9.1 Magma Generation
Magma is generated within the Earth when solid rock partially melts. This process does not occur everywhere in the mantle—specific physical and chemical conditions must be met for the solidus temperature to be exceeded. Three principal mechanisms drive melting in different tectonic settings: decompression melting at mid-ocean ridges and hotspots, flux melting at subduction zones where volatiles lower the solidus, and conductive heating where hot material raises the temperature of adjacent rock above its solidus.
Understanding magma generation requires knowledge of the phase relations of mantle rocks, the thermodynamics of partial melting, and the physics of melt segregation and transport. These topics form the foundation for interpreting the composition, volume, and distribution of volcanic activity on Earth.
Solidus & Liquidus Boundaries
The solidus is the temperature at a given pressure below which the rock is entirely solid. The liquidus is the temperature above which the rock is entirely liquid. Between these two boundaries lies the zone of partial melting, where a mixture of crystals and melt coexists. The solidus and liquidus both increase with pressure (depth), but at different rates, defining a wedge-shaped melting interval in P–T space.
Clapeyron Slope for Dry Peridotite
\[ \frac{dT_{\text{solidus}}}{dP} \approx 130 \;^{\circ}\text{C/GPa} \]
For dry (anhydrous) peridotite, the solidus rises at approximately 130°C per GPa of pressure increase. At the surface (P ≈ 0), dry peridotite begins to melt near ~1100°C; at 3 GPa (~100 km depth), the solidus is approximately ~1500°C. The liquidus lies ~600°C above the solidus at a given pressure, but the bulk of melt production occurs in the lower portion of this interval.
| Depth (km) | Pressure (GPa) | Dry Solidus (°C) | Wet Solidus (°C) | Liquidus (°C) |
|---|---|---|---|---|
| 0 | 0 | ~1100 | ~1000 | ~1700 |
| 30 | 1.0 | ~1230 | ~1000 | ~1830 |
| 60 | 2.0 | ~1360 | ~1020 | ~1960 |
| 100 | 3.3 | ~1520 | ~1050 | ~2100 |
| 150 | 5.0 | ~1700 | ~1100 | ~2300 |
Approximate values from experimental petrology compilations (Hirschmann, 2000; Katz et al., 2003).
Three Mechanisms of Mantle Melting
1. Decompression Melting
When mantle rock rises adiabatically (without heat exchange), its temperature decreases slowly along an adiabatic gradient (~0.3–0.5°C/km), which is much less steep than the solidus gradient (~4°C/km). As the ascending mantle crosses the solidus, partial melting begins. This is the dominant melting mechanism at mid-ocean ridges and beneath hotspot swells.
At mid-ocean ridges, upwelling mantle at potential temperature Tp ≈ 1350°C intersects the dry peridotite solidus at approximately 60 km depth. Melting continues as the material rises, producing a triangular melting region beneath the ridge axis. The final melt fraction depends on how far above the solidus the mantle ascends.
For each 1 km of additional ascent above the solidus intersection, the melt fraction increases by approximately 0.3–0.5%, yielding a total of ~15–20% melting for the ~60 km melting column beneath a normal mid-ocean ridge.
2. Flux Melting (Volatile-Induced Melting)
The addition of volatiles—primarily H2O and CO2—dramatically lowers the solidus temperature of peridotite. Water is especially effective: the wet solidus of peridotite lies 200–400°C below the dry solidus at pressures of 2–5 GPa. This is the principal melting mechanism at subduction zones.
In subduction zones, hydrous minerals (serpentine, chlorite, amphibole, lawsonite) in the descending slab progressively break down with increasing pressure and temperature, releasing water into the overlying mantle wedge. The influx of water triggers partial melting in the mantle wedge at temperatures that would otherwise be below the dry solidus.
The resulting hydrous magmas are enriched in incompatible elements and are characteristically more oxidized than MORB, producing the distinctive calc-alkaline volcanic suite of island arcs.
3. Conductive Heating
When hot magma intrudes into cooler crustal rock, heat conduction can raise the wall-rock temperature above its solidus. This mechanism is important for generating felsic melts by partial melting of the lower continental crust (anatexis) when basaltic magma ponds at the base of the crust (underplating). It also plays a role in contact metamorphism aureoles around large intrusions.
Conductive heating is inherently slow compared to decompression or flux melting, but it can generate volumetrically significant granitic magma in settings such as continental arcs and large igneous provinces.
Melt Fraction & Melting Models
The degree of partial melting is quantified by the melt fraction F, defined as the mass fraction of liquid produced from a given source rock. Two end-member models bracket the range of possible melting behavior.
Batch (Equilibrium) Melting
All melt remains in chemical equilibrium with the residual solid until extraction. The melt fraction as a first approximation:
\[ F \approx \frac{T - T_{\text{solidus}}}{T_{\text{liquidus}} - T_{\text{solidus}}} \]
This linear parameterization is an idealization. In reality, the melt productivity dF/dP varies with pressure and composition. The trace element concentration in the batch melt is given by:
\[ \frac{C_L}{C_0} = \frac{1}{D_0 + F(1 - D_0)} \]
where CL is the concentration in the liquid, C0 is the initial source concentration, and D0 is the bulk distribution coefficient.
