Table 1.
List of Parameters Used in This Study
| Parameter | Definition | Unit |
|---|---|---|
| Geometry | ||
| a | Radius of spherical or semimajor axis of ellipsoidal magma reservoir | m |
| c | Semiminor axis of ellipsoidal magma reservoir | m |
| d | Depth of magma reservoir center | m |
| a c | Radius of conduit | m |
| L c | Length of conduit | m |
| Rheological Properties | ||
| η m | Viscosity of magma | Pa s |
| η r | Viscosity of crustal rocks | Pa s |
| ρ m | Density of magma | kg/m3 |
| