Upper Plate Faults May Contribute to the Paleoseismic Subsidence Record Along the Central Hikurangi Subduction Zone, Aotearoa New Zealand

Earthquake‐driven subsidence can cause cascading hazards at the coast by exacerbating relative sea level rise, storm surges, tsunami, and tidal flooding. At Ahuriri Lagoon near Napier, Aotearoa New Zealand, paleoseismic uplift and subsidence are typically attributed to upper plate faults and subduction interface earthquakes, respectively. We test this assumption with elastic dislocation models of upper plate and subduction interface earthquakes informed by historical events, seismic surveys, and modern interface coupling data. We compared our surface deformation results to paleoseismic records preserved at Ahuriri Lagoon, which includes eight rapid subsidence (c. 0.5–1.2 m) and two rapid uplift events over the last c. 7 kyr. Our models demonstrate that offshore upper plate faults could cause subsidence of c. 0.5–1 m at Ahuriri Lagoon at recurrence intervals of c. 2 kyr. A range of subduction interface earthquakes can also produce subsidence at Ahuriri Lagoon, and may explain larger (>1 m) subsidence, but must rupture the currently creeping (i.e., aseismic) portions of the interface. We demonstrate that both upper plate fault and subduction interface earthquakes may have contributed to the Ahuriri Lagoon records, and that interface coupling may be more spatially or temporally heterogeneous than modern geodetic data suggest. Models of sea‐level rise and earthquake multi‐hazards that do not include the effects of upper plate faulting may mischaracterize risk at the coast.

nation, which reflects both Māori and English names) (Figure 1), encapsulates many of the challenges involved in using pre-instrumental vertical coastal motions to constrain subduction behavior and associated seismic hazard.Numerous upper plate faults are present in onshore and offshore Hawke's Bay (Figure 1) and contribute to vertical motions at Ahuriri Lagoon.The M w 7.8 1931 Napier earthquake ruptured the steep reverse-oblique Awanui fault and uplifted Ahuriri Lagoon by 1-2 m (Figure 1) (Haines & Darby, 1987;Hull, 1990).The c. 7 kyr paleoseismic record there includes sudden subsidence (c.0.5-1.2m per event) in eight inferred paleoearthquakes, as well as uplift in a further two events (including 1931 CE) (e.g., Hayward et al., 2016;Hull, 1990).
Attributing specific fault sources to events at Ahuriri Lagoon and other sites along the Hikurangi margin is made difficult by wide displacement and age uncertainties, short record lengths, limited spatial preservation, and intertwined signals from subduction and upper plate fault earthquakes (e.g., Clark et al., 2019).Slip on upper-plate structures clearly control the topography and sedimentary basin structure of the area over 10-100 kyr timescales (e.g., Barnes et al., 2002;Berryman et al., 2011;Hull, 1987;Litchfield et al., 2022;Paquet et al., 2009).Despite this established role of upper-plate faulting in the structural evolution of the region, previous work has not identified upper-plate earthquake sources that explain coseismic subsidence at the lagoon.Consequently, paleoseismic subsidence at Ahuriri Lagoon has been tentatively attributed to subduction earthquakes, which are responsible for significant long-wavelength coseismic subsidence along other subduction margins (e.g., Atwater, 1987;Melbourne et al., 1997;Plafker, 1969;Subarya et al., 2006).
There have been no large subduction earthquakes along the Hikurangi margin in historical times that could guide expected patterns of coastal deformation.At many subduction zones, the spatial pattern of coupled or partially coupled segments corresponds to slip patches in past great earthquakes (e.g., Chlieh et al., 2008;Loveless & Meade, 2011;Perfettini et al., 2010) and therefore persistent coupling may inform future earthquake behavior (e.g., Chlieh et al., 2011;Kaneko et al., 2010;Lay & Nishenko, 2022;Uchida & Bürgmann, 2021;L. Wang et al., 2015).Geodetic observations suggest predominantly low modern coupling on the central Hikurangi subduction zone, meaning convergence is currently accommodated through slow-slip and creep (Wallace et al., 2004;Woods, 2022).The current understanding of strain accumulation and release generally suggests that creeping portions of subduction zones are not expected to host large megathrust earthquakes (e.g., K. Wang et al., 2012).Is modern Hikurangi interface behavior and coupling long-lived, and if so, which fault sources produced the coseismic subsidence observed at Ahuriri Lagoon?
The scarcity of subduction zone paleoseismic records along the Hikurangi margin highlights the importance of the relatively long record at Ahuriri Lagoon (Clark et al., 2019).The discrepancy between the inferred earthquakes in the Ahuriri Lagoon record and the modern low coupling along the central margin is difficult to reconcile.The current New Zealand National Seismic Hazard Model (NZ NSHM) takes a conservative approach to this problem and incorporates a higher coupling coefficient for the central Hikurangi interface than the geodetically derived values (Van Dissen et al., 2022;Wallace, 2020).Therefore, the Ahuriri Lagoon paleoseismic record currently underpins models that ultimately inform building codes, and improvements to fault source characterizations will have a direct impact on future mitigation.
In this study, we use elastic dislocation modeling to address two questions: (a) can recognized upper plate faults produce coseismic subsidence at Ahuriri Lagoon and (b) what is the range of plausible subduction earthquakes that can cause subsidence at Ahuriri Lagoon?These slip models can explore a greater suite of potential earthquakes and resulting coastal deformation from upper plate faults and the subduction interface than the spatially limited, short, and fragmentary paleoseismic records.This approach also allows for variations based on uncertainties in fault source geometries, kinematics, and slip which have never before been applied to the Ahuriri Lagoon paleoseismic records and are rarely considered elsewhere.Our results challenge the current paradigm that sudden coastal subsidence at Ahuriri Lagoon is only caused by megathrust earthquakes.

