Coseismic Throw Variation Across Along‐Strike Bends on Active Normal Faults: Implications for Displacement Versus Length Scaling of Earthquake Ruptures

Fault bends, and associated changes in fault dip, play a key role in explaining the scatter in maximum offset versus surface rupture length fault scaling relationships. Detailed field measurements of the fault geometry and magnitude of slip in the 2016–2017 Central Italy earthquake sequence, alongside three examples from large historical normal‐faulting earthquakes in different tectonic settings, provide multiple examples in which coseismic throw increases across bends in fault strike where dip also increases beyond what is necessary to accommodate a uniform slip vector. Coseismic surface ruptures produced by two mainshocks of the 2016–2017 Central Italy earthquake sequence (24 August 2016 Mw 6.0 and 30 October 2016 Mw 6.5) cross a ~0.83‐km amplitude along‐strike bend, and the coseismic throws for both earthquakes increase by a factor of 2–3, where the strike of the fault changes by ~28o and the dip increases by 20–25o. We present similar examples from historical normal faulting earthquakes (1887, Sonora earthquake, Mw 7.5; 1981, Corinth earthquakes, Mw 6.7–6.4; and 1983, Borah Peak earthquake, Mw 7.3). We demonstrate that it is possible to estimate the expected change in throw across a bend by applying equations that relate strike, dip, and slip vector to horizontal strain conservation along a nonplanar fault for a single earthquake rupture. The calculated slip enhancement in bends can explain much of the scatter in maximum displacement (Dmax) versus surface rupture length scaling relationships. If fault bends are unrecognized, they can introduce variation in Dmax that may lead to erroneous inferences of stress drop variability for earthquakes, and exaggerate maximum earthquake magnitudes derived from vertical offsets in paleoseismic data sets.


Introduction
Displacement versus length scaling relationships derived from earthquake ruptures are commonly used to infer magnitudes from paleoseismic data and measurements of active fault length and also to calculate stress drops during earthquakes (e.g., Cinti et al., 2011;Dolan et al., 1997;Galadini & Galli, 2000, 2003Galli et al., 2017;Galli & Peronace, 2014;Manighetti et al., 2007;Pantosti et al., 1996;Villamor & Berryman, 2001). These displacement versus length scaling relationships (e.g., Leonard, 2010;Manighetti et al., 2007;Stirling et al., 2002;Wells & Coppersmith, 1994;Wesnousky, 2008) are widely utilized, yet they are formulated upon data which contains significant scatter in coseismic maximum displacement (Dmax) for a given fault length ( Figure 1). In this paper we study this scatter and point out that (1) normal faulting earthquake ruptures commonly occur on faults with along-strike bends; (2) these bends appear to be characterized by relatively steep fault dips, as suggested by the five large normal faulting earthquakes studied in this paper; and (3) dip increases within the bends will necessitate an increase in the magnitude of the coseismic slip vector because the coseismic throw and displacement must increase if the coseismic strain is maintained along strike. Our main conclusion is that the increase in the magnitude of the coseismic slip vector, if not recognized, can produce scatter in Dmax values for a given fault length, overestimating the value calculated from scaling relationships, and we discuss the implications of this finding.
A key point we make is that bends in fault strike appear to be causal in controlling fault dip (see Figure 2) and the dip is then causal in controlling increases in throw and the magnitude of the slip vector in bends. First, we explain our reasoning concerning how along-strike fault bends form and exert a control on fault dip IEZZI ET AL. 1 ( Figure 2). Second we explain how dip changes in along-strike bends control the throw and hence magnitude of coseismic slip vectors (Figures 1c and 1d).
First, in terms of how along-strike fault bends form and exert a control on fault dip, we point out that faults grow and link through time (e.g., Mansfield & Cartwright, 2001; Figure 2). What is clear from analogue models for the growth of normal faults (Mansfield & Cartwright, 2001) and fault growth histories in nature described by stratigraphic evolution underpinned by 3-D seismic reflection and age control from well data (e.g., McLeod et al., 2000) is that (1) initially separate faults grow by tip propagation, with en echelon map geometries common; (2) new faults begin to grow in the relay zones between en echelon fault tips as incipient breach faults (see McLeod et al., 2000 Wilkinson et al., 2015). The distance 0 km represents the center of the fault, with values increasing moving toward the tip of the fault. Graphs show that instead of having a regular decrease of throw moving toward the tip of the fault, the throw increases within an along-strike fault bend, which is located within 1,500 and 2,500 m. This variation of throw across the fault bend is not accompanied by anomalies in the strain rate distribution along the fault, which decreases regularly toward the tip. (d) Graphs showing relationships between the throw rate and fault strike and dip across a fault bend, with constant strain rate (adapted from Figure 7c and Figure 8c of Faure Walker et al., 2009). Green lines show the variability of the throw rate of the fault caused by the variation of the angle between the fault strike and the slip vector and by the variation of the fault dip within the fault bend. Black triangles are values obtained from Wilkinson et al., 2015, showed in (c).

