The Role of Fluid Seepage in the Erosion of Mesozoic Carbonate Escarpments

Mesozoic submarine carbonate escarpments are erosional features that host box canyons, the formation of which had been attributed to seepage erosion in view of their similarity to subaerial box canyons. The latter had been cited as diagnostic of groundwater activity, although the efficacy of fluid seepage as an erosive agent in bedrock remains controversial. Here we use multibeam echosounder data from the Blake, Campeche, Malta and Florida Escarpments to demonstrate that box canyon formation is, in general, a significant process eroding carbonate escarpments. Numerical modeling based on parameters from the Florida Escarpment shows that box canyons can initiate and retrogressively evolve by fluid seeping via joints, which causes a reduction in rock strength due to fluid pressure and dissolution, resulting in periodic block failure at the canyon head. Box canyon elongation is promoted by an exponential distribution of joint density, an increase in joint density, joints oriented perpendicular and parallel to the escarpment, or an increase in the thickness of the flowing groundwater zone and slope gradient of the escarpment. The angularity of the canyon head decreases with a decrease in joint density and when joint density is uniform, whereas the canyon width is regulated by the extent of the joint set zone. Since the key factors contributing to box canyon formation along the Florida Escarpment appear to characterize the Blake, Campeche and Malta Escarpments, the groundwater model for box canyon formation should be applicable to these escarpments as well.


Knowledge Gaps
In subaerial settings, fluid seepage has been shown to unambiguously lead to the formation of box canyons only in unconsolidated sand to gravel sized sediments (Lapotre & Lamb, 2018;Lobkovsky et al., 2007;Micallef et al., 2021;Schumm et al., 1995). The efficacy of fluid seepage as an erosive agent in bedrock remains disputed, however, and there is no unambiguous example of a bedrock box canyon formed by seepage erosion (Lamb et al., 2006). The mechanisms and rates of seepage weathering and erosion processes in subaerial bedrock are poorly constrained, and it is still unclear how box canyon geometries are generated (Lamb et al., 2006(Lamb et al., , 2008. There are a number of reasons for these gaps in knowledge. Field observations and experimental simulations of box canyon formation in bedrock are complicated by the long timescales involved and the overprinting of surface erosion processes. Experimental and numerical analyses have been based on simplistic assumptions related to flow processes and hydraulic characteristics, and they rarely take into consideration geologic heterogeneities or weathering (e.g., Luo & Howard, 2008;Nagihara, 1996;Pelletier & Baker, 2011). Subaerial box canyons can also be formed by surface water erosion without the need of groundwater flow, for example, in substrate with stratigraphic contrasts and vertical joints, waterfall erosion by abrasion, and megaflooding (Amidon & Clark, 2015;Lamb et al., 2006Lamb et al., , 2007Lamb et al., , 2008Lamb et al., , 2014Ryan & Whipple, 2020;Scheingross & Lamb, 2017). In view of the above, a re-evaluation of the role of groundwater in eroding submarine escarpments is necessary.

Objectives of This Study
In this study we combine morphological observations from multibeam echosounder data with 3-D numerical modeling to: (i) Determine if and how groundwater seepage can drive the formation of box canyons in submarine carbonate escarpments; (ii) Assess the relative importance of box canyon formation as an erosional process across a carbonate escarpment.
The study focuses on the Florida Escarpment to address objective (i), and it also takes into consideration the Blake, Campeche and Malta Escarpments to fulfill objective (ii) (Figure 1). We have chosen these escarpments because they are amongst the best mapped and investigated globally. The Florida Escarpment, in particular, has been the most intensively studied and is the only escarpment where fluid seepage has been documented thus far.

Motivation
An improved understanding of carbonate escarpment evolution is of interest from both an academic and an applied standpoint. First, exposed submarine carbonate escarpments provide modern analogs of their buried counterparts. Carbonate escarpments are common in the geological record, with buried Mesozoic carbonate platform edges rimming much of the North Atlantic and passive continental margins along the Tethyan Seaway during the Mesozoic (Arthur et al., 1979;Given, 1977;Goldflam et al., 1980;Lancelot & Seibold, 1977;Locker & Buffler, 1983;Schlee et al., 1979). Second, carbonate escarpments are commonly eroded by submarine canyons and landslides. The dynamics and controls associated with these processes are poorly constrained because most studies have focused on siliciclastic margins. As a result, our ability to estimate the hazards from these submarine processes to coastal communities and seafloor infrastructures is still poor. Third, carbonate platforms, slopes, and syn-stratigraphic units can host petroleum or ore bodies due to their high porosity and permeability. Knowledge on the geometry of these formations in the sub-surface and their controls is valuable to resource prospecting. 10.1029/2021JF006387 4 of 25

