Comparison of geodetic slip-deficit and geologic fault slip rates reveals that variability of elastic strain accumulation and release rates on strike-slip faults is controlled by the relative structural complexity of plate-boundary fault systems

Comparisonof geodeticslip-deficit rateswith geologicfaultslip rateson major strike-slip faults reveals marked differences in patterns of elastic strain accumulation on tectonically isolated faults relative to faults that are embedded within more complex plate-boundary fault systems. Specifically, we show that faultsthatextendthroughtectonicallycomplexsystemscharacterizedbymultiple,mechanicallycomplemen-taryfaults(thatis,differentfaultsthatareallaccommodatingthesamedeformationfield),whichwereferto ashigh-CoefficientofComplexity(orhigh-CoCo)faults,exhibitratiosbetweengeodeticandgeologicrates thatvaryandthatdependonthedisplacementscalesoverwhichthegeologicslipratesareaveraged.This indicatesthatelasticstrainaccumulationratesonthesefaultschangesignificantlythroughtime,whichin turnsuggeststhattheratesofductileshearbeneaththeseismogenicportionoffaultsalsovarythroughtime. Thisisconsistentwithmodelsinwhichmechanicallycomplementaryfaultstradeoffslipintimeandspace inresponsetovaryingmechanicalandstressconditionsonthedifferentcomponentfaults.Inmarkedcon-trast,structurallyisolated(orlow-CoCo)faultsexhibitgeologicslipratesthataresimilartogeodeticslip-deficit rates,regardlessofthedisplacementandtimescalesoverwhichtheslipratesareaveraged.Suchfaultsexpe-riencerelativelyconstantgeologicfaultslipratesaswellasconstantstrainaccumulationrate(asidefrombrief, rapidpost-seismicintervals).Thissuggeststhatlow-CoCofaults“keepup”withtherateimposedbytherela-tiveplate-boundarycondition,sincetheyaretheonlystructuresintheirrespectiveplate-boundaryzonethat caneffectivelyaccommodatetheimposedsteadyplatemotion.Wehypothesizethatthediscrepanciesbe-tweenthesmall-displacementaveragegeologicslipratesandgeodeticslip-deficitratesmayprovideameans ofassessingaswitchofmodesforsomehigh-CoCofaults,transitioningfromaslowmodetoafastermode,or viceversa.Ifso,thedifferencesbetweengeologicslipratesandgeodeticslip-deficitratesonhigh-CoCofaults mayindicatechangesinafault’sbehaviorthatcouldbeusedtorefinenext-generationprobabilisticseismic hazardassessments.


Introduction
Unravelling the relationship between geologic fault slip rates and rates of strain accumulation as measured by geodesy is critically important for developing a better understanding of the mechanics of faults and the seismic hazards that they pose.Whereas some major faults exhibit constant behavior, with relatively steady geologic slip rates spanning a range of time and displacement scales (e.g., Kozacı et al., 2009Kozacı et al., , 2011;;Berryman et al., 2012;Salisbury et al., 2018;Grant Ludwig et al., 2019), other faults exhibit highly irregular slip rates through time, with centennial to millennial periods of relatively fast slip rate spanning multiple earthquake cycles, separated by prolonged periods of slower or no slip rate (e.g., Benedetti et al., 2002;Friedrich et al., 2003;Bull et al., 2006;Dolan et al., 2016;Hatem et al., 2020;Zinke et al., 2017Zinke et al., , 2019Zinke et al., , 2021)).
Elastic strain accumulation rates inferred from analysis of geodetic data reflect the shearing velocity of the seismogenic faults' underlying ductile roots, and have been suggested to be relatively constant beyond the single-earthquake scale (i.e., once fast post-seismic and slower interseismic rates have been averaged out).Indeed, comparisons of geodetic slip-deficit and geologic rates have been used to infer near-constant interseismic rates.For example, in one of the largest such compilations to date, Meade et al. (2013) compared geologic fault slip rates and geodetic slip-deficit rates for 15 major continental strike-slip faults around the world.Their results suggest that, as an ensemble, these faults exhibit a near 1:1 relationship (with a slope of 0.94 ± 0.09) between geologic and geodetic rates.Slight differences between the datasets could be attributable to shortlived periods of higher-than-average strain accumulation during the post-seismic period.The geologic rates used as inputs into the analysis of Meade et al. (2013) span a huge range of displacement and time scales, from as small as ~13 m to as large as ~600 m, and as short as 2 ky to as long as 160 ky.We recently presented results that demonstrate that, for faults that lie within complex plate-boundary fault networks, geologic slip rates vary depending on the displacement scale over which the slip rate is estimated; on the other hand, structurally isolated faults that accommodate most of the relative motion within simple plate boundaries exhibit steadier slip rates (Gauriau and Dolan, 2021).These observations lead us to explore the possibility that differences between geodetic slip-deficit rates and geologic slip rates might also be sensitive to the relative complexity of the surrounding fault network.If they are, this would require that geodetic-geologic rate comparisons consider time and displacement scales over which incremental slip rates are averaged, as well as the relative structural complexity of the surrounding fault system, especially in structurally complex plate boundaries (e.g., northern and southern California, Marlborough fault system in New Zealand), that are characterized by multiple, mechanically complementary faults.
In this paper, we explore the potential constancy, or lack thereof, of the elastic strain accumulation rate patterns on active strike-slip faults.Specifically, we aim to investigate the relative constancy and potential variability of elastic strain accumulation rates on faults characterized by temporally constant geologic slip rates, on the one hand, and faults that exhibit temporally variable geologic slip rates, on the other.Comparing elastic strain accumulation rates derived from geodesy with geologic slip rates has been done in several studies (e.g., Kozacı et al., 2009;Meade et al., 2013;Tong et al., 2014;Dolan and Meade, 2017;Evans et al., 2016) but never in light of the relative complexity of the plate-boundary fault systems being considered.

