999). Rigidity variations with depth along inter- plate megathrust faults in subduction zones, Nature 400, 443–446, doi: 10.1038/22739. Blaser, L., F. Krüger, M. Ohrnberger, and F. Scherbaum (2010). Scaling relations of earthquake source parameter estimates with special focus on subduction environment, Bull. Seismol. Soc. Am. 100, 2914–2926, doi: 10.1785/0120100111. Chini, M., F. R. Cinti, and S. Stramondo (2011). Co-seismic surface effects from very high resolution panchromatic images: The case of the 2005 Kashmir (Pakistan) earthquake, Nat. Hazards Earth Syst. Sci. 11, 931– 943, doi: 10.5194/nhess-11-931-2011. Chiou, B., R. Darragh, N. Gregor, and W. Silva (2008). NGA project strong- motion database, Earthq. Spectra 24, 23–44, doi: 10.1193/1.2894831. Christensen, D. H., and L. J. Ruff (1988). The seismic coupling of outer rise earthquakes, J. Geophys. Res. 93, 13,421–13,444, doi: 10.1029/ JB093iB11p13421. Diao, F., T. R. Walter, M. Motagh, P. Prats-Iraola, R. Wang, and S. V. Samsonov (2015). The 2015 Gorkha earthquake investigated from ra- dar satellites: Slip and stress modeling along the MHT, Front. Earth Sci. 3, doi: 10.3389/feart.2015.00065. Dong, S., Y. Zhang, Z. Wu, N. Yang, Y. Ma, W. Shi, Z. Chen, C. Long, and M. An (2008). Surface rupture and co-seismic displacement produced by the Ms8.0 Wenchuan earthquake of May 12th, 2008, Sichuan, China: Eastwards growth of the Qinghai-Tibet plateau, Acta Geol. Sin. 82, 938–948, doi: 10.1111/j.1755-6724.2008.tb00649.x. Duputel, Z., H. Kanamori, V. C. Tsai, L. Rivera, L. Meng, J.-P. Ampuero, and J. M.Stock (2012). The2012Sumatra great earthquakesequence, Earth Planet. Sci. Lett. 351/352, 247–257, doi: 10.1016/j.epsl.2012.07.017. Eberhart-Phillips, D., P. J. Haeussler, J. T. Freymueller, A. D. Frankel, C. M. Rubin, P. Craw, N. A. Ratchkovski, G. Anderson, G. A. Carver, A. J. Crone, et al. (2003). The 2002 Denali fault earthquake, Alaska: A large magnitude, slip-partitioned event, Science 300, 1113–1118, doi: 10.1126/ science.1082703. Ekström, G., M. Nettles, and A. M. Dziewoński (2012). The global CMT project 2004–2010: Centroid-moment tensors for 13,017 earthquakes, Phys. Earth Planet. In. 200/201, 1–9, doi: 10.1016/j.pepi.2012.04.002. Haeussler, P. J., D. P. Schwartz, T. E. Dawson, H. D. Stenner, J. J. Lienkaem- per, B. Sherrod, F. R. Cinti, P. Montone, P. A. Craw, A. J. Crone, et al. (2004). Surface rupture and slip distribution of the Denali and Tot- schunda faults in the 3 November 2002 M 7.9 earthquake, Alaska, Bull. Seismol. Soc. Am. 94, S23–S52, doi: 10.1785/0120040626. Hanks, T. C., and W. H. Bakun (2002). A bilinear source-scaling model for M-log A observations of continental earthquakes, Bull. Seismol. Soc. Am. 92, 1841–1846, doi: 10.1785/0120010148. Hayes, G. P., H. M. Benz, and W. D. Barnhart (2015). Near realtime, multi- approach earthquake source inversion, and an extensive, consistent finite fault database, Seismol. Res. Lett. 86, no. 2B, 711 pp. Hayes, G. P., D. J. Wald, and R. L. Johnson (2012). Slab1.0: A three- dimensional model of global subduction zone geometries, J. Geophys. Res. 117, no. B1, doi: 10.1029/2011JB008524. Heuret, A., S. Lallemand, F. Funiciello, C. Piromallo, and C. Faccenna (2011). Physical characteristics of subduction interface type seismo- genic zones revisited, Geochem. Geophys. Geosys. 