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Article

A Probabilistic Assessment Framework for Submarine Landslide Susceptibility in Continental Slopes with Rich Gas Hydrates

by
Lin Tan
1,2,
Mingliang Zhou
1,2 and
Feiyang Wang
3,*
1
State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
2
Key Laboratory of Geotechnical and Underground Engineering (Tongji University), Ministry of Education, Shanghai 200092, China
3
Department of Civil Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
*
Author to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2023, 11(7), 1366; https://doi.org/10.3390/jmse11071366
Submission received: 24 May 2023 / Revised: 20 June 2023 / Accepted: 3 July 2023 / Published: 5 July 2023
(This article belongs to the Special Issue Advances in Gas Hydrate Development: Experimental and Numerical Simulation)
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Abstract

:
Submarine landslides in regions enriched with gas hydrates pose a significant threat to submarine pipelines, cables, and offshore platforms. Conducting a comprehensive regional-scale susceptibility assessment is crucial for mitigating the potential risks associated with submarine landslides in gas hydrate enrichment regions. This study conducted a preliminary exploration by presenting a probabilistic assessment framework that integrated database construction, rapid prediction model training, and landslide susceptibility assessment in hydrate enrichment regions. The database was a virtual repository constructed using numerical simulations of hydrate dissociation under various combinations of factors, including water depth, geothermal gradients, seafloor slope gradients, the seafloor temperature’s rate of increase, gas hydrate saturation, and the strength and permeability of sediments. The rapid prediction model was trained using machine learning techniques, relying on the virtual database. A probabilistic assessment was performed using Monte Carlo simulations, with the landslide susceptibility determined by the rapid prediction model. The probability of landslide susceptibility exceeding a certain threshold served as an indicator for classifying the susceptibility of the study area. The proposed framework was implemented in the Shenhu area of the South China Sea, which is a representative region known for its substantial hydrate enrichment and well-developed landslides. The trained rapid prediction model for landslide susceptibility exhibited a speed advantage of over 60,000 times compared to traditional numerical calculation methods. The statistical analysis of the results in Monte Carlo simulations suggested that the landslide susceptibility was subjected to a high level of uncertainty due to limited survey data availability. Based on the probability of landslide susceptibility exceeding 0.4 in Monte Carlo simulations, the study area was classified into three zones of susceptibility: low, moderate, and high levels.

