Landslide hazard cascades can trigger earthquakes

Domain: earth_science
Published: 2024-04-08
Editorial outcome: accept

Abstract
While earthquakes are well-known to trigger surface hazards and initiate hazard cascades, whether surface hazards can instead trigger earthquakes remains underexplored. In 2018, two landslides on the Tibetan plateau created landslide-dammed lakes which subsequently breached and caused catastrophic outburst floods. Here we build an earthquake catalog using machine-learning and cross-correlation-based methods which shows there was a statistically significant increase in earthquake activity (local magnitude ≤ 2.6) as the landslide-dammed lake approached peak water level which returned to the background level after dam breach. We further find that ~90% of the seismicity occurred where Coulomb stress increased due to the combined effect of direct loading and pore pressure diffusion. The close spatial and temporal correlation between the calculated Coulomb stress increase and earthquake activity suggests that the earthquakes were triggered by these landslide hazard cascades. Finally, our Coulomb stress modeling considering the properties of landslide-dammed lakes and reservoir-induced earthquakes globally suggests that earthquake triggering by landslide-dammed lakes and similar structures may be a ubiquitous phenomenon. Therefore, we propose that earthquake-surface hazard interaction can include bidirectional triggering which should be properly accounted for during geological hazard assessment and management in mountainous regions.

Introduction
Mass movements such as landslides, avalanches, and debris flows are regarded as both major hazards and key forms of geomorphic evolution in mountainous regions1–3. These surface processes can be triggered by many factors including rainfall4,5, snow melt6,7, and human activities8,9. In seismically active regions, the risk is also heightened since large earthquakes can induce widespread mass wasting with devastating effects10,11. When these mass movements block rivers and form landslide-dammed lakes (LDLs), subsequent dam breaches may cause catastrophic outburst floods which significantly increase the degree and scope of the disaster12,13. For example, the 1933 M7.5 Diexi earthquake in the eastern Tibetan plateau directly caused ~7000 fatalities and triggered many large landslides, some of which dammed rivers. These LDLs breached in the following days, generating catastrophic outburst floods which then resulted in >2500 additional fatalities14. Therefore, the response of surface processes to earthquakes has been studied extensively, in particular the failure mechanisms of earthquake-triggered landslides11,12, the quantification and prediction of the spatial distribution of mass movements13,15, and the geomorphic evolution after earthquakes in mountainous areas16,17, to improve our ability to mitigate the impact of these complex hazard cascades.

To date, studies about the interaction between earthquakes and mass movements have focused mainly on how earthquakes trigger mass movements and initiate hazard cascades, while a potential earthquake response to mass movements and their hazard cascades has received less attention. However, various studies have shown that processes which change the stress state of the Earth’s crust by surface loading and/or fluid diffusion18,19, such as earth tides20, water storage behind dams21, hydraulic fracturing22, waste fluid disposal23, and lake filling24–27 can trigger/induce earthquakes when the stress increase on neighboring active faults exceeds a critical threshold28,29. Since hazardous mass movements and their complex hazard cascades are often accompanied by sediment redistributions and changes in water storage and associated surface loads3,13, it is conceivable that the resulting stress changes can trigger earthquakes30–33. This would have important implications for hazard management in seismically active mountain regions.

Here, we use the 2018 Baige landslide hazard cascades (Fig. 1) on the Tibetan plateau as a case study to investigate earthquake triggering by LDLs. We quantify the spatiotemporal evolution of seismicity and stress changes on a surrounding fault system due to this hazard cascade. We further use Coulomb stress modeling based on a global LDL database to explore the potential for LDLs to trigger earthquakes.

Results
2018 Baige hazard cascades
At 22:05 China Standard Time (CST) on 10 October 2018, a massive landslide occurred at the Baige village on the Tibetan plateau34–38 (Fig. 1 and S1) and deposited 2.5 × 107 m3 of sediments into the Jinsha River35. This created a landslide dam with ~1500 m length, >450 m width, and ~60 m height35–37 (Fig. S1). With an upstream inflow of 1680 m3/s (ref. 35), the water level of the LDL gradually increased from ~2880 m asl to a peak of ~2932 m asl at 00:45 CST on 13 October (Fig. 2c), corresponding to inundation up to ~45 km upstream and a peak volume of ~2.9 × 108 m3 (refs. 35–37). As the water naturally overflowed the west of the dam, the landslide dam breached rapidly. The outburst flood’s discharge reached a peak of 10,000 m3/s at 06:00 CST on 13 October while the LDL’s water level rapidly decreased. Eight hours later at 14:00 CST, the discharge was reduced to that of the upstream lake inflow. However, due to the residual dam, the water level upstream of the dam (~2893 m asl) remained higher than before the landslide.

About three weeks later at 17:40 CST on 3 November 2018, materials at the trailing edge of the first landslide’s scar suddenly failed and the resulting landslide deposited an additional 8.7 × 106 m3 of sediments on the residual dam formed by the first landslide35–37. This formed a new >96 m high landslide dam and a new LDL35–37. To mitigate the potential impact of another outburst flood, the Chinese government trenched an artificial spillway of 220 m length, 15 m depth, and >3 m width on the west side of the dam36,37. Water entered the spillway at 04:45 CST on 12 November marking the initiation of a second outburst flood and the LDL reached a peak water level of 2957 m asl at 13:40 CST on 13 November (Fig. 2c), corresponding to inundation up to ~70 km upstream and a peak volume of ~5.8 × 108 m3 (refs. 35–37). At 18:00 CST on 13 November, the outburst flood’s discharge reached a maximum of 31,000 m3/s (refs. 35–37). Fourteen hours later at 08:00 CST on 14 November, the discharge decreased to the upstream inflow of ~600 m3/s. Like for the first LDL outburst, the water level upstream of the dam (2906 m asl) remained higher than before the landslide due to the residual dam (Fig. 2c).

Seismicity rate increase after Baige LDLs’ formation
Using continuous seismic data recorded by 13 nearby seismic stations from January 2014 to January 2023, we apply machine-learning and cross-correlation-based methods to build an earthquake catalog which contains ~3970 earthquakes with documented magnitude within a region of ~1° × 1° (Fig. 1b). 244 of these earthquakes within 10 km of the LDLs occurred after May 2018 when a denser seismic network began operation. It is well-established that earthquakes can trigger surface hazards and initiate hazard cascades5–7,12. However, the Baige landslides were not triggered by earthquakes34–38 as no earthquakes with magnitude M ≥ 3.5 were recorded within 50 km in the 3 preceding years39 (Figs. 1 and 2). Instead, in the week (10 to 16 November) when the second LDL approached its peak water level, 61 earthquakes with local magnitude up to ~2.6 occurred within 10 km of the LDLs.

As the second LDL approached peak water level, the number and magnitude of earthquakes started increasing as the water level rised and then peaked together with the water level peak (Fig. 2 and S2). Subsequently, as the LDL water level decreased following the dam breach, the earthquake activity gradually decreased back to the background rate. 45 of the 61 events in this earthquake sequence occurred before the largest magnitude (M 2.6) earthquake, and other M > 2.6 earthquakes during our observation period all had fewer than 4 aftershocks in the following week (Fig. S3). Therefore, this earthquake sequence is unlikely to be primarily an aftershock sequence of the largest magnitude event. We further verified that only 5 earthquakes (all with M < 2.0) occurred within 60 km of the LDLs besides this earthquake sequence as the second LDL approached peak water level (Fig. 1b), and the largest earthquake that occurred within 60 km of the LDLs in the 6 months before this earthquake sequence has M 2.7 (Fig. S4). Therefore, the earthquake sequence within 10 km of the LDLs is unlikely to have been triggered by surrounding large earthquakes.

We estimate the magnitude of completeness (Mc) to be 1.1 (ref. 40; Fig. 1c) for the earthquakes within 10 km of the LDLs. There are 62 earthquakes between May 2018 and January 2023 with local magnitude M ≥ 1.1, 16 of which occurred in the week when the second LDL approached its peak water (Table S1). We then perform declustering using the Reasenberg method41, leaving us with 54 events (Fig S5), 9 of which occurred in the week the second LDL approached its peak water level (Fig. S5, Table S1). In comparison, there were only 8 earthquakes in the previous 27 weeks (seismicity rate of ~0.3 events/week) and 37 earthquakes in the subsequent ~224 weeks (seismicity rate of ~0.2 events/week) in this region (Table S1). For each of ≥ Mc and declustered catalogs, we consistently find that the increase in seismicity rate is statistically significant at a >99% level based on both the statistic P (ref. 42) and statistic Z (ref. 43) tests (Methods). We further confirm that the increase in seismicity rate is also statistically significant at a >99% level (Table S1) based on both the improved statistic based on Poisson probability44 and an empirically derived statistic45 (Fig. S6) tests (Methods) which were developed to determine statistically significant changes in earthquake rate under small background rate. Hence, the significant increase in seismicity rate starting when the second LDL approached peak water level (Fig. 2 and S2) suggests that the two are related.

Stress changes caused by Baige LDLs
We further investigate whether the LDLs could have triggered the earthquakes by modeling the Coulomb failure stress changes (ΔCFS) on the surrounding fault systems. In our study region, there are three local faults Boluo-Tongmai, Jinshajiang, and Gangtuo-Yidun faults (from west to east) with similar surface traces of ~N50°W (ref. 46; Fig. 1a) though the exact fault dip and slip directions are unknown. Nevertheless, since January 2014, four M > 3.5 earthquakes occurred at distances between 16 and 35 km from the LDLs and have similar left-lateral strike-slip focal mechanisms with strikes that are also ~N50°W and dips of ~75°NE (ref. 39; Fig. 1a). In addition, we find that the first motions recorded by surrounding seismic station of the two largest earthquakes (M 2.6 and 1.9) as the second LDL approached peak water level are generally consistent with the left-lateral strike-slip focal mechanisms of these surrounding large earthquakes (Fig. S7). Therefore, we take these as our receiver fault geometry for the ΔCFS modeling (Methods). Furthermore, the receiver faults are assumed to be planar and located at 4.5 km depth which is deeper than 95% of our observed seismicity (Fig. S8) and corresponds to ~ −0.5 km asl because ~80% of our study area is at elevation between 4 and 5 km asl35.

We find that as the LDLs’ water level increased following the landslides, the ΔCFS in the seismic region generally increased due to both the direct gravitational loading of the LDL and pore pressure diffusion, while ΔCFS decreased when the LDLs’ water level decreased following the dam breaches (Fig. 2 and S9). The larger and longer-lasting LDL generated greater ΔCFS. The ΔCFS due to the first, smaller, and shorter-duration LDL peaked at 0.007 MPa which is smaller than the stress increase of >0.01 MPa typically associated with stress triggering of earthquakes (refs. 47,48; Fig. 2d). This could explain why there was no significant increase in seismicity rate associated with the first LDL’s formation (Fig. 2c). In comparison, about 3 weeks later on 3 November, the second landslide formed a larger LDL. The ΔCFS due to this second LDL peaked at 0.024 MPa when the LDL’s water level approached its peak, coinciding with maximum earthquake activity (Fig. 2c). Although the subsequent dam breach lowered the LDL’s water level which decreased the ΔCFS due to direct gravitational loading, the pore pressure diffusion effect kept the ΔCFS elevated which might explain why earthquake activity continued over the next few days (Fig. 2c).

While direct loading resulted in a decrease in ΔCFS directly below the LDL, it resulted in a slight increase in ΔCFS in surrounding regions (Fig. S9a). On the other hand, fluid diffusion significantly increased the pore pressure around the LDL, and the ΔCFS in regions closer to the LDL were larger (Fig. S9b). Therefore, due to the combined effect of direct loading and pore pressure diffusion, the ΔCFS around the LDL increased, especially on its east side. We find that ~90% of the earthquakes locate within regions of positive ΔCFS (Fig. 2a). The close spatial and temporal correlation between the calculated positive ΔCFS and the statistically significant increase in earthquake activity suggest that the earthquakes were likely triggered by the LDL.

Earthquake triggering by LDLs
Considering the fundamental mechanism of earthquake triggering by LDLs and reservoir-induced earthquakes is similar, we further explore the potential for other LDLs to trigger earthquakes. Based on HiQuake, currently the most complete and up-to-date freely available database of ~226 cases of reservoir-induced earthquakes spanning the period 1933-2019 globally49, we find that the minimum and median heights of ~190 reservoirs with documented height that induced earthquakes are ~13 and 110 m, respectively (Fig. 3a). In comparison, from a global database of ~410 LDLs with dams >1 million m3 in volume reported worldwide spanning the period 1900–2018 (ref. 50), we find that of the ~300 LDLs with documented dam height, ~73% and ~10% were higher than the minimum and median heights of reservoirs which induced earthquakes, respectively (Fig. 3a). Therefore, some LDLs globally are of similar heights as reservoirs which induced earthquakes.

We further calculate the stress response of surrounding faults in our study area to an LDL with a depth of 30 m which is the median dam height in the global LDL database50 (Fig. 3b). In this case, the ΔCFS at a given point (Figs. 2a and 3d) would exceed 0.01 MPa after ~11 days due to direct loading and pore pressure diffusion if the dam does not breach (Fig. 3c). The stress responses to this typical LDL at different sites can vary (Fig. 3d) and depend on factors such as the fault types51 (Fig. S10), geometries (Fig. S11), and depths (Fig. S11). Nevertheless, our modeling shows that both the fault types and geometries primarily affect stress distribution rather than amplitude of ΔCFS (Figs. S10 and S11), and stress changes caused by the LDLs are larger at shallower depths (Fig. S11). Considering ~64% of the ~145 LDLs in the global database with documented duration lasted more than 11 days before dam breach (Fig. 3b) with no correlation with dam height (Fig. S12), our modeling suggests that other LDLs globally have the potential to trigger earthquakes if there are critically stressed faults nearby.

Methods
Earthquake catalog building
We adopt an AI-based workflow to develop a new earthquake catalog from 2014 to 2023 based on the 13 permanent seismic stations57 (Fig. 1). We first use the machine-learning-based detector, PhaseNet58, to identify P- and S-wave arrival times from the continuous waveforms. Subsequently, these P- and S-wave arrival times are associated into earthquake events using PyOcto59, resulting in 6692 earthquakes within a region of 2.5° × 3° (latitude: 30° to 32.5°; longitude: 97° to 100°). We then manually inspect the waveforms of 859 earthquakes around our target area (latitude: 30.7° to 31.7°; longitude: 98.1° to 99.2°) to exclude 112 non-tectonic or unreasonably associated events. We then use the absolute location method Hypoinverse61 to further refine the hypocenters of the remaining 747 events and calculate their location uncertainties.

We also estimate the local magnitudes for all retained earthquakes based on their S-wave amplitudes and a recently improved national standard magnitude scale that is specific to the Sichuan region, China62,63. The maximum amplitudes of horizontal component waveforms are measured after deconvolving the instrument response from the raw waveforms and then convolving the obtained signal with the theoretical Wood–Anderson seismometer response. The measured waveform window starts 0.5 s before the P wave arrival and is twice the predicted S–P travel time in length. Note that we only estimate magnitudes for 669 events with at least two stations having signal-noise ratio larger than 3. The estimated magnitudes range from 1.1 to 4.2. The 1-D velocity model used in the above absolute earthquake location was adopted in GPU-M&L as well. Note that in GPU-M&L, we relocate the epicenters of detections through a grid search method with searching space 1.2 × 1.2 km in the horizontal direction and searching interval of 0.06 km if template and continuous waveforms were recorded by at least three seismic stations. Otherwise, the locations of detections will be defined as that of the templates. By manually inspecting these detections, the detection threshold is defined as correlation coefficient of 0.3 and 12 times median absolute deviation (MAD) if the common component number between template and continuous waveforms is ≥ 9. Otherwise, the detection threshold is defined as correlation coefficient of 0.5 and 15 times MAD. In total, GPU-M&L resulted in 4294 detections including the 669 template events. The magnitudes of the newly detected earthquakes are estimated based on the local magnitudes of the templates and the amplitude ratio between these detections and their corresponding templates65. Note that due to the poor local seismic station coverage with available data before May 2018, 22 earthquakes that occurred from March 2014 to May 2018 in the routine catalog, which utilized data from the entire China, were not detected. Thus, these missing earthquakes are manually added to our earthquake catalog.

Declustering and seismicity rate change analysis
Using the approach from Reasenberg41, we identified 5 clusters of earthquakes containing a total of 13 events (5 main earthquakes and 8 foreshocks/aftershocks) out of 62 events which occurred over ~5 years, using the following input parameters41: look-ahead time from 0.5 to 3 days, confidence probability of 0.9, effective min magnitude cutoff of 1.1, the increase in lower cutoff magnitude during clusters of 0, and the number of crack radii surrounding each earthquake of 5.