Definitions
In this paper the following definitions are used ( Figure 2). A carbonate platform is an extensive submarine, gently sloping plateau constructed primarily by biological precipitation of calcium carbonate. Here reference is only made to the morphology and composition, and there is no differentiation between carbonate factories (sensu Schlager, 2005) or based on whether the platform is active or drowned. The ramp is an area of increased slope gradient in the outer part of the carbonate platform, where the gradient is <5° (Mullins et al., 1988). A carbonate escarpment is steep seafloor (>5°) with exposed bedrock, in places covered by a thin sediment cover, located between the outer platform or ramp and the abyssal plain.

Florida Escarpment
The Florida Escarpment is ∼640 km long and 1,600 m high, with a maximum local slope gradient of 74°. It marks the western boundary between the Florida-Bahama platform and ramp, and the deep waters of the Gulf of Mexico. The contact between the base of the escarpment and the abyssal plain of the Gulf of Mexico deepens from 2,600 to 3,400 m from north to south and has been buried by rapidly accumulating distal Mississippi Fan sediments (Paull et al., 1984;Twichell et al., 1990). Rocks exposed across the Florida Escarpment include bedded Early to Late Cretaceous, platform-interior lagoonal skeletal limestones and crystalline dolomite (Carannante et al., 1988;Corso et al., 1989;Freeman-Lynde, 1983;Paull, Freeman-Lynde, et al., 1990;Paull, Spiess, et al., 1990;Paull, Twichell, et al., 1991). Dredged and submersible samples show a change in age from Lower Aptian at the base of the escarpment to Upper Cenomanian at a depth of 1, 950-2,200 m (Freeman-Lynde, 1983;Paull, Freeman-Lynde, et al., 1990). Above a depth of 1,500 m are gently sloping ramps covered by pelagic sediments deposited during the Tertiary (Carannante et al., 1988). Normal faults occur throughout the Lower Cretaceous and Jurassic sections (Corso et al., 1989;Shaub, 1984). They are concentrated in the Tampa and South Florida Basins, and may be due to basin subsidence and/or the collision of Cuba with the Florida-Bahama platform in the Early Cenozoic (Klitgord & Schouten, 1986;Twichell et al., 1990). There is little indication of faulting across the Tertiary to recent section (Corso et al., 1989;Shaub, 1984). Joints are oriented parallel and perpendicular to the escarpment face; they may be a relatively surficial characteristic in response to spalling or, more likely, reflect a regional fabric. The latter is generated by either the interaction of the Caribbean and North American plates during the Late Cretaceous and Tertiary (Klitgord & Schouten, 1986;Uchupi & Emery, 1968), or by differential subsidence across the basement features (Klitgord et al., 1984). Active chemosynthetic biological communities, commonly referred to as cold seeps, were first discovered at the base of the Florida Escarpment, along with unique sedimentary deposits that contain anomalous amounts of authigenic sulphide minerals, carbonate cements and mussel shell hash Commeau et al., 1987;Hecker, 1985;Paull et al., 1984Paull et al., , 1992. Seepage is estimated to be occurring along ∼10% of the base of the Florida Escarpment . The chemical and isotopic signatures of seep fluids suggest it consists of 6% platform formation brines and 94% seawater (Chanton et al., , 1993Martens et al., 1991;Paull et al., 1984). The brines consist of sulphide-rich fluids, due to dissolution of evaporite sulphate deposits within the platform, which are also rich in ammonium, methane, chloride and alkaline earth elements. Fluid circulation within the Florida-Bahama platform is density-driven and occurs at depths of >1 km. Seawater enters the carbonate platform along its exposed flanks below an impermeable anhydrite formation, percolates downwards through the platform, and seeps at the base after encountering an impermeable sill of hemipelagic sediments Fanning et al., 1981;Hughes et al., 2007;Kohout, 1965;Manheim & Horn, 1968;Paull & Neumann, 1987). Mixing between the brines and the seawater at the seepage sites is thought to give rise to corrosion as a result of mixing of waters of different salinities and the generation of acidic fluid due to seafloor oxidation of dissolved sulphide species Hanshaw & Back, 1980;Paull & Neumann, 1987;Paull, Spiess, et al., 1990;Plummer, 1975;Twichell et al., 1991). The effect of active corrosion has been observed in the form of pitted and fluted stratal surfaces, joint planes that are opened and enlarged, absence of Fe-Mn oxide coating and fine sediment drape where seepage occurs, and etched calcareous nannofossils in seep sediments at the base of the escarpment (Chanton et al., 1993;Paull & Neumann, 1987). Seepage and corrosion have also been inferred along terraces above the Florida Escarpment base, which mark the location of permeability horizons within the platform and suggest that seepage may occur at different depths Twichell et al., 1991). Seeps are also associated with downslope, density-driven flows of briny fluids, generating fanshaped deposits on the abyssal plain (Paull et al., 1992).