Figure 2.
Diagram showing the 3-D evolution of an along-strike fault bend through fault propagation, linkage, and coalescence. This model is adapted from McLeod et al. (2000) and Mansfield and Cartwright (2001). The fault surface at point Z forms after the bend forms at point Y. The dip at point Z for the five earthquakes described in this paper is steeper than for the fault surfaces outside the bend, suggesting this may be typical for such locations. (a) 3-D diagram of the eventual geometry of an along-strike fault bend that developed from two initial en echelon normal faults at depth, which grew through along strike and updip propagation, eventually coalescing into one linked fault surface through time. the strain in the relay zone and the regional kinematics (Roberts, 2007; we show below that all the examples presented in this paper have steeper fault dips in the bend); (4) faults then link across the relay zones through tip propagation, followed by coalescence and linkage of breach faults and the initial en echelon faults; and (5) the newly linked fault propagates up and down dip to increase the fault surface area through progressive deformation. The key point is that the dip value for the breach fault, which eventually becomes the fault bend, forms after the formation of the initial en echelon faults and, in updip and downdip locations, after the formation of a throughgoing fault within a bend (see time 6 in Figure 2). In other words, the change in strike across the incipient bend sets up the situation that controls the dip of the eventual fault within the structural bend. The 5 earthquakes described in this paper suggest that relatively steep dips typify such locations (see below). The formation of a steeply dipping breach fault necessitates an increase in throw across the bend if the strain is to be conserved along strike (Faure Walker et al., 2009). Thus, bends in fault strike appear to be causal in controlling steeper fault dips which result in local increases in throw and the magnitude of the slip vector in along-strike fault bends. In summary, along-strike bends are likely to be places where the dip varies and hence the throw varies.
Second, Faure Walker et al. (2009Walker et al. ( , 2010 show that the vertical offset (throw) across a given location on an active normal fault is controlled by the regional strain the fault must accommodate and the local nonplanar fault geometry. In response to the change in obliquity of the slip across an along-strike fault bend, the throw rate and fault dip must vary locally if the long-term horizontal strain rate across the fault is to be maintained (Faure Walker et al., 2009, 2010, 2015. For an example normal fault from the central Apennines, Italy, local variation in fault strike coincides with a local maximum in throw rate, with preservation of the horizontal strain rate, which decreases linearly toward the fault tip ( Figure 1d; Wilkinson et al., 2015). The relationship is confirmed by natural examples of long-term throw rates across faults (e.g., 15 ± 3 ka; Faure Walker et al., 2009;Wilkinson et al., 2015), and individual coseismic ruptures with larger coseismic Dmax within fault bends (Mildon et al., 2016;Wilkinson et al., 2015). If Dmax increases in along-strike fault bends, with steep fault dips, compared to straight faults, and this phenomenon is not recognized, we hypothesize that databases such as that in Wells and Coppersmith (1994), and other published scaling relationships, may contain a mixture of ruptures across along-strike bends and those along straight faults and this may cause scatter in Dmax for a given fault length. This could lead to erroneous inferences about stress drop and maximum magnitude.
To improve our understanding of coseismic throw variations associated with along-strike fault bends with steep fault dips, we present measurements and analysis of the surface ruptures to the 24 August 2016 M w 6.0 and the 30 October 2016 M w 6.5 earthquakes that both ruptured the southern part of the Mt. Vettore active normal fault in the central Apennines, Italy. We show that the Mt. Vettore fault exhibits a prominent bend in strike with an associated increase in local fault dip, and a relatively high value of total finite throw and coseismic throw in this bend. We measured the coseismic throw, heave, and displacement independently, with heave derived with trigonometry when it was not possible to measure it directly, within the vertical plane containing the slip vector. The orientation of the slip vector was recorded by mud smears on the fault planes that were striated during coseismic slip, and piercing points in ruptured colluvial deposits. We compare the along-strike profiles of coseismic throw for these two earthquakes with the structural relief and the long-term throw profile of the fault, constructed through geological cross sections, to understand how throw in these earthquakes compares with the longer-term throw of the Mt. Vettore fault. We adapt existing quantitative relationships for the conservation of the horizontal extensional strain rate across fault bends (Faure Walker et al., 2009, 2015 so that they are suitable for single ruptures, to explain the large coseismic throw within the along-strike bend on the Mt. Vettore fault and within along-strike bends for three other large magnitude normal faulting earthquakes. We use these observations to discuss the observed scatter in Dmax in displacement versus length scaling data, and the implications of this for calculating stress-drop variability and maximum estimated magnitudes for paleoearthquakes.

Geologic Background
The 2016-2017 Central Italy seismic sequence began on the 24 August 2016 with a M w 6.0 earthquake that killed 302 people ( Figure 3). The earthquake ruptured both the north western part of the Laga fault and the south eastern part of the Mt. Vettore fault with reports of surface ruptures confined to the latter . On 26 October 2016, two earthquakes (M w 5.4 and 5.9) ruptured the northern part of the Mt. Vettore fault, but it is unclear if they produced surface ruptures. It is unclear because on the 30 October 2016, before field surveys of the 26 October earthquakes, a M w 6.5 earthquake ruptured the total length of the Mt. Vettore fault, rerupturing locations that slipped in the 24 August 2016 earthquake and perhaps those on the 26 October (see Figures 2, 3, and 4;Calderoni et al., 2017;Cheloni et al., 2017;Chiaraluce et al., 2017;Civico et al., 2018;Falcucci et al., 2018;Ferrario & Livio, 2018;Lavecchia et al., 2016;Mildon et al., 2017;Pavlides et al., 2017;Perouse et al., 2018;Pizzi et al., 2017;Porreca et al., 2018;Scognamiglio et al., 2018;Verdecchia et al., 2018;Walters et al., 2018). Meter-scale offset across surface ruptures was measured with near-field 1-Hz global navigation satellite system for the 30 October ruptures, revealing that the ruptures formed within 2-4 s and, before peak ground acceleration, supporting the primary tectonic origin of the ruptures (Wilkinson et al., 2017; Figure 3).
The Mt. Vettore fault dissects the western slope of the Sibillini Mountain range (Figures 2-4). The fault is about 30 km in length, and its 10 6 -year activity has produced an internally draining intramontane basin and lake bed, and a large footwall escarpment (up to 1,000 m of relief). Despite clear geomorphic evidence of Holocene active faulting, there is no record of prior historical earthquakes on the Mt. Vettore fault (see Galadini & Galli, 2000). Paleoseismological analyses of the Mt. Vettore fault suggest a minimum throw rate of 0.11-0.36 mm/year, a recurrence interval that could span at least 4,690 years and a minimum elapsed time of 1,300-1,500 years, but possibly up to 4,155 years since the last paleoearthquake (Galadini & Galli, 2003).

