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Data sourcesEighteen rice-producing countries were selected for our analysis (Supplementary Table 1). Those countries account for 88 and 86% of global rice production and harvested rice area2, respectively (FAOSTAT, 2015–2017). We followed two steps to select the dominant cropping systems in each country. Within each country, our study focused on the main rice-producing area(s) (Supplementary Tables 2 and 3). For example, in the case of Brazil, we selected the southern and northern regions, which together account for nearly all rice production in this country. In the case of Vietnam, we selected the Mekong Delta region, which accounts for nearly 60% of national rice production57. While we tried to cover all major rice cropping systems in each country, this was not possible in the case of rainfed lowland rice cropping systems in northeastern Thailand and eastern India because of lack of reliable estimates of yield potential and access to farmer yield and management data. Once the main rice-producing region(s) in each country was (were) identified, we then determined the dominant rice cropping system(s) for each of them (Supplementary Table 3). We note that “cropping system” refers to a unique combination of a number of rice crops planted on the same piece of land within a 12-month period (and their temporal arrangement), water regime (rainfed or irrigated), and ecosystem (upland or lowland) (Supplementary Fig. 1 and Supplementary Table 2). In our study, rice cropping systems are single-, double-, or triple-season rice; none of the cropping systems are ratoon rice. Following the previous examples, two cropping systems were selected for Brazil (rainfed upland single rice and lowland irrigated single rice in the northern and southern regions, respectively) and two systems (double and triple) were selected for the Mekong Delta region in Vietnam. These systems account for nearly all rice harvested areas in these regions. We distinguished between rice-based cropping systems sowing hybrid versus inbred cultivars in the southern USA. Across the 18 countries, this study included a total of 32 rice cropping systems, which, in turn, covered 51% of the global rice harvested area (Supplementary Tables 1 and 3). Note that the area coverage reported here corresponds to that accounted by 32 cropping systems (and not by the countries where the cropping systems were located). These systems portrayed a wide range of biophysical and socio-economic backgrounds (Supplementary Figs. 1 and 2 and Supplementary Tables 1 and 2), leading to average rice yields ranging from 2–10.4 Mg ha−1 (Supplementary Fig. 3). For data analysis purposes, rice cropping systems were classified into tropical and non-tropical9,58,59 and also based upon water regime and crop season.Agronomic information was collected via structure questionnaires completed by agricultural specialists in each country or region (Supplementary Table 6). The collected data included field size, tillage method, crop establishment method, degree of mechanization for each field operation, seeding rate, crop establishment, and harvest dates, nutrient fertilizer rates, manure type, and rate, pesticides (number of applications, products, and rates), irrigation amount (in irrigated systems), energy source for irrigation pumping, labor input, and straw management (Supplementary Tables 4 and 5). Average values for each cropping system reported by country experts were retrieved from survey data available from previous projects (Supplementary Table 7). Rice grain yield was reported at a standard moisture content of 140 g H2O kg−1 grain, separately for each crop cycle, using data from, at least, three recent cropping seasons in each cropping system. In the case of irrigated rice cropping system in Nigeria and Mali, data were only available for one crop cycle in double-season rice. In this case, we assumed management and actual yield to be identical in the two crop cycles.In all cases, and wherever possible, data were cross-validated with other independent datasets (e.g., FAOSTAT, World Bank, IFA, and published journal papers), which gives confidence about the representativeness and accuracy of the survey data. For example, we estimated area-weighted national yield according to actual yield provided for each cropping system and annual rice harvested area in each system for each of the 18 countries. Comparison of these yields against those reported by FAOSTAT2 showed a strong association and agreement between data sources (Supplementary Fig. 10). We also cross-validated actual yield, N fertilizer, labor, and