Blake, Campeche and Malta Escarpments
The characteristics of the Blake, Campeche and Malta Escarpments are summarized in Table 1. Their description is less detailed than for the Florida Escarpment because our modeling is only carried out for the latter (Section 3.2). Total escarpment lengths vary between 290 km (Malta Escarpment) and 810 km (Campeche Escarpment). Blake Escarpment is the highest (3,300 m) and steepest (83°) of the four escarpments. All three escarpments consistently correspond to sections composed of Mesozoic strata. The base of the escarpments comprises a sharp concave change in slope and a linear plan shape. Above the escarpments, the ramps are predominantly concave in profile and their downslope limit consists of a sharp to gentle convex change in slope. The ramps of the Campeche and Malta Escarpments, located above 2 km water depths, consist of Cenozoic age strata. In the case of the Blake Escarpment, the ramp comprises the broad and nearly flat Blake Plateau at water depths shallower than 1,500 m. The Campeche Escarpment has undergone geologically instantaneous margin collapse as a result of the Chicxulub meteorite impact, which generated erosive gravity flows that were the source of the Cretaceous-Tertiary boundary deposit in the Gulf of Mexico (Bralower et al., 1998;Denne et al., 2013;Paull et al., 2014). The Malta Escarpment, on the other hand, is thought to have been exposed down to a depth of 2 km and eroded during the Messinian salinity crisis . Since the onset of plate convergence between Africa and Europe during the Late Cretaceous, the Malta Escarpment was transformed from a passive margin into a mega-hinge fault system with an additional sinistral strike-slip component (Argnani & Bonazzi, 2005;Gutscher et al., 2016;Reuther et al., 1993).

3-D Distinct Element Modeling
The commercially available software 3DEC (https://www.itascacg.com/software/3dec) was used to address the question of whether fluid seepage via joints can lead to their widening by fluid pressure (pore and joint fluid pressure) and dissolution, reduce the rock strength, and ultimately result in slope failure and the upslope evolution of a box canyon. A 3-D Distinct Element Model consists of discrete blocks represented as polyhedrons with planar boundaries that correspond to joints in a rock mass. The blocks are allowed to deform and they are internally discretized into finite-difference tetrahedral elements (Cundall & Strack, 1979). Displacements along joints, as well as rotations and collapse of blocks, are allowed. Fluid propagates through the model primarily through joints, and equations of motion are solved using an explicit solution scheme. 3DEC uses a finite volume formulation for calculating stress, strain and displacement.

Joint Fluid Flow
As a first approximation, the fluid flow along a joint is modeled as flow between two parallel plates with constant hydraulic aperture (b h ), as described by the "cubic law" (Snow, 1965): is the Laplacian, t is the time, and D is the scalar hydraulic diffusivity (Hummel & Müller, 2009), which is defined by: where S i is intrinsic storativity, S is the increase in the weight of fluid stored per unit area of a joint, K is hydraulic conductivity, and T is the rate at which groundwater flows horizontally (transmissivity) (Cappa et al., 2008;Domenico & Schwartz, 1997). The latter is defined according to the parallel plate flow concept as: where k nif is the initial joint normal stiffness, σ ni is the initial effective normal stress, b hi is the initial hydraulic aperture at the initial effective stress, and   n E is the initial effective normal stress.