We then evaluate the statistical significance of the observed seismicity rate change based on statistic P (ref. 42) and statistic Z (ref. 43). The statistic Z is defined as follows:

Z = (N/tN - M/tM) / sqrt(N/tN^2 + M/tM^2) (1)

Where N and M represent the number of earthquakes after and before an event in time windows Δt N and Δt M, respectively. When N and M are sufficiently large and in the null hypothesis of no seismicity rate change, Z follows a Gaussian distribution with zero mean and unit standard deviation. Statistic Z was first proposed by Habermann43 to evaluate the statistical significance of seismicity rate changes. After declustering, there were 9 earthquakes in the week (10 to 16 November) when the second LDL approached its peak water level. There were only 8 earthquakes in the previous 6 months (~27 weeks) which translates to a seismicity rate of 0.3 events/week. Based on Eq. 1, we obtain a Z value of 2.90 taking N, M, Δt N, and Δt M as 9, 8, 1, and 27, respectively. A change is considered statistically significant if |Z| > 2 (ref. 43), and our observed seismicity rate increase after declustering41 is statistically significant at a 99.62% level based on statistic Z.

In the null hypothesis that the seismicity rate in the week after (Poisson process with mean rate λ N) and the week before (Poisson process with mean rate λ M) an event is the same, the statistic P reads:

P(λ N > λ M) = 1 - ∑ (N! M! / (N+M)!) ∫ (e^-x x^M Γ(N+1, x) dx) (2)

Where Γ(n, x) = ∫ t^n-1 e^-t dt is the incomplete Gamma function and follows a uniform distribution between 0 and 1 (ref. 42). 1-P gives us the probability that an observed value could be obtained by chance if the null hypothesis of no rate change is true42. While there were no earthquakes in the ~1 month before the second LDL, we still take the seismicity rate for the week before the second LDL approached its peak water level as 0.3 events/week based on the average seismicity rate in the previous 6 months to be conservative. Based on Eq. 2, we obtain a P value of 0.9982 taking N and M as 9 and 0.3, respectively. This implies that the probability that our observed seismicity rate increase occurred by random chance is 0.18%. Therefore, our observed seismicity rate increase after declustering41 is statistically significant at a >99.82% level based on statistic P.

We further evaluate the statistical significance of the observed seismicity rate change based on both an improved statistic based on Poisson probability44 and an empirically derived statistic45 which were developed to determine statistically significant changes in earthquake rate under small background rate. We assumed that earthquakes occur independently at a constant rate, following a Poissonian distribution44. To determine the statistical significance of seismicity rate increase, we compare the number of expected earthquakes in a 1-week window to the number of earthquakes in the 1-week window after the trigger and calculate the Poisson probability of obtaining the number of earthquakes (ν) in the 1-week window after the trigger given the expected number of events (μ) in the 1-week window.

P(ν) = e^-μ μ^ν / ν! (3)

For this case of low background seismicity rate, similar to the idea of ref. 44, we conservatively regard the largest number of earthquakes (3) in a 1-week window over our observation period, except for this earthquake sequence, as the expected number of events (μ) in a 1-week window. Based on Eq. 3, we obtain a P value of 0.0027 taking μ and ν as 3 and 9, respectively. This implies that our observed seismicity rate increase after declustering41 is statistically significant at a >99.73% level.

We also use the empirical statistical method of ref. 45 to determine the significance in the seismicity rate change. First, we count the number of earthquakes in each 1-week time window incorporating a 1-day sliding window. There are >1700 windows from May 2018 to January 2023. We then assign the number of earthquakes N count within each window to a timestamp at the start of the window. We next build a histogram of N count values (Fig. S6). Finally, using percentile measurements, the >99% statistically significant level is 3 earthquakes in a 1-week window. We observed 9 earthquakes (after declustering) as the second LDL approached the peak water level, hence this seismicity rate increase is statistically significant at a >99% level.

We also tested the impact of different input parameters on the declustering based on the approach from Reasenberg41. We identified 4 clusters of earthquakes containing a total of 16 events (4 main earthquakes and 12 foreshocks/aftershocks) out of 62 events which occurred over ~5 years, using other suggested input parameters41: look-ahead time from 1 to 10 days, confidence probability of 0.95, effective min magnitude cutoff of 1.5, the increase in lower cutoff magnitude during clusters of 0.5, and the number of crack radii surrounding each earthquake of 10. While the declustered earthquake catalogs with different input parameters are different, we further confirm that this seismicity rate increase is statistically significant at a >~90% level based on the four above statistical tests (Table S1).

Coulomb stress change calculation
Coulomb stress change (ΔCFS) on the surrounding fault systems due to the LDL is a result of the combined effect of direct gravitational loading and pore pressure diffusion. We model ΔCFS due to both direct loading and pore pressure diffusion using the GeoTaos software66. Since the direct gravitational loading effect can be regarded as the result of point forces acting vertically on the surface of a homogeneous elastic half-space, the loading from the LDL can be calculated by the convolution of the Green’s function and the distributed surface forces. The distributed surface forces can be estimated based on the spatiotemporal evolution of the LDL’s water level. To quantify the spatiotemporal evolution of the LDL’s water level, the LDL is mapped as a series of square cells with a size of 200 by 200 m. The elevation of each square cell is estimated from the GDEM V3 30 m. Based on the elevation of each cell, the water depth of each cell can then be estimated. Therefore, the distributed surface forces and thus the direct gravitational loading effect of each cell can be calculated using the water depth of each cell. Note that we ignore the ΔCFS resulting from gravitational loading of landslide sediments, since these landslide sediments are not a new source of mass but only the very local redistributions (~1–2 km) of sediments along the landslide sliding path.

Uncertainty analyses
Before more seismic stations became operational in May 2018, no earthquakes were detected within 10 km of the LDLs due to limited station coverage and/or low seismicity rate. Nevertheless, in the ~250 weeks of observation period since May 2018 for which we have an improved earthquake catalog, 61 earthquakes occurred within 10 km of the LDLs during the week when the second LDL’s water level almost peaked, while only 183 earthquakes occurred in the period of ~247 weeks in the background. Therefore, our catalog shows that the seismicity rate during the LDL is significantly higher than the background seismicity rate of the region. We chose to focus on earthquakes that occurred within 10 km of LDLs since the region with stress increase of >0.01 MPa is always located within 10 km of the LDLs (Fig. 2a). Nevertheless, the earthquake activity within larger and smaller regions shows a similar accelerated trend during the landslide hazard cascades (Fig. S16).

As the second LDL approached peak water level, ~50% and ~95% of the hypocenters in the earthquake sequence were at depths of <1.2 and <4.5 km, respectively (Fig. S8). Similarly, for the earthquake catalog before template matching, the median depth of these triggered earthquakes is ~1.2 km (Fig. S8). However, the mean horizontal and vertical location uncertainties of our cataloged earthquakes are ~4 and ~8 km, respectively. To further constrain the likely depths of these events, we look at the larger earthquakes which are more accurately located since they are recorded by more stations. We find that the median depth of all M > 1.1 earthquakes during the second LDL is ~1.5 km with average depth uncertainty of ~6 km. Our modeling shows that ΔCFS down to a depth of 7 km can reach levels that trigger earthquakes (Fig. S11d), and the ΔCFS is larger at shallower depths (Fig. S11). Furthermore, ~60% of reservoirs with documented earthquake depths have induced earthquakes up to ~8 km depth (Fig. S17). Therefore, we conclude that the earthquake sequence can be triggered by stress changes due to the LDL.

The stress change on surrounding faults due to the LDLs partly depends on the fault geometry. In contrast to the well-documented fault strike, the dip of the fault is less well constrained. We assume a fault dip of 75°NE based on the focal mechanisms of four M > 3.5 earthquakes nearby and the consistency of the first motions of the two largest earthquakes (ML 2.6 and 1.9) as the second LDL approached peak water level with these focal mechanisms (Fig. S7), though we cannot confirm that the focal mechanisms of the smaller earthquakes necessarily share similar geometries. Nevertheless, our modeling shows that the fault dip mainly affects the spatial distribution and amplitude of ΔCFS but not its sign, and the seismicity generally locates within regions of positive ΔCFS for a range of different assumed fault dips (Fig. S11e–h). Hence, the dip uncertainty has minimal effect on our conclusion that landslide hazard cascades can trigger earthquakes.