Measurements
We conducted field mapping of the surface ruptures immediately after the 24 August and 30 October 2016 earthquakes (Figures 4 and 5). The full extent of the 24 August 2016 surface rupture was mapped within a few weeks after the earthquake, and before the occurrence of the 30 October 2016 earthquake . For the 30 October earthquake, we focused our work on constraining the large coseismic throws around a prominent bend near the southern end of the Mt. Vettore fault (bend A-B, Figure 5), which also ruptured in the earlier 24 August earthquake. We conducted most of the mapping for the 30 October 2016 earthquake from the 2-6 November 2016 but completed a section of the mapping across the A-B bend in June 2017, due to bad weather after the 6 November 2016; the absence of measured postseismic slip larger than~5 cm, constrained by remeasuring the offset at given sites, allowed us to combine the November and June data sets. The fault trace shows a second prominent along-strike fault bend along its northern half (C-D, Figure 5), which also ruptured during the 30 October M w 6.5 earthquake . We were unable to map ruptures across this fault bend with the detail required for this paper in the time available, but those ruptures are described by Civico et al. (2018) and .
We measured the strike, dip, slip vector azimuth, plunge of the slip vector, slip vector magnitude, throw, heave, and displacement associated with the ruptures, using steel rulers, compass clinometers, and handheld global positioning system (Figures 3a, 4-8 and S2 in the supporting information). Measurements were made every 2-10 m along strike and every 10-50 m along strike, following the 24 August 2016 earthquake and the 30 October 2016 earthquake, respectively. We plotted these measurements as a function of distance along a line oriented parallel to the regional strike (163°) of the Mt. Vettore fault (Figures 6 S2, and S3).
Where the ruptures occurred directly on the bedrock fault plane, they revealed a freshly exposed lightcolored stripe in the limestone bedrock ( Figure 4). In these locations we measured throw and displacement in the vertical plane containing the slip vector, defined by striations on mud smears (Figures 4c and 5), and used trigonometry to derive the heave. The longer-term slip vector orientation was confirmed by kinematic indicators on the fault plane, such as tool marks and frictional wear striae cut into the limestone fault gouge, and measurements of the strike and dip of fault planes.
In places, the ruptures also stepped a few decimeters to meters into the hangingwall of the main bedrock scarp to offset colluvial deposits. To obtain accurate measurements and avoid the effects of disaggregation on colluvial scarps, we used two methods: (1) We measured the slip vector azimuth and the displacement along preserved continuous striae on fault planes cutting through the fine matrix of coarse-grained mixed scree, debris flow, and colluvial deposits, and also the magnitude of the slip vector where possible; (2) where striae were not preserved, we measured the slip vector by matching piercing points on the footwall and hangingwall cutoffs defined by clasts and holes left by clasts in the colluvium (see Figures 4bii and 4cii).
To understand how the offsets produced by these earthquakes compare to offsets that have developed over the long-term history of the Mt. Vettore fault, we compared the along-strike profiles of coseismic throw for the two earthquakes with the long-term throw profile of the fault, constructed from 10 serial geological cross sections across prerift strata, based on the geological map published in Pierantoni   field observations ( Figure 8; see supporting information S1; Mildon et al., 2017). We also compared these alongstrike profiles with (1) the large-scale relief associated with the footwall escarpment on the Mt. Vettore fault obtained using topographic profiles derived from a 10-m resolution digital elevation model (Tarquini et al., 2007(Tarquini et al., , 2012 and (2) the location of Middle Pleistocene-Holocene lake deposits in the hangingwall (from Pierantoni et al., 2013), to ascertain the position and dimensions of areas of maximum subsidence ( Figure 8).
We have also compared the long-term deformation with the locations of maximum coseismic subsidence determined from preliminary interferometric synthetic aperture radar results (InSAR; Figure 8).

The Relationship Between Strain, Fault Geometry, and Coseismic Throw
We calculated predicted throws across fault bends by adapting the methodology published in Faure Walker et al. (2009) so that it can be used with individual ruptures, using field measurements as input (Figures 8 and 9). We define an "along-strike bend" as a portion of the fault where the strike is not perpendicular to the regional extension direction. We define outer faults as portions of the fault either side of the bend with strikes that are perpendicular to the regional extension direction.  (2010), shows how strain rate along a specified direction, φ, is calculated using field measurement of strike, dip, slip vector azimuth, and coseismic throw. To calculate the expected coseismic throw across the bend, we rearrange equation (1) to express throw as a function of strain and field measurements of strike, dip, and slip vector azimuth across the bend (equation (2)). In our calculations of throw across the bend, the inferred strain magnitude across the fault bend is assumed to be the mean of the strain calculated on the outer faults either side of the bend.
T ¼ mean strain across outer faults per given length with B representing the value within the bend, α = principal angle of the outer fault segments measured clockwise from north (Faure Walker et al., 2010;Fung, 1977), and p (plunge) is defined as Given the values of strain, strike, and slip vector azimuth at the bend, we iterate the fault dip in order to obtain a coseismic throw consistent with the field measurements of throw across the bend. The consistency between the iterated dip necessary to obtain a modeled throw consistent with field measurements of throw and the field measurements of dip indicates that the anomalously large throw (and hence large magnitude of the slip vector) across the bend can be explained by the relationship between horizontal strain and fault geometry.
To obtain strike values that represent the overall character of the fault bend and of the outer faults, for distances of hundreds of meters along the fault, strike lines (also known as structure contours) were constructed. Strike lines are horizontal lines joining points of equal elevation on a structure such as the hangingwall cutoff ( Figure 5b; see details in Figure S4). We used our field measurements to obtain the dip ( Figure 6). We used published structural data to study coseismic throw across along-strike fault bends for other active normal ruptures (1887, Sonora earthquake, M w 7.5, Suter, 2008aSuter, , 2008bSuter, , 20151981, Corinth earthquake, M w 6.7-6.4, Jackson et al., 1982;Morewood & Roberts, 2001;1983, Borah Peak earthquake, M w 7.3, Crone et al., 1987; Figure 10a) and supplemented data for the Corinth example with our own fieldwork results. The above data were used to predict the coseismic throw in along-strike fault bends for comparison with measurements of the same, as was done for the Mt. Vettore earthquake sequence studied herein.
The reader should note that the above calculations apply only once a rupture is throughgoing and has crossed a bend. We emphasize this because there are natural examples of normal faulting ruptures that terminated at along-strike fault bends. Biasi and Wesnousky (2017) discuss the termination of some ruptures at fault bends, and it is beyond the scope of this paper to discuss this further, but we point out that all five of the earthquake ruptures we describe in this paper did cross fault bends.