Elastic Hydromechanical Behavior of Joints
The relationship between effective normal stress (  n E ), normal stress ( n E ) and fluid pressure ( f E P ) is described by the effective stress law (Biot, 1941;Terzaghi, 1923): where  E is the Biot effective stress constant.
where S c is the ratio of the contact area to total joint surface.
The storativity (S e ) expresses the increase in the weight of fluid stored per unit area of a joint in response to a unit increase in pressure, and can be defined according to Domenico and Schwartz (1997) as: where A is the area of the joint plane and f E V is the fluid volume between the two joint faces.
Under normal stress, the coupling between joint flow and normal deformation is modeled according to the "modified cubic law" (Witherspoon et al., 1980): where hi E b is the initial hydraulic aperture at the initial effective stress and E f is a factor reflecting the influence of roughness on the tortuosity of flow. This law associates the joint hydraulic aperture Joint displacements are induced by a change in the effective stress field acting on the joint. The relationship between stresses and joint displacement is described by the relation between the change in joint normal and shear displacements (respectively, noted U n and U s ) caused by a change in effective normal (  n E ) and shear (  s E ) stresses (Goodman, 1970): where k n and k s are the normal and shear stiffness, respectively.

Joint Dissolution
Joint dissolution cannot be explicitly modeled with a Distinct Element Model. This process was therefore simulated by assuming that the change in joint volume with time (ΔV(t)) is equivalent to the volume of dissolved mineral (Vm), which was calculated as follows (adapted from Garcia-Rios et al., 2015): where Q is the flow rate and k is a constant.  (Table 2) are for dolomite and derived from borehole data, seafloor imagery and geophysical surveys from onshore/offshore Florida and elsewhere. Groundwater, driven by a hydraulic head, is supplied from the landward side of the carbonate platform, and the direction of groundwater flow is from the escarpment into the ocean. The base of the model is considered impermeable. The initial pore water pressure within the escarpment was estimated by accounting for a 500 m high seawater column above the top of escarpment, and was added to all nodes of the model. This value was chosen because the boundary between the ramp and outer platform above the Florida Escarpment is located at a water depth of ∼500 m.

Model Parameters for Florida Escarpment
For the main model, the following parameters were used: (a) a constant slope gradient of 70° for the escarpment; (b) a 100 m thick flowing groundwater zone at the base (i.e., half the vertical extent of the domain); (c) two basic (intrinsic) joint sets with a uniform density of 0.2 per m with orientations perpendicular and parallel to the escarpment ( Figure 4; Table 2). A third joint set, assumed to result from external processes (e.g., faulting, tectonics), was imposed across the joint set zone, which is a central 500 m wide section of the escarpment (Figure 4). This joint set is oriented perpendicular to the escarpment and entails an exponential decrease in joint density from 2 per m at the center to 0.2 per m at the boundaries (i.e., correlation between joint density and distance is exponential). Such a spatial variation in joint density is representative of field observations of fracture distribution across fault zones (e.g., Caine et al., 1996;Liao et al., 2019;Sagy et al., 2001;Wilson et al., 2003).
In addition, a number of additional simulations were carried out by individually changing the following parameters to test their influence on the shape, size and evolution of box canyons: 1. A linear decrease in joint density across the joint set zone from a maximum of 2 per m at the center to a maximum of 0.2 per m at the boundaries; 2. A uniform joint density of 0.4 per m across the joint set zone; 3. Thickness of the flowing groundwater zone above the base of 25 m; 4. Basic joint density divided by 5; Bulk density kN/m 3 29.5 Koumantakis and Sachpazis (1989), Yasar and Erdogan (2004) Joint direction°0, 90 Paull, Spiess, et al. (1990) Joint density m −1 0. 2 Paull, Spiess, et al. (1990) Friction angle°48 Nguyen (

Simulations
Each model simulation entailed a total of 4 million calculation cycles. Each cycle is composed of a sequence of operations based on one year of groundwater flow. The boundary conditions evolved as the model domain changed due to removal of blocks. In our model, the rock blocks disappeared once they became detached from the cliff face. In addition, the enhancement of dissolution at the seepage sites due to the mixture of waters with different salinities was ignored.

