Geomorphometric Analysis of Submarine Mud Volcanoes: Variability, Evolutionary Trends, and Geohazard Implications

Abstract

The systematic morphometric analyses of submarine mud volcanoes are widespread yet still poorly understood geological features. Our study reveals that submarine mud volcanoes show significant variability in size and geometry, independent of water depth. Specifically, the mean height-to-radius (H/R) ratio is ~0.14 ± 0.08 (±1σ). This study focuses primarily on submarine mud volcanoes in the Mediterranean, which account for approximately 58% of the dataset and include structures reaching heights of up to ~500 m with mean diameters of up to 8000 m. These edifices display a range of basal geometries, from sub-elliptical (e.g., North Alex, off the coast of Egypt) to super-elliptical (e.g., Alberto da Ottaviano in the Mediterranean Ridge Accretionary Complex). A comparative analysis of morphometric parameters distinguishes mud cones from mud pies globally, with the latter generally lacking large examples (mean diameter >10 km). The results suggest distinct evolutionary pathways, beginning with small simple cones (~100 m³ in volume), analogous to arc volcanoes in other geological settings. This study integrates fundamental marine geology with applied geohazard considerations, serving as an initial step toward enhancing shared knowledge of submarine mud volcanoes. By improving the understanding of their formation, morphometric variability, and spatial distribution, this research supports better-informed decisions regarding submarine geohazards.

1. Introduction

Fluid leakage from the seabed is a common process that occurs worldwide from coastal to abyssal plain environments [1,2]. It can give rise to a wide range of morphologies, classified as “Fluid Escape Structures” or more recently as ‘’Seabed Fluid Flow Morphologies” [2], whose morphological characteristics are believed to be strictly dependent on the type of fluid involved and the geological setting where they are found [3]. The main superficial expressions of seabed fluid flow are represented by pockmarks and mud volcanoes, respectively [4,5], which comprise engineering challenges and hazards for seabed infrastructure and exploration drilling [6]. Mud volcanoes (MVs) are positive reliefs formed by the vertical migration of overpressured fluids (e.g., CH₄, CO₂, and water) mixed with fine sediments named mud breccia (i.e., structureless pebbly mud containing predominantly angular, semi-indurated clasts) [7,8]. They occur globally in various geological settings, particularly in compressional tectonic zones and regions with high sedimentation rates, such as deltas, sedimentary basins, and accretionary prisms. Submarine MVs are identified by their subcircular shape and gas plumes escaping from the seabed [9] and can be found across a wide range of water depths [10] (Figure 1).

Figure 1. Location and size of submarine mud volcanoes (N = 1003) divided by size (small, medium, large, or giant). Unclassified submarine MVs, i.e., those without morphometric parameters are shown as red points (data from Napoli et al., 2025 [11]).

Figure 1. Location and size of submarine mud volcanoes (N = 1003) divided by size (small, medium, large, or giant). Unclassified submarine MVs, i.e., those without morphometric parameters are shown as red points (data from Napoli et al., 2025 [11]).

MVs morphologically vary depending on factors such as the viscosity of mud breccia, eruption frequency, and conduit size [8,12]. Conical MVs, for example, are generated through successive mud flow deposits, whereas mud pies (i.e., low cone slope < 5%) or plateau-like MVs result from high water content in the mud breccia [13,14]. In both cases, the mud shows plastic behavior, with the yield strength decreasing as porosity increases [15]. The genesis of MVs is driven by pore-fluid pressure, buoyancy contrasts, and tectonic forces, with two primary models proposed: (1) the “solid model”, where MVs develop on mud diapirs, and (2) the “fluid model”, where fluidized mud arise along faults and fractures [10,16]. Recent studies indicate that MV morphology may serve as a potential indicator of regional tectonic stress [17]. Moreover, submarine MVs play a significative role in seafloor methane release, contributing between 2.2 and 6 Tg yr⁻¹ of methane to the atmosphere, with deep-water MVs potentially emitting up to 27 Tg yr⁻¹ [10], which requires further investigation taking into account episodic mud emissions and variability in the state of activity (quiescent versus eruptive) [18]. In addition to their environmental impact, MVs pose significant geohazards, including seafloor instability, slope failure, and occasional explosive eruptions [19].

