# Mid-Ocean Ridges: Geodynamics Written in the Seafloor

Jean-Arthur Olive

► To cite this version:

Jean-Arthur Olive. Mid-Ocean Ridges: Geodynamics Written in the Seafloor. João C. Duarte. Dynamics of Plate Tectonics and Mantle Convection, Elsevier, pp.483-510, 2023, 9780323885867. 10.1016/B978-0-323-85733-8.00018-4. hal-04040211

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# Mid-Ocean Ridges: geodynamics written in the seafloor

in: *Dynamics of Plate Tectonics and Mantle Convection - 1st Edition*, edited by J. Duarte

Jean-Arthur Olive¹

¹Laboratoire de Géologie, CNRS - Ecole Normale Supérieure - PSL University, Paris, France.

## Abstract

Mid-ocean ridges are divergent plate boundaries where new oceanic crust and lithosphere form through a complex interplay of magmatic, hydrothermal and tectonic processes. Magma is generated tens of km below the ridge by adiabatic decompression of upwelling asthenosphere. It ascends and collects at the ridge axis, where it is emplaced as oceanic crust, bringing heat that fuels hydrothermal convection. Repeated intrusions of melt into the lithosphere accommodate a sizeable fraction of plate divergence, thereby modulating the properties of faults that take up the remaining fraction. This chapter uses simple analytical models to draw connections between the thermal state of the sub-ridge asthenosphere, its magmatic productivity, and the thermo-mechanical properties of young oceanic lithosphere, which deforms in the presence of magma to shape the Earth's seafloor. This provides first-order guidelines to interpret the ~200 Myr-long seafloor record in terms of the transient dynamics of the upper mantle.

## 1. Introduction

About 2/3 of Earth's surface is paved with oceanic crust that formed somewhere along the global mid-ocean ridge (MOR) system (Searle, 2013) (Fig. 1A). This ~65,000 km-long, seismically and volcanically active boundary accommodates the divergent motion of two tectonic plates, which induces upwelling and partial melting of the underlying mantle. The asthenosphere rises up to mere kilometers below the axis of MORs, bringing along specific and latent heat. Conduction and hydrothermal circulation transfer this heat to the ocean across a thin boundary layer, which ultimately thickens as it becomes new oceanic lithosphere. By bringing hot, reduced mantle in close proximity to the cold, oxidizing ocean, global convection effectively makes MORs crucial thermo-chemical valves between the deep Earth and hydrosphere. The heat lost through recently accreted (<10 Ma) seafloor is for example on the order of 10 TW (Stein and Stein, 1992), a sizeable fraction of Earth's total heat loss (~42 TW).
Conduction and hydrothermal circulation continuously cool upwelling rocks as they transition from vertical to horizontal motion. Colder rocks become able to withstand large stresses imparted by plate divergence until they develop fractures and faults. At the same time, magma generated 10s of kms below the axis ascends and becomes emplaced a few kms below seafloor to form the oceanic crust, which is also subject to cooling and fracturing. Overall, new oceanic lithosphere is formed by a delicate balance of tectonic, magmatic, and hydrothermal processes. The relative contribution of each process depends on large-scale mantle and lithosphere dynamics. For example, the flux of magma reaching the axis is modulated by the local plate divergence rate, which reflects the self-organization of mantle convection on a global scale. Magma supply also reflects local properties of the mantle such as its potential temperature, fertility and heterogeneity. These properties are ultimately encoded in the composition and architecture of the oceanic crust / lithosphere, as well as the texture of the overlying seafloor (Menard and Mammerickx, 1967; MacDonald et al., 1996; Cannat, 1993; Goff et al., 1997; Buck et al., 2005).

As new lithosphere moves off-axis, it continues to cool but mostly ceases to deform. The characteristics it inherited at the ridge are thus largely preserved, making the seafloor a ~200 Myr-long record of MOR activity that can be leveraged to infer the transient thermo-chemical state of the upper mantle, the mechanical properties of the oceanic lithosphere, and the history of plate motions. This of course requires a solid understanding of how tectonic, magmatic and hydrothermal processes interact to shape the seafloor and oceanic lithosphere, and how they respond to changes in mantle dynamics and associated melt production— in other words: an understanding of the grammar that lets us read geodynamics in the ocean floor.

This chapter is intended as a brief overview of the ways MORs encode first-order information on upper mantle and lithosphere dynamics in the seafloor. I begin with a synthetic overview of seafloor spreading modes, from fully magmatic to amagmatic. Emphasizing simple scaling relations and analytical models, I then describe how mantle dynamics controls magma production below ridges, and how hydrothermal cooling modulates the strength of axial oceanic lithosphere. This allows me to relate styles of seafloor spreading to lithosphere strength and MOR magma supply, providing quantitative guidelines to decipher the seafloor record.

## 2. Mid-ocean ridge systematics

### 2.1. A bit of history

Line soundings revealed a broad zone of relatively shallow seafloor in the middle of the North Atlantic Ocean as early as the mid-19th century (Maury, 1860). Later expeditions established the north-south continuity of this feature (e.g., Tizard, 1876), now known as the Mid-Atlantic Ridge (Fig. 1C). Other elongated ridges were identified in all major ocean basins by the early 20th century. The development of echo-sounding techniques in the 1920s was a game changer that revealed the texture of the seafloor, first punctually, then along a single beam following the path
of a ship. As these types of measurements became more widely available in the 1950s, the picture of a globally continuous MOR system with contrasting axial morphologies emerged, largely thanks to the extensive compilation and physiographic interpretations of Marie Tharp and Bruce Heezen (e.g., *Heezen and Tharp*, 1957). Echo-sounding technologies later evolved to allow measurements along a whole swath ~5 times wider than the water column is thick, along the path of a ship. As of 2022, these techniques have enabled the mapping of less than 20% of the global seafloor at ~100 m resolution. The rest is known only at a resolution of a few kms through satellite measurements of the Earth's gravity field (Smith and Sandwell, 1997).

In the 1960s, progress in geophysical instrumentation revealed a narrow band of seismicity within 10s of km of the ridge axis (Isacks et al., 1968) and, crucially, a pattern of lineated magnetic anomalies showing remarkable symmetry about the ridge axis (Vine and Matthews, 1963). The understanding that magnetic anomalies arise from basaltic rocks recording the ever-reversing magnetic field of the Earth as they cool, and then carry this recording with them as they move away from the ridge axis was at the heart of the Plate Tectonics revolution. From then on, MORs were understood as divergent boundaries between rigid tectonic plates. Dating of magnetic anomalies enabled the determination of seafloor spreading rates (Fig. 1), which range from ~1 cm/yr (ultraslow) to ~18 cm/yr (fast/superfast), and were key to constraining the global kinematics of tectonic plates (Heirtzler et al., 1966; Le Pichon, 1968). Finally, progress in understanding MOR dynamics closely followed these major kinematic developments. MORs were swiftly interpreted as the surface manifestation of upwelling zones in a convecting mantle, and their relatively high elevation was attributed to elevated near-surface temperatures (Dietz, 1961; Hess, 1962). Today, MORs are widely understood as divergent plate boundaries where new oceanic crust and lithosphere are continuously accreted, and where divergence drives passive upwelling largely confined to the upper mantle.

Geodynamic modeling of mid-ocean ridges is a relatively young field, that was kick-started with pioneering thermal studies in the 1970s (e.g., Sleep, 1975). The 1980s and early 1990s saw great progress in the modeling of ridge magmatism (e.g., McKenzie, 1984; Whitehead et al., 1984; Sparks and Parmentier, 1991), and the late 1990s saw the rise of thermo-mechanical models that could simulate elasto-visco-brittle deformation of the lithosphere (e.g., Poliakov and Buck, 1998). I entered this game when I crossed the Mid-Atlantic Ridge in the late 2000s, at a time when ridge models started to couple magmatism and tectonics in 2 dimensions (Buck et al., 2005; Behn and Ito, 2008). At MIT/WHOI and then at Lamont, we modeled the impact of MOR tectonics on crustal architecture (Olive et al., 2010), applied the concepts of MOR tectono-magmatic interactions to explain large-scale ocean floor textures (Olive et al., 2015), and worked to expand these notions to three dimensions (Howell et al., 2019). Because I often worry that simulations may end up just as complicated as the Earth itself, I greatly value simple, analytical models that capture the essential physics of tectonic processes. These are the kinds of models I chose to emphasize in the present chapter. Since I crossed the Mid-Atlantic Ridge back to Paris
in 2018, I became interested in linking the mechanics of seafloor spreading as they operate over millions of years to their short-term manifestation on “human time scales”, e.g., earthquakes and eruptions (Olive and Dublanchet, 2020). My hope is that such approaches will foster new collaborations between marine and “sub-aerial” tectonophysicists, and that this chapter will be a pleasant first dive for all into the fascinating mechanics of the seafloor.