1. Introduction

Submarine landslides are widespread in hydrate-enriched continental slopes [1,2,3,4,5], such as the submarine landslides occurring in the north continental slope of the South China Sea, which are enriched with natural gas hydrates [1,6]. Submarine landslides have the potential to destroy submarine pipelines [7,8], cables [9,10], and offshore platforms [11] and to generate destructive waves, even causing tsunamis [12]. The rising demand for oceanic energy has led to significant growth in the exploration and extraction of offshore natural resources, including oil, gas, and natural gas hydrates [13]. In particular, natural gas hydrates have caught global attention as a potential alternative energy source due to their substantial reserves, high energy density, and lower pollution rates. However, gas hydrates can also serve as a potential trigger for submarine landslides. Hance [14] estimated that approximately 10% of submarine landslides were triggered or promoted by gas hydrate dissociation. In view of this, assessing the submarine landslide susceptibility, a commonly used measure to map landslide-prone zones, in hydrate enrichment regions is of essential importance for disaster prevention and reduction.
Natural gas hydrates are ice-like crystalline compounds composed of water molecules and trapped methane gas. They are widely distributed in marine sediments under intermediate pressure and low temperature [15]. Hydrates dissociation can be caused by changes in climate, such as seafloor warming [16] and sea level drop [17], as well as anthropogenic disturbances, including activities related to oil and gas production [18]. The dissociation of gas hydrates releases large amounts of methane gas, resulting in cementation loss and excess pore pressure buildup, which may cause or promote instability in submarine slopes. The recognition of hydrate dissociation as a potential trigger for submarine landslides has motivated extensive research efforts to understand the underlying mechanisms and susceptibility assessment of submarine landslides. The instability mechanisms of hydrate-bearing slopes are explored through physical laboratory experiments [19,20,21,22,23] and numerical simulations [24,25,26]. However, research on landslide susceptibility assessment in marine hydrate enrichment regions is still in the preliminary stage of qualitative analysis [27]. The challenges of quantitative assessments of these regions stem from the limited availability of comprehensive survey data at a regional scale and the unmatured approaches for assessing submarine landslide susceptibility.
Landslide susceptibility assessment entails the evaluation of the likelihood of a landslide occurring in a specific area based on geological and terrain conditions [28]. Assessment approaches for terrain landslides can be categorized into statistically based and physically based methods [29]. Statistically based methods use statistical analysis to establish correlations between landslide occurrence and various factors, including the slope gradient, soil properties, land use, and vegetation [30,31]. These methods require a comprehensive inventory of the historical landslides coupled with information on related factors. Collecting such data for marine sediments over an extensive region poses a great challenge. In contrast, physically based methods use theoretical frameworks linking terrain, geological, and geotechnical conditions based on reasonable simplification [32,33,34]. Geotechnical analysis is used to reproduce the physical processes that govern landslide occurrence. Physically based methods are more suitable for assessing submarine landslides and have been used to assess the susceptibility of seismically induced submarine landslides in the South China Sea [35,36,37].
Physically based methods require the use of sufficient and accurate input parameters in the geotechnical analysis to achieve an accurate assessment [33]. These parameters, such as water depth, temperature, geothermal gradient, terrain slope gradient, soil strength, permeability, and hydrate distribution, exhibit inherent spatial heterogeneity in hydrate enrichment regions [38,39]. As a result, uncertainties are inevitably involved in the process of determining these parameters, primarily due to the extensive study area and limited sampling, especially in the case of marine sediments. Therefore, the accuracy and precision of a deterministic assessment of an extensive area will be unsatisfactory because of the challenges involved in obtaining, checking, and processing large spatial datasets related to submarine environments [40]. Probabilistic approaches that consider the uncertainties in the input parameters are more appropriate for assessing the susceptibility of submarine landslides.
Probabilistic approaches usually utilize Monte Carlo simulations and statistical analysis to assess the landslide occurrence probability [41,42]. Monte Carlo simulations of hydrate-induced landslides necessitate substantial numerical modelings of the hydrate dissociation process for slope stability analysis. However, hydrate dissociation is a complex thermo–hydro–mechanical–chemical coupling process [43]. It includes heat transfer, phase exchange between gas–water fluids and solid gas hydrates, fluid seepage, and deformation of the soil skeleton [44,45]. The hydrate dissociation/formation process is governed by the thermodynamic stability of hydrates, which is influenced by the pore pressure and temperature fields [15]. The dissociation/formation of hydrates can change the mechanical properties and seepage characteristics of the reservoir sediments [46,47,48], thereby influencing the deformation of the soil skeleton and the fluid seepage process. The exothermic/endothermic effects during hydrate dissociation/formation and the convective heat generated by fluid seepage can impact the heat conduction process [49]. Soil skeleton deformation modifies the sediment’s permeability and, thus, impacts the seepage and heat conduction processes [50]. It would be too expensive and time-consuming to conduct the substantial numerical modeling of such a complicated process involved in the Monte Carlo simulations for a regional-scale probabilistic analysis. As a result, the determination of landslide susceptibility in a sloping hydrate reservoir requires a rapid prediction model.
In developing a rapid prediction model of landslide susceptibility, machine learning techniques offer an effective alternative, which has seen significant growth in various engineering disciplines for predicting complex system behaviors [51,52,53,54,55]. For example, Zhou et al. [51] proposed a meta-model based on an artificial neural network algorithm, which efficiently predicted the responses of a hydrate reservoir during gas production with reduced computational demand. Vikara et al. [52] discussed a systematic approach for assessing the production potential of oil and gas wells by using artificial intelligence and machine learning to investigate shale-controlling factors. The framework considered geologic properties and well design attributes to draw a comprehensive evaluation. Furthermore, Sinha et al. [53] emphasized the importance of automated monitoring tools for carbon capture and storage projects to mitigate the risk of stored carbon dioxide leakage. However, like the drawback of the statistically based methods for submarine susceptibility assessment, training a rapid prediction model based on machine learning also needs a database of landslide susceptibility and the input parameters to establish their relationship.
Altogether, landslide susceptibility assessment in marine hydrate enrichment regions is still in the preliminary stage of qualitative analysis due to the limited survey data, the spatial heterogeneity in the influencing parameters, and the complicated mechanism of hydrate dissociation. This study presents a preliminary exploration of a quantitative assessment framework for susceptibility assessment of submarine landslides induced by hydrate dissociation. This framework combines virtual database construction, rapid prediction model training, and probabilistic assessment based on Monte Carlo simulations. It is applied to a representative hydrate enrichment region with well-developed submarine landslides, namely, the Shenhu area of the South China Sea, and presents a landslide susceptibility zonation map.