Studied faults and terminology
In this study, we use the recently developed Coefficient of Complexity (CoCo) method (Gauriau and Dolan, 2021), which quantifies the relative structural complexity of the fault network surrounding a fault of interest by integrating the density and displacement rates of the faults in the plate-boundary network at a specific radius (here, 100 km) around the site of interest.The method is illustrated in Figure 1.We use CoCo values calculated for 18 major strike-slip faults for which both geologic incremental slip-rate records and geodetic slipdeficit rates are available (Figure 2, Table 1).In total, we work with 24 different fault sites where these two kinds of data are available and approximately collocated.The comparison of the CoCo values for all sites is then enabled by the standardization of the CoCo values by the respective plate-motion rate, totaled for the observation area of 100 km radius.This allows direct comparisons of the intensity of fault activity in different plate-boundary fault networks that move at different relative plate motion rates.
We divide the available geologic slip-rate data into two groups: large-displacement slip rates and smalldisplacement slip rates (usually referred to as "longterm" and "short-term" slip rates, respectively), which are averaged over large (> ~50 m) and small (< ~50 m) displacements, respectively (Table 1).The reasons for this are twofold: (a) This allows us to discuss fastand slow-slipping faults with comparable parameters and hence by considering similar numbers of earthquakes on faults that have widely different recurrence intervals, and (b) displacement, not time, may be what matters most in terms of the mechanisms governing fault behavior in complex plate-boundary fault systems (Dolan et al., 2007;Cawood and Dolan, submitted;Dolan et al., 2024).In addition, we use the terms "geodetic slip-deficit rates" to refer to any rate that was obtained on the basis of space geodetic measurements of surface ground displacement over multi-annual to decadal time scales, such as Global Positioning System (GPS) or Interferometric Synthetic Aperture Radar (InSAR), and which has been modeled to characterize the most recent rate of elastic strain accumulation for the studied strike-slip faults.

Consideration of elapsed time since most recent event relative to sampling geodetic slip-deficit rates
In order to evaluate potential differences in behavior of faults embedded within structurally simple fault systems (i.e., low-CoCo faults) versus faults embedded within structurally complex fault networks (i.e., high-CoCo faults), we compare geodetic slip-deficit rates with geologic fault slip rates that are averaged over both small displacements and large displacements.We first introduce a few key considerations that allow us to carry out this comparison between geodetic and geologic data.
* rate calculated between MRE and given offset marker § based on several studies cited in Haddon et al. (2016), with offsets ranging from 3 m (1 earthquake) to 19 m, and respective ages ranging from 600 years ago and 25 ka $ averaged over the past four historical earthquakes # first age relates to boulder samples, second age refers to sediment samples ( 10 Be technique) ¤ using their upper-terrace reconstruction (Cowgill et al., 2009), as for the small-displacement slip rate as well as an estimate of their mean earthquake recurrence interval.For a majority of the faults we study, it has been at least 100 years since the MRE, as documented historically (e.g., the 1717 Alpine fault earthquake, the 1857 Fort Tejon earthquake on the San Andreas fault, the 1872 Owens Valley earthquake) or on the basis of paleoseismological evidence (e.g., the ca.1800-1840 CE earthquake on the Conway section of the Hope fault; Hatem et al., 2019).In a few instances, the MRE occurred more recently, such as the series of earthquakes on the North Anatolian fault between 1939 and 1999 (Barka, 1992;Barka et al., 2002), the 2002 Denali earthquake (Haeussler, 2004), or the Kahramanmaraş earthquake (e.g., Barbot et al., 2023) that occurred in Februray 2023 on the East Anatolian fault (for which we use a geodetic rate that was acquired before the earthquake).
Table S1 summarizes the MRE dates and the available mean recurrence intervals for the fault locations we study.In most of the examples, we are well into at least the middle part of the elastic strain accumulation cycle, likely well past any rapid post-seismic deformation (with the possible exceptions of the 1992 Landers, 1999Izmit, 1999Düzce, 1999Hector Mine, and 2002 Denali earthquakes).

Relative structural complexity of the surrounding fault network in interpretation of geodetic slip-deficit rate and geologic slip-rate comparisons
In our original formulation of the CoCo metric (Gauriau and Dolan, 2021), we categorized faults as either lowor high-CoCo.To determine the CoCo metric for each fault study site, we apply a system in which we recognize that the degree of structural complexity surrounding a fault is a continuum, with no hard boundary between high-and low-CoCo faults.Whereas many of the faults we study can be readily categorized as either high-CoCo faults (e.g., the Hope fault or the Mojave section of the San Andreas fault) or low-CoCo faults (e.g., the southern Alpine fault, the central San Andreas fault), some of the faults exhibit intermediate CoCo values reflecting a surrounding plate-boundary zone that shows minor to moderate complexity.The two faults that fall in this inbetween area are the Central Denali fault ( 16), characterized by a standardized CoCo value of 1.62•10 -2 yr -1 and the Altyn Tagh fault (18), characterized by a standardized CoCo value of 1.56•10 -2 yr -1 .Based on these two values, we use a standardized CoCo value of 1.6•10 -2 yr -1 as the dividing line between what we will refer to hereafter as low-and high-CoCo faults.With this boundary defined, we can explore the behaviors exhibited by these two categories of faults, as shown in Figure 2b, c (see Figure 3 for standardized CoCo values of all faults).