Given the global importance of submarine MVs and their direct links to geological processes (e.g., tectonic deformations, subduction), as well as their potential but poorly understood impacts on marine ecosystems, this study seeks to better understand their variability and evolutionary trends. Through morphometric analysis of a wide range of morphologies, valuable insights are provided into the dynamic processes governing their formation, development, and associated geohazard implications.

This study aims to conduct a systematic morphometric analysis of submarine mud volcanoes to enhance understanding of their size, geometry, and distribution. Using a large, publicly available dataset [11], we investigate the intrinsic variability of submarine mud volcanoes, with a particular focus on those in the Mediterranean, which represent a significant portion of the dataset. Additionally, this study aims to distinguish morphometric differences between mud cones and mud pies, exploring their evolutionary trends.

2. Materials and Methods

In this study, we use the “Global inventory of submarine mud volcanoes” available in Zenodo (https://zenodo.org/records/13120956, accessed on 10 March 2025) [11]. The input database includes data (e.g., location, height, diameter, and, when available, water depth and mean slope) obtained from the scientific articles published in the last 30 years [20,21,22,23] as well as derived data (e.g., perimeter, area, volume, aspect ratio, and height/radius ratio).

Submarine MVs have been classified according to morphological types [8] (i.e., mud cones and mud pies) and based on size [24] (i.e., small, medium, large, and giant), allowing their analysis and comparison. The plan shapes of the basic areas were distinguished according to recent literature [25] (i.e., circular, sub-elliptical, elliptical, elliptical elongated, and super elliptical). In addition, MV classifications [26,27] were applied to identify potential matches with terrestrial onshore and Martian mud volcanoes. In the Global inventory of submarine mud volcanoes [28], tabulated submarine MVs without previous designations are labeled as “unnamed” and carry sequential identification numbers. Finally, for cases where different authors report submarine MVs with the same name, there are distinctive acronyms. A semi-automatic method has recently been adopted to extract key parameters [11,28], following recent literature on submarine volcanic settings [29,30,31]. Morphometric characterization (e.g., size, slope, shape, and morphological type) of submarine MVs may provide clues into the mechanisms and factors that drive their growth and evolution [32,33,34]. In the following section, we provide a brief description of this approach (Figure 2).

Submarine Mud Volcanoes. A total of 782 submarine MVs were analyzed morphometrically. For each submarine mud volcano, the following morphometric parameters were extracted:

i.

Size parameters: maximum (D_max), minimum (D_min), mean diameter (D_mean), basic area, basal perimeter, height, and volume. The basic perimeters are respectively calculated as 2π(√(D_max² + D_min²)/2) or 2πR, the basic areas as πD_maxD_min/4 or πD_mean²/4, and the volumes as πD_maxD_minH/12 or πD_mean²H/12 (Figure 2).

ii.

Shape parameters: basal ratio (bsr, d/D), axis ratio (D_max/ D_min), height versus radius of the mud volcano’s body (H/R ratio), vertical relief to area ratio (Height/Area), compactness factor (comf = Perimeter/(√4*π*Area)), ellipticity index (ei = (π*(D_max /2)²)/Area), dissection index (di = (Perimeter/2*Area)*(√(Area/π)), and eccentricity (e = (√(D_max/2)² − (D_min/2)²/D_max/2).

iii.

Slope parameters: mean slope (arctan(H/R)).

