Dating submarine landslides using the transient response of gas hydrate stability


 Submarine landslides are prevalent on the modern-day seafloor, yet an elusive problem is constraining the timing of slope failure. Herein, we present a novel technique for constraining the age of submarine landslides without sediment core dating. Underneath a submarine landslide in the Orca Basin, Gulf of Mexico, in 3D seismic data we map an irregular bottom simulating reflection (BSR), which mimics the geometry of the pre-slide seafloor rather than the modern bathymetry. Based on the observed BSR, we suggest that the gas hydrate stability zone (GHSZ) is currently adjusting to the post-slide sediment temperature perturbations. We apply transient conductive heat flow modeling to constrain the response of the GHSZ to the slope failure, which yields a most likely age of ~8 ka demonstrating that gas hydrate systems can respond to slope failures even on the millennia timescales. We also provide an analytical approach to rapidly determine the age of submarine slides at any location.

the accumulation of free gas below the BSR 16 . The base of the GHSZ is a sensitive interface controlled by a combination of four factors: pressure, temperature, gas composition, and pore water salinity 18,20 .
Typically, the four factors remain regionally uniform and the BSR parallels the sea oor gently deepening with increasing water depth, which causes an increase in hydrostatic pressure 17 . Yet, there are irregular BSRs that deviate from the sea oor bathymetry. Such BSRs indicate there may be lateral changes in the temperature gradient [21][22][23] , gas composition 24 or salinity 25 . Although less common, BSRs can appear as multiple re ections named double BSRs, possibly indicating presence of thermogenic gas 26-28 , high sedimentation rates, and/or recent tectonic shifts [29][30][31] .
Here, we analyze an irregular BSR underlying a landslide scarp and MTD in the Orca Basin, Gulf of Mexico. The BSR in this location deviates from the modern sea oor bathymetry due to slide-induced temperature perturbations imposed upon the sediments. We determine the age of the submarine landslide using the deviation of the observed BSR from its steady-state depth, the reconstructed pre-slide bathymetry, the modeled post-slide sediment temperature and gas hydrate stability.

Geologic Setting
The Orca Basin in the Gulf of Mexico is a salt-withdrawal minibasin that is well known for a large (123 km 2 ) anoxic hypersaline brine pool occurring at the bottom of the basin 32 . The water depths in the basin range from 1600 to 2600 m ( Figure 1A). The sea oor of the Orca Basin is marked by prominent escarpments and rugged topography resulting from slump deposits and rafted blocks produced by multiple submarine slide events 33,34 (Figure 1A, B).
Our study area is located at the southern ank of the Orca Basin where a sharp ~ 90 m tall sea oor escarpment marks the head of a submarine slide described in a previous study 33 ( Figure 1A). The slide area exhibits an ~3 x 7.5 km excavation underlain by a salt body. Previous study also reported an accumulation of MTDs at the basin oor that were sourced from the slides above 33 (Figure 1A, B). The BSR was previously mapped 35 and further analyzed in this study over an area of 44.3 km 2 ( Figure 1C).
Gas hydrates were also identi ed in industry wells anking the escarpment ( Figure 1D).

Irregular BSR In The Orca Basin
In the depth-migrated 3D seismic data, we observe multiple negative-amplitude BSRs that crosscut stratigraphy ( Figure 1D, 2A). The BSRs are distinct and located at depths between 2300-3500 meters below sea level (mbsl) (230-1130 meters below sea oor (mbsf) ( Figure 1C). The large BSR depth range is surprising given that BSRs are typically subparallel to the sea oor. The irregular BSR con guration is especially well-observed along seismic section c-d extending across the southern rim and slope of the Orca Basin (Figure 2A, B). The shallowest BSR occurs within the slide escarpment area upslope (~200 mbsf) and the deepest BSR occurs below the MTD downslope (~1110 mbsf) (Figure 2A, B).
There are several possible explanations for the southward shallowing BSRs. First, it could be caused by the higher sediment temperature over the heat-conductive salt body; this would drive the base of the GHSZ shallower. Similar effects have been previously analyzed within the roofs of salt bodies [37][38][39] . The geothermal gradients required to explain the depths of the observed BSR along the pro le c-d show a signi cant increase from 16.3°C/km downslope to as high as 43°C/km above the salt summit ( Figure 2A, see methods).
The second explanation is based on the fact that the BSR is in a striking agreement with the reconstructed pre-slide bathymetry of the Orca Basin southern rim (Figure 2A, B, see methods). The observed BSR lies at an approximately constant depth below the reconstructed pre-slide sea oor both, within the slide escarpment upslope and downslope, where the pre-slide sea oor submerges along the base of the MTD (Figure 2A, B). Such a con guration is observed over a wide area as illustrated by the thickness maps ( Figure 1C). The thickness between the BSR and the pre-slide sea oor (~400-550 m) is more uniform over the study area as compared to the thickness between the BSR and the modern sea oor (~230-1130 m). This suggests the base of the GHSZ in the Orca Basin still closely re ects the pre-slide sea oor con guration.
To understand the temperature effect of the salt body on the observed BSR shape, we constrain the regional average geothermal gradient and run a 2D conductive heat ow model along pro le c-d ( Figure   1). We then model the response time of the GHSZ to the slide-induced sediment temperature change and compare the results with the observed BSR depth to de ne the age of the slope failure.