The stress change on surrounding faults caused by LDL is also related to the fault friction coefficient and the fluid diffusion coefficient. We assumed a friction coefficient of 0.5 for our ΔCFS modeling. However, the chosen friction coefficient has minimal effect on both the spatial distribution and amplitude of ΔCFS (Fig. S18). In addition, due to differences in rock properties and depth-dependent confining pressure, crustal hydraulic diffusivity has been found to range from 0.01 to 5 m2/s (refs. 67,68). Both the geometry and closure of faults and fractures also cause significant spatial variation in hydraulic diffusivity69,70. These factors make it challenging to obtain a precisely constrained hydraulic diffusivity for the calculation of ΔCFS. Nevertheless, higher fluid diffusivity causes the pore water pressure to increase faster, which increases the amplitude of ΔCFS over a wider area. Our chosen value of 0.3 m2/s is on the lower end of observed values and is a typical value observed in fluid-driven seismic swarms in different regions71–73. While hydraulic diffusivity strongly influences the time at which ΔCFS exceeds a certain threshold, we further confirm that ΔCFS exceeds 0.01 MPa for hydraulic diffusivities ranging from 0.02 to 2 m2/s. On the day of peak seismicity rate, the relative contribution to ΔCFS of pore pressure increases from ~0.1 to 0.9 as the assumed hydraulic diffusivity increases from 0.02 to 2 m2/s (Fig. S14). We conclude that our main conclusion that LDLs can trigger earthquakes is robust to changes in the discussed parameter choices.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "• What are the noteworthy results?\nThis is generally a well wriften paper with a provocafive suggesfion, that landslides could potenfially\ncreate a large enough of stress disturbance that will trigger earthquakes. This assertafion is not far-\nfetched, as we see many are documenfing induced seismicity throughout the world, from gas\nextracfions, enhanced oil recovery, hydraulic fracturing, reservoir induced seismicity, and even seismicity\nfrom glacial retreat. However, this work depends heavily on the earthquake catalog that the authors did\nnot produce, and I worry that all of uncertainfies are not explored, making the case very weak. In its\ncurrent state, I cannot recommend this paper for publicafion.\n• Does the work support the conclusions and claims, or is addifional evidence needed?\nThe previously exisfing seismic network was enhanced in May 2018, and because of this, the sensifivity\nof the network changed, allowing for more small magnitude earthquakes to be detected and located.\nThus, it is difficult to determine the background seismicity rate prior to the landslide in Nov. 2018, and\nthe seismicity rate of the region in general. Furthermore, the authors do not plot the stafion distribufion\n(before or after May 2018), and the depth uncertainfies are not stated. If these events are deep in the\ncrust, making the case for induced seismicity becomes very difficult. Even if they were shallow, we have\nno idea of the stafion distribufion and true depth uncertainly, plus the diffusivity should be known to\nmake any connecfion to water migrafion and the fiming of the proposed induced seismicity. To have\ngood depth determinafion, a seismic stafion must be within a focal depth to have any chance of\nconstraining depth, plus having a well calibrated velocity model is crifical for accurate depth esfimates.\nThere is no menfion of the stafion distribufion, the local velocity model, the locafion errors, and the\nnumber of stafions that recorded the events. Furthermore, these are catalog events, and perhaps the\nseismicity is clustered near the landslide itself. Using an approach like HypoDD (double difference) might\nshow that the events are clustered spafially, invalidafing the argument that the events are spread\nthroughout the region of inundafion. None of these locafion approaches are explored; thus, the\ncorrelafion with the landslide is tenuous at best. Lastly, all of the triggered events seem to be less than\nM1.4. These are micro earthquakes, and they are difficult to locate and analyze. The seismology for\nthese earthquakes will have to be more clearly documented for this work to be convincing.\n• Are there any flaws in the data analysis, interpretafion and conclusions? Do these prohibit publicafion\nor require revision?\nAlthough not under the author’s control, the number and magnitude of earthquakes are small, and\nrunning stafisfics on these small numbers is difficult. The authors decluster the catalog and use a couple\nof stafisfical methods to determine a change in seismicity rate. Complicafing this, associafing the events\nto the water inundafion caused by landslide proves difficult given the fime delay (two weeks) before the\nonset of seismicity. I would explore the use of other stafisfics used for dynamic triggering studies (works\nof Z. Peng, K. Pankow, R. Alfaro-Diaz, D. Kilb, E. Brodsky). If these events are indeed triggered, they would\nbe classified as delayed triggering, which even is harder to show stafisfically. Finally, seismicity also\nappears widespread in the region, not necessarily on the faults. Again, this may be the result of poor\nlocafions. There is simply no way to assess given the informafion given in the study.\n• Is the methodology sound? Does the work meet the expected standards in your field?\nStress modeling also depends on assumed faults. The fault informafion also appears not well\ndocumented (orientafion of the faults are not known). Determining focal mechanism would help, but\nthese are small earthquakes. Perhaps a composite focal mechanism can be used to determine what the\nstress direcfion is that would be released with increase pore pressure. Furthermore, how deep are these\nfaults, and how long would it take for the water to reach these faults?", "reviewer_2": "Zhang et al. focuses on the potenfial impact of landslide-dammed lakes on the triggering of earthquakes\non nearby faults. The paper is easy to read and addresses an interesfing issue, which I feel deserves to\nreceive the aftenfion of a high-impact journal. Too few studies have indeed focused on the impact of\nsurface processes during extreme events on the triggering of earthquakes and deformafion. I was\ntherefore thrilled to receive this paper for a review.\nUnfortunately, I have found too many major weaknesses that at this stage prevent, in my opinion, the\npaper from being published. Despite that, I also feel that most of these major issues can be thoroughly\naddressed by the authors, and I therefore would ask the editor and authors to consider a phase of major\nrevisions, but not necessarily of rejecfion (or otherwise with the opportunity for resubmission). I want to\nthank the authors for this interesfing manuscript, and I hope they will receive most of these comments\nas a means to increase the quality of their manuscript, and not only as a crificism.\nI first summarize below my main comments and then describe my other comments line-by-line.\nWith my best regards,\nPhilippe Steer\nMain comments:\n• False claim of the manuscript: The manuscript repeats several fimes (lines 14-15, 49-52, in conclusion\nas well) that this is the first fime that a link between surface hazards/processes (or erosion or landslides)\nand the triggering of earthquakes is made. This is simply wrong and surprising to see this affirmafion, as\nseveral visible papers in high-impact journals were published on this subject during the last 15 years:\nCalais et al. (2010 - Nature), Steer et al. (2014 - Nature Communicafions), Steer et al. (2020 - Scienfific\nreports), Jeandet Ribes et al. (2020 - GRL), and probably others. Moreover, several papers have already\nshown that lake water variafion can impact seismicity and trigger earthquakes (Gough & Gough, 1970;\nKebeasy & Gharib, 1991; Simpson et al., 2018; and many more). This paper is therefore not the first one\nto address the issue of the triggering of earthquakes because of surface hazards, landslides, or erosion,\nnor it is the first one to show the impact of lake water level fluctuafion on earthquake triggering. The\nmanuscript by Zhang et al. therefore needs to account for these previous studies, in parficular in the\nfitle, introducfion, discussion and conclusion, and to correct the importance of their study respecfively\nto what was already demonstrated by these previous studies. This manuscript is however the first one (if\nI have not missed a previous arficle) to address the issue of the response of seismic acfivity to landslide-\ndammed lakes filling. But this is largely different from what the current manuscript claims.\n• Issue with declustering: The manuscript uses two classical approaches to decluster the earthquake\ncatalog they invesfigate. However, only 3 over 39 earthquakes are idenfified as aftershocks and removed\nfrom the catalog. This is a very unusually low number of earthquake removal by declustering. I idenfify\ntwo issues that need to be addressed by the manuscript: 1) The manuscript does not menfion the values\nof the numerous parameters of the Reasenberg algorithm (the minimum look-ahead fime for building\nclusters, the maximum look-ahead fime for building clusters, a confidence probability, the effecfive lower\ncutoff magnitude, the increase in lower cutoff magnitude during clusters, and the number of crack radii\nsurrounding each earthquake), while these parameters can have a profound impact on the results of the\ndeclustering; 2) The manuscript seems to ignore the earthquakes occurring outside the study area or\npreviously to 2018. This is problemafic has these un-considered earthquakes have local magnitude up to\n5, while the largest earthquake in the space-fime window considered is only a magnitude of 1.4 (which is\nextremely low). It is unclear to me that there is no stafisfical link between what is observed in the study\narea and what occurred before or outside. The manuscript needs to befter address this issue and\ndemonstrate that there is no link.\n• Computafion of pore pressure and the issue of fime variafion: The manuscript uses (in its main text)\nonly one value of the coefficient of pore pressure diffusion D but evaluates the DCFS obtained when\nchanging this coefficient D in the supplementary. On Fig 2 c, one can indeed observe that the modeled\nsignal of pore pressure change, with D=0.3 m2/s could be a good candidate for explaining the observed\nchange in earthquake frequency. However, not only does the amplitude of the pore pressure signal\nchanges with D, but the diffusion fimescale also as it scales with L/sqrt(D), with L being the distance\nbetween the pore pressure source and the observed change in pore pressure. And it is relafively well\nadmifted that D is not well constrained and could vary by orders of magnitude (which the manuscript\nfairly menfions lines 206-210). This means that the fiming of when pore pressure increases or peaks is\ndirectly determined by D. There is in my opinion, no clear reason to choose D=0.3, except that it gives a\ngood match with the change in earthquake acfivity. But using this argument would lead to a circular\nargument, which must be avoided. I would like the authors to account for the issue of the fiming of pore\npressure change, and to show/discuss the impact of changing pore pressure through fime. The\nmanuscript also needs to clearly menfion/explain to what temporal state their maps of DCFS or pore\npressure refer to (I have not found this informafion in the manuscript).\n• Heterogeneous value of the coefficient of pore pressure diffusion: Moreover, the value of D changes\nspafially, in parficular in areas crossed by faults or structural disconfinuifies (which is the case of this\nstudied area where a fault is almost below the lake). This means that the spafial and temporal response\nto the filling of the lake is probably not the one of a homogeneous medium. The authors do not menfion\nthis possibility, nor discuss the implicafions of this heterogeneity.\n• The issue of depth: As shown by Figure S6, most earthquakes possibly triggered by the filling of the\nLDLs are located at a depth deeper than 5 km (about 6 km below the surface). This is puzzling, as the\nDCFS is likely to be significantly higher closer to the surface. Steer et al. (2014) or De Novellis et al. (2020,\n2021) have clearly shown this dependency on depth. And some earthquakes can occur at shallower\ndepths than 5-6 km. For instance, De Novellis et al. (2020) reports a depth of 1-2 km. So, my quesfion is\nwhy the earthquakes you believe were triggered by filling of the LDLs do not occur at shallower depths,\nwhere the DCFS and pore pressure are likely to be of greater amplitude? This study need to make a clear\ninvesfigafion of the role of depth on DCFS and pore pressure (accounfing for fime as well), to show\nwhether the earthquakes occur at an opfimal depth, and if it is note the case, if other factors (such as\nthe rheological nature of the faults – for instance the a and b parameters of the rate-and-state law)\nprevent earthquakes occurring at shallower depths than the one observed. A second quesfion: what is\nthe uncertainty of the depth esfimate of these earthquakes? Generally, the depth is less well constrained\nthan the horizontal posifion.\n• Issue with the global study on the effect of LDL: the last part of the manuscript is dedicated to\ninvesfigafing how LDL could globally impact seismicity. However, I am not convinced by this part. First,\nthe manuscript considers that all LDLs occur in a similar structural-tectonic sefting, dominated by strike-\nslip faults, while this is likely to be incorrect. What would be the effect of considering normal or reverse\nfaults? The localizafion of the faults and the orientafion of the plane also significantly mafters, but this is\nnot considered in the manuscript. This study really needs to go deeper into this issue, or otherwise\nremove it as it is currently unconvincing.\n• The paper correctly menfions that the geometry of the faults (except that they are likely in strike-slip\nregimes) are unknow. This study needs either to test the sensifivity of the DCFS results to the geometry\nat depth of the faults or to propagate the uncertainty on the geometry of these faults on the obtained\nvalues of DCFS.\nLine comments:\n• Lines 70-71 “deposited 2.5 x 10^7 m3 of sediments intor the river” – How do you know?\n• Line 72 “upstream inflow of 1,680 m3/s” – Same, how do you know?\n• Lines 72-75 – How were all these measurements obtained? Gauging stafions, geotechnical reports, … ?\n• Line 83 “Nafional Earthquake Data Center” – of which country?\n• Lines 108-109: It is generally recommended to use more than 100 earthquakes to characterize mc and\nb.\n• Lines 206-209: “S5). In addifion, since crustal hydraulic diffusivity has been found to range from 0.01 to\n5 m2/s (ref.45,46),we conservafively assume a diffusion coefficient of 0.3 m2/s” – In this case this is not a\nconservafive esfimate – please correct.\n• Lines 226-227: “Wenchuan earthquake triggered more than 10,000 landslides” - Available landslide\ncatalogs point towards more than 100,000 landslides and near 200,000 (e.g, Xu et al., 2014). Of course\nthere is a large uncertainty, but sfill, more than 10,000 does not make jusfice to the esfimated number of\nlandslides.\n• Lines 229-232: Reading these two sentences can wrongly give the impression to the reader that these\nnumerous post-Wenchuan earthquakes were triggered by LDLs, which is obviously wrong. Of course,\nthere are some aftershocks after a Mw7.9 mainshock. The effect of LDLs, if demonstrated, is likely to be\nnegligible by orders of magnitude.\n• Line 240-241: “Since landslide materials are denser than water, landslides smaller than our LDLs can\nresult in comparable DCFS.” - Since landslides do not represent a new source of mass (but only the very\nlocal displacement of material, along the landslide path), this statement is likely wrong (except for very\nshallow faults of a few 100 m depths at more). The removal by erosion and sediment transport could\nplay a role (Steer et al., 2020; Jeandet-Ribes et al., 2020), but this is different from what is menfioned\nhere.", "reviewer_3": "This manuscript aims to understand the potenfial link between the Baige landslide dam and triggered\nsmall earthquakes in this region. It‘s intriguing to explore the interacfion between earthquakes and\nsurface hazards. The Baige landslide dam may indeed trigger some small earthquakes, but the current\nevidence is insufficient or inconclusive. Firstly, the observafion period in 2018-2022 is relafively short and\nthe network coverage is not shown in this study. Secondly, the limited number of events (39 with\nML<=1.4) near the LDLs may not be representafive of the earthquake acfivity in the study region.\nThirdly, the esfimate of Mc for 0.3 may not be reliable from the frequency-magnitude distribufion of\nevents with ML mostly less than 1 and a limited number of earthquakes (< 50). The locafions of potenfial\ntriggered earthquakes seem to be best correlated with the area with posifive stress caused by the pore\npressure changes than the stress due to the change of surface loads. It remains unclear whether fluids can\ninfiltrate to the median hypocentral depth of 6 km within ~10 days. My other comments are listed below\nLines 69-71: To give a befter overview of the Baige landslide dam, authors can provide a few photos of\nlandslide-dammed lakes (e.g. photos shown in Zhang et al. Landslides, 2019) in the supplementary\nmaterials. It is not easy to follow the descripfion of texts in Lines 70- 101 without a good figure. How\nlandslide materials distribute in space during the first and second landslides and where the LSDs are\nlocated during two sliding events?\nLines 104-109: Please plot the locafion of seismic stafions in Figure 1. The Baige landslide occurred on\nthe Tibetan plateau where the stafion coverage may be insufficient to have the magnitude of\ncompleteness (Mc) of 0.3. In addifion, most events have magnitudes ranging from 0 to 1 (Fig. 1b), is the\nvalue of Mc a robust esfimate? Given only 48 events in May 2018 – Dec. 2022 and 36 events left after\nperforming declustering, the temporal paftern of seismicity may be quesfionable.\nLines 113-114 The authors need to provide a detailed figure showing the fime series of earthquake\nnumber and water level (daily sampling?) in the week of 12 to 18 November after the second LDL\napproached its peak water level. Why they choose earthquakes within 15 km of the LDLs but not a larger\nor smaller area? Are those chosen earthquakes shown as green dots in Fig. 2? Figure 1 shows\nearthquakes in this region and the seismicity acfivity seems to be high to the southeast of the study area\nwith a subtle influence of LDLs. If authors choose earthquakes in different regions, how figure 2b varies\naccordingly?\nLine 127-137, Please shows the locafions of earthquakes before and after performing declustering. After\ndeclustering, where and how deep are the remaining eight earthquakes located? As authors claimed the\nlargest magnitude (ML) is 1.4 during their observafion period, maybe declustering is not necessary. Since\nthere are only eight events (within 15 km of LDLs) left after declustering, I’m not sure the stafisfic test for\nthe significance of increasing seismicity rate is meaningful given very few earthquakes in this period.\nLines 140-148: Since most earthquakes occurred after the second LDL are very small (ML<1.4), it is\nunclear whether these earthquakes truly occurred on the surrounding fault system. Is the Coulomb\nstress esfimated at the depth of 6 kn in Fig. 2a? If so, please add it in the figure capfion.\nLines 149-159: Please add a new figure to show the earthquake number from Nov. 10th to 20th where\nmost earthquakes occurred. The stress due to fluid pressure diffusion reached peak about 12-13 days\nafter the formafion of landslide dam on Nov. 3rd. However, most of the hypocentral depths range from 5\nto 15 km (median at 6 km) and it is unclear whether fluids can infiltrate to such great depths within ~10\ndays. About 80% of the earthquakes locate within regions of posifive ΔCFS (Fig. 2a). However, the ΔCFS in\nFig. 2a is mainly contributed by fluid pressure diffusion instead of direct loading.\nLine 179: What are the minimum and median heights of reservoirs?