Comparison of geologic slip rates and geodetically based slip-deficit rates on strike-slip faults
Figure 2 illustrates the comparison between geologic and geodetic slip-deficit rates for the 24 different sites on the studied strike-slip faults.It reveals marked differences in the consistency of the values of the geodetic/geologic-rate pairs for high-CoCo faults relative to low-CoCo faults.Specifically, comparison of geodetic slip-deficit rates with large-displacement and small-displacement average geologic slip rates (displayed as squares and circles, respectively, in Figure 2) reveals that these rates are similar for faults characterized by low CoCo values (displayed in blue in Figure 2), whereas they differ for the faults characterized by high CoCo values (displayed in red in Figure 2).This observation is a corollary to the main conclusion of our previous study (Gauriau and Dolan, 2021), in which we showed that low-CoCo faults slip at relatively constant rates through time whereas high-CoCo faults exhibit long-term slip rates that are potentially different from the slip rates averaged over small displacements.In other words, the displacement over which the slip rate is averaged does not matter for low-CoCo faults, since any geologic slip rate will give the same value.In contrast, geologic slip rates for high-CoCo faults that are averaged over one particular displacement range may differ from the slip rate averaged over a different displacement range.
Figure 2a shows a comparison of geologic slip rates and geodetic slip-deficit rates.Figure 2b shows that low-CoCo strike-slip fault sites plot on (or near) the 1:1 line, reflecting the similarity of their short-term geodetic strain accumulation rates and both their smalldisplacement and large-displacement geologic strainrelease rates.This can be further illustrated statistically, since the coefficient of determination obtained from an ordinary least squares regression for the low-CoCo faults is 0.983 for geologic rates averaged over large displacements, and 0.978 for geologic rates averaged over small displacements (Figure S1).Assuming a linear relationship between geologic slip rates and geodetic slip-deficit rates going through the origin, we find scaling lines with best-fit slopes and respective 1σ confidence of 0.945 ± 0.028 and 1.103 ± 0.050 for the low-CoCo faults using the large-displacement and smalldisplacement average geologic rates, respectively (see Figure S1a and b).These results show that for these low-CoCo faults, geodetic rates provide a reliable proxy for the geologic slip rate of the fault of interest.
That geodetic slip-deficit rates are a reliable proxy for geologic slip rate is not the case for high-CoCo faults (Figure 2c).Specifically, there is wide dispersion amongst the geodetic slip-deficit and both large-and small-displacement geologic slip rates (Figure 3).This observation requires that geodetic slip-deficit rates cannot be used as a proxy for geologic rates for high-CoCo faults, whether the rate is averaged over small displacements or large displacements.For these high-CoCo faults, the coefficient of determination obtained from an ordinary least squares regression between geologic Figure 1 Schematic explanation of the rationale of the Coefficient of Complexity (CoCo) analysis for a hypothetical fault network.The calculation of CoCo for a given radius is shown on top.The radius over which CoCo is calculated is 100 km.Within a structurally complex fault system (numerous, and relatively fast-slipping faults), shown to the left, the CoCo value will be higher than within a structurally simple fault system (few or zero neighboring faults), shown to the right.The quantification of complexity, done with the CoCo analysis, correlates with the relative steadiness of geologic slip-rate record, as shown in our recent study (Gauriau and Dolan, 2021).
rates and geodetic slip-deficit rates is 0.396 for geologic rates averaged over large displacements, and 0.350 for geologic rates averaged over small displacements (Figure S1c, d).Scaling lines between geologic rates and geodetic rates for these faults, assuming a linear relationship going through the origin (as in Meade et al., 2013) are characterized by the best-fit slopes of 0.751 ± 0.162, using the small-displacement geologic rates, and 0.696 ± 0.140, using the large-displacement geologic rates (Figure S1c and d).These linear regressions seem to imply a global trend where geologic slip rates are faster than geodetic slip-deficit rates, but we suggest that these best-fit slope values are not meaningful, and are rather artifacts of the current limited state of available data.Reinforcing this idea is the observation that the dispersion of the data, shown by the standard deviations of the best-fit slopes, demonstrates that there is no good correlation between geodetic slip-deficit and geologic slip rates for high-CoCo faults.Figure 3 further illustrates this result, by displaying the ratio between the geodetic slip-deficit rates and the geologic rates averaged over large or small displacements.Figure 3b plots a measure of distance from the data points to the 1:1 ratio line with varying CoCo values, and emphasizes the dispersion of the data for higher-CoCo faults (see details of the dispersion calculation in the Supplementary Materials); the relatively sharp increase in dispersion at standardized CoCo ~0.0015-0.002yr -1 likely reflects the presence of major secondary faults that can accommodate significant portion of relative plate motions.6 Fault loading rates…

…are constant on low-CoCo faults
Our analysis reveals that low-CoCo faults are characterized by geodetic rate/geologic rate ratios very close to one, regardless of the displacement scale over which the geologic slip rate is measured (Figures 2, 3).Geologic slip rates estimated from offset landforms at widely different displacements are the same for these faults, showing that the elastic strain release remains constant over the time intervals over which these displacements have accumulated.Furthermore, the current elastic strain accumulation rate (as constrained by the geodetic slip-deficit rate) is equal to strain release rates (as constrained by geologic slip rates) at all measured displacement scales.This indicates that for these faults, the elastic strain accumulation rate provided by the geodetic slip-deficit rate remains constant during the interseismic period (Figure 4), following the shortduration periods of fast post-seismic deformation at the beginning of each cycle, as originally noted by Meade et al. (2013).

