Episodic fluid venting from sedimentary basins fueled by pressurized mudstones

Significance Sedimentary basins can provide the capacity to sequester carbon dioxide and store hydrogen fuel. However, reliable containment requires a robust, impermeable seal. Natural fluid vents in sedimentary basins demonstrate that even highly impermeable salt seals can be breached, allowing fluids to escape. We investigate the pressure dynamics associated with fluid venting in the Levant Basin as a means to better understand the conditions leading to seal failure. We show that, contrary to what is commonly assumed, mudstone sedimentary layers can act to store pressure and feed it into reservoir layers. This helps to explain the unexpectedly high frequency of venting. Hence, it is important to measure the pressure stored in mudstones during risk assessment of sequestration and borehole drilling projects.

Sedimentary successions often include high-permeability sandstone units enveloped by thick, low-permeability mudstone units.Because the surrounding mudstones can act as barriers to fluid leakage, these sandstones are often viewed as sealed reservoirs and therefore as targets for the large-scale sequestration of waste or storage of sustainable fuels (Krevor et al. 2023, Heinemann et al. 2021, Ringrose et al. 2021).However, fluid injection can pressurise such a reservoir to the point of triggering hydraulic fractures that breach the mudstone seal, enabling rapid depressurisation by fluid venting.This mechanism of sediment depressurisation has been recognised for several decades (Noble 1963, Cathles & Smith 1983, Roberts & Nunn 1995).It is generally believed that pressures below this failure threshold will dissipate by poroelastic diffusion through sealing mudstones over thousands of years (Muggeridge et al. 2004, 2005, Chang et al. 2013, Luo & Vasseur 2016).However, this slow depressurisation relies on the assumption that the mudstones themselves will remain at low pressure over these long timescales, whereas a variety of natural mechanisms are known to gradually pressurise the entire sedimentary column (Osborne & Swarbrick 1997).Luo & Vasseur (Luo & Vasseur 2016) showed that overpressured mudstones can, in theory, act as a pressure source rather than as a pressure sink, re-pressurising a sandstone reservoir after natural fluid venting.They proposed that this mechanism could fuel further episodes of venting.Kearney et al. (2023) recently developed a poroelastic model of episodic venting that supports and extends this basic concept.However, the predictions of these theoretical studies are difficult to test against observational evidence due to the long timescale associated with mudstone pressure evolution.
Here, we test the hypothesis that mudstones can act as sources of pressure, fuelling fluid venting from sedimentary basins.The geological record of episodic fluid venting in the Levant Basin (Fig. 1A) provides a rare opportunity to elucidate the role of mudstones in the pressure evolution of sedimentary basins.These vents release overpressure in localised fluid-expulsion events that transport fluid through kilometres of low-permeability rock via cylindrical conduits known as fluid-escape pipes (Cartwright et al. 2018).These pipes provide a high-permeability pathway to the surface, where they terminate as pockmarks, each recording a discrete episode of venting.Field observations of relict fluid-escape pipes consistently show evidence of fracturing (Huuse et al. 2005, Roberts et al. 2010, Løseth et al. 2011), suggesting that these pipes form by hydraulic fracturing (Cartwright & Santamarina 2015).Hydraulic fracturing typically requires the pore pressure to exceed the local compressive stress; indeed, drilling in a region of active venting has revealed near-lithostatic pore pressures (Reilly & Flemings 2010).Furthermore, the resulting pockmarks enable stratigraphic estimates of the time of each venting episode and thus constrain the rate of pressure recharge between episodes.when corrected for relative salt translation rates (Oppo et al. 2021).