3. Results and Discussion

3.1. Global Morphometric Characters of Submarine MVs

In this study, we conduct a morphometric analysis of 782 submarine mud volcanoes (MVs) selected from those listed in Tables S1 and S2 [28]. The submarine MVs are extremely variable in size and shape regardless of the water depth, such as for the mean H/R ratio ranging around 0.14 ± 0.08 (±1σ). Heights of submarine MVs vary from only 2 m to over 2 km (e.g., Honza in Izu-Ogasawara Trench [35]), with a mean (median) value of 174 m (130 m) (

Table 1. Summary of main morphometric parameters of 782 submarine MVs (i.e., 570 mud cones and 212 mud pies) scattered around the world. H/R is the shape parameter corresponding to the ratio of height to radius of the submarine mud volcano. The minimum (min), maximum (max), mean (mean), median (median), standard deviation (std), variance (var), skewness (skew), and kurtosis (kurt) values are reported as shown.

Submarine MVs (N = 782)	Height (m)	Perimeter (m)	Area (km2)	Volume (km3)	Mean Diameter (m)	Radius (m)	Height/Area (m−1)	H/R	Mean Slope (°)
min	2.00	31.00	0.00	0.00	10.00	5.00	0.000	0.01	0.38
max	2364.00	131,947.00	1385.44	1091.73	42,000.00	21,000.00	0.051	0.80	38.70
mean	174.49	9155.87	15.41	5.30	2893.82	1446.92	0.000	0.14	7.84
median	130.00	7620.07	4.56	0.20	2420.00	1210.00	0.000	0.12	7.10
std	214.92	10,799.20	73.80	48.76	3405.73	1702.86	0.003	0.08	4.47
var	46,192.39	116,622,700.00	5445.83	2377.99	11,598,990.00	2,899,726.00	0.000	0.01	19.97
skew	5.54	5.63	11.80	16.75	5.67	5.67	19.584	2.59	1.98
kurt	40.05	42.78	178.17	337.33	43.43	43.43	384.429	14.85	8.18

and Figure 3). The radii range from very few meters to ∼21 km (e.g., Big Blue in the Mariana Forearc region [36]), with a mean (median) value of 1447 m (1210 m). Their mean slopes are also highly variable (Figure 3), from much less than 1° on extremely flattened forms (e.g., Atlante and Cyclops offshore Barbados [37]) to a max value usually of ~27° on purely conical forms (e.g., Chueca and Demetrio de Armas in the Gulf of Cadiz [34]; Figure 3) with a mean value of ~7.8°± 4.5° (±1σ) (Table 1).

Size Classification:

• Small mud volcanoes (N = 94; area < 0.5 km²), bound to a weak driving force, show a mean height of ~41 m (range = 2–183 m), a mean diameter of ~472 m (range = 10–800 m), a mean volume of ~0.004 km³ (range = 100 m³–0.02 km³), and a mean slope of ~10.8° (range = 0.7–38.7°). Note that some documented cases can reach heights up to ~340 m (e.g., El Cid in the Gulf of Cadiz was excluded from the analysis as complete morphometric values are not available).
• Medium mud volcanoes (N = 486; area 0.5–9 km²) show a mean height of ~138 m (range = 10–477 m), a mean diameter of ~2069 m (range = 800–3380 m), a mean volume of ∼0.21 km³ (range = 0.002–1.06 km³), and a mean slope of ∼8° (range = 1–26.5°).
• Large to giant mud volcanoes (N = 202; area > 9 km²), related to massive upwellings of mud breccia, show a mean height of ∼ 325 m (range = 14–2364 m), a mean diameter of ∼6006 m (3990–42,000 m), a mean volume of ∼20 km³ (range = 0.06–1092 km³), and a mean slope of ∼6.1° (range = 0.4–15.9°).

Giant mud volcanoes, unlike the globally widely distributed small and medium-sized ones, are mostly found in the Mariana region, in the south Caspian Sea, in the Mediterranean region (Calabrian accretionary wedge, Mediterranean Ridge accretionary complex, and west Nile deep-sea fan), in the Gulf of Cadiz, and off the Antarctic Peninsula (Figure 1). In this significant group are the best-known active mud volcanoes, among which are Conical and South Chamorro serpentinite mud volcanoes (resulting from the extrusion of serpentinite-rich mud) in the Mariana forearc [36] or unnamed mud volcanoes with recurrent eruptions from the south Caspian Sea [38].