12, no. Q01004, doi: 10.1029/2010GC003230. Horspool, N., I. Pranantyo, J. Griffin, H. Latief, D. H. Natawidjaya, W. Kongko, A. Cipta, B. Bustaman, S. D. Anugrah, and H. K. Thio (2014). A prob- abilistictsunamihazardassessmentforIndonesia,Nat.HazardsEarthSyst. Sci. 2, 3105–3122, Discussion Paper, doi: 10.5194/nhessd-2-3423-2014. Hyndman, R. D., M. Yamano, and D. A. Oleskevich (1997). The seismo- genic zone of subduction thrust faults, Isl. Arc 6, 244–260, doi: 10.1111/j.1440-1738.1997.tb00175.x. Jade,S., M. Mukul,I. A. Parvez, M. B.Ananda, P. D. Kumar, and V. K. Gaur (2002). Estimates of coseismic displacement and post-seismic defor- mation using Global Positioning System geodesy for the Bhuj earth- quake of 26 January 2001, Curr. Sci. 82, 748–752. Jayangondaperumal, R., and V. C. Thakur (2008). Co-seismic secondary sur- face fractures on southeastward extension of the rupture zone of the The objective for developing rupture-scaling relation- ships of offshore earthquakes is to better determine the area of strong-motion generation and slip for both earthquake- and tsunami-hazard modeling. These alternative models will allow hazard modelers and practitioners to explore the epistemic uncertainty among existing rupture-scaling rela- tions for subduction and other offshore earthquakes for a variety of applications (e.g., PSHA, PTHA, and scenario ground shaking and tsunami modeling). Furthermore, the scaling models proposed herein could be used in concert with pre-existing models of subducting slab geometries (e.g., Hayes et al., 2012) to generate rapid empirical fault- rupture models for near-real-time earthquake ground-shak- ing and impact assessments. This approach is likely to be better—in the immediate aftermath of a large earthquake, and prior to the availability of a teleseismic inversion-based FFRM—than assuming a point-source rupture. Conse- quently, areas potentially affected by strong ground shaking could be rapidly assessed, which may facilitate improved impact assessments and response. Data and Resources Most finite-fault rupture models (FFRMs) used in this study were obtained from the U.S. Geological Survey’s Advanced National Seismic System Comprehensive Catalog (ComCat; https://earthquake.usgs.gov/data/comcat/, last ac- cessed February 2017), whereas others were calculated speci- fically for this study. Sources for rupture parameters of other interface earthquakes are referenced in the article. The SciPy ODRPACK functions were used for the orthogonal regres- sions. Further details on the method can be obtained from SciPy.org (last accessed February 2017). Acknowledgments Many thanks to Roy Hyndman, Kelin Wang, William Levandowski, and an anonymous reviewer for their thoughtful reviews of this article. Andreas Skarlatoudis is thanked for providing updated parameterization for the Somerville et al. (2015) non-self-similar L and W scaling models. References Akaike, H. (1973). Information theory as an extension of the maximum likelihood principle, in B. N. Petrov and F. Csaki (Editors), Second International Symposium on Information Theory, Akaemiai Kiado, Budapest, Hungary, 267–281. Aki, K. (1966). Generation and propagation of G waves from the Niigata earthquake of June16, 1964. Part 2. Estimation of earthquake moment, released energy, and stress-straindrop from the G wavespectrum,Bull. Earthq. Res. Inst. 44, 73–88. Allen, T. I., and G. P. Hayes (2015). Subduction interface fault scaling relationships to facilitate rapid ground-shaking and impact assess- ments, Seismol. Res. Lett. 86, no. 2B, 618. Allmann, B. P., and P. M. Shearer (2009). Global variations of stress drop for moderate to large earthquakes, J. Geophys. Res. 114, no. B01310, doi: 10.1029/2008JB005821. Ammon, C. J., H. Kanamori, and T. Lay (2008). A great earthquake doublet and seismic stress transfer cycle in the central Kuril Islands, Nature 451, 561–565, doi: 10.1038/nature06521. BSSA Early Edition

