Alluvial fan response to Alpine Fault earthquakes on the Westland piedmont, Whataroa, Aotearoa‐New Zealand

We examined the stratigraphy of alluvial fans formed at the steep range front of the Southern Alps at Te Taho, on the north bank of the Whataroa River in central West Coast, South Island, New Zealand. The range front coincides with the Alpine Fault, an Australian‐Pacific plate boundary fault, which produces regular earthquakes. Our study of range front fans revealed aggradation at 100‐ to 300‐year intervals. Radiocarbon ages and soil residence times (SRTs) estimated by a quantitative profile development index allowed us to elucidate the characteristics of four episodes of aggradation since 1000 CE. We postulate a repeating mode of fan behaviour (fan response cycle [FRC]) linked to earthquake cycles via earthquake‐triggered landslides. FRCs are characterised by short response time (aggradation followed by incision) and a long phase when channels are entrenched and fan surfaces are stable (persistence time). Currently, the Te Taho and Whataroa River fans are in the latter phase. The four episodes of fan building we determined from an OxCal sequence model correlate to Alpine Fault earthquakes (or other subsidiary events) and support prior landscape evolution studies indicating ≥M7.5 earthquakes as the main driver of episodic sedimentation. Our findings are consistent with other historic non‐earthquake events on the West Coast but indicate faster responses than other earthquake sites in New Zealand and elsewhere where rainfall and stream gradients (the basis for stream power) are lower. Judging from the thickness of fan deposits and the short response times, we conclude that pastoral farming (current land‐use) on the fans and probably across much of the Whataroa River fan would be impossible for several decades after a major earthquake. The sustainability of regional tourism and agriculture is at risk, more so because of the vulnerability of the single through road in the region (State Highway 6).


| INTRODUCTION
Alluvial fans occur in a variety of settings (Blair & McPherson, 2009;Keefer, 1999;Mather et al., 2017) and are sensitive recorders of environmental change and landscape dynamics (Bull, 1977;Field, 2001;Mouchené et al., 2017). The behaviour of alluvial fans is controlled by both allogenic (external) and autogenic (internal) forcing, the effects of which may be difficult to distinguish in their sedimentary archives (Ventra & Nichols, 2014). Autogenic dynamics arise from topographic constraints on sediment accommodation on the fan (causing channel avulsion) and intrinsic feedbacks between channel gradient and sediment supply (triggering aggradation or incision). Despite these internal dynamics, allogenic controls on net fan building or erosion leave recognisable stratigraphic signatures (Ventra & Nichols, 2014) and have been linked to climate variability (Assine et al., 2014), tectonic activity (DeCelles & Cavazza, 1999), base-level oscillations (Harvey, 2002) or a combination of those factors (Abrams & Chadwick, 1994;Dade & Verdeyen, 2007;Schlunegger & Norton, 2015;Ventra & Nichols, 2014). An allogenic forcing of alluvial fans that has received relatively little attention (Keefer, 1999) is earthquake-triggered landsliding and the effects of the consequent increase in sediment supply (see the review by Fan et al., 2019). The responses to local non-earthquake-triggered landslides provide a general understanding (Davies & Korup, 2007) Langridge et al., 2018;Wells et al., 1999) culminated a sequence of paleoearthquakes that occurred at semi-regular intervals of 249 ± 58 years , over fault section lengths of 250-400 km, producing large to great earthquakes (Mw ≥ 7.5). There has been no rupture in the time of written record since European colonists arrived in Aotearoa-New Zealand about 1840, but a young event may have occurred on the northern section of the fault in the interval 1813-1848 CE (Langridge et al., 2021). The paleoseismic record indicates that there is a 75% probability of rupture on the central section (single section or multisection) in the next 50 years  and efforts to increase preparedness are underway (Orchiston et al., 2018).  (Cochran et al., 2017); HC is Hokuri Creek (Berryman et al., 2012); LE is Lake Ellery (Howarth et al., 2016); LP is Lake Paringa (Howarth et al., 2014), LM is Lake Mapourika (Howarth et al., 2014); and LK is Lake Kaniere (Howarth et al., 2014;Howarth et al., 2016). Red circles show the location of the study site at Whataroa (WH) and Hokitika (HK) as the principal town of Westland. MFS is the region of the Marlborough Fault System, including the Hope Fault as its southern component. (c) The paleoseismic record showing the timing and likely extent of ruptures on the Alpine Fault in the past 2000 years. Question marks indicate uncertainty in the extent of ruptures across section boundaries. The most recent event (1813-1848 CE) is from fault trenches at the Toaroha River near Lake Kaniere (Langridge et al., 2021). All other events come from Table S6 of Howarth et al. (2021). The extent of this rupture on the North Westland section of the Alpine Fault is unknown. Source: Figure  The sedimentary record of earthquakes preserved in lake deposits has been particularly important along the central section of the fault. Here, there are few opportunities to trench the fault with much likelihood of being able to date the coarse alluvium typically present in the vicinity of the fault. The most recent reviews of the large earthquake history of the fault, which include the results from lake paleoseismology , indicate the most recent, penultimate and antepenultimate (third to last) events that occurred 1701-1732 CE (most probably 1717 CE based on tree ring studies), 1384-1400 and 1148-1179 CE, respectively. Each of these events appears to have ruptured the southern and central sections of the fault over distances of >300 km in ca. Mw8 earthquakes.
Prior events appear to have sometimes ruptured just the central or southern sections (Figure 1). An important observation from lake record studies is that 40% of all sediment entered the studied lakes in the 50 years following an Alpine Fault event .