Results And Discussion
The regional average geothermal gradient of 25.5°C/km is derived from the three BSR depths where sediment temperature is assumed to be at steady-state: away from the heat-conductive shallow salt, outside of the slide escarpment and outside of the MTD (red, yellow and white stars in the inset of Figure  2A). The 2D heat ow model shows a pronounced heat ow increase directly above the top of salt and elevated heat ow ~4000 m southward and northward along the pro le c-d ( Figure 3, see methods). The geothermal gradient predicted by the 2D heat ow model over the salt body is 30°C/km, and it gradually decreases to the average regional 25.5°C/km ~4000 m northward from the salt summit ( Figure 3). However, these variations are insu cient to explain the shape of the irregular BSR, which requires geothermal gradients increasing from 16.3°C/km downslope to as high as 43°C/km above salt ( Figure   2A).
Moreover, the 2D heat ow model predicts where the base of GHSZ would be at steady-state, and indicates that the sediments are still undergoing the residual post-slide temperature adjustment ( Figure  3). To analyze this adjustment, pro le c-d can be divided into three areas ( Figure 2B): 1) the upslope area where the removal of the overburden is cooling the shallow sediments and drives the base of GHSZ down ( Figure 2B, Figure 3), 2) the downslope area where the warming effect due to the deposition of the MTD drives the base of GHSZ upward, and 3) the areas outside of the MTD and slide escarpment where the GHSZ is relatively steady-state ( Figure 2B, Figure 3). The fact that the BSR still closely mimics the preslide sea oor implies that the temperature adjustment is not yet signi cant, and that the landslide is relatively young. The following time-transient heat ow model provides constraints on the age of the slope failure.

1D Transient Heat Flow Models
We model the transient post-slide temperature eld at the upslope slide location where sediments experience cooling, and at the downslope MTD location, where the sediments undergo warming ( Figure  2A, B, see methods). We use a bottom water temperature of 4.2°C for the upper boundary condition. To constrain the lower boundary at each location, we apply constant heat ow that corresponds to the steady-state geothermal gradients predicted by the 2D heat ow model: 30°C/km at the upslope location and 25.5°C/km at the downslope location ( Figure 3). Based on the 1D heat ow modeling (see equation (1) in methods), we de ne the transient temperature changes in the sediment column and derive the temperature pro les at certain times (time-temperature pro les) after the slide for both locations (see methods). Finally, to de ne the age of the slide event in the Orca Basin, we nd the crossover of the three functions: the methane phase boundary curve, the observed BSR depth (re ecting the modern temperature), and the corresponding time-temperature pro le (insets of Figure 2B).
2D steady-state conductive heat ow model used to estimate the effect of the salt body on the geothermal gradients along seismic section c-d (located in Figure 1). The model domain is 14 km deep and 16.5 km wide with constant basal heat ow. The properties of the sediment (i.e. thermal conductivity) vary with porosity and the properties of the salt vary with temperature (see methods and supplementary material). The model predicts an elevated geothermal gradient over salt (~30°C/km) and regional average geothermal gradient below the MTD (~25.5°C/km), which is however insu cient to explain the observed shift in the BSR in the Orca Basin ( Figure 2A). We use the observed gradients at the upslope (30°C/km) and downslope (25.5°C/km) locations for our one-dimensional simulations ( Figure 4).