irrigation from our database with those reported by previous studies (published after the year 2000) based on on-farm data collected in ten selected countries. Due to the lack of on-farm data on irrigation, we used published data collected from experiments that follow typical farmer irrigation practices. In the case of irrigation, our cross-validation differentiated between crop seasons (wet versus dry) in the case of irrigated double-season rice cropping systems. In all cases, average yield, N fertilizer, labor, and irrigation from our database fell within (or very close) the range of values reported in previously published studies for those same cropping systems (Supplementary Table 8). Measured daily weather data, including daily solar radiation, minimum and maximum temperatures, and precipitation, were derived from representative weather stations in each region (Supplementary Fig. 2 and Supplementary Table 9). Data on per-capita gross domestic product (GDP) during 2015–2017 were retrieved for each country to explore relationships between yield gap and economic development60 (Supplementary Fig. 9 and Supplementary Table 1).Estimation of yield gapsThe yield gap is defined as the difference between yield potential and average farmer yield. Estimates of yield potential for irrigated rice or water-limited yield potential for rainfed rice were adopted from Global Yield Gap Atlas (GYGA)61 (Supplementary Table 7). Yield potential simulation in GYGA was performed using crop growth and development model ORYZA2000 or ORYZA (v3) (except for APSIM in the case of India) and based on actual data on crop management, soil data, measured daily weather data, and representative rice varieties planted in each region (see details for yield potential simulation in Supplementary Information Text Section 1). Data on yield potential were not available for Australia (AUIS) in GYGA; hence, we used estimates of yield potential from Lacy et al.62. Yield potential (or water-limited yield potential for rainfed rice) and average yields were computed separately for each rice crop in each rice cropping system (Supplementary Fig. 3). The coefficient of variation (CV) of yield potential (or water-limited yield potential) was estimated for each cropping system (Supplementary Fig. 4). In this study, average rice yield was expressed as percentage of the yield potential (or water-limited yield potential for rainfed rice) for each cropping system (Fig. 1 and Supplementary Fig. 5). In those cropping systems where more than one rice crop is grown within a 12-month period, we estimated yield potential and average yield on both per-crop and annual basis by averaging and summing up the estimates for each rice crop, respectively. In the case of per-crop averages, for those cropping systems in which the harvested rice area changed between crop cycles, we weighted the values for each cycles based on the associated harvested rice area. However, for simplicity, the main text reports only the values on a per-crop basis; annual estimates are provided in the Supplementary Information. Normalizing average yield by the yield potential at each site provides a direct comparison of yield gap closure across systems with diverse biophysical backgrounds (e.g., variation in solar radiation, temperature, and water supply). Without this normalization, one might make biased assessment in relation to the available room for improving yield. For example, an actual yield of 8 Mg ha−1 is equivalent to 80% of yield potential in the cropping system of central China, whereas a yield of 8 Mg ha−1 achieved by irrigated rice farmers in Brazil only represents 55% of yield potential (Supplementary Fig. 3).Quantifying resource-use efficiencyWe assessed the performance of rice production by calculating the following metrics: global warming potential (GWP), fossil-fuel energy inputs, water supply (irrigation plus in-season precipitation), number of pesticide applications, nitrogen (N) balance, and labor input, each expressed on an area and yield-scaled basis (Figs. 2, 3 and 4 and Supplementary Figs. 6, 7 and 11). We estimated metrics on both per-crop and annual basis and report the values on a per-crop basis in the main text while the annual estimates are provided in the Supplementary Information. In the case of GWP, it includes CO2, CH4, and N2O emissions (expressed as CO2-eq) from (i) production, packaging, and transportation of agricultural inputs (seed, fertilizer, pesticides, machinery, etc.), (ii) fossil-fuel energy directly used for farm operations (including irrigation pumping), and (iii) CH4 and N2O emission during rice