| Landsliding and landscape response
Landsliding and aggradation at and west of the range front are recognised as significant, acute and recurrent hazards on account of the possibility of (1) dam-burst floods emanating from landslide dams F I G U R E 2 Location diagram showing the Te Taho fans along the range front of the Southern Alps adjacent to the Alpine Fault. Background imagery is a hillshade model developed from a 25-m DEM (https://lris.scinfo.org.nz/layer/48127-nzdem-south-island-25-metre/). River polygons from LINZ data service (https://data.linz.govt.nz/layer/50328-nz-river-polygons-topo-150k/). Geology and the delineation of the Alpine Fault trace are from QMap 1:250 000 mapping (Cox & Barrell, 2008). MIS refers to Marine Isotope Stages. The summit of Mt Adams is shown with the location of the 1999 landslide (Korup et al., 2004). Area of Figure 12 is shown as a red rectangle. Source: This work includes Toit u Te Whenua Land Information New Zealand data, which are licensed by Toit u Te Whenua Land Information New Zealand for re-use under the Creative Commons Attribution 4.0 International licence [Color figure can be viewed at wileyonlinelibrary.com] in alpine sections of the river (Robinson & Davies, 2013;Wells & Goff, 2006) and (2) flooding and sedimentation-induced damage to farms and property, and infrastructural lifelines (Orchiston et al., 2018). Most of the understanding of related sediment fluxes is based on (1) decadal landslide inventories in the Southern Alps (Hovius et al., 1997); (2) experience from non-earthquake-related landslides in individual catchments (e.g., Korup, 2005); and (3) volumes of landslidegenerated sediment from elsewhere in New Zealand or globally, calibrated against modern sediment loads and an assumption of steady state processes in the Southern Alps where denudation balances mountain building. Current models of landslide generation, sediment flux and hazard for the West Coast invoke an earthquake trigger and have large model uncertainties (Robinson et al., 2016). However, it remains unclear if Alpine Fault and other earthquakes are always the trigger of regionwide landsliding and how well current models capture event-to-event variability in terms of magnitude and locus.
Pre-historic botanical records offer the best potential for assessing the timing and magnitude at a regional scale of past aggradation events on the Westland piedmont. Goff (2006, 2007) used ages of discrete cohorts of trees on coastal dunes to show that dune formation was episodic and closely tied to Alpine They showed that forest re-established in two phases corresponding closely to inferred Alpine Fault earthquakes. Moreover, they showed that spatial patterns of regeneration differed, from which they inferred different magnitudes of flooding-or aggradation-related disturbance between the two events. Blagen et al. (2022) expanded on Cullen et al.'s (2003) data set by including tree age data from fan-floodplain complexes north and south of the Whataroa. They concluded similarly that large-scale aggradation was punctuated and consequent on catastrophic landsliding associated with earthquakes on the Alpine Fault or other Southern Alps faults.

| Purpose
Tree age-based analyses of past aggradation timing and extent are essentially a biologically based surface exposure dating technique.
Such studies are limited by (1) the longevity of trees (ca. <1000 years for New Zealand podocarps species); (2) loss of the older part of the disturbance record due to overprint by recent events; and (3) no discrimination between flooding-or aggradation-driven disturbance that initiated establishment of new cohorts of trees. In this paper, we take a single-catchment scale, geological approach to the question of the timing and magnitude of aggradation response to Alpine Fault earthquakes. We consider the stratigraphic record of alluvial fans near Whataroa, which record sedimentation over a period of $2 ka. We exploit natural exposures in small range front fans, which coalesce and interact with the larger Whataroa River fan. From the stratigraphy and ages of these fans, we interpret fan evolution and the behaviour of the larger Whataroa fan to which they grade. The stratigraphy, aggradation and soil formation age model we develop provide a basis for (1) considering the link between Alpine Fault earthquakes and alluvial fan sedimentation; (2) quantifying the magnitude and rate of aggradation events; and (3) inferring hazard to infrastructure and economic activity locally and, by extrapolation, to the wider Westland region.