The Levant Basin
In the North Levant Basin, located in the Eastern Mediterranean (Fig. 1B), more than 300 fluid-escape pipes have been documented, recording episodic fluid venting from 13 fixed locations across the region.For one of these locations, named Oceanus (Fig. 1C), Cartwright et al. (2021) calculated that the initiation of venting via hydraulic fracturing requires ∼30 MPa of overpressure.Tectonic compression and marginal uplift have been proposed as the main overpressuring mechanisms in the region (Oppo et al. 2021, Cartwright et al. 2021).The Levant Basin resides within a compressive tectonic regime stemming from the collision of the African and Eurasian plates.We estimate the strain at Oceanus to be less than 10% (Supplementary Material S1).Within the Levant Basin is a ∼3 km-thick Oligo-Miocene clastic succession consisting of turbiditic sandstones of Late Oligocene to Early Miocene age that are encased by mudstone.Many of these sandstone reservoirs host biogenic methane accumulations in NE-SW trending anticlines.The Levant pipes source methane and water from these anticline reservoirs and terminate at the seafloor as pockmarks (Fig. 1A).The pipes penetrate through a ∼1.5 km-thick layer of salt deposited during the Messinian Salinity Crisis (Ryan 2009).Recent activity of the Levant Fracture System has been uplifting the eastern margin of the basin, leading to gravity-driven, basinward salt flow since ∼2 Ma, contemporaneous with the formation of pipes in the area.
Each pipe forms vertically but the basinward viscous flow of salt advects existing pipes away from their initial positions, such that subsequent venting from the same reservoir requires the formation of a replacement pipe (Fig. 1C).Repetition of this process leads to the 13 observed trails of pipes in the North Levant Basin (Cartwright et al. 2018, Oppo et al. 2021).Thus, each pipe trail records episodic fluid venting from a single reservoir, suggesting that these reservoirs are repeatedly repressurised.From the spatial distributions of pockmarks within each pipe trail, the time of formation of each pipe can be estimated (Fig. 1D) using the methods of Oppo et al. (2021) and Cartwright et al. (2021).These approaches reveal that for each trail, pipe formation typically occurs every ∼100 kyr.Since fluid-escape pipes record critical subsurface pressures, the Levant pipe trails enable us to distinguish between theories for pressure redistribution between sedimentary layers.The timings of the pockmarks of the isolated Oceanus pipe trail are particularly well constrained as it is situated in a less tectonically-active region of the basin.Oceanus is therefore less susceptible to local stress changes that might affect the recharge mechanics.We thus focus our analysis on the Oceanus trail.The remaining 12 trails are distributed along the active basin margin and are used to extend our inferences from Oceanus to a more complex system.
To test the pressure-source hypothesis, we develop a novel stochastic model of reservoir pressure evolution and use it to invert the Levant pipe trail data under a Bayesian framework for model parameters such as the pressure-recharge rate.Using basic physical arguments, we then estimate recharge rates for each candidate overpressure mechanism and compare with the inferred rates.In particular, Kearney et al. (2023) showed that pressure diffusion from mudstones amplifies the rate of pressure recharge generated by tectonic compression.In mudstone-dominated basins like the Levant Basin, pressurerecharge rates can be amplified by a factor of ∼10.Therefore if this hypothesis is correct, then we expect that the inferred recharge rate is a factor of ∼10 greater than that predicted for tectonic compression alone.