## 2.2. Large-scale ridge morphologies

Mid-ocean ridges typically lie 2–3 km above the surrounding abyssal plains (~5–6 km depth). In the North Atlantic, the ridge domain transitions to the abyssal plains over a distance of ~2000 km (Fig. 1C). This distance is ~4 to 8 times longer in the Pacific (Fig. 1B), a direct consequence of spreading rates being 4 to 8 times faster at the East Pacific Rise compared to the Mid-Atlantic Ridge (Fig. 1A). At the ridge axis, mantle upwelling brings heat from the Earth’s interior, resulting in elevated temperatures ($T_M$ ~ 1300–1400°C) close to the seafloor. As a piece of new oceanic lithosphere moves off-axis at an absolute velocity $U$ (close to half of the ridge spreading rate), heat is transferred to the cold ocean ($T_0$ ~ 4°C) by vertical conduction. The thermal diffusivity of the oceanic lithosphere is on the order of $\kappa$ ~ 10⁻⁶ m²/s. This means that after a time $\tau$, the lithosphere has moved by a horizontal distance $d_x = U\tau$ and cooled over a characteristic vertical distance $d_z = \sqrt{\kappa\tau}$. Its thermal structure $T(x, z)$ is well described by the half-space cooling model (Turcotte and Schubert, 2002, Fig. 1B, C):

$$T(x, z) = T_0 + (T_M - T_0) \operatorname{erf} \left( \frac{z^*}{2\sqrt{x^*}} \right), \quad (1)$$

where $x^*$ and $z^*$ respectively denote distance from the ridge axis and depth normalized by a characteristic advection-diffusion length:

$$L = \frac{\kappa}{U}. \quad (2)$$

As the lithosphere cools, its average density increases, and the seafloor must lie at a lower elevation such that vertical stresses can remain constant along a horizontal compensation level located deep within the weak asthenosphere. This simple Pratt isostasy model explains the observed trend of seafloor deepening $\Delta d$ as the square root of distance to the axis (or seafloor age), illustrated in Fig. 1B, C:

$$\Delta d(x^*) = L \frac{\rho_m \alpha (T_M - T_0)}{(\rho_m - \rho_w)} \frac{2}{\pi} \sqrt{x^*}. \quad (3)$$

In equation (3), $\rho_m$ and $\rho_w$ are the reference density of the mantle and the density of the ocean, respectively, and $\alpha$ is the mantle’s thermal expansion coefficient (~10⁻⁵ K⁻¹). This thermal model is also consistent with heat flow measurements near and away from the ridge axis, with important deviations from the model in seafloor younger than ~50 Ma, attributed to hydrothermal heat extraction at shallow levels (Stein and Stein, 1992), and in seafloor older than ~70 Ma, attributed to heat being supplied by mantle convection below old oceanic lithosphere (i.e., the plate thermal
model). It is interesting to note that while the relative elevation of mid-ocean ridges is
maintained by convection bringing hot mantle close to the surface, it cannot be referred to as
"dynamic topography", since it is well explained by isostatic equilibrium (Molnar et al., 2015).

## 2.3. Ridge axis morphologies

Zooming in on scales of ~10s of km around the ridge axis reveals systematic trends in seafloor morphology (Fig. 2), crust and lithosphere structure, as well as tectonic styles as a function of spreading rate (Fig. 3). To first-order, the texture of the seafloor at this scale is dominated by regularly-spaced topographic highs that are elongated in the along-axis direction (Goff et al., 1997). The morphological characteristics of these abyssal hills can be straightforwardly related to the morphology of the MOR where they originated (Fig. 1D).

Fast-spreading ridges (e.g., the East Pacific Rise, Fig. 2A) are typically associated with an axial high ~10 km wide and ~100s of meters high, whose flanks are dissected by many axis-facing and outward-facing faults with offsets limited to ~10 m. Axis-facing faults become dominant at the edge of the axial high (Escartín et al., 2007). They offset and tilt seafloor paved with overlapping basaltic lava flows, thereby abyssal hills < 100 m high, typically spaced by ~1–3 km (Fig. 3A, B) (Macdonald et al., 1996). These faults cut through the brittle portion of the axial lithosphere, which is likely thinner than ~2km, as indicated by the depth distribution of microseismicity (Fig. 3D). Summing fault offsets shows that they account for a very small fraction (<5%) of the total plate separation, suggesting that M > 95% of the plate divergence is accommodated by magmatic emplacement. In the following we refer to the magmatic fraction of plate separation M (Fig. 3E) as the time-averaged rate of magmatic intrusion into the brittle lithosphere, divided by the plate separation rate (2U). The oceanic crust is ~6 km thick at fast MORs (Fig. 3C), with a basaltic upper section consisting of lava flows and dikes down to ~1.5 km: the depth of the axial melt lens (AML, Fig. 1D). Below the AML, the lower oceanic crust mainly consists of gabbros that likely accrete through a complex plumbing system involving multiple melt lenses (Kelemen et al., 1997; Marjanović et al., 2014) within a crystal mush zone (Sinton and Detrick, 1992). Finally, the axial high hosts multiple hydrothermal vents that spew metal-rich fluids at temperatures >350°C. These vents cluster within hydrothermal fields, each accounting for a heat flux on the order of ~100s of MW (Fig. 3F). Hydrothermal fields lie above fluid upwelling zones that are part of along-axis convection cells within the thin brittle lithosphere (Tolstoy et al., 2008). Hydrothermal circulation is fueled by heat from the underlying AML (Lowell et al., 2013), and likely involves fluid recharge in the cross-axis direction beneath the axial high (Hasenclaver et al., 2014).

Intermediate-spreading ridges share many characteristics of fast-spreading ridges, with the main exception that they can be straddled either by an axial high or an axial valley (e.g., the Chile Ridge, Figs. 1D, 3C). In the latter case, the axis consists of a ~10 km-wide depression with ~1 km negative relief, bound on either side by axis facing normal faults. These faults can
accumulate greater offsets than fast-spreading ridge faults, and end up accommodating a greater fraction of the total plate divergence (~5–30%, Fig. 3E). They outline abyssal hills of slightly greater amplitude (~100s of m), with spacing as large as ~3–5 km (Fig. 3A, B). The axial lithosphere is slightly thicker, and AMLs, when imaged, tend to lie at a slightly greater depths (~2-3 km) (Fig. 3D). Remarkably, the overall thickness of the magmatic crust (as estimated through seismic imaging) changes very little across intermediate and fast spreading rates (Fig. 3C). High-temperature hydrothermal fields have also been extensively documented above AMLs at intermediate spreading ridges (e.g., *Tivey and Johnson*, 2002).

The above described trends continue as spreading rates further decrease, albeit with more spectacular changes below ~4 cm/yr. These include more widely spaced, greater amplitude abyssal hills (Fig. 2D, Fig. 3A, B), thicker axial lithosphere (Fig. 3D), and a reduced contribution of magmatism to the accommodation of plate divergence (Fig. 3E). The most crucial change is the increased variability in ridge characteristics along axis, which manifests as increased scatter in the data plotted in Fig. 3. This variability exists at the scale of individual ridge segments, which are 10s of km long. The centers of slow-spreading ridge segments are associated with thicker crust, shallower seafloor and more intense magmatic activity compared to segment ends (located near transform faults or non-transform offsets), which have thinner crust (~4 km), a deeper, wider axial valley, and larger-offset faults that accommodate a greater fraction of plate separation (Kuo and Forsyth, 1988; Cannat, 1996; Tucholke and Lin, 1994). Some normal faults —often located at the inside corner of ridge-transform intersections— accumulate offsets greater than ~10 km and result in asymmetric seafloor morphology that contrasts with the staircase-like symmetric topography of segment centers (Fig. 2D). These large-offset faults are referred to as detachments, and exhume lower crustal and mantle units directly at the seafloor within dome-shaped bathymetric highs (Tucholke et al., 1998) (Fig. 2E).