| The study area
The Whataroa locality in central Westland lies a few kilometres west of the steep range front of the Southern Alps in the central section of the Alpine Fault (Figures 1 and 2). The topographic divide of the Southern Alps parallels the range front about 20 km to the southeast.
Between the two lie steep slopes, fissile metamorphic rocks (Alpine Schist) and very high precipitation. From the range front, mean annual rainfall increases from about 5000 mm to reach a peak west of the main divide of about 12 000 mm (Griffiths & McSaveney, 1983). This domain is recognised as having high background erosion rates (Griffiths, 1979;Hovius et al., 1997;Korup, 2005) and efficient fluvial transport of sediment on to the piedmont.
The Whataroa River is the dominant local agent of landscape change on the piedmont. The Whataroa is a large gravel-bed river whose catchment is bounded by the main divide of the Southern Alps in the southeast and covers 453 km 2 . The mean annual flow is 134 m 3 s À1 generated by a spatially averaged mean annual rainfall of about 8000 mm (Hicks et al., 2011). With a catchment average erosion rate of $7 mm year À1 (Larsen et al., 2014) and a suspended sediment yield estimated to be in the order of 5 Mt year À1 , the river delivers more than 5% of the South Island's total suspended sediment budget (Hicks et al., 2011).
At the time of our investigation, the Whataroa River was incised into its fan head ( Figure 3) and, at Te Taho on its true right bank, it was carving laterally immediately west of the Alpine Fault. Across the piedmont, the Whataroa River forms an alluvial fan confined by last glacial maximum (32-18 ka) lateral moraines and the Tasman Sea to the northwest ( Figure 2). The fan is largely of late Holocene age and represents the upper part of a 400-to 700-m thickness of Quaternary sediment (Davey, 2010). Much of the original podocarp-angiosperm forest of the fan has been cleared in historical times for pastoral farming now comprising a large proportion of intensive dairying.
Our study exploits the exposures of stratigraphy in range front alluvial fans at Te Taho. This setting allows us to quantify landscape evolution in a geomorphic system with large to great earthquakes (Mw ≥ 7.5) occurring at intervals of 200-300 years, a steep range front with slope angles of 30-45 ( Figure 3) and annual rainfall of $5000 mm.
The catchments of the fans we studied are entirely within the amphibolite facies of the Haast Schist on the Alpine Fault hanging wall (Figures 2 and 4). The rocks include abundant pelitic schist (Cox & Barrell, 2008) although mylonitic rocks occur immediately adjacent to the fault (Sibson et al., 1981). Accordingly, the alluvium comprising the fans differs from that of the Whataroa River, which rising close to the Main Divide, is dominated by greywacke lithologies. Thus, the presence or absence of greywacke allowed us to unequivocally distinguish the provenance of coarse clastic sediment in the fans.  Organic material from SSUs and intervening sediment packages were collected for radiocarbon dating, with a preference for woody material. Large trees were preserved in association with some SSUs, a few remaining in growth position. From some of these trees, we took samples from two growth rings referenced to ring counts. In this way, we could use Bayesian statistics incorporating age F I G U R E 5 Little Man fan stratigraphy and radiocarbon ages along (a) Tahi stream and (b) the fan toe. The nomenclature of sediment packages (L1, L2 etc.), soil stratigraphic units (S1 SSU, S2 SSU etc.) and soil residence times (SRTs) are discussed in the text and Table 1. Section locations and radiocarbon ages are listed in Table S1. The horizontal distance scale is metres southward from the confluence of Little Man River and the Whataroa River, or Tahi stream with Little Man River. Panel (c) shows the location of each on an oblique aerial photograph showing the incised state of the Little Man River from the fan head to the confluence with the Whataroa River, and fan toe erosion by lateral migration of the Whataroa River. The fan toe exposures are approximately 15-20 m high. Source: Photograph courtesy of Graham Hancox, GNS Science sequence information to reduce uncertainties on estimates of calibrated radiocarbon ages and estimate the time of tree germination and tree death. When estimating the age of land surface stabilisation using tree germination age, a lag of 23 ± 8 years was added. Here, we assume a normally distributed population of lag times with a mean of 23 years (Wells et al., 1999) and a standard deviation of 8 years. This distribution gives a 95% confidence interval (CI) of 7-39 years, close to the range of germination lags derived by Wells et al. (1999) for podocarps. The Waikato (Wk numbers) or Rafter (NZA numbers) radiocarbon laboratories carried out the analyses. All radiocarbon ages were calibrated against the SHCal20 calibration curve (Hogg et al., 2020) in OxCal (Version 4.4 online, Bronk Ramsey, 2009). We also used increment borers to take cores of living trees to constrain the age of the modern ground surface soil. Tree rings from discs or increment cores were made after sanding to a fine grit. All tree ring counts were assumed to have a ±5% counting error (Wells et al., 1999).
At representative profiles of fine-textured (sandy sediment or finer) surface soil and buried SSUs, we used a corer of 5.4 cm diameter to take soil samples of known volume, which we oven dried and sieved to <2 mm. From these samples, we calculated the bulk density (kg m À3 ) and then quantified the concentration of secondary pedogenic oxides extractable by acid ammonium oxalate (McKeague & Day, 1966). This reagent extracts poorly crystalline and organically complexed secondary Fe and Al compounds, which are diagnostic of weathering and pedogenesis under the acid leaching regime of the high rainfall West Coast region (Eger et al., 2011;Tonkin & Basher, 1990). The gravimetric oxide concentrations were adjusted to account for Fe and Al extractable at time zero, that is, from unweathered parent material. This baseline value was estimated by analysing the extractable Fe and Al from fresh alluvial sand. After adjustment, gravimetric concentrations were converted to areal masses (kg m À2 ) by multiplying by the sample increment thickness (m) and the bulk density. We then calculated a profile areal mass of oxalate extractable Fe and Al to the base of a B horizon or 20 cm into the C horizon if no B horizon was present. Thus, the profile aerial mass (PAM) of each analyte is given by where X i refers to oxalate extractable Fe or Al concentration. The index k refers to the kth sample of the solum of the (buried) soil, whereas pm refers to the unweathered parent material. A normalised profile development index (PDI) was calculated by dividing the profile aerial masses for each analyte by the corresponding values from a calibration soil of known age, summing and dividing by 2. Thus, the calibration site's PDI evaluated to unity: The calibration soil (Wh 65, Figure where τ S , PDI S and τ ref are the residence time of soil S, the PDI of soil S and the residence time of the soil at the calibration site, respectively.
The uncertainty in τ s was propagated from the uncertainty in age of stabilisation of the surface the tree established on, which determined τ ref .
The chronostratigraphy for each fan was derived using the aggradation (burial) events defined as Boundaries stratigraphically above them. SRTs were introduced using the Before constraint to require that the burial of SSU t occurred before burial of SSU t + 1 À τ t + 1 . Thus, the age of burial of an SSU minus its SRT established a Terminus ante quem for the burial of the immediately underlying SSU. This construction allowed the duration of aggradation to be implicitly determined. Uncertainties in SRTs were determined from the uncertainty in the slope of the PDI versus τ relationship ( Figure 6) or from the standard error of the mean (SEM) where more than one estimate of τ from an SSU existed. For trees with more than one radiocarbon dated ring, germination ages, ages of land surface stabilisation and ages of tree death were estimated in distinct Sequence models. The models used the D-   formed by sapping erosion in response to base level lowering by trimming of the fan toe formed between 690 and 740 m (Gully-700) and between 970 and 1000 m (Gully-1000).
Five buried SSUs were recognised along the fan toe exposure, of which three were also found in Tahi stream. The SSUs are labelled S1-5 from stratigraphically lowermost to uppermost, and the intervening sediment packages are labelled L1-6 in the same stratigraphic order.