cultivation63. Emissions from agricultural inputs were calculated on application rates and associated GHG emissions factors (see details in Supplementary Information Text Section 2, Supplementary Table 10). In the case of fossil fuel used for field operations, it was calculated based on the number and type of farm operations and associated fuel requirements (Supplementary Table 11). Total N2O emissions were calculated as the sum of direct and indirect N2O emissions. A previous meta-analysis including rice showed that direct soil N2O emissions can be estimated from the magnitude of N-surplus, which was calculated as applied N inputs minus accumulated N in aboveground biomass at physiological maturity21. Therefore, direct soil N2O emissions for a given rice crop cycle were estimated following van Groenigen et al. N-balance approach21. Indirect N2O emissions were estimated based on the Intergovernmental Panel on Climate Change (IPCC) methodology64, assuming indirect N2O emissions represent 20% of direct N2O emissions. The CH4 emissions from rice paddy field were calculated following IPCC65. Following this approach, CH4 emissions are estimated considering the duration of the rice cultivation period, water regime during the cultivation period and during the pre-season before the cultivation period, and type and amount of organic amendment applied (e.g., straw, manure, compost) based on a baseline emission factor. We assumed no net change in soil carbon stocks as soil organic matter is typically at steady state in lowland rice66. We did not attempt to estimate changes on soil C in the upland rice system in Brazil. All emissions were converted to CO2-eq, with GWP for CH4 set at 25 relatives to CO2 and 298 for N2O on a per mass basis over a 100-year time horizon67. For each rice crop cycle in each of the 32 rice systems, GWP was calculated as the sum of CO2, CH4, and N2O emissions expressed as CO2-eq. (Details on N2O and CH4 emissions estimates and GWP calculations are provided in Supplementary Information Text Section 2).Calculation of energy inputs was similar to that of GWP and was based on the reported rates of agricultural inputs and field operations and associated embodied energy (see details for energy input estimates in Supplementary Information Text Section 2, Supplementary Table 12). Human labor was also included in the calculation of energy inputs. There was a strong positive relationship between energy input and GWP on both per-crop (r = 0.81; p  More

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The Chaihuín stratigraphyCore transects (Fig. 2b) reveal three sand layers, intercalated between herbaceous peats, that are laterally extensive over 600 m across the marsh (Fig. 3a). In all cases, the sand layers have sharp lower contacts and transitional upper contacts. Ten accelerator mass spectrometric (AMS) radiocarbon dates modelled using a Bayesian phased sequence model provide the chronology (Fig. 3c and Supplementary Table 1). The age of plant macrofossils immediately beneath the upper layer, sand A, are consistent with burial by the 1960 tsunami. The age model places the deposition of the middle sand B at 1600–1820 and lower layer, sand C, at 1486–1616 CE. The calibrated age ranges for sands B and C are reasonably broad due to plateaux in the radiocarbon calibration curve, which affect dates from the seventeenth to twentieth centuries21.Fig. 3: Geological evidence from Chaihuín.a Stratigraphy of selected coring transects showing three laterally extensive sand sheets. Transect locations X–X’ and Y–Y’ shown on Fig. 2; b sedimentology of sand sheets, including grain size, sorting and clastic composition (%) classified relative to six modern environments established by discriminant analysis (see Supplementary Discussion), with images of sands A and B in CN17/8. Box-and-whisker plots show the statistical parameters measured in sand samples with the horizontal line inside the box representing the median, the box representing the upper and lower quartiles, the whiskers representing the minimum and maximum values excluding any outliers and the crosses the extreme outlier values. The number within each box indicates the number of samples in each group; c probability density functions (95.4%) of radiocarbon dates and modelled ages for the three earthquakes. Full radiocarbon results in Supplementary Table 1.Full size imageThe sedimentology and mineralogical signatures of the sand sheets are described in detail elsewhere based on over 100 hand-driven cores22 and summarised in Supplementary Discussion; here we analyse diatoms in three representative cores and present