…vary on high-CoCo faults
In contrast, high-CoCo faults, embedded within more complex structural settings, display no consistent relationship between geodetic slip-deficit and geologic slip rates.As noted above, these results reinforce the point that geodetic slip-deficit rates cannot be used as reliable proxies for geologic slip rates on high-CoCo faults.Moreover, although the mismatch between geodetic slip-deficit rates and small-displacement geologic slip rates could conceivably be due to short-term variations in fault slip rate, the mismatch between geodetic slipdeficit rates and large-displacement geologic slip rates, which are averaged over >50 to hundreds of meters of slip (see Table 1) and numerous individual earthquakes, and will thus average over any shorter-term/smallerdisplacement accelerations or decelerations of fault slip, indicates that elastic strain accumulation rates on the high-CoCo faults must vary through time.Specifically, at these large-displacement scales, the fault slip rate spanning numerous earthquakes will provide a robust estimate of the average rate of strain release on that fault through time.Insofar as the elastic strain accumulation rate must equal the elastic strain release rate (i.e., fault slip) over long time intervals, the mismatch that we document between geodetic slip-deficit rates and geologic slip rates averaged over large displacements requires that elastic strain accumulation rates as measured by geodetic slip-deficit rates must vary through time.
Further examination of the results displayed in Figure 3 helps us distinguish several types of behaviors amongst the high-CoCo faults.Those behaviors can be defined depending on whether the geodetic slip-deficit rate is equal to, slower than, or faster than either the large-displacement average geologic rate, or the smalldisplacement average geologic rate (Figure 4).
These differences between geodetic and geologic rates reveal the following fundamental point: Faults for which the current loading rate does not equal the average large-displacement geologic slip rate overly a ductile shear zone that must be creeping at either a slower or a faster rate than the long-term average slip rate.If, furthermore, the geodetic rate differs from the smalldisplacement rate, the rate of elastic strain accumulation consequently has to vary over the same periods of accelerations and decelerations that are averaged over in these small-displacement geologic rate values.
We suggest that using the mismatches between geodetic slip-deficit and small-displacement geologic rates can help us infer the current behavior of the faults that may be most representative of the nearfuture likelihood of major earthquake recurrence.Mismatches between elastic strain accumulation rates and small-displacement geological rates reveal three different modes for the high-CoCo faults.These are: faults that are storing elastic strain energy more slowly than their small-displacement geologic slip rates; faults that exhibit a current rate of elastic strain accumulation that is faster than the small-displacement geologic slip rate; and faults in which the geodetic slip-deficit rate approximately equals the youngest average geologic slip rate.In the following, we describe the details of the behavior of faults that fall within these three categories and discuss a model that attempts to explain the observations in terms of faults switching from one mode to another.
In the first case, geodetic slip-deficit rates are slower than the small-displacement (short-term) geologic slip rates measured on these faults.The Garlock (numbered 1 in Figures 2 and 3), the Mojave segment of the San Andreas (2), Wairau (8), Hope (9), Awatere (10), and Yammouneh ( 14) faults are all characterized by geodetic rate values that are slower than their respective geologic slip rates (both large-and small-displacement).For example, the central Garlock fault experienced a cluster of four large earthquakes between 0.5 and 2.0 ka (Dawson et al., 2003), resulting in a small-displacement (26 m) slip rate averaged over these four events through to the present of 14 +2.2 −1.8 mm/yr (Dolan et al., 2016).Modeling of geodetic data consistently yields very slow rates of elastic strain accumulation on the central Garlock fault, with a best estimate of ~2.6 mm/yr (Evans, 2017b), potentially including almost no elastic strain accumulation.In contrast, the large-displacement (long-term) slip rate averaged over the most recent 70 m of slip on this section of the Garlock fault is 8.8±1.0 mm/yr (Fougere et al., 2023, submitted).While this is slower than the small-displacement geologic rate, it is at least three times faster than the current rate of elastic strain accumulation.This mismatch suggests that the Garlock fault has recently entered into a "slow" mode of elastic strain accumulation, likely as a result of a decreased shearing rate on the underlying ductile shear zone.But why is the youngest, small-displacement rate so fast?We suggest that the switch in behavior of the Garlock fault from the 0.5 -2 ka "fast" mode ended with the final earthquake in the cluster, either because the fault (including the upper seismogenic part and the ductile shear zone roots) strengthened during the fast period encompassing the four-event cluster and became more difficult to slip (Dolan et al., 2007; Cawood and Dolan, The geologic rate values are averaged over large or small displacement (as in Figure 2).The numbering of the fault sites is referred to in Figure 2 and Table 1.The dashed arrows refer to a ratio of geodetic/geologic rate that would reach infinity, with a geological rate close or equal to 0 mm/yr, if the fault has not slipped for a long time since the MRE (see text for details).(b) Diagram showing the dispersion of the ratio (geodetic to geologic rates) values varying with the CoCo values.The higher the CoCo value, the more scattered the data (i.e., the farther from the 1:1 ratio line they tend to plot).The measure of the dispersion is detailed in the Supplementary Materials.Although we cannot calculate an exact CoCo value for the Queen Charlotte fault (15), because of our inability to include all active faults within a 100 km radius of the slip-rate site, we assign it a CoCo value of zero, since this fault accommodates >95 % of the total Pacific/North America plate-motion rate (NUVEL-1A; DeMets and Dixon, 1999).submitted), and/or because the Garlock fault has exhausted what Dolan et al. (2024) refer to as the "crustal strain capacitor" (similar to Mencin et al. (2016) "strain reservoir"), that is, the shear strain stored in the crust surrounding this section of the Garlock fault.In this view, the current slip rate (or, equivalently in this context, the "most recent geologic slip rate") of the Garlock fault since the most recent earthquake (MRE) ca.500 years ago has been 0 mm/yr, reflecting the current very slow rate of elastic strain accumulation on the Garlock fault.
Similarly, the geodetic slip-deficit rate on the Wairau fault in New Zealand (2.8 +2.4 −0.8 mm/yr; Johnson et al., 2022) is slower than the small-displacement rate of 4.5±1.0mm/yr (Zinke et al., 2021), calculated for the preceding fast period of slip between a geomorphic offset dated at ca. 5.4 ka and the ca. 2 ka MRE.This contrast highlights a period of fast slip on the fault during this time interval.Yet, 2,000 years have elapsed since the MRE on the Wairau fault (relative to an average Holocene recurrence interval of ca.1,000 years Nicol and Dissen, 2018), which we suggest indicates a "most recent geologic slip rate" since the MRE of 0 mm/yr.Thus, the averaging of the small-displacement rate over Figure 4 Observed modes of fault behavior, with time shown as the horizontal dimension of the block, and with relative slip rate displayed with a color gradient.In (a), we show that whatever the time over which its behavior is averaged, a low-CoCo fault's slip rate is constant and thus equals its elastic strain accumulation rate, as shown in the left hand-side, hence the same color at each point in time and in the brittle and ductile parts of the fault.Note that we are not considering singleearthquake time scales.In contrast, high-CoCo faults (b and c) exhibit several types of behaviors, as discussed in the text.In (b), we illustrate a fault that has a short-term (small-displacement) geologic slip rate that is slower than its long-term (largedisplacement) rate.For this fault, the current elastic strain accumulation (ductile shear of the ductile roots) is slower than the short-term geologic slip rate, and therefore might be entering what we refer to as a slow mode.In (c), we show another example of a fault whose long-term geologic slip rate is faster than its short-term geologic slip rate.This fault is entering a fast mode since its elastic strain accumulation is much faster than its short-term geologic slip rate.
the past 5,400 years through to the present may be masking a switch of the Wairau fault from a fast mode between 2 and 5 ka, to the current slow mode that has prevailed since the MRE at 2 ka.In both the Wairau and Garlock faults examples, if we were to use the inferred most recent geologic slip rate of 0 mm/yr as the best representation of the small-displacement slip rate, the geodetic/small-displacement rate ratios would soar, as the dashed arrows in Figure 3a illustrate.
Although the small-displacement slip-rate of the Hope fault (8.2 +5.4  −3.0 mm/yr; Hatem et al., 2020) is likely faster than the geodetic slip-deficit rate estimate (5.8 +1.8 −1.1 mm/yr; Johnson et al., 2022), their respective 2σ uncertainties overlap (Table 1), which does not allow us to strongly affirm a potential switch of mode for this fault.However, the difference between these estimates might suggest that the Hope fault is currently in a slower mode, and may have exhausted its strain capacitor in the past five earthquakes, which generated 20-30 m of fault slip over the past ~1,500 years (Hatem et al., 2019(Hatem et al., , 2020)).The thus-reduced shear stress stored in the crust surrounding the Hope fault might explain the lack of significant slip on the Hope fault in the 2016 Kaikōura earthquake sequence (e.g., Hamling et al., 2017), despite its proximity to the faults that initially ruptured in the sequence.Indeed, both Ulrich et al. (2019) and Nicol et al. (2023) have suggested that the lack of significant 2016 coseismic slip on the Hope fault could be due to the low stresses in play across the Hope fault prior to the Kaikōura earthquake.
A final example is the Mojave section of the San Andreas fault (SAFm), which is characterized by an elastic strain accumulation rate (15.1±2.3 mm/yr; Evans, 2017b) that is much slower than its small-displacement slip rate (~27-29 mm/yr; Weldon et al., 2004;Dolan et al., 2016) (Figures 3, 4, Table 1).The MRE occurred 167 years ago on the SAFm, whereas the mean recurrence interval for this stretch of the fault is about 100 years (e.g., Scharer et al., 2017).The absence of any earthquakes since the 1857 MRE led to much speculation in earlier decades, when some scientists suggested that the SAFm was "overdue" (e.g., Weldon and Sieh, 1985).These early ideas of earthquake recurrence patterns were based on the assumption of steady elastic strain accumulation rates.If, instead, elastic strain accumulation rates vary, as we show here, then the long elapsed time since the 1857 earthquake may at least partially be a consequence of reduced loading rates in this section of the SAF, as reflected in the current geodetic rate.All of this suggests that the SAFm (2) may have entered a "quieter mode".
A partial, potential alternative explanation for this situation was provided in Hearn et al. (2013) and Hearn (2022), who suggested that some of this slow elastic strain deformation rate on the SAFm might be due to a so-called "ghost transient" related to long-term viscoelastic relaxation of the lithospheric mantle and lower crust following the 1857 Fort Tejon earthquake.However, this would only explain 5 mm/yr of the apparent ~14 mm/yr difference between the geodetic slip-deficit rate and the small-displacement slip rate.In marked contrast to the SAFm, Hearn et al. (2013) also noted that there is no such "ghost transient" associated with the Garlock fault, which ruptured most recently in 1450-1640 CE (Dawson et al., 2003).
Our analysis reveals another type of behavior, in which faults exhibit geodetic slip-deficit rates that are faster than their geologic slip rates.We suggest that these faults may have switched from a slow mode to a fast mode.This behavior characterizes the Clarence fault (9), the northern Dead Sea fault (nDSF -13), the northern strand of the North Anatolian fault system (nNAF -23), and the Pazarcık segment of the East Anatolian fault (EAF -24) (Figure 3).The Clarence fault (9) has a geodetic slip-deficit rate (8.6 +1.5  −1.1 mm/yr; Johnson et al., 2022) that is faster than both its smalldisplacement and large-displacement geologic rates, although its small-displacement slip rate (2.0 ± 0.4 mm/yr) is half as fast as its large-displacement slip rate (4.2 ± 0.5 mm/yr; Zinke et al., 2019).Similarly, the nDSF stores elastic strain energy at a rate of 4.8 ± 0.3 mm/yr (Gomez et al., 2020) and is characterized by a slower small-displacement slip rate of 3.5 ± 0.2 mm/yr (Wechsler et al., 2018).For the nNAF, considering the large uncertainties on the large-displacement geologic slip rate (18.5 +10.9 −5.9 mm/yr, measured over a 500 My time scale; Kurt et al., 2013), we cannot confidently infer that it is slower than the reported geodetic slip-deficit rate (28.6 mm/yr;DeVries et al., 2016), but we can more confidently state that the small-displacement geologic rate (15 ± 6 mm/yr; Meghraoui et al., 2012) is slower that the geodetic rate, as suggested by Dolan and Meade (2017).The EAF (24) has a geodetic slip-deficit rate (10.3 ± 0.6 mm/yr; Aktug et al., 2016) that is nearly twice as fast as the available large-displacement geologic slip rate (5.6 ± 0.3 mm/yr; Yönlü and Karabacak, 2023).Notably, this section of the EAF ruptured in the 2023 M w 7.8 Kahramanmaraş earthquake.
The Calico fault (6) may also fall within this type of behavior, with a switch from a previous slow mode to a current faster mode.Although the data currently available for the Calico fault do not allow us to infer a small-displacement slip rate, the current loading rate (7.4±3.4 mm/yr; Evans, 2017b) is much faster than its large-displacement slip rate (1.6±0.2 mm/yr; Oskin et al., 2007) (Figure 3).Specifically, the Calico fault has generated four surface-rupturing earthquakes within the past ~9,000 years (Ganev et al., 2010), which coincide with periods of clustered moment release identified on other faults in the eastern California shear zone (ECSZ) (Rockwell et al., 2000).The MRE on the Calico fault occurred sometime between 0.6 and 2 ka, likely as part of an ongoing cluster of earthquakes that has been occurring over the past 1-1.5 ky in the ECSZ (Rockwell et al., 2000), including most recently the 1872 Owens Valley, 1992 Landers, 1999 Hector Mine, and 2019 Ridgecrest earthquakes.Geodetic data suggest that the Calico fault, and potentially other nearby faults in the ECSZ, are likely experiencing a period of anomalously fast loading (Oskin et al., 2007;Dolan et al., 2007), as originally suggested by Peltzer et al. (2001), and further discussed by Oskin et al. (2008).Peltzer et al. (2001) showed that active dextral shear associated with the ECSZ extends across the Garlock fault, which does not exhibit any accumulation of left-lateral shear strain energy, emphasizing the idea that the Garlock fault has entered a slow mode (Evans et al., 2016;Evans, 2017a).These observations are consistent with kinematic models that suggest that the Garlock fault is currently storing and releasing elastic strain energy at much slower-than-average rates, whereas the ECSZ subsystem is storing and releasing energy at faster-than-average rates (Dolan et al., 2007(Dolan et al., , 2016;;Hatem and Dolan, 2018;Peltzer et al., 2001).Farther north in the ECSZ-Walker Lane system, the Owens Valley fault exhibits a geodetic slip-deficit rate estimate (2.7±1.4 mm/yr; Evans, 2017b) that may be faster than its small-displacement slip-rate (1.3±0.8 mm/yr; Haddon et al., 2016), consistent with a period of faster-thanaverage elastic strain accumulation.It is worth noting however, that these rate estimates overlap at 95% uncertainty (Table 1).
In addition to these behaviors, the San Jacinto fault (4) exhibits a small-displacement geologic slip rate (15.6±2.3 mm/yr; Onderdonk et al., 2015) that is similar to the current loading rate (13.2±4.6 mm/yr; Evans, 2017b) within 2σ uncertainties.However, there is currently no well-constrained, large-displacement (> 50 m) geologic slip rate available for the San Jacinto fault.Thus, the similarity of the geodetic and smalldisplacement geologic rates might suggest that the San Jacinto fault may have been captured in the middle of either a fast period (i.e., cluster) or a slow period, but in the absence of a large-displacement slip rate, we cannot say definitively which.
It is worth noting that the slip rate of high-CoCo faults does not seem to affect their behavior; both fast-slipping and slow-slipping high-CoCo faults exhibit significant dispersion of geodetic/geologic ratios.Dispersion analysis indicates that fast-slipping, high-CoCo faults exhibit larger dispersion of geodetic/geologic ratios than for slower-slipping high-CoCo faults (see Supplementary Materials), contrary to what Cowie et al. (2012) obtained from their simulations of elastic interactions between growing faults.However, we suspect that the dispersion values we determine are not particularly meaningful given the dearth of slip-rate data from fastslipping, high-CoCo faults.
One key element to highlight is the potential difficulty in capturing any switches from fast to slow mode (or vice versa) with the available incremental fault sliprate data, which in some instances may not be detailed enough over the appropriate displacement intervals to capture these switches in mode.This challenge will typically lie in the resolution at which the increments of the incremental slip-rate record are obtained, and if the slip-rate data are not detailed enough over the appropriate time and displacement intervals, the switches in mode may not be observable.Assuming, however, that the input data we use in this study provide sufficient information to constrain the timing of these switches in mode, our results imply that the elastic strain accumulation rate keeps up with or controls fast and slow fault slip periods, which challenges the suggestion by Weldon et al. (2004) that the strain release rate varies while the strain accumulation rate does not (i.e., their "strainpredictable behavior").