Stochastic Model of Pressure Evolution
We assume that a fluid-escape pipe forms via hydraulic fracturing when the pore pressure exceeds the critical fracture pressure p f , which is the sum of the minimum horizontal compressive stress σ min and tensile strength σ T of the overlying mudstone (Price & Cosgrove 1990, Scandella et al. 2011), where we take compression to be positive.Once venting begins, the pressure drops rapidly until the pathway closes, which we assume occurs when the pressure reaches σ min .Once closed, we expect fractures to self-seal via swelling and mineral precipitation (Bock et al. 2010).Roberts & Nunn (Roberts & Nunn 1995) predict fluid venting durations of order years, which may be considered instantaneous relative to recharge times, of order 100 kyrs.Over the latter timescale, pressure will become spatially uniform within a high-permeability reservoir.We thus assume that reservoir pressure depends on time only.For multiple venting episodes to be sourced from the same reservoir, the reservoir pressure must recharge between episodes.We consider generic pressure recharge at an average rate Γ, such that the corresponding time ∆t between events is ∆t = Fractures exploit pre-existing rock weaknesses that change over geologic time, such that σ T will vary between events.We model this variability by asserting that σ T is a normally distributed random variable with mean σ T and standard deviation s T .Equation ( 2) then implies that ∆t ∼ N (σ T /Γ, s T /Γ).Thus, the mean and standard deviation of inter-event times of a trail of pockmarks can be used to infer the underlying recharge rate.
As this is a limited dataset that has been produced by an inherently stochastic process, Bayesian inference is used to invert the pipe trail data for the full probability distribution of each parameter and quantify their uncertainty.Our prior estimates of each parameter (Γ, σ T , s T ) are updated by evaluating the data with a likelihood function to recover the posterior probability distributions of each parameter.The likelihood function provides a statistical measure of modeldata agreement by calculating the probability of observing the data given a set of model parameters.The simplicity of our physical model enables the likelihood function to be expressed analytically (Supplementary Material S2).We apply a conservative Gaussian prior for σ T ∼ N (2.0, 1.0) MPa, since mudstone tensile strengths are typically a few MPa (Okland et al. 2002, Raaen et al. 2006); in particular, Roberts & Nunn (Roberts & Nunn 1995) predict a pressure drop of ∼2 MPa from venting.The posterior distributions of each parameter are sampled using the Metropolis-Hastings algorithm (Hastings 1970)

Oceanus Pockmark Trail
From the posterior distributions inferred for the isolated Oceanus trail (Supplementary Material S4), we use the mean posterior parameter values as input for our stochastic model to simulate an instance of linearised pressure evolution (Fig. 2A).
The qualitative similarity between the pockmark data and the model output is apparent (Fig. 2A, lower panel).For statistical comparison, we use samples from the posterior parameter distributions to calculate a range of posterior time interval distributions (Fig. 2B) that agree well with the data; variations between samples indicate the level of uncertainty in the inference.We note that as we have inferred the time-averaged recharge rate, this linearised pressure evolution resembles the sawtooth behaviour that is predicted for recharge from tectonic compression only (Cartwright et al. 2021, Kearney et al. 2023).However, our statistical model makes no physical assumptions regarding the mechanism or dynamics of pressure recharge between venting episodes.

Levant Margin Pockmark Trails
To the east of Oceanus are 12 other trails distributed along the basin margin (Oppo et al. 2021).Some of these trails originate from the same anticline, separated only by ∼1 km, and thus may be in hydraulic communication.To account for this possibility, we introduce pressure coupling as a feature of the model.For a coupled system of pipes, after any one pipe vents, the pressures of all pipes coupled to it reset to σ min and a new σ T is sampled for each.Therefore, the pipe that vents pressure temporarily inhibits any coupled pipes from venting.Consequently, the pipes in a coupled system form complementary pockmark series (Supplementary Material S5).If a group of pipes are instead uncoupled, each pipe behaves independently.This contrast between independent and complementary venting behaviour is a qualitative diagnostic for pressure coupling.
To evaluate whether a pair of adjacent trails are coupled, we calculate the Bayes factor of the coupled model M c and uncoupled model M u (Supplementary Material S2).The Bayes factor B cu of two models M c and M u is given by the ratio of probabilities of observing the data t given each model, i.e., (Kass & Raftery 1995) state that Bayes factors in the range 10-100 are 'strong' and above 100 are 'decisive'.We use this interpretation to assess the couplings of the pipe trails.For the Levant margin pipe data (Fig. 3A), we infer similar recharge rates to those inferred for Oceanus, although mean recharge rates range up to 66 MPa/Myr for pipe trail 8 (Fig. 3B).Fig. 3C shows Bayes factors of pairwise analysis of adjacent trails.Triple-wise analysis leads to the same conclusions, but has been omitted to simplify the interpretation (Supplementary Material S6).The model identifies all adjacent pipes that are greater than 10 km apart as decisively uncoupled.Furthermore, the inverted model indicates hydraulic connectivity between pipes 3, 4 and 5, each located along the same anticline, as well as trails 7 and 8 (Fig. 3C).
The inferences for pressure coupling are in agreement with the qualitative diagnostic behaviour.For example, the complementary venting behaviour of trails 3, 4 and 5 is visually evident.Conversely, trails 10, 11 and 12 are statistically inferred to be uncoupled and exhibit independent venting behaviour.Bayes factors with magnitudes below 10 exist for trail pairs {1, 2}, {2, 3} and {5, 6}, indicating a lack of preference for either coupling or not.We attribute this neutrality to features in the data that obscure the underlying recharge mechanics.These features are likely due to local stress variations caused by, for example, faulting.Nonetheless, since the majority of results do have strong preferences to one model or another, we assert that the physical model captures the main pressure behaviour, both spatially and temporally.This result lends support to our statistical inferences of pressure-recharge rates.

