Paleoseismicity of the western Humps fault on the Emu Plain, North Canterbury, New Zealand

ABSTRACT The 2016 MW 7.8 Kaikōura Earthquake nucleated on The Humps fault, which ruptured across the Emu Plain in North Canterbury. The paleoearthquake history of the fault was poorly constrained prior to the 2016 earthquake. To determine the timing and single-event displacements (SED) of earthquakes on the fault we use Optically Stimulated Luminescence (OSL) and radiocarbon dates of faulted stratigraphy and analysis of faulting (i.e. geometry and slip) at the McLean-1 trench site. At the trench the fault trace trends east–west and primarily accommodated right-lateral strike-slip in 2016 (2 ± 0.2 m strike slip and 0.35 ± 0.05 m vertical slip northside downthrow). The Humps fault is more seismically active than previously thought and accrued slip during at least six surface rupturing paleoearthquakes. The timing of these earthquakes was: 9.8–15.3 ka BP (Event 1), 8.6–11.5 ka BP (Event 2), 8.1–10.9 ka BP (Event 3), 6.0–8.6 ka BP (Event 4), 1840 AD to 4.5 ka (Event 5), and 2016 AD (Event 6). These earthquakes have a mean recurrence interval of 1.8–3.4 kyr and could have recurrence intervals up to ~9 kyr. Kaikōura-type ruptures could occur as frequently as every ∼2 kyr and maybe longer if The Humps fault rupture geometries are not characteristic.


Introduction
The 2016 Kaikōura Earthquake nucleated on The Humps fault and subsequently ruptured a complex network of at least 17 active faults at the ground surface (Figure 1), which vary in length, slip sense, slip rate and their proximity to the Hikurangi plate interface (e.g. Hamling et al. 2017;Litchfield et al. 2018;Mouslopoulou et al. 2019). At the time of the earthquake, no published paleoseismic data were available for the faults that ruptured in 2016 with surface slip >1 m (including The Humps fault). South of the Hope fault ( Figure 1) most of the faults that ruptured in 2016 were either not mapped as active, or mapped as discontinuous active traces significantly shorter than the 2016 ground ruptures (Warren 1995;Pettinga et al. 2001;Rattenbury et al. 2006; Barrell and Townsend 2012;Nicol et al. 2018). Based on their geomorphic expression and the estimated ages of displaced geomorphic surfaces, active faults south of the Hope fault were estimated to have slip rates of <2.5 mm/yr and typical recurrence intervals (RIs) for surface-rupturing earthquakes of >5 kyr (Pettinga et al. 2001; Barrell and Townsend 2012;Stirling et al. 2012). These relatively long RIs have been used to infer that Kaikōura-type earthquakes (i.e. rupturing the main faults that slipped in 2016) occur no more frequently than every ∼5 kyr (Litchfield et al. 2018;Nicol et al. 2018).
In this paper, we document the paleoseismic history of The Humps fault at one site on the Emu Plain ( Figure 2). The Humps fault is key for understanding the Kaikōura Earthquake because the earthquake nucleated on this structure and it has been used to infer the minimum RI of Kaikōura-type earthquakes (Litchfield et al. 2018;Nicol et al. 2018). Prior to the 2016 earthquake, The Humps fault was mainly mapped in the Mount Stewart Range and on the eastern margin of the Emu Plain (Figure 2A), where it was estimated to have a vertical slip-rate of ∼0.2 mm/yr and a RI of 13 ± 8.7 kyr (Barrell and Townsend 2012). The large uncertainty in RI for The Humps fault highlights the lack of available paleoearthquake data prior to 2016, and the need for additional study of this fault. Here we use data from the McLean-1 trench site on The Humps fault (see Figures 1 and 2 for location) together with Optically Stimulated Luminescence (OSL) and radiocarbon dating of faulted strata to constrain the paleoseismicity of the fault since ∼18 ka. This study shows that The Humps fault has RIs shorter than previously estimated and, on average, probably generates surface-rupturing earthquakes about every two to three thousand years. The data help address the question, 'how frequently could Kaikōura-type earthquakes occur?' and provide key paleoseismic input for seismic hazard assessment in the North Canterbury region of the South Island, where information on the magnitude and RIs of past surface-rupturing earthquakes is sparse (e.g. Nicol et al. 1994;Pettinga et al. 2001; Barrell and Townsend 2012).   Begg and Johnston 2002;Rattenbury et al. 2006;Forsyth et al. 2008), active faults (black lines from Langridge et al. 2016) and November 14 2016 Mw 7.8 Kaikōura Earthquake fault ruptures (red lines with key fault names shown). The offshore fault is the Hikurangi subduction thrust. The Pacific Plate motion vector relative to the Australian Plate is from Beavan et al. (2002). The epicentral locations of the Kaikōura Earthquake (blue star; Nicol et al. 2018) and large historical Cheviot and Motunau earthquakes (from Downes and Dowrick 2015) in the North Canterbury Domain are shown. The onshore topographic basemap is an 8 m hillshade DTM from LINZ and bathymetry is from NIWA. MFS: Marlborough Fault System; NCD: North Canterbury Domain.