…on high-CoCo faults
The variations in strain accumulation rate described above likely record variations in the rate of shear along the ductile shear zone roots of seismogenic faults.Here we discuss the mechanisms that might control the behavior of ductile shear zones on high-CoCo faults.
The different behaviors exhibited by the high-CoCo faults can be explained by mechanisms that occur at the plate-boundary scale, such as the shared accommodation of slip in complex plate-boundary structural settings (Peltzer et al., 2001;Dolan et al., 2016), as well as by mechanisms at the scale of the fault zone, with potential strengthening and weakening processes over the ductile shear zone and the coupling between the brittle and the ductile parts of a fault (e.g., Peltzer et al., 2001;Oskin et al., 2008;Dolan et al., 2007).In structurally complex, high-CoCo settings, mechanically complementary faults within the system can share the load by trading off slip while maintaining a relatively constant overall system-level rate that keeps pace with the relative platemotion rate (Dolan et al., 2024).In these structurally complex plate-boundary fault systems, when one fault slips much faster than its average rate throughout multiple earthquakes, the other faults of the system slip more slowly or not at all as the overall fault system works together to maintain constant average rate.Acceleration of the ductile shear zone rate will create a positive feedback loop in which faster shear on the ductile shear zone roots will drive the occurrence of more frequent, large earthquakes (i.e., an earthquake cluster) in the seismogenic part of the fault, which will in turn accelerate underlying ductile shear rates through viscous coupling, increasing driving stress, and potentially by addition of fluids into the nominally ductile uppermost parts of the ductile shear zone roots (Ellis and Stöckhert, 2004;Cowie et al., 2012;Mildon et al., 2022;Dolan et al., 2007).But eventually, either through exhaustion of the crustal strain capacitor of stored elastic strain energy on the fault in question, and/or through increases in ductile shear zone strength (i.e., resistance to shear), the fault will enter a slow mode of strain release as deformation shifts to a mechanically complementary, weaker fault within the system (Dolan et al., 2024).
These accelerations and/or decelerations of the faults' ductile shear roots of a complex fault network might be explained by strength changes (e.g., strain hardening and weakening).Dolan et al. (2007Dolan et al. ( , 2016) ) and Dolan and Meade (2017), for instance, suggested that ductile shear zone roots can harden during fast slip periods, leading to lulls in ductile shear and hence earthquake lulls in the upper crust.In this model, the ductile shear roots of faults are accumulating elastic strain energy more slowly than their long-term slip rate, after having been "exhausted" during a period of rapid ductile shearing and fast fault slip in clusters of earthquakes (Dolan et al., 2024).Other potential mechanisms occurring within ductile shear zones that could give rise to a change in shearing rate and associated elastic strain accumulation rates of the overlying fault include changes in fluid concentration (e.g., Mancktelow and Pennacchioni, 2004;Okazaki et al., 2021), changes in grain size (e.g., Handy, 1989;Okudaira et al., 2017), macroscopic fault evolution (e.g., Handy et al., 2007) and fabric development (e.g., Carreras et al., 2005;Melosh et al., 2018) (see Cawood and Dolan, submitted, for details on these mechanisms).All these mechanisms could drive the crustal "strain capacitor" to either its exhaustion or its replenishment (Dolan et al., 2024;Cawood and Dolan, submitted).