  14. 14 T. I. Allen and G. P. Hayes 2005 Kashmir earthquake, Tectonophysics 446, 61–76, doi: 10.1016/j. tecto.2007.10.006. Johnson, J. M., and K. Satake (1999). Asperity distribution of the 1952 great Kamchatka earthquake and its relation to future earthquake potential in Kamchatka, Pure Appl. Geophys. 154, 541–553, doi: 10.1007/978-3- 0348-8679-6_8. Johnson, J. M., K. Satake, S. R. Holdahl, and J. Sauber (1996). The 1964 Prince William Sound earthquake: Joint inversion of tsunami and geo- detic data, J. Geophys. Res. 101, 523–532, doi: 10.1029/95JB02806. Johnson, J. M., Y. Tanioka, L. J. Ruff, K. Satake, H. Kanamori, and L. R. Skyes (1994). The 1957 great Aleutian earthquake, Pure Appl. Geophys. 142, 3–28, doi: 10.1007/BF00875966. Leonard, M. (2010). Earthquake fault scaling: Self-consistent relating of rupture length, width, average displacement, and moment release, Bull. Seismol. Soc. Am. 100, 1971–1988, doi: 10.1785/0120090189. Lin,A.,F.Fu,J.Guo,Q.Zeng,G.Dang,W.He,andY.Zhao(2002).Co-seismic strike-slipandrupturelengthproducedbythe2001Ms8.1CentralKunlun earthquake, Science 296, 2015–2017, doi: 10.1126/science.1070879. Liu-Zeng, J., Z. Zhang, L. Wen, P. Tapponnier, J. Sun, X. Xing, G. Hu, Q. Xu, L. Zeng, L. Ding, et al. (2009). Co-seismic ruptures of the 12May 2008, Ms8.0 Wenchuanearthquake, Sichuan:East–westcrustal shortening on oblique, parallel thrusts along the eastern edge of Tibet, Earth Planet. Sci. Lett. 286, 355–370, doi: 10.1016/j.epsl.2009.07.017. Mai, M., and G. C. Beroza (2000). Source scaling properties from finite- fault-rupture models, Bull. Seismol. Soc. Am. 90, 604–615, doi: 10.1785/0119990126. Mai, M., and K. K. S. Thingbaijam (2014). SRCMOD: An online database of finite-fault rupture models, Seismol. Res. Lett. 85, 1348–1357, doi: 10.1785/0220140077. Mooney, W. D., G. Laske, and T. G. Masters (1998). CRUST 5.1: A global crustal model at 5° × 5°, J. Geophys. Res. 103, 727–747, doi: 10.1029/ 97JB02122. Moreno, M. S., J. Bolte, J. Klotz, and D. Melnick (2009). Impact of megathrust geometry on inversion of coseismic slip from geodetic data: Application to the 1960 Chile earthquake, Geophys. Res. Lett. 36, L16310, doi: 10.1029/2009GL039276. Murotani, S., H. Miyake, and K. Koketsu (2008). Scaling of characterized slip models for plate-boundary earthquakes, Earth Planets Space 60, 987–991, doi: 10.1186/BF03352855. Murotani, S., K. Satake, and Y. Fujii (2013). Scaling relations of seismic moment, rupture area, average slip, and asperity size for M ∼ 9 sub- duction-zone earthquakes, Geophys. Res. Lett. 40, 5070–5074, doi: 10.1002/grl.50976. Pagani, M., D. Monelli, G. Weatherill, L. Danciu, H. Crowley, V. Silva, P. Henshaw, R. Butler, M. Nastasi, L. Panzeri, et al. (2014). OpenQuake Engine: An open hazard (and risk) software for the Global Earthquake Model, Seismol. Res. Lett. 85, 692–702, doi: 10.1785/0220130087. Rhie, J., D. Dreger, R. Bürgmann, and B. Romanowicz (2007). Slip of the 2004 Sumatra–Andaman earthquake from joint inversion of long- period global seismic waveforms and GPS static offsets, Bull. Seismol. Soc. Am. 97, S115–S127, doi: 10.1785/0120050620. Rogozhin, E. A., A. N. Ovsyuchenko, A. V. Marakhanov, and S. S. Novikov (2009). Tectonic position and geological manifestations of the 2006 Olyutor earthquake in Koryakia, Geotectonics 43, 443, doi: 10.1134/ S0016852109060016. Satake, K., and Y. Tanioka (1999). Sources of tsunami and tsunamigenic earthquakes in subduction zones, Pure Appl. Geophys. 