Faults in the NCD are mainly northeast-striking with oblique reverse and right-lateral displacements (e.g. Nicol et al. 1994;Barnes 1996;Pettinga et al. 2001;Rattenbury et al. 2006;Forsyth et al. 2008;Barrell and Townsend 2012;Vanderleest et al. 2017). Ongoing active deformation in the NCD is indicated by active fault traces (e.g. Pettinga et al. 2001;Rattenbury et al. 2006;Forsyth et al. 2008;Barrell and Townsend 2012), uplift of marine terraces (e.g. Nicol et al. 1994;Vanderleest et al. 2017), tilting of alluvial terraces (e.g. Nicol et al. 1994) and historical moderate to large magnitude earthquakes. Prior to the Kaikōura Earthquake, the M w 6.8 1901 Cheviot and M w 6.4 1922 Motunau earthquakes were the largest historical events in the NCD, although neither ruptured the ground surface and direct evidence for these earthquakes would be difficult to observe today if they occurred prehistorically (see Downes and Dowrick 2015, for descriptions of the earthquakes and Figure  1 for their locations).
The Humps fault is located in the northern part of the NCD ∼10 km south of the Hope fault (Figure 1). At the surface the fault is ∼36 km in length from a free trip in the west to its intersection with the Leader fault in the east Brough 2019) ( Figure 1). The fault has been divided into two main sections which, based on changes in strike and dip, have been referred to as The Humps West and The Humps East . The Humps West section of the fault is ∼25 km long and traverses the Emu Plain, which comprises alluvial surfaces with estimated ages of ∼70 ka to Holocene (Clayton 1968;Rattenbury et al. 2006;Brough 2019). The 2016 surface rupture generated new scarps and reoccupied preexisting fault traces, some of which had previously been mapped by Barrell and Townsend (2012). Not all previously mapped active fault traces on the Emu Plain ruptured in 2016. Fault traces that ruptured in 2016 generally strike east to east-northeast (∼070-090°) across the Emu Plain and at the surface typically dip steeply (>60°) to the south Brough 2019). Faults that did not rupture in 2016 strike east to east-northeast and north to northnorthwest.
The Humps West fault section forms a segmented array of fault traces with segmentation occurring on decimetre to kilometre scales ( Figure 2). On the kilometre scale, the western ∼8 km of The Humps fault comprises one main fault trace, which was sampled by the McLean-1 trench and, bifurcates further east where it comprises two primary fault traces ( Figure  2A). During the Kaikōura Earthquake, The Humps West primarily accommodated right-lateral strikeslip of up to 3.9 ± 0.4 m (mean ∼1.4 ± 0.4 m) with <1.2 ± 0.2 m vertical displacement (mean 0.5 ± 0.2 m) mainly up-to-the-south (Litchfield et al. 2018;Nicol et al. 2018;Brough 2019). The highest vertical displacements on the Emu Plain were recorded at pop-up structures and pull-apart basins, consistent with the fault being mainly right-lateral strike-slip Brough 2019).

Data and methods
To constrain the timing, RIs and single event displacement (SED) for surface-rupturing earthquakes on The Humps fault we use data from the McLean-1 trench, fault-trace mapping and measurement of displacements, and dating of faulted cover-bed stratigraphy. Fault traces that ruptured in 2016 on the Emu Plain and close to the trench site were mapped across agricultural pasture using four main datasets: (i) a 1 m resolution Digital Elevation Model (DEM) derived from light detecting and ranging (lidar) data collected in December 2016 (source: NZTA; New Zealand Transport Authority, Land Information New Zealand; New Zealand Land Information, ECAN; Environment Canterbury, and AAMNZ ltd) ( Figure 2); (ii) a ∼0.1 m Digital Surface Model (DSM) constructed from dronebased Structure-from-Motion (SfM) photogrammetry ( Figure 2C west of fence line); (iii) field measurements using hand-held GPS (Global Positioning System); and (iv) Real Time Kinematic (RTK) Global Navigational Satellite System (GNSS) data. The combination of all altitude data was used to record fault scarps with heights as small as ∼0.1 m (Figures 2 and 3). Fault rupture mapping and vertical displacement measurements for 2016 ruptures at the trench site were augmented by differential lidar produced by subtracting the pre-and post-earthquake lidar elevations (i.e. 2013 ECAN and 2016 AAMNZ lidar surveys) ( Figure  3). Field mapping and lidar data were also used to measure 2016 displacements of cultural markers (e.g. fences, roads, farm animal tracks and plough lines). The 2016 surface displacements constrain SED at the trench site, while cumulative apparent vertical displacements of cover-bed stratigraphy in the trench walls record slip that accrued during multiple earthquakes.