Even more spectacular variability can be observed from segment to segment along slow and ultraslow MORs. About 50% of the Northern Mid-Atlantic Ridge axis is for example populated by “symmetric” segments with a well defined axial valley that is ~10 km wide and >1 km deep (Escartín et al., 2008). These sections produce abyssal hills that are ~2–8 km apart and reach amplitudes of ~1 km (Fig. 2D). The hills are bound by axis-facing normal faults that accommodate ~15 to ~40% of plate separation (Fig. 3E), meaning that magma emplacement accounts for ~60 to 85% of the divergence rate. These segments are associated with a “normal” crustal thickness of ~6 km, or sometimes more (Fig. 3C). Some, like the Lucky Strike segment of the Mid-Atlantic Ridge, likely host an AML at depths of 3–4 km (Singh et al., 2006), but such a feature is thought to be more transient than at fast-spreading MORs (Phipps Morgan and Chen, 1993). By contrast, the remaining ~50% of the Northern Mid-Atlantic Ridge axis consists of highly asymmetric sections where detachment faulting plays a key role in lithosphere accretion (Fig. 2E). These sections are associated with thicker on-axis lithosphere (~10–12 km, Fig. 3D), greater seismicity rates, stronger hydrothermal activity, and basalts with major element
compositions that suggest fractionation at depths greater than basalts erupted at symmetric segments (Escartín et al., 2008). Because faults can accumulate very large offsets in these areas, they can take up a large fraction (up to ~50%) of total plate separation (Buck et al., 2005; Behn and Ito, 2008; Schouten et al., 2010). The resulting crustal structure is highly discontinuous, with a basaltic section virtually absent where detachment faults exhume serpentinized mantle and gabbro bodies (Dick et al., 2008).

The contrast between magmatically-robust, symmetric sections and detachment-bearing sections is even more extreme at ultraslow-spreading MORs such as the Southwest Indian Ridge. This ridge comprises amagmatic segments where the seafloor appears “smooth” (Cannat et al., 2006), and almost exclusively consists of detachment surfaces exposing serpentinized mantle (Sauter et al., 2013). There, seafloor spreading proceeds by prolonged slip on large-offset faults that “flip-flop”, i.e., initiate sequentially with alternating polarities (Reston, 2018; Cannat et al., 2019a), and shape horst blocks with spectacular relief (>4 km, Fig. 2F). These faults root to a depth of at least ~16 km, as evidenced by the distribution of microseismicity (Chen et al., 2020). A few tens of km further along the ridge, the seafloor sharply transitions to a more symmetric morphology, and mostly consists of basaltic rocks. In fact, magmatic sections of the Southwest Indian Ridge are just as extreme as their amagmatic counterparts, as they feature some of the thickest known oceanic crust outside the region of influence of hot spots. For example, the crust is 9.5 km-thick at Segment 27 of the Southwest Indian Ridge (Jian et al., 2017), whose morphology suggests an extremely strong contribution of magmatic emplacement to total plate separation (>92%, Chen et al., 2021b) (Fig. 3C, E). This suggests that the local supply of magma can vary drastically along the axis of slow and ultraslow MORs, from an entirely amagmatic end-member to another extreme akin to an intermediate or fast-spreading MOR. This is particularly evident at MOR sections influenced by a nearby hot spot such as the Reykjanes Ridge south of Iceland (Fig. 2B).

### 3. From decompression melting to oceanic crust emplacement

#### 3.1. Magma generation

Spreading centers are systematically underlain by a region of upwelling asthenosphere (Fig. 4A, B). This flow is thought to be largely passive, i.e., driven by plate separation. Its characteristic vertical velocity thus scales with the MOR's spreading half-rate (Fig. 4A). A parcel of hot mantle rising at speeds of ~cm/yr can advect heat faster than heat can escape conductively. Mantle ascent below MORs thus occurs adiabatically, along a geotherm characterized by a low gradient (~0.3°C/km) given by:

$$ \frac{\partial T}{\partial z_{adiab}} = \frac{\alpha g T_M}{c_P}. \quad (4) $$

In equation (4), $c_P$ denotes the heat capacity of the mantle (~1000 J/kg), $g$ is gravity, and $T_M$ is the mantle's potential temperature, i.e., the temperature a mantle parcel would retain if it could
rise adiabatically all the way to the surface. This of course cannot happen because a rising parcel must eventually enter the lithosphere, where significant conductive heat loss occurs. Below the lithosphere, however, the mantle is sufficiently hot to cross the dry peridotite solidus as it ascends (Fig. 4). At any given depth z, the solidus temperature can be expressed as:

$$T_S(z) = T_{S0} + \gamma \rho_m g z, \quad (5)$$

with γ the Clausius-Clapeyron slope (~6×10-8 K/Pa). The crossing depth zM, where the first melts are produced (Fig. 4E, F), is thus given by

$$z_M = \frac{T_M - T_{S0}}{\gamma \rho_m g - \frac{\alpha g T_M}{c_p}}. \quad (6)$$

This depth is typically ~60–70 km below MORs, although other depths are possible depending on the local potential temperature (Fig. 4C–F) or compositional variability of the mantle (not accounted for in the simplified model presented here) (Langmuir and Forsyth, 2007). The sub-ridge region where the mantle is hotter than the solidus ($T(z)>T_S(z)$) is called the melting regime, and typically has the shape of a triangle (because isotherms deepen off-axis, Fig. 1B, C) with a flat base at zM. The melt fraction F(z) within the triangle can be estimated to first order by balancing the mantle’s specific heat (in excess of the solidus) with the latent heat needed to drive partial melting, assuming a latent heat of fusion $L_M \sim 4 \times 10^5$ J/kg. This yields (Crowley et al., 2015):

$$F(z) = \frac{c_p}{L} \left( \gamma \rho_m g - \frac{\alpha g T_M}{c_p} \right) (z_M - z), \quad (7)$$

with typical values of F below MORs ranging between 0 and ~20% (Fig. 4 E, F). Every time a cubic meter of mantle ascends by 1 meter, it produces a mass of melt equal to $\rho_m \left|\frac{\partial F}{\partial z}\right|$. This quantity is known as the adiabatic productivity of the mantle (Π), and can be expressed as:

$$\Pi = \rho_m g \frac{\gamma c_p \rho_m - \alpha T_M}{L}. \quad (8)$$

If the mantle upwells at a characteristic rate U within a triangular (cross-axis) area of height ~zM (assuming the thickness of the axial lithosphere is small compared to zM) and width wM (Fig. 3A, C, D), this region produces a total mass flux of magma equal to:

$$\Phi = \Pi U \frac{1}{2} z_M w_M, \quad (9)$$

in kg/s per meter along the ridge axis. Assuming all this magma, of density ρc, ultimately gets emplaced at shallow depths to form an oceanic crust of thickness HC, and neglecting density changes associated with crystallization, the corresponding crustal mass flux is

$$\Phi = 2U \frac{H_C}{\rho_c}. \quad (10)$$

Equating (9) and (10) yields the following expression for crustal thickness:
$$H_C = \frac{1}{2} \Pi \rho_c \frac{z_M w_M}{\overbrace{A_m}^{A_m}}. \quad (11)$$

The first thing to note in equation (11) is that because *U* cancels out of equations (9) and (10), crustal thickness does not depend on spreading rate. This accounts for the remarkable uniformity of crustal thickness measurements (~6–7 km) at ridges that spread faster than ~4 cm/yr (Fig. 4C). The second takeaway point of equation (11) is that the potential temperature of the mantle *T*<sub>M</sub> exerts a crucial control on crustal thickness, primarily through the *z*<sub>M</sub> term (equation 6). Simply put, a hotter mantle intersects the solidus at a greater depth, resulting in a larger melting column (Fig. C, E vs. D, F) and greater magma production (e.g., Forsyth and Langmuir, 2007). This is likely to occur at hot spot influenced sections of MORs such as Iceland, where the thickness of the oceanic crust can exceed 20 km. In practice, the simple model presented here would attribute the formation of a 20-km thick crust to a thermal anomaly on the order of ~100°C in the sub-ridge mantle, relative to a “standard” setting that produces a 6-km thick crust. Additional effects relative to composition and differences in mantle fertility can be considered to refine these estimates.

The sharp decrease in crustal thickness observed at MORs slower than ~4 cm/yr (Fig. 3C) can also be interpreted in light of equation (11). First, it is apparent from equations (1–2) and Fig. 4A that, because the characteristic advection-diffusion distance *L* increases at slower spreading rates, the isotherm that defines the top of the melting regime steepen more sharply off-axis, leading to a narrower melting triangle (e.g., Fig. 1B vs. 1C). Second, a greater *L* means a greater axial lithospheric thickness (Fig. 4A), which is no longer negligible compared to *z*<sub>M</sub>. This drastically reduces the height of the melting regime. Overall, it is largely the reduction in the area of the melt production region (*A*<sub>M</sub> in equation 11) that accounts for the lesser magmatic productivity of slow/ultraslow MORs.