Field Observations
In the 24 August 2016 earthquake, surface ruptures formed either on the bedrock fault scarp, forming a freshly exposed stripe on the fault plane, or a few meters into the hangingwall, for a length of about 5 km along strike, propagating across a prominent along-strike fault bend (Figures 3, 4, 5 and S2). Surface ruptures were identified on the Mt. Vettore fault with a footwall made of competent limestone, whereas there are few clear signs of surface ruptures on the Laga fault, which has a footwall made mainly by less competent flysch . On the Mt. Vettore fault, the ruptures were continuous for about 2 km across the fault bend.
The rupture was less continuous toward the SE and NW terminations of the rupture. The surface ruptures were organized as sets of well-defined partially overlapping traces, tens of meters in length, each with a local Dmax. Rupture traces were arranged with both right-and left-stepping en echelon relay zones placing overlapping tip zones a few decimeters to meters apart across strike. Ruptures could be traced along strike from fault traces within colluvial deposits onto bedrock fault planes and vice versa (Figure 4b).
The combined effect of the 26 October 2016 M w 5.4 and 5.9 and the 30 October 2016 M w 6.5 earthquakes appears to have ruptured the entire Mt. Vettore fault, reactivating the surface ruptures produced by the 24 August M w 6.0 earthquake ( Figure 5). Given the location of the mainshock, the 26 October M w 5.9 earthquake appears to have ruptured only the northern part of the fault (Figure 3). Due to the short temporal interval between the 26 October and 30 October events, we were unable to determine whether the surface ruptures of the northern part of the fault were in part caused by the 26 October Mw 5.4 and 5.9 earthquakes or if the measured surface rupture was formed entirely by the larger 30 October M w 6.5 earthquake, so these northern parts of the rupture were not included in this study. The surface ruptures in the central and southern parts of the fault, on which we focused our field mapping, were all attributable to the 30 October M w 6.5 earthquake, based on the magnitude of slip and their timing of formation . The 30 October surface ruptures were significantly longer and more continuous, with more slip for each rupture trace, than ruptures associated with the 24 August earthquake. The ruptures mainly occurred on bedrock fault planes, and as synthetic ruptures in colluvial deposits adjacent to the main Mt. Vettore fault escarpment. However, in places, synthetic and antithetic ruptures occurred a few tens to a few thousand meters into the hangingwall ( Figure 5). Where it ruptured on bedrock, the coseismic slip produced a second freshly exposed stripe on the fault plane (Figures 4ci, 4civ, 4cv, and 4d). Presence of a mud smear covering the fault plane ( Figure 4ciii) allowed us to define portions of the fault plane exhumed by the 24 August (white stripe, no mud smear due to wind and rain since 24 August) and the 30 October earthquakes (mud smear deformed by tool tracks and frictional wear striae observed a few days after the event). By June 2017, mud smears on the fault planes were no longer preserved, but it was still possible to recognize two generations of light-colored stripe on the fault planes, belonging to the two different earthquakes (Figures 4ci and 4d).
All the parameters measured in the field show high variability along strike, even over a few tens of meters ( Figure 6; see Figure S2 for details of the 24 August ruptures). This is because individual rupture traces were as short as a few meters to tens of meters, and we were able to capture changes in parameters along each individual rupture trace due to our dense sampling. Despite the small-scale variability revealed by our measurements, we point out four overall features: 1. The range of strike values for the surface ruptures is similar between the two different earthquakes. Measurements of both the coseismic ruptures in colluvium and the strike of the bedrock fault planes show a large variability of values: The strike ranges between N110°and N210°for ruptures in colluvium ( Figure 6a) and between N110°and N178°for bedrock fault planes (Figure 6h). Such variation is common on bedrock fault scarps where multiple measurements are available to constrain variability (Roberts, 2007;Figure 7. Comparison between the measured slip vector azimuths from both earthquakes (red lines) and the slope dip directions (green arrows). The slope dip directions are derived from a 10-m resolution DEM (Tarquini et al., 2007(Tarquini et al., , 2012. Slip vector azimuths are also shown in Figure 6b. The photo in the inset shows an uphill-facing rupture with slip vectors across and/or almost opposite to the slope dip direction (two people provide scale). Our interpretation is that the direction of the measured slip vectors does not correlate with the slope dip directions; hence, this does not support the hypothesis that gravitational processes generate the surface ruptures.

Journal of Geophysical Research: Solid Earth
IEZZI ET AL. Figure S3). Fault plane orientations are organized so that the fault can accommodate the slip vector, so individual compass measurements of fault plane strike are not a good indicator of the overall strike of the fault (see Figure S3). Strike lines, which are a better way to gain the overall strike of the fault over along-strike distances of hundreds to thousands of meters, show that the fault strike is~N163°to the north-west and south-east of the bend and N135°within it ( Figure 5). 2. The dip of the bedrock fault plane is steeper in the fault bend, where it ranges between 70°and 88°, compared with ranges between 50°and 70°on the outer faults (Figure 6i). 3. The slip vector azimuths are very similar for both earthquakes: They range between N210°and N270°, which is consistent across the mapped fault strands (Figure 6b) and consistent with the regional stress field and 2016 focal mechanisms (Mariucci & Montone, 2016). We derived the overall azimuth of the slip vector across the fault bend and the outer faults by combining measurements of the coseismic slip vector azimuth with calculations of the best fit to poles of fault planes (see Roberts, 2007, and Figure S3 for explanation of the latter method). This shows that the slip vector azimuth is relatively constant along the fault trace (Figures 6b, 7 and S3). The overall coseismic slip vector azimuth is thought to be best represented by measurements close to the center of mapped ruptures (Roberts, 2007), and our measurements suggest a value of~253°(see Figure S3), perpendicular to the overall fault strike, and oblique to the bend A-B again consistent with the regional NE-SW orientated extensional stress field and 2016 focal mechanisms (Mariucci & Montone, 2016). The plunge of the slip vector is also similar between the two earthquakes, with values increasing within the fault bend, where it ranges between 60°and 80°, compared to values along the outer faults, where it ranges between 40°and 70° (Figure 6c). The change in the plunge of the slip vector within the fault bend suggests that the Mt. Vettore fault is not a perfectly corrugated fault surface, in fact exhibiting a noncylindrical geometry (see Roberts, 2007, for explanation). 4. Values recording the magnitude of slip appear to increase across the bend for both surface-rupturing earthquakes (Figures 6d, 6e, 6f and S2). The throw for the 24 August earthquake is less than 12 cm along the southern outer fault and increases to a maximum of 29 cm within the bend (Figures 6f and S2). For the 30 October earthquake, throw is less than 90 cm along the southern outer fault, increases within the fault bend to a maximum of 234 cm, and decreases across the northern outer fault to less than 150 cm (Figure 6f). Similar patterns are evident for field measurements of displacement (Figures 6d and S2). Evidence for along-strike variability for heave is less clear, suggesting that the magnitude of horizontal extension was, in general, conserved across the bend, away from the tips of the overall ruptures (Figures 6e and S2). Importantly, values for offset do not appear to be affected by propagating through different materials (e.g., colluvial deposits and carbonate bedrock) with similar values where ruptures propagated from one material to the other (Figure 4bi).
To assess whether the observed scarps could be related to shallow gravitational motions (e.g., Huang et al., 2017, for the 24 August 2016 earthquake) instead of coseismic slip, we compared the azimuth of slip vectors measured across the ruptures with slope dip directions, derived from a 10-m resolution digital elevation model (Tarquini et al., 2012, Figure 7). The slip vector azimuths associated with the two earthquakes appear to be independent of the slope dip direction. In particular, the coseismic slip vector azimuth points across the slope or upslope in some locations, especially near the southern end of the rupture trace. Our interpretation is that the overall uphill-facing scarp geometry near its southern termination, and the lack of correlation between slip vector azimuths on the faults and the dip direction of the local slope, indicates a primary tectonic origin of the surface ruptures. We suggest that coseismic slip from depth propagated upwards to offset the ground surface, consistent with results measured with Global Navigation Satellite System (GNSS) located in the footwall and hangingwall of the Mt. Vettore fault, which recorded the very rapid formation of the ruptures (2-4 seconds) (Wilkinson et al., 2017).
Overall, the key observation is that the fault bend A-B was the site of anomalously large throw and displacement in both the 24 August and 30 October earthquakes; this is where the fault strike changes by about 28°a nd the dip steepens by about 20 o .