Brough (2019) excavated two trenches and here we re-examine and report the McClean-1 trench, which is the only one to provide paleoseismic information (For information on the McLean-2 trench refer to Brough 2019; see Figure 2C for location of McLean-2). The McLean-1 trench was excavated into an alluvial fan surface of assumed Holocene age, to a depth of about 3 m, perpendicular to the 2016 fault-rupture trace. In addition, three holes were augered to a depth of 3.5 m below the trench base to locate the top of gravel Unit 1 on the downthrown northern side of the fault (Figures 4 and 5). The trench site was selected because: (i) the upslope-facing scarp had the potential to pond sediments, (ii) the 2016 fault zone comprised one main strand and was sufficiently narrow to be captured by a single trench < 20 m long and, (iii) the 2013 lidar showed a ∼40 cm high fault scarp demonstrating prior movement on the fault (Figure 3, 2013 ground surface). Both walls of the trench were cleaned, photographed and logged at 1:20 scale (Figures 4-6). Constraints on the timing of paleoseismic events and the ages of displaced landforms were provided by radiocarbon and Optically Stimulated Luminescence (OSL) dates (Table 1). Two radiocarbon ages are from adjacent charcoal fragments preserved in silts (Unit 6C, Figure  4) dated by the University of Waikato Radiocarbon Laboratory (see Table 2 for further details). OSL dates of silt layers are from laboratories at Victoria University of Wellington (VUW, N = 4) and Utah State University (USU, N = 2). OSL dates from each laboratory were single aliquot samples comprising multiple grains of feldspar (VUW) and quartz (USU). All uncertainties for radiocarbon and OSL dates are quoted at the 95% confidence level, with radiocarbon samples presented in calibrated years before present (cal. yrs BP), where the present is taken to be 1950. Within the uncertainties of the dates the majority of the radiocarbon and OSL ages are consistent with their relative stratigraphic positions (i.e. ages for strata deeper in the stratigraphic section are older). OSL sample WLL1298 (14.8 ± 2.8 ka, Table 1) is older than the stratigraphically higher and lower OSL ages in the east wall of the trench ( Figure 4) and seems inconsistent with other dates in the trench. Its inclusion would mean that the entire stratigraphic sequence from the base of Unit 2 to Unit 6a (up to 4 m of sediment, including ∼1.5-2 m of low energy silty clay in Unit 2) was deposited very rapidly, which we think is unlikely. Therefore, we infer that this date includes inherited grains that were not exposed to sufficient sunlight to reset them when they were last transported.
The earthquake timings quoted in this paper were calculated with OxCal v4.3.2 using the SHCal13 Southern Hemisphere calibration for radiocarbon ages (Bronk-Ramsey 2017). In the models, we made minimal assumptions about the relative ordering of events within units except where our interpretations required them (e.g. the stratigraphic position and timing of EQ1 within Unit 2; Figure 7). For simplicity, we assumed the two radiocarbon ages were splits of the same sample (i.e. same source of charcoal and all uncertainty is due to analytical error), though changing this input parameter had a negligible effect on output. We could not achieve a reasonable OxCal output including both OSL samples WLL1298 and USU-2902; doing so results in an overall agreement index of ∼10, meaning the age 'shifts' between input (measured) and posterior (modelled) age distributions required to meet stratigraphic constraints were large. Thus, we have explored a range of models including two simple, mutually exclusive models that (i) omit sample WLL1298 (preferred model) or (ii) retain WLL1298 but omit sample USU-2902 (alternate model). The omission of sample USU-2902 leads to a reasonable output that we think is less geologically feasible than the preferred model. Below, we report ages (Tables 1 and 2) and discuss event timings for our preferred model, while OxCal outputs for both preferred and alternate models can be found in the supplementary information to this article (Supplementary Material Figures S1 and S2; Tables S1 and S2 at https://doi.org/10.5281/zenodo.5523324).