## 3.2. Magma ascent and focusing

The simple model summarized above assumes that all the magma produced in the melting region instantaneously ascends and accretes as a homogeneous oceanic crust. The reality is of course far more complex. Partial melts fill the pore space between minerals, and their migration involves a complex feedback with the viscous deformation of the porous mantle (McKenzie, 1984). The velocity of the melt relative to the velocity of the mantle depends on the permeability of the mantle (a strong function of porosity, i.e., local melt fraction), the viscosity of the magma, and gradients in magma pressure. The positive buoyancy of the melt is the strongest contributor to the pressure gradient, accounting for largely vertical melt trajectories within the melting triangle (e.g., Hebert and Montési, 2011; Fig. 4B). Feedbacks between melt fraction and permeability can prompt the development of permeable channels that focus melts during ascent (Sparks and Parmentier, 1991; Aharonov et al., 1995). This is particularly thought to occur along
the base of the lithosphere: as vertically traveling melts reach a permeability barrier —which roughly coincides with the 1240°C isotherm (Montési and Behn, 2007)— some of them crystallize, which decompacts the porous mantle and forms an oblique channel through which melts can travel towards the ridge axis (Fig. 4A, B). This process explains how melt produced near the sides of the melting triangle can be collected at the ridge axis. Lateral variations in mantle viscosity and magma production rates may also induce gradients in compaction pressure that further complicate the trajectories of the melt (Turner et al., 2017). However, the first-order model involving magma generation, ascent, and axis-ward focusing along the base of the lithosphere (Fig. 4B) has proven successful at predicting oceanic crustal thickness from a known mantle flow and thermal structure (Bai et al., 2017).

This conceptual model also sheds light on the remarkable variability of seafloor spreading styles along the axis of slow and ultraslow ridges, compared to the relative uniformity of intermediate- and fast-spreading MORs (Fig. 3). The thermal structure of slow ridges is indeed known to be strongly three-dimensional (Fig. 1E), with thinner lithosphere at segment centers and thicker lithosphere at segment ends (e.g., Cannat, 1996; Cannat et al., 2019a). This structure favors focusing of melt towards segment centers and away from segment ends, resulting in thicker crust at segment centers (Kuo and Forsyth, 1988). At ultraslow-spreading ridges, along-axis changes in thermal regime can be even more drastic and prompt extreme along-axis focusing of melt, leaving entire ridge sections devoid of magma while others accrete an abnormally thick (10+ km) oceanic crust (Dick et al., 2003; Cannat et al., 2019a; Chen et al., 2021b). Of course collecting and emplacing more magma in regions of hotter, thinner lithosphere exerts a self-reinforcing feedback on the thermal structure of the ridge. It is therefore not entirely clear which process(es) shape this along-axis variability in the first place. One possibility could be a form of gravitational instability developing within the zone where melts pool at the base of the lithosphere, leading to zones of melt upwelling that are regularly spaced along axis (Whitehead et al., 1984).

### 3.3. *Building the crust*

Once magma reaches very shallow depths below seafloor, it gets emplaced and crystallizes to form new oceanic crust. Studies of ophiolites and tectonic windows at MORs have led to a widely accepted model for the structure of the oceanic crust formed at intermediate and fast ridges (Fig. 1D; e.g., Penrose Conference, 1972), in which the lower crust consist primarily of gabbro. Seismic imaging studies (e.g., Detrick et al., 1987) later revealed that the lower crust is topped by magma-filled sills that are ~1.5–3 km deep, ~100 m thick and span kms or 10s of kms along the axis of fast/intermediate MORs. These axial melt lenses are thought to be the primary locus for melt pooling and fractionation, before magma intrudes the upper crust as dikes that feed lava flows at the seafloor. The detailed mechanisms of lower crust accretion are still somewhat debated. One end-member, the so-called “gabbro glacier” model postulates that the lower crust is
shaped by the downward and outward flow of a crystal mush zone initiating at the axial melt lens (*Phipps Morgan and Chen*, 1993). Another end-member model describes the lower crust as a stack of gabbroic sills that have intruded each other and accreted the crust “in-situ” (*Kelemen et al.*, 1997). While real systems likely combine elements from both models, new imaging of several regularly spaced melt lenses beneath the axial melt lens (*Marjanovic et al.*, 2014) now point to the possibility that deep pockets of melt may be inherently dynamic features, akin to porosity waves that travel upward through the lower crustal mush zone (Fig. 1D), ultimately feeding the uppermost axial melt lens (*Carbotte et al.*, 2020).

Unsurprisingly, the modes of crustal accretion at slow and ultraslow spreading ridges are more diverse and complex. While the crust formed at symmetric sections of slow ridges, paved with basaltic flows (Fig. 3D), likely resembles that formed at faster rates, magma-poor sections of ultraslow ridges (Fig. 3F) primarily expose serpentinized peridotites with a patchy cover of basaltic flows (*Sauter et al.*, 2013). These areas, where the lithosphere is at least ~15 km thick, are thus not entirely amagmatic but do receive transient inputs of magma that can reach the surface and erupt (*Fan et al.*, 2020). The overall magma supply is too reduced and scattered, however, to build a continuous magmatic crust. This is also seen at detachment-bearing sections of slow MORs (Fig. 3E), where the footwalls of large-offset faults exhume a composite lower crust made of discrete gabbro bodies embedded in serpentinized peridotites (*Blackman et al.*, 2002; *Dick et al.*, 2008). In a nutshell, the specificity of these settings is that the thickness of their axial lithosphere typically exceeds that of the magmatic crust (or the magmatic crust that would accrete if the supply of magma was continuous, e.g., solid vs. thin dashed line in Fig. 3D). This is unlike faster ridges where the axial lithosphere is confined to the uppermost levels of the magmatic crust. Because slow, magma-poor ridges lack a steady magmatic plumbing system where melt is continuously delivered to a shallow axial melt lens, it is mechanically difficult for magma to travel upwards through the brittle lithosphere and erupt at the seafloor. Magma transport also likely involves a significant along-axis component, away from magma-rich sections or segment centers. These complex magma pathways across the lithosphere result in multiple gabbroic intrusions, possibly sill-like, emplaced over a wide range of depths and temperatures (*Chen et al.*, 2022). To further complicate matters, the architecture of slow-spread crust is heavily reworked by slip on large offset faults that can alternate in polarity (*Cannat et al.*, 2006; *Olive et al.*, 2010).

## 4. Cooling and building the oceanic lithosphere

The oceanic lithosphere is by definition a layer where large deviatoric stresses, on the order of 10s to 100s of MPa, can accumulate before rocks yield in a brittle or ductile fashion. In mafic to ultramafic lithologies deformed at tectonic strain rates, the brittle-ductile transition roughly corresponds to the ~650–750°C isotherm (*Mackwell et al.*, 1998; *Karato and Wu*, 1993). At temperatures exceeding ~1200°C, thermally-activated creep mechanisms become so efficient that
mantle rocks can flow easily, relaxing any deviatoric stress on yearly time scales (Karato, 2008). The ~1200–1300°C isotherm marks the transition between lithosphere and asthenosphere. Is therefore clear that the thermal structure of a MOR strongly determines its strength profile, which has a strong impact on seafloor spreading modes.

The thermal structure of MORs reflects a balance between heat advected upwards by the upwelling asthenosphere (and the melt it produces), and heat transferred across the lithosphere which is ultimately lost to the ocean. In the lithosphere, heat is primarily transferred by diffusion and hydrothermal circulation, i.e., the convective and reactive flow of seawater through fissures and pores. To first order, the on-axis thickness of the oceanic lithosphere is an advection-diffusion length scale (L, equation 2). Montési and Behn (2007) for example modeled a generic ridge thermal structure non-dimensionalized by L, in which the lithosphere-asthenosphere boundary (and permeability barrier where melts pool) is located on-axis at a depth of ~5L, while the base of the seismogenic zone (brittle-ductile transition) lies at a depth of ~2.5L (Fig. 4A). This simple framework explains why the seismogenic thickness of MOR axes increases sharply as spreading rate approaches zero (Fig. 3D). It can be extended to include the effect of hydrothermal circulation as “enhanced diffusion”. This involves multiplying the thermal diffusivity of the lithosphere by an ad-hoc factor called the Nusselt number to parameterize the efficient extraction of heat by hydrothermal flow (Fig. 5A). To produce a thermal structure that is compatible with observed seismogenic thicknesses and the depth of axial melt lenses, models must invoke Nusselt numbers on the order of 4–8 in shallow regions colder than 600°C (Phipps Morgan and Chen, 1993). This is compatible with the notion that viscous creep should prevent the opening of fissures, and therefore prevent the vigorous circulation of fluids, at high temperatures. This class of models is broadly applicable to fast and intermediate-spreading MORs, where the axial brittle lithosphere is thinner than the magmatic crust (Fig. 3D).