…on low-CoCo faults
In contrast, tectonically isolated, primary low-CoCo plate-boundary faults (e.g.central SAF, central and eastern NAF, Alpine fault), are characterized by interseismic rates that correlate well with geologic slip rates that are averaged over both small and large displacements (Figure 3).This suggests that such low-CoCo faults must "keep up" with the relative plate-motion rate over short time and small displacement scales because there are no other mechanically complementary faults in such systems to share the load.In other words, even though all of the potential strengthening and weakening mechanisms we discuss for high-CoCo faults must be operating on low-CoCo faults as well, these processes will be overwhelmed by steady increases in driving stress related to relative plate motion.All or most of the relative plate motion must be accommodated on the primary fault in the absence of other major faults that could potentially share the work required to move the plates past each other.Moreover, the similarity of geodetic slipdeficit rates and small-displacement geologic slip rates on low-CoCo faults requires that the fault responds to steady increases in driving stress at scales of no more than a few tens of meters of relative plate motion.This is consistent with the long-held notion embodied in elastic rebound theory (Reid, 1910) that the crust can only store a given amount of elastic strain energy before the weakest element of the system (i.e., the structurally isolated primary fault) slips in an earthquake.In turn, this line of reasoning implies that the single, isolated fault either has to be weak all the time -as soon as it stores no more than a few tens of meters of elastic strain energy, it is ready to slip -or it cyclically becomes weak when stress is approaching the rupture limit.A key question is whether this near-1:1 relationship between "energy in" (as manifest in geodetic slip-deficit rates) and "energy out" (i.e., fault slip rates) on low-CoCo faults extends to single-earthquake scales.The few available earthquake-by-earthquake age plus displacement-perevent datasets that are available from low-CoCo faults suggest that, at least generally, this may be the case.Specifically, the relatively regular timing (CoV ~0.3) of surface ruptures on the Alpine fault at Hokuri Creek, coupled with similar ~7.5 m horizontal displacements in the two most recent earthquakes (Berryman et al., 2012;De Pascale and Langridge, 2012;Sutherland et al., 2006), and the similar displacements in the four most recent earthquakes and relatively regular timing of earthquakes on the NAF at Demir Tepe (Kondo et al., 2010) are consistent with the idea that this may extend to sin-gle earthquake scales.If this is generally true, then low-CoCo faults may release much of, and perhaps almost all, of the shear stress accumulated since the previous event during each rupture.It is worth noting, however, that even at the Hokuri Creek site on the low-CoCo Alpine fault (Berryman et al., 2012), which is characterized by quasi-periodic earthquake recurrence, the 24event record cannot be fit precisely with either time-or slip-predictable models (Shimazaki and Nakata, 1980), and may best be explained by an underlying chaotic behavior (Gauriau et al., 2023).