Dating of stratigraphy in the trench walls constrains the timing and associated uncertainties of individual earthquakes (Figure 7). The modelled ages for each sample have been used to estimate the RIs between consecutive earthquakes and the uncertainties of these RIs. Because the uncertainties on the RIs can be as large as the RIs, we have adopted a Monte Carlo approach to generate frequency histograms of RIs that honour the available earthquake ages and their uncertainties. The Monte Carlo method employed here is outlined briefly below (for more detailed discussion see Nicol et al. 2016a). A Probability Density Function (PDF) was assigned to the timing of each event determined from the OxCal analysis. The uncertainty bounds of the underpinning data are assumed to represent the 95% confidence limit of each PDF and are equally distributed about the mean. As the probability distribution between the 95% limits is unknown, for the standard model we assume that all events in the central 95% of the distribution have equal probability. The central 95% is bounded by two 2.5% tails decreasing in probability with  Table 1 for details of the OSL dating and Table 2 for radiocarbon dates. For a photomosaic of the trench wall refer to Appendix 5 of Brough (2019). increasing distance from the mean (the decay being equivalent to that of a normal distribution). Our sensitivity tests suggest that using box-car, normal and triangular PDFs does not impact the first-order results. The resulting RI frequency histograms were generated for 5000 earthquakes and rerun 20 times to test the stability of the results. The general shape of the histograms presented in Figure 8 is replicated in all 20 runs and is assumed to be representative of the fault RIs and their uncertainties.

Fault geometry, slip and paleoearthquake timing
The McLean-1 trench provides information on the timing of multiple (e.g. ≥6) paleoearthquakes on The Humps fault in the last ∼18 kyr. In early 2018, when the trench was excavated, the fault trace at the trench site was defined by a furrow up to 2 m wide associated with an en-echelon array of left-stepping synthetic Riedel (R) shears ( Figure 2C). At the trench site the fault trace has a general east-west trend (∼95°), with individual R Riedel shears typically trending ∼105°. In the trench walls the subsurface faultzone width varies from 3 to 5 m and comprises up to 6 main fault traces (Figures 4 and 5). These faults dip predominantly to the south (mean 75°south) and range from 65°north to 20°south. In the east wall of the trench the fault bifurcates in the upper 2.5 m of strata to form a geometry consistent with that of a negative flower structure (Figure 4). In both walls of the trench many of the secondary splays do not reach the ground surface, with slip in 2016 mainly confined to a zone <1 m wide and defined by faults A and E (Figures 4 and 5).
At the trench, the fault has a mainly right-lateral strike-slip sense of motion, with minor reverse slip (south-side up). Left-stepping synthetic R Riedel shears observed in map view ( Figure 2C The maximum stratigraphic thickness of units above the basal gravel in the trench (including the auger holes) is about 6.5 m and mainly comprises interbedded gravel and silts (Figures 4 and 5; see also detailed descriptions in Table 3.1 of Brough 2019). The clay plugged gravel unit at the base of the sequence (Unit 1) is immediately below the OSL (sample WLL1297) dated silty clay (Unit 2) which returned an age of 15.1 ± 3.0 ka (Table 1) and thus the entire sequence above the gravel is interpreted to post-date the ∼30-18 ka Last Glacial Maximum (LGM; Alloway et al. 2007). The main stratigraphic layers can be correlated across the fault and between trench walls (Figures 4 and 5), indicating that these units probably have lateral continuity of at least 10 m. Many of the units appear to thicken into the downthrown side of the fault (e.g. units 2 and 6 show 2 and 0.6 m thickening, respectively, in the east wall of the trench; Figure 4). The silty clay Unit 2 also thins dramatically (>1 m) in the immediate upthrown side of faults A (east wall, Figure 4) and G (west wall, Figure 5), suggesting that a scarp of approximately 1 m in height formed and was then partially eroded prior to deposition of Unit 3. Despite the inferred erosion of Unit 2, there is little evidence for significant erosion of units 3-6, while the mixed silt and gravel Unit 7 is restricted to a fault-bounded depression (i.e. proposed negative flower structure) Table 1. Summary of OSL samples and dates from the McLean-1 trench. Trench location is latitude 42°37 ′ 56.97 ′′ and longitude 172°57 ′ 16.12 ′′ at an elevation of 180 m (see Figure 1 and its caption for location). See Figure 4 for locations of OSL samples in the east wall of the trench.  (2000). b Samples analysed at Utah State University laboratory. Age analysis using the single-aliquot regenerative-dose procedure of Murray and Wintle (2000) on 1-2 mm small-aliquots of quartz sand. c For unit descriptions refer to Figure 4 and Table 1 of Brough (2019). d All ages reported at the 95% confidence level with ages and uncertainties reported to 1 decimal place. and may have formed in association with erosion from the fault scarps that formed the depression (Figure 4). In addition to local scarp erosion, some sedimentary infilling of the structural depression on the downthrown side of the fault occurred (e.g. units 2-6 collectively thicken by ∼3.5 m across the fault in the east wall, Figure 4).