Fractional (Rayleigh) Melting
Melt is extracted continuously as it forms, so that each infinitesimal increment of liquid is in equilibrium only with the residue at that instant. This is more physically realistic because melt tends to segregate at low melt fractions (~1–2%).
\[ \frac{C_L}{C_0} = \frac{1}{D_0} \left(1 - F\right)^{(1/D_0 - 1)} \]
Fractional melting produces first melts that are strongly enriched in highly incompatible elements (D << 1), while later melt increments are progressively depleted. The aggregate fractional melt integrates all extracted increments and differs subtly from batch melting at the same total F.
Parameterized Melting
Modern computational models use empirically calibrated parameterizations that express the melt fraction as a function of temperature, pressure, and water content:
\[ F = f\left(T, \; P, \; X_{\text{H}_2\text{O}}\right) \]
The widely used Katz, Spiegelman & Langmuir (2003) parameterization fits experimental data for peridotite melting across a wide P–T range, including the effects of water content on solidus depression and melt productivity. These parameterizations are incorporated into geodynamic codes (e.g., ASPECT, CitcomS) to model melt production in convecting mantle.
Melt Segregation & Migration
Once partial melt forms, it must segregate from the residual solid matrix and migrate upward toward the surface. The physics of melt migration through a porous, deformable matrix is governed by two-phase flow theory, where the melt (liquid) and solid (matrix) interact through viscous and buoyancy forces.
Darcy's Law for Melt Flow
The velocity of melt relative to the solid matrix is governed by a modified form of Darcy's law:
\[ \mathbf{v}_{\text{melt}} = \frac{k}{\eta_{\text{melt}}} \left( \Delta\rho \, \mathbf{g} + \nabla P \right) \]
k = permeability of the solid matrix (m²)
ηmelt = dynamic viscosity of the melt (~1–100 Pa·s for basalt)
Δρ = density contrast between solid and melt (~500 kg/m³)
g = gravitational acceleration (9.81 m/s²)
∇P = pressure gradient driving flow (includes dynamic pressure from matrix compaction)
Permeability–Porosity Relation
The permeability of a partially molten aggregate depends strongly on the melt fraction (porosity φ):
\[ k = \frac{a^2 \, \phi^n}{b} \]
a = grain size (~1–5 mm for upper mantle)
φ = porosity (melt fraction), typically 0.001–0.05
n ≈ 2–3 (exponent from experimental and theoretical models)
b ≈ 200–3000 (geometric constant depending on melt geometry)
The strong nonlinearity (k ∝ φ² to φ³) means that permeability increases very rapidly with small increases in melt fraction. At φ = 1%, a grain size of 3 mm, and n = 3, typical permeabilities are ~10&sup{-13}–10&sup{-12} m², yielding melt velocities of order 1–10 m/yr.
Melt Focusing at Mid-Ocean Ridges
A fundamental puzzle in ridge magmatism is that the melting region beneath a ridge extends laterally to ~100 km on each side (the width of the triangular melting regime), yet volcanism is narrowly focused into a neovolcanic zone only ~1–2 km wide at the ridge axis. Two mechanisms are invoked to explain this focusing:
Pressure-Driven Focusing
The tilted base of the thermal lithosphere creates a sloping permeability barrier. Melt rising from the broad melting region encounters this impermeable boundary and migrates up-slope toward the thin lithosphere at the ridge axis, analogous to oil migrating along a tilted cap rock. Dynamic pressure gradients from mantle corner flow also contribute to directing melt inward.
Buoyancy-Driven Focusing
Reactive porous flow can create high-porosity channels in the mantle. As melt dissolves pyroxene and precipitates olivine, it increases local porosity, attracting more melt in a positive feedback loop. These channels coalesce toward the ridge axis, forming a network of high-permeability conduits. This mechanism may also produce the observed dunite channels found in ophiolite mantle sections.
Trace Element Consequences
The choice between batch and fractional melting has major consequences for the trace element composition of extracted magmas. Elements are classified by their partition coefficient D:
| Element Type | D Value | Behavior | Examples |
|---|---|---|---|
| Highly Incompatible | D << 1 | Strongly enriched in first melts | Th, U, Nb, La |
| Moderately Incompatible | D ≈ 0.1–0.5 | Enriched in melt, depleted in residue | Nd, Sm, Ti |
| Compatible | D ≈ 1–5 | Retained in the solid residue | Ni, Cr, Sc |
| Highly Compatible | D >> 1 | Strongly retained in residual minerals | Os, Ir (in sulfides) |
For highly incompatible elements (D → 0), the batch melting equation simplifies to CL/C0 ≈ 1/F: a 10% melt is enriched 10-fold relative to the source. In fractional melting, the very first melt increment can be enriched by 1/D0(potentially hundreds-fold for D = 0.001), but the enrichment drops off rapidly as the source becomes depleted. The aggregate (pooled) fractional melt approaches the batch melt composition at the same total F.
Key Takeaways
- Magma generation requires crossing the solidus via decompression, volatile addition, or heating
- The dry peridotite solidus increases at ~130°C/GPa; water lowers it by 200–400°C
- Mid-ocean ridge melting initiates at ~60 km depth beneath mantle at Tp ≈ 1350°C
- Batch melting keeps melt in equilibrium with residue; fractional melting extracts melt continuously
- Melt migration is governed by Darcy's law with permeability k ∝ φ2–3
- Melt from a broad melting region is focused to the narrow ridge axis by pressure and buoyancy mechanisms
- Incompatible elements are strongly concentrated in low-degree melts; compatible elements stay in the residue