| Little Man fan SRTs and chronostratigraphy
SRTs were estimated from their PDI and a linear relationship between PDI and soil age calibrated against the calibration site on Spider Island.   Table S1) and one sample from 540 m along the fan toe exposure (sample Wh 57 in Figure 5 and Table S1). Three of the ages' 95% CIs closely overlapped in the range 251-631 CE (Table S1; see light grey probability density functions [PDFs] in Figure 7). The fourth age had a 95% CI of 654-987 CE. All ages came from roots. The closely aligned ages suggest that this soil was buried by sediment package L2 at 251-631 CE but that sediment package was locally eroded to allow a later generation of trees  to exploit the S1 SSU and introduce younger roots. The three sampled soil profiles of the S1 SSU produced a mean residence time of 746 ± 57 years, which when subtracted from the date of that SSU's burial provides a constraint on the end of aggradation of sediment package L1 in which it formed.
Age constraints on the burial of the S2 SSU (formed in sediment package L2) come from Tahi stream gully at or near site Wh 50 where three samples of roots or disseminated organics from within the organic upper horizon gave a range of 773-1207 CE (samples S_Wh 50a_2, Wh 50a-Sb and Wh 50a.2 in Table S1; see light grey PDFs in Figure 7). Fine roots in the S2 SSU from site Wh 53 (Wh 53_Sb in  Table S1). The tree had 196 rings but a rotten centre-most 40 mm. By combining the radiocarbon ages and the tree ring count data in OxCal ( Figure S3A) and assuming that accumulation of sediment package L4 killed the tree, the S3 SSU was bur- by sediment package L3, in which the S3 SSU forms, suggesting that aggradation of L3 may have been short-lived.
The burial of the S4 SSU by sediment package L5 is dated from the trees in growth position in Tahi stream gully (Wh 50b-d in Table S1; see light grey PDFs in Figure 7) and on the fan toe (Stuart's Folly in Table S1) two trees (Wh 50c,d) suggests that they established in a subsequent phase of recruitment in an existing forest stand.
A maximum age for burial of the S5 SSU and thus the time of arrival of the uppermost sediment package, L6, is provided by a set of radiocarbon ages from wood material in the SSU (Table S1). The calibrated age ranges are wide, spanning the period 1503-1950 CE (see light grey PDFs in Figure 7), because the calibration curve has a shallow slope and is distinctly non-monotonic through this age range. The S5 SSU contains two prone trees, which we radiocarbon dated. At Wh 45 (located at 70-m distance in Figure 5), a large tree in a prone position (Wh 45a in Table S1) with a total of 430 rings yielded radiocarbon ages of 1220-1383 CE 146 rings from the centre and 1421-1624 CE 414 rings from the centre.
Combining the radiocarbon ages and ring count information in OxCal afforded a germination date of 1028-1201 CE and death at 1478-1652 CE ( Figure S3B). Both ages suggest that the tree has inbuilt age and neither its germination nor death relates to the S5 SSU. The following appear reasonable: It germinated on sediment package L3 at a similar time to the tree Wh 40; it was killed in place by sediment package L4; and it was felled and transported with sediment package L6, which buries the S5 SSU. Another prone and highly rotted tree (Wh 46 in Table S1) occurred immediately above the S5 SSU on the true right of the Gully at 700-m distance in Figure 5 ($68 m ASL) ( Figure S4A). The calibrated radiocarbon date of 1441-1629 CE from the outer part of the tree is also out of stratigraphic order and suggests that it was another tree similarly killed by sediment package L4 but snapped later and incorporated into sediment package L6. We excavated the tree and found no root plate ( Figure S4B).  Table 2) are recognised with a precision (95% CI) ranging from 85 to 463 years for those with bracketing radiocarbon constraint.
The oldest event, Event VI, is dated only by the interval between it and Event V as determined by the residence time of the S1 SSU and it has low precision (range = 1036 years) (

| Stratigraphy
Five buried SSUs were recognised along the fan toe exposure. The SSUs are labelled S1-5 from stratigraphically lowermost to uppermost, and the intervening sediment packages are labelled L1-5 (L2 is a composite unit with S2 within the sediment package on the north exposure) (Figures 9 and 10).