Variations in the thickness and lithologies of stratigraphy adjacent to the fault, together with upward terminations of faults and dating of the strata, provide key constraints for the paleoearthquake history of The Humps fault at this site (Figures 4-7). Here these paleoearthquakes are discussed from oldest (Event 1) to youngest (Event 6, 2016 Kaikōura Earthquake). The oldest displacement event(s) in the trench are recorded by thickness changes of Unit 2 across faults A and G (Figures 4 and 5). Given the thickening of Unit 2 by 2.5 m and the decrease in apparent vertical displacement from ∼3.5 m at the base of the Unit 2 to ∼0.7 m on the Table 2. Summary of radiocarbon samples and Accelerator Mass Spectrometry dates from the McLean-1 trench. Trench location is latitude 42°37 ′ 56.97 ′′ and longitude 172°57 ′ 16.12 ′′ at an elevation of 180 m (see Figure 1 and its caption for location). See Figure  4 for locations of radiocarbon samples in the east wall of the trench.  Figure 4 and Table 1 of Brough (2019). c Conventional radiocarbon age in years before Present (BP), where BP is before AD1950. Result is following Stuiver and Polach (1977) and based on the Libby half-life of 5568 yr with correction for isotopic fractionation applied. d Calibrated ages reported at 95.4% probability, calculated using OxCal v 4.3.2 Bronk Ramsey (2017) and the SHCal13 atmospheric carbon curve of Hogg et al. (2013). e Posterior ages modelled using OxCal v 4.3.2 Bronk Ramsey (2017). Charcoal calibrated dates are assumed to be splits of the same sample and combined to produce a single model age. base of Unit 3 (Table 1, Figures 4 and 5), we interpret that multiple earthquakes contributed to the creation of the accommodation space and erosion associated with Unit 2. As Unit 2 is poorly bedded it was not possible to determine precisely the stratigraphic location of the event horizon(s) and the timing of the earthquake(s) during deposition of this unit. We hypothesise that at least two earthquakes (here referred to as events 1 and 2) occurred during deposition of Unit 2, one to create the accommodation space into which the over thickened Unit 2 silty clay was deposited and a second to produce the fault scarp that resulted in strong erosion at the top of Unit 2 in the immediate up-thrown side of faults A and G (Figures 4 and 5). The younger of the two events is consistent with the upward terminations of faults D, F and G (south splay) at the top of, or within, the upper part of Unit 2 in the west wall of the trench ( Figure 5). Therefore, the event horizon for event 2 is inferred to be at the top of Unit 2 and this earthquake may have created the accommodation space indicated by thickening of gravel units 3 and 5 on the north side of the fault. OSL dates USU-2902, WLL1297 and WLL1299 (Table 1, Figure 4), in combination with OxCal analysis, suggest that Event 1 occurred between 9.8-15.3 ka and Event 2 at 8.6-11.5 ka ( Figure 4, Table 1). Given the ∼3.5 m apparent displacement on the top of the Unit 1 gravel, additional events during deposition of Unit 2 are possible and the pre-Holocene record of surface-rupturing earthquakes in the McLean-1 trench may be incomplete. Event 3 is marked by the upward terminations of faults C and G (north splay) in the west wall of the McLean-1 trench (Figures 5 and 6B,C). The top of units 3, 4 and 5 have approximately constant apparent vertical displacements along fault G, suggesting that this fault did not accrue slip during deposition of these units (Figure 5). Fault G also displaced Unit 6A and is overlain by Unit 6B (i.e. does not displace 6B), which indicates that event 3 is defined by an event horizon at the boundary between units 6A and 6B (Figures 5 and 6B). A similar relationship can be observed for fault C, although in this case units 6A and 6B could not be distinguished in the hangingwall of the fault and the stratigraphic position of the event is more ambiguous (Figures 5 and 6C). The timing of Event 3 is constrained by dates from OSL2 and OSL6 (Table 1) which, in combination with OxCal analysis, indicate an age of 8.1-10.9 ka, similar to the age range for Event 2. Although the precise age of events 2 and 3 remains uncertain, the available data supports a model in which The Humps fault experienced at least two surface-rupturing earthquakes in the earliest Holocene, with the interval between these events being no greater than ∼3.4 kyr.