reconstructions of marsh surface elevation change over time from a diatom-based transfer function (Fig. 4 and Supplementary Data 1). From diatom analysis of the three cores, we identified 170 species indicative of differing tolerances to tidal inundation. Only 14 species were absent from a previously published modern training set that includes 29 samples from Chaihuín20, and 9 of these species constituted 2% of any sample (comprising 4–5% in 2 non-sand samples).Fig. 4: Diatom assemblages and estimates of land-level change derived from a regional south-central Chile transfer function for three cores from Chaihuín.a–c Diatom assemblage summaries and dominant taxa in cores CN14/5 (a), CN17/8 (b) and CN18/11 (c) at elevations of 0.88, 0.89 and 1.10 m above mean sea level (MSL), respectively. Elevation optima of diatom species are classified based on weighted averaging of the modern training set and reported relative to mean higher high water (MHHW). The modern analogue technique was used to calculate the squared chord distance to the closest modern analogue, and the threshold for a fossil sample having a close modern analogue is defined as the 20th percentile of the dissimilarity values (MinDC) for the modern training set44. Reconstructed palaeomarsh surface elevations (PMSE) and coseismic subsidence are shown from the weighted averaging partial least squares (WA-PLS) model only. d Estimates of coseismic subsidence in 1737 from three cores and three different diatom-based transfer function approaches, showing 95.4% uncertainties.Full size imageThe laterally extensive uppermost coarse to medium-grained sand sheet (A) is mid grey, varies in thickness between 1 and 19 cm, has a median grain size of 0.49 mm and is upwards fining (0.27–0.71 mm) in 61 cores (80% of those in which A is preserved, massive in the others). The marsh grades steeply into freshwater scrub, and there is no sand unit in cores just above the high marsh limit. There is an abrupt contact between the sand and dark brown silty herbaceous peat below, which contains plant material including below-ground stems (rhizomes) of Scirpus americanus. In many cores, there are rip-up clasts (~2 cm) of peat encased in the sand sheet, as well as vegetation rooted in the peat below. The peat below the sand sheet contains a diatom assemblage that is almost entirely composed of species found on the contemporary high marsh above mean higher high water (MHHW) (e.g. Eunotia praerupta, Nitzschia acidoclinata), with higher elevation optima than the diatoms found in the herbaceous peat above the sand unit (e.g. Rhopalodia constricta) (Fig. 4a). The overlying peat also contains low, albeit important, percentages (5–24%) of taxa with elevation optima below MHHW. By contrast to the peats, sand A is dominated by species with lower elevation optima (59–72% of the total assemblage have optima below MHHW), including Achnanthes reversa and Planothidium delicatulum.The middle brown-grey to dark grey mica-rich coarse to medium-grained sand sheet (B) is similarly laterally extensive across the entire marsh, varying in thickness between 2 and 32 cm. It has a median grain size of 0.47 mm and is upwards-fining (0.38–0.68 mm) in 31 cores (50% of those in which B is preserved, massive in others), but rip-up clasts of peat were only occasionally observed. In some cases, we observe a 2–4-cm-thick cap of horizontally bedded detrital plant fragments and wood at the top of the sand layer. The sand sheet abruptly overlays a red-brown to dark brown silty herbaceous peat with variable silt content and humification. Humidophila contenta dominates the diatom assemblage in the peat below sand B (up to 37% of the assemblage) and is also present in the peat overlying the sand sheet, which remains dominated by species with elevation optima above MHHW. In the core from the lowest contemporary marsh elevation (CN14/5, Fig. 4a), there is an increase in low marsh diatom species (elevation optima below MHHW) above the sand compared to below (e.g. A. reversa, P. delicatulum). Diatom assemblages are relatively consistent across the five samples from the sand unit, with 54–76% of the assemblages being species with elevation optima below MHHW, including A. reversa, Fallacia tenera and P. delicatulum.A third sand deposit (C) is found in 16 cores at the southern end of the marsh, although still traceable over 200 m and across most cores that penetrated deep enough to potentially sample sand C. The deposit is a dark grey fine to medium-grained massive sand (median grain size 0.25 mm, range 0.22-0.29 mm), with a maximum thickness of 51 cm and contains occasional rip-up clasts