\nLine 180-181: Fig 3a show the height of LDLs which induced earthquakes are generally lower than the\nheights of reservoirs induced earthquakes. I don’t understand the logic of “Therefore, a significant\nnumber of LDLs globally are of similar heights as reservoirs which induced earthquakes.”\nLine 286: How did authors obtain distributed surface forces?\nFigure 1 is not very informafive. Please mark the downstream direcfion. A more detailed map of LDLs."}, "author_response": "Response to Reviewer #1:\n• What are the noteworthy results?\nThis is generally a well written paper with a provocative suggestion, that landslides\ncould potentially create a large enough of stress disturbance that will trigger\nearthquakes. This assertation is not far-fetched, as we see many are documenting\ninduced seismicity throughout the world, from gas extractions, enhanced oil recovery,\nhydraulic fracturing, reservoir induced seismicity, and even seismicity from glacial\nretreat. However, this work depends heavily on the earthquake catalog that the authors\ndid not produce, and I worry that all of uncertainties are not explored, making the case\nvery weak. In its current state, I cannot recommend this paper for publication.\nWe would like to thank you for the specific and constructive comments you provided\nfor this manuscript. These comments are really helpful and greatly improve this\nmanuscript. We are honored that you are interested in our results and agree that a high-\nquality earthquake catalog is critical for strengthening our main conclusion that\nlandslide hazard cascades can trigger earthquakes. Therefore, in the revised manuscript,\nbased on the continuous seismic waveforms from January 2014 to January 2023,\nwe use machine learning and cross-correlation-based methods to build an earthquake\ncatalog which contains ~5 times more events than the previously presented catalog. We\nfind that ~61 earthquakes of magnitudes up to 2.6 occurred in the week when the second\nlandslide-dammed lake LDL was near peak water level, substantially strengthening our\nmain novel conclusion that landslide hazard cascades can trigger earthquakes.\nFurthermore, we discuss in detail the uncertainties in earthquake location and stress\ncalculations based on this high-quality earthquake catalog and confirm that our main\nconclusions still stand after considering these uncertainties. We believe that this revised\nmanuscript has addressed your major concerns and look forward to receiving further\nfeedback.\n• Does the work support the conclusions and claims, or is additional evidence needed?\nThe previously existing seismic network was enhanced in May 2018, and because of\nthis, the sensitivity of the network changed, allowing for more small magnitude\nearthquakes to be detected and located. Thus, it is difficult to determine the background\nseismicity rate prior to the landslide in Nov. 2018, and the seismicity rate of the region\nin general.\nThank you for your comments. We used cross-correlation and machine learning based\nmethods to build an enhanced earthquake catalog from January 2014 to January 2023\nwhich allows good estimation of the background seismicity rate of the region.\nBefore more seismic stations became operational in May 2018, no earthquakes were\ndetected within 10 km of the LDLs due to limited station coverage and/or low seismicity\nrate. Nevertheless, in the ~250 weeks of observation period since May 2018 for which\nwe have an improved earthquake catalog, 61 earthquakes occurred within 10 km of the\nLDLs during the week when the second LDL’s water level almost peaked while there\nwere only 183 earthquakes over the ~247 weeks outside the time period of the two LDLs\ni.e., a background seismicity rate of only ~0.7/week over ~5 years (Table S1). Therefore,\nour catalog shows that the seismicity rate during the LDL is significantly higher than\nthe background seismicity rate of the region.\nFurthermore, the authors do not plot the station distribution (before or after May 2018),\nand the depth uncertainties are not stated. If these events are deep in the crust, making\nthe case for induced seismicity becomes very difficult. Even if they were shallow, we\nhave no idea of the station distribution and true depth uncertainly, plus the diffusivity\nshould be known to make any connection to water migration and the timing of the\nproposed induced seismicity. To have good depth determination, a seismic station must\nbe within a focal depth to have any chance of constraining depth, plus having a well\ncalibrated velocity model is critical for accurate depth estimates. There is no mention\nof the station distribution, the local velocity model, the location errors, and the number\nof stations that recorded the events. Furthermore, these are catalog events, and perhaps\nthe seismicity is clustered near the landslide itself. Using an approach like HypoDD\n(double difference) might show that the events are clustered spatially, invalidating the\nargument that the events are spread throughout the region of inundation. None of these\nlocation approaches are explored; thus, the correlation with the landslide is tenuous at\nbest. Lastly, all of the triggered events seem to be less than M1.4. These are micro\nearthquakes, and they are difficult to locate and analyze. The seismology for\nthese earthquakes will have to be more clearly documented for this work to be convincing.\nThank you for these comments. We now show the distribution of seismic stations in Fig.\n1.\nFig. 1 | Study site and seismicity. a Distribution of seismic stations. Red box marks\nthe region covered by the earthquake catalog we built. Black and green triangles\nindicate seismic stations that started operating since January 2014 and May 2018,\nrespectively. b Map of seismicity from January 2014 to January 2023. Red beach\nballs depict focal mechanisms available from the National Earthquake Data Center of\nstrike-slip earthquakes39. Red and gray dots represent earthquakes which occurred\nwhen the second landslide-dammed lake (LDL) almost reached peak water level and\nearthquakes beyond that, respectively. Red box marks the region shown in (d). c\nMagnitude-frequency distribution of earthquakes from May 2018 to January 2023\nwithin 10 km of the LDLs. Magnitude of completeness (Mc) and a- and b-values\nwere calculated using the ZMAP software40. d Distribution of earthquakes from May\n2018 to January 2023 within 10 km of the LDLs. Red and gray dots represent\nearthquakes that occurred when the second LDL almost reached peak water level and\nearthquakes beyond that, respectively.\nWe also introduce the methods of earthquake detection, location, magnitude calculation,\nand discuss the location uncertainties in detail.\nWe adopt an AI-based workflow to develop a new earthquake catalog from 2014 to\n2023 based on the 13 permanent seismic stations57 (Fig. 1). We first use the machine-\nlearning-based detector, PhaseNet58, to identify P- and S-wave arrival times from the\ncontinuous waveforms. Subsequently, these P- and S-wave arrival times are associated\ninto individual earthquakes using a high-throughput seismic phase associator,\nPyOcto59, and a local 1-D velocity model60. A threshold of two P picks, one S pick, and\na total of five P and S picks is adopted during the PyOcto association, resulting in 6,692\nearthquakes within a region of 2.5° × 3° (latitude: 30° to 32.5°; longitude: 97° to 100°).\nWe then manually inspect the waveforms of 859 earthquakes around our target area\n(latitude: 30.7° to 31.7°; longitude: 98.1° to 99.2°) to exclude 112 non-tectonic or\nunreasonably associated events. We then use an absolute location method\nHypoinverse61 to further refine the hypocenters of the remaining 747 events and\ncalculate their location uncertainties.\nWe also estimate the local magnitudes for all retained earthquakes based on their S-\nwave amplitudes and a recently improved national standard magnitude scale that is\nspecific to the Sichuan region, China62,63. The maximum amplitudes of horizontal\ncomponent waveforms are measured after deconvolving the instrument response from\nthe raw waveforms and then convolving the obtained signal with the theoretical Wood-\nAnderson seismometer response. The measured waveform window starts 0.5 seconds\nbefore the P wave arrival and is twice the predicted S–P travel time in length. Note that\nwe only estimate magnitudes for 669 events with at least two stations having signal-\nnoise ratios of S waves larger than 3. The estimated magnitudes range from M 0.1 to\nL\n4.2.\nTo further improve the magnitude of completeness, we use a template matching\ntechnique, Graphics Processing Unit-based match and locate technique (GPU-M&L)64,\nto detect and locate more earthquakes based on the 669 retained earthquakes with\nestimated magnitude. P- and S-waves of these events are simultaneously used in GPU-\nM&L. The length of template window is 6 s starting 1 s before the P- and S-wave\narrivals picked by PhaseNet. We filter the continuous and template waveforms from 2\nto 8 Hz. The 1-D velocity model used in the above earthquake absolute location was\nadopted in GPU-M&L as well. Note that in GPU-M&L, we relocate the epicenters of\ndetections through a grid search method with searching space 1.2 km × 1.2 km in the\nhorizontal direction and searching interval of 0.06 km if template and continuous\nwaveforms were recorded by at least three seismic stations. Otherwise, the locations of\ndetections will be defined as that of the templates. By manually inspecting these\ndetections, the detection threshold is defined as correlation coefficient of 0.3 and 12\ntimes median absolute deviation (MAD) if the common component number between\ntemplate and continuous waveforms is ≥ 9. Otherwise, the detection threshold is\ndefined as correlation coefficient of 0.5 and 15 times MAD. In total, GPU-M&L resulted\nin 4,295 detections including the 669 template events. The magnitudes of the newly\ndetected earthquakes are estimated based on the local magnitudes of the templates and\nthe amplitude ratio between these detections and their corresponding templates65. Note\nthat due to the poor local seismic station coverage with available data before May 2018,\n22 earthquakes that occurred from March 2014 to May 2018 in the routine catalog,\nwhich utilized data from the entire China, were not detected. Thus, these missing\nearthquakes are manually added to our earthquake catalog.\nWe also attempted to use HypoDD to relocate the seismic events we detected. However,\ndue to the limited seismic station coverage, many outliers appear in the relocation\nresults hence we decided not to include the HypoDD results in the manuscript.\nNevertheless, our new enhanced earthquake catalog shows that the earthquakes during\nthe landslide hazard cascades were closely related to the LDLs in space (Fig. 2a) and\ntime (Figs. 2c and S2) after location and depth uncertainties are taken into account,\nwhich supports our main conclusions:\nFig. 2 | Earthquakes triggered by 2018 Baige landslide-dammed lake. a Spatial\ndistribution of Coulomb stress change (∆CFS) at depth of 4.5 km corresponding to -0.5\nkm asl on 13 November 2018 and earthquakes from 10 November to 16 November 2018\nwithin 10 km of the landslide-dammed lakes (LDLs). ∆CFS is from the combined effect\nof direct gravitational loading and fluid pressure diffusion (Fig. 2d). b Cumulative\nnumber of earthquakes and weekly seismicity rate over a five-year period. Arrows mark\nthe timings of the two 2018 Baige landslides. c Earthquake magnitudes and LDL water\nlevel over a fifty-day period. d Temporal evolution of ∆CFS and pore pressure at point\nP (Fig. 2a).\nFig. S2 | Daily seismicity rate, earthquake magnitudes, and LDL water level over a\ntwenty-day period.\nAs the second LDL approached peak water level, ~50% and ~95% of the hypocenters\nin the earthquake sequence are at depths of <1.2 and <4.5 km, respectively (Fig. S8).\nHowever, the mean horizontal and vertical location uncertainties of our cataloged\nearthquakes are ~4 and ~8 km, respectively. To further constrain the likely depths of\nthese events, we look at the larger earthquakes which are more accurately located since\nthey are recorded by more stations. We find that the median depth of all M >1.1\nL\nearthquakes during the second LDL is ~1.5 km with average depth uncertainty of ~6\nkm. Our modelling shows that ∆CFS down to a depth of 7 km can reach levels that\ntrigger earthquakes (Fig. S11d), and the ∆CFS is larger at shallower depths (Fig. S11).\nFurthermore, ~60% of reservoirs with documented earthquake depths have induced\nearthquakes up to >8 km depth (Fig. S14). Therefore, we conclude that the earthquake\nsequence can be triggered by stress changes due to the LDL.\nFig. S8 | Earthquake depth over an eight-day period.\nFig. S11 | Coulomb stress change (∆CFS) map on 13 Nov 2018. a-d ∆CFS, as in\nFigure 2, assuming different fault depths. e-h ∆CFS assuming different fault dip values.\nFurthermore, we realize that the earthquake magnitudes used in our previous\nmanuscript initially reported in the China Unified Earthquake Catalog were\nunderestimated. For the same earthquakes, our estimated local magnitude is 0.8-1.2\nlarger than the previous magnitude and consistent with the final report of the China\nEarthquake Networks Center. Therefore, the triggered events have M up to 2.6.\nL\n• Are there any flaws in the data analysis, interpretation and conclusions? Do these\nprohibit publication or require revision?\nAlthough not under the author’s control, the number and magnitude of earthquakes are\nsmall, and running statistics on these small numbers is difficult. The authors decluster\nthe catalog and use a couple of statistical methods to determine a change in seismicity\nrate. Complicating this, associating the events to the water inundation caused by\nlandslide proves difficult given the time delay (two weeks) before the onset of\nseismicity. I would explore the use of other statistics used for dynamic triggering studies\n(works of Z. Peng, K. Pankow, R. Alfaro-Diaz, D. Kilb, E. Brodsky). If these events\nare indeed triggered, they would be classified as delayed triggering, which even is\nharder to show statistically. Finally, seismicity also appears widespread in the region,\nnot necessarily on the faults. Again, this may be the result of poor locations. There is\nsimply no way to assess given the information given in the study.\nThank you for your suggestion. We agree with your concerns about how to confirm the\nspatiotemporal evolution relationship between these triggered earthquakes and the\nsecond landslide hazard cascade. Our new earthquake catalog gives us the opportunity\nto better analyze the evolution of this earthquake sequence. Based on the enhanced\nearthquake catalog, we observed that as the second LDL approached peak water level,\nthe number and magnitude of earthquakes started increasing as the water level rises\nand then peaked together with the water level peak (Figs. 2 and S2). Subsequently, as\nthe LDL water level decreased following the dam breach, the earthquake activity\ngradually decreased back to the background rate.\nFurthermore, following your suggestion, we now also quantify the change in seismicity\nrate using the improved statistic based on Poisson probability (Alfaro-Diaz et al.,\n2020)44 and an empirically derived statistic (Pankow and Kilb, 2020)45 (Fig. S6)\ntests (Methods) which were developed to determine statistically significant changes in\nearthquake rate under small background rate:\nWe further evaluate the statistical significance of the observed seismicity rate change\nbased on both an improved statistic based on Poisson probability44 and an empirically\nderived statistic45 which were developed to determine statistically significant changes\nin earthquake rate under small background rate. We assumed that earthquakes occur\nindependently at a constant rate, following a Poissonian distribution44. To determine\nstatistical significance of seismicity rate increase, we compare the number of expected\nearthquakes in a 1-week window to the number of earthquakes in the 1-week window\nafter the trigger, and calculate the Poisson probability of getting the number of\nearthquakes (𝜈) in the 1-week window after the trigger given the expected number of\nevents (𝜇) in the 1-week window.\n𝜇𝜈\n𝑃 (𝜈) = 𝑒−𝜇 (3)\n𝜇 𝜈!\nFor this case of low background seismicity rate, similar to the idea of Alfaro-Diaz et al.\n(2020)44, we conservatively regard the largest number of earthquakes (3) in a 1-week\nwindow over our observation period, except for this earthquake sequence, as the\nexpected number of events (𝜇) in a 1-week window. Based on Equation 3, we obtain a\nP value of 0.0027 taking 𝜇 and 𝜈 as 3 and 9 respectively. This implies that our\nobserved seismicity rate increase after declustering41 is statistically significant at\na >99.73% level.\nWe also use empirical statistical method of Pankow and Kilb (2020)45 to determine the\nsignificance in the seismicity rate change. Firstly, we count the number of earthquakes\nin each 1-week time window incorporating a 1-day sliding window. There are >1,700\nwindows from May 2018 to January 2023. We then assign the number of earthquakes\nN within each window to a timestamp at the start of the window. We next build a\ncount\nhistogram of N values (Fig. S6). Finally, using percentile measurements, the >99%\ncount\nstatistically significant level is 3 earthquakes in a 1-week window. We observed 9\nearthquakes (after declustering) as the second LDL approached the peak water level,\nhence this seismicity rate increase is statistically significant at a >99% level.\nFig. S6 | Number of earthquakes in a given 1-week time window using the\nearthquakes from May 2018 to January 2023. The inset figure zooms into the smaller\nvalues of the histogram.\nRegarding your concern of running statistics on small numbers, our enhanced catalog\nnow contains more earthquakes and we also perform four different statistical tests\n(including one developed to determine statistically significant changes in earthquake\nrate under small background rate) using the whole, >Mc, and declustered catalogs,\nall of which confirm that the increase in seismicity rate is statistically significant at >99%\nlevel.\nTable S1 | Seismicity rate change and statistical significance.\nSeismicity rate per week\nTime window\nAll events >Mc events Declustered events\n1 week during the second LDL* 61 16 9\n27 weeks before the second LDL 0.7 0.3 0.3\n(Total number of earthquakes) (19) (9) (8)\n224 weeks after the second LDL 0.7 0.2 0.2\n(Total number of earthquakes) (164) (37) (37)\nMaximum over observation\n14 3 3\nperiod besides the second LDL\nStatistical significance\nStatistical tests\nAll events >Mc events Declustered events\nStatistic P 100.00% 100.00% 99.82%\nStatistic Z 100.00% 100.00% 99.62%\nImproved statistic based on\n100.00% 100.00% 99.73%\nPoisson probability\nEmpirically derived statistic 99.88% 99.71% 99.71%\n* 1 week (10 to 16 November) when the second LDL approached its peak water level\nFinally, the locations of the triggered earthquakes in our enhanced earthquake catalog\nare mainly distributed near previously mapped faults (Fig. 1). The triggering is also not\ndelayed since the seismicity rate started increasing as the second LDL approached peak\nwater level (Fig. 2c).\n• Is the methodology sound? Does the work meet the expected standards in your field?\nStress modeling also depends on assumed faults. The fault information also appears not\nwell documented (orientation of the faults are not known). Determining focal\nmechanism would help, but these are small earthquakes. Perhaps a composite focal\nmechanism can be used to determine what the stress direction is that would be released\nwith increase pore pressure. Furthermore, how deep are these faults, and how long\nwould it take for the water to reach these faults?\nThank you for your suggestion. The fault information is indeed limited because large\nearthquakes occur rarely in this region. Nevertheless, since January 2014, four M>3.5\nearthquakes occurred at 16 to 35 km from the LDLs and have similar left-lateral strike-\nslip focal mechanisms. While the small event sizes and limited station coverage prevent\nus from directly inverting for the focal mechanisms of the earthquake sequence during\nthe LDL, we find that the first motions recorded by surrounding seismic stations of the\ntwo largest earthquakes as the second LDL approached peak water level are generally\nconsistent with the left-lateral strike-slip focal mechanisms of the surrounding large\nearthquakes (Fig. S7). Finally, these focal mechanisms are also consistent with the\nstrike and fault type documented based on field investigations. Therefore, we believe\nour assumed fault geometry is reasonable.