Morphology
Canyons and scars are the most common landforms in all four carbonate escarpments.
Overall, v-shaped canyons are consistently more prevalent (Table 3); they are located either on the ramp or gently sloping (<10°), concave sections of the escarpment. In the Campeche and Malta Escarpments, they tend to be located where the 120 m isobath (Last Glacial Maximum palaeo-coastline) is closest to the escarpment top. Box canyons are only found at the base of escarpments. The Florida Escarpment has the largest number of canyons (n = 301). Box canyons are concentrated in two areas-between 24°20'N and 25°35'N, and between 26°30'N and 27°N. The largest canyon on the Florida Escarpment is the Florida Canyon, which is a 20 km long and 4 km wide box canyon (Paull, Spiess, et al., 1990). The ratio of area per length is higher for box canyons than for v-shaped canyons in the Campeche, Florida and Malta Escarpments, and vice-versa for the Blake Escarpment ( Table 3). The Campeche Escarpment has the highest area of box canyons, both total and per escarpment length (Table 3), of any escarpment, and it also hosts the largest box canyon, which is 24 km long and 7.6 km wide.

Scars
Scars are downslope-oriented depressions with low aspect ratios. The headwalls of the scars are generally steep (10-25°) and linear to arcuate in plan shape. At their distal limit, most scars connect to either another scar or a canyon. The seabed within these scars is typically relatively smooth and planar. Scars are predominantly located on the ramps (Table 3), where they have a mean area of ∼10 km 2 and headwall heights of 100-200 m. The largest scar has an area of 480 km 2 (in the Campeche Escarpment). The smallest scars are located along the heads and walls of submarine canyons. The Florida Escarpment has the largest area of scars per escarpment length, although the largest area of scars across the escarpment face is observed at the Campeche Escarpment (Table 3).

Numerical Simulations
The results of all numerical simulations are presented as four consecutive snapshots of a duration of 1 million cycles (Figure 10). For the main model, a box canyon-with a theater-shaped head, linear thalweg profile, steep to vertical wall gradients, and a length of 423 m-develops by the end of the simulation ( Figure 10). The initial stages involve the development of a recess and an overhang along the base of the escarpment. This eventually leads to loss of support and failure of the cliff face via toppling and rock fall.

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12 of 25 Recurrence of these mechanisms results in the landward retreat of the canyon head; this retreat is faster at the center and slower at the sides due to the lateral variability in joint density across the joint set zone.
The results from the additional simulations using different parameters are summarized in Table 4.

Origin of V-Shaped Canyons and Scars
In siliciclastic margins, gravity flows are known to incise submarine canyons characterized by v-shaped cross-sectional shapes, concave thalweg profiles and dendritic network patterns (Gerber et al., 2009;Mitchell, 2005;Pratson et al., 2009). In view of the similarity with such morphologies, v-shaped canyons in carbonate escarpments have been associated with pelagic and hemipelagic sediments traveling as channelized debris flows and turbidity currents, collectively referred to here as gravity flows. The latter are thought to mechanically erode the v-shaped canyons and form debrites, turbidites and extensive carbonate lenses at the foot of the escarpment (Casero et al., 1984;Holmes, 1985;Lindsay et al., 1975;Micallef et al., 2019;Paull, Freeman-Lynde, et al., 1990;Paull, Spiess, et al., et al., 1990;Twichell et al., 1996). Most gravity flows are sourced by terrestrial sediments during sea-level lowering (e.g., subaerial fluvial discharge, hyperpycnal flows), failure of pelagic and hemipelagic sediments, or strong surface current flowing across platforms (Casero et al., 1984;Lindsay et al., 1975;Micallef et al., 2019;Wilson & Roberts, 1992). The former is supported by the spatial correlation of v-shaped canyons on escarpments with sea-level lowstand coastlines in the Campeche and Malta Escarpments.
On escarpments, erosion by gravity flows is thought to be restricted to the sediment veneer (Bryant et al., 1969;Freeman-Lynde, 1983;Paull, Freeman-Lynde, et al., 1990;Twichell et al., 1996). However, we do see a stark difference in the morphology of the escarpments-gentler slope gradient, convex slope profile-where the v-shaped canyons are located. This suggests that the Mesozoic carbonate bedrock has been eroded, and this may be attributed to quarrying and plucking by the gravity flows, which is particularly effective in jointed bedrock (Mitchell, 2014).
Scars are the result of submarine mass movements triggered by loss of support and steepening associated to erosion downslope Mullins & Hine, 1989;Twichell et al., 1990Twichell et al., , 1996. The larger, more prevalent scars are the result of failure in sedimentary drape across the ramp. The morphological differences between carbonate escarpments, in terms of v-shaped canyons and scars, can be attributed to the following: 1. High sedimentation rates (up to 6-11 m per 1 ka, as estimated from scientific drilling samples) during the Cenozoic (Kohl, 1985) may explain why the upper Campeche and Florida Escarpments host the largest landslides and have the highest scar area per escarpment length on their ramps. 2. Blake Escarpment features the lowest frequency of canyons and scars, which may be attributed to low sedimentation supply since the Palaeocene/Eocene due to the presence of the Florida Current (Gulf Stream). The latter eroded young sediments, prevented terrigenous sediment input to the Blake Plateau and reduced erosive mass wasting downslope (Dillon & Popenoe, 1988;Dillon et al., 1985;Popenoe, 1985;Sheridan, 1981). 3. The highest percentage of v-shaped canyons is observed across the ramp of the Malta Escarpment, and this is likely due to subaerial exposure and fluvial incision during the Messinian salinity crisis .