Event 4 is best preserved in the east wall of the trench where it is recorded by faulting and bed rotations of units 6B and 6C (Figure 4). Displacement of these units produced a structural depression in the fault zone into which Unit 7, a mixed gravelly silt, was deposited. The gravel cobbles in Unit 7 have no preferred orientation and are poorly sorted, and this unit is interpreted to be a colluvial 'wedge' derived from gravel and silt in Unit 6 exposed by fault scarps. Units 6, 6C and 7 are overlain by Unit 8 which has significantly less deformation than the immediately underlying units (i.e. 6-7). The event (4) horizon is inferred to be at the top of Unit 6C and to predate deposition of units 7 and 8 (Figure 3). The timing of this event is constrained by OSL dates of 5.8 ± 0.6 and 7.7 ± 1.4 ka immediately below and above the event horizon respectively (Figure 4, Table 1). Using these dates and OxCal analysis the timing of Event 4 is estimated to be 6.0-8.6 ka.
The penultimate earthquake on The Humps fault is constrained by the northern splays of fault A and splays B2 and B3 of fault B on the east wall of the trench. These displace the top and base of Unit 8 by up to 0.3 m but do not appear to displace the ground surface ( Figure 4). It is also possible that displacements along the top boundary of Unit 8 formed in 2016, although Unit 9 is thin (∼10-20 cm) and we would expect to see deformation of the ground surface, particularly above the northern splays of Fault A (Figure 4), which we do not. The presence of a ∼0.4 m high fault scarp at the trench site prior to 2016 (Figure 3, 2013 ground surface) suggests that slip on faults A, B and E likely displaced Unit 8 and at least part of Unit 9, which supports the case for a post-Unit 8 and pre-2016 event (Figures 4 and 5). Event 5 may have produced the fissure filled by Unit 10 in the eastern wall of the trench (Figure 4). The fissure was filled with a mix of material from units 6C, 7 and 8, while the active soil layer (Unit 9) appears to pass undisrupted across the top of the fissure, suggesting that the fissure mostly pre-dates formation of Unit 9. The Event 5 horizon is inferred to post-date the onset of formation of the Unit 9. However, because this unit is within the zone of microbial and chemical activity, and has experienced anthropogenic agricultural disturbance through ploughing, it is not possible Figure 8. Four representative recurrence interval frequency histograms for The Humps fault generated using the data in Figure 7 and the Monte Carlo method outlined in Nicol et al. (2016a). Each of the histograms were generated for 5000 earthquakes, which produced a median RI of 2.5 and a range from 0.1 to 6.95 at the 95% confidence level.
to identify the precise location of an event horizon. If a penultimate event occurred after deposition of Unit 8, it would post-date the ages of charcoal within Unit 8 of 4790-4430 (Wk-47373) and 4820-4520 (Wk-49900) cal. years BP (Table 2), and likely predates European settlement of the area at ∼1840 AD. The preferred OxCal age for this event is younger than 4.5 ka.

Paleoearthquake SED, RIs and slip rate
Slip at the ground surface during individual earthquakes (i.e. SED) typically varies along the length of faults during individual earthquakes, with both strike-slip and vertical displacement varying along The Humps fault in 2016 . The mean strike-slip and vertical SED for The Humps fault on the Emu Plain are 1.4 ± 0.2 m and 0.5 ± 0.2 m, respectively . These values are comparable to the 2.0 ± 0.2 m and 0.35 ± 0.05 m observed at the trench site for strike slip and vertical displacements in 2016, respectively. At the present time there is little information to constrain the net SED of prehistoric events at the trench site, however, the pre-2016 fault scarp and analysis of stratigraphy in the east wall of the trench suggest apparent vertical displacements of ∼0.4 (similar to 2016) and ∼1 m for events 5 and 2, respectively. The factor of two difference between apparent vertical SED during events 2 and 5 raises the possibility that the H:V ratio was lower in Event 2 than Event 5 (and 6) and/or that the SED in Event 2 was larger than Event 5. In either case, the data, and our interpretation of the trench log, indicate that vertical SED at a point varied between earthquakes and may not have been characteristic (i.e. uniform) through time.