Type classification:

• The mud cones (N = 570; mean slope > 5°) show extremely variable heights from 4 m up to 2364 m, with a mean height of ~203 m. Their mean diameters are between 10 m and ~42 km, with a mean diameter equal to ~2804 m. The mean slope value is ~9.5°. The mud cones are characterized by an H/D ratio between 0.02 and 0.4 and a vertical relief to an area up to 0.05 m⁻¹. Of these, 153 mud cones show an ellipticity index (ei) between 1 and 2.74 and a dissection index (di) included between 1 and 1.25. Their basal ratio (bsr) ranges from 0.37 to 1.
• The mud pies (N = 212; mean slope < 5°) show lower heights from only 2 m up to 828 m, with a mean height of ~97 m. Their diameters range between hundreds of meters and ~22 km and the mean diameter is ~3136 m. The mean slope value is ~3.5°. The mud pies are characterized by an H/D ratio between 0.003 and 0.07 and a vertical relief to an area up to 0.00017 m⁻¹. Of these, 78 mud pies show an ellipticity index (ei) between 1 and 5.82 and a dissection index (di) between 1 and 1.73. Their basal ratio (bsr) ranges from 0.17 to 1.

3.2. Geomorphometric Comparison and Evolutionary Trends

According to the “Global inventory of submarine mud volcanoes” [11], mud pies appear to be smaller than mud cones or at least lack very large cases (D_mean > 10 km; only Blue Moon in the Marianas in Figure 4). Scatterplots a and b in Figure 5 show how mud pies are generally more elongated in plan than mud cones (i.e., smaller bsr and greater deformability resulting from mud breccia with usually higher water content). Alberto da Ottaviano in the Mediterranean Ridge Accretionary Complex and MV69 in the south Caspian Basin offshore Azerbaijan are examples of irregular mud pies, characterized by super-elliptical plan shape, with high dissection index (di) and ellipticity index (ei). Mud breccia viscosity, pressure, conduit resistance versus edifice resistance, and the presence of fluid migration pathways such as local faults and/or fractures play a crucial role in influencing these distinct evolutionary trends [8,33,39]. As visible in Figure 4, the smaller steep mud cones (volume ~100 m³) represent the morphometric starting points (two overlapping submarine MVs named MSPs); the associated steepness could depend on the eruptive style and the composition of the mud breccia. These features align geometrically (i.e., simple conical shapes) with the morphometric starting points of the arc volcanoes described. In fact, we applied the classical morphological approach traditionally used for these features [33]. Although there are evident differences, the processes that regulate mud and magmatic volcano systems are thought to be dynamically similar [17,40].

Following the morphometric evolutionary trend and the corresponding type (mud cone or mud pie) (Figure 4), significant height gaps are identified within submarine MVs, such as 258–329 m and 511–611 m. These gaps become particularly evident in the transition from submarine MVs to the Mariana serpentinite MVs (i.e., 350–828 m; 611–720 m). The internal gaps may reflect critical thresholds beyond which two distinct evolutionary paths are possible: very large mud cones and mud pies continue to grow upward delineating steeper-sided morphologies (e.g., in the mud pie transition 329–350 m, from MV74 to Phytagoras; in the serpentinite mud cone transition 1461–1645 m, from Pacman to Fujin), or they grow laterally in diameter delineating gentler morphologies with even greater volumes (e.g., in the mud pie transition 258–329 m, from MV65 to MV74; in the mud cone transition 511–611 m, from unnamed 94 to MV55).

The morphometric evolutionary trend shown in Figure 4 displays that the giant mud cones (i.e., MV55) and mud pies (i.e., MV74) from sub elliptical to elliptical elongated of the south Caspian Sea (offshore Azerbaijan)—“the land of eternal fire” [41] with high density of submarine MVs [12]—represent the closest terms in size to the serpentinite mud volcanoes of the Marianas (Figure 4).