Comparison Between Long-Term and Coseismic Activity of Mt. Vettore Fault
The long-term fault offset varies along the strike of the Mt. Vettore fault, with local maxima evident within the along-strike fault bends (Figure 8). The maximum total throw for the Mt. Vettore fault is~1,400 m since the initiation of faulting at 2-3 Ma (Roberts & Michetti, 2004;Roberts et al., 2002), and it is located within October M w 6.5 earthquakes. For each of the earthquakes, we report field measurements of coseismic throw (panels ai and bi), measurements of the strike of the bedrock fault plane (panels aii and bii), measurements of the dip of bedrock fault plane (panels aiii and biii), measurements of the plunge of the slip vector (panels aiv and biv), and the relative fault traces (panels av and bv). We have used these field measurements to model the throw and dip values across the fault bend, given the conservation of the strain and constant slip vector azimuth along the fault. In each panel colored lines represent the values that have been used in the calculation. Across the outer faults, we used the arithmetic mean of the field measurement for throw, dip, and plunge of the slip vector to calculate the strain. For strike measurements (panels aii and bii), we have used the values of strike derived from strike lines. Across the bend, iterated fault dips (reported as green lines in panels aiii and biii) are needed to obtain a coseismic throw consistent with field measurements, constant slip vector azimuth and with constant strain (green lines in panels ai and bi). In fault trace panels (av and bv), we report the subdivision of the fault in outer faults and fault bend, and the overall slip vector azimuth that we have used in the calculations (see text for details of how the slip vector azimuth is defined from field measurements). This shows that the elevated coseismic throw values can be explained by the presence of the bend and its associated steep fault dip.

Journal of Geophysical Research: Solid Earth
IEZZI ET AL.
the fault bend A-B (Figure 8a). A second local maximum abuts the fault bend C-D (Figure 8a). The faultcontrolled relief, which developed at least partially since 2-3 Ma, reaches a maximum value of~1,000 m within the fault bend A-B, again with a second maximum close to the bend C-D (Figure 8b). Where the hangingwall profile is higher than the footwall profile, this indicates uphill facing scarps (southeastern termination, see Figure 7 inset) or erosion of the footwall by fluvial drainage. The maximum fault-related subsidence since the Middle Pleistocene is centered opposite fault bend A-B indicated by the local presence of fluvio-lacustrine sediments in the hangingwall (Figure 8e); this is consistent with the notion that rates of vertical motion are relatively high within the fault bend since the middle Pleistocene, including the incremental offset of post last glacial maximum units within the valley (Villani & Sapia, 2017). Moreover, the maximum coseismic subsidence indicated by preliminary InSAR results for both earthquakes show maxima located near the lake bed ( Figure 8e). Overall, Figure 8 suggests that the along-strike fault bend A-B, and perhaps also C-D, have been persistent features that have influenced the development of vertical motions across the Mt. Vettore fault for a time period encompassing hundreds to thousands of earthquakes.

Modeling the Expected Throw Within Fault Bends 4.3.1. Earthquakes on the Mt. Vettore Fault
We apply equations (1) and (2) using field measurements of the Mt. Vettore earthquakes. The fault strike values derived from strike lines for the Mt. Vettore fault are N163°for the outer fault segments and N135°f or the bend (Figure 5b). We use a dip of 60°for the outer fault segments, which is the arithmetic mean of the measured dips. We set the slip vector azimuth to N253°on the entire fault, consistent with our field measurements (Figures 6 and S3). We set values for coseismic throws for the outer fault segments using the arithmetic means of our field measurements for each earthquake, including all the measurements obtained on the outer faults. We have used those parameters to constrain the outer faults, in order to calculate the modeled throw and dip within the bend.
For the 24 August earthquake, we used a value of 9 cm for the throw on the southern outer fault and 14 cm for the northern outer fault. We found that a fault dip in the bend of 77°produces a modeled throw of 29 cm. The iterated dip across the bend, which is necessary to model a throw value consistent with field measurements (maximum measured throw 29 ± 5 cm), is consistent with field measurements of dip across the bend (mean of measured dip 75 o ± 6 o (±1σ)).
For the 30 October earthquake, we used throws across the outer faults of 39 and 46 cm. We found that a fault dip in the bend of 84°produces a modeled throw of 233 cm, which is consistent with the maximum measured throw of 234 ± 6 cm. The 84°dip is a value consistent with our measurements of dip at locations of maximum throw, with arithmetical mean of 86°± 3°(±1 σ).
Overall, for the Mt. Vettore earthquakes our model iterations suggest throw values consistent with field measurements of throw across the bend, and field measurements of fault dips within the bend. This suggests that the conservation of the strain within an along-strike fault bend influences the coseismic throw values (Figure 9). This suggests that the 29-and 234-cm coseismic throws across the fault bend for the two earthquakes are required to preserve the extensional strain along the strike of the studied portion of the Mt. Vettore ruptures. This also further supports the interpretation that the observed offsets are due to primary tectonic faulting that propagated to the surface from seismogenic depths, rather than resulting from shallow gravitational processes (cf. Huang et al., 2017, for the 24 August 2016 earthquake).