Formation of Box Canyons by Fluid Seepage at the Florida Escarpment
The results of our numerical simulations confirm that fluid seeping via joints can lead to the retrogressive evolution of a box canyon at the base of the Florida Escarpment via episodic block failure at the head due to a reduction in rock strength (Figures 10 and 11). A box canyon formed at the end of all simulations, even when the model parameters were changed ( Figure 10). According to Table 4, the box canyon tends to be longer when:  ger et al., 2007;Singh et al., 2002]); 2. The basic joint density is higher (a higher joint density results in smaller blocks that are easier to mobilize); 3. The distribution of joint density across the joint set zone is exponential (such a distribution is associated with the highest overall joint density across the joint set zone); 4. The thickness of the flowing groundwater zone is higher (fluid pressure and dissolution affect a larger extent of the escarpment); 5. The slope gradient of the escarpment is higher (slope failure is facilitated by steeper slopes). The angularity of the canyon head tends to decrease when the joint density across the joint set zone is uniform or when the basic joint density is lower ( Figure 10). In our simulations, the width of the box canyon is controlled by the width of the joint set zone.
The observations at the base of the Florida Escarpment are consistent with the model predictions. The occurrence of patches of talus composed of rectangular blocks on the canyon floors, indicative of periodic collapse, are more common at the base of the canyon heads . The growth rate of the box canyon in our main scenario is estimated at 10 km per 100 Ma, which compares well with the escarpment retreat of 8 km in the last 100 Ma inferred from geophysical data (Corso & Buffler, 1985;Freeman-Lynde, 1983;Paull, Freeman-Lynde, et al., 1990).
The occurrence of box canyons across the Florida Escarpment coincides with the location of basins (e.g., Tampa Basin, South Florida Basin) under the west Florida shelf, where faulting of the Cretaceous and Jurassic strata is concentrated (Ball et al., 1988;Twichell et al., 1990). The location of basins also coincides with more abundant anhydrite (Applin & Applin, 1965), which implies a larger source of dense, sulphide-rich brines discharging along the escarpment.
Based on the above, we conclude that there are three main factors supporting box canyon formation along the base of the Florida Escarpment: (a) an internal, density-driven fluid circulation system that leads to the seepage of corrosive fluids at the base of the escarpment (Chanton et al., , 1993Paull & Neumann, 1987;Paull et al., 1988), (b) limestone and dolomite outcrops that are susceptible to dissolution, and (c) fabric (joints, faults), which enhances groundwater flow to and seepage across the escarpment, and facilitates fragmentation and failure of massive rock faces. Figure 9. Plots of mean and standard deviation of morphologic parameters for v-shaped and box canyons for all carbonate escarpments. The parameters were measured as follows: (i) Length:width ratio-thalweg length divided by width. (ii) Drainage density-Total thalweg length of a canyon system (including tributaries) divided by area. (iii) Mean spacing-Linear distance between center points of two adjacent canyons. (iv) Bifurcation angle-angle at the bifurcation of a canyon into two tributaries. (v) Cross-sectional shape-Calculated by normalizing each side of a cross-sectional profile, reducing them into a power law curve, and using the exponent as a shape indicator (Brook et al., 2006). Exponent of ∼1 represents a V-shaped canyon. The value 2 describes a U-shaped canyon, >2 denotes a wide flat valley bed and is typical of a box canyon. (vi) Wall gradient-Slope gradient of the steepest wall for an individual canyon. Number of canyons at each escarpment: Blake (90), Campeche (281), Florida (301), Malta (153).