2. Methodology

2.1. Workflow

A framework based on machine learning was devised for a probabilistic assessment of hydrate-associated landslide susceptibility. Figure 1 illustrates the overview of the entire workflow. The first step involves constructing a virtual database that encompasses landslide susceptibility and its influencing factors. The study area is rasterized into a grid composed of cells. Each cell represents an infinite slope, which is subdivided into an array of elements. The survey data of the influencing parameters are interpolated into this grid to generate a geological model, including the spatial distribution of water depth, seafloor slope gradient, geothermal gradient, hydrate saturation, cohesion, and permeability. The process of hydrate dissociation in each cell is numerically modeled to calculate the transient pore pressure and strength parameters. Subsequently, these results are utilized within the framework of the limit equilibrium method to construct a stability analysis of the infinite slope. The analysis of the slope’s stability results in a dimensionless index that characterizes the landslide susceptibility. The input parameters, along with the calculated landslide susceptibility index at each cell, constitute a sample, and all cells within the study area form the sample database required for machine learning. As a result, a virtual database pertaining to the susceptibility of hydrate-associated landslides is established.
In the second step, a rapid landslide susceptibility prediction model is developed based on the virtual database. Machine learning techniques are used to establish the connections between landslide susceptibility and the influencing parameters. The training model utilizes the widely acclaimed and efficient XGBoost model, which is currently one of the most popular choices.
Finally, the trained rapid prediction model of landslide susceptibility is subsequently implemented to construct a probabilistic assessment of submarine landslide susceptibility. The landslide susceptibility is classified according to its exceeding probability, which is determined through Monte Carlo simulations considering the variation in the input parameters at each cell. The landslide susceptibility index in the Monte Carlo simulations is determined using the rapid prediction model. Statistical analysis of the Monte Carlo simulations gives rise to an exceeding probability of landslide susceptibility index, namely, the frequency at which the landslide susceptibility exceeds a critical value [41,42]. The exceeding probability of susceptibility is ranked, classifying the susceptibility into three levels: high, moderate, and low. According to the classification, the assessment provides the landslide susceptibility zonation map of the study area.

2.2. Susceptibility Analysis Based on the Physical Model

The slope stability analysis is performed using the limit equilibrium method [24,56]. This study focused on a one-dimensional infinite slope undergoing hydrate dissociation, which leads to the buildup of pore pressure and a reduction in shear strength. It is assumed that a planar potential sliding surface runs parallel to the seafloor, which is widely used, particularly for submarine slides with lateral–longitudinal dimensions much greater than the thickness [56,57,58]. The slope safety factor, expressed as the ratio of shear stress to shear strength, was used as an indicator of slope stability. As the pore pressure develops and the cohesion reduces during hydrate dissociation, the safety factor varies over time. The time-dependent safety factors were formulated by Liu et al. [24] and are expressed as
F s ( t ) = τ f ( t ) τ d ( t ) = c ′ ( t ) + [ σ 0 ′ − u e ( t ) ] tan φ ′ ( t ) γ ′ H ( t ) sin β cos β
where t denotes time; τd and τf are the shear stress and the shear strength on the failure plane that are located at a depth of H; β is the slope angle; γ′ represents the buoyant unit weight of the sediments; σ′0 is the initial effective overburden stress on the failure plane; ue is the transient excess pore pressure that varies over time; and c′ and φ′ are the effective cohesion and internal friction angles of the sediments, respectively. Refer to [24] for the derivation of this equation and the determination of its parameters.
Numerical simulation of hydrate dissociation is used to determine the transient excess pore pressure and cohesion using the numerical simulator TOUGH + HYDRATE [59]. This simulator was developed by the Lawrence Berkeley National Laboratory and widely used for modeling geologic systems containing gas hydrates [60,61,62]. It is assumed that the fluid follows Darcy’s law and that the soil skeleton is poroelastic. TOUGH + HYDRATE can deal with phase change, heat transport, and fluid flow through porous media during hydrate dissociation by solving the coupled equations of mass and heat balance. The transient cohesion is calculated using a linear relationship with gas hydrate saturation. The internal friction angle is assumed to remain unchanged according to the laboratory tests [46,63].
Seafloor warming is adopted as the hypothetical landslide trigger. The evolution of the safety factor under the hypothetical scenario is derived using the aforementioned slope stability analysis model. The landslide onset time is determined by monitoring the time-dependent safety factor and identifying the point where it reaches below one. Then, the landslide onset time is converted to a dimensionless index to characterize the landslide susceptibility.

2.3. XGBoost-Based Machine Learning Description

The machine learning framework in this study adopts XGBoost as the primary algorithm to establish the linkages between the landslide susceptibility and the input parameters. XGBoost, an abbreviation for eXtreme Gradient Boosting, was proposed by Chen and Guestrin [64]. It is built on the gradient boosting approach [65], using the ensemble learning technique to combine multiple weak learners. XGBoost is an efficient and scalable implementation of the gradient boosting framework, which features the integration of several classification and regression trees to optimize the gradient tree boosting system. Additionally, XGBoost automatically runs parallel computation and accepts sparse inputs, which significantly enhances its speed. During the training process, shrinkage and column subsampling techniques are used to prevent overfitting and enhance accuracy. A more detailed explanation can be found in [64].
XGBoost supports multiple objective functions, including regression and classification. The XGBoost tree model utilizes ensemble learning with a classification and regression tree (CART) and implements data training with gradient boosting. In addition, this model can accurately predict high-quality results by effectively extracting features and their combinations from the data. XGBoost consists of multiple decision trees [66], where each tree predicts the residual value between the true value and the sum of predictions from all previous decision trees. The final result is obtained by summing the predicted values of all decision trees.