Coseismic Offsets for Other Large Normal Faulting Earthquakes
To evaluate whether bends influence offsets elsewhere, we examined displacement data from surface ruptures for the 1887 M w 7.5 Sonora earthquake (Suter, 2008a(Suter, , 2008b(Suter, , 2015, 1981 Corinth M w 6.7-6.4 earthquake (Jackson et al., 1982;Morewood & Roberts, 2001;Roberts, 1996), and the 1983 M w 7.3 Borah Peak earthquake (Crone et al., 1987; Figure 10a). In addition, we carried out new fieldwork on the 1981 Corinth ruptures in 2017 to update values from Roberts (1996). Fault traces for these earthquakes show prominent along-strike fault bends, 2-10 km long, whose presence are confirmed by the construction of strike lines (Figure 10a, panels iii, vi, and ix; see also Figure S4). Other smaller bends may exist, but we were unable to verify these because of the resolution of the field measurements of throw (average spacing of measurements for the Sonora earthquake is 528 m, for the Corinth earthquake is 1,070 m, for the Borah Peak earthquake is 426 m). We can only resolve variation in throw across bends with along-strike length longer than the average spacing of the field measurements of throw, so we concentrated on the prominent along-strike fault bends, which are also identifiable with strike lines (Figure 10a, panels iii, vi, and ix). These We have applied the methodology explained in section 3.2 to investigate whether the fault bends explain coseismic throw maxima. As for the Mt. Vettore earthquakes, for each earthquake we derived fault strike values from strike lines, and fault dips and throws for the outer faults as the arithmetical means of field measurements reported along the entire fault traces outside the bends, and the slip vector azimuth from field measurements. We then iterated the fault dip angles within the bends, in order to derive modeled throws across the fault bends to check for consistency with field measurements (see Figures 10a and S6 for details about input values used for each earthquake).
For the Sonora earthquake, where ruptures outside the bend show a Dmax of about 400 cm, the iterated fault dip value of 79°produces a modeled throw across the bend of 498 cm; these values are consistent with field measurements (arithmetic mean of dip 79°, maximum measured throw 495 cm, from Suter et al., 2008aSuter et al., , 2008bSuter et al., , 2015 see Figures S5a and S6 for details).
For the Corinth earthquake, where ruptures outside the bend show a Dmax of about 100 cm, the iterated dip value of 76°produces a modeled throw across the bend of 148 cm, consistent with field measurements (maximum measured dip across the bend of 77°, from our field measurements; maximum measured throw at bend 150 cm, by Jackson et al., 1982; see Figure S5b).
For the Borah Peak earthquake, where ruptures outside the bend show a Dmax of about 200 cm, the iterated dip value of 79°produces a modeled throw across the bend of 270 cm, consistent with the maximum field measurements of 270 cm by Crone et al. (1987). The 79 o dip is similar to that shown by a field photo within the bend (see Figure 6 of Crone et al., 1987) and agrees with measurements of fault dips between 60°and 90°m entioned in Crone et al. (1987).
Thus, for the 1981 Corinth M w 6.7-6.4 and for the 1887 Sonora M w 7.5 earthquakes, we suggest that the required fault dip angles across the bends are consistent with field measurements. The required fault dip across the bend for the 1983 Borah Peak M w 7.3 earthquake is a plausible value for normal faults that represent testable hypotheses given further fieldwork, but similar to that shown in field photos. Hence, it appears that along-strike fault bends may be a key control on coseismic offset. This has implications for how Dmax relates to rupture length and magnitude if coseismic throws from bends are converted to displacement and/or reported as Dmax and included in calculations to gain Daverage.
A note on the modeling is that the results for modeled throw replicate the measured values very well (R 2 = 0.999) but the results are highly sensitive to the iterated dip and less sensitive to the input strike (see Figure S7). This highlights the importance of dip measurements; future rupture mapping and paleoseismic studies should report the dip of the fault as fully as possible if the approach advocated here is to be used. Also, it is important to note that we have applied our modeling for bends with changes in strike angle of less than 28°(compare with Biasi & Wesnousky, 2017). We did not test our model for bends with greater angles, up to a case-limit of a transform fault connecting two normal faults.

Comparison Between Field Measurements and Predictions of Dmax From Existing Scaling Relationships
To investigate whether existing, empirically derived scaling relationships (e.g., Wells & Coppersmith, 1994) adequately predict measured displacement values for faults with along-strike bends, we compare the Dmax and M w for the two Mt. Vettore earthquakes, and the Sonora, Borah Peak, and Corinth earthquakes with the same values implied by existing scaling relationships of Dmax versus surface rupture length (LogDmax = À1.38 + 1.02xlog(L)) and M w versus Dmax (M = 6.61 + 0.71xlog(Dmax); published in Wells and Coppersmith, 1994; Figure 10b; see also Figure S9). We have used both the all kinematics and normal scaling relationships expressed in Wells and Coppersmith (1994). We have used the all kinematics Dmax versus fault length scaling relationship because it covers the full range of fault lengths of our examples, including those from the literature (the range of surface rupture length in our examples is 5-100 km, the normal kinematic scaling relationship from Wells & Coppersmith, 1994, is valid for cases within a range of 3.8-75 km). We have used the normal kinematics M w versus Dmax scaling relationship in agreement with the kinematics of the earthquakes on the Mt. Vettore fault and of the historical earthquakes. For the two Mt. Vettore earthquakes we have used the Dmax derived from our own field measurements; for the other historical earthquakes studied we have calculated the Dmax from measured throws at bends, on a fault plane with value of dip given by the iterated dip at bends obtained from our modeling.
The measured Dmax values shown in Figure 10bi for the five studied earthquakes with fault bends are consistently higher than the Dmax predicted from their lengths using the Wells and Coppersmith (1994) Dmax versus surface rupture length scaling relationship. The M w predicted from the observed Dmax for the five studied earthquakes are perhaps larger than the M w predicted based on the Dmax predicted from the surface rupture length, although error bars overlap for some examples (Figure 10bii). Although we are aware that slip for the earthquakes in the Wells and Coppersmith (1994) database may well be influenced by a variety of parameters (e.g., depth of moment centroid, fault strength, and seismogenic thickness), our interpretation is that fault bends may form an important part of the explanation for the~1 order of magnitude scatter in Dmax for a given fault length (Figure 1; Wells & Coppersmith, 1994).
To explore whether fault bends can produce the high values and scatter seen in Dmax versus surface rupture length scaling, we used equations (1) and (2) to calculate the expected throw across a bend for a variety of fault lengths and increasing fault dips within the bend, in agreement with field observations of steeper fault dips at bends, as shown by our five examples from the two Mt. Vettore earthquakes, and the Sonora, Corinth, and Borah Peak earthquakes. We followed the methodology outlined in section 3.2. For each fault rupture length, we calculated the strain across the outer faults with an assigned 40°fault dip (see Figure S8), pure dip slip kinematics, and a value of coseismic throw calculated using the Dmax versus surface rupture length scaling relationship in Wells and Coppersmith (1994), LogDmax = À 1.38 + 1.02Log(L). Again, we have used the all kinematics scaling relationship because it covers the total range of rupture length explored. Across the bend, we maintain constant strain and slip vector azimuth and calculate the predicted throw by varying the fault dip in the bend in 5°increments from 40°to 85° (Figure 11a; see Figure S8). The range of dips explored (40°-85°) represents the range of dips that have been documented in databases containing many thousands of measurements from normal faults (e.g., Roberts, 2007). From each of the modeled throws we have calculated the expected Dmax on a fault plane dipping with the value used in the calculation, and we have compared those with the Dmax versus surface rupture length scaling relationship from Wells and Coppersmith (1994). We have also calculated the above for the scaling relationship in Wesnousky (2008); see Figure S9.
The results show that changing the fault dip can produce dramatic variability in the coseismic Dmax within the fault bend (Figures 11a and S9a). The value of Dmax can increase by~1 order of magnitude for a fault bend with dip angle of 85°compared to one with a dip of 40°. A comparison between these results and measurements for normal faulting earthquakes in Wells and Coppersmith (1994) shows a similar range in Dmax for a given fault length (~1 order of magnitude; Figure 11b). This suggests that the effect of fault bends is a likely contributor to the scatter in coseismic throw for a given fault length recorded in natural data sets.