Fault's near-future behavior, and further applications for PSHA
Our results may provide new insight into how slip rates can be better used as basic inputs into probabilistic seismic hazard assessment (PSHA) methods.For low-CoCo faults, the outcome is straightforward -both the slip rate averaged over large displacements and the slip rate averaged over small displacements are similar to the geodetic slip-deficit rate.Therefore, any of these values can be used as an input into a PSHA.Despite this relative constancy of both strain accumulation and release rates in the behavior of a low-CoCo fault, any attempt towards formulating earthquake prediction focused on timing of earthquake occurrence on a specific fault may be functionally impossible (e.g., Chen et al., 2020;Gauriau et al., 2023).Therefore, a probabilistic methodology is required for any seismic hazard assessment.
For high-CoCo faults, the outcome is less straightforward, since such faults exhibit variable strain accumulation and release rates through time.The question arises as to what slip-rate value is the best to use in PSHA?There are three possible strategies for incorporating incremental slip-rate data into PSHA, as originally suggested by van Dissen (2020): (a) incorporating the large-displacement average slip rate by neglecting any incremental rate changes, which in a long-term statistical sense can be viewed as variations about the mean rate; (b) using the full error range associated with all available incremental slip rates, or (c) favoring the most recent (smallest-displacement multipleearthquake) incremental slip rate as the most appropriate one.
Here we propose a potential solution to this conundrum by comparing the small-displacement and largedisplacement rates with the elastic strain accumulation rates.Geodetic slip-deficit rates have been suggested as primary inputs into seismic hazard assessment (e.g., Bird and Kreemer, 2014;Hussain et al., 2018), but never in light of comparison to available geologic slip-rate records.The examples listed in paragraph 6.2., however, illustrate the current limitations on using smalldisplacement rates (suggestion c) as a proxy for the most recent phase of fault behavior without considering the possibility that the fault may have switched modes in the interval since displacement of the most-recent available small-displacement slip-rate data.We suggest that a potential path forward is to use the comparison of the geodetic slip-deficit rates with small-displacement geologic rates of high-CoCo faults to forecast the near-future behavior that might be expected on a given fault.While we suggested in our earlier paper (Gauriau and Dolan, 2021) that option (c), i.e., implementing the shorter-term slip rate into a PSHA, would lead to a more reliable forecast of the near-future behavior of the fault, the current analysis suggests that deviations of geodetic rates from the small-displacement geologic slip rates might better illustrate the future behavior of high-CoCo faults.
Specifically, we propose that a geodetic slip-deficit rate that is slower than the small-displacement slip rate might indicate lower near-future hazard, because the fault is storing elastic strain energy more slowly than average (Figure 5).This is exemplified by the cases of the Garlock fault, the SAFm, and the Hope fault.Conversely, geodetic rates that are faster than the smalldisplacement rate on faults that have not experienced a recent earthquake (i.e., those not experiencing a post-seismic strain transient) may indicate higher nearfuture hazard, as illustrated by the nNAF, the Clarence fault, and the nDSF.In support of this idea, the 2023 M w 7.8 Kahramanmaraş earthquake occurred on a section of the EAF that exhibited a geodetic slip-deficit rate, prior to the earthquake, that was almost twice as fast as the long-term geologic slip rate.In the case of the San Jacinto fault, and other faults with a geodetic rate that equals the small-displacement slip rate, we suggest that the near-future hazard can be best represented by the small-displacement slip rate and/or the geodetic rate (Figure 5).
One possible route towards using these observations in improved PSHA would be to evaluate geodetic and geologic rate discrepancies using the smallestdisplacement incremental slip rate for a fault to infer the current mode of fault behavior.