At fast and intermediate-spreading MORs, hydrothermal convection is confined to along-axis cells within the upper crust (lava flows and sheeted dikes), with additional recharge of fluids occurring in the cross-axis direction (Tivey and Johnson, 2002; Tolstoy et al., 2008; Hasenclaver et al., 2014). Fluids can circulate in close proximity to the axial melt lens and efficiently mine magmatic heat through a thin conductive boundary layer sandwiched between the base of the permeable hydrothermal system ($T_H$ ~ 600°C at the most) and the top of the axial melt lens ($T_L$ ~ 1200°C, the basaltic liquidus) (Lowell and Germanovich, 2004; Liu and Lowell, 2009; Fig. 5A). The thickness of this boundary layer is estimated at $\delta$~10–100 m from outcrops of the dike-gabbro transition at ophiolites and MORs (Gillis, 2008). Introducing $\lambda$, the thermal conductivity of the crust (~3 W/K/m), the corresponding heat flux writes:

$$q_{CBL} = \lambda \frac{T_L - T_H}{\delta}. \quad (12)$$

This heat is collected over a horizontal area $A_{CBL}$, which is particularly difficult to estimate without knowledge of the fluid pathways at the base of the upper crust. Using the map view
extent of imaged axial melt lenses below hydrothermal fields, Lowell et al. (2013) proposed values on the order of 10⁶–10⁷ m². This is consistent with the heat flow measured at many high-temperature hydrothermal fields, typically on the order of ~100s of MW (Fig. 3F), which roughly matches the integrated flux: $q_{CBL}A_{CBL}$. In the simple single-pass model of hydrothermal convection of Lowell and Germanovich (2004), this heat is transferred vertically in narrow fluid upwelling (discharge) zones that feed hydrothermal fields at the seafloor (Fig. 5A). The size and spacing of these pipe-like structures can be inferred from the demagnetization they impart on the basaltic crust (Tivey and Johnson, 2002), or from the distribution of micro-earthquakes along the path of the fluids (Tolstoy et al., 2008). The characteristic diameter of upflow zones is ~100 m, which means they must account for a vertical heat flux on the order of 1000s of W/m² ($q_{CBL}A_{CBL}/A_{upflow}$). In comparison, vertical heat conduction from a melt lens emplaced 2 km below seafloor barely accounts for a few W/m², illustrating how much more efficient hydrothermal convection can be at evacuating heat across the lithosphere.

The vertical flow of seawater in discharge zones is reasonably well modeled as Darcy flow driven by the buoyancy of hot fluids. In this framework, the upwelling velocity of the fluids writes:

$$v_f = \frac{k_d}{\nu_f} \alpha_f (T_H - T_0) g, \quad (13)$$

where $k_d$ is the permeability of the upflow zone, $\nu_f$ and $\alpha_f$ are the kinematic viscosity (~10⁻⁷ m²/s) and thermal expansion coefficient (~10⁻³ K⁻¹) of the hydrothermal fluids, $T_H$ is the temperature of the fluid at the base of the hydrothermal system and $T_0$ is the temperature of the ocean. Assuming fluids travel fast enough not to lose heat conductively to the upper crust, they can retain a temperature close to $T_H$ during ascent. Introducing $\rho_f$ (~1000 kg/m³) and $c_{Pf}$ (~1000s of J/kg/K) the reference density and heat capacity of the fluids, we can write the advective heat flux $q_H$ associated with fluid upflow:

$$q_H = \rho_f c_{Pf} (T_H - T_0) v_f = \frac{k_d \alpha_f \rho_f c_{Pf} g}{\nu_f} (T_H - T_0)^2. \quad (14)$$

Using the characteristic values of all the parameters listed above, we find that fluxes $q_H$ ~ 1000s of W/m² require an upflow zone permeability on the order of 10⁻¹⁴–10⁻¹³ m² (Lowell et al., 2013). These values are consistent with independent estimates of permeability that rely on the poro-elastic response of hydrothermal systems to tides (Barreyre et al., 2018). However, this permeability should be understood as an effective value averaged over the entire discharge zone, as it is well known that the permeability of the oceanic crust can span multiple orders of magnitude depending on depth, lithology, degree of fracturing, precipitation of minerals, and many other factors (Fisher, 1998). The assumption of constant fluid properties is also an oversimplification, as parameters such as viscosity, heat capacity and density vary significantly and non-linearly across the range of hydrothermal fluid temperatures. Accounting for these
variations reveals a trade-off between permeability and fluid venting temperatures (Driesner, 2010). Specifically, the thermodynamic properties of seawater are such that a low-temperature (<100°C), high-permeability (>10⁻¹² m²) system can account for the same heat flux as a high temperature (>300°C), low-permeability (<10⁻¹⁴ m²) upflow. High-temperature “black smoker”-type vents are thought to be the seafloor expression of pipe-like flows of moderate permeability, effectively sealed from the rest of the crust by mineral precipitation (Coumou et al., 2008). Smokers are often surrounded by lower temperature “diffuse flow” that likely result from mixing of hot upwelling fluids with seawater in a shallow, high permeability layer (Fig. 5A). Although less spectacular than smokers, diffuse vents are pervasive and likely account for a sizeable portion of the heat output of many hydrothermal fields (Mittelstaedt et al., 2012).

The above description of hydrothermal systems mainly applies to intermediate and fast MORs with a robust and steady magma supply. Liu and Lowell (2009) specifically showed that in order to maintain the kinds of heat fluxes documented at these ridges, the axial melt lens must to be continuously replenished at rates ~10⁶ m³/yr. These rates exceed the fluxes needed for long-term crustal accretion (equation 10), but are on par with rates inferred at terrestrial volcanoes. In the absence of magma replenishment, the axial melt lens would cool and crystallize in a few decades. This is clearly not happening at the East Pacific Rise or the Costa Rica ridge, where axial melt lenses have been surveyed since the 1980s and 1990s (Marjanovic et al., 2014; Lowell et al., 2020). On the other hand, slow and ultraslow mid-ocean ridges challenge the above paradigm in a variety of ways. Hydrothermal activity has for example been documented in quasi-amagmatic sections of ultraslow ridges (Baker et al., 2004; Cannat et al., 2019b). High-temperature seafloor venting could be a transient feature that occurs whenever a gabbro sill is intruded within the lithosphere (Fan et al., 2021), and lasts for tens of years (Liu and Lowell, 2009). A sluggish, lower temperature hydrothermal system may be maintained over thousands to tens of thousands of years if hydrothermal cooling induces grain-scale fracturing that allows fluids to penetrate deeper and mine heat from the lithosphere (Lister, 1974; Olive and Crone, 2018). Additional heat sources may include the heat released by exothermic alteration reactions such as serpentinization (Lowell, 2010). Beyond the vigor and temporal stability of magma-poor hydrothermal systems, another crucial question is their depth extent. Suppose for example that confining pressure prevents any cracking, and consequently the development of any significant permeability at depths greater than a few kilometers below seafloor (Kuang and Jiao, 2014). Then the area of enhanced heat extraction, manifesting as a high Nusselt number, should be confined to the uppermost portion of the lithosphere. If magmas preferentially pool near the base of the lithosphere, the conductive boundary layer separating the magmatic heat source from the hydrothermal system would be kilometers wide, resulting in very low heat fluxes ($q_{CBL} < 1$ W/m²). Such systems would not be particularly efficient at cooling the oceanic lithosphere, and are unlikely to account for the thick seismogenic zone (~16 km: Chen et al., 2020) observed at quasi-amagmatic sections of the Southwest Indian Ridge, unless the heat advected from the
rising asthenosphere is particularly low and the supply of magma is particularly scarce (Fan et al., 2021). Alternatively, a model in which fluids can convect vigorously down to ~15 km (e.g., Tao et al., 2020), perhaps aided by tectonically driven fracturing, would straightforwardly account for a thick axial lithosphere underlain by a thin boundary layer that allows efficient heat extraction. A corollary to such a model would be that large portions of the lithosphere (e.g., down to depths ~10-15 km, where temperatures do not exceed ~400°C) should be serpentinized owing to the sustained input of seawater in direct contact with mantle peridotites. This is however at odds with seismic imaging studies which reveal P-wave velocities characteristic of fresh peridotites at depths as shallow as ~5 km (Momoh et al., 2017). While there is petrological evidence for lithosphere hydration at depths > 15 km in transform settings (e.g., Prigent et al., 2020), the presence of water does not imply a vigorous convective system that can effectively extract heat. Resolving the issue of how deep hydrothermal circulation may occur is now crucial to further our understanding of the thermo-mechanical state of slow-spread oceanic lithosphere, as well as its degree of hydration, which has implications for the deep water cycle.

## 5. Shaping the seafloor through tectono-magmatic interactions

Now that we understand how basaltic melts are produced and form the oceanic crust, and how hydrothermal circulation modulates the thermo-mechanical structure of young oceanic lithosphere, the last piece of the puzzle is to understand how brittle deformation of the lithosphere interacts with magma emplacement to shape the fabric of the seafloor.