| Blackburn exposure SRTs and chronostratigraphy
Radiocarbon ages from which the chronostratigraphy of the Blackburn exposure was developed, along with descriptions of SSUs and sediment packages, are presented in Figure 11. Two radiocarbon ages, both from organic (peaty) silts in the surface of the S1 SSU, one from  F I G U R E 8 Synthesis of all data pertaining to the evolution of (a) the Little Man fan and (b) the Blackburn exposure for the past $3 ka. Data include event timing and duration of aggradation based on OxCal models (Table 2 and Figures 7 and 11) of all radiocarbon ages (Table S1), soil residence times (Table 1), correlation with the most recent compilation of timing of Alpine Fault (yellow boxes) and a presumed Southern Alps earthquake (grey box). Event ages have age ranges (horizontal blue bars). Aggradation depth-time is shown by stippled polygons. Soil residence time (τ) as given has quantified or assumed uncertainties in the order of 21%. No data on the SRT for S3 SSU or S5 SSU are available. Incisionaggradation trajectories are drawn so that incision begins contemporaneously with the beginning of pedogenesis (with uncertainty) of SSUs as indicated by SRTs. The subsequent aggradation trajectory is drawn so that pedogenesis of an SSU is curtailed by burial due to the aggradation.  (Table S1). The PDI of an example of this SSU (Wh 62 at 110-m distance of the north section- Figure 9) calibrated to a residence time in the order of 1200 years. The directly overlying SSU in the north section, the S2 SSU, had no age control but similar SRT (Table 1).
The age control on the S3 SSU from the north section near Wh 61 ($100-m distance- Figure 9) came from wood, twigs, peat and other organic material (MLG_S2_3, MLG_S2_4, MLG_S2_5, Wh 61/7Bb_PS2 and Wh 61 Bc_PS2 in Table S1) that spanned the age range from 221 to 987 CE ( Figure 11). This wide age range is inconsistent with the relatively short residence time (240 years) indicated by the example of this SSU we sampled at Wh 61 (Wh 61-PS2). Near the origin of the north section, the age range of the S3 SSU widened (S1_FACE_GG_S1_1, GG_S1_1, N1_GG_S1_1 and N2_GG_S1_1 in Table S1) to 35 BCE to 1281 CE and included an age characteristic of the overlying SSU (S4); we suspect that the SSUs in this area represent soils that form a composite (merged or 'welded', Morrison, 1998;Ruhe & Olson, 1980) profile as intervening fluvial sediments thin (to the north) and, thereby, host at least two populations of organic material. The S3 SSU in the south section yielded ages (PT3, PT (a), PT (b), Blackburn 3 in Table S1) that overlapped those of the S3 SSU on the north section but covered the narrower range of 675-1130 CE. A prone tree in the S3 SSU at 410 m along-section (E8582/101-105T in Table S1) with a ring count of 304 rings gave an age of 431-637 CE from the 105th ring from the centre. Allowing for the offset, the outside of the tree had an age of 647-860 CE, which aligns it with the age of sample Blackburn 3 (twigs; 675-889 CE).
Three ages (S_SECT18_1, Wh 65-PT4 and Wh 14/27 in Table S1) from the thick alluvial fill burying the S3 SSU (sediment package L3) on the north and south sections ranged from 993 to 1214 CE, which overlapped the ages from the underlying SSUs but had a younger  with later aggradation (burying the S5 SSU) than on the north section.
The large living matai (Prumnopitys taxifolia) tree ( Figure 10) growing F I G U R E 9 Blackburn exposure stratigraphy and radiocarbon ages along (a) the fan toe north of Sheet Creek and (b) the fan toe south of Sheet Creek. The nomenclature of sediment packages (L1, L2 etc.), soil stratigraphic units (S1 SSU, S2 SSU etc.) and soil residence times (SRTs) are discussed in the text and Table 1. Section locations and radiocarbon ages are listed in Table S1. The distance scale is metres southward from the start of exposure as shown in panel ( Table S1). The tree was clearly buried part way up its trunk ( Figure S6A). We felled the tree and dated two rings from a disc with 662 rings, one at the 84th ring from the centre (894-1154 CE) and the other from the 304th ring (1189-1385 CE). Modelling the sequence in OxCal gave times of establishment (allowing for the 23 ± 8-year lag for germination) and death of 865-1042 and 1553-1729 CE, respectively ( Figure S6C).
We dug at the tree's base and exposed a soil very similar to that at Wh 61 and Wh 67 described above ( Figure S6B). At 2.17-m depth, we hit roots and a buried A horizon, possibly implying the tree established in the S4 SSU, which is buried at about that depth on the north section fan toe. However, when we tried to insert the tree establishment age in this stratigraphic position in the OxCal model, it produced poor agreement. We favour the interpretation that we uncovered a higher tier of roots that were the tree's response to an initial phase of burial and the tree instead established on sediment package L2, in the S3 SSU. Our interpretation implies that the tree is buried by as much as 5 m of fan sediment and our tree-ring-based ages may be significant under-estimates given that the time for the tree to reach about 6.5-m height is not accounted for. Nonetheless, even with an age under-estimation, the residence time of the S3 SSU accommodates the germination of the tree.
Our OxCal sequence model of the Blackburn stratigraphy (model agreement index 91.4%; Bronk Ramsey, 1995) does not include the old and conflicting ages associated with the S1 SSU, although they do suggest an approximate date of 0-2 ky BCE (Table S1). The model indicates reasonable estimates for the timing of three aggradation events ( Figure 11 and Table 2)  and Table 2). The behaviour of the fans at the Blackburn exposure over the last ca. 1 ka is summarised in Figure 8b.
Evidence of fan aggradation before Event III is preserved on the north section, corresponding to the southern flank of Vine Creek fan.
F I G U R E 1 0 Photograph looking south over the Blackburn exposure with stratigraphy exposed in a small fan toe sapping gully north of Sheet Creek. The pronounced unconformity is the edge of an infilled gully cut through the fan sequence at 160 m in Figure 9. Here, most of the sediment is sandy and fine gravelly, packages of sediment between SSUs are thin, and SSUs are well developed. This evidence suggests that the Vine Creek fan was relatively quiescent in the early to mid-late Holocene, depositing dominantly overbank sediment with only slowly accreting ground surfaces that allowed soils with multi-centennial to millennial residence times to form (SRT for S1 estimated at 1288 years) (Table 1).