\nFig. S7 | Focal mechanism of M 3.7 earthquake and the first motions of two M >1.8\nL L\nearthquakes at their surrounding seismic stations. Red beach balls depict focal\nmechanisms of M 3.7 earthquake that occurred on 30 June, 2023 (striking: 323o, dip:\nL\n74o, slip: -16o) in Fig. 2b. For the earthquake sequence which occurred within 10 km\nof the LDL as the second LDL approached peak water level, the first motions of the two\nlargest earthquakes (M 2.6 (a) and M 1.9 (b)) at surrounding seismic stations are\nL L\nmarked. Black and white dots represent upward and downward motions, respectively.\nFinally, in the revised manuscript we also discuss the effects of fault depth and dip on\nstress changes on surrounding faults and confirm that our main conclusions stand after\nconsidering these uncertainties.\nThe stress change on surrounding faults due to the LDLs partly depends on the fault\ngeometry. In contrast to the well-documented fault strike, the dip of the fault is less well\nconstrained. We assume a fault dip of 75°NE based on the focal mechanisms of four\nM>3.5 earthquakes nearby. In addition, our modelling shows that the fault dip mainly\naffects the spatial distribution and amplitude of ∆CFS but not its sign, and the seismicity\ngenerally locate within regions of positive ∆CFS for a range of different assumed fault\ndips (Fig. S11e-h). Hence, the dip uncertainty has minimal effect on our conclusion that\nlandslide hazard cascades can trigger earthquakes.\nResponse to Reviewer #2:\nZhang et al. focuses on the potential impact of landslide-dammed lakes on the triggering\nof earthquakes on nearby faults. The paper is easy to read and addresses an interesting\nissue, which I feel deserves to receive the attention of a high-impact journal. Too few\nstudies have indeed focused on the impact of surface processes during extreme events\non the triggering of earthquakes and deformation. I was therefore thrilled to receive this\npaper for a review.\nUnfortunately, I have found too many major weaknesses that at this stage prevent, in\nmy opinion, the paper from being published. Despite that, I also feel that most of these\nmajor issues can be thoroughly addressed by the authors, and I therefore would ask the\neditor and authors to consider a phase of major revisions, but not necessarily of rejection\n(or otherwise with the opportunity for resubmission). I want to thank the authors for\nthis interesting manuscript, and I hope they will receive most of these comments as a\nmeans to increase the quality of their manuscript, and not only as a criticism.\nI first summarize below my main comments and then describe my other comments line-\nby-line.\nWith my best regards,\nPhilippe Steer\nWe would like to thank you for your very constructive comments on our manuscript.\nThey have helped to significantly improve this manuscript in all aspects. We have\nrevised the manuscript according to your great suggestions and comments.\nMain comments:\n• False claim of the manuscript: The manuscript repeats several times (lines 14-15, 49-\n52, in conclusion as well) that this is the first time that a link between surface\nhazards/processes (or erosion or landslides) and the triggering of earthquakes is made.\nThis is simply wrong and surprising to see this affirmation, as several visible papers in\nhigh-impact journals were published on this subject during the last 15 years: Calais et\nal. (2010 - Nature), Steer et al. (2014 - Nature Communications), Steer et al. (2020 -\nScientific reports), Jeandet Ribes et al. (2020 - GRL), and probably others. Moreover,\nseveral papers have already shown that lake water variation can impact seismicity and\ntrigger earthquakes (Gough & Gough, 1970; Kebeasy & Gharib, 1991; Simpson et al.,\n2018; and many more). This paper is therefore not the first one to address the issue of\nthe triggering of earthquakes because of surface hazards, landslides, or erosion, nor it\nis the first one to show the impact of lake water level fluctuation on earthquake\ntriggering. The manuscript by Zhang et al. therefore needs to account for these previous\nstudies, in particular in the title, introduction, discussion and conclusion, and to correct\nthe importance of their study respectively to what was already demonstrated by these\nprevious studies. This manuscript is however the first one (if I have not missed a\nprevious article) to address the issue of the response of seismic activity to landslide-\ndammed lakes filling. But this is largely different from what the current manuscript\nclaims.\nWe are very sorry that we have overlooked these important references. We have\nmodified the relevant descriptions in our manuscript (including title, abstract and\nconclusion) to include these important references and communicate the novelty of our\nspecific results while acknowledging the contributions of these previous studies.\n• Issue with declustering: The manuscript uses two classical approaches to decluster the\nearthquake catalog they investigate. However, only 3 over 39 earthquakes are identified\nas aftershocks and removed from the catalog. This is a very unusually low number of\nearthquake removal by declustering. I identify two issues that need to be addressed by\nthe manuscript: 1) The manuscript does not mention the values of the numerous\nparameters of the Reasenberg algorithm (the minimum look-ahead time for building\nclusters, the maximum look-ahead time for building clusters, a confidence probability,\nthe effective lower cutoff magnitude, the increase in lower cutoff magnitude during\nclusters, and the number of crack radii surrounding each earthquake), while these\nparameters can have a profound impact on the results of the declustering; 2) The\nmanuscript seems to ignore the earthquakes occurring outside the study area or\npreviously to 2018. This is problematic has these un-considered earthquakes have local\nmagnitude up to 5, while the largest earthquake in the space-time window considered\nis only a magnitude of 1.4 (which is extremely low). It is unclear to me that there is no\nstatistical link between what is observed in the study area and what occurred before or\noutside. The manuscript needs to better address this issue and demonstrate that there is\nno link.\nThank you for your suggestion. Using continuous seismic data recorded by 13 nearby\nseismic stations from January 2014 to January 2023, we apply machine-learning and\ncross-correlation-based methods to build an enhanced earthquake catalog which\ncontains 3,970 earthquakes with documented magnitude within a region of ~1o × 1o\n(Fig. 1b). 244 of these earthquakes within 10 km of the LDLs occurred after May 2018\nwhen a denser seismic network began operation.\nFig. 1 | Study site and seismicity. a Distribution of seismic stations. Red box marks the\nregion covered by the earthquake catalog we built. Black and green triangles indicate\nseismic stations that started operating since January 2014 and May 2018, respectively.\nb Map of seismicity from January 2014 to January 2023. Red beach balls depict focal\nmechanisms available from the National Earthquake Data Center of strike-slip\nearthquakes39. Red and gray dots represent earthquakes which occurred when the\nsecond landslide-dammed lake (LDL) almost reached peak water level and earthquakes\nbeyond that, respectively. Red box marks the region shown in (d). c Magnitude-\nfrequency distribution of earthquakes from May 2018 to January 2023 within 10 km\nof the LDLs. Magnitude of completeness (Mc) and a- and b-values were calculated\nusing the ZMAP software40. d Distribution of earthquakes from May 2018 to January\n2023 within 10 km of the LDLs. Red and gray dots represent earthquakes that occurred\nwhen the second LDL almost reached peak water level and earthquakes beyond that,\nrespectively.\nTo estimate the earthquake activity in our study area, we estimate the magnitude of\ncompleteness (Mc) to be 1.1 (ref.40; Fig. 1c) for the earthquakes within 10 km of the\nLDLs. There are 62 earthquakes between May 2018 and January 2023 with local\nmagnitude M ≥1.1, 16 of which occurred in the week when the second LDL approached\nL\nits peak water (Table S1). We then perform declustering using the Reasenberg method41,\nleaving us with 54 events (Fig S5), 9 of which occurred in the week the second LDL\napproached its peak water level (Fig. S5, Table S1). For your two specific questions,\nwe have made the following revisions:\nFig. S5 | Earthquakes after performing declustering. a Distribution of earthquake\nfrom May 2018 to January 2023 within 10 km from LDLs. Red and blue dots represent\nthe locations of earthquakes that were left and removed after performing declustering,\nrespectively. b Earthquake magnitudes and LDL water level over a twenty-day period.\nc Earthquake depths over a twenty-day period.\n1) Values of the numerous parameters of the Reasenberg algorithm: Using the\napproach from Reasenberg41, we identified 5 clusters of earthquakes containing a\ntotal of 13 events (5 main earthquakes and 8 foreshocks/aftershocks) out of 62\nevents which occurred over ~5 years, using the following input parameters41: look-\nahead time from 0.5 to 3 days, confidence probability of 0.9, effective min\nmagnitude cutoff of 1.6, the increase in lower cutoff magnitude during clusters of 0,\nand the number of crack radii surrounding each earthquake of 5. Most events are\nnot identified as aftershocks which makes sense since the largest events are small\n(M <2.7) and the events are spaced out in time (event rate of ~0.7/week).\nL\n2) Statistical link between what is observed in the study area and what occurred before\nor outside: We further verified that only 5 earthquakes (all with M <2.0) occurred\nL\nwithin 60 km of the LDLs besides this earthquake sequence as the second LDL\napproached peak water level (Fig. 1b), and the largest earthquake that occurred\nwithin 60 km of the LDLs in the six months before this earthquake sequence has M\nL\n2.7 (Fig. S4), hence the earthquake sequence within 10 km of the LDLs is unlikely\nto have been triggered by surrounding large earthquakes.\nFig. S4 | Distribution of M >2.5 earthquake from May 2018 to November 2018. Time\nL\nand magnitude of the earthquakes are marked.\n• Computation of pore pressure and the issue of time variation: The manuscript uses (in\nits main text) only one value of the coefficient of pore pressure diffusion D but evaluates\nthe DCFS obtained when changing this coefficient D in the supplementary. On Fig 2 c,\none can indeed observe that the modeled signal of pore pressure change, with D=0.3\nm2/s could be a good candidate for explaining the observed change in earthquake\nfrequency. However, not only does the amplitude of the pore pressure signal changes\nwith D, but the diffusion timescale also as it scales with L/sqrt(D), with L being the\ndistance between the pore pressure source and the observed change in pore pressure.\nAnd it is relatively well admitted that D is not well constrained and could vary by orders\nof magnitude (which the manuscript fairly mentions lines 206-210). This means that\nthe timing of when pore pressure increases or peaks is directly determined by D. There\nis in my opinion, no clear reason to choose D=0.3, except that it gives a good match\nwith the change in earthquake activity. But using this argument would lead to a circular\nargument, which must be avoided. I would like the authors to account for the issue of\nthe timing of pore pressure change, and to show/discuss the impact of changing pore\npressure through time. The manuscript also needs to clearly mention/explain to what\ntemporal state their maps of DCFS or pore pressure refer to (I have not found this\ninformation in the manuscript).\nThanks for your comments and suggestions. We have added Fig. S16 to show the\ntemporal evolution of pore pressure and the ∆CFS in the revised manuscript. We further\nconfirm that the temporal evolutions of ∆CFS at a given point are similar for different\nhydraulic diffusivity, and that the peak seismicity rate coincides with the peak amplitude\nof ∆CFS assuming different hydraulic diffusivity (Fig. S16).\nFig. S16 | Coulomb stress change (∆CFS) and earthquakes triggered by 2018 Baige\nlandslide-dammed lake. a Earthquake magnitudes and LDL water level over a fifty-\nday period. Temporal evolution of ∆CFS (b) and pore pressure (c) at point P (Fig. 2a)\nassuming different hydraulic diffusivity coefficient values.\nFurthermore, we marked the date of ∆CFS in Figs. 2a and S15 in the legend: 13\nNovember 2018, corresponding with peak water level of the second LDL.\nFig. S15 | Coulomb stress change (∆CFS) on 13 November 2018. a-d ∆CFS, as in\nFigure 2, assuming different friction coefficient values. e-h ∆CFS assuming different\nhydraulic diffusivity coefficient values.\nFinally, we have added some description about the timing of pore pressure change and\nthe temporal state of ∆CFS in the revised manuscript.\n…The ∆CFS due to the first, smaller, and shorter-duration LDL peaked at 0.007 MPa\nwhich is smaller than the stress increase of >0.01 MPa typically associated with stress\ntriggering of earthquakes47,48. …In comparison, about three weeks later on 3 November,\nthe second landslide formed a larger LDL. The ∆CFS due to this second LDL peaked\nat 0.024 MPa when the LDL’s water level approached its peak, coinciding with\nmaximum earthquake activity (Fig. 2).…\n• Heterogeneous value of the coefficient of pore pressure diffusion: Moreover, the value\nof D changes spatially, in particular in areas crossed by faults or structural\ndiscontinuities (which is the case of this studied area where a fault is almost below the\nlake). This means that the spatial and temporal response to the filling of the lake is\nprobably not the one of a homogeneous medium. The authors do not mention this\npossibility, nor discuss the implications of this heterogeneity.\nAccording to your suggestion, we have added some description about the heterogeneity:\nThe stress change on surrounding faults caused by LDL is also related to the fault\nfriction coefficient and the fluid diffusion coefficient. We assumed a friction coefficient\nof 0.5 for our ∆CFS modelling. However, the chosen friction coefficient has minimal\neffect on both the spatial distribution and amplitude of ∆CFS (Fig. S15). In addition,\ndue to differences in rock properties and depth-dependent confining pressure,\ncrustal hydraulic diffusivity has been found to range from 0.01 to 5 m2/s (ref.67,68).\nBoth the geometry and closure of faults and fractures also cause significant spatial\nvariation in hydraulic diffusivity69,70. These factors make it challenging to obtain a precisely-\nconstrained hydraulic diffusivity for the calculation of ∆CFS. Nevertheless, higher fluid\ndiffusivity causes the pore water pressure to increase faster, which increases the\namplitude of ∆CFS within a wider area. Our chosen value of 0.3 m2/s is on the lower\nend of observed values and is a typical value observed in fluid-driven seismic swarms\nin different regions71,72,73.\n• The issue of depth: As shown by Figure S6, most earthquakes possibly triggered by\nthe filling of the LDLs are located at a depth deeper than 5 km (about 6 km below the\nsurface). This is puzzling, as the DCFS is likely to be significantly higher closer to the\nsurface. Steer et al. (2014) or De Novellis et al. (2020, 2021) have clearly shown this\ndependency on depth. And some earthquakes can occur at shallower depths than 5-6\nkm. For instance, De Novellis et al. (2020) reports a depth of 1-2 km. So, my question\nis why the earthquakes you believe were triggered by filling of the LDLs do not occur\nat shallower depths, where the DCFS and pore pressure are likely to be of greater\namplitude? This study need to make a clear investigation of the role of depth on DCFS\nand pore pressure (accounting for time as well), to show whether the earthquakes occur\nat an optimal depth, and if it is note the case, if other factors (such as the rheological\nnature of the faults – for instance the a and b parameters of the rate-and-state law)\nprevent earthquakes occurring at shallower depths than the one observed. A second\nquestion: what is the uncertainty of the depth estimate of these earthquakes? Generally,\nthe depth is less well constrained than the horizontal position.\nThanks for your comment. Based on the continuous seismic waveforms from January\n2014 to January 2023, we use machine learning and cross-correlation-based methods\nto build an enhanced earthquake catalog. As the second LDL approached peak water\nlevel, ~50% and ~95% of the hypocenters in the earthquake sequence are at depths of\n<1.2 and <4.5 km, respectively (Fig. S8). However, the mean horizontal and vertical\nlocation uncertainties of our cataloged earthquakes are ~4 and ~8 km, respectively.\nTherefore, the improved earthquake locations confirm that these triggered earthquakes\nare indeed located at shallow depths.\nFig. S8 | Earthquake depths over an eight-day period.\nFurthermore, we perform a detailed analysis of the location uncertainties and confirm\nthat these earthquakes occurred within a depth range where LDL filling can trigger\nearthquakes after accounting for the depth uncertainties. To further constrain the likely\ndepths of these events, we look at the larger earthquakes which are more accurately\nlocated since they are recorded by more stations. We find that the median depth of all\nM >1.1 earthquakes during the second LDL is ~1.5 km with average depth uncertainty\nL\nof ~6 km. Our modelling shows that ∆CFS down to a depth of 7 km can reach levels\nthat trigger earthquakes (Fig. S11d), and the ∆CFS is larger at shallower depths (Fig.\nS11). Furthermore, ~60% of reservoirs with documented earthquake depths have\ninduced earthquakes up to >8 km depth (Fig. S14). Therefore, we conclude that the\nearthquake sequence can be triggered by stress changes due to the LDL.\nFig. S11 | Coulomb stress change (∆CFS) map on 13 Nov 2018. a-d ∆CFS, as in\nFigure 2, assuming different fault depths. e-h ∆CFS assuming different fault dip values.\n• Issue with the global study on the effect of LDL: the last part of the manuscript is\ndedicated to investigating how LDL could globally impact seismicity. However, I am\nnot convinced by this part. First, the manuscript considers that all LDLs occur in a\nsimilar structural-tectonic setting, dominated by strike-slip faults, while this is likely to\nbe incorrect. What would be the effect of considering normal or reverse faults? The\nlocalization of the faults and the orientation of the plane also significantly matters, but\nthis is not considered in the manuscript. This study really needs to go deeper into this\nissue, or otherwise remove it as it is currently unconvincing.\nThanks for your comment. To demonstrate that these LDL triggered earthquakes we\nshown are not special cases, we statistically analyzed global LDLs’ characteristics, such\nas duration and dam height. Compared to reservoirs which induced earthquakes (Figs.\n3a and 3b), we find that some LDLs also have the potential to trigger earthquakes.\nFig. 3 | General properties of landslide-dammed lakes. a Frequency distribution and\ncumulative distribution function of the height of reservoirs documented to have induced\nearthquakes and landslide-dammed lakes worldwide. b Frequency distribution and\ncumulative distribution function of the duration of landslide-dammed lakes worldwide.\nc Temporal evolution of ∆CFS and pore pressure at point P (Fig. 3d) and water surface\nelevation for a 30-m deep LDL. d Spatial distribution of ∆CFS at depth of 4.5 km\ncorresponding to -0.5 km asl, 11 days after the formation of a 30-m deep LDL. ∆CFS is\nfrom the combined effect of direct gravitational loading and fluid pressure diffusion.\nFurthermore, we acknowledge that it is unreasonable to use a similar structural-tectonic\nsetting to calculate ∆CFS. Therefore, based on your suggestion, we state that the stress\nresponses to this typical LDL at different sites can vary (Fig. 3d) and depend on factors\nsuch as the fault types51 (Fig. S10), geometries (Fig. S11), and depths (Fig. S11).