Discussion
The along-strike throw profiles of five different coseismic surface ruptures associated with normal faulting earthquakes show that the coseismic throw, and therefore the coseismic Dmax, increases where ruptures propagate across along-strike fault bends characterized by steep fault dips. Quantitative relationships can explain these larger throws in terms of conservation of strain across the fault bend, where the fault dip becomes steeper.
Note that in our examples ruptures propagate across bends and do not terminate at these structural changes, as is the case for examples in the literature (e.g., Biasi & Wesnousky, 2017). Biasi and Wesnousky (2017) suggest that stiffening of mechanical resistance for dip slip ruptures occurs for bends with change in strike angle of about 50°. We hypothesize that our model is applicable for ruptures that do propagate across fault bends up to a change in strike of about 45°, corresponding to the limiting point at which the bend would be classified as a normal fault, rather than an oblique-slip or strike-slip fault. However, we note we have only tested our model herein for examples where propagation of ruptures across fault bends occurs and where the change in strike angle is up to 28°.
In terms of the relevance of our results to databases that have compiled Dmax and rupture length (e.g., Leonard, 2010;Manighetti et al., 2007;Wells & Coppersmith, 1994;Wesnousky, 2008), it is unfortunately uncommon for the data sources that support these compilations to report whether data were collected from fault bends with strikes oblique to the extension direction or portions of faults striking perpendicular to the 10.1029/2018JB016732

Journal of Geophysical Research: Solid Earth
IEZZI ET AL. Figure 11. (a) Dmax versus surface rupture length scaling relationships obtained by varying the fault dip angle from 40°to 85°across an along-strike fault bend. Each Dmax value has been calculated from modeled throws across an along-strike fault bend, derived using equation (2). To model throws across bends, we set values for throw on the outer faults as the Dmax value calculated with the Wells and Coppersmith (1994) Dmax versus surface rupture length scaling relationship for each fault length, and a fault dip of 40°. We calculated the throw at the bend by varying values of fault dip every 5°between 40°and 85°(see Figure S8 for details). The continuous orange line represents the Wells and Coppersmith (1994), relationship. Dashed orange line is the upper 95% confidence interval of the Wells and Coppersmith (1994) relationship. Dashed black line represent values of throw for a bend with 85°fault dip angle. See Figure S9 for a similar figure for scaling relationships in Wesnousky (2008). (b) Superposition of the normal faulting earthquakes reported in Wells and Coppersmith (1994), Dmax versus surface rupture length graph, and related scaling relationship (continuous orange line) and 95% confidence interval (dashed orange lines), with plots of expected Dmax with variable dip angle across along-strike fault bend at 85°. (c) M w derived from each Dmax calculated in Figure 11a. For each fault length, we have calculated the expected M w from the modeled values of Dmax showed in Figure 11a using the M w versus Dmax scaling relationship from Wells and Coppersmith (1994). Results are plotted with fault length on the x-axis to show that for each fault length, the variability of Dmax given by the fault bend causes a large variability in the expected M w , when it is derived with Wells and Coppersmith (1994)  extension direction, and, in general, they do not report the geometry and kinematics of the faulting for each measurement. The observed scatter in Dmax for a given fault length (Figure 1) has been interpreted as indicating significant scatter in implied stress drop (Manighetti et al., 2007). Values of Dmax are also used in some examples to infer paleoearthquake magnitudes from paleoseismic studies, (e.g., Cinti et al., 2011;Dolan et al., 1997;Galadini & Galli, 2000, 2003Galli et al., 2017;Galli & Peronace, 2014;Pantosti et al., 1996;Villamor & Berryman, 2001). Although careful consideration of paleoseismic uncertainties are often completed when completing state-of-the-science level hazards (e.g., Working Group on Utah Earthquake Probabilities [WGUEP], 2016), it is not a ubiquitous practice for individual investigators to consider if measurements are impacted by the effect of along-strike fault bends. We have shown that local variations in fault geometry and kinematics can produce variations in coseismic throw values, and therefore in the coseismic displacement associated with the earthquake. This leads to uncertainty in paleoearthquake magnitudes and implied variations of stress drops for a given fault length if the effect of fault bends is not considered when collecting data along prehistoric or modern fault ruptures.
We concede that it might be possible that high slip patches occur at depth, possibly propagating to the surface without the influence of fault bends, although this is difficult to prove with direct measurements at depth. Our analysis of five surface-rupturing normal fault earthquakes shows that fault bends are a plausible explanation for patches of high slip measured at the surface and that the detailed characterization of fault bend geometry allows prediction of the magnitude of the slip anomaly. Fault bends are also likely to exist at depth, and these may even be responsible for suggested high slip patches at depth. This suggests that (1) nonplanar fault geometry may be an alternative explanation of high spatial variability within slip distributions for finite fault inversions of major normal faulting earthquakes and (2) finite fault inversions should include variable fault geometry at depth, to derive the best representation of the slip distribution along the fault.
We also address how variable coseismic throws across fault bends impact calculations of M w from Dmax. If the reported Dmax value comes from a fault bend with a high dip value, and this is not recognized, by how much might the M w be overestimated compared to a straight fault? To answer this question, for each fault length we have calculated the expected M w for all the plausible Dmax for values within the fault bend (shown in Figure 11a), using the M w versus Dmax scaling relationship in Wells and Coppersmith (1994), M = 6.61 + 0.71 log (Dmax), (Figure 11c). The graph shows that for a given fault length, the variability of Dmax across fault bends leads to a large variability of M w estimates if M w is derived using the M w versus Dmax scaling relationship in Wells and Coppersmith (1994). This is important because fault bends, and their associated fault dip angles, are not commonly considered when using displacements measured in paleoseismic trenches to infer M w for paleoearthquakes. It appears that this can introduce a large uncertainty of M w into paleoseismic estimates of past seismicity.
The effect of the variability of Dmax on the estimation of the M w also raises the question of how the variability in Dmax due to fault bends affects calculations of seismic moment and stress drop associated with normal faulting earthquakes. It is known that seismic moment and stress drop should be calculated using the Daverage (Kanamori & Anderson, 1975;Scholz, 2002). We also know that Dmax~2*Daverage for most large earthquakes (e.g., Manighetti et al., 2005) and the presence of fault bends on normal faults contributes to Dmax being larger than Daverage. Therefore, we suggest that the presence of fault bends may produce bias in calculation of Daverage for two reasons. First, given limitations in the field due to accessibility and quality of exposure, it is possible that measurements may be focused in locations where the ruptures are more impressive and have larger offsets, which may be located within fault bends. Thus, the derived Daverage may contain sampling bias and overestimate the true Daverage if bends with high dip angles are included, but not recognized. Second, as fault bends with high dip angles produce higher values of throw, the calculated Daverage for a data set where measurements have been made at regularly spaced intervals along strike will contain values influenced by the high dip angles in the fault bend. Therefore, a fault with an along-strike bend with high dip angle, sampled at regular distances along strike, would have higher Daverage compared to that for a straight fault. Thus, claimed Daverage values could be biased and affect calculation of seismic moment and stress drop if the effect of bends and high dip angles are not recognized. To investigate this, we examine the worst case where Daverage equals Dmax, a scenario that could be approached if fault bends have not been considered at all, and a relatively large portion of the rupture occurs within a bend like the 24 August Mt. Vettore example.