Significance of Box Canyon Formation in Escarpment Erosion
Across the Campeche, Florida and Malta Escarpments, box canyons are, in terms of areal extent, more prevalent than either v-shaped canyons or scars (Table 3). Box canyons also cover a greater proportion of the escarpment area than scars at the Blake Escarpment. Box canyon formation is, therefore, a significant erosive process across carbonate escarpments.

Implications for Other Carbonate Escarpments
Is the model for box canyon formation proposed for the Florida Escarpment ( Figure 11) applicable to the Blake, Campeche and Malta Escarpments?
All three sites share lithological similarities with the Florida Escarpment, with outcrops of limestone and dolomite (Table 1), and with joints being similarly ubiquitous. Box canyons at the Blake Escarpment have been linked to jointing due to a regional fabric, uneven erosional unloading of the escarpment's face, or differential subsidence across the fracture zone (Dillon et al., 1987(Dillon et al., , 1993Paull, Twichell, et al., 1991). Little is known of the fabric of the Campeche Escarpment, although offsets of up to 100 m have been observed in seismic reflection profiles, some of which are likely related to the Chicxulub impact structure (Gulick et al., 2013;Morgan et al., 1997). The Malta Escarpment exhibits both Mesozoic normal block faulting and a more recent sinistral strike-slip component (Catalano et al., 2000;Grasso, 1993;Gutscher et al., 2016;Pedley et al., 1993;Reuther, 1990;Reuther et al., 1993;Scandone et al., 1981), whilst vertical jointing is clearly visible in seafloor images (Biju-Duval et al., 1982).
Although fluid seepage has only been documented at the base of the Florida Escarpment, density-driven circulation cells may be active in other carbonate escarpments as well. At the Florida Escarpment, the occurrence of evaporites is the main reason for the development of an outward flow at the base of the escarpment. There are indications for the occurrence of evaporites in the other escarpments. Evaporites have been reported in onshore and offshore wells at depths of 1 and 5 km in the Malta Plateau (Bishop & Debono, 1996;Gatt, 2012 Canyon area was estimated based on the boundaries of submarine canyons delineated semi-automatically using morphometric attribute maps (slope gradient, slope aspect, profile curvature), flow accumulation map and water basin analysis.

Table 3 Number and Area a of Canyons and Scars and Across the Ramps and Escarpments
from ODP Site 1052, drilled in the Blake Escarpment, show significant increases in salinity, chloride, and sodium concentrations with depth, which may indicate the presence of an evaporite sequence in the underlying Cretaceous and Jurassic units (Norris et al., 1998). In addition, circulation cells within carbonate platforms can also be stimulated by lateral thermal differences and changes in sea level, among others (Hughes et al., 2007;Kohout, 1965;Manheim, 1967). Escarpments are also fundamental hydrological boundaries, with their base acting as a "triple point" between the abyssal seawater and the waters within the platform Figure 10. Evolution of box canyon morphology during four consecutive intervals, as simulated for the Florida Escarpment, for different parameters. Each interval is 1 million calculation cycles, which is equivalent to 1 Ma. and the basinal sediments. The likelihood of fluid seepage in the Blake, Campeche and Malta Escarpments, either at present or in the past, is therefore high.
Since the three main factors supporting box canyon formation along the Florida Escarpment also occur in the Blake, Campeche and Malta Escarpments, the model for box canyon formation proposed for the Florida Escarpment should also be applicable to these. This may be valid for other carbonate escarpments that have been mapped and studied in less detail. The 3,300 m high Bahama Escarpment, for example, exposes Early to middle Cretaceous platform interior jointed limestones (Cavailhes et al., 2020;Freeman-Lynde et al., 1981) (Figure 2). The escarpment geometry indicates an erosional origin with a retreat of 5 km at its base since the Lower Cretaceous, predominantly by spalling, current erosion, slope failure and dissolution (Freeman-Lynde et al., 1981;Freeman-Lynde & Ryan, 1985;Mullins & Hine, 1989;Schlager et al., 1984;Walles, 1993). Saline water and brines, generated by the dissolution of anhydrite , are thought to seep at the base of the Bahama Escarpment (Henderson et al., 1999). The 1,000 m high Apulian Escarpment in the central Mediterranean Sea (Figure 2), on the other hand, comprises Late Cretaceous shallow water limestones that feature box canyons (Bosellini, 2002;Groupe Escarmed, 1983;Volpi et al., 2011). Other similar features occur offshore Grand Banks, which comprises a Jurassic to Cretaceous 5-km-high escarpment hosting submarine canyons , the Mazagan Escarpment offshore Morocco (Auzende et al., 1983;Ruellan et al., 1984;Winterer & Hinz, 1984), and offshore northwestern Australia (Veevers, 1974).
A rock fabric conducive to fluid seepage is commonly found in carbonate platforms globally. Syn-depositional fractures, especially margin perpendicular fractures, are widely recognized in carbonate platforms (Cozzi, 2000;Frost & Kerans, 2009;Guidry et al., 2007;Lehner, 1991). Factors leading to their development include gravity, antecedent topography, and tectonics. Recently it has been suggested that such fractures can develop without the influence of regional tectonic stress (Nooitgedacht et al., 2018). Margin parallel fractures are localized around platform margin, suggesting a gravitational driver for the formation of tensile   stress. Perpendicular fractures, on the other hand, form sub-vertical dikes and fracture corridors. They are a systematic feature in the slopes of flat-topped carbonate platforms and are generated by downslope loading and differential compaction.