154, 467– 483, doi: 10.1007/978-3-0348-8679-6_5. Schellart, W. P., and N. Rawlinson (2013). Global correlations between maximum magnitudes of subduction zone interface thrust earthquakes and physical parameters of subduction zones, Phys. Earth Planet. In. 225, 41–67, doi: 10.1016/j.pepi.2013.10.001. Skarlatoudis, A. A., P. G. Somerville, and H. K. Thio (2016). Source-scaling relations of interface subduction earthquakes for strong ground motion and tsunami simulation, Bull. Seismol. Soc. Am. 106, no. 4, 1652, doi: 10.1785/0120150320. Somerville, P., A. Skarlatoudis, and H. K. Thio (2015). Source scaling relations of subduction earthquakes for strong ground motion and tsu- nami prediction,URS Group,Inc.Award Number:G13AP00028, 25pp. Sørensen, M., M. Spada, A. Babeyko, S. Wiemer, and G. Grünthal (2012). Probabilistic tsunami hazard in the Mediterranean Sea, J. Geophys. Res. 117, no. B01305, doi: 10.1029/2010JB008169. Stewart, J. P., S. Midorikawa, R. W. Graves, K. Khodaverdi, T. Kishida, H. Miura, Y. Bozorgnia, and K. W. Campbell (2013). Implications of the Mw 9.0 Tohoku-Oki earthquake for ground motion scaling with source, path, and site parameters, Earthq. Spectra 29, S1–S21, doi: 10.1193/1.4000115. Strasser, F. O.,M. C. Arango,and J. J. Bommer(2010). Scalingof the source dimensions of interface and intraslab subduction-zone earthquakes with moment magnitude, Seismol. Res. Lett. 81, 941–950, doi: 10.1785/gssrl.81.6.941. Tajima, R., Y. Matsumoto, and K. Irikura (2013). Comparative study on scal- ing relations of source parameters for great earthquakes in inland crusts and on subducting plate-boundaries, Zisin 66, 31–45, doi: 10.4294/zi- sin.66.31 (in Japanese with English abstract). Thio, H.-K., and W. Li (2015). Probabilistic tsunami hazard analysis of the Cascadia subduction zone and the role of epistemic uncertainties and aleatory variability, 11th Canadian Conf. on Earthquake Engineering, Victoria, Canada, Paper 98815. Wagenmakers, E.-J., and S. Farrell (2004). AIC model selection using Akaike weights, Psychon. Bull. Rev. 11, 192–196, doi: 10.3758/BF03206482. Wang, K., and Y. Fialko (2015). Slip model of the 2015 Mw7.8 Gorkha (Nepal) earthquake from inversions of ALOS-2 and GPS data, Geophys. Res. Lett. 42, 7452–7458, doi: 10.1002/2015GL065201. Wells, D. L., and K. J. Coppersmith (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seismol. Soc. Am. 84, 974–1002. Ye, L., T. Lay, H. Kanamori, and L. Rivera (2016). Rupture characteristics of major and great (Mw≥7:0) megathrust earthquakes from 1990 to 2015: 1. Source parameter scaling relationships, J. Geophys. Res. 121, 826–844, doi: 10.1002/2015JB012426. Yue, H., T. Lay, and K. D. Koper (2012). En échelon and orthogonal fault ruptures of the 11 April 2012 great intraplate earthquakes, Nature 490, 245–249, doi: 10.1038/nature11492. Zhou, Y., J. R. Elliott, B. Parsons, and R. T. Walker (2015). The 2013 Ba- lochistan earthquake: An extraordinary or completely ordinary event? Geophys. Res. Lett. 42, doi: 10.1002/2015GL065096. Zinke,R., J. Hollingsworth, and J. F. Dolan (2014).Surface slip and off-fault deformation patterns in the 2013 Mw7.7 Balochistan, Pakistan earth- quake: Implications for controls on the distribution of near-surface coseismic slip, Geochem. Geophys. Geosys. 15, 5034–5050, doi: 10.1002/2014GC005538. Pacific Geoscience Centre Natural Resources Canada 9860 West Saanich Road Sidney, British Columbia Canada V8L 4B2 trevor.allen@ga.gov.au (T.I.A.) National Earthquake Information Center U.S. Geological Survey PO Box 25046, MS-966 Denver, Colorado 80225 ghayes@usgs.gov (G.P.H.) Manuscript received 8 August 2016; Published Online 21 March 2017 BSSA Early Edition