3. Study Area

The proposed framework was applied to the Shehu area of the South China Sea, a typical submarine landslide region enriched with gas hydrates [1,6] (Figure 2). The submarine environment of this region is characterized by favorable conditions for hydrate formation, namely, high pressure and low temperature. The seafloor has a slope gradient between 2 and 10 degrees and is located at a water depth ranging from 600 to 1600 m. The seafloor temperature varies between 4.8 °C and 6.4 °C, with a geothermal gradient that spans a range of 44 °C/km to 116 °C/km. Gas hydrates are present at a depth of around 100~300 m below seafloor (mbsf), with hydrate saturation achieving up to an impressive 78% [38]. Most of the gas hydrates in the Shenhu area occur within Late Miocene–Quaternary unconsolidated clayey silt and silty clay [67,68]. These hydrate-bearing sediments are typically characterized by low permeability [68]. There is a series of northwest-trending submarine canyons (each about 30~60 km long) alternating with submarine ridges [69]. The hydrate reservoirs contain various focused fluid flow structures, such as landslides, faults, mud diapirs, gas chimneys, and mud volcanoes. These structures provide conduits for gas migration from deep to shallow strata and offer storage capacity for hydrate formation [70].

4. Construction of Virtual Database

This section presents the construction of the virtual database comprising the input parameters and the calculated landslide susceptibility. The survey data demonstrate that the study area contains three layers from top to bottom: the overburden layer, the hydrate reservoir, and the underburden layer. Liu et al. [24] suggested that the thickness, cohesion, and permeability of the overburden layer play important roles in slope stability. The overburden thickness is governed by water depth, seafloor temperature, and geothermal gradient. In addition, slope stability is influenced by the seafloor slope gradient and excess pore pressure during hydrate dissociation, according to Equation (1). The buildup of excess pore pressure is related to the hydrate saturation, overburden permeability, and the seafloor temperature’s rate of increase. Therefore, the input parameters for the rapid prediction model of landslide susceptibility involve the water depth, geothermal gradient, seafloor slope gradient, rate of seafloor temperature increase, hydrate saturation, overburden cohesion, and permeability. Geological models of these factors were constructed based on a grid of 70 × 61 = 4270 cells, with each cell covering an area of approximately 460 m × 460 m.

4.1. Geological Parameters

Due to the difficulty in obtaining field measurements of the input parameters, the published data from the literature were collected. The isobaths from Figure 1b of [71] were digitized and converted into a raster format by means of the topo-to-raster tool in ArcGIS, a geographic information system that provides functions of geostatistical analyses and a coding environment for customizing data processing (Esri, https://www.esri.com/en-us/home, access on 23 May 2023). Figure 3a presents the bathymetric map of the Shehu area. Statistical analysis of the interpolated water depth in Figure 3b shows that the water depth ranged from 608 m to 1624 m, with a median value of 1147 m. The distribution followed a normal distribution, with a mean of 1130 m and a standard deviation of 241 m.
The geothermal gradient map in Figure 3c was created by interpolating scatter data using the topo-to-raster tool in ArcGIS. The scatter data were collected from published papers [72,73,74,75,76,77,78,79]. The interpolated geothermal gradient ranged from 44 °C/km to 116 °C/km, with a median value of 78 °C/km. Figure 3d depicts the histogram of the geothermal gradient, along with a normal distribution curve showing a mean of 77.70 °C/km and a standard deviation of 17.42 °C/km.
The map of the seafloor slope gradient (Figure 3e) was derived from the bathymetric map. Statistical analysis of the derived slope gradients in the study area (Figure 3f) showed that the minimum, median, and maximum slope angles are 0.01°, 2.28°, and 10.97°, respectively. The slope angle followed a lognormal distribution, with a mean of 2.54° and a standard deviation of 1.49°. The mean and standard deviation values for the logarithmic slope angle were calculated as 0.74 and 0.67, respectively.
The hydrate saturation distribution in the reservoir was derived from the drilling data. Since 2007, the Guangzhou Marine Geology Survey (GMGS) has conducted four gas hydrate survey drilling expeditions in the study area [80,81,82,83]. We collected the gas hydrate saturation data from pressure cores from the survey sites of the GMGS1, GMGS3, and GMGS4 expeditions, as shown in Figure 4. Using the sequential Gaussian simulation method, a subsurface hydrate distribution model was constructed based on the assumption that hydrate saturation adheres to a lognormal distribution. Figure 3g presents the subsurface model of hydrate saturation. The interpolated reservoir model indicates that hydrate saturation ranges from 0.07 to 0.80 with a median of 0.23 and conforms to a lognormal distribution with a mean of 0.24 and a standard deviation of 0.16, as presented in Figure 3h. In addition, the logarithmic mean and standard deviation of hydrate saturation are −1.47 and 0.33, respectively.