Upslope Location
Given the 30°C/km steady-state geothermal gradient, the pre-slide temperature at the level of the modern sea oor (~220 meters below the pre-slide sea oor) was 10.7°C ( Figure 4A). After the instantaneous 220-meter sea oor drop caused by the slide, these warmer sediments were exposed to cooler bottom waters with a temperature 4.2°C ( Figure 4A). Over thousands of years, the temperature within the subsea oor sediments gradually cools to adjust to the new boundary condition as shown by the timetemperature pro les ( Figure 4A).
Based on the steady-state geothermal gradient, the pre-slide BSR would have been at ~ 465 m below the pre-slide sea oor (~245 meters relatively to the modern sea oor) (Figure 4a, black 0 kyr pro le), and it will reach its post-slide steady-state depth at ~505 mbsf approximately 200 kyr after the slide event. Timetemperature pro les show the base of the GHSZ approaches approximately half-way to its steady-state depth during the rst ~20 kyrs after the slope failure. Figure 4a shows that the intersection of the modern BSR (~342 mbsf, blue line in Figure 4a) and methane phase boundary curve corresponds to the ~8 kyr time-temperature pro le (red curve in Figure 4A), which constrains the upslope location age estimate for the Orca submarine slide.

Downslope Location
At the downslope location, we model a 400-meter thick sediment mass added to the top of the pre-slide sea oor to simulate the deposition of the MTD ( Figure 4B). The initial temperature pro le within the MTD is somewhat ambiguous because slope failure is a chaotic process involving sediment redeposition and unpredictable rates of mixing with the cold bottom water. We select a uniform 7.5°C temperature throughout the MTD for the model, which was the mean temperature in the ~220 m thick upslope sediment column prior to failure ( Figure 2B, 4B). The temperature at the top of the MTD is 4.2°C.
The model shows that at the downslope location the depth of the pre-slide BSR was ~720 meters below the pre-slide sea oor (~1120 mbsf) ( Figure 4B). It will reach its post-slide steady-state depth at 680 mbsf approximately 250 kyrs after the slide event, whereas complete steady state will be reached in ~350 kyrs ( Figure 4B). The modern BSR is observed in the seismic data at ~1090 mbsf, which is only 30 m above its pre-slide location (Figures 3, 4B). The modern BSR depth and methane phase boundary intersection corresponds to the ~14 kyr time-temperature pro le (red line in Figure 4B), which constrains the downslope location age estimate for the Orca submarine slide.
A) Transient 1D heat ow modeling at the upslope location ( Figure 2B) showing the time-temperature pro les after the slope failure (removal of overburden). The gure shows the intersection of methane phase boundary (black curve) and modern BSR depth (blue line) corresponds to an 8 kyr timetemperature pro le (red line) indicating the age of the Orca slide derived from the upslope location. B) Transient 1D heat ow modeling at the downslope location ( Figure 2B) showing the time-temperature pro les after the MTD deposition. The model shows that the intersection of methane phase boundary (black curve) and modern BSR depth (blue line) corresponds to a 14 kyr time-temperature pro le (red line). For the upper boundary condition, we use a bottom water temperature of 4.2°C. At the lower boundary, we apply constant heat ow that corresponds to 30°C/km geothermal gradient at the upslope location and 25.5°C/km at the downslope location (see supplementary material for thermal conductivity and diffusivity depth pro les). Front panel shows that both slide ages determined for the Orca Basin correlate with a rapid post-glacial sea level rise 40 , which could cause increased slope instability across the worldwide continental margins 13 .