Comparison of Candidate Overpressure Mechanisms
The venting observations could plausibly be explained by various overpressure mechanisms that have been previously proposed.We next show that these mechanisms are inconsistent with our inferred recharge rates.Tectonic compression has been proposed as a major contributor to overpressure in the region (Cartwright et al. 2021).Previous numerical modelling of tectonic compression indicates that overpressures of 11-14 MPa in total can be generated from 10% strain (Obradors-Prats et al. 2016).At Oceanus, the strain accumulated since at least the Messinian Salinity Crisis, 5-6 Ma, is less than 10%.This implies a maximum recharge rate of ∼3 MPa/Myr from tectonic compression, which is insufficient to reproduce the observations (Fig. 4).However, Kearney et al. (2023) showed that pressure diffusion from mudstones amplifies the tectonic pressure-recharge rate in adjacent sandstones by a factor of (1 + ν/γ).The factor is termed the venting frequency multiplier and ν/γ is a ratio of dimensionless numbers that quantifies the relative effects of diffusion and compression.The dimensionless quantity γ measures the tectonic pressure-recharge rate of the sandstone relative to that of the mudstone; ν is hydraulic capacitance of the mudstone relative to that of the sandstone.The hydraulic capacitance of a layer is the product of compressibility and thickness.Typically, ν/γ ≫ 1 in basins composed primarily of mudstone (Kearney et al. 2023), like the North Levant Basin.Due to the wide range of uncertainty in mudstone permeabilities (Yang & Aplin 2007, Chang et al. 2013), it might be expected that the uncertainty in the recharge rate from mudstone pressure diffusion would span many orders of magnitude.However, the venting frequency multiplier is independent of the mudstone permeability (Kearney et al. 2023).This result enables us to calculate the recharge rate from the combined effect of diffusion and compression using prior distributions of each constituent parameter, giving a probability distribution that largely overlaps with inferred recharge rates (Fig. 4).Other candidate mechanisms predict much lower recharge rates than those inferred from the data (Fig. 4).The details of how we estimate the pressure-recharge rates from each mechanism are found in Supplementary Material S7.Oppo et al. (2021) proposed that marginal uplift generates significant overpressures at the basin margin by driving lateral fluid migration from the highly overpressured deep basin.If pressure is transferred laterally along a connected, high-permeability sandstone unit, the venting periods would be several orders of magnitude lower than are observed.However, it is likely that there is poor lateral reservoir connectivity in the area (Cartwright et al. 2021) and our analysis above supports this idea, indicating that many relatively nearby pipes are likely to be hydraulically independent (Fig. 3C).As a result, the only pathway for lateral fluid migration is via mudstones, thus implicitly requiring pressure diffusion from mudstones for reservoir recharge.Marginal uplift may also generate overpressure by flow focusing (Flemings et al. 2002), though this mechanism likely produces insufficient recharge rates (Fig. 4).Flow focusing due to fold amplification (Flemings et al. 2002) merely generates overpressures at a rate less than ∼1 MPa/Myr.Furthermore, hydrocarbon generation likely cannot generate the required recharge rate since the additional head required from buoyancy is greater than ∼1 km/Myr and most thermogenic gas generation was likely complete by 5-6 Ma (Al-Balushi et al. 2016).We cannot rule out the possibility of weak pressure recharge from biogenic gas generation, though petroleum systems modelling of the region favours biogenic gas accumulation via lateral migration from the deep basin (Bou Daher et al. 2016, Ghalayini et al. 2018, Nader et al. 2018).However, due to poor lateral reservoir connectivity, lateral gas migration is rate-limited by pressure diffusion (as for the case of marginal uplift).While lateral transfer produces insufficient recharge rates, vertical pressure transfer from a deeper reservoir along faults or fractures has been associated with fluid venting in other regions (see Grauls & Baleix 1994, Tingay et al. 2007, Cathles 2019).In the Levant basin, however, there is no evidence to support vertical fluid migration.Moreover, vertical transfer cannot explain the observed regular periodicity of venting.Disequilibrium compaction due to the small, post-salt sediment accumulation of ∼300 m (Cartwright et al. 2021) creates a negligible pressurisation rate of ∼1 MPa/Myr.Sea-level fluctuations may trigger venting episodes (see Scandella et al. 2011), though this mechanism alone provides no net pressure recharge.
The venting observations from the Levant fluid-escape pipe trails are consistent with predictions deriving from the hypothesis that pressure diffusion from mudstones fuels episodic venting in the region.Therefore, the Levant pipe trails provide strong spatiotemporal evidence supporting this hypothesis.In doing so, the pipe trails support a more general idea-that pressure diffusion from mudstones plays an important role in pressure redistribution between sedimentary layers-and provide observational evidence that was previously lacking from the theoretical literature (e.g., Muggeridge et al. 2004, 2005, Luo & Vasseur 2016, Kearney et al. 2023).It is likely that tectonic compression and marginal uplift were the main mechanisms for slowly pressurising the basin to near-lithostatic by ∼2 Ma.This pressurisation initiated basin-wide fluid venting by hydraulic fracturing, sourced by high-permeability, pre-salt sandstone reservoirs.Tectonic compression continued to slowly pressurise (∼3 MPa/Myr) the entire sedimentary succession while poroelastic pressure diffusion from mudstones recharged the sandstone reservoirs back to failure at a rate of ∼30 MPa/Myr.This combination of pressure diffusion and tectonic compression, with minor contributions from hydrocarbon generation and disequilibrium compaction, led to episodic fluid venting with a typical venting period of ∼100 kyr.While this is not a universal result for pipes in any basin, pressure diffusion exists wherever the corresponding reservoir unit is encased by highly overpressured, low-permeability rocks.Furthermore, the effect of pressure diffusion is intensified in sedimentary basins composed mostly of mudstone (Kearney et al. 2023), where fluid venting phenomena are commonly observed (Cartwright & Santamarina 2015).In many cases, liquefied mudstone is vented in addition to basinal fluids (e.g., Cartwright et al. 2023).The diverse roles of mudstones in pressure-driven, focused fluid venting provides an impetus to improve our mechanistic models of such venting phenomena.