10.1029/2018JB016732
To calculate the scalar seismic moment, we used the equation M 0 = μAD, where μ is the shear modulus (considered herein as 3 × 10 10 Pa), A is the seismogenic area, and D is the Dmax across fault bend, derived from values in Figure 11a (Figure 11d). We set the thickness of the seismogenic layer to be 15 km. We assumed a circular fault when the fault length (L) is <15 km, and rectangular faults with increasing aspect ratio for faults with L values progressively larger than 15 km. The fault width (downdip dimension in the plane of the fault) has been corrected for different dip angles. For each fault length, the seismic moment is calculated for each displacement associated with variable fault dip. Variable displacement across fault bends can produce almost 1 order of magnitude of variability in the seismic moment estimations (Figures 11d and S9c).
To calculate stress drops, we used the equation Δσ ¼ c M0 A 3=2 (Kanamori & Anderson, 1975;Scholz, 2002;Figures 11e and S9), where C is a nondimensional shape factor (≈1 from Kanamori & Anderson, 1975). We used the M 0 values shown in Figures 11d and S9c to evaluate the effect of variable Dmax across fault bends. The results show that the variable displacement across a fault bend can produce~1 order of magnitude of variability in stress drop values for each fault length (Figures 11e and S9d). Although this effect may be overestimated, because we are considering the worst case where Dmax equals Daverage, this result is important because information on the geometry and kinematics of faulting are not commonly considered when using D values to calculate stress drop.
Overall, we suggest that along-strike fault bends, where the fault strike becomes oblique to the slip vector azimuth and the fault dip steepens beyond what is required to maintain the slip vector, strongly influence values of coseismic throw and displacement within the bend, and thus Dmax. This influences the estimation of M w from paleoseismic studies and stress drop from field data on surface ruptures. Furthermore, our findings suggest that Dmax to length scaling data sets are even more valuable than previously envisaged because it appears that the scatter of Dmax for a given length provides information about how earthquake strain and moment release are partitioned along the strike of nonplanar faults.

Conclusions
The 24 August 2016 M w 6.0 and 30 October 2016 M w 6.5 earthquakes ruptured the Laga and Mt. Vettore faults, in the central Apennines, Italy, producing anomalously large coseismic surface ruptures within an along-strike fault bend with steep fault dips on the Mt. Vettore fault. The bend has an amplitude of 0.83 km, which changes the fault strike and dip by~25°. We characterize the surface ruptures across the bend through detailed field mapping. The fault bend and its steep dip appear to have produced (1) a local maximum in total finite slip across the fault from offset of pre-rift strata, (2) a local maximum in fault-related relief, and (3) internal drainage on the hangingwall, all three of which developed over several million years, testifying to the long-term influence of the fault bend on the coseismic throw during earthquakes.
The application of the quantitative relationships (Faure Walker et al., 2009, 2010, 2015 on field data related to these two earthquakes shows that the relatively large coseismic throw observed across the bend (29 and 234 cm for the 24 August M w 6.0 and 30 October M w 6.5 earthquakes, respectively) are required by the geometry and kinematics of the faulting to maintain the horizontal extensional strain along strike and across the fault bend with its high fault dip (Figure 9).
Increases of coseismic throw in fault bends are also investigated for some of the largest historic normal faulting earthquakes (1887, Sonora earthquake, M w 7.5; 1981, Corinth earthquake, M w 6.7-6.4; and 1983, Borah Peak earthquake, M w 7.3). The same equations can explain the anomalously large coseismic Dmax values in terms of conservation of the horizontal extensional strain along-strike and across the fault bends with their high fault dips. Thus, this paper provides the first multiple examples from different normal faulting regions showing that coseismic throw depends on fault geometry. Furthermore, it is possible to quantify and explain changes in observed coseismic throws across fault bends in addition to longer-term changes in throw rates across fault bends.
We suggest that along-strike fault bends are a plausible explanation of the scatter of Dmax values for normal faulting earthquakes in Dmax versus surface rupture length scaling relationships (e.g., Wells & Coppersmith, 1994). Thus, if the role of bends and high dips in those bends are not considered, this can produce misleading interpretations of (1) M w from Dmax values gathered during paleoseismological studies, (2) seismic moments, and (3)  the role of fault bends and their dips in influencing the magnitude of coseismic displacements associated with surface ruptures because it appears that the scatter of Dmax for a given length provides information about how earthquake strain and moment release are partitioned along the strike of nonplanar faults.