Age Of The Orca Submarine Slide
At the upslope location, we predict an age of ~8 ka for the Orca submarine slide, whereas at the downslope location we predict an age of ~14 ka. We consider the 8 ka age estimate to be more accurate for two reasons. First, sediment removal upslope was likely a single fast-moving event. In contrast, the MTD at the downslope location may be an amalgamation of several landslides that occurred around the rim of the Orca basin 33 . Thus, the temperature pro le within the sediments at the downslope may record a number of slides, some older than the one released at the upslope location. Second, the depth interval between the pre-slide and modern BSR is wider and shallower at the upslope location compared to the downslope location ( Figure 4A, B). Within this interval upslope, the thermal signal propagates faster resulting in the wider-spaced time-temperature pro les. Thus, the upslope location provides better age resolution than the densely clustered pro les at the downslope location.
The impact of slope failures on gas hydrate accumulations is different in the interval below the MTD than below the slide escarpments. Below the MTDs, there would be gas hydrate dissociation as the base of GHSZ rises with the temperature increase ( Figure 2B). Gas hydrate dissociation below the MTDs (i.e. the downslope location) is an endothermic reaction 41 that would draw the heat from the sediments, slow the general warming trend, and consequently increase the modeled slide age. In contrast, below the slide escarpments (i.e. the upslope location), the deepening GHSZ entraps the underlying gas, which forms hydrate ( Figure 2B). Gas hydrate formation is an exothermic process accompanied by heat release, which may slow the general cooling trend and likewise increase the modeled slide age. Therefore, the ~8 ka is the youngest age estimate for the Orca landslide. Accurate quantitative characterization of hydrate formation and dissociation depends on gas hydrate and gas saturations over the area, which are not available. In any case, our modeling shows that the effect of slope failures on gas hydrate systems can continue over tens of thousands of years after the slide events.
Our inferred age of the Orca slide (~8 ka) coincides with the nal stage of rapid late Pleistocene-early Holocene sea level rise in the Gulf of Mexico averaging at ~12 mm/yr between 14.5 and 8 ka 40 (inset of Figure 4B). An earlier study showed that this fast post-glacial sea-level rise could induce seismicity along faults on passive continental margins and increase the frequency of submarine slides worldwide 13 (inset of Figure 4). A similar mechanism could be responsible for the activation of deep-rooted and supra-salt faults, triggering submarine slides in the Gulf of Mexico, including the Orca Basin.

Model Sensitivity
Our landslide age estimates may be affected by factors that control gas hydrate stability, such as the presence of heavy hydrocarbons (ethane, propane, butane, pentane), and high salinity. In addition, geologic factors can also in uence hydrate stability by altering temperature and pressure, such as elevated post-slide sedimentation rates and eustatic sea level change. These factors can contribute to the depth of the GHSZ, yet the impact on our age estimates is unlikely to be signi cant.
First, the presence of heavy hydrocarbons and/or elevated salinity in the shallow subsea oor sediments would provide the opposite effects at the upslope and downslope locations. Higher salinity would shift the methane hydrate phase boundary leftward in Figure 4 and result in a younger modeled slide age at the downslope location and older slide age at the upslope location. The presence of heavy hydrocarbons would shift the methane-hydrate phase boundary rightward in Figure 4 and result in the older modeled slide age at the downslope locations and younger age upslope. Neither salinity anomalies nor thermogenic gas are supported by our well log and seismic data.
Second, the high post-slide sediment deposition rate would result in a younger modeled slide age at the downslope location and older age at the upslope location. Based on the 3D seismic data, the hemipelagic drape within the slide escarpment is absent or <8 m thick, indicating that the effect of the sediment deposition is negligible. Additionally, the thin layer of post-slide sediments supports the relatively young age of the slide.
Third, the post-glacial sea level rise in the Gulf of Mexico 40 would only result in <7 m uncertainty in the pre-slide base of GHSZ based on the corresponding shift of the methane-hydrate phase boundary pro le. This slightly affects the pre-slide BSR location but provides negligible effect on the slide age.
Universal Approach To Submarine Slide Dating Using BSRs Equation (2) (see methods) provides a simple analytical method for a quick-look slide age (t slide , s) estimate using the modern BSR depth (z bsr , m) below slide escarpments (similar to the Orca upslope location) with a known temperature at the BSR depth (T bsr ) (Figure 2A). We further nd that parameter ) all fall into one curve at different locations with different water depths, temperature gradients, thermal diffusivities, BSR temperatures and/or landslide thicknesses ( Figure 5: red curve). This means that the age of a submarine landslide t slide can be estimated simply from the diagram shown in Figure 5 with easily accessible parameters (z bsr , z bsr , o , z bsr , 1 , κ). It is evident that the BSR shift from the pre-slide to post-slide steady-state (z bsr , 1 − z bsr , o ) can be roughly equated to the thickness of a submarine slide ( Figure 4A, 5).
The analytical solution (see equation (2) in methods), which estimates submarine slide age using BSR depths under the landslide escarpments, similar to the upslope location at Orca. z bsr is calculated from equation (2) by assuming a constant, known temperature at the BSR depth (T bsr ) during the evolution. z bsr , 0 is the depth of a pre-slide steady-state BSR that can be estimated based on the thickness of removed sediments; z bsr , 1 is the depth of a post-slide steady-state BSR; κ is the average thermal diffusivity of the subsea oor sediment (see supplementary material); t slide is the age of a submarine landslide. The analytical solution for the Orca upslope location using 30°C/km geothermal gradient (red dashed arrows) dates the slide to ~7.8 ka, which is similar to the result of our numerical simulation. Gray dashed lines show the sensitivity of the analytical solution to the varying geothermal gradients.
The age of the Orca slide from the analytical solution is ~7.8 ka, which is in a good agreement with our numerical solution ( Figure 5). The discrepancy between the analytical and numerical solutions may be caused by a difference in domains; the numerical solution is solved for a nite domain, whereas the analytical solution is solved for a semi-in nite domain. There are also slightly different physical properties with depth that could cause variation in the results as the numerical solution has varying porosity and thermal diffusivity, whereas the analytical solution assumes homogeneous sediments properties with depth.
Our seismic and modeling-based landslide dating technique is a novel method for dating submarine landslides without core data. Because gas hydrate systems occur worldwide and often coexist with submarine landslides, there may be many locations where our approach can be applied. Moreover, this technique is especially relevant given the expanding public seismic databases worldwide. The following are only few examples where published seismic data appear to show irregular BSRs deviating from the sea oor bathymetry below the landslide escarpment and/or below MTDs: the Cape Fear slide complex offshore the US East Coast 42 , offshore Oregon, USA 43 , the Storegga slide offshore southern Norway 44 , the Brunei slide offshore Brunei 45 , and the Hinlopen megaslide offshore Svalbard 46,47 .