General Implications
There are three main general implications associated with our results. First, the location, and possibly geometry/dimension of box canyons, may provide insights into carbonate platform structure, as well as its hydrogeology (e.g., extent of fluid seepage and its fluxes) and the potential occurrence of chemosynthetic communities. This is particularly relevant for the Campeche and Malta Escarpments, which host the highest areas of box canyons per escarpment length (Table 3). Second, the slow development of box canyons at multi-km depth by low frequency head failure suggests that these features do not comprise a significant geohazard. V-shaped canyons are conduits for higher frequency sedimentary flows and they are expected to be more hazardous, especially for submarine cables. With respect to tsunami generation, the highest risk is posed by submarine landslides on ramps, in view of their large area and shallow depths (e.g., Chaytor et al., 2016). Third, the model for box canyon formation in carbonate escarpments may be applicable to other bedrock margins, involving different lithologies (e.g., sandstone) and fluids (meteoric), where similar landforms have been documented, for example, Norwegian margin (Hong et al., 2019;Rise et al., 2013) and SE Australian margin (Mitchell et al., 2007;Varma & Michael, 2012).

Conclusions
Based on analyses of multibeam echosounder data from the Blake, Campeche, Malta and Florida Escarpments, and 3-D numerical modeling of the latter, we infer that groundwater plays a key role in the geomorphic evolution of carbonate escarpments. Our main conclusions are the following: 1. Box canyon formation is, in general, a significant erosive process across carbonate escarpments. 2. While v-shaped canyons across the gentler sloping and convex sections of carbonate escarpments likely correspond to bedrock erosion by gravity flows, box canyons are attributed to fluid seepage. 3. 3-D Distinct Element Modeling shows that the initiation and retrogressive evolution of a box canyon can be driven by fluid seeping via joints, which leads to a reduction in rock strength due to fluid pressure (pore and joint fluid pressure) and dissolution, resulting in periodic block failure at the canyon head. The efficacy of these processes was demonstrated using geological, geotechnical and hydraulic parameters from the Florida Escarpment. 4. The modeling reveals that box canyon elongation is promoted by: (a) an exponential distribution of joint density across a joint set zone, (b) perpendicular and parallel orientations of basic joints relative to the escarpment, (c) an increase in the basic joint density, the thickness of the flowing groundwater zone, or the slope gradient of the escarpment. The angularity of the canyon head tends to decrease with a decrease in the basic joint density, or when the distribution of joint density across a joint set zone is uniform. The width of the box canyon is controlled by the width of the joints set zone. 5. The main factors supporting box canyon formation along the base of the Florida Escarpment are: (a) an internal, density-driven fluid circulation system that gives rise to seepage of corrosive fluids at the base of the escarpment, (b) limestone and dolomite outcrops that are susceptible to dissolution, and (c) fabric (joints, faults) that enhances groundwater flow to, and seepage across, the escarpment, and which facilitates fragmentation and failure of rock faces. Since these elements also appear to occur in the Blake, Campeche, and Malta Escarpments, the groundwater model for box canyon formation should be applicable to these escarpments as well.