from the buried organic unit below encased in the sand. The basal contact is abrupt, with the sand overlying a brown clayey silt with occasional herbaceous plant remains, humified organic matter and woody plant material. The organic horizon below sand C contains more diatom species typically found at lower elevations in the tidal frame than the peats below A and B (Fig. 4a). There is also a change in species composition approaching the top of the peat, with abundances of Opephora pacifica and Pseudostaurosira perminuta decreasing and H. contenta and E. perpusilla increasing from the base to top of the peat below sand C. Also in contrast to the other two buried organic deposits, there is a change in species composition approaching the top of the peat and samples immediately above and below sand unit C have very similar diatom assemblages, dominated by H. contenta and E. perpusilla. Diatom preservation in the sand unit was very poor, and it was not possible to obtain representative counts from this unit.Brown silty herbaceous peats separate the three sand sheets, deposited intertidally on the basis of their diatom composition. In addition to the relative variations in freshwater and brackish diatom composition of peats described above, the peat units also vary in their degree of humification. While peats below sands A and C contain humified organic matter, the peat below sand B is unhumified. Additionally, two layers of highly humified black peat were observed immediately above and below sand A in low marsh cores from the southwest of the marsh, varying in thickness between 1 and 15 cm.Evidence for a locally sourced tsunamiWe interpret all three sand sheets as being deposited by locally sourced tsunamis, rather than far-field tsunamis or non-seismic processes (e.g. storms, river floods or aeolian processes). This is based primarily on coincident land deformation, and also upon their lateral extent, diatom composition, and sedimentological signatures. Dealing first with the latter lines of reasoning, sands A and B are not only dominated by marine sublittoral and epipsammic diatom species but also contain substantial numbers of benthic silty intertidal mudflat and freshwater taxa, which also dominate the underlying peats. This is consistent with mixed diatom assemblages in tsunami deposits worldwide and indicative of tsunamis eroding, transporting and redepositing diatoms from diverse environments as they cross coastal and inland areas23,24,25,26. The presence of marine and tidal flat diatoms excludes deposition of sand by river flooding25,27, and statistical comparison of the sedimentological and mineralogical signatures of the sands with modern depositional environments, reported by Aedo et al.22 and summarised in Supplementary Discussion, further supports a seaward rather fluvial sediment source. We observe a maximum sedimentary contribution of 12% from upstream fluvial sources (Fig. 3b) and do not observe erosional or depositional features characteristic of fluvial flood deposits, such as a high basal mud content reflective of suspended loads during the initial stages of flooding or inverse grading as energy increases28.Meteorologically driven deposition of the sands, either during storm surges or other transient sea-level fluctuation events (e.g. El Niño), is discounted as the diatoms in the overlying organic units demonstrate lasting ecological change27,29. While a non-tsunamigenic earthquake followed closely in time by a large storm surge may impact diatom assemblages in the same way, there are several further characteristics of the three sand sheets which are consistent with a tsunami origin, even though these, in themselves, are not diagnostic. These include the lateral extent (traceable across 230 m), upwards-fining grain size of sand sheets A and B, and clasts of underlying peats observed within sands A and C and occasionally within B. The absence of extreme climatic phenomena, such as hurricanes and tropical storms, in the Chaihuín area during the historic period also minimises the possibility of finding storm deposits. However, while it is recognised that the above criteria cannot be used individually to confirm tsunami deposition, it is the combination of all sedimentological and diatom evidence that we use here in support of the most compelling evidence for tsunami deposition, which comes from the accompanying abrupt land-level change. The latter rules out deposition by tsunamis sourced in the far-field, storms or aeolian processes.Evidence for coseismic land-level changeFollowing established criteria30,31, we use the sedimentary and diatom evidence to propose