| Other sites
Two other locations, one on the distal downstream toe of Little Man fan and the other on the middle of the piedmont reach of the Whataroa River, provided insights into the chronology of aggradation of the Whataroa River.
Site Wh 8 (Figures 2 and S7) exposed 6 m of fan-floodplain sediment with three intercalated buried soils at 2.5-, 3.5-and 6.0-m depth. We took woody material from a buried A horizon at 2.5-m depth, which returned a calibrated age of 1640 CE to present (Table S1). The soil was buried by sandy and loamy sediment with multiple rudimentary A horizons indicating incremental sediment accumulation, possibly coinciding with Event I or II on Little Man fan.
The dated soil sat atop fine gravelly sands and silt lying over the second buried soil at 3.5 m, which we did not date. An auger boring below 3.5 m exposed loamy sands above another buried peat at 6-m depth. The peat gave a calibrated radiocarbon age of 685-998 CE (Table S1). This time period, when peat was accumulating at Wh 8, overlaps with the residence time of the S2 SSU at Little Man fan.
About midway (12 km) between the range front and the Tasman Sea at site Wh 13 (Figures 2 and S8), the Whataroa River exposed a stand of snapped trees in growth position in the river bed. We dated the outside of one tree to 778-1139 CE (Wh 13-  (Horrell et al., 2012), but we see no aggradation signal of the Te Taho fans at this timescale. Second, there is a close coincidence with known major earthquakes on the Alpine Fault (see Table 3 and discussion below). Autogenic responses in different fans are very unlikely to be coeval because they rely on subtle internal variations in the threshold of critical power related to changes in discharge, fan sediment reworking and channel gradient, amongst other effects.

Additionally, aggradational responses on individual range front fans in
Westland to landslides have been documented historically (Korup et al., 2004).

| Fan evolution
In Table 3 out, but we note that a peak in tree recruitment on the lower Whataroa floodplain at ca. 1650-1675 CE (Cullen et al., 2003) suggests that aggradation was waning or complete by then. If these trees established on deposits related to aggradation 2, then allowing for a decadal timescale for aggradation (Table 2 and modern examples), the onset of aggradation must have been close to the 1605 CE older age limit; hence, the delay between earthquake and aggradation may range from sub-decadal to ca. 50 years.
An absence of aggradation events corresponding to some Alpine Fault earthquakes (Table 3) indicates that the fan deposits described in our study are an incomplete record, which is not surprising given (1) the $30% exposure we have available for study ( Figure 4); (2) the proclivity of fan sedimentation to result in spatially discrete sediment packages corresponding to avulsion events (Field, 2001); and (3) repeated cut and fill especially along the fan axis. Our data show that at least the distributive components of sediment pulses are frequently stacked in a sequence enabling the analysis we have undertaken on the elapsed time for each phase of the fans' response. Thus, despite the record we document being incomplete, we believe it captures the essence of range front fan response to earthquake-induced sediment pulses. Moreover, the contrast in provenance of the alluvium between the fans and the Whataroa River also allows us to infer aspects of the interaction of the small range front fans and the larger Whataroa River draining from the main divide of the Alps; and importantly, we believe the system we study provides a model for much of the $200 km of the central section of the Alpine Fault.