### 5.1. Lithospheric thickness and the lifespan of normal faults

The state of stress within the lithosphere at a MOR axis combines lithostatic pressure (partially relieved by pore fluids) and a component of horizontal tension, such that the principal stresses $σ_1$ (most compressive, i.e., most negative) and $σ_3$ are respectively vertical and horizontal. Normal faults form when the differential stress ($Δσ = σ_3 - σ_1$) in the lithosphere exceed a frictional, e.g., Mohr-Coulomb, threshold:

$$ \Delta\sigma^{\text{BREAK}} = 2 \frac{C + \mu \rho g (1 - \lambda) z}{\mu + \sqrt{1 + \mu^2}}, \quad (15) $$

where C and μ denote the cohesion and friction coefficient of unfaulted lithosphere. ρ is its average density, z is depth below seafloor and λ is the ratio of pore fluid pressure to lithostatic pressure. This differential stress prompts the formation of optimally-oriented faults, with dips equal to:

$$ \theta^{\text{OPT}} = \frac{\pi}{4} + \frac{\tan^{-1}(\mu)}{2}. \quad (16) $$

Breaking faults with dips θ other than $θ^{OPT}$ is possible, but requires a differential stress greater than $Δσ^{BREAK}$ given by:
$$ \Delta\sigma(\theta) = \frac{C + \mu\rho g(1 - \lambda)z}{\cos\theta \sin\theta + \mu \sin^2\theta}. \quad (17) $$

For friction coefficients typical for silicate rocks (~0.6–0.85) [Byerlee, 1978], the optimal dip of a normal fault is close to 60°. Integrating equation (15) over the thickness $H$ of the brittle lithosphere yields the force required to break an optimally-oriented fault:

$$ F_{\text{BREAK}} = \frac{2CH + \mu\rho g(1 - \lambda)H^2}{\mu + \sqrt{1 + \mu^2}}. \quad (18) $$

As soon as a normal fault accumulates some finite offset, a number of processes act jointly to lower the force necessary to sustain slip. On the one hand, fault localization amounts to a loss of cohesion, and the development of a phyllosilicate bearing gouge can lead to a reduction in fault friction: $\mu_F < \mu$ (Escartín et al., 1997; Collettini and Sibson, 2001). Fault gouges may contain weak minerals such as clays, chlorite ($\mu_F \sim 0.4$), serpentine ($\mu_F \sim 0.3–0.45$), or talc ($\mu_F \sim 0.1$). The latter however requires silica-rich fluids, for example supplied by the alteration of gabbroic bodies. On the other hand, accumulating offset on a normal fault up- and down-warps its footwall and hanging wall blocks, respectively, over characteristic distances controlled by $H$ (Vening-Meinesz, 1950; Weissel and Karner, 1989; Buck, 1988). Flexure in turn rotates the fault towards gentle dips (Choi and Buck, 2012), at rates (i.e., degrees of rotation per unit increment of offset) inversely proportional to $H$ (Olive and Behn, 2014; Olive et al., 2014). Consequently, integrating equation (17) yields the force required to sustain slip on a fault that has developed an horizontal offset $h$, and has rotated down to a dip $\theta_{(h)}$ (Behn and Ito, 2008):

$$ F_F(h) = \frac{\mu_F \rho g (1 - \lambda_F) H_{(h)}^2}{\cos \theta_{(h)} \sin \theta_{(h)} + \mu_F \sin^2 \theta_{(h)}}. \quad (19) $$

The $H_{(h)}$ term accounts for the fact that as the fault grows, it may migrate off-axis and encounter thickening lithosphere.

Flexure of the footwall and hanging-wall blocks, and the associated build-up of topography can be thought of as resisting the accumulation of offset on a normal fault (Forsyth, 1992). These effects can be parameterized as an additional force $F_B(h)$ required to sustain fault slip. Buck [1993] quantified this force as the derivative of the strain energy stored in the faulted blocks with respect to $h$. Accounting for inelastic deformation prompted by large flexural stresses, he showed that this force peaks at a value proportional to $H^2$ which increases with fault dip. Behn and Ito [2008] approximated $F_B(h)$ as a plateauing exponential function of $h$, based on empirical fits to numerical simulations:

$$ F_B(h) = A H^2 \left(1 - e^{-B \frac{h}{H}}\right), \quad (20) $$

where $A$ (Pa/m) and $B$ (dimensionless) are constants which are larger in stronger elasto-plastic lithosphere. In this framework, a normal fault can grow as long as the total amount of force required to sustain slip is lower than the force required to break intact lithosphere. This writes:

$$ F_F(h) + F_B(h) < F_{\text{BREAK}}. \quad (21) $$
The maximum offset on a fault ($h_{MAX}$) can then be determined by combining equations (19–21). Because both $F_F$ and $\max(F_B)$ scale as $H^2$ while $F_{BREAK}$ contains a term that only scales linearly with $H$, it can be shown that faults can accumulate greater offsets in thinner lithosphere, and that there exist a threshold lithospheric thickness below which $h_{MAX}$ can be infinite (Buck, 1993; Lavier et al., 2000; Behn and Ito, 2008; Olive and Behn, 2014). This threshold thickness increases with lithosphere cohesion (Lavier et al., 2000).

This simple model has important implications for mid-ocean ridges. First, it explains why normal faults preferentially form at the axis, where $H$ and therefore $F_{BREAK}$ are minimized. Second, it explains why faults stop growing tens of km away from the axis. Conductive cooling of the lithosphere indeed increases both $F_F$ and $F_B$, such that sustaining slip on off-axis faults eventually requires a greater force than breaking a new fault on-axis.

## 5.2. Magma-rich mid-ocean ridges

The key to using the above framework to explain MOR faulting styles is to understand how quickly faults may migrate off-axis and encounter thicker lithosphere (Fig. 5B). Buck et al. (2005) proposed that a fast rate of dike intrusions through the axial lithosphere, by accommodating a large fraction $M$ of the total plate separation rate (see section 2.3), prompts the rapid migration of faults away from the axis. They specifically showed that the migration rate of an active fault $U_{AF}$, assuming a single normal fault is active on one side of the axis at any given time (Fig. 5B), writes

$$U_{AF} = 2U(M - 0.5). \quad (22)$$

In equation (22), $U_{AF}>0$ corresponds to fault migration away from the axis, and requires $M>0.5$, i.e., a moderate-to-very robust magma supply. In that case, the horizontal offset $h$ on the fault increases at a rate equal to $U - U_{AF}$. A model for fault rotation with increasing offset (e.g., Olive et al., 2014) can be used to estimate fault dip throughout the lifespan of said fault $\theta_{(h)}$. The rate at which the lithosphere thickens off-axis (e.g., the slope of the lithosphere-asthenosphere boundary, on the order of 15–30°; Behn and Ito, 2008) can be inferred from thermal modeling (e.g., Fig. 4A), yielding $H_{(h)}$. We then have all the information needed to estimate the total force $F_F(h) + F_B(h)$ needed to keep a fault active as it weakens, accumulates offset, rotates, bends its footwall and hanging wall, and moves through thicker and thicker lithosphere (Behn and Ito, 2008). When this force reaches $F_{BREAK}$, the fault has reached its maximum offset $h_{MAX}$ (equation 21). This happens after a time

$$t_{MAX} = \frac{h_{MAX}}{U - U_{AF}}, \quad (23)$$

during which the fault has moved off-axis by a distance equal to $t_{MAX}/U_{AF}$. At this point, the now inactive fault continues to move off-axis, but at the same velocity as the oceanic plate it dissects (i.e., the spreading half-rate $U$, if spreading occurs symmetrically). Meanwhile, a new
fault forms at the axis, for example on the conjugate plate. Repeating this basic cycle (Fig. 5B) leads to a succession of faults that are evenly spaced by a distance:

$$S = h_{MAX} \frac{M}{1 - M}. \quad (24)$$

Each of these faults offsets and tilts oceanic crust, forming an abyssal hill. Therefore, the distance S can be thought of as a characteristic length scale of seafloor roughness.

This very simplified model does a good job at explaining observed trends of abyssal hill spacing and height (related to maximum fault offset) across slow-to-fast spreading rates (Fig. 3A, B; Olive et al., 2015), provided a correspondence between spreading rate and M can be established (Fig. 3E; Olive and Dublanchet, 2020). It primarily applies to MOR settings where faulting is staircase-like and symmetric about an axial valley (Fig. 6), as it the case at many intermediate spreading ridges (M ~ 0.7–0.9; Fig. 2C) and symmetric sections of slow-spreading ridges (M ~ 0.6–0.8; Fig. 2D; Escartín et al., 2008). There, the axial lithosphere is thin (<10 km), which means faults would build infinitely long offsets if they could remain fixed at the axis. Decreasing M values approaching ~0.6 lead to widely spaced (5+ km), tall (100s of m) hills at slow MORs (Fig. 3A, B, E). On the other hand, the greater the M, the faster faults are pushed off-axis through thicker lithosphere and de-activated. The corresponding fault spacing (equation 24) is drastically reduced to a near constant, low value (~1–3 km) as M approaches 1 at fast-spreading MORs (Fig. 3A, E).