\nNevertheless, our modelling shows that both the fault types and geometries mainly\naffect stress distribution rather than amplitude of ∆CFS (Figs. S10 and S11), and stress\nchanges caused by the LDLs are larger at shallower depth (Fig. S11).\nFig. S10 | Coulomb stress change (∆CFS) map on 13 Nov 2018. a and b ∆CFS on the\nsurrounding normal and reverse fault systems due to the LDL’s direct gravitational\nloading and fluid pressure diffusion.\nFinally, based on the characteristics of global LDL and calculated ∆CFS in a similar\nstructural-tectonic setting, we only state in the revised manuscript that other LDLs also\nhave the potential to trigger earthquakes rather than give unconvincing specific number\nof LDLs which can trigger earthquakes. Considering ~64% LDLs of the ~145 LDLs in\nthe global database with documented duration lasted more than 11 days before dam\nbreach (Fig. 3b) with no correlation with dam height (Fig. S12), our modelling suggests\nthat other LDLs globally have the potential to trigger earthquakes if there are critically\nstressed faults nearby.\n• The paper correctly mentions that the geometry of the faults (except that they are\nlikely in strike-slip regimes) are unknow. This study needs either to test the sensitivity\nof the DCFS results to the geometry at depth of the faults or to propagate the uncertainty\non the geometry of these faults on the obtained values of DCFS.\nBased on your suggestion, we added a test for the sensitivity of ∆CFS to both depth\nand dip of faults.\nOur modelling shows that ∆CFS down to a depth of 7 km can reach levels that trigger\nearthquakes (Fig. S11d), and the ∆CFS is larger at shallower depths (Fig. S11).\nThe stress change on surrounding faults due to the LDLs partly depends on the fault\ngeometry. In contrast to the well-documented fault strike, the dip of the fault is less well\nconstrained. We assume a fault dip of 75°NE based on the focal mechanisms of four\nM>3.5 earthquakes nearby. In addition, our modelling shows that the fault dip mainly\naffects the spatial distribution and amplitude of ∆CFS but not its sign, and the seismicity\ngenerally locate within regions of positive ∆CFS for a range of different assumed fault\ndips (Fig. S11e-h). Hence, the dip uncertainty has minimal effect on our conclusion that\nlandslide hazard cascades can trigger earthquakes.\nLine comments:\n• Lines 70-71 “deposited 2.5 x 10^7 m3 of sediments intor the river” – How do you\nknow?\nThe two landslide hazard cascades are very well documented. There are many studies\non these two events that present these field measurements in detail. We have added\nthese references in the revised manuscript.\n• Line 72 “upstream inflow of 1,680 m3/s” – Same, how do you know?\nSimilarly, we have added these references in the revised manuscript.\n• Lines 72-75 – How were all these measurements obtained? Gauging stations,\ngeotechnical reports, … ?\nSimilarly, we have added these references in the revised manuscript.\n• Line 83 “National Earthquake Data Center” – of which country?\nWe have removed this sentence in the revised manuscript because we built an enhanced\nearthquake catalog by ourselves.\n• Lines 108-109: It is generally recommended to use more than 100 earthquakes to\ncharacterize mc and b.\nSince an enhanced earthquake catalog was built, we now have more than 100\nearthquakes to evaluate Mc and b values in the revised manuscript.\n• Lines 206-209: “S5). In addition, since crustal hydraulic diffusivity has been found to\nrange from 0.01 to 5 m2/s (ref.45,46), we conservatively assume a diffusion coefficient\nof 0.3 m2/s” – In this case this is not a conservative estimate – please correct.\nDone. Our chosen value of 0.3 m2/s is on the lower end of observed values and is a\ntypical value observed in fluid-driven seismic swarms in different regions71,72,73.\n• Lines 226-227: “Wenchuan earthquake triggered more than 10,000 landslides” –\nAvailable landslide catalogs point towards more than 100,000 landslides and near\n200,000 (e.g, Xu et al., 2014). Of course there is a large uncertainty, but still, more than\n10,000 does not make justice to the estimated number of landslides.\nDone. …the 2008 M7.9 Wenchuan earthquake triggered more than 100,000 landslides\nand formed a few hundred LDLs52,53,54\n• Lines 229-232: Reading these two sentences can wrongly give the impression to the\nreader that these numerous post-Wenchuan earthquakes were triggered by LDLs, which\nis obviously wrong. Of course, there are some aftershocks after a Mw7.9 mainshock.\nThe effect of LDLs, if demonstrated, is likely to be negligible by orders of magnitude.\nTo avoid misleading readers, we have removed this sentence describing the aftershocks.\n• Line 240-241: “Since landslide materials are denser than water, landslides smaller\nthan our LDLs can result in comparable DCFS.” - Since landslides do not represent a\nnew source of mass (but only the very local displacement of material, along the\nlandslide path), this statement is likely wrong (except for very shallow faults of a few\n100 m depths at more). The removal by erosion and sediment transport could play a\nrole (Steer et al., 2020; Jeandet-Ribes et al., 2020), but this is different from what is\nmentioned here.\nThanks for your comments, we have removed these descriptions in the revised\nmanuscript.\nResponse to Reviewer #3:\nThis manuscript aims to understand the potential link between the Baige landslide dam\nand triggered small earthquakes in this region. It‘s intriguing to explore the interaction\nbetween earthquakes and surface hazards. The Baige landslide dam may indeed trigger\nsome small earthquakes, but the current evidence is insufficient or inconclusive. Firstly,\nthe observation period in 2018-2022 is relatively short and the network coverage is not\nshown in this study. Secondly, the limited number of events (39 with ML<=1.4) near\nthe LDLs may not be representative of the earthquake activity in the study region.\nThirdly, the estimate of Mc for 0.3 may not be reliable from the frequency-magnitude\ndistribution of events with ML mostly less than 1 and a limited number of earthquakes\n(< 50). The locations of potential triggered earthquakes seem to be best correlated with\nthe area with positive stress caused by the pore pressure changes than the stress due to\nthe change of surface loads. It remains unclear whether fluids can infiltrate to the\nmedian hypocentral depth of 6 km within ~10 days. My other comments are listed\nbelow\nWe would like to thank you for the specific and constructive comments you provided\nfor this manuscript. We have studied these valuable comments carefully and tried our\nbest to revise the manuscript according to these comments. Below is our point-to-point\nresponse to your concerns:\nFirstly, regarding the issue of relatively short observation period in 2018-2022: Based\non machine-learning and cross-correlation-based methods, we build an enhanced\nearthquake catalog based on the continuous waveforms from January 2014 to January\n2023 recorded by 13 permanent seismic stations within ~200 km of the LDLs, of which\n8 of these seismic stations have been operational since May 2018. Furthermore, we\nshow the distribution of seismic stations in Fig.1\nFig. 1 | Study site and seismicity. a Distribution of seismic stations. Red box marks the\nregion covered by the earthquake catalog we built. Black and green triangles indicate\nseismic stations that started operating since January 2014 and May 2018, respectively.\nb Map of seismicity from January 2014 to January 2023. Red beach balls depict focal\nmechanisms available from the National Earthquake Data Center of strike-slip\nearthquakes39. Red and gray dots represent earthquakes which occurred when the\nsecond landslide-dammed lake (LDL) almost reached peak water level and earthquakes\nbeyond that, respectively. Red box marks the region shown in (d). c Magnitude-\nfrequency distribution of earthquakes from May 2018 to January 2023 within 10 km\nof the LDLs. Magnitude of completeness (Mc) and a- and b-values were calculated\nusing the ZMAP software40. d Distribution of earthquakes from May 2018 to January\n2023 within 10 km of the LDLs. Red and gray dots represent earthquakes that occurred\nwhen the second LDL almost reached peak water level and earthquakes beyond that,\nrespectively.\nBefore more seismic stations became operational in May 2018, no earthquakes were\ndetected within 10 km of the LDLs due to limited station coverage and/or low seismicity\nrate. Nevertheless, in the ~250 weeks of observation period since May 2018 for which\nwe have an improved earthquake catalog, 61 earthquakes occurred within 10 km of the\nLDLs during the week when the second LDL’s water level almost peaked while there\nwere only 183 earthquakes over the ~247 weeks outside the time period of the two LDLs\ni.e., a background seismicity rate of only ~0.7/week over ~5 years (Table S1). Therefore,\nour catalog shows that the seismicity rate during the LDL is significantly higher than\nthe background seismicity rate of the region.\nSecondly, regarding the limited number of events: Based on the continuous seismic\nwaveforms from January 2014 to January 2023, we use machine learning and cross-\ncorrelation-based methods to build an enhanced earthquake catalog which contains ~5\ntimes more events than the previously presented catalog. We find that ~61 earthquakes\nof magnitudes up to 2.6 occurred in the week when the second landslide-dammed lake\nLDL was near peak water level, substantially strengthening our main novel conclusion\nthat landslide hazard cascades can trigger earthquakes.\nUsing continuous seismic data recorded by 13 nearby seismic stations from January\n2014 to January 2023, we apply machine-learning and cross-correlation-based\nmethods to build an earthquake catalog which contains 3,970 earthquakes with\ndocumented magnitude within a region of ~1o × 1o (Fig. 1b). 244 of these earthquakes\nwithin 10 km of the LDLs occurred after May 2018 when a denser seismic network\nbegan operation. It is well-established that earthquakes can trigger surface hazards\nand initiate hazard cascades5,6,7,12. However, the Baige landslides were not triggered by\nearthquakes34,35,36,37,38 as no earthquakes with magnitude M ≥3.5 were recorded within\nL\n50 km in the three preceding years (Figs. 1 and 2). Instead, in the week (10 to 16\nNovember) when the second LDL approached its peak water level, 61 earthquakes with\nlocal magnitude up to ~2.6 occurred within 10 km of the LDLs. In comparison, there\nwere only 19 earthquakes in the previous 27 weeks (~0.7 event/week) and 164\nearthquakes in the subsequent ~224 weeks (~0.7 event/week) (Fig. 2, Table S1) in this\nregion.\nThirdly, regarding the estimation of Mc given the small magnitude and limited number\nof events: Since an enhanced earthquake catalog was built, we now have enough\nearthquakes to better evaluate Mc and b values (Fig. 1c). Furthermore, we realize that\nthe earthquake magnitude used in our previous manuscript initially reported in the\nChina Unified Earthquake Catalog was underestimated. For the same earthquakes, our\nestimated local magnitudes are 0.8-1.2 larger than the previous magnitudes and\nconsistent with the final report of the China Earthquake Networks Center. Therefore,\nthe triggered events have M up to 2.6.\nL\nFourthly, the issue of location: As the second LDL approached peak water level, ~50%\nand ~95% of the hypocenters in the earthquake sequence are at depths of <1.2 and\n<4.5 km, respectively (Fig. S8). However, the mean horizontal and vertical location\nuncertainties of our cataloged earthquakes are ~4 and ~8 km, respectively. To further\nconstrain the likely depths of these events, we look at the larger earthquakes which are\nmore accurately located since they are recorded by more stations. We find that the\nmedian depth of all M >1.1 earthquakes during the second LDL is ~1.5 km with\nL\naverage depth uncertainty of ~6 km. Our modelling shows that ∆CFS down to a depth\nof 7 km can reach levels that trigger earthquakes (Fig. S11d), and the ∆CFS is larger\nat shallower depths (Fig. S11). Furthermore, ~60% of reservoirs with documented\nearthquake depths have induced earthquakes up to >8 km depth (Fig. S14). Therefore,\nwe conclude that the earthquake sequence can be triggered by stress changes due to\nthe LDL.\nFig. S8 | Earthquake depth over an eight-day period.\nFig. S11 | Coulomb stress change (∆CFS) map on 13 Nov 2018. a-d ∆CFS, as in\nFigure 2, assuming different fault depths. e-h ∆CFS assuming different fault dip values.\nLines 69-71: To give a better overview of the Baige landslide dam, authors can provide\na few photos of landslide-dammed lakes (e.g. photos shown in Zhang et al. Landslides,\n2019) in the supplementary materials. It is not easy to follow the description of texts in\nLines 70-101 without a good figure. How landslide materials distribute in space during\nthe first and second landslides and where the LSDs are located during two sliding events?\nThank you for your suggestion. We have added some satellite images of these\nlandslides in Fig. S1, and marked the spatial distribution of landslides, landslide dams\nand LDLs.\nFig. S1 | Sentinel-2 images near the Baige landslides. Dashed yellow and red lines\noutline the landslides and dams in b, c, and d. Time of these images are shown using\nyyyy-mm-dd format in each panel.\nLines 104-109: Please plot the location of seismic stations in Figure 1. The Baige\nlandslide occurred on the Tibetan plateau where the station coverage may be\ninsufficient to have the magnitude of completeness (Mc) of 0.3. In addition, most events\nhave magnitudes ranging from 0 to 1 (Fig. 1b), is the value of Mc a robust estimate?\nGiven only 48 events in May 2018 – Dec. 2022 and 36 events left after performing\ndeclustering, the temporal pattern of seismicity may be questionable.\nFirstly, we plotted the locations of the seismic stations in Fig. 1. Furthermore, as you\nhave seen, based on the continuous seismic waves from January 2014 to January 2023\nrecorded by 13 seismic stations, we use machine-learning and cross-correlation-based\nmethods to build an enhanced earthquake catalog which contains 3,970 earthquakes\nwith documented magnitude within a region of ~1o × 1o (Fig. 2a). 244 of these\nearthquakes within 10 km of the LDLs occurred after May 2018 when a denser seismic\nnetwork began operation.\nFig. 1 | Study site and seismicity. a Distribution of seismic stations. Red box marks the\nregion covered by the earthquake catalog we built. Black and green triangles indicate\nseismic stations that started operating since January 2014 and May 2018, respectively.\nb Map of seismicity from January 2014 to January 2023. Red beach balls depict focal\nmechanisms available from the National Earthquake Data Center of strike-slip\nearthquakes39. Red and gray dots represent earthquakes which occurred when the\nsecond landslide-dammed lake (LDL) almost reached peak water level and earthquakes\nbeyond that, respectively. Red box marks the region shown in (d). c Magnitude-\nfrequency distribution of earthquakes from May 2018 to January 2023 within 10 km\nof the LDLs. Magnitude of completeness (Mc) and a- and b-values were calculated\nusing the ZMAP software40. d Distribution of earthquakes from May 2018 to January\n2023 within 10 km of the LDLs. Red and gray dots represent earthquakes that occurred\nwhen the second LDL almost reached peak water level and earthquakes beyond that,\nrespectively.\nWe estimate the magnitude of completeness (Mc) to be 1.1 (ref.40; Fig. 1c) for the\nearthquakes within 10 km of the LDLs. There are 62 earthquakes between May 2018\nand January 2023 with local magnitude M ≥1.1, 16 of which occurred in the week\nL\nwhen the second LDL approached its peak water (Table S1). We then perform\ndeclustering using the Reasenberg method41, leaving us with 54 events (Fig S5), 9 of\nwhich occurred in the week the second LDL approached its peak water level (Fig. S5,\nTable S1).…\n…. Using the approach from Reasenberg41, we identified 5 clusters of earthquakes\ncontaining a total of 13 events (5 main earthquakes and 8 foreshocks/aftershocks) out\nof 62 events which occurred over ~5 years, using the following input parameters41:\nlook-ahead time from 0.5 to 3 days, confidence probability of 0.9, effective min\nmagnitude cutoff of 1.6, the increase in lower cutoff magnitude during clusters of 0,\nand the number of crack radii surrounding each earthquake of 5.…\nLines 113-114 The authors need to provide a detailed figure showing the time series of\nearthquake number and water level (daily sampling?) in the week of 12 to 18 November\nafter the second LDL approached its peak water level. Why they choose earthquakes\nwithin 15 km of the LDLs but not a larger or smaller area? Are those chosen earthquakes\nshown as green dots in Fig. 2? Figure 1 shows earthquakes in this region and the\nseismicity activity seems to be high to the southeast of the study area with a subtle\ninfluence of LDLs. If authors choose earthquakes in different regions, how figure 2b\nvaries accordingly?\nWe appreciate your suggestions. We have plotted a figure showing the time series of\nearthquake number and water level (Fig. S2). Furthermore, we chose to focus on\nearthquakes that occurred within 10 km of LDLs since the region with stress increase\nof >0.01 MPa is always located within 10 km of the LDLs (Fig. 2a). Nevertheless, the\nearthquake activity within larger and smaller region shows a similar accelerated trend\nduring the landslide hazard cascades (Fig. S13).\nFig. S2 | Daily seismicity rate, earthquake magnitudes, and LDL water level over a\ntwenty-day period.\nFig. S13 | Cumulative numbers of earthquakes occurred within 8 km (a), 12 km (b),\nand 14 km (c) of LDLs over a five-year period. Arrows mark the timings of the two\nLine 127-137, Please shows the locations of earthquakes before and after performing\ndeclustering. After declustering, where and how deep are the remaining eight\nearthquakes located? As authors claimed the largest magnitude (ML) is 1.4 during their\nobservation period, maybe declustering is not necessary. Since there are only eight\nevents (within 15 km of LDLs) left after declustering, I’m not sure the statistic test for\nthe significance of increasing seismicity rate is meaningful given very few earthquakes\nin this period.\nWe have shown the locations and depth of earthquakes after performing declustering\nin Fig. S5. For the new earthquake catalog, we estimate the magnitude of completeness\n(Mc) to be 1.1 (ref.40; Fig. 1c) for the earthquakes within 10 km of the LDLs. There are\n62 earthquakes between May 2018 and January 2023 with local magnitude M ≥1.1,\nL\n16 of which occurred in the week when the second LDL approached its peak water\n(Table S1). We then perform declustering using the Reasenberg method41, leaving us\nwith 54 events (Fig S5), 9 of which occurred in the week the second LDL approached\nits peak water level (Fig. S5, Table S1).\nFig. S5 | Earthquakes after performing declustering. a Distribution of earthquake\nfrom May 2018 to January 2023 within 10 km from LDLs. Red and blue dots represent\nthe locations of earthquakes that were left and removed after performing declustering,\nrespectively. b Earthquake magnitudes and LDL water level over a twenty-day period.\nc Earthquake depths over a twenty-day period.\nFurthermore, we confirm that the increase in seismicity rate is also statistically\nsignificant at a >99% level (Table S1) based on both the improved statistic based on\nPoisson probability44 and an empirically derived statistic45 (Fig. S6) tests (Methods)\nwhich were developed to determine statistically significant changes in earthquake\nrate under small background rate.\nFig. S6 | Number of earthquakes in a given 1-week time window using the\nearthquakes from May 2018 to January 2023. The inset figure zooms into the smaller\nvalues of the histogram.\nRegarding your concern that the statistically significance of increasing seismicity rate\nis due to very few earthquakes: our enhanced catalog now contains more earthquakes\nand we also perform four different statistical tests (including one developed to\ndetermine statistically significant changes in earthquake rate under small background\nrate) using the whole, >Mc, and declustered catalogs, all of which confirm that the\nincrease in seismicity rate is statistically significant at >99% level. Therefore, the\nstatistical significance of our result is not an artefact of having very few events.