Broader Implications
Because understanding subsurface pressure is crucial to prevent unwanted fluid leakage, these results have wider implications for risk assessment during borehole drilling and the sequestration of waste such as CO 2 .Fluid leakage resulting from reservoir pressurisation by mudstones may be a risk in a broad range of geological settings, requiring only that the mudstones are overpressured relative to the reservoir.This overpressure can be retained even after several episodes of fluid venting (Kearney et al. 2023), and can be generated by various means, not limited to horizontal compression.Indeed, Kearney et al. (2023) show that disequilibrium compaction (i.e., vertical compression) leads to mathematically equivalent behaviour.Therefore, even tectonically inactive regions like passive margins are prone to episodic venting if they are subjected to, for example, high sedimentation rates.Indeed, fluid-escape pipes are commonly observed in passive margin settings (Cartwright & Santamarina 2015).Passive margins also provide the largest and likely most cost-effective large-scale CO 2 storage resource (Ringrose & Meckel 2019).Therefore, fluid-escape pipes may pose a significant threat to offshore storage projects.This work highlights the importance of considering pressure diffusion from mudstones when assessing reservoir overpressures.This is especially true for sequestration sites with evidence of previous fluid venting, like the Sleipner field (Arts et al. 2004, Cavanagh & Haszeldine 2014).While the relict fluid-escape pipes at Sleipner are unlikely to be a result of CO 2 injection (Cavanagh & Haszeldine 2014), they serve as an example of the risks to containment associated with fluid venting.Although the dissolution of injected CO 2 can act to depressurise a storage reservoir (Akhbari & Hesse 2017), evidence from a natural CO 2 reservoir suggests that the rate of depressurisation from CO 2 dissolution is ∼1 MPa/Myr (Sathaye et al. 2014).This is much less than the recharge rates from pressure diffusion that we infer in the Levant Basin, suggesting that CO 2 dissolution is unlikely to prevent leakage in regions where pressure diffusion from mudstones is active.Thus, for storage projects in regions with pressurised mudstones, our results indicate that reservoir pressure monitoring over several millenia may be required to ensure containment.