A corollary to this framework is that a value of M < 1 cannot account for the formation of axial highs (Fig. 6), which are observed along many intermediate and fast-spreading ridges (Fig. 2A; Buck et al., 2005; Ito and Behn, 2008; Liu and Buck, 2018). Buck et al. (2005) attributed axial highs to flexural isostasy driven by magma buoyancy in settings where magmatism is sufficiently intense to accommodate ~100% of plate divergence. Ito and Behn (2008) nuanced this idea by proposing alternating phases of fully magmatic and amagmatic accretion could still lead to an axial high, provided the amagmatic phases are not much longer than the magmatic phases, and that the axial lithosphere is weak enough for positive relief to grow quickly in response to magma buoyancy during a magmatic phase. The dense population of inward and outward facing faults documented on axial highs (Escartín et al., 2007) are thought to form through lithosphere unbending as it subsides off-axis. Short-offset (< 100 m) axis-facing faults accommodating mere percents of the plate divergence may further develop beyond the axial high, outlining small-amplitude abyssal hills spaced by ~2 km (Fig. 3A).

### 5.3. Detachment-dominated and quasi-amagmatic seafloor spreading

Detachment faults are normal faults that have accumulated offsets on par with the thickness of the brittle layer they dissect (~10 km). Their footwalls, which are not significantly eroded in the submarine environment, consequently experience large amounts of rotation (Buck, 1988; Sandiford et al., 2021) and expose lower crustal and mantle units at the seafloor in dome-shaped
core complexes (Fig. 2E). The formation of these structures can be understood in our simple model if the local *M* value is close to 0.5 (Buck *et al.*, 2005), between ~0.3 and ~0.6 (Olive *et al.*, 2010). As mentioned earlier, this range of *M* minimizes the rate of off-axis fault migration (equation 22), meaning faults are free to grow indefinitely in thin axial lithosphere and become detachments (Howell *et al.*, 2019). This view is akin to a Goldilocks range for the formation of detachments (Fig. 6), requiring neither too much, nor too little magma (Tucholke *et al.*, 2008). Olive *et al.* (2010) amended this idea by showing that only the rate of magma emplacement in the brittle lithosphere matters to the formation of faults. In other words, as long as *M* is moderate in the brittle lithosphere, large amounts of magma can be intruded in the underlying asthenosphere without disrupting the growth of detachments. This magma ultimately ends up exposed as gabbro bodies in core complexes.

Our standard model is however strongly challenged by quasi-amagmatic sections of ultraslow-spreading MORs (Fig. 2F) where “smooth” seafloor is shaped by faults with offsets ~10 km that dip both towards and away from the axis, and cut through a brittle layer that is at least 15 km thick (Fig. 6). The lack of a fixed, steady magmatic injection zone means that the basic setup of Fig. 5B does not apply. Further, the cold thermal regime and lack of magma means that the lithosphere comprises a strong ductile layer at depths where the temperature falls between ~600 and ~1200°C (e.g., 15–20 km, Fan *et al.*, 2021). This is very different from the settings considered above, where robust magmatic emplacement maintains a thin (~100 m) boundary layer between the 600 and 1200°C isotherm (see section 4), resulting in a primarily brittle lithosphere. A lithosphere with a thick brittle layer and a strong ductile base does not favor the prolonged growth of detachment faults, because strong flexural stresses and viscous flow act to defocus deformation onto multiple shorter-offset faults (Buck, 1993; Nagel and Buck, 2006). Explaining the growth of flip-flopping detachments in this context must then involve some form of rheological weakening (e.g., lowering the *F*<sub>F</sub> term in equation 21). Lowering fault friction through the precipitation of weak minerals (e.g., Escartín *et al.*, 1997) is an appealing solution, provided these minerals are indeed found in real fault zones. Pervasive alteration and/or damaging of the lithosphere away from major faults may also play a role, as well as the localization of weak shear zones in the ductile lithosphere through grain size reduction (Bickert *et al.*, 2020).

**6. A seafloor record of interior dynamics**

We are now armed with a (very) first-order understanding of how the morphology of the seafloor, the architecture of the oceanic crust and the thermo-mechanical structure of the oceanic lithosphere reflect the plate divergence rate and local magma supply. While spreading rate is set by dynamic equilibria at the scale of the entire mantle convection system (e.g., *Coltice*, this volume), magma supply reflects the local thermo-chemical state of the upper mantle, which can vary through time, leaving a distinct signature in the seafloor.
Temporal variability in seafloor spreading has been documented along virtually all spreading centers over a range of time scales. Christeson et al. (2020) recently conducted a transect along a plate flowline away from the Southern Mid-Atlantic Ridge, into the South American plate (Fig. 7). Combining bathymetric, magnetic, gravity and seismological observations, they documented an increase in crustal thickness on the order of ~3 km over time scales of ~30 Myrs, starting at ~60 Ma (Fig. 7B). These changes correlate well with a ~60% increase in spreading rate from a slow rate (~3 cm/yr full rate), accompanied by a 50% reduction in the characteristic amplitude of abyssal hills (Fig. 7C). Such variations are consistent with the global trends highlighted in Fig. 3B, C, and E. Between 60 Ma and 30 Ma, spreading at the Southern Mid-Atlantic Ridge accelerated, prompting a greater magmatic production, a thicker crust, greater rates of magmatic emplacement into the lithosphere (increased *M*) which led to shorter-offset, more closely-spaced faults outlining smaller abyssal hills. In the framework of our simple models, this could have occurred at a near constant mantle potential temperature, but with a change in sub-ridge thermal structure that led to a taller melting triangle, producing thicker crust.

Comparable changes can also occur without significant changes in spreading rate. Using gravity measurements along the Vema transform fault, Bonatti et al. (2003) documented a gradual increase in oceanic crustal thickness in this region by ~1 km over the last 20 Myrs. They attributed this trend to a warming mantle (increased $T_M$ in the model of section 3.1), possibly reflecting a gradual change in the convective regime of the upper mantle. They also found oscillations in crustal thickness on time scales of ~3 Myrs, superimposed on this long-term trend, also present in the chemistry of abyssal peridotites dredged along the transform valley wall, which are thought to be the residue of mantle melting. Thus, the degree of melting that has fed the crust in the Vema region has both increased and oscillated over the last 20 Myrs. Such oscillations were attributed to the dynamics of melt extraction, but could have a number of explanations (Fig. 1E). Mantle heterogeneities manifesting as more or less fusible patches tens of kilometers wide could for example lead to fluctuations in magma production on time scales of millions of years if they ascend through the melting regimes at ~1 cm/yr. Such variability could leave a detectable signature in the texture of the seafloor, the thickness of the oceanic crust, and the geochemistry of erupted basalts. Variability in magma production has also been documented on shorter time scales, between ~100 kyrs and 1 Myr (Canales et al., 2000; Shinevar et al., 2019; Parnell-Turner et al., 2020), and on even shorter time scales < 100 kyrs (Boulahanis et al., 2020). These are more commonly attributed to variability in the magma ascent and focusing mechanisms (Figs. 1E; 4B), e.g., the development of porosity waves bringing a larger supply of magma to the axis every ~400 kyr at the Southeast Indian Ridge (Parnell-Turner et al., 2020). Very rapid fluctuations have even been attributed to changes in magma production, on the order of 10%, induced by sealevel change on Milankovitch time scales (Crowley et al., 2015). Although these are less likely to leave a clear signature at the seafloor (Olive et al., 2015), they
may be expressed as subtle oscillations in crustal thickness, particularly at fast MORs
(Boulahanis et al., 2020).

Overall, new modeling frameworks are needed to understand and exploit the seafloor record in terms of the thermo-chemical state of the sub-ridge mantle. Combined with progress in global seafloor mapping and automated techniques for bathymetric analyses, this exciting area of research will likely provide new constraints on the transient dynamics of our solid Earth, and inform global convection models.

**7. Conclusions and Perspectives**

In this chapter, I presented a synthetic overview of how the interaction between magmatic, hydrothermal and tectonic processes shape the oceanic lithosphere, emphasizing simplified analytical models over an exhaustive overview of seafloor spreading in all its fascinating complexity. These clearly oversimplified models are nonetheless useful to develop a physical intuition of the processes at play, and work towards physics-informed interpretations of seafloor data. An exciting perspective would be to infer transient geodynamic properties of the upper mantle (e.g., temperature, compositional heterogeneity...) from bathymetric data, on Earth or other planetary bodies that experience processes akin to seafloor spreading.