\nTable S1 | Seismicity rate change and statistical significance.\nSeismicity rate per week\nTime window\nAll events >Mc events Declustered events\n1 week during the second LDL* 61 16 9\n27 weeks before the second LDL 0.7 0.3 0.3\n(Total number of earthquakes) (19) (9) (8)\n224 weeks after the second LDL 0.7 0.2 0.2\n(Total number of earthquakes) (164) (37) (37)\nMaximum over observation\n14 3 3\nperiod besides the second LDL\nStatistical significance\nStatistical tests\nAll events >Mc events Declustered events\nStatistic P 100.00% 100.00% 99.82%\nStatistic Z 100.00% 100.00% 99.62%\nImproved statistic based on\n100.00% 100.00% 99.73%\nPoisson probability\nEmpirically derived statistic 99.88% 99.71% 99.71%\n* 1 week (10 to 16 November) when the second LDL approached its peak water level\nLines 140-148: Since most earthquakes occurred after the second LDL are very small\n(ML<1.4), it is unclear whether these earthquakes truly occurred on the surrounding\nfault system. Is the Coulomb stress estimated at the depth of 6 kn in Fig. 2a? If so,\nplease add it in the figure caption.\nIn the revised manuscript, based on the continuous seismic waveforms from January\n2014 to January 2023, we use machine learning and cross-correlation-based methods\nto build an earthquake catalog which contains ~5 times more events than the previously\npresented catalog. Our new enhanced earthquake catalog shows that the earthquakes\nduring the landslide hazard cascades were closely related to the LDLs in space (Fig.\n1d) and time (Figs. 1d and S2) after location uncertainties are taken into account, which\nsupports our main conclusions. Furthermore, we estimate location uncertainties using\nthe Hypoinverse. As the second LDL approached peak water level, ~50% and ~95% of\nthe hypocenters in the earthquake sequence are at depths of <1.2 and <4.5 km,\nrespectively (Fig. S8). However, the mean horizontal and vertical location uncertainties\nof our cataloged earthquakes are ~4 and ~8 km, respectively. To further constrain the\nlikely depths of these events, we look at the larger earthquakes which are more\naccurately located since they are recorded by more stations. We find that the median\ndepth of all M >1.1 earthquakes during the second LDL is ~1.5 km with average depth\nL\nuncertainty of ~6 km. Our modelling shows that ∆CFS down to a depth of 7 km can\nreach levels that trigger earthquakes (Fig. S11d), and the ∆CFS is larger at shallower\ndepths (Fig. S11).\nFig. S8 | Earthquake depth over an eight-day period.\nFinally, the Coulomb stress estimated at 4.5 km depth which is deeper than 95% depth\nof our observed seismicity (Fig. S8) and corresponds to ~-0.5 km asl because ~80% of\nour study area is at elevation between 4 and 5 km asl35. We added the depth for\ncalculating Coulomb stress in the figure caption (Figs 2 and 3).\nLines 149-159: Please add a new figure to show the earthquake number from Nov. 10th\nto 20th where most earthquakes occurred. The stress due to fluid pressure diffusion\nreached peak about 12-13 days after the formation of landslide dam on Nov. 3rd.\nHowever, most of the hypocentral depths range from 5 to 15 km (median at 6 km) and\nit is unclear whether fluids can infiltrate to such great depths within ~10 days. About\n80% of the earthquakes locate within regions of positive ΔCFS (Fig. 2a). However, the\nΔCFS in Fig. 2a is mainly contributed by fluid pressure diffusion instead of direct\nloading.\nWe show the daily number of earthquakes in Fig S2, and show that the largest number\nof earthquakes occurs on November 13, which corresponds to the peak water level of\nthe second LDL.\nFig. S2 | Daily seismicity rate, earthquake magnitudes, and LDL water level over a\ntwenty-day period.\nFurthermore, as the second LDL approached peak water level, ~50% and ~95% of the\nhypocenters in the earthquake sequence are at depths of <1.2 and <4.5 km, respectively\n(Fig. S8). However, the mean horizontal and vertical location uncertainties of our\ncataloged earthquakes are ~4 and ~8 km, respectively. To further constrain the likely\ndepths of these events, we look at the larger earthquakes which are more accurately\nlocated since they are recorded by more stations. We find that the median depth of all\nM >1.1 earthquakes during the second LDL is ~1.5 km with average depth uncertainty\nL\nof ~6 km. Our modelling shows that ∆CFS down to a depth of 7 km can reach levels\nthat trigger earthquakes (Fig. S11d), and the ∆CFS is larger at shallower depths (Fig.\nS11). Furthermore, ~60% of reservoirs with documented earthquake depths have\ninduced earthquakes up to >8 km depth (Fig. S14). Therefore, we conclude that the\nearthquake sequence can be triggered by stress changes due to the LDL.\nLine 179: What are the minimum and median heights of reservoirs?\n…we find that the minimum and median heights of ~190 reservoirs with documented\nheight that induced earthquakes are ~13 and 110 m, respectively (Fig. 3a).\nLines 180-181: Fig 3a show the height of LDLs which induced earthquakes are\ngenerally lower than the heights of reservoirs induced earthquakes. I don’t understand\nthe logic of “Therefore, a significant number of LDLs globally are of similar heights as\nreservoirs which induced earthquakes.”\nWe revised some descriptions: In comparison, from a global database of ~410 LDLs\nreported worldwide spanning the period 1900-2018 (ref.50), we find that of the ~300\nLDLs with documented dam height, ~73% and ~10% were higher than the minimum\nand median heights of reservoirs which induced earthquakes, respectively (Fig. 3a).\nTherefore, some LDLs globally are of similar heights as reservoirs which induced\nearthquakes.\nLine 286: How did authors obtain distributed surface forces?\nWe added some descriptions: The distributed surface forces can be estimated based on\nthe spatiotemporal evolution of the LDL’s water level. To quantify the spatiotemporal\nevolution of the LDL’s water level, the LDL is mapped as a series of square cells with\na size of 200 by 200 m. The elevation of each square cell is estimated from the GDEM\nV3 30 m. Based on the water depth at the dam (Figs. 2 and 3) and the elevation of each\ncell, the water depth of each cell can then be estimated. Therefore, the distributed\nsurface forces, the direct gravitational loading effect of each cell, can be calculated\nusing the water depth of each cell.\nFigure 1 is not very informative. Please mark the downstream direction. A more\ndetailed map of LDLs.\nWe completely revised Fig. 1 and marked the flow direction. We also added Fig. S1 to\nshow the distribution of landslides, landslide dams, and LDLs in detail.\nFig. S1 | Sentinel-2 images near the Baige landslides. Dashed yellow and red lines\noutline the landslides and dams in b, c, and d. Time of these images are shown using\nyyyy-mm-dd format in each panel.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nOverall, I commend the authors for addressing my concerns by conducfing new analysis, specifically,\nlocafing earthquakes using the available data. The depth uncertainty is sfill a bit ambiguous because of\nthe lack of explorafion of velocity models, and the reporfing of the errors is realisfic. Thus, the analysis is\nmuch stronger. My only comment on this draft is in regards to clarifying the figure capfions (see below).\nSpecific Comments.\nFigure 1: Need to state what the orange line is. I assume it is where the water was impacted. I also do\nnot understand the red/grey circle descripfion. Grey circles are earthquakes that occurred before the\npeak LDL? Red after?\n“Red beach balls depict focal mechanisms…”. Beach balls are not what many like to refer these to. I\nwould reword: “Focal mechanisms (red/white circles)…” The same style can be used throughout the\ncapfion:\nHere’s a suggested re-write of the Figure capfion:\nFig. 1: Study site and seismicity. a) Distribufion of seismic stafions operafing since January 2014 (black\ntriangles) and May 2018 (green triangles). Red box marks the specific study region where we developed\nthe earthquake catalog. b) Seismicity map from January 2014 to January 2023 showing strike-slip focal\nmechanisms (red/white circles) available from the Nafional Earthquake Data Center plus earthquakes\nthat occurred before (grey filled circles) and after (red filled circles) when the second landslide-dammed\nlake (LDL) almost reached peak water level. Red box marks the region shown in (d). c) Magnitude-\nfrequency distribufion of earthquakes from\nMay 2018 to January 2023 within 10 km of the LDLs. Magnitude of completeness (Mc)and a- and b-\nvalues were calculated using the ZMAP software. d) Distribufion of\nearthquakes from May 2018 to January 2023 within 10 km of the LDLs.\nI would recommend re-wrifing all capfions for clarity, as illustrated above.\nReviewer #2 (Remarks to the Author):\nDear authors,\nI wish to thank you for the hard and thorough work you have made to answer my comments as well as\nthe comments of the other reviewers. The quality and robustness of the manuscript have both been\nsignificantly improved thanks to that. If the manuscript sfill relies on some debatable assumpfions (as in\nmost Earth Sciences paper), they are now clearly stated and well discussed or jusfified. Demonstrafing\nthe link between an LDL event and few potenfially triggered earthquakes (of small magnitudes) is\nstafisfically difficult. Yet, the authors have made a real effort to strengthen this link by improving the\nquality of the catalog and by exploring in more details the parametrizafion of the processes (pore\npressure diffusion and direct gravitafional loading) which could trigger earthquakes in relafion to LDL\nwater level rise.\nI therefore suggest the editor to accept the paper for publicafion after some minor revisions (see below).\nBest regards,\nPhilippe Steer\nMinor comments\n• Abstract: please explicitely state (line 21) that the observed increase in seismicity rate after the LDL\nonly applies to low magnitude earthquakes\n• Concerning pore pressure and its temporal evolufion: Thank you for having added Fig. S16. However, I\ndisagree with the interpretafion that “the temporal evolufions of ΔCFS at a given point are similar for\ndifferent hydraulic diffusivity, and that the peak seismicity rate coincides with the peak amplitude of\nΔCFS assuming different hydraulic diffusivity (Fig. S16).” (as menfioned in your rebuftal lefter and paper).\nTheory of pore pressure diffusion demonstrates that the pore pressure front progressively propagates\nfrom a point source at a distance d that is funcfion of fime t and Diffusivity D as d=sqrt(4 pi D t) [see for\ninstance Shapiro et al., 1997]). Therefore, diffusivity strongly impacts the fiming of the arrival of the peak\nof pore pressure, as well as its amplitude, beneath the LDL. Fig. S16 (b and c) is also clearly showing that.\nYou could strengthen your manuscript by 1) menfioning the range of D are consistent with having a DCFS\nabove >0.01 MPa, and 2) by mentioning the relafive contribufion to DCFS of gravitafional loading and\npore pressure for these different values of D.\n• Declustering: the manuscript only considers the lower ranges of accepted parameters for declustering\nusing the Reasenberg approach (see for instance Table 3 of van Sfiphout et al., 2012\nhftp://dx.doi.org/10.5078/corssa-52382934). Please make addifional tests with standard parameters and\nwith the one of the lower range.\nReviewer #3 (Remarks to the Author):\nThe revised manuscript represents a significant improvement over the previous version, parficularly in\nterms of the earthquake catalog and stafisfical analysis. However, I sfill have two principal concerns\nregarding the triggering mechanisms and earthquake stafisfics. While the manuscript has made notable\nimprovements, addressing these concerns will enhance the clarity and credibility of the research\nfindings.\nMan comments:\n(1) While the manuscript provides a more comprehensive earthquake catalog and stafisfics, the\ncorrelafion between the spafiotemporal occurrence of earthquakes and pore pressure changes remains\nunclear. It is noteworthy that most events (ML > 1.1) occurred near the peak of the water level. However,\nthe manuscript does not sufficiently elucidate the role of pore pressure throughout the enfire process.\nFurther clarificafion on how pore pressure influences seismic acfivity is warranted to enhance the\nunderstanding of the triggering mechanisms.\n(2) It appears that the authors evaluate the stafisfical significance of the observed seismicity rate change\nby including events lower than the completeness magnitude (Mc). This approach may introduce biases\nand potenfially obscure the true significance of seismicity rate changes. Revisifing the stafisfical analysis\nmethodology to ensure that only events above the completeness magnitude are considered would\nstrengthen the robustness of the findings and their interpretafion.\nOther comments:\n1. Lines 121-124: By reviewing Figure 2 and the esfimafion of the number of events per week, it appears\nthat the authors have included events with magnitudes lower than the completeness magnitude (Mc).\nAs such, discussions regarding the seismic rate without considering Mc may lack meaningful\ninterpretafion. Therefore, I suggest removing these sentences for clarity and accuracy.\nFigure 2:\nPlot the cumulafive number of earthquakes with magnitudes greater than or equal to Mc (1.1) in Figure\n2b. This adjustment will provide a clearer representafion of the seismic acfivity relevant to the study's\nobjecfives.\nIn Figure 2c, mark the value of Mc to highlight its significance in the context of the\nseismicity analysis. Addifionally, plot the cumulafive number of events since November 3 and compare the temporal\nevolufion with the increase in water level. This comparison will offer valuable insights into the\ncorrelafion between seismic acfivity and water level fluctuafions.\n2. Lines 167-180: The manuscript discusses Coulomb failure stress changes in the context of triggered\nseismic events, which predominantly exhibit small magnitudes (ML less than 2). It is important to note\nthat small events may not necessarily share similar geometries with adjacent fault systems.\n3. Ling 179: I have observed that the hypocentral depths of many events in the dataset appear to be\npinned at specified depths (Fig S8). Consequently, these events may not be suitable for esfimafing the\nmedian depth of triggered earthquakes.\n4. Lines 181-184: It appears that the authors solely esfimated the increase in water level following the\nLSL, without accounfing for the weight of the landslide sediments (8.7 × 10^6 m^3 as menfioned in Lines\n98-99). Considering the substanfial mass of the landslide sediments, which could exert gravitafional\nloading, it is crucial to evaluate its potenfial contribufion to induced seismicity alongside the rise in water\nlevel.\n5. Lines 227-229: How to esfimate the temporal evolufion of water level rise after the formafion of LDL?\n6. Lines 182-183: The manuscript lacks clarity regarding how the authors evaluate the contribufions from\ndirect gravitafional loading of LDL and fluid pressure diffusion to induced seismicity. Despite the reported\nrise in water level, there is no discernible spafiotemporal migrafion of earthquakes associated with this\nincrease. Notably, most events cluster near the peak of the water level, raising quesfions about the\nprecise mechanisms driving seismic acfivity. Given the absence of clear migrafion pafterns and the\nlimited magnitudes of events, it remains uncertain whether the observed seismicity results from direct\ngravitafional loading, fluid pressure diffusion, or other factors.\nFigure 1 Cayan or Green triangles? Gray and red dots are too big.\nFigure 2 See my earlier comment\nResponse to Reviewer #1:\nOverall, I commend the authors for addressing my concerns by conducting new analysis,\nspecifically, locating earthquakes using the available data. The depth uncertainty is still\na bit ambiguous because of the lack of exploration of velocity models, and the reporting\nof the errors is realistic. Thus, the analysis is much stronger. My only comment on this\ndraft is in regards to clarifying the figure captions (see below).\nWe are honored that you recognized our efforts to address your concerns. We would\nlike to thank you for your great comments on our manuscript. They have helped to\nimprove this manuscript in all aspects.\nSpecific Comments.\nFigure 1: Need to state what the orange line is. I assume it is where the water was\nimpacted. I also do not understand the red/grey circle description. Grey circles are\nearthquakes that occurred before the peak LDL? Red after? “Red beach balls depict\nfocal mechanisms…”. Beach balls are not what many like to refer these to. I would\nreword: “Focal mechanisms (red/white circles)…” The same style can be used\nthroughout the caption:\nHere’s a suggested re-write of the Figure caption:\nFig. 1: Study site and seismicity. a) Distribution of seismic stations operating since\nJanuary 2014 (black triangles) and May 2018 (green triangles). Red box marks the\nspecific study region where we developed the earthquake catalog. b) Seismicity map\nfrom January 2014 to January 2023 showing strike-slip focal mechanisms (red/white\ncircles) available from the National Earthquake Data Center plus earthquakes that\noccurred before (grey filled circles) and after (red filled circles) when the second\nlandslide-dammed lake (LDL) almost reached peak water level. Red box marks the\nregion shown in (d). c) Magnitude-frequency distribution of earthquakes from May\n2018 to January 2023 within 10 km of the LDLs. Magnitude of completeness (Mc)and\na- and b-values were calculated using the ZMAP software. d) Distribution of\nearthquakes from May 2018 to January 2023 within 10 km of the LDLs.\nI would recommend re-writing all captions for clarity, as illustrated above.\nThanks for your suggestion. The orange line is LDLs - this is denoted in the figure\nlegend. According to your suggestion, we have rewritten the figure captions:\nFig. 1 | Study site and seismicity. a Distribution of seismic stations operating since\nJanuary 2014 (black triangles) and May 2018 (cyan triangles). Red box marks the\nspecific study region where we developed the earthquake catalog. b Seismicity map\nfrom January 2014 to January 2023 (grey filled circles) showing strike-slip focal\nmechanisms (red/white circles) available from the National Earthquake Data\nCenter39 plus earthquakes that occurred during the week (10 to 16 November 2018)\nwhen the second landslide-dammed lake (LDL) reached peak water level (red filled\ncircles). Red box marks the region shown in (d). c Magnitude-frequency distribution\nof earthquakes from May 2018 to January 2023 within 10 km of the LDLs. Magnitude\nof completeness (Mc) and a- and b-values were calculated using the ZMAP\nsoftware40. d Distribution of earthquakes from May 2018 to January 2023 (grey filled\ncircles) within 10 km of the LDLs plus earthquakes that occurred during the week (10\nto 16 November 2018) when the second LDL reached peak water level (red filled\ncircles).\nFig. 2 | Earthquakes triggered by 2018 Baige landslide-dammed lake. a Spatial\ndistribution of Coulomb stress change (∆CFS) at depth of 4.5 km corresponding to -0.5\nkm asl on 13 November 2018 and earthquakes from 10 to 16 November 2018 (green\nfilled circles) within 10 km of the landslide-dammed lakes (LDLs). ∆CFS is from the\ncombined effect of direct gravitational loading and pore pressure diffusion (Fig. 2d). b\nCumulative number of earthquakes with local magnitudes greater than or equal to the\nmagnitude of completeness (Mc = 1.1) and weekly seismicity rate over a five-year\nperiod with timings of the two 2018 Baige landslides (black arrows). Gray bar marks\nthe period shown in (c and d). c Earthquake magnitudes and measured LDL water\nlevel35,36,37 over a fifty-day period. Gray dashed line marks Mc. d Temporal evolution of\n∆CFS at point P (Fig. 2a).