4.2. Geotechnical Properties

As the available data about the cohesion and permeability of submarine sediments are too sparse to support an accurate estimate, their values were determined by referring to experimental tests [67,68,84]. To account for the uncertainty in these two parameters, we generated random fields for them by means of the sequential Gaussian simulation method (Figure 5). As shown in Figure 5b, the logarithmic permeability was assumed to follow a normal distribution, with a mean of −20.30 and a standard deviation of 1.12. The cohesion uncertainty for sand and clay was considered through two separate random fields, shown in Figure 5c,e. The random fields were generated based on a lognormal distribution. The logarithmic mean and standard deviations were 8.40 and 0.44 for sandy formations and 10.45 and 0.14 for clayey formations, respectively.

4.3. Landslide Susceptibility Calculation

Considering the effects of the input parameters on landslide susceptibility, six regional-scale assessments were carried out to construct a virtual database for machine learning, with the parameter settings outlined in Table 1. The spatial distributions of water depth, geothermal gradient, slope gradient, and hydrate saturation were more reliable, as they were derived from the collected data. All cases used the same spatial distribution of these four parameters, which were determined in Section 4.1. In Case 1, the values of permeability and cohesion of the overburden layer were assumed to be uniform. The values were set to 1 × 10−19 m2 and 35 kPa, respectively, according to the experimental results of this area [68]. In addition, the seafloor temperature’s rate of increase was set to 3 °C/century. The permeability in Case 2 was set to the random field in Figure 5a. In Case 3 and Case 4, the cohesion was described using the random fields in Figure 5c,e, respectively. Case 5 and Case 6 varied the seafloor temperature’s rate of increase to 1 and 5 °C/century, respectively.
Figure 6 illustrates the landslide onset time map of Case 1, along with the corresponding histogram. The cumulative distribution function was derived from the cumulative distribution of the landslide onset time (Figure 6b), which shows a normal distribution. Based on this derived cumulative distribution function, the landside onset time was converted to a dimensionless landslide susceptibility index, Is, via Equation (2):
I s = P ( t > t f ) = 1 − y 0 − A ∫ − ∞ t f 1 2 π σ e − ( t − μ ) 2 2 σ 2 d t
where tf is the landslide onset time; μ and σ represent the expectation and the standard deviation of the normal distribution; and y0 and A are the fitting parameters. Figure 7a displays the landslide susceptibility map of Case 1, derived from Figure 6a. Similarly, landslide susceptibility maps for the remaining five cases were obtained, as shown in Figure 7b–f. Each case included 61 × 70 = 4270 cells and all six cases constituted a virtual database of 4270 × 6 = 25,620 samples for machine learning.

5. Training of the Rapid Prediction Model

The constructed virtual database was divided into a training set (80% of data) and a testing set (20% of data). As the susceptibility index is a continuous value, the objective function in the XGBoost model was set to be linear regression. The gradient boosting used a tree model, and the maximum depth of each tree was designated as 6, restraining the leaf nodes to six layers. Using the XGBoost-based machine learning model with these settings, the rapid prediction model of landslide susceptibility was trained. Its accuracy and efficiency are evaluated in the following sections. Furthermore, the controlling factors were investigated via an importance analysis of the input parameters.

5.1. Accuracy of the Predicted Landslide Susceptibility

To evaluate the overall accuracy of the rapid prediction model, the numerically calculated susceptibility index was plotted against its predicted values from the rapid model in both the training and testing sets (see Figure 8). The plot contained a reference line with a slope of 1. The scatters were distributed around the reference line, indicating a good match between the predicted results and the calculated results. Moreover, the values of the mean squared errors (MSE), mean absolute error (MAE), and coefficients of determination (R2) were summarized in the inserted tables to evaluate the performance of the trained model. The training set exhibited an MSE of 0.005, an MAE of 0.05, and an R2 score of 0.93. Similarly, the testing set yielded an MSE of 0.006, an MAE of 0.06, and an R2 score of 0.92. The combination of low MSE and MAE values along with high R2 scores indicated that the trained rapid model yielded accurate predictions of the landslide susceptibility index. Its accuracy and efficiency are evaluated in the following sections. However, it is worth noting that the rapid model tends to overestimate the susceptibility index of samples with values below 0.2.
Applying the rapid prediction model to Case 1, we obtained the predicted landslide susceptibility map shown in Figure 9. A noticeable discrepancy between the rapid prediction and the physically based map (Figure 7a) was observed in the low-susceptibility zone located in the southeastern part of the study area, as depicted in Figure 10. This discrepancy could be attributed to the rapid prediction model’s tendency to overestimate the susceptibility for samples with low values. Despite this discrepancy, it remained within an insignificant range of −0.1 to 0.1, as indicated in Figure 11. Furthermore, a high level of agreement between the predicted and physically based maps was evident, as demonstrated by the comparison between Figure 7a and Figure 9. In conclusion, we can affirm that the rapid prediction model was able to effectively predict the landslide susceptibility index within an acceptable margin of error.