Conclusions
We estimate the age of the submarine landslide on the southern bank of the Orca Basin to be ~8 ka based on the modern depth of the bottom simulating re ection in seismic data coupled with numerical heat ow models. This new approach does not require seismic stratigraphic correlations or sediment core dating. We also provide an analytical solution that can be used for quick-look submarine slide age estimates elsewhere. Our study shows that the Orca and similar gas hydrate systems expand below the slide escarpments and dissociate below the MTDs. Finally, we nd such transformations can be still ongoing thousands of years after the slope failures indicating long-lasting dynamic behavior of slideimpacted gas hydrate systems.

3D seismic data and pre-slide sea oor reconstruction
The sea oor, BSR, and salt surface are mapped in the 3D seismic data sampled to 4.8 m. We use depthmigrated 3D seismic data, which was originally converted from time to depth by WesternGeco. The seismic data provide accurate depths within the GHSZ (our target interval), which is supported by a good correlation between the depths of major seismic horizons (e.g. sea oor and salt top) and corresponding responses in resistivity and gamma ray well logs available in the study area. The frequency of the processed seismic data ranges from 5-55 Hz providing ~7-9 m vertical resolution at the BSR level.
We use the sea oor seismic re ection to reconstruct the pre-slide sea oor geometry and infer the base of the GHSZ before the slide event. For this reconstruction, we use manual and automatic interpolation of the bathymetric contours from the sea oor surface surrounding each headwall scarp. The approach provides a reasonable estimate of the change in water depth after the slide event and with it, the total volume of the slide ( Figure 1B, Figure 2A, B). Under the basin oor, we extend the pre-slide sea oor surface along the base of the MTD marked by a distinct trough-leading re ector indicating more consolidated slide sediments onlapping the ancient sea oor (Figure 2A).

Gas hydrate stability and geothermal gradients
The gas hydrate phase boundary was estimated assuming 100% methane concentration, 3.5% NaCl, and hydrostatic pressure 48 . The assumption of pure methane gas is supported by the seismic data showing no deep-rooted gas chimneys that could source heavier hydrocarbons towards the base of the GHSZ. To estimate the mean geothermal gradient, we apply linear temperature approximation between the sea oor and the BSR, using a bottom water temperature of 4.2°C, the BSR depth, and the methane hydrate phase boundary diagram.
2D heat ow modeling across the slope We use a 2D plane-strain nite-element model to simulate the potential effect of a salt body on the heat ow and the base of GHSZ. The geometry of the salt body and the seabed topography are obtained from the 3D seismic data (Supplementary Figure 1A). Heat ow in the model occurs only through conduction, which assumes that heat advection due to pore uid migration is negligible. The radiogenic heat, which produces heat in addition to the basal heat ow, is absent in salt and 1.0E-6 W/m 3 in the sediments 49 .
The boundary conditions include a uniform temperature of 4.2°C at the sea oor, no heat ow at the side boundaries, and a uniform basal heat ow of 0.0234 W/m 2 (Supplementary Figure 1A). The basal heat ow is constrained by the sea oor temperature and regional average geothermal gradient of 25.5°C/km (see main text). The thermal conductivity of salt varies with temperature 37 , ranging from ~5 W/m °C at the base of the salt body to ~7 W/m °C at the top of the model (Supplementary Figure 1B). The thermal conductivity of sediments (~1 to 2 W/m °C) is proportional to the porosity and the mineralogy, and the porosity decreases with depth according to observations in shallow marine sediments in the Gulf of Mexico 50 (Supplementary Figure 1C).