The Mariana serpentinite MVs (grouped in Figure 4; the lower end is Sumisu, the upper one is Big Blue), among which Quaker, Conical, Celestial, Honza, and Big Blue with calculated volumes, respectively, ranging from ∼ 212 km³ to ∼ 1092 km³ are the largest mud volcanoes on Earth [42]. They represent dimensional outliers compared to the others.

Figure 4. On the left scatter plot, Height (m) vs. Mean diameter D_mean (m) of submarine MVs (N = 782). The data shows upper limits and internal gaps for the two different morphological classes, suggesting potential critical maximum heights and diameters of development. The associated equations corresponding to the best-fitting second-degree polynomial model of each category are as follows: Mud cones y = 0.0016x² + 12.251x + 154.56 (R² = 0.91), Mud pies y = 0.0017x² + 24.195x + 769.65 (R² = 0.78), and Submarine MVs y = 0.0019x² + 11.326x + 769.49 (R² = 0.82) (Modified from Kioka and Ashi (2015)) [43]. On the right scatter plot, Height (m) versus Volume (km³) (N = 782) shows submarine mud cones and mud pies divided according to their sizes. MSPs are two morphometric starting points from which the different trends depart. Some data points definable as outliers (e.g., MV35 in the Caspian Sea) deviate from the corresponding associated trends.

Figure 4. On the left scatter plot, Height (m) vs. Mean diameter D_mean (m) of submarine MVs (N = 782). The data shows upper limits and internal gaps for the two different morphological classes, suggesting potential critical maximum heights and diameters of development. The associated equations corresponding to the best-fitting second-degree polynomial model of each category are as follows: Mud cones y = 0.0016x² + 12.251x + 154.56 (R² = 0.91), Mud pies y = 0.0017x² + 24.195x + 769.65 (R² = 0.78), and Submarine MVs y = 0.0019x² + 11.326x + 769.49 (R² = 0.82) (Modified from Kioka and Ashi (2015)) [43]. On the right scatter plot, Height (m) versus Volume (km³) (N = 782) shows submarine mud cones and mud pies divided according to their sizes. MSPs are two morphometric starting points from which the different trends depart. Some data points definable as outliers (e.g., MV35 in the Caspian Sea) deviate from the corresponding associated trends.

Figure 5. (a) Scatter plot of Height (m) versus Aspect ratio bsr (D_min/D_max) of submarine MVs (N = 231), subdivided into Mud cones (red dots) and Mud pies (purple dots). (b) Scatter plot of Mean diameter D_mean (m) versus Aspect ratio bsr (D_min/D_max) of submarine mud volcanoes (N = 231), where D_mean = (D_min + D_max)/2. A smaller bsr indicates that the submarine mud volcano is more elongated in plain view, while a larger bsr indicates a sub-circular plan view shape. Modified from Kioka and Ashi (2015) [43].

Figure 5. (a) Scatter plot of Height (m) versus Aspect ratio bsr (D_min/D_max) of submarine MVs (N = 231), subdivided into Mud cones (red dots) and Mud pies (purple dots). (b) Scatter plot of Mean diameter D_mean (m) versus Aspect ratio bsr (D_min/D_max) of submarine mud volcanoes (N = 231), where D_mean = (D_min + D_max)/2. A smaller bsr indicates that the submarine mud volcano is more elongated in plain view, while a larger bsr indicates a sub-circular plan view shape. Modified from Kioka and Ashi (2015) [43].

3.3. Submarine MVs in the Mediterranean Sea

The Mediterranean Sea, likely due to extensive research in a scientifically and economically advanced region, hosts ~58% of the submarine mud volcanoes reported in the global MVs database [11]. Submarine MVs are clustered in several areas across a wide range of water depths (5–3600 m). The highest density occurs within the western Nile deep-sea fan [22] with eight submarine MVs per 100 km² (Figure 6). The density of submarine MVs decreases considerably up to 0.3 per 100 km² in the northern or southeastern Tyrrhenian Sea [44].