Expected Vertical Deformation From Upper Plate Fault and Subduction Earthquakes
Coastal coseismic deformation above the Hikurangi subduction zone is likely dictated by a complex interaction between slip along the subduction interface as well as from multiple smaller upper plate faults (Figure 1).Both interface and upper plate fault earthquakes can produce uplift and subsidence (Figure 2).Coseismic vertical deformation at the coast, such as at Ahuriri Lagoon, depends on the site location in relation to the source fault and rupture patch as well as fault dip.Steeper reverse faults produce significant hanging wall uplift and little-to-no 10.1029/2023GC011060 3 of 21

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4 of 21 hanging wall subsidence and may cause subsidence in the near-fault footwall; a similar signal occurred during the 1931 Napier earthquake (Figures 1 and 2a) (e.g., Haines & Darby, 1987;Hull, 1990).Gently dipping reverse faults (upper plate fault or interface) produce uplift above the updip portion of the rupture patch and subsidence above the down-dip limit of the rupture patch (Figures 2b-2d) (e.g., Meltzner et al., 2006), or along strike from the slip patch (Briggs et al., 2014).Listric (curved) faults can produce large uplift near the fault tip and subsidence above the down-dip limit of the rupture patch due to steep dips at shallow depths and gentle dips at deeper depths (Figure 2c) (e.g., Cochran et al., 2006).Little is known about the subsurface geometry of coastal upper plate faults, but primary structures typically dip northwest.(c) Major active faults and key paleoseismic sites near central Hawke's Bay.Northwest-dipping faults typically control slip and continue to interface; southeast-dipping faults are typically shallow back thrusts that splay from other faults (e.g., Mountjoy & Barnes, 2011;Paquet et al., 2009Paquet et al., , 2011)).Data: bathymetric DEM, Mitchell et al. (2012); onshore DEM, Landcare Research NZ Ltd. (2011), onshore faults, Langridge et al. (2016) and Lee et al. (2020); offshore faults, Paquet et al. (2009Paquet et al. ( , 2011) ) and Mountjoy and Barnes (2011); Hikurangi Plateau thickness, Davy and Wood (1994); and paleoseismic data, Clark et al. (2019) (and references within).These expected deformation patterns are the basis for many studies where coastal deformation records inform past earthquake behavior (e.g., Atwater & Hemphill-Haley, 1997;Clark et al., 2015;Cochran et al., 2006;Hayward et al., 2016;Witter et al., 2022) and longer-term subduction zone behavior (Meltzner et al., 2010(Meltzner et al., , 2012;;Sieh et al., 2008;Tsang et al., 2015;Woods, 2022).The dual uplift and subsidence record at Ahuriri Lagoon suggests that at least two source faults contribute to coseismic deformation there (e.g., Hull, 1990).Attributing fault source and other interpretations from paleoseismic site data typically include assumptions about the source fault and slip behavior, but become less clear if multiple fault sources can produce similar coastal deformation signals at any one site (e.g., McNeill et al., 1999).In order to build realistic elastic dislocation models, we summarize below the known seismogenic fault sources in central Hawke's Bay and evidence that informs expected earthquake behavior at Ahuriri Lagoon.

Hikurangi Subduction Zone Behavior
Large-magnitude subduction earthquakes have not been observed on the Hikurangi margin since European colonization in 1840 CE.Therefore, much of the subduction zone earthquake characterization, expected slip behavior, and hazard forecasts are heavily informed by interface coupling models (e.g., Van Dissen et al., 2022).Coupling estimates use modern geodetic motions to infer the degree of interface locking across the plate margin (e.g., Johnson et al., 2022;Wallace et al., 2004).Megathrust earthquakes are thought to occur in highly coupled (locked) zones, while aseismic processes, such as slow slip and creep, are inferred to dominate in zones of low coupling (e.g., Herman & Furlong, 2021;Witter et al., 2014).The central Hikurangi margin has low coupling and has experienced multiple slow slip events in recent decades (Wallace et al., 2004(Wallace et al., , 2009)).Some locking may occur near the trench, but geodetic data there, and thus coupling models, are poorly constrained (Wallace et al., 2004(Wallace et al., , 2009;;Woods, 2022).Other studies that use vertical derivatives of horizontal strain suggest more heterogeneous coupling near Hawke's Bay with smaller locked patches between slow-slip event extents (Dimitrova et al., 2016).The relatively rough central Hikurangi interface, caused by subducted sea mounts and a change in interface protolith, likely contributes to the creeping and slow slip behavior and lack of large magnitude earthquakes (e.g., K. Wang & Bilek, 2014).
The paleoseismic record along the central margin shows evidence of both large vertical displacements and tsunami deposits, indicative of larger magnitude stick-slip earthquake behavior, which is seemingly at odds with modern low coupling and slow-slip behavior (Clark et al., 2019;Hayward et al., 2016;Wallace et al., 2009).Whether the interpreted contemporary coupling reflects long-term subduction behavior, and whether the central margin will host great subduction earthquakes, remains unknown (Clark et al., 2019).

Coastal Uplift Records
The M w 7.8 1931 Napier earthquake (also referred to as the 1931 Hawke's Bay earthquake, see McGinty et al. (2001)) is the only earthquake since 1840 CE that deformed the Hawke's Bay coast and likely occurred on the Awanui fault (Figure 1c) (Hull, 1990;Kelsey et al., 1998).The earthquake produced a >90-km-long uplifted dome with 2.5 m peak uplift and c. 1.5 m uplift at Ahuriri Lagoon, as well as up to 1.1 m of localized onshore subsidence in the proximal fault footwall (Figure 1c) (Hull, 1990).Two additional paleoseismic uplift events are recorded in the combined Ahuriri Lagoon and Pakuratahi Valley sediments since 7 ka (Figure 3) (Hayward et al., 2016;Pizer et al., 2023).These uplift events are attributed to the Awanui fault or similar faults in that zone.
Uplifted marine terraces farther east provide longer-term, time-averaged uplift records as well as individual paleoearthquake uplift data (Figure 3).Mahia Peninsula uplift is considered to be dominantly controlled by the northwest-dipping Lachlan fault (discussed further below), and provides general constraints for a fast-slipping and well-characterized offshore structure (Figure 1c) (Berryman, 1993a;Berryman et al., 2018;Clark et al., 2019).Uplifted terraces there record a minimum of five earthquakes since c. 4,500 years BP, per-event uplift of 1.4-3.1 m, and longer-term uplift rates up to 1.9 ± 0.5 mm/yr since 40 ka (Figure 3) (Berryman, 1993a(Berryman, , 1993b;;Berryman et al., 2018).
Farther south, uplifted Holocene marine terraces are preserved at Cape Kidnappers, Waimārama, and Aramoana and are attributed to earthquakes on the northwest-dipping Kidnappers Ridge, Waimārama, and Kairākau fault network (Figure 1c) (Hull, 1987;Litchfield et al., 2022;Miyauchi et al., 1989;Paquet et al., 2011).These sites record one to three paleoearthquakes since c. 5.5 ka.The large height difference between some Holocene terraces indicates additional intermediate terraces, and thus records of past earthquakes, may have eroded away (Figure 3) (Clark et al., 2019;Hull, 1987;Litchfield et al., 2022;Miyauchi et al., 1989).Pleistocene strandlines in central Cape Kidnappers provide an uplift rate of 1.6 mm/yr since c. 120 ka (Hull, 1985;Paquet et al., 2011).Other less well-preserved Pleistocene strandlines at the eastern Cape Kidnappers margin have been used to infer an uplift gradient across Cape Kidnappers; however, both strandlines are undated (Figure S1 in Supporting Information S1).We use only the central, better-preserved strandline for constraints in this study.