that the Chaihuín sequence records three earthquake events, associated with vertical coseismic deformation and tsunami deposition. Diatom assemblages from immediately below sand layers A and B are characterised by species with higher elevation preferences than those found immediately above the sands, suggesting decreases in marsh surface elevation consistent with coseismic subsidence (Fig. 4). Diatom assemblages show minimal change across sand layer C; instead a transition occurs prior to event C whereby species with lower elevation preferences are replaced by those with higher elevation preferences, indicating net emergence prior to event C followed by minimal coseismic subsidence.The transfer function reconstructs 0.35 ± 0.42 m of subsidence occurred in event A, which local testimony and radiocarbon dating confirm to be the 1960 earthquake. Compared to our previous estimate for this event20, refining the transfer function method and expanding the modern training set here, reduces the uncertainty by 0.26 m. Reconstructed subsidence agrees with observations of 0.7 ± 0.4 m19. By contrast, the transfer function reconstructs very minor subsidence of 0.10 ± 0.36 m occurred in event C, but this needs confirmation from analyses of additional cores.The transfer function predicts that coseismic subsidence occurred in event B, with reconstructions varying between 0.10 ± 0.33 and 0.52 ± 0.39 m, and averaging 0.22 ± 0.38 m (Fig. 4d). While this is close to the detection limit of coseismic land-level change30 and the error term is large compared to the amount of deformation, we interpret event B as being associated with net submergence for two reasons. First, changes in diatom-inferred marsh elevations between pre- and post-earthquake samples are greater than other sample-to-sample changes. Second, all nine reconstructions, regardless of core location or transfer function approach, indicate submergence rather than a mixture of submergence and emergence (Fig. 4d).Linking the geologic and historical recordsDespite the broad modelled age ranges for events B and C of 1600–1820 and 1486–1616 CE, respectively, each range only includes one historically reported earthquake. If the historical catalogue is complete, sands B and C represent tsunamis accompanying the 1737 and 1575 earthquakes, respectively. Although other great tsunamigenic earthquakes occurred in the time range of event B (1657, 1730, 1751), their rupture areas have been placed much further north8,32 and therefore are very unlikely sources for the observed deformation. Age ranges do not include 1837; therefore, absence of evidence for this earthquake at Chaihuín supports the chronicle-based interpretation that the 1837 rupture area lies further south11,16. The preservation of turbidites from 1837 at sites to the north of Chaihuín14 is consistent with observations of earthquake-triggered turbidites some distance outside the rupture zone, as observed for the Mw 8.8 2010 Maule earthquake14.Implications for the rupture depth in 1737The Chaihuín record provides the first evidence for crustal deformation during the 1737 earthquake and the first evidence for the earthquake being tsunamigenic. While the nearshore bathymetry and orientation of the coastline may amplify tsunami inundation and the abundant sediment source may enhance the potential for evidence creation during even moderate tsunamis, the direction of land-level change at Chaihuín (subsidence) calls for reconsideration of the associated rupture depth. While correlation with evidence of shaking-induced turbidites from Calafquén and Riñihue lakes14, along with the absence of a 1737 event in sedimentary records from Río Maullín and Chucalén to the south9,11, supports the hypothesis that a smaller section of the plate interface ruptured in 1737 (between 39 and 41°S) than in 1960 and 157514, the Chaihuín record also forms an important constraint on the depth of local slip in 1737.By combining deformation and tsunami modelling, we show that our evidence of coastal subsidence and tsunami inundation at Chaihuín is better explained by offshore, shallow megathrust slip rather than by deeper slip below land as previously suggested16 (Fig. 5 and Supplementary Fig. 1). This is demonstrated by a simple numerical experiment designed to find the most likely depth range of the causative earthquake rupture that can explain the coastal subsidence inferred at Chaihuín and also the tsunami inundation.Fig. 5: Results of model tests to show that the 1737 rupture must have been confined to the offshore region at shallower fault depths than previously proposed.a The lower panel shows the