Submarine MVs in the Mediterranean Sea (N = 459) have heights up to 511 m (i.e., unnamed 94 in the western Nile deep-sea fan, offshore Egypt [22]) with a mean (median) value of ~169 m (150 m) and mean diameters up to 8000 m (i.e., Pythagoras in the Calabrian accretionary prism, Ionian Sea, one of the largest submarine mud volcanoes in the entire Mediterranean Sea [45]) with a mean (median) value of ~2750 m (2710 m). They cover surfaces ranging between ~80 m² and ~49.5 km² (mean value of ~7 km²) and have volumes between 10–7 km³ and ~5.8 km³ (mean value of ~0.48 km³) (Figure 7).

Submarine MVs, as highlighted by their axis ratio, generally have sub elliptical (1–1.5; e.g., Amon and North Alex in the central Nile deep-sea fan, off the coast of Egypt [46]) or elliptical base (1.5–2; e.g., Luigi and Sorrento in Mediterranean Ridge Accretionary Complex [23]), although in some cases elliptical elongated (2–2.5, e.g., Pan di Zucchero-2 and Procida in Mediterranean Ridge Accretionary Complex [23]), or super elliptical (>2.5; e.g., Pan di Zucchero and Alberto da Ottaviano in Mediterranean Ridge Accretionary Complex [23]).

Submarine MVs have a great morphological variability as they can be defined as flat-topped (e.g., Amsterdam, Giza, and Novorossiysk in the Eastern Mediterranean [47]), dome-shaped (Lich and Napoli in the Eastern Mediterranean [48,49]), slightly conical (e.g., Kazan in the Anaximander Mountains, Eastern Mediterranean [50]), and conical mud volcanic edifices (e.g., unnamed 207 in the western Nile deep-sea fan, offshore Egypt [22]).

The most common submarine MVs in the Mediterranean are represented by medium-sized mud cones (slice in blue in Figure 7). Examples of these are, respectively, Saint Ouen l’Aumône and Kula [51] in the Eastern Mediterranean and Giunone [52] in the Calabrian accretionary prism in the Ionian Sea.

Figure 7. Pie chart and 3D scatter plot relative to submarine MVs of the Mediterranean Sea (N = 459), differentiated by morphological type and size. In the 3D scatter plot, each data point represents a specific submarine mud volcano, characterized by H/R ratio (i.e., the ratio of the height to the radius) on the x-axis, Height (m) on the y-axis, and Volume (km³) on the z-axis. Within each category, different trends are visible and the range of values of the morphometric parameters is circumscribed (e.g., large mud cones with H/R ratio up to 0.29, heights up to 511 m, and volumes up to 2.69 km³; small mud cones with the widest range of H/R ratio values, i.e., up to 0.8, heights up to 183 m, and volumes up to 0.014 km³). Note that there are very few examples of small mud pies mentioned in scientific literature in the Mediterranean (e.g., Marrakech from the Alborán Sea [53]). This spatial distribution may be influenced by technological bias, as the resolution of vessel-mounted multibeam echo sounders decreases exponentially with increasing water depth. Additionally, it may reflect the limited availability of high-resolution bathymetric data in deep-sea environments.

Figure 7. Pie chart and 3D scatter plot relative to submarine MVs of the Mediterranean Sea (N = 459), differentiated by morphological type and size. In the 3D scatter plot, each data point represents a specific submarine mud volcano, characterized by H/R ratio (i.e., the ratio of the height to the radius) on the x-axis, Height (m) on the y-axis, and Volume (km³) on the z-axis. Within each category, different trends are visible and the range of values of the morphometric parameters is circumscribed (e.g., large mud cones with H/R ratio up to 0.29, heights up to 511 m, and volumes up to 2.69 km³; small mud cones with the widest range of H/R ratio values, i.e., up to 0.8, heights up to 183 m, and volumes up to 0.014 km³). Note that there are very few examples of small mud pies mentioned in scientific literature in the Mediterranean (e.g., Marrakech from the Alborán Sea [53]). This spatial distribution may be influenced by technological bias, as the resolution of vessel-mounted multibeam echo sounders decreases exponentially with increasing water depth. Additionally, it may reflect the limited availability of high-resolution bathymetric data in deep-sea environments.