Coastal Subsidence Records
Localized footwall subsidence in the 1931 Napier earthquake is the only historical coseismic subsidence in central Hawke's Bay (Figure 1c).Longer records of coseismic subsidence in Hawke's Bay are inferred from lagoon sediments that record repeated rapid relative sea level rise events.Long-term uplift rates (italics) are derived from uplifted Pleistocene marine terraces.(b) Age data for rapid uplift (red) and subsidence (blue) events attributed to paleoearthquakes, presented at 2σ (95%).Question marks indicate suspected erosion and potentially missing uplifted Holocene terraces.Simplified fault mapping from Mountjoy and Barnes (2011) and Paquet et al. (2009Paquet et al. ( , 2011)).Paleoseismic data from Clark et al. (2019) (and references within), Litchfield et al. (2022) and Pizer et al. (2023).
The best-studied and most complete records are from Ahuriri Lagoon, which shows eight subsidence events ranging from 0.5 to 1.2 m over the last c.7 ka (Figure 3) (Hayward et al., 2015(Hayward et al., , 2016;;Hull, 1986).These geologic records provide evidence for abrupt subsidence events (i.e., from earthquakes) rather than gradual interseismic processes.The lagoon records have large vertical displacement uncertainties (c.0.3-0.5 m), which sum the uncertainties from paleo-sea level, modern sediment core elevation, and estimated sediment compaction beneath the sample since deposition (Hayward et al., 2016).The resolution of the lagoon records is not precise enough to distinguish pre-or post-seismic deformation (Hayward et al., 2016).Post-seismic deformation from afterslip and visco-elastic rebound, however, is much smaller than paleoseismic record uncertainties (<4% peak coseismic slip) (e.g., Luo & Wang, 2022).An additional 1.6-2 m of subsidence since over the last c.7 kyr was also documented at Ahuriri Lagoon that could not be confidently attributed to earthquakes (Hayward et al., 2016).
Initial studies of coseismic subsidence at Ahuriri Lagoon did not interpret possible source faults for these events, but recognized a potential link to the overall fold structure between Napier and Cape Kidnappers (Hull, 1986).The 1931 Napier earthquake source fault, other upper plate faults, and the seismogenic potential of the subduction zone were not understood at the time.More recent studies inferred that some, if not all, subsidence events were caused by subduction interface earthquakes because similar phenomena occurred along other margins (Hayward et al., 2006(Hayward et al., , 2016)).Some Ahuriri Lagoon subsidence events correlate with paleoseismic events elsewhere along the Hikurangi margin (≥70 km along-margin distance), suggesting widespread deformation and strong ground motions, and thus a larger (i.e., subduction interface) fault source (Clark et al., 2019;Hayward et al., 2016;Pizer et al., 2023).The adjacent Pakuratahi Valley and more northerly Te Paeroa/Opoho sites also record multiple rapid subsidence and tsunami deposits in the Holocene, some of which have overlapping age distributions with Ahuriri Lagoon records (Figure 3) (Clark et al., 2019;Cochran et al., 2006;Pizer et al., 2023).None of the rapid subsidence events at Ahuriri Lagoon correlate with the preserved Holocene uplift events at Cape Kidnappers, as would be expected from a nearby upper plate fault earthquake, though this could be due to incomplete preservation at either site (Hull, 1987).The age of one Ahuriri Lagoon subsidence event does overlap with terrace uplift at Waimārama at c. 5 ka (Figure 3) (Clark et al., 2019;Pizer et al., 2023).
Longer term (c.400 ka) subsidence near Ahuriri Lagoon is recorded in the numerous forearc basins in offshore and near-shore Hawke's Bay; these basins (e.g., the Kidnappers Basin) are located between active thrust-faultcontrolled ridges and develop in response to changes in climate, sedimentation, and tectonic processes (Figure 1c) (e.g., Dravid & Brown, 1997;Paquet et al., 2011).The basin-scale records are too coarse to resolve individual earthquake histories, but indicate that cumulative fault displacements follow expected upper plate fault deformation patterns (i.e., hanging wall uplift and footwall subsidence; Figure 2), and across the Awanui fault, mimic the 1931 event displacement profile (e.g., Begg et al., 2022;Dravid & Brown, 1997;Hull, 1986).

Upper Plate Faults
The active offshore and nearshore faults in Hawke's Bay are generally characterized as out-of-sequence thrust faults that maintain the accretionary wedge taper (Figure 1c) (Barnes et al., 2010).Published seismic survey data indicate the presence of predominantly northwest-dipping listric faults, which result from the reactivation of extensional faults preceding the current convergent regime (Figure 1b) (Barnes & Nicol, 2004;Barnes et al., 2010).The fault tips are generally buried in the near-surface below anticline ridges that are separated by sedimentary basins (e.g., Barnes et al., 2002;Paquet et al., 2009Paquet et al., , 2011)).Southeast-dipping backthrusts are relatively shallow features (i.e., limited to the upper few kilometers) that splay from the primary northwest-dipping structures (e.g., Barnes et al., 2002;Paquet et al., 2009Paquet et al., , 2011)), and are therefore unlikely to be independently seismogenic.
Farther south are the Waimārama, Kairākau, and Kidnappers Ridge faults (Figure 1c) (e.g., Paquet et al., 2011).Kidnappers Ridge is a zone of uplifted and folded sea floor that is cored by several active but unnamed northwest-dipping, listric reverse faults and a southeast dipping backthrust (the Kidnappers fault) (Figure 1c) (Barnes et al., 2002).The northwest-dipping faults likely continue along strike under Cape Kidnappers, though the surface expression there is less clear and the fault tip may be buried (Figure 1c) (Paquet et al., 2011).The Waimārama-Kairākau thrust faults dip steeply northwest in the near-surface and are inferred to be listric, similar to other nearby faults, but cannot be imaged at depth by marine surveys (Figure 1c) (Mountjoy & Barnes, 2011).
The slip vector rake for these upper plate faults is poorly constrained.Due to the obliquity of plate convergence compared to fault strike, these faults likely contain a variable component of dextral slip (Figure 1) (e.g., Barnes & Nicol, 2004;Barnes et al., 2002).Thus, reported dip-slip and vertical separation rates represent a minimum of the full slip rate or single-earthquake slip values.