The time intervals between successive paleoearthquakes on individual faults (i.e. RI) can be estimated by the data from the trench and, on average, appear to be several thousand years (Figure 7). The mean RI represented by units 2-10 is 2.3 ± 0.5 ka; calculated by dividing the 14.3 ± 2.7 ka OxCal age for the base of Unit 2 ( Figure 4 and Table 1) by the interpreted six events. This RI will decrease if we have missed earthquakes during deposition of Unit 2 and increases to 3.1 ± 0.3 kyr if we exclude the 2016 earthquake (i.e. assuming this study was conducted prior to 2016). Alternatively, if we only use data for strata above Unit 2 over the last 12.1 ± 1.4 ka (OxCal age for sample USU2902, Table 1) and assume that this age defines the oldest event and 2016 the youngest event, the four intervening RIs would average ∼2.7-3.4 kyr. Collectively these calculations suggest a mean RI for the western Humps fault is likely to be in the range of 1.8-3.4 kyr (i.e. 2.6 ± 0.8 ka). The mean RI estimated from the McLean-1 trench is less than the 13 ± 8.7 kyr proposed by Barrell and Townsend (2012) who acknowledged significant uncertainties in their estimate. Based on the new earthquake timing data, we propose that The Humps fault accommodates more frequent surface rupturing earthquakes than previously inferred.
Using the dating results and OxCal analysis of these dates the precise timing of some earthquakes (e.g. 1 and 5; Figure 7) from the trench are poorly constrained, which means that RIs between consecutive earthquakes on The Humps fault can carry significant uncertainties (e.g. ±0.85-2.7 ka). Our Monte Carlo RI frequency analysis accounts for uncertainties and produces a range in RIs from 0 to 9 kyr for 20 models (e.g. Figure 8). The resulting frequency histograms in Figure 8 present four of these models and all generally show a decrease in RI frequencies smaller than about 1.5 kyr with a long tail of RIs between 5 and~9 kyr ( Figure 8) which is common for paleoseismic data on New Zealand faults (Nicol et al. 2016a). The long RIs (e.g. >5 kyr) are largely due to events 1 and 2 and may partly or entirely arise from incompleteness of the pre-Holocene record in the trench. Therefore, additional data is required to test the validity of the long RI tail in the distribution. Although the histogram in Figure 8 does not strongly resemble a normal distribution, the median (∼2.5 ka) and standard deviation (1.7 ka) for RI appears to provide a reasonable first-order approximation for the recurrence behaviour of The Humps fault. These values produce a coefficient of variation (CV = standard deviation / mean) of 0.71, consistent with RIs being quasi-random (for random distributions the CV = 1), which has been observed for some low slip rate (<2 mm/yr) faults in New Zealand (Nicol et al. 2016a). The large standard deviation highlights the importance of explicitly including some measure of RI variability for faults in seismic hazard analysis.
Vertical and strike-slip rates for The Humps fault have been estimated at 0-0.2 mm/yr and 0.4-0.7 mm/yr, respectively (Barrell and Townsend 2012;Brough 2019). In the McLean-1 trench the 3.5 ± 0.5 m apparent vertical displacement and 14.3 ± 2.7 ka OxCal age for the top of Unit 1 (sample WLL1297, Figure 4, Table 1) produce an apparent vertical slip rate of ∼0.28 ± 0.08 mm/yr. This slip rate is slightly higher than previous estimates and, to a large extent, reflects the high vertical displacements during deposition of Unit 2. We have no data to constrain strike-slip rates in the McLean-1 trench, however, if we assume that the 2.0 ± 0.2 m strike slip at the trench site in 2016 represents the mean SED and use the mean RI of 2.6 ± 0.8 kyr from trench analysis the resulting slip rate would be 0.87 ± 0.35 mm/yr. Slip rate estimates from this study and Brough (2019) indicate that values of 0.4-1 mm/yr are most likely. However, if we are missing events in the trench (i.e. the mean RI is shorter than estimated) it is possible that the slip rate is higher than ∼1 mm/yr. Given the uncertainties in the data, further work is required to refine the slip rate estimate.