5.2. Enhanced Efficiency

The computational efficiency of the rapid prediction model was demonstrated by comparing its processing time with that of the numerical model. Both the numerical calculation and the rapid prediction were carried out on a desktop computer equipped with two Intel Core E5-2630 Central Processing Units (CPU) and 16 GB of random access memory (RAM). The numerical calculation of the regional-scale landslide susceptibility assessment for Case 1 took around one week, whereas the rapid prediction model completed the task within a mere one second. Notably, the prediction model exhibited a computational efficiency that was over 60,000 times faster than the numerical calculation. This superiority will be even more significant when the numerical calculation involves complex constitutive models of the hydrate-bearing sediments and the heterogeneity of the input parameters.

5.3. Importance Analysis

The importance of the input parameters was comprehensively evaluated to identify the controlling factors, as shown in Figure 12. This evaluation was based on their weights, which represent the number of features used during the splitting of the subtree model. As a result of the evaluation, five primary factors were identified from the seven input parameters. These factors were ranked in descending order of importance as follows: geothermal gradient, water depth, overburden permeability, overburden cohesion, and hydrate saturation. The effects of seafloor slope gradient and the rate of seafloor temperature increase were even lower compared with the five primary factors. The geothermal gradient and water depth play critical roles in determining the burial depth of the hydrate-bearing layer, which controls the initial effective overburden stress, i.e., σ′0 in Equation (1). Overburden permeability and hydrate saturation affect the buildup and diffusion of excess pore pressure during hydrate dissociation. Finally, as a critical factor determining soil strength, overburden cohesion directly influences the stability of the sloping reservoir.

6. Probabilistic Susceptibility Assessment

6.1. Monte Carlo Simulation

We conducted 10,000 Monte Carlo simulations for a probabilistic submarine landslide susceptibility assessment for the Shenhu area. In these simulations, the input parameters for each cell in Case 1 were adjusted by introducing errors that were assumed to be uniformly distributed within a specific range, as presented in Table 2. Due to the lack of detailed survey data, the error margins were arbitrarily specified in reasonable ranges. Subsequently, we utilized the rapid model to predict the landslide susceptibility index of each cell based on these adjustments.

6.2. Statistical Analysis

Figure 13 displays the average landslide susceptibility predicted by 10,000 Monte Carlo simulations. The discrepancy and standard deviation, as shown in Figure 14, were used to evaluate the assessment result’s accuracy and precision, respectively. It was evident that the discrepancy between the predicted and calculated results is positive in the southeast part of the study area and negative in the northwest part, as shown in Figure 14a. This indicates that the landslide susceptibility from the numerical simulation was underestimated in the southeast part and overestimated in the northwest part. Comparing Figure 14a with the spatial distribution of the water depth (Figure 3a) and the geothermal gradient (Figure 3c) suggested that the underestimated regions were deep and cold, namely, with deep water and a low geothermal gradient, while the overestimated regions were shallow or warm. Moreover, in the deep cold regions, the landslide susceptibility assessment also exhibited low precision, characterized by the high standard deviation shown in Figure 14b.
The probability density distribution of the discrepancy (Figure 15a) revealed that the positive errors were primarily within 0.2, which was an acceptable range. However, the negative errors were within −0.5, which was considerably large. As shown in Figure 15b, the third quartile of the standard deviation of the Monte Carlo simulation results was 0.07, indicating that the landslide susceptibility in 25% of cells in the study area had a deviation above 0.07. It is evident that areas with larger discrepancies exhibit higher standard deviations. Hence, the landslide susceptibility in this region is characterized by significant uncertainty, underscoring the necessity of conducting a probabilistic assessment in this submarine hydrate enrichment region.