Previous Elastic Dislocation Modeling
Previous studies used forward elastic dislocation models to estimate tsunami hazard or to determine source faults for historic earthquake and paleoseismic records along the central Hikurangi margin (Cochran et al., 2006;Fraser et al., 2014;Hayward et al., 2016;Litchfield et al., 2022;McGinty et al., 2001).The 1931 Napier earthquake coseismic surface deformation was fitted using steep planar faults, rupture from 5 km depth to the interface, and up to 8 m each of dextral and reverse slip (Haines & Darby, 1987;McGinty et al., 2001).Cochran et al. (2006) investigated sources for subsidence at Te Paeroa and Opoho and uplifted terraces at Mahia Peninsula (Figure 3).Results indicated that both a gently dipping Lachlan fault and subduction interface sources could contribute to uplift and subsidence there, either synchronously or separately, but subduction rupture was required for the larger subsidence (>0.9 m) records (Cochran et al., 2006).Fraser et al. (2014) presented forward elastic dislocation models of the Lachlan fault and subduction interface to estimate tsunami inundation hazard at Napier.Those Lachlan fault scenarios used a planar, steep fault (60° dip) and uniform slip that resulted in negligible hanging wall and coastal subsidence.The subduction rupture followed interface geometry (i.e., not planar) with a slip distribution informed by contemporary coupling patterns; several central margin rupture scenarios (M w 8.2-8.4) and multi-segment scenarios (M w 8.8-9.0)result in subsidence between 0.3 and 0.6 m near Napier (Fraser et al., 2014).Litchfield et al. (2022) showed that reverse slip on the Kairākau fault could produce observed meter-scale terrace uplift at Aramoana, and potentially other coastal sites, but subsidence from that fault did not reach Ahuriri Lagoon.Hayward et al. (2016) provided one subduction interface elastic dislocation model that produces subsidence at Ahuriri Lagoon and the Hawke's Bay coastline, but provided no information on the earthquake source parameters or magnitude.None of the existing dislocation models explore subsidence at Ahuriri Lagoon from smaller subduction interface earthquakes (<M w 8.2) or closer offshore upper plate faults.

Elastic Dislocation Modeling Methods
We used elastic dislocation models to test whether recognized upper plate fault and subduction interface sources could produce recorded subsidence (≥0.5 m) at Ahuriri Lagoon.The models focus on the Kidnappers Ridge, Waimārama, and Kairākau upper plate faults because these structures have gentle dips at depth and likely extend near or below Ahuriri Lagoon and are thus capable of producing subsidence there (e.g., Figure 2c).Closer faults (e.g., Awanui and Tukituki faults) are likely to produce uplift at Ahuriri Lagoon based on the proximal hanging wall location, as seen in the 1931 earthquake (Figures 1c, 2b, and 2c) (Haines & Darby, 1987;Hull, 1990;McGinty et al., 2001).There are no mapped, active, northwest-dipping reverse faults northwest of Ahuriri Lagoon that could produce coseismic footwall subsidence there.
We also modeled displacements from several possible subduction zone rupture scenarios.Those elastic dislocation models explore how slip location on the interface affects coseismic subsidence at Ahuriri Lagoon and whether those slip distributions reflect modern coupling.

Upper Plate Fault Elastic Dislocation Models
We present two upper plate fault model geometries: a listric fault based on seismic survey data and a planar fault as represented in the Community Fault Model (Seebeck et al., 2022).Both listric and planar fault geometries use the same simplified trace of the combined Kidnappers Ridge, Waimārama, and Kairākau faults with a strike of 227° and total fault length of 75 km.Fault length is based on the distribution of mapped fault traces, which could conceivably link during an earthquake, and the 80-km-long Napier earthquake rupture (McGinty et al., 2001).All upper plate scenarios use 8 m peak slip, informed by average earthquake dip-slip estimates on the Lachlan fault (5-9 m for single segment, 4-7 m for multi segment) (Barnes et al., 2002) and the dislocation modeling discussed above in Section 2.5 (Cochran et al., 2006;Fraser et al., 2014;McGinty et al., 2001).
The planar upper plate fault model dips uniformly at 40° from the surface to the subduction interface at 15.7 km depth.The listric upper plate fault model dip changes from 80° at 0-1 km depth to 22° at 6 km depth, and continues at 22° from 6 to 21 km depth (to the intersection with the interface).For both upper plate fault shapes, we test whether allowing additional slip on the subduction interface (up to 3 km depth) affects the slip distribution and deformation pattern.This configuration approximates one type of interface-upper plate joint rupture, as well as possible triggered slip or afterslip on the interface (e.g., Gomberg & Sherrod, 2014;Melnick et al., 2012;T. Wang et al., 2018).Since rake is not well constrained, all upper plate dislocation models are run twice: once with pure reverse rake (90° rake) and again with oblique reverse-dextral rake (135°).
Model geometries were discretized into 3 by 3 km patches.Green's functions representing vertical displacements at Ahuriri Lagoon for 1 m of slip on each patch were calculated using the method of Okada (1985), assuming a Poisson ratio () of 0.25.We acknowledge that incorporation of more realistic, spatially, heterogeneous elastic properties could change modeled slip by up to 20% at the depths of interest (Williams & Wallace, 2018).However, we do not include such heterogeneity in our models because that process would be computationally expensive and would influence the results much less than the other parameters, such as fault geometry and slip distribution.Similarly, we do not investigate sensitivity of results to Poisson's ratio because previous work suggests that doing so would have a negligible effect on modeled vertical deformation (Hsu et al., 2011).
We use a combination of slip inversions and forward models to investigate the plausibility of subsidence at Ahuriri Lagoon due to upper plate earthquakes.Our inversions solve for slip distributions on upper plate faults that maximize subsidence at the lagoon.We emphasize that there is no unique solution to this inversion-clearly, the range of values of single-event vertical motions at a single site cannot constrain the 3,600 parameters required to define a slip distribution on our modeled listric fault, even if the uncertainty in this geometry is ignored.The inversion results are highly sensitive to specified fault geometry, rake, maximum slip, and smoothing parameters, but are useful for three reasons.First, they test whether an upper-plate earthquake could cause subsidence at Ahuriri Lagoon, although that test could also be done using forward models.Second, they help identify the optimal location for slip that promotes subsidence at Ahuriri Lagoon (within the constraints of the parameters above).It would be possible to search for this optimal location using a grid search or forward models and a trial-and-error approach; however, our inversions allow for more freedom in the shape of the slip distribution than these other approaches.Third, inverting for slip allows us to estimate an approximate maximum magnitude for subsidence, again assuming the orientation, smoothness and maximum magnitude of slip.
Since there are few constraints on slip distributions that could cause subsidence at Ahuriri Lagoon, we also run a suite of forward models to investigate the sensitivity of vertical motions at the lagoon to different parameters, including slip taper width, down-dip extent, and updip extent.The forward models use the same fault geometry as the inversion and hold all other parameters the same in each trial (further details in Text S1 in Supporting Information S1, Delano et al., 2023).
We experimented with different relative weights for Laplacian smoothing and penalized slip on all the modeled fault edges.This slip taper also approximates a buried fault rupture tip, where slip is zero along the top 3 km of the fault (i.e., one tile length), consistent with 1931 Napier earthquake modeled slip and fault propagation folds beneath Cape Kidnappers and in Hawke Bay (Barnes & Nicol, 2004;Haines & Darby, 1987;McGinty et al., 2001).