trench-normal section of the megathrust and seafloor geometry at the latitude of Chaihuín used in the modelling experiment. The upper panel shows the bell-shaped slip distributions for a suite of eight earthquake ruptures and the middle panel shows the modelled vertical surface deformations using an elastic dislocation model (see “Methods”). The red and blue curves are the deep and shallow ruptures used as illustrative examples in the text. In this suite of models, the rupture width and peak slip are fixed at 100 km and 1 m, respectively, and the rupture location is systematically shifted horizontally in the trench-normal direction to represent ruptures at different depths. b Summary plot showing the modelled coastal uplift (left vertical axis) and tsunami runup (right vertical axis) predicted by the suite of models. Note that coastal subsidence can only be produced by offshore ruptures, with slip shallower than ~20 km. Ruptures deeper than this produce uplift at the coast. This opposing pattern of coastal deformation between shallow versus deeper ruptures is insensitive to how much slip is prescribed at the fault. Supplementary Fig. 1 shows the results for two different suite of models, in which the rupture width varies by fixing the updip (Supplementary Fig. 1a) and downdip (Supplementary Fig. 1b) limits.Full size imageOur numerical approach (see also “Methods”) leverages the sensitivity of the deformation sign (uplift or subsidence) and tsunami size at the Chaihuín coast to the depth of megathrust slip33 (Fig. 5). An earthquake rupture with maximum slip at 33 km fault depth (Fig. 5a, red model), as previously inferred from historical records16, will result in coastal uplift and a relatively small tsunami. Instead, if the rupture occurs offshore (Fig. 5a, blue model), the deformation will result in coastal subsidence and a much larger tsunami. From a systematic analysis in which the hypothetical rupture models are shifted horizontally in the trench-normal direction or vertically in the depth direction (Fig. 5a, upper panel), we conclude that subsidence at the Chaihuín coast could only be produced by ruptures placed mainly offshore, at average megathrust depths shallower than 20 km (Fig. 5b, downward triangles). Deeper ruptures will produce coastal uplift and consequent smaller tsunamis (Fig. 5b). The same conclusion is reached by varying the rupture width with fixed updip and downdip limits (Supplementary Fig. 1).Our conclusions are independent of the use of a normalised unit displacement in all models (i.e. 1 m at the centre of its corresponding bell-shaped rupture) because the opposing effects of deep versus shallow ruptures at Chaihuín are insensitive to the magnitude of slip involved and depend on its locus. The amount of slip determines the magnitude of deformation but not its sign due to the elastic response of the crust during earthquakes34. However, with evidence at only one location we only feel confident to constrain the depth range but not the magnitude nor along-strike extent of the causative slip. Therefore, from our numerical experiment we conclude that to produce subsidence at the Chaihuín coast, an offshore rupture likely shallower than 20 km is required as a deeper source would result in coastal uplift. This is also consistent with the inferred tsunami heights (Fig. 5b), which are larger for a shallower rupture and therefore more likely to produce inundation on land independent of the local topography. This geologically-based inference of an offshore rupture (blue curve in Fig. 5b) contrasts with the deeper rupture below land (red curve in Fig. 5b) previously inferred from historical observations alone16.Implications for tsunami recurrence intervalsThe average interval between the three events preserved at Chaihuín, 193 years, is shorter than the interval proposed for full segment 1960-style ruptures of 270-280 years9,11,14. This supports the notion that the Chilean subduction zone displays a variable rupture mode, in which the size, depth, tsunamigenic potential and recurrence interval vary between earthquakes10. Of greatest importance, however, is the shorter average recurrence interval of tsunami inundation than previously reported. With the addition of the 1737 tsunami alongside previously known events in 1960, 1837 and 1575, the historical recurrence interval for tsunamis generated anywhere along the Valdivia segment of the Chilean subduction zone is reduced to 130 years. This holds even if the inferred tsunami inundation is not associated with the 1737 earthquake, but with another earthquake of similar age missed in the historical catalogue. More