6.3. Landslide Susceptibility Zonation

The landslide susceptibility in the probabilistic assessment was represented by the susceptibility’s exceeding probability, namely, the probability that the susceptibility exceeds a critical value. Figure 16 illustrates the exceeding probability maps with critical values of 0.3, 0.4, and 0.5. The map generated with a critical susceptibility of 0.4 exhibited good agreement with the reported zones where historical landslides were identified through seismic data analysis by He et al. [1]. Based on the exceeding probability with a critical susceptibility of 0.4, P(Is > 0.4), a zoning map of landslide susceptibility was generated, as illustrated in Figure 17. The susceptibility was classified into three levels by means of natural breaks: low (P(Is > 0.4) ≤ 0.21), moderate (0.21 < P(Is > 0.4) ≤ 0.69), and high (0.69 < P(Is > 0.4) ≤ 1).

7. Conclusions and Discussion

This paper presents a preliminary exploration of a probabilistic assessment framework for predicting the susceptibility of submarine landslides in a hydrate enrichment region. The assessment mapped the exceeding probability of landslide susceptibility and classified it into three levels: low, moderate, and high. The proposed framework was applied to the Shenhu area of the South China Sea, which is a representative hydrate enrichment region with well-developed submarine landslides. Through numerical simulations of hydrate dissociation, a virtual database of 25,620 samples was constructed, based on which the rapid prediction model of landslide susceptibility was trained. The rapid prediction model was over 60,000 times faster than the numerical simulation. Using the rapid prediction model to determine the landslide susceptibility, 10,000 Monte Carlo simulations were conducted to perform a probabilistic assessment. The landslide susceptibility showed low accuracy and precision in 25% of the study area, suggesting that the probabilistic method is necessary to conduct a submarine landslide susceptibility assessment of a hydrate enrichment region with limited data. Finally, a landslide susceptibility zonation map, with the low, moderate, and high levels, was created with a critical susceptibility index of 0.4. The high-susceptibility zones were consistent with the reported historical landslide development areas.
We must highlight the limitation of this study. The available data of the study area are too sparse to form an accurate subsurface model, which leads to high uncertainty in the assessment results. As more data become available in the study area, the assessment susceptibility zonation map could become more precise. Moreover, this study only considered the geological and geotechnical parameters of the hydrate-bearing sediments but ignored the influence of the shallow focused fluid flow system, faults, and earthquakes, which also play important roles in the instability of submarine landslides [37,85]. These important factors should be involved in a future assessment. The challenge of this work is that slope stability analysis needs a more sophisticated approach, for example, a shear band propagation method [86].

Author Contributions

Conceptualization, L.T.; Data curation, L.T.; Methodology, F.W. and L.T.; Software, M.Z. and L.T.; Formal analysis, F.W.; Writing—original draft preparation, L.T.; writing—review and editing, M.Z. and F.W.; Project administration, M.Z. and L.T.; Funding acquisition, L.T. and M.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Natural Science Foundation Committee Program of China, grant number 42206219, U20B6005, 41907245; the Science and Technology Commission of Shanghai Municipality, China, grant number 22YF1429900.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data associated with this research are available and can be obtained by contacting the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