Subduction Interface Elastic Dislocation Models
We used forward elastic dislocation models to investigate if subduction interface earthquakes, informed by modern coupling and slow-slip event locations, produce subsidence at Ahuriri Lagoon.Wallace (2020) show that over decadal timescales, the central Hikurangi interface has low coupling (i.e., is creeping).However, between slow-slip events on annual timescales, the slow-slip source areas are more coupled (Wallace, 2020).We therefore test rupture patches that only include the shallow, more permanently locked interface as well as those that include the slow-slip source area.We also tested slip on the interface patches located between slow-slip events, which may be partially or heterogeneously coupled based on vertical derivative of horizontal strain data (Dimitrova et al., 2016;Wallace, 2020).Finally, we estimate the location and slip patch for the smallest interface earthquake capable of producing 0.5 m subsidence at Ahuriri Lagoon, irrespective of the modern coupling data.
We calculated surface displacements using the method of Nikkhoo and Walter (2015) and the Poisson ratio above (0.25).The interface is represented by a triangular mesh surface with 3 km triangles that follows the geometry of Williams et al. (2013).The scenarios used average slip that follows the magnitude-area scaling relationship from Stirling et al. (2021) with a C value of 4.0 (Gerstenberger et al., 2022).Interface slip tapers to zero over 12 km to the patch edge (approximately matching upper plate fault inversion taper).The rake for each subduction interface patch is from Wallace et al. (2012).

Elastic Dislocation Modeling Results
The paleoseismic subsidence records at Ahuriri Lagoon provide minimum constraints on coastal deformation preservation potential (Figure 3).The eight documented coseismic subsidence events range from 0.5-1.2m (average 0.85 m) subsidence, and the smallest subsidence is estimated at 0.5 ± 0.5 m (Hayward et al. (2015).These values are similar to subsidence documented at Te Paeroa and Opoho, where the smallest measured coseismic subsidence was c. 0.5-1.0m and the largest subsidence was c. 1.0-2.0m (Cochran et al., 2006), and at Pakuratahi Valley, with >0.5 m estimated coseismic subsidence (Figure 3) (Pizer et al., 2023).It is therefore probable that subsidence events <0.5 m would not be reliably preserved and resolved in the geological record at Ahuriri Lagoon, and we adopt c. 0.5 m as a minimum threshold.

Upper Plate Fault Inversion Model Results
Both the modeled listric and planar fault geometries can produce subsidence of at least 0.5 m at Ahuriri Lagoon with reasonable slip magnitudes and distributions (Figure 4).The listric fault inversion models produce 0.73 and 0.72 m subsidence for reverse and oblique rakes, respectively, without any slip on the subduction interface.The resulting earthquake magnitudes are M w 7.7 (Figure 4).Allowing additional slip on the subduction interface increased the maximum subsidence to 0.96 m for the oblique rake model, but did not increase subsidence for the pure reverse rake model (Figure S2 in Supporting Information S1).
For the planar fault, subsidence at Ahuriri Lagoon only occurs when slip continues onto the subduction interface.This results in subsidence of 0.61 and 0.48 m with reverse and oblique rakes, respectively, and results in a magnitude of M w 7.6 (Figure 4c) (see Supporting Information S1 for additional results; Delano et al., 2023).The planar fault has a steeper average fault dip compared to the listric fault models.This contributes to slightly larger uplift values near the updip portion of the fault, given the same rake (e.g., Figures 2a and 2b).
In all upper plate fault models, variations in rake influence the spatial pattern of surface deformation.Oblique slip shifts peak subsidence southwest (i.e., opposite the direction of rake) and peak uplift northeast compared to pure reverse rake (Figure 4,Figures S4 and S5 in Supporting Information S1).
In addition to rake, the location of peak uplift and subsidence, and thus our modeled subsidence at Ahuriri Lagoon, is dependent on the extent of slip at depth.We reiterate that these subsidence values and exact locations are non-unique results (Figures S4 and S5 in Supporting Information S1).However, the inversion results demonstrate that sizable subsidence from upper plate faults is plausible and consistent with a range of slip distributions and geometries.We explore those results in more detail below.

Sensitivity of Subsidence at Ahuriri Lagoon to Modeled Slip Distribution
The forward models demonstrate how certain inversion parameter choices (i.e., slip taper, updip, down-dip, and lateral slip extent) might change our findings (Figures S4-S8 in Supporting Information S1; additional details in Text S1 in Supporting Information S1).Changing the updip slip extent only affects subsidence insofar as it changes the overall slip area, and thus maximum displacement.These effects are negligible for subsidence at Ahuriri Lagoon in our models (Figure S3 in Supporting Information S1).The down-dip slip extent model variations show that subsidence is largest at Ahuriri Lagoon when slip terminates underneath, or just updip of, Ahuriri Lagoon (Figures S6-S8 in Supporting Information S1).The range of subsidence values at Ahuriri Lagoon is small (c.0.2 m) for ruptures that terminate between 9 km updip and 9 km down-dip of the upper plate-interface intersection, given the same slip taper width (Figures S6-S8 in Supporting Information S1).The slip taper width (i.e., how sharply slip tapers) affects Ahuriri Lagoon subsidence by moving the peak slip values, and thus peak subsidence, closer or father away (e.g., compare Figures S6d-S8d in Supporting Information S1).For the same down-dip slip extent, our taper widths (9, 15, and 21 km) change Ahuriri Lagoon displacement by <0.2 m.
Variations in along-strike rupture extent result in translations of surface displacement.The resulting changes in subsidence at Ahuriri Lagoon are more pronounced for oblique rakes because maximum subsidence is not orthogonal to fault strike (Figures S4 and S5 in Supporting Information S1).In the oblique rake inversion model, for example, slip is primarily east of the lagoon to maximize subsidence at the lagoon (Figure 4).If slip instead extends along the entire modeled fault, peak slip is shifted southwest and Ahuriri Lagoon subsidence is slightly reduced (Figure S5 in Supporting Information S1).This relationship is also why additional slip on the interface results in greater subsidence at Ahuriri Lagoon for oblique rakes, but not for pure reverse rake (Figure S2 in Supporting Information S1).
The individual effects of slip taper, down-dip slip terminations, and lateral slip terminations are relatively minor and lend confidence that our interpretations based on inversion results are valid.Together, they indicate that a rupture that terminates or has peak slip far away from Ahuriri Lagoon (e.g., Figures S6a and S8d in Supporting Information S1) will be less likely to produce subsidence ≥0.5 m at Ahuriri Lagoon.In other words, if earthquakes on these upper plate faults terminate at especially shallow or deep depths rather than near upper plate fault-interface transition, or too far away along strike, subsidence may not be large enough to be preserved and resolved at Ahuriri Lagoon.Conversely, they indicate that there are a wide range of slip distributions capable of producing subsidence ≥0.5 m at Ahuriri Lagoon.