S2.1 Likelihood function
Given a model, the likelihood function is the joint probability of the observed data.Here, the observed data is the set of all venting times t = {t n } N n=1 .The likelihood function can be decomposed in the following way: where f is the probability density and the history H tn is the set of all event times until (but not including) t n .Since the proposed model asserts that the pressure resets to σ min after each event, the pressure 'memory' of the system extends only from the most recent event so H tn = t n−1 .We can therefore write where ∆t n = t n − t n−1 .For coupled systems we must additionally consider the mark of each pipe κ, denoting where each event originated.It can be shown that for a set of K coupled pipes, where f k and F k are the uncoupled probability and cumulative density functions of pipe κ = k, respectively, and δ is the Kronecker delta.We utilise these likelihood functions to model the probability density of any coupling configuration of pipes.

S2.2 Bayes factor
To evaluate whether a pair of adjacent trails are coupled, we calculate the Bayes factor of the coupled model M c and the uncoupled model M u .The Bayes factor B cu of two models M c and M u is given by the ratio of probabilities of observing the data t given each model, i.e, For example, if B cu > 1 then M c is preferred over M u .Here, M c is the coupled model and M u is the uncoupled model.Kass & Raftery (1995) state that Bayes factor magnitudes between 10-100 are 'strong' and above 100 are 'decisive'.We define a new parameter ϕ ∈ {0, 1} such that ϕ = 1 indicates the coupled model M c and ϕ = 0 indicates the uncoupled model M u .The Bayes factor can be rewritten in terms of ϕ as In this form, the Bayes factor can be calculated with MCMC methods.We assume a prior distribution for ϕ ∼ Bernoulli( 1 2 ).Using the likelihood functions of the coupled and uncoupled models, the posterior distribution P(t | ϕ) can be sampled (using e.g., the Metropolis-Hastings algorithm) from which the Bayes factor can be calculated.

S3. INVERSION TESTS
Inversions are performed on synthetic data to test the accuracy and sensitivity of our inversion method.Here, we apply uniform prior distributions to assess the effectiveness of the likelihood function alone.We nondimensionalise the parameters (Γ, σ T , s T ) to Γ * = Γ/σ T and s * T = s T /σ T .

S3.1 One pipe
Inversions of a single pipe trail perform well if the true s * T < 1.When s * T > 1, the distribution of ∆t begins to be significantly truncated for ∆t < 0 and tends towards a uniform distribution for larger s * T .Henceforth, we analyse simulations with s * T < 1.