3.4. Submarine MVs Frequency–Area Distribution

Scale-invariant size statistics have been documented for various natural phenomena [54]. They describe a statistical property in which size distributions follow the same pattern across different scales, indicating the absence of a characteristic or preferred size. This often appears as a power-law distribution, where smaller and larger structures maintain a consistent ratio regardless of the scale of observation. A prominent example is the frequency–magnitude relationship of earthquakes [55]. This approach has been crucial for estimating the recurrence time of earthquakes and for characterizing different seismotectonic regions based on the power-law exponent (β), which refers to the slope of the heavy tail seismicity distribution [56]. Consequently, this has direct implications for seismic hazard assessment. There has been growing interest in modeling other natural phenomena using similar statistical approaches, particularly in cases where collecting extensive samples is challenging [57]. This idea was further explored and consolidated in the context of geomorphology [58], including landslides, wildfires, and floods [59]. All these processes appear to follow a power-law behavior, which can also be fitted using a number of univariate statistical distributions. Their power-law exponents mark the decay trend of the given phenomenon, with larger values indicating a more rapid decrease in the number of observed processes, given their large spatial extent.

To the best of our knowledge, scale-invariant size statistics have not been tested yet on mud volcanoes. Therefore, characterizing the power-law exponent of mud volcanoes remains a task to be undertaken to match standard applications so common in other scientific branches. Here, we address this by fitting a double-Pareto simplified distribution separately for mud cones and pies. The choice of the double-Pareto simplified distribution is due to the dataset exhibiting heavy variability in both directions, meaning it contains both very small and very large values. Figure 8 demonstrates that a β value of approximately −2 is diagnostic of a distribution where the bulk is concentrated around small to very small submarine MVs, and only few extremely large ones occupy the right tail. Both mud cones and pies behave quite similarly, with the latter being characterized by a slightly larger power-law exponent. As no frequency–area distributions (FADs) appeared so far in marine geological literature, we opted to offer this as a reference analysis for future comparisons. Being a fractal diagnostic tool for magnitude, its value becomes evident in a comparative manner, as it may contextually inform on the state of development of MVs according to their spatial extent and numbers across any geographic scale.

3.5. Geohazard Implications

Mud volcanoes can be a threat to submarine infrastructures, as they may affect drilling operations, stability pipeline routings, and the anchoring of wind farms [10]. A well-documented historical example of an explosive (earthquake-triggered) eruption of a submarine mud volcano was reported on the western Mediterranean Ridge in the Ionian Sea in August 1886 [60]. Another example of violent gas emissions is provided by the deep-sea subcircular Haakon Mosby mud volcano, located in the western Barents Sea. Here, a colossal methane plume, reaching 600 m in height, was visible on echo sounder systems during several cruises. Furthermore, methane jets emitted from the seafloor were systematically observed during diving with submarines [9].

In shallow water, gas eruptions from submarine mud volcanoes may threaten navigation [61]. Strong single-gas explosions are very dangerous because they can cause changes in water density and ship buoyancy [62]. In September 1952, a gas outburst from a submarine mud volcano sank the Kayo Maru 5, a Japanese science vessel, killing all 31 crew members [63]. More recent eruptions from very shallow mud volcanoes in the northern Tyrrhenian Sea (M1 Sp and M2 Sp [11]) have been documented by concerned local fishermen [64]. Therefore, shallow water mud volcanoes, such as Amfilochia Bay MV (Figure 9) with the top only 5 m deep in the water column [65], deserve special attention.