Subduction Interface Model Results
In our subduction interface forward models, subsidence did not exceed 0.5 m at Ahuriri Lagoon when slip occurred in areas that are assumed to be locked or partially locked, even at great magnitudes (≥M w 8.5) (Figure 5a).The same is true for areas where geodetic data show shallow slow slip (Figure 5b).The subduction interface rupture scenarios only produce subsidence ≥0.5 m at Ahuriri Lagoon when the down-dip termination of the slip patch is approximately below Ahuriri Lagoon (Figures 5c and 5d, Figure S9 in Supporting Information S1).Importantly, that part of the interface is between slow-slip patches and in a zone that is considered creeping over decadal timescales (Wallace, 2020); however, it does overlap with a possible smaller locked interface patch shown by Dimitrova et al. (2016).Our smallest subduction interface rupture that produced ≥0.5 m subsidence at Ahuriri Lagoon had a magnitude of M w 7.6 (Figure 5d).Both uplift and subsidence from the M w 7.6 scenario diminish to near-zero over a short distance (c.50 km).These rupture scenarios are not exhaustive or predictive, but take into consideration how interface slip extent translates to surface deformation and the minimum requirements to produce sizable coastal subsidence.Different magnitude events or alternative slip distributions will change the absolute vertical deformation values, but the overall patterns would remain similar.Even a whole-margin rupture (i.e., c. M w 9.0) will not produce significant subsidence at Ahuriri Lagoon if slip only occurs within the currently fully coupled portions of the interface.

Can Slip on Upper Plate Faults Cause Subsidence at Ahuriri Lagoon?
Our results demonstrate that both upper plate fault and subduction interface earthquakes may produce coseismic subsidence of at least 0.5 m at Ahuriri Lagoon.These scenarios and slip suggest that coseismic subsidence at Ahuriri Lagoon can be produced from several fault sources and rupture scenarios, given our current (albeit limited) understanding of these structures.
For the elastic dislocation models presented here, the greatest Ahuriri Lagoon subsidence is caused by a gently dipping fault with a slip patch southeast (i.e., on the updip side) of Ahuriri Lagoon.Our results also imply that multi-fault or multi-segment ruptures on the Kidnappers Ridge, Waimārama, and Kairākau fault systems are required to produce similar-sized or larger earthquakes (Figure 1).How these structures may link at depth remains unknown, but given the similarity in orientation, close proximity, and short steps between fault traces, it is reasonable that these faults may rupture together (e.g., Clark et al., 2017;Litchfield et al., 2022).If the upper plate faults are significantly steeper at depth than considered here, or have moderate dips and do not rupture with the subduction zone interface, then surface displacement may be dominated by uplift (e.g., Figure 2a).
Earthquakes smaller than c.M w 7.5 may not produce enough subsidence for preservation in the lagoons, though smaller amounts of coastal subsidence would still present significant coastal hazard and risk.The estimated magnitude for a full Lachlan fault rupture is M w 7.8-8.0(Barnes et al., 2002;Mountjoy & Barnes, 2011); the Kidnappers Ridge, Waimārama, and Kairākau faults are less well characterized but their similar geometry suggests comparable earthquake potentials.If these faults rupture with the subduction interface, their potential earthquake magnitudes could be greater.

Are Subduction Earthquakes Required to Explain the Ahuriri Lagoon Record?
We have shown that upper plate faults can cause subsidence at Ahuriri Lagoon, but here we consider whether known faults in Hawke Bay have fast enough slip rates, short enough recurrence times, or large enough earthquake slip to account for all Holocene geologic subsidence records at Ahuriri Lagoon.
Ahuriri Lagoon records eight rapid subsidence events over the last c.7°ka with an average inter-event time of 900 years (Figure 3) (Hayward et al., 2016;Hull, 1986).Our simplified upper plate fault elastic dislocation models produce an average 4 m slip per earthquake, similar to models of the 1931 Napier event.For a minimum slip rate of 2.0 mm/yr on the Kidnappers Ridge-Waimārama faults (see justification in Text S1 in Supporting Information S1), this corresponds to an average recurrence interval of 2,000 years.This is a crude estimate; coseismic displacement distributions and sedimentary environment conditions mean not all earthquake subsidence may be recorded (resulting in a longer apparent recurrence interval), while the minimum slip rate means earthquakes may have a shorter recurrence interval.Despite these caveats, the substantial difference between the c. 900 years average inter-event time recorded at Ahuriri Lagoon and the 2,000 years estimated upper plate fault recurrence interval range shows that some additional source other than upper plate faults is likely needed to produce all subsidence events recorded at Ahuriri Lagoon.Barring an unmapped, fast-slipping upper plate fault, the subduction interface is the most feasible alternate contributor to subsidence at Ahuriri Lagoon.Alternatively, faults may have temporally variable slip rates or exhibit earthquake clustering.
In the paleoseismic record, there is only one interpreted earthquake that potentially indicates synchronous coseismic marine terrace uplift and lagoon subsidence near Napier (Figure 3) (Clark et al., 2019;Pizer et al., 2023).This possible event is recorded by 0.5 ± 0.5 m rapid (i.e., coseismic) subsidence at Ahuriri Lagoon at 5,205-4,625 cal yr B.P (Clark et al., 2019;Hayward et al., 2016), rapid subsidence at Pakuratahi Valley at 4,837-4,584 cal yr B.P (Pizer et al., 2023), and 3.5 m of terrace uplift at Waimārama at 5,030-4,490 cal yr B.P (Figure 3) (Clark et al., 2019;Miyauchi et al., 1989).The overlap between these records could suggest the same earthquake affected all sites, or multiple closely timed events.If these records are from a single event, the deformation fits the expected uplift and subsidence profile from an upper plate fault source (Figure 3).
The lack of other correlating paleoearthquakes across all sites is perhaps not surprising given that vertical deformation from upper plate sources is more sensitive to the slip patch location and rake than a larger subduction interface event.It is possible that some upper plate fault earthquakes may not generate both a subsidence record and uplifted terrace due to a non-optimal slip patch.Alternatively, coastal erosion and sea level rise may remove marine terrace evidence while better preserving subsidence (e.g., Dura et al., 2016;Hull, 1987).
An alternative way to distinguish Ahuriri Lagoon paleoearthquake sources is through the magnitude and extent of subsidence, since subduction earthquakes can produce larger and more widespread coseismic subsidence than upper plate faults (Figure 2).At Ahuriri Lagoon, most event subsidence is estimated at <1 m (0.5-0.9 ± 0.5 m), but two Ahuriri Lagoon paleoearthquakes show subsidence ≥1.0 m (1.0 ± 0.3 and 1.2 ± 0.4 m, Hayward et al., 2016).In each instance, the wide paleoseismic displacement uncertainties prevent a robust interpretation of the source; however, in our elastic dislocation models, only larger magnitude (>M w 8.0) interface earthquakes were capable of maximum hanging wall subsidence ≥1 m (Figure 5, Figure S9 in Supporting Information S1).Larger subsidence events may be more reasonably explained by a subduction interface source (or combination upper plate and subduction) than upper plate faults alone, similar to conclusions from Te Paeroa and Opoho (Figure 3) (Cochran et al., 2006).Additionally, several of the Ahuriri Lagoon records have been correlated elsewhere along the margin, suggesting a larger source with broader deformation (Clark et al., 2019).However, the age control on these events can span hundreds of years and it is difficult to distinguish between closely timed, smaller earthquakes and more widespread synchronous deformation.