References

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Figure 1. A workflow for a probabilistic assessment of submarine landslide susceptibility associated with gas hydrates.
Figure 1. A workflow for a probabilistic assessment of submarine landslide susceptibility associated with gas hydrates.
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Figure 2. The location of the Shenhu area, outlined with a box, on the northern continental slope of the South China Sea.
Figure 2. The location of the Shenhu area, outlined with a box, on the northern continental slope of the South China Sea.
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Figure 3. The spatial and statistical characterizations of the geological conditions and hydrate distribution: (a,b) water depth; (c,d) geothermal gradient; (e,f) seafloor slope gradient; (g,h) hydrate saturation.
Figure 3. The spatial and statistical characterizations of the geological conditions and hydrate distribution: (a,b) water depth; (c,d) geothermal gradient; (e,f) seafloor slope gradient; (g,h) hydrate saturation.
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Figure 4. Hydrate saturation profiles from the pressure cores and chloride anomaly in sites of expeditions GMGS1, GMGS3, and GMGS4. THOZ: top of hydrate occurrence zone; BHSZ: base of hydrate stability zone; BHOZ: base of hydrate occurrence zone.
Figure 4. Hydrate saturation profiles from the pressure cores and chloride anomaly in sites of expeditions GMGS1, GMGS3, and GMGS4. THOZ: top of hydrate occurrence zone; BHSZ: base of hydrate stability zone; BHOZ: base of hydrate occurrence zone.
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Figure 5. The random fields and histograms of permeability (a,b) and cohesion (c–f).
Figure 5. The random fields and histograms of permeability (a,b) and cohesion (c–f).
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Figure 6. Slope stability results of Case 1: (a) landslide onset time map and (b) the corresponding histogram plot, as well as the inferred curve of the cumulative distribution function.
Figure 6. Slope stability results of Case 1: (a) landslide onset time map and (b) the corresponding histogram plot, as well as the inferred curve of the cumulative distribution function.
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Figure 7. Landslide susceptibility maps from numerical calculation of cases listed in Table 1.
Figure 7. Landslide susceptibility maps from numerical calculation of cases listed in Table 1.
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Figure 8. Calculated landslide susceptibility of the sloping reservoirs against the predicted values for (a) the training set and (b) the testing set.
Figure 8. Calculated landslide susceptibility of the sloping reservoirs against the predicted values for (a) the training set and (b) the testing set.
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Figure 9. The landslide susceptibility map predicted using the rapid model.
Figure 9. The landslide susceptibility map predicted using the rapid model.
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Figure 10. Discrepancy map between the predicted and calculated landslide susceptibility.
Figure 10. Discrepancy map between the predicted and calculated landslide susceptibility.
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Figure 11. The probability density distribution of the discrepancy between the predicted and calculated landslide susceptibility.
Figure 11. The probability density distribution of the discrepancy between the predicted and calculated landslide susceptibility.
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Figure 12. Weight of the input parameters.
Figure 12. Weight of the input parameters.
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Figure 13. The map of average landslide susceptibility from the Monte Carlo simulations.
Figure 13. The map of average landslide susceptibility from the Monte Carlo simulations.
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Figure 14. Maps of (a) discrepancy between the average of predicted susceptibility index in Monte Carlo simulations and the calculated susceptibility and (b) standard deviation of Monte Carlo simulations.
Figure 14. Maps of (a) discrepancy between the average of predicted susceptibility index in Monte Carlo simulations and the calculated susceptibility and (b) standard deviation of Monte Carlo simulations.
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Figure 15. The probability density distribution of the (a) discrepancy between the average of predicted susceptibility index in Monte Carlo simulations and the calculated susceptibility and (b) standard deviation of Monte Carlo simulations.
Figure 15. The probability density distribution of the (a) discrepancy between the average of predicted susceptibility index in Monte Carlo simulations and the calculated susceptibility and (b) standard deviation of Monte Carlo simulations.
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Figure 16. Exceeding probability of landslide susceptibility with critical values of (a) 0.3, (b) 0.4, and (c) 0.5. The shadow areas are the reported zones where historical landslides were identified through seismic data analysis by He et al. [1].
Figure 16. Exceeding probability of landslide susceptibility with critical values of (a) 0.3, (b) 0.4, and (c) 0.5. The shadow areas are the reported zones where historical landslides were identified through seismic data analysis by He et al. [1].
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Figure 17. Zoning map of landslide susceptibility in the Shenhu area.
Figure 17. Zoning map of landslide susceptibility in the Shenhu area.
Jmse 11 01366 g017
Table
Table 1. Parameter setting in numerical analysis cases.
Table 1. Parameter setting in numerical analysis cases.
CasesWater DepthGeothermal GradientSlope GradientHydrate SaturationPermeabilityCohesionTemperature Increase Rate
Case1Figure 3aFigure 3cFigure 3eFigure 3g1 × 10−19 m235 kPa3 °C/century
Case2Figure 5a35 kPa3 °C/century
Case31 × 10−19 m2Figure 5c3 °C/century
Case41 × 10−19 m2Figure 5e3 °C/century
Case51 × 10−19 m235 kPa1 °C/century
Case61 × 10−19 m235 kPa5 °C/century
Table
Table 2. The error ranges of the input parameters in Monte Carlo simulation.
Table 2. The error ranges of the input parameters in Monte Carlo simulation.
ParametersError Range
Water depth (m)[−50, 50]
Slope angle (°)[−0.1, 0.1]
Geothermal gradient (°C/km)[−1, 1]
Hydrate saturation[−0.05, 0.05]
Logarithmic permeability [−0.5, 0.5]
Cohesion (kPa)[−2, 2]
Temperature increase rate (°C/century)[−0.1, 0.1]
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Tan, L.; Zhou, M.; Wang, F. A Probabilistic Assessment Framework for Submarine Landslide Susceptibility in Continental Slopes with Rich Gas Hydrates. J. Mar. Sci. Eng. 2023, 11, 1366. https://doi.org/10.3390/jmse11071366

AMA Style

Tan L, Zhou M, Wang F. A Probabilistic Assessment Framework for Submarine Landslide Susceptibility in Continental Slopes with Rich Gas Hydrates. Journal of Marine Science and Engineering. 2023; 11(7):1366. https://doi.org/10.3390/jmse11071366

Chicago/Turabian Style

Tan, Lin, Mingliang Zhou, and Feiyang Wang. 2023. "A Probabilistic Assessment Framework for Submarine Landslide Susceptibility in Continental Slopes with Rich Gas Hydrates" Journal of Marine Science and Engineering 11, no. 7: 1366. https://doi.org/10.3390/jmse11071366

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