Conclusions
Our comparison of geologic fault slip rates with geodetic slip-deficit rates from strike-slip plate-boundary faults reveals markedly different strain accumulation and release behavior on structurally isolated faults relative to those that extend through structurally complex regions.Our main take-away is that elastic strain accumulation rates on high-CoCo faults must vary through time, whereas they remain relatively constant on low-CoCo faults.This can potentially be applied to faults exhibiting other kinematics, such as extensional or compressional fault systems, where both fault interactions and slip-rate variability have also been studied (e.g., Luo and Liu, 2010;Mildon et al., 2022).
High-CoCo faults have geodetic-to-geologic ratios that vary widely, demonstrating that rates of elastic strain accumulation vary significantly through time at scales that are longer than individual earthquake cycles.This is particularly clear from the differences observed between the short-term geodetic slip-deficit rate data with long-term, large-displacement geologic slip rates, which will average over any shorter-term and smaller-displacement accelerations and decelerations of fault slip that typify faults in such settings (Gauriau and Dolan, 2021).Presumably, these changes reflect temporally variable rates of shear on the ductile shear zone roots of brittle faults, which we infer are related to the more complicated history of strain accumulation and release among regional fault interactions at displacement scales of a few tens of meters and centennial to millennial time scales.Specifically, geodetic slip-deficit rates that neither match large-displacement nor small-displacement average slip rates indicate that the elastic strain accumulation rate must vary over time scales corresponding to the deceleration and acceleration periods over which smallest-displacement geologic rates are averaged.
In contrast, low-CoCo faults are characterized by steady elastic strain accumulation and release rates, which indicate that such faults need to "keep up with" the relative plate motion rate at short-time and small-displacement scales, overwhelming any potential strengthening and weakening mechanisms that might be operating on such faults.Consequently, the geodetic slip-deficit rate observed on a low-CoCo fault can be used as a proxy for its geologic rate, which itself can be assumed to be relatively constant.
Finally, we suggest that the discrepancies between short-term geologic slip rates and geodetic slip-deficit rates for high-CoCo faults might represent a switch of mode, revealing either an accelerating or a decelerating phase.A geodetic slip-deficit rate that is faster than the most recent geologic incremental slip rate would imply a potential higher near-future seismic hazard, whereas a geodetic rate that is slower than the smallestdisplacement slip rate would signal a lower near-future seismic hazard.These discrepancies could be used to refine PSHA models, not only in strike-slip fault systems, as highlighted in this study, but potentially to any type of plate-boundary kinematics.The importance and current relative dearth of robust incremental slip rate records highlights the need to develop more such records from more faults around the world to enable better PSHA.

Figure 3
Figure 3 Variations of geodetic to geologic slip-rate ratios against CoCo values standardized by plate rate over a 100 km radius.(a) Ratios of geodetic slip-deficit rate to geologic rate plotted against CoCo.The geologic rate values are averaged over large or small displacement (as in Figure2).The numbering of the fault sites is referred to in Figure2and Table1.The dashed arrows refer to a ratio of geodetic/geologic rate that would reach infinity, with a geological rate close or equal to 0 mm/yr, if the fault has not slipped for a long time since the MRE (see text for details).(b) Diagram showing the dispersion of the ratio (geodetic to geologic rates) values varying with the CoCo values.The higher the CoCo value, the more scattered the data (i.e., the farther from the 1:1 ratio line they tend to plot).The measure of the dispersion is detailed in the Supplementary Materials.Although we cannot calculate an exact CoCo value for the Queen Charlotte fault (15), because of our inability to include all active faults within a 100 km radius of the slip-rate site, we assign it a CoCo value of zero, since this fault accommodates >95 % of the total Pacific/North America plate-motion rate (NUVEL-1A; DeMets and Dixon, 1999).

Figure 5
Figure 5 Schematic illustration of modes of behavior defined in this paper, according to the CoCo values and the geodetic/geologic rate ratio, and their potential meaning in terms of near-future hazard.

Table 1
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