Megathrust Slip Behavior Through Multiple Seismic Cycles
The subduction interface scenarios constrained by the contemporary locked or partially locked interface do not produce sizable subsidence at Ahuriri Lagoon (Figure 5).If any of the Ahuriri Lagoon paleoseismic subsidence events are from subduction earthquakes, as suggested by paleoseismic interpretations, they likely included slip on the interface currently dominated by creep (e.g., Figure 5c, Figure S9 in Supporting Information S1).Spatial heterogeneity in coupling on the central Hikurangi interface may provide a mechanism for deeper subduction slip and coseismic coastal subsidence (e.g., Dimitrova et al., 2016).Whether these potentially locked patches rupture in smaller earthquakes, or include more of the interface in larger events, remains unknown.
The mismatch between low modern coupling and paleoseismic evidence has also been noted along the Aleutian margin (Kelsey et al., 2015;Witter et al., 2019), with proposed explanations such as transient interseismic coupling over one or more seismic cycles, heterogeneous megathrust rupture properties, non-megathrust fault sources for tsunami deposits, or dynamic rupture processes.Dynamic weakening can cause slip into creeping segments of a fault when an earthquake initiates in a more locked section (Noda & Lapusta, 2013).Temporally variable coupling has been observed on the Chilean and Sumatran subduction zones over multi-year and decadal time scales when previous ruptures enhance shear stress on adjacent interface patches (Loveless, 2017;Melnick et al., 2017;Philibosian et al., 2017).However, the slow-slip and creeping behavior on the central Hikurangi subduction zone appears correlated to the interface roughness, subducting sediment composition and supply, and other more long-lived conditions, and therefore may not change over relatively short geologic time intervals (Gao & Wang, 2014;Gase et al., 2022).Additional monitoring is needed to evaluate the spatial and temporal variability in coupling on the Hikurangi subduction zone.
In light of our results, other proxies that inform our understanding of the seismic cycle of subduction zones should account for potential upper plate faulting.For example, coral microatolls are one of the most important ways of tracking coupling and subduction zone behavior through time (e.g., Mallick et al., 2021;Meltzner et al., 2015;Philibosian et al., 2017).At a minimum, upper plate faulting may add noise to signals that have previously been attributed to subduction zone processes; in margins with significant upper plate faulting, previous interpretations may need re-evaluation to account for vertical deformation from non-subduction sources.

Tectonic Contributions to Present-Day Vertical Land Movements in Hawke's Bay
Elastic earthquake behavior suggests that coseismic subsidence at Ahuriri Lagoon should be the counterpart of gradual interseismic uplift (e.g., Savage, 1983;Sieh et al., 1999;Wesson et al., 2015).Over multiple earthquake cycles, long-term tectonic vertical deformation should be near zero from the subduction interface and distal offshore upper plate faults (i.e., Waimārama, Kairākau, and Kidnapper Ridge faults) (e.g., Briggs et al., 2008), or slightly positive from the nearby Awanui fault (Figure 1).
Actual land movements reflect more than tectonic deformation.Modern geodetic data show that the east coast of the North Island is subsiding, with rates up to 5 mm/yr near Napier (Hamling et al., 2022).Ahuriri Lagoon shows up to c. 8-9 m net subsidence between c. 7,500°ka and the 1931 Napier earthquake, taking into account sediment compaction and changes in sea level (Hayward et al., 2016).The 8-9 m lagoon subsidence was previously attributed to permanent coseismic or aseismic tectonic deformation (Hayward et al., 2016).
Neither the short-term geodetic nor significant permanent lagoon subsidence are consistent with the expected elastic behavior from the subduction interface or offshore upper plate faults, or permanent uplift from the Awanui fault.This implies one or both of the following: the central Hikurangi margin does not fit with the conventional seismic cycle model of coseismic recovery of interseismic strain accumulation, or other factors besides earthquake cycle strain recovery, such as groundwater removal (Naish et al., 2022), may contribute to subsidence over 10 1 -10 3 yr timescales.