In the scientific literature, it is reported how the summit crater diameter/basal diameter ratio can be a proxy of the magnitude of explosive activity [66]. High values suggest a more intense eruption and vice versa [67]. Unfortunately, the available scientific literature lacks systematic measurements at the summit part of submarine MVs. Nonetheless, considering the main outcomes coming out from Napoli et al. (2025) [11], we highlight some individual key points that should be considered in the geohazard assessment. A high and narrow submarine mud volcano (i.e., high H/R ratio >> 0.14; e.g., unnamed 185 in the western Nile deep-sea fan) is gravitationally more unstable than a short and wide one (i.e., low H/R ratio << 0.14; e.g., MV31 in the Caspian Sea) for very different reasons (e.g., higher center of mass, possible over steepening, significant hydrostatic pressure differences, differential erosion) representing a geohazard for the infrastructures (e.g., platforms, wind farms, pipelines) and human activities. Indeed, mass failures of submarine MVs can often act as tsunami triggers [19]. Furthermore, a high H/R ratio (i.e., H/R mud cones > 0.14 and H/R mud pies > 0.06; values calculated excluding the Mariana serpentinite MVs and not to be taken into account for them) (e.g., Napoli and Jessica in the eastern Mediterranean Sea, MV74 and MV88 in the Caspian Sea, DDS13 and DDS19 on the northeastern continental slope of the South China Sea [11]), while for small volumes may mainly reflect the viscosity of the extruded mud breccia [15], for larger volumes it may primarily indicate particularly recurrent emission activity over time (e.g., mud flows and/or aqueous fluid seepage) that affect surrounding areas and the marine ecosystem [13,16,68].

4. Conclusions

The main outcomes of this study can be an important baseline for understanding the formation and growth of submarine mud volcanoes (MVs) and their geohazard potential. The morphometric analysis of 782 MVs revealed significant variability in size and shape, independent of water depth. Heights range from 2 m to over 2 km, with radii up to ~21 km and slopes varying from <1° to ~27° (mean ~7.8°). MVs are categorized by size: small (N = 94, <0.5 km²), medium (N = 486, 0.5–9 km²), and large to giant (N = 202, >9 km²). Small MVs are steeper (~10.8°) and ~41 m high, while medium MVs reach ~138 m with gentler slopes (~8°). Large to giant MVs, linked to massive mud breccia upwellings, have an average height of ~325 m with slopes of ~6.1°. Giants MVs are concentrated in regions like the Mariana forearc, Caspian Sea, and Mediterranean Ridge. Two primary MV types emerge: mud cones (N = 570) and mud pies (N = 212). Mud cones are steeper (~9.5°) and taller (up to 2364 m), while mud pies have lower slopes (~3.5°), broader diameters, and more deformable elliptical shapes due to differences in viscosity, pressure, and fluid migration. Morphometric trends highlight distinct growth patterns that originate from very small mud cones. Internal gaps suggest key critical thresholds in MV evolution. The largest known MVs, such as Mariana serpentinite MVs, are dimensional outliers, reaching volumes up to ~1092 km³. In the Mediterranean (N = 459), MVs cluster in specific areas, with the highest density in the western Nile deep-sea fan (eight submarine MVs per 100 km²). They show varied morphologies, including flat-topped, dome-shaped, and conical forms. Medium-sized cones dominate, while smaller mud pies may be underrepresented due to mapping limitations. A frequency–area distribution (FAD) analysis shows power-law behavior (β ~−2), suggesting most MVs are small, with a few exceptionally large ones.

Furthermore, our findings contribute to both fundamental marine geology and applied geohazard assessment, ultimately supporting informed decision-making regarding submarine geohazards. Historical events, such as the 1886 Ionian Sea eruption and methane emissions from Haakon Mosby MV, highlight the significant geohazards posed by submarine MVs. Their eruptions can disrupt drilling, submarine infrastructure, and offshore wind farms. In shallow water, sudden gas expulsions may also endanger navigation. Finally, this study advances our understanding of MV morphology, classification, and hazards. Future research should employ high-resolution mapping and geophysical monitoring to refine hazard assessments and predictive models.