| The range front fan response cycle
Based on the consistent tempo of fan aggradation events and their coincidence with Alpine Fault or other earthquakes, we hypothesise a fan response cycle (FRC) linked to the earthquake cycle. We adopt the terminology of Bull (2008) to discuss phases of the FRC ( Figure 13). An FRC begins with an earthquake, which perturbs the system by generating co-and post-seismic landslides (Fan et al., 2019), providing sediment for the fan.  (Howarth et al., 2012;Robinson et al., 2016) of which, at least, 40%-60% (by volume) is likely to be directly connected to rivers (Li et al., 2016;Roback et al., 2018). Landslide sediment delivered to a fan causes a reaction, whose lag from the triggering earthquake (the reaction time) we expect to be short given the high (>5 m) rainfall, short (3-6 km) steep gradients and historical analogues. In our chronology from the Te Taho fans (Table 3), aggradation and earthquake timings are mostly indistinguishable, and hence, the reaction time is too short for us to resolve. The two case studies of landslide-induced aggradation suggest sub-decadal reaction time, which we would not expect to resolve with radiocarbon. The style of initial reaction of the river is likely to include infilling of an incised channel at the fan head with the development of prograding fans on to the axial river floodplain at the trimmed fan toes (Leeder & Mack, 2001). The gravel we encountered in the range front fans was all schist derived, confirming that the initial aggradational response was to over-supply of sediment and not rising base level (i.e., aggrading axial river). Rising base level would have seen greywacke lithologies intercalated in the fan sediments (the 'axial alluvium' of Leeder & Mack, 2001).
Relaxation time corresponds to the period of mining of landslidegenerated sediment in the catchment and its transport onto the fan or beyond ( Figure 13). We infer this involves backfilling of an incised stream channel then avulsion and sedimentation on the fan by distributory lobes. On the Little Man fan, the exposure near the fan axis where the current river is incised shows cut-and-fill gravel packages.
Away from the fan axis, sediment tended to be finer, consistent with distributory lobes and associated overbank sediment on a fan with no confined stream. Relaxation time represents the greatest instability on the broadest part of the fan surfaces, and therefore, in future, this will be when infrastructure and economic activity are most compromised. (2013)  of 2-4 m and assume no sediment bypass in the calculation. It is likely that the catchments of the range front fans generate disproportionately high yields compared with the region-wide average sediment yields proposed by Robinson and Davies (2013) because of their proximity to the fault, steeper than average slopes and weak cataclastic rocks. Our 95% CI estimates of the duration of the relaxation phase (duration of aggradation) range from effectively instantaneous to nearly two centuries based on OxCal models (Table 2)  These average rates obscure the likely punctuated and locally thick sedimentation that would make maintaining pasture and farm infrastructure impossible, as demonstrated by the Poerua River aggradation following the 1999 Mt Adams landslide (Davies & Korup, 2007).

Robinson and Davies
Towards the end of the relaxation time, probably decades after initiating earthquakes, farming may once again become feasible, especially with some river control measures. SSUs and surface soils formed on aggradation packages often have cumulate B horizons, indicating that upbuilding pedogenesis (Almond & Tonkin, 1999) is common, whereby soil formation rates keep pace with sediment accumulation.
Stream incision ends the period of relaxation whereupon the fan becomes dominantly stable, forest establishes broadly and soils shift from upbuilding to topdown pedogenesis (Almond & Tonkin, 1999) once the fan surface receives only rare and localised pulses of sediment.
The cycle ends with persistence time after the fan stream adjusts to lower sediment supply by incising, forming a lower gradient channel. During this phase, there is an approximate balance between sediment flux and the background catchment sediment yield. It is likely that, simultaneously, the axial river to which the fans grade has excess transport capacity and is capable of eroding sediment from its bed completely covered by forest. In contrast, there is almost no forest cover on the fans now. Therefore, the hydraulic roughness of the fan surfaces is markedly less and the character of aggradation is likely to be different in future. We speculate that aggradation may take place in future via more discrete channelised deposition involving bedload and suspended load and less distributed deposition as in the past. Blagen et al. (2022) suggest that this effect may lead to less aggradation at fan heads and more towards fan toes, with a more rapid progression of aggradation down-fan. Robinson and Davies (2013) noted that few alluvial fans are currently aggrading and that most fan heads are incised, as we see at the Te Taho fans. Therefore, most West Coast alluvial fans responding to Alpine Fault earthquakes are likely to have relatively short response times as Davies and Korup (2007) (Wang et al., 2017). Wang et al. (2017) suggest that it will be years to decades for the sedimentation rate to decay to preearthquake levels in the Longmenshan Range.
Although there are many similar characteristics between landslides and sediment transfer in the Te Taho fans and historic international events, there are marked differences in some of the key drivers of fan building particularly related to river power. River power in West Coast rivers and streams is substantially greater than in Taiwan where maximum rainfall is about 4000-5000 and $1000 mm year À1 in the Longmenshan Range of China (Gao et al., 2016). So, in both locations, annual rainfall is lower than the West Coast setting and, additionally, the West Coast rivers and streams have at least twice the gradient of catchments affected by the Chi Chi and Wenchuan earthquakes (Croissant et al., 2017). Thus, our assessment that the Te Taho range front fans respond very rapidly to earthquake forcing and have the ability to transport the debris quickly and efficiently to the piedmont is consistent with international observations, but we suggest that they may represent an extreme of sediment transport efficiency and response time (see fig. 4 of Croissant et al., 2017  colonisation was estimated to be 1425 CE. Assuming that the terrace is aggradational, the 1400 CE event had culminated before 1425 CE and must postdate the age from 20-m depth in the DFDP-2B core described above. An OxCal model of the sequence (Table S3) constrains the aggradation event and duration of aggradation in the alpine reach of the river to 1293-1433 CE and 34-170 years, respectively.
These ranges are indistinguishable from those of Te Taho aggradation 3 (Tables 2 and 3), meaning if there is any lag in response or difference in tempo of aggradation between the range front fans and the Whataroa River, it is undetectable by our means. As discussed above, a histogram of tree colonisation dates from the lower Whataroa fan (Cullen et al., 2003) suggests that a pulse of aggradation was complete before 1650 CE and another by 1725 CE. These dates of culmination of aggradation are consistent with the Whataroa fan aggrading coeval with the Te Taho fans (see aggradation onsets 2 and 1, respectively, Table 3). In summary, and with reference to the discussion above, we have no reason to believe the range front fans and the Whataroa fan do not aggrade or incise in-step. Thus, we feel confident that the range front fans are a reliable proxy for behaviour of the Whataroa fan whose behaviour presents the greatest hazard locally (Blagen et al., 2022).