Mid-ocean ridges are a fantastic playground for geodynamic modelers. They combine faults, magmas and fluids in small-scale systems that can be better characterized than many terrestrial volcanoes or diffuse continental plate boundaries. One of today's most pressing research questions arguably pertains to the modes of magma transport and emplacement through young oceanic crust and lithosphere (Keller et al., 2013). Specifically, for a given input of magma reaching the base of the crust from the melting region, how much of it will be intruded through the lithosphere, setting the value of *M* that modulates faulting and thermal structure, and how much will be emplaced at depth to form lower crustal units? Recent work has begun to address feedbacks between *M* and lithospheric stresses, whether topographic (Liu and Buck, 2020) or tectono-magmatic (Olive and Dublanchet, 2020), relaxing the need to prescribe an ad-hoc value of *M* based on seafloor measurements. These studies emphasize the discrete nature of emplacement events, and the stress changes they impart. This opens further research questions on how our limited observations of seafloor spreading “events” (dike intrusions, eruptions, large normal faulting earthquakes) may be extrapolated to geological time scales. This is particularly critical at a time where seafloor observatories are being deployed to monitor the activity of MORs in quasi real time (Kelley et al., 2014).
Acknowledgements

I would like to thank João Duarte for inviting me to write this chapter, in which I did my best to synthesize 15 years of passionate mid-ocean ridge discussions with Mark Behn, Javier Escartín, Roger Buck, Mathilde Cannat, Thibaut Barreyre, Garrett Ito, Eric Mittelstaedt, and many others, who I thank for their support and guidance through my subaquatic journey.

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**Figure captions**

**Figure 1** – **A.** Map of seafloor spreading rates (Seton et al., 2020) showing the global mid-ocean ridge system and its associated transform faults (black lines). Other types of plate boundaries (Bird, 2003) shown in yellow. MAR: Mid-Atlantic Ridge. RR: Reykjanes Ridge. GR: Gakkel Ridge. JdF: Juan de Fuca Ridge. GSC: Galapagos Spreading Center. EPR: East Pacific Rise. CR: Chile Ridge. PAR: Pacific-Antarctic Ridge. SWIR: Southwest Indian Ridge. SEIR: Southeast Indian Ridge. CIR: Central Indian Ridge. Red dots are sites shown in Fig. 2. Dashed lines are transects shown in panels B & C. **B.** Bathymetric transect across the EPR (Ryan et al., 2009), along with modeled bathymetry assuming Pratt isostasy and a half-space cooling model with a full spreading rate of 17 cm/yr (dashed) and a 1400°C deep mantle. Red line shows 1300°C isotherm. **C.** Same across the Mid-Atlantic Ridge. Half-space cooling model assumed a full spreading rate of 2.5 cm/yr. **D.** First-order structure of a MOR axis, with bathymetry from the Chile Ridge (modified from Olive et al., 2015). **E.** Sources of variability in MOR magma supply and oceanic crustal thickness, reproduced from Shinevar et al. (2019).

**Figure 2** – Axial morphology of various mid-ocean ridges (locations shown in Fig. 1). All panels are to scale. DF: Detachment fault. Panels A–F are roughly ordered by decreasing magma supply. Bathymetry data from the GMRT synthesis (https://www.gmrt.org/index.php) and Sauter et al. (2013).

**Figure 3** – Key trends in mid-ocean ridge characteristics across spreading rates. **A.** Spacing of abyssal hills determined by geology-agnostic bathymetric processing (crosses: Macario et al., 1994; Goff et al., 1997) and by identification of hill-bounding faults (circles: Carbotte and MacDonald, 1994; Cowie et al., 1994; Escartín et al., 1999; Malinverno and Pockalny, 1990; Ito and Behn, 2008). Gray line shows model from Behn and Ito (2008) and Olive et al. (2015) assuming the gray trends in axial lithosphere thickness and *M* shown in panels D and E, respectively. Dashed and solid black lines are models that use corresponding trends in panels D and E. **B.** Characteristic height of abyssal hills (RMS amplitude: Macario et al., 1994; Goff et al., 1997). **C.** Seismically-determined crustal thickness (circles: White et al., 2001; Jian et al., 2017) and simple analytical model (Eq. 11 in main text). **D.** Proxies for the thickness of the brittle lithosphere on-axis. Vertical lines: extent of seismogenic zone (Grevemeyer et al., 2019; Wilcock et al., 2002; Bohnenstiehl et al., 2008). Circles: depth of axial melt lens (AML) reflector. Solid black line shows on-axis depth of ~700°C isotherm according to the thermal model of Montési and Behn (2007). Thick dashed line is an ad-hoc trend designed as a thin end-member of axial thickness (Olive and Dublanchet, 2020). Thin dashed line shows modeled crustal thickness from panel C for reference. **E.** Magmatic fraction of plate separation (*M*) estimated by summing fault heaves in bathymetric transects (Ito and Behn, 2008; Cowie et al., 1993; Olive and Escartín,
2016; Howell et al., 2016; Chen et al., 2021b; Parnell-Turner et al., 2020). Lines show models of *Olive and Dublanchet* (2020) corresponding to trends of axial lithosphere thickness shown in panel D, all assuming inflation rates in crustal magma chambers proportional to spreading rate. **F. Heat flow at high-temperature hydrothermal sites as compiled by Lowell et al. (2013). Lines indicate heat supplied by crustal emplacement along 1 and 10 km along the ridge axis, as estimated by Humphris and Cann (2000).

**Figure 4** – Magma generation and ascent below MORs. **A.** Universal ridge thermal structure computed by Montési and Behn (2007), non-dimensionalized by the advection-diffusion length scale *L* (equation 2). Thick lines correspond to the permeability barrier that collects melts towards the ridge axis (shallower and deeper line for *L* = 0 and 2.5 km, respectively). **B.** Generic model for magma production, ascent and focusing, reproduced from Gregg et al., 2012. **C.** Mantle flow lines and melting triangle for a “cold” mantle potential temperature, and **D.** for a hotter mantle. **E.** and **F.** Corresponding geotherms and mantle solidus. Panels C–F reproduced from Langmuir and Forsyth, 2007.

**Figure 5** – Hydrothermal and tectonic processes shaping the axis of magma-rich ridges. **A.** Schematic illustration of the single-pass hydrothermal circulation model, reproduced from Lowell and Germanovich (2004). **B.** Schematic faulting cycle for ridges with $0.5 \le M < 1$, resulting in regularly-spaced, fault-bounded abyssal hills.

**Figure 6** – Major modes of seafloor spreading as a function of spreading rate and magma supply, modified from *Olive and Dublanchet* (2020), and *Escartín and Olive* (2022).

**Figure 7** – Temporal variability in seafloor spreading recorded along a 70 Myr-long transect in the South Atlantic, reproduced from Christeson et al. (2020). **A.** Location of the transect. **B.** Spreading rate inferred from magnetic anomalies, from Kardell et al. 2019, with regional trend shown as smoothed curve. Triangles show seismically determined crustal thickness at selected points along the transect. **C.** Characteristic amplitude of abyssal hills along the transect.
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>
A. East Pacific Rise (9°N):

<figure><img src="image_7.png" /></figure>

B. Reykjanes Ridge (59°N):

<figure><img src="image_8.png" /></figure>

C. Chile Ridge (38°S):

<figure><img src="image_9.png" /></figure>

D. Mid-Atlantic Ridge (14°N):

<figure><img src="image_10.png" /></figure>

E. Mid-Atlantic Ridge (13°N):

<figure><img src="image_11.png" /></figure>

F. Southwest Indian Ridge (62°E):

<figure><img src="image_12.png" /></figure>
A.

abyssal hill
spacing (km)

<figure><img src="image_13.png" /></figure>

C.

crustal
thickness (km)

<figure><img src="image_14.png" /></figure>

E.

magmatic
fraction M

<figure><img src="image_15.png" /></figure>

spreading rate (cm/yr)

B.

abyssal hill
height (m)

<figure><img src="image_16.png" /></figure>

D.

axial brittle
thickness (km)

<figure><img src="image_17.png" /></figure>

F.

hydrothermal
heat flow (MW)

<figure><img src="image_18.png" /></figure>

spreading rate (cm/yr)
<figure><img src="image_19.png" /><figcaption>B.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>C.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>COLD ascending mantle</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>HOT ascending mantle</figcaption></figure>

<caption>depth (km)</caption>

<figure><img src="image_23.png" /><figcaption>F.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>temperature</figcaption></figure>
<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>
SPREADING RATE

Magma
Supply

ultraslow

slow

intermediate

fast

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

M ~ 0.95

<figure><img src="image_30.png" /></figure>

symmetric
abyssal hills

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

~ 10 km

detachment

<figure><img src="image_33.png" /></figure>

M ~ 0.5

flip-flopping
detachments

<figure><img src="image_34.png" /></figure>

M ~ 0

~ 10 km

<figure><img src="image_35.png" /></figure>
A.

<figure><img src="image_36.png" /></figure>

B.

<figure><img src="image_37.png" /></figure>

C.

<figure><img src="image_38.png" /></figure>