\nResponse to Reviewer #2:\nDear authors,\nI wish to thank you for the hard and thorough work you have made to answer my\ncomments as well as the comments of the other reviewers. The quality and robustness\nof the manuscript have both been significantly improved thanks to that. If the\nmanuscript still relies on some debatable assumptions (as in most Earth Sciences paper),\nthey are now clearly stated and well discussed or justified. Demonstrating the link\nbetween an LDL event and few potentially triggered earthquakes (of small magnitudes)\nis statistically difficult. Yet, the authors have made a real effort to strengthen this link\nby improving the quality of the catalog and by exploring in more details the\nparametrization of the processes (pore pressure diffusion and direct gravitational\nloading) which could trigger earthquakes in relation to LDL water level rise.\nI therefore suggest the editor to accept the paper for publication after some minor\nrevisions (see below).\nBest regards,\nPhilippe Steer\nWe would like to thank you for the specific and constructive comments you provided\nfor this manuscript. These comments are really helpful and greatly improve this\nmanuscript.\nMinor comments\n• Abstract: please explicitely state (line 21) that the observed increase in seismicity rate\nafter the LDL only applies to low magnitude earthquakes\nDone.\n…there was a statistically significant increase in earthquake activity (local magnitude\n≤ 2.6)…\n• Concerning pore pressure and its temporal evolution: Thank you for having added Fig.\nS16. However, I disagree with the interpretation that “the temporal evolutions of ΔCFS\nat a given point are similar for different hydraulic diffusivity, and that the peak\nseismicity rate coincides with the peak amplitude of ΔCFS assuming different hydraulic\ndiffusivity (Fig. S16).” (as mentioned in your rebuttal letter and paper). Theory of pore\npressure diffusion demonstrates that the pore pressure front progressively propagates\nfrom a point source at a distance d that is function of time t and Diffusivity D as d=sqrt(4\npi D t) [see for instance Shapiro et al., 1997]). Therefore, diffusivity strongly impacts\nthe timing of the arrival of the peak of pore pressure, as well as its amplitude, beneath\nthe LDL. Fig. S16 (b and c) is also clearly showing that. You could strengthen your\nmanuscript by 1) mentioning the range of D are consistent with having a DCFS\nabove >0.01 MPa, and 2) by mentioning the relative contribution to DCFS of\ngravitational loading and pore pressure for these different values of D.\nThank you for your suggestion. According to your suggestion, we calculated the\nrelative contribution to DCFS of pore pressure for these different values of D and added\nsome description:\nWhile hydraulic diffusivity strongly influences the time at which ∆CFS exceeds a certain\nthreshold, we further confirm that ∆CFS exceeds 0.01 MPa for hydraulic diffusivities\nranging from 0.02 to 2 m2/s. On the day of peak seismicity rate, the relative contribution\nto ∆CFS of pore pressure increases from ~0.1 to 0.9 as the assumed hydraulic diffusivity\nincreases from 0.02 to 2 m2/s (Fig. S14).\nFig. S14 | Coulomb stress change (∆CFS) and earthquakes triggered by 2018 Baige\nlandslide-dammed lake. a Earthquake magnitudes and LDL water level over a fifty-\nday period. Gray dashed line marks Mc. b Temporal evolution of ∆CFS due to the\ncombined effect of direct gravitational loading and pore pressure diffusion at point P\n(Fig. 2a) assuming different hydraulic diffusivity coefficient values. c Temporal\nevolution of ∆CFS due to pore pressure diffusion at point P (Fig. 2a) assuming different\nhydraulic diffusivity coefficient values. d Relative contribution to ∆CFS of pore\npressure at point P (Fig.2a) assuming different hydraulic diffusivity coefficient values.\n• Declustering: the manuscript only considers the lower ranges of accepted parameters\nfor declustering using the Reasenberg approach (see for instance Table 3 of van\nStiphout et al., 2012 http://dx.doi.org/10.5078/corssa-52382934). Please make\nadditional tests with standard parameters and with the one of the lower range.\nDone.\nWe also tested the impact of different input parameters on the declustering based on the\napproach from Reasenberg41. We identified 4 clusters of earthquakes containing a total\nof 16 events (4 main earthquakes and 12 foreshocks/aftershocks) out of 62 events which\noccurred over ~5 years, using other suggested input parameters41: look-ahead time\nfrom 1 to 10 days, confidence probability of 0.95, effective min magnitude cutoff of 1.5,\nthe increase in lower cutoff magnitude during clusters of 0.5, and the number of crack\nradii surrounding each earthquake of 10. While the declustered earthquake catalogs\nwith different input parameters are different, we further confirm that this seismicity rate\nincrease is statistically significant at a > ~90% level based on the above four statistical\ntests (Table S1).\nResponse to Reviewer #3:\nThe revised manuscript represents a significant improvement over the previous version,\nparticularly in terms of the earthquake catalog and statistical analysis. However, I still\nhave two principal concerns regarding the triggering mechanisms and earthquake\nstatistics. While the manuscript has made notable improvements, addressing these\nconcerns will enhance the clarity and credibility of the research findings.\nWe would like to thank you for the specific and constructive comments you provided\nfor this manuscript. These comments are really helpful and greatly improve this\nmanuscript. We have tried our best to resolve the issues you are still concerned about.\nWe hope our revisions have addressed your concerns.\nMan comments:\n(1) While the manuscript provides a more comprehensive earthquake catalog and\nstatistics, the correlation between the spatiotemporal occurrence of earthquakes and\npore pressure changes remains unclear. It is noteworthy that most events (ML > 1.1)\noccurred near the peak of the water level. However, the manuscript does not\nsufficiently elucidate the role of pore pressure throughout the entire process. Further\nclarification on how pore pressure influences seismic activity is warranted to\nenhance the understanding of the triggering mechanisms.\nThank you for your suggestion. We have added some description of the correlation\nbetween the spatiotemporal occurrence of earthquakes and pore pressure changes, and\ndiscuss the relative contributions from direct gravitational loading of LDL and pore\npressure diffusion in triggering seismicity.\nWhile gravitational loading can cause Coulomb stress to decrease in some areas, pore\npressure always causes an increase in ΔCFS with its amplitude gradually decreasing\naway from the LDLs (Fig. S9). For earthquakes that occurred in regions where\ngravitational loading resulted in a decrease in Coulomb stress, it is clear that pore\npressure is the primary mechanism triggering these events, though we neglect the\ncoupling effect between pore pressure diffusion and gravitational loading24,25,26,27.\nHowever, for those earthquakes that occurred in regions where gravitational loading\nresulted in an increase in Coulomb stresses, both gravitational loading and pore\npressure may jointly control the triggered seismicity. After the second LDL formed,\nwhile the water level rises and seismicity begins to occur from 10 to 13 November (Fig.\nS2), the relative contribution to ΔCFS of gravitational loading decreases gradually\nfrom 0.45 to 0.41 (Fig. S13). Subsequently, after the dam breached on 13 November\nwhich is the day of peak seismicity rate, the water level rapidly decreased and the\nrelative contribution to ΔCFS of gravitational loading decreases sharply from 0.41 to\n0.19 so pore pressure becomes the dominant triggering mechanism. However, the\nrelative contribution to ∆CFS of pore pressure depends on the assumed hydraulic\ndiffusivity (Fig. S14). In addition, since the pore pressure diffusion is from a long\nwinding river (LDLs) instead of a point source, there is no obvious migration pattern\nin seismicity with time (Fig. S15).\nFig. S13 | Relative contributions to Coulomb stress change (∆CFS) of pore pressure\nand direct loading and earthquakes triggered by 2018 Baige landslide-dammed lake.\na Earthquake magnitudes and LDL water level over a fifty-day period. Gray dashed\nline marks Mc. Relative contributions to ∆CFS of pore pressure (b) and direct loading\n(c) at point P (Fig.2a).\nFig. S15 | Coulomb stress change (∆CFS) maps at depth of 4.5 km and earthquakes\nthat occurred before (grey filled circles) and on (green filled circles) each day from\n10 to 16 Nov 2018.\n(2) It appears that the authors evaluate the statistical significance of the observed\nseismicity rate change by including events lower than the completeness magnitude\n(Mc). This approach may introduce biases and potentially obscure the true\nsignificance of seismicity rate changes. Revisiting the statistical analysis\nmethodology to ensure that only events above the completeness magnitude are\nconsidered would strengthen the robustness of the findings and their interpretation.\nThanks for your comment. We apologize for the misunderstanding that may have\noccurred because we analyzed the seismicity rate without considering Mc, in addition\nto statistical tests on ≥Mc and declustered events. To avoid confusion, we have now\nremoved discussion regarding statistical analysis of the seismicity rate without\nconsidering Mc and only keep the discussion regarding statistical analysis on ≥Mc and\ndeclustered events:\nFor each of ≥Mc and declustered catalogs, we consistently find that the increase in\nseismicity rate is statistically significant at a > 99% level based on both the statistic P\n(ref.42) and statistic Z (ref.43) tests (Methods). We further confirm that the increase in\nseismicity rate is also statistically significant at a >99% level (Table S1) based on both\nthe improved statistic based on Poisson probability44 and an empirically derived\nstatistic45 (Fig. S6) tests (Methods) which were developed to determine statistically\nsignificant changes in earthquake rate under small background rate.\nTable S1 | Seismicity rate change and statistical significance.\nSeismicity rate per week\nTime window Declustered events Declustered events\n≥Mc events\nwith input I** with input II***\n1 week during the second LDL* 16 9 5\n27 weeks before the second LDL 0.3 0.3 0.3\n(Total number of earthquakes) (9) (8) (8)\n224 weeks after the second LDL 0.2 0.2 0.2\n(Total number of earthquakes) (37) (37) (37)\nMaximum over observation\n3 3 3\nperiod besides the second LDL\nStatistical significance\nStatistical tests\n≥Mc events Declustered events Declustered events\nStatistic P 100.00% 99.82% 97.41%\nStatistic Z 100.00% 99.62% 96.52%\nImproved statistic based on\n100.00% 99.73% 89.92%\nPoisson probability\nEmpirically derived statistic 99.71% 99.71% 99.71%\n* 1 week (10 to 16 November 2018) when the second LDL approached its peak water\nlevel\n** look-ahead time from 0.5 to 3 days, confidence probability of 0.9, effective min\nmagnitude cutoff of 1.1, the increase in lower cutoff magnitude during clusters of 0,\nand the number of crack radii surrounding each earthquake of 5\n*** look-ahead time from 1 to 10 days, confidence probability of 0.95, effective min\nmagnitude cutoff of 1.5, the increase in lower cutoff magnitude during clusters of 0.5,\nand the number of crack radii surrounding each earthquake of 10\nOther comments:\n1. Lines 121-124: By reviewing Figure 2 and the estimation of the number of events\nper week, it appears that the authors have included events with magnitudes lower\nthan the completeness magnitude (Mc).\nAs such, discussions regarding the seismic rate without considering Mc may lack meaningful\ninterpretation. Therefore, I suggest removing these sentences for clarity and accuracy.\nWe have removed these sentences in the manuscript.\nFigure 2:\nPlot the cumulative number of earthquakes with magnitudes greater than or equal to\nMc (1.1) in Figure 2b. This adjustment will provide a clearer representation of the\nseismic activity relevant to the study's objectives.\nIn Figure 2c, mark the value of Mc to highlight its significance in the context of the\nseismicity analysis. Additionally, plot the cumulative number of events since\nNovember 3 and compare the temporal evolution with the increase in water level. This\ncomparison will offer valuable insights into the correlation between seismic activity\nand water level fluctuations.\nWe now plot the cumulative number of earthquakes with magnitudes greater than or\nequal to Mc (1.1) in Fig. 2b. We also marked Mc in Fig. 2c. Considering the layout of\nFigure 2, there is indeed no space to add a new panel. Therefore, we plot the cumulative\nnumber of events since November 3 and the temporal evolution of water level in Fig.\nS2a.\n2. Lines 167-180: The manuscript discusses Coulomb failure stress changes in the\ncontext of triggered seismic events, which predominantly exhibit small magnitudes\n(ML less than 2). It is important to note that small events may not necessarily share\nsimilar geometries with adjacent fault systems.\nThank you for your suggestion.\nBased on reviewer 1's comment, in the last round of revisions, we have check that the\npolarities of two M2.6 and 1.9 are consistent with the focal mechanisms of those large\nevents:\nIn addition, we find that the first motions recorded by surrounding seismic station of\nthe two largest earthquakes (ML 2.6 and 1.9) as the second LDL approached peak water\nlevel are generally consistent with the left-lateral strike-slip focal mechanisms of the\nsurrounding large earthquakes (Fig. S7).\nAlso, we agree with your concern that some small earthquakes may not necessarily\nshare similar geometries with adjacent fault systems. Therefore, we added some\ndiscussion in the revised manuscript:\nWe assume a fault dip of 75°NE based on the focal mechanisms of four M>3.5\nearthquakes nearby and the consistency of the first motions of the two largest\nearthquakes (ML 2.6 and 1.9) as the second LDL approached peak water level with\nthese focal mechanisms (Fig. S7), though we cannot confirm that the focal mechanism\nof the smaller earthquakes necessarily share similar geometries.\n3. Ling 179: I have observed that the hypocentral depths of many events in the dataset\nappear to be pinned at specified depths (Fig S8). Consequently, these events may\nnot be suitable for estimating the median depth of triggered earthquakes.\nThanks for your comment. For events detected using template matching, their depths\nare assumed to be the same as the depths of the template. However, we have confirmed\nthat after removing events detected by template matching, the estimated median depth\nis still ~1.2 km (Fig. S8):\nSimilarly, for the earthquake catalog before template matching, the median depth of\nthese triggered earthquakes is also ~1.2 km (Fig. S8).\nFig. S8 | Earthquake depths in complete catalog (a) and in catalog before template\nmatching (b) over an eight-day period. Median earthquake depths in complete catalog\nand in catalog before template matching are 1.19 and 1.24 km, respectively.\n4. Lines 181-184: It appears that the authors solely estimated the increase in water\nlevel following the LSL, without accounting for the weight of the landslide\nsediments (8.7 × 10^6 m^3 as mentioned in Lines 98-99). Considering the\nsubstantial mass of the landslide sediments, which could exert gravitational\nloading, it is crucial to evaluate its potential contribution to induced seismicity alongside the\nrise in water level.\nThanks for your comment. Regarding the potential of landslide gravitational loading to\ntrigger earthquakes, as reviewer 2 mentioned in the previous round of reviews,\nlandslides do not represent a new source of mass, but only the very local redistributions\nof sediments along the landslide path. In our study case, these landslide sediments only\ntraveled ~1-2 km that is even smaller than the mean horizontal location uncertainty (4\nkm) of our cataloged earthquakes, so we do not expect to be able to resolve the\ncontribution of the redistribution of the landslide sediments in triggering seismicity.\nFurthermore, we admit that calculating the gravitational loading of landslide sediments\nis a challenge due to the lack of data regarding their spatiotemporal distribution. We\nalso added some description:\nNote that we ignore the ∆CFS resulting from gravitational loading of landslide\nsediments, since these landslide sediments are not new sources of mass but only the\nvery local redistributions (~1-2 km) of sediments along the landslide sliding path.\n5. Lines 227-229: How to estimate the temporal evolution of water level rise after the\nformation of LDL?\nThe temporal evolution of water level rise at the dam is from field measurements. After\nthese two landslides, the Chinese government immediately launched emergency\nobservation and response. There are some studies on these two LDLs that present these\n these\nfield measurements. We have added these references in the revised manuscript.\nZhong, Q., Chen, S., Wang, L. & Shan, Y. Back analysis of breaching process of\nBaige landslide dam. Landslides 17, 1681-1692 (2020).\nGao, Y., Zhao, S., Deng, J., Yu, Z. & Rahman, M. Flood assessment and early warning\nof the reoccurrence of river blockage at the Baige landslide. Journal of Geographical\nSciences 31, 1694-1712 (2021).\n6. Lines 182-183: The manuscript lacks clarity regarding how the authors evaluate the\ncontributions from direct gravitational loading of LDL and fluid pressure diffusion\nto induced seismicity. Despite the reported rise in water level, there is no discernible\nspatiotemporal migration of earthquakes associated with this increase. Notably,\nmost events cluster near the peak of the water level, raising questions about the\nprecise mechanisms driving seismic activity. Given the absence of clear migration\npatterns and the limited magnitudes of events, it remains uncertain whether the\nobserved seismicity results from direct gravitational loading, fluid pressure\ndiffusion, or other factors.\nThanks for your comment. Similar to your comment above, to address your concerns,\nwe have added the following description and discussion:\nWhile gravitational loading can cause Coulomb stress to decrease in some areas, pore\npressure always causes an increase in ΔCFS with its amplitude gradually decreasing\naway from the LDLs (Fig. S9). For earthquakes that occurred in regions where\ngravitational loading resulted in a decrease in Coulomb stress, it is clear that pore\npressure is the primary mechanism triggering these events, though we neglect the\ncoupling effect between pore pressure diffusion and gravitational loading24,25,26,27.\nHowever, for those earthquakes that occurred in regions where gravitational loading\nresulted in an increase in Coulomb stresses, both gravitational loading and pore\npressure may jointly control the triggered seismicity. After the second LDL formed,\nwhile the water level rises and seismicity begins to occur from 10 to 13 November (Fig.\nS2), the relative contribution to ΔCFS of gravitational loading decreases gradually\nfrom 0.45 to 0.41 (Fig. S13). Subsequently, after the dam breached on 13 November\nwhich is the day of peak seismicity rate, the water level rapidly decreased and the\nrelative contribution to ΔCFS of gravitational loading decreases sharply from 0.41 to\n0.19 so pore pressure becomes the dominant triggering mechanism. However, the\nrelative contribution to ∆CFS of pore pressure depends on the assumed hydraulic\ndiffusivity (Fig. S14). In addition, since the pore pressure diffusion is from a long\nwinding river (LDLs) instead of a point source, there is no obvious migration pattern\nin seismicity with time (Fig. S15).\nFigure 1 Cayan or Green triangles? Gray and red dots are too big.\nWe've changed \"blue\" to \"cyan\" and made the gray and red dots smaller.\nFigure 2 See my earlier comment\nDone.\nREVIEWERS' COMMENTS\nReviewer #3 (Remarks to the Author):\nThe authors have addressed all of my comments. The paper can be accepted in its present form.\nResponse to Reviewer #3:\nThe authors have addressed all of my comments. The paper can be accepted in its\npresent form.\nWe would like to thank you for the specific and constructive comments you provided\nfor this manuscript. These comments are really helpful and greatly improve this\nmanuscript."}]

Decision letter