Earthquake and Tsunami Hazard Implications
The sizable subsidence difference between the listric and planar upper plate fault models presented here highlights that simplifying fault geometry may be adequate for some hazard applications (e.g., ground shaking) but underestimates hazard for other applications (e.g., displacement hazards) (Figure 4).A gentler average fault dip increases the maximum possible rupture width and affects the expected location and amount of surface deformation (Barnes et al., 2002).Thus, displacement-based hazard models should incorporate more realistic fault geometries (e.g., listric) or values that better represent dips at depth.Fault source geometry can affect tsunami inundation because lower dips produce more coastal subsidence and thus greater flow depths and inundation extent.The previous tsunami inundation model for Napier overestimates dip on the Lachlan fault and therefore underestimates subsidence, though coseismic subsidence at Napier is likely minimal from that fault (Fraser et al., 2014).The Kidnappers Ridge, Kairākau, and Waimārama fault sources were not investigated in the previous tsunami inundation model for Napier, but produce up to c. 0.7 m subsidence at Napier in our models.However, these faults are included as fault sources in the National Tsunami Hazard Model that estimates wave heights along a fixed coastline (Power, 2013).The wave height models incorporate uncertainties by modeling a larger-than-expected event, and are thus less susceptible to hazard underestimations caused by fault geometry (Power, 2013).
In addition to fault geometry, modeled rake clearly impacts the spatial distribution of uplift and subsidence (Figure 4) and is therefore an important parameter in displacement hazard analyses.We note that the Community Fault Model rake (90° ± 20°) gives equal probability of a minor sinistral or dextral component of slip (Seebeck et al., 2022).A more realistic rake range for faults in Hawke Bay based on the oblique orientation to convergence is 90°-135°, which spans from pure reverse to equal parts reverse and dextral slip (Figure 1).
The extent of subduction interface slip drastically affects expected earthquake size, deformation, and hazard potential.The NZ NSHM incorporates the subduction interface coupling distribution for estimating shaking hazard from the subduction zone (Van Dissen et al., 2022).Because the paleoseismic record in Hawke's Bay indicates past large earthquakes, but the modern coupling distribution shows almost no slip deficit (i.e., no coupling), the hazard model manually imposes a slip deficit of 20% to the central Hikurangi margin.Therefore, resolving the relationship between earthquakes on upper plate faults and the subduction interface has direct implications for the NZ NSHM and downstream policies.Our new insights into upper plate fault earthquakes as a cause of subsidence at Ahuriri Lagoon may justify reducing the influence of the Ahuriri record on the imposed slip deficit in future revisions of the NZ NSHM.

Conclusions
Understanding potential fault sources directly affects hazard planning and mitigation efforts.Hazards from ground motions, coastal vertical deformation, and tsunami-exacerbated by ongoing sea-level rise worldwidevary greatly between great subduction earthquakes and upper plate faults.Elastic dislocation modeling of upper plate fault and subduction interface earthquakes provides a means to test possible sources for repeated coseismic subsidence at Ahuriri Lagoon near Napier, Aotearoa New Zealand.We find that both sources can produce subsidence ≥0.5 m at Ahuriri Lagoon.Our preferred upper plate fault source scenarios include more accurate listric fault geometry with gentle dips based on seismic reflection data.Simpler fault models that use steeper, planar faults do not resultin coastal subsidence and are likely inadequate for modeling coastal deformation in this setting.
The modeling results, along with slip rate and recurrence data, suggest that at least some of the eight paleoseismic subsidence events at Ahuriri Lagoon since 7 ka could be caused by slip on upper plate structures.This result deviates from many interpretations of coastal subsidence records, both in New Zealand and along other subduction margins, where megathrust events are typically the default source without significant evidence to the contrary.In Hawke's Bay, the upper plate structures may be important drivers of coseismic subsidence and should be considered as possible sources for the paleoseismic records there.
Our subduction earthquake model scenarios also showed that interface earthquakes only caused sizable subsidence at Ahuriri Lagoon when slip occurred on currently creeping parts of the interface.Paleoseismic data recording large single-event subsidence and margin-wide correlations suggest that megathrust events have occurred in the past.This apparent discrepancy between expected and past earthquake behavior suggests that modern coupling patterns are either more spatially and temporally heterogeneous than modern measurements, or that earthquake rupture can include creeping portions of the interface.

Figure 1 .
Figure 1.Tectonic setting of the Hawke's Bay region.(a) Plate boundaries and simplified tectonic regimes of the North Island.Hawke's Bay is located near the transition from upper plate accretionary wedge thrust faults to the North Island Dextral Fault System (NIDFS).(b) Cross-section of the Hikurangi subduction zone with schematic upper plate faults.Little is known about the subsurface geometry of coastal upper plate faults, but primary structures typically dip northwest.(c) Major active faults and key paleoseismic sites near central Hawke's Bay.Northwest-dipping faults typically control slip and continue to interface; southeast-dipping faults are typically shallow back thrusts that splay from other faults (e.g.,Mountjoy & Barnes, 2011;Paquet et al., 2009Paquet et al., , 2011)).Data: bathymetric DEM,Mitchell et al. (2012); onshore DEM, Landcare Research NZ Ltd. (2011), onshore faults,Langridge et al. (2016) andLee et al. (2020); offshore faults,Paquet et al. (2009Paquet et al. ( , 2011) ) andMountjoy and Barnes (2011); Hikurangi Plateau thickness,Davy and Wood (1994); and paleoseismic data,Clark et al. (2019) (and references within).

Figure 2 .
Figure 2. Generalized vertical deformation from various fault sources, assuming simple uniform reverse slip on (a) steeply dipping planar upper plate, (b) gently dipping upper plate, (c) listric upper plate, and (d) subduction interface faults.Both upper plate faults and subduction zone earthquakes can produce sizable subsidence depending on interest location relative to the fault, fault dip angle, and slip amount.Overall deformation patterns are based on the method of Okada (1985); values are schematic.

Figure 4 .
Figure 4. Select elastic dislocation model results for listric and planar upper plate faults (see Data Repository for additional results; Delano et al., 2023).These models have set geometry, rake, peak slip, and slip taper conditions and are inverted for the slip distribution that produces maximum subsidence at Ahuriri Lagoon (A.L.).(a) The listric upper plate fault with pure reverse motion and (b) listric upper plate fault with oblique motion both can produce at least 0.5 m of subsidence at Ahuriri Lagoon with reasonable magnitudes and slip distributions.(c) The steeper, planar fault only produces 0.5 m subsidence at Ahuriri Lagoon when substantial slip also occurs on the subduction interface.C.K. = Cape Kidnappers.Gray contour interval = 1 m vertical displacement; blue dashed contour = −0.5 m vertical displacement.

Figure 5 .
Figure 5. Forward elastic dislocation model results of subduction interface earthquakes.(a) Interface earthquakes on the locked or partially locked Hikurangi margin result in offshore subsidence but no subsidence at Ahuriri Lagoon (A.L.).Coupling boundary (gray dashed line) from Wallace et al. (2012).(b) Earthquakes on the locked interface and adjacent, shallow slow-slip event (SSE) extent do not produce significant subsidence at A.L. Teal dotted polygon = 20 mm cumulative slip contour from 2006 to 2008 SSEs; teal dashed polygons = 100 mm cumulative slip contour from 2002 to 2014 SSEs (Wallace, 2020).(c) Slip between modern SSEs on the currently creeping interface produces moderate subsidence at Ahuriri Lagoon.(d) Smaller magnitude interface earthquakes can produce c. 0.5 m of subsidence at Ahuriri Lagoon with an optimally located slip patch that terminates down-dip below Ahuriri Lagoon.C.K. = Cape Kidnappers.Listric upper plate fault geometry used in the main text shown as a gray-dashed line in the cross sections.