| Implications for hazard and risk
Our data on the history and evolution of the Te Taho fans provide high-resolution information on likely future hazard and risk when the Alpine Fault next ruptures in the anticipated M8 earthquake. Most of the findings confirm the basis for prior hazard and risk assessments (Blagen et al., 2022;McDonald et al., 2018;Orchiston, 2013;Orchiston et al., 2018;Robinson & Davies, 2013;Westland District Council, 2006).
From our data, the relaxation time of the Te Taho fans (basically the aggradation phase) is estimated to range from years to decades but <200 years (Table 2), in keeping with historic events in New Zealand and international literature. Many studies infer an initial decadal reaction time (Croissant et al., 2017). In the initial relaxation phase, one can imagine that the Te Taho fan location would be too unpredictable for safe or effective occupation with stream avulsion, continued high rates of aggradation especially at times of large rainfall events or aftershocks.
The economic and psychosocial effects if farming of the fans was attempted are likely to be profound. Alongside the immediate impacts of aggradation on pasture productivity, animals and farm infrastructure, and seismically induced damage to infrastructure (shaking, liquefaction and landslide damage) (Westland District Council, 2006), up to a decade of aftershocks would add to the stress burden. Our data also suggest that the larger area of the Whataroa floodplain would experience disastrous disturbances with similar timing and tempo. Our results show ( Figure S8C) that as much as 5 m of sediment ranging from silt to fine gravel has accumulated 12 km down-valley from the range front in the last ca. 1000 years. This result corroborates findings from tree ages and confirms that most of the Whataroa fan will experience protracted aggradation that threatens livelihoods, exacerbating the acute hazard of flooding of an aggrading river. Later in the relaxation phase, it may be possible, with active management of stream courses, excavation of sediment from channels and warning systems for the transport route and farming to resume.
The singularity and fragility of SH 6 is well known even under non-earthquake conditions (Gorman, 2019;Westland District Council, 2006). Our data from Whataroa provide an indication of the

| CONCLUSIONS
Our study of the range front fans at Te Taho on the north side of the Whataroa River has involved mapping and dating exposures of multiepisode fans at the fan toe where they have been trimmed by the incised and laterally migrating Whataroa River. Complementary exposures were provided by local streams graded to the larger Little Man River or Whataroa River, and sapping gullies eroding back from the trimmed toe locations. The sequences exposed on the Little Man fan and Blackburn exposure are similar for the past several cycles but differ in detail of aggradation deposits and depth of stream incision.
Comparing FRCs with the timing of known Alpine Fault earthquakes confirms that initial aggradation is very likely to be earthquake triggered. However, not all fan building episodes are exposed in our study and, thus, our sequence is incomplete, with bypassing of fan aggradation in successive events a likely cause. Nevertheless, we have identified and dated four major episodes of fan building since 1000 CE.
Sixty-two radiocarbon ages, SRTs and stratigraphic ordering have been used as input to OxCal sequence models for the Little Man fan (30 ages) and Blackburn exposure (19 ages) (Figures 7 and 11) that constrain event times to 1041-1130, 1318-1445, 1605-1754 and 1652-1800 CE. SRTs quantify the duration of periods when rates of aggradation were minimal or nil and hence have allowed us to constrain the duration of rapid aggradation (Table 2 and  Our data on the evolution of the Te Taho fans are consistent with other historic non-earthquake events on the West Coast but faster than other earthquake sites in New Zealand and internationally where rainfall and elevation gradients (the basis for stream power) are lower.
Judging from the thickness of fan deposits exposed in the fan toe areas of the Te Taho fans and the short duration of aggradation (Table 2), we conclude that current farming practices on the fans and probably across much of the Whataroa River fan are most unlikely to be sustainable for a decade to several decades after a major earthquake. We partly base this conclusion on observations from nonearthquake, localised landslides that occurred in range front catchments at Gaunt Creek and Poerua River. The recovery after aggradation, including re-establishment of farm infrastructure and productive pasture, represents a further delay, which remains poorly quantified.
The sustainability of current land-use practices, regional tourism and agriculture are at risk, more so because of reliance on infrastructure including the highly vulnerable single arterial highway (SH 6; see Westland District Council, 2006).

AUTHOR CONTRIBUTIONS
All authors contributed to conceptualisation, methodology and investigation. Berryman secured funding. Almond, Berryman, Villamor and Alloway wrote, reviewed and edited the draft manuscript.