Transient 1D heat ow modeling
We use a numerical model 51 with a vertical grid size of 10 m to simulate the transient temperature change below the slide-impacted sea oor upon an instantaneous temperature change at the sea oor. At time 0, we set the temperature at the sea oor to 4.2°C and keep it constant with time; the base of the model is at the depth that is ~5 times the depth of the BSR, where there is a constant geothermal heat supply that correlates with the local geothermal gradients predicted by the 2D heat ow model. In addition, we assume the pores are fully saturated with water. The temperature is calculated from the energy conservation equation: where t is time (s); z is depth below the sea oor (m); T is temperature (°C); C bulk is the bulk heat capacity (J kg −1 o C −1 ) of the sediment; λ bulk is the bulk thermal conductivity (W m −1 o C −1 ). C bulk and λ bulk increase with depth as the porosity decreases (see supplementary material for the calculations of λ bulk and C bulk and physical properties of the sediments).

Analytical solution below slide escarpments
For more general cases, it is possible to assume homogeneous sediment properties and a constant geothermal heat ux below the slide escarpments. By solving equation (1) with constant λ bulk and C bulk we obtain an analytical expression for the depth evolution of the GHSZ (z bsr , m) with a known temperature at the BHSZ (T bsr , °C) 52 : 52 where T s , 0 and T s , 1 are the sea oor temperature before and after the change, respectively (°C); T z , 0 is the initial temperature below the sea oor at depth z (°C) (see Figure 4A); T bsr can be derived from the modern BSR depth (the intersection between the in situ temperature pro le and the methane hydrate phase boundary) (see Figure 4A); κ is the average thermal diffusivity of the subsea oor sediment (see supplementary material); t is time.

Data Availability
The 3D seismic data are not publicly available due to its proprietary status. The data that support the ndings of this study may be available on request from the corresponding author A.P.
Declarations extent and depth (mbsl). Pink line outlines the slide escarpment over the gray shaded bathymetry surface. The two panels on the right show the highly variable BSR depth below the modern sea oor (upper) and more coherent BSR depth below the reconstructed pre-slide sea oor (lower). D) Seismic cross section a-b shows three industry wells (labeled white lines) with plotted gamma ray (green) and resistivity (red) logs. Figure 1A, B, C. Gas hydrates are evident from the highresistivity intervals above the BSR in the wells WR143-001 and WR143-003.

Figure 2
Irregular bottom simulating re ection (BSR) under the slide-impacted sea oor. A) Seismic cross-section cd showing the BSR, which is not parallel to the modern sea oor (blue arrows), but strikingly parallel to the reconstructed pre-slide sea oor (red dotted line). Steady-state geothermal gradients required to explain the depth of the bottom simulating re ection (BSR) using pre-slide sea oor (red) show better consistency than those calculated using the BSR and modern sea oor depths (green); Tgrad-geothermal gradient. The left inset shows three BSR locations (stars) outside of the slide escarpment (pink line) and away from the shallow salt (colored surface in mbsf) selected for calculation of the regional average geothermal gradient in our study area (25.5 °C/km). B) Interpreted seismic section c-d showing the pre-slide sea oor, modern BSR, mass transport deposits (MTD), upslope and downslope locations selected for modeling analyses and other elements of the slide-gas hydrate system labeled. Insets show schematic adjustment of the temperature eld after the slope failure (cooling effect at the upslope location and warming effect at the downslope location) leading to the reciprocal BSR shifts (blue arrows). SF-sea oor; PSF -pre-slide sea oor; T-temperature; D-depth; t0-n -time-temperature pro les.

Figure 3
Two-dimensional steady-state conductive heat ow model.  Transient 1D heat ow modeling at the upslope and downslope locations.

Figure 5
Analytical solution for submarine landslide dating.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. Supplementaryinformation.docx