Discussion
The Humps fault was largely undetected across much of the Emu Plain prior to the 2016 earthquake, which reemphasises the incompleteness problem inherent in the New Zealand active faults database (see Nicol et al. 2016b for further discussion). This incompleteness was highlighted by the Greendale fault, which ruptured in the 2010 Mw 7.1 Darfield Earthquake (Elliot et al. 2012;Quigley et al. 2012), where fault slip rates were low (∼0.2 mm/yr) and fault traces prior to 2010 were buried by fluvial aggradation deposits (Hornblow et al. 2014). The Humps fault remained undetected on post-LGM fan surfaces and unreported in national active fault databases (e.g. Litchfield et al. 2014;Langridge et al. 2016) even though these surfaces were ruptured by multiple scarp-forming earthquakes. The difficulty in mapping The Humps fault across the Emu Plain prior to the 2016 earthquake can be attributed to a variety of reasons including erosion of, or deposition on, the fault scarp; ground surface displacements being predominately strike-slip; and/or a lack of detailed topographic data on the Emu Plain. Therefore, pre-2016 scarp heights were typically <1 m and generally below the routine resolution limit for 1:16000-1:25000 aerial photograph stereoscopic analysis. Inspection of the 2013 lidar model enables the pre-2016 scarp to be mapped across the Emu Plain and suggests that the mapped active-fault trace would have been longer prior to 2016 if higher resolution data were available and utilised for fault mapping. Given the higher resolution of lidar (compared to ∼1:20,000 aerial photographs) we expect that with collection of nationwide lidar the number of active faults with low scarp heights (e.g. <1 m) and slip rates (e.g. < 1 mm/yr) will increase. On a regional scale these undetected faults may be accounted for by background seismicity in the New Zealand National Seismic Hazard Model. However, where presently undetected faults are located close to the main urban areas, knowing their location and earthquake potential will likely be important for quantifying seismic hazard.
Questions remain about how often multi-fault events occur throughout New Zealand and, specifically, how frequently Kaikōura-type events occur across the NCD and MFS boundary (Figure 1). Litchfield et al. (2018) and Nicol et al. (2018) estimated that Kaikōura-type events (i.e. earthquakes involving the specific faults that ruptured in 2016) happen no more frequently than every ∼5 kyr, based on the RIs for The Humps, Conway-Charwell and Stone-Jug faults in the NCD. Paleoseismic studies have been completed, or are well advanced, on all of the main faults that ruptured in the NCD (e.g. The Humps, Conway-Charwell, Leader, Stone-Jug faults and Hundalee faults), and provide new insights into how often Kaikōura-type events could occur. Like our data from The Humps fault, these studies typically show mean RIs of 2-4 kyr for faults in the NCD (Hyland-Brook 2018; Scott 2019; Bushell et al. 2020;Barrell et al. this volume). The conclusion we draw is that, for faults throughout the NCD, RIs are generally shorter and large magnitude earthquakes more frequent than previously thought. Because RIs are now considered shorter on faults in the NCD we can update the original conclusions of Litchfield et al. (2018) and Nicol et al. (2018) by suggesting that Kaikōura-type events could occur as frequently than every ∼2 kyr. We should, however, remind ourselves that, because RIs on the Kekerengu fault are hundreds of years in duration (mean 375 ± 32 years: Little et al. 2018;Morris 2020) and an order of magnitude shorter than those presented here, many of the earthquakes that rupture the Kekerengu fault are unlikely to rupture south of the Hope fault onto The Humps fault . These data highlight the requirement that future seismic hazard models include (i) earthquakes that rupture the Kekerengu fault only, (ii) earthquakes that rupture the Kekerengu together with other faults in the MFS, (iii) relatively rare events that rupture the Kekerengu fault and specific faults in the NCD (e.g. The Humps, Leader, Stone jug and Hundalee faults), (iv) earthquakes that only rupture faults in the NCD together (e.g. The Humps and Leader faults, Bushell et al. 2020), and (v) rupture of The Humps fault only. Which of these options most commonly applies to The Humps fault remains uncertain.

Conclusions
The 2016 M W 7.8 Kaikōura Earthquake nucleated on The Humps fault in the North Canterbury region of the South Island. The earthquake ruptured pre-existing fault scarps on the Emu Plain, which were largely unidentified prior to the earthquake, resulting in mainly right-lateral strike-slip on east-west striking and steeply dipping faults. For the first time, the timing and SEDs for paleoearthquakes on The Humps fault have been estimated by mapping faults and stratigraphy exposed in the walls of a trench and dating of variably deformed strata. Trench data indicate the timing of six surface rupturing paleoearthquakes at: 9.8-15.3 ka BP (Event 1), 8.6-11.5 ka BP (Event 2), 8.1-10.9 ka BP (Event 3), 6.0-8.6 ka BP (Event 4), 1840 AD to 4.5 ka (Event 5), and 2016 AD (Event 6). These earthquakes have a mean RI of 2.6 ± 0.8 kyr with individual RIs possibly ranging up to~9 kyr. Our mean RIs suggest that The Humps fault is more seismically active than previously proposed and that Kaikōura-type earthquakes may occur as frequently as every ∼2 kyr.