S3.2 Two pipes
We similarly perform inversions on synthetic data from simulations of two uncoupled pipes, shown in Fig. S3, and two coupled pipes, shown in Fig. S4.In these figures, each point represents results from Bayesian inversion applied to a simulated sequence of 40 venting times from two pipes.The number of venting times was chosen to investigate the level of uncertainty in the inversion for a pair of Levant pipe trails, which each typically comprise ∼20 venting times.In each case, the predicted Γ * is in agreement with the true value; the uncertainty in the inference of s * increases with increasing true s * .
WUXH  The model for tectonic compression developed by Kearney et al. (2023) is highly simplified; to ensure an accurate estimation of Γ s we use results from previous numerical modelling of tectonic compression (Obradors-Prats et al. 2016).Obradors-Prats et al. (2016) estimate overpressures between 11-14.2MPa from 10% strain at different rates, implying that 1.1-1.4MPa of overpressure is generated per % strain.Using seismic imaging, we estimate the strain at Oceanus to range from 1% to 10%, which we assume has been accumulating since the Messinian Salinity Crisis, between 5 Ma to 6 Ma.Flow focusing due to marginal uplift can lead to overpressure generation.For a flat sandstone of length L s in a mudstone with pressure gradient ρ m g, uplifting one side by dz leads to an equilibration of pressures at the new sandstone centroid, dz/2 (Flemings et al. 2002).Therefore, tilting the sandstone by an angle θ gives an overpressure of If the sandstone reservoir has a growing parabolic profile, then the overpressure rate generated at the crest by flow focusing is given by (Flemings et al. 2002)

S7.2 Pressure diffusion
where the factor of 2/3 appears because the sandstone and mudstone pressures equilibrate at ∆h/3.

Figure 1 :
Figure 1: Fluid escape pipe trails in the Levant Basin.(A) Overview of base-salt surface, showing sub-salt anticlines and the elevated margin platform, adjacent to the normally faulted deeper basin; adapted from Oppo et al. (2021), where lighter colours indicate larger depth.(B) Study area located on the North Levant Basin margin, offshore Lebanon.(C) General mechanism for fluid escape pipe trail formation, adapted from Cartwright et al. (2018), with (i) as the formation of the initial pipe at 1.7 Ma and (ii) as the present-day arrangement.(D) Pipe trails labelled 1-12 and Oceanus from panel (A) when corrected for relative salt translation rates(Oppo et al. 2021).

Figure 2 :
Figure 2: Results of Bayesian inference applied to the Oceanus pockmark trail.(a) Lower panel: Time-transformed pockmark data (blue) and stochastic model instances of venting history using inferred posterior mean (dark green) and sample parameters (translucent green).Upper panel: Stochastic instance of linearised pressure evolution using inferred posterior mean parameters (dark green), with pressures in excess of the minimum compressive stress corresponding to the mean tensile strength (dashed line) and corresponding to tensile strength values within one standard deviation of the mean (grey shaded area).(b) Posterior mean (dark green) and sample (translucent green) time interval distributions compared with Oceanus data.

Figure 3 :
Figure 3: Results of Bayesian inference applied to Levant margin data.(a) Time-transformed data from Oppo et al. (2021).Dashed lines divide pipe clusters that are separated by more than 10 km.(b) Violin plot of posterior recharge rate distributions for each pipe trail.(c) Bayes factors of pairwise pipe analysis, where a positive value implies the coupled model is more likely.

Figure 4 :
Figure 4: Comparison of pressure-recharge rates inferred from Levant pipe trail data with estimated recharge rates from candidate mechanisms.

Figure S2 :
Figure S2: Showing inversion results for simulated synthetic data.Each simulation uses a pair of values for Γ * and s * T to generate a sequence of 1000 venting times.(a) Predicted mean Γ * versus the true assigned Γ * for that simulation.(b) Predicted mean s *T versus the true assigned s * T for that simulation.Black points represent inversion results from simulations with true s * < 1 and red points with true s * > 1.

Figure S3 :Figure S4 :Figure S5 :
Figure S3: Showing inversion results for simulated synthetic data of two uncoupled pipes.Each simulation uses a pair of values for Γ * and s * T to generate 40 events in total.The inversion of each simulation generates two points, one for pipe 1 (blue) and one for pipe 2 (orange).(a) Predicted mean Γ * versus the true assigned Γ * for that simulation.(b) Predicted mean s * T versus the true assigned s * T for that simulation.

S7. 5
Disequilibrium compactionParameter Description mean std.dev.min.max.Reference ρ ps (kg/m 3 ) post-salt sediment density to post-salt sedimentation contributes to overpressure in the North Levant Basin.For a change in post-salt sediment thickness ∆h ps over a time ∆t c with density ρ ps , the maximum overpressure rate is given by the change in total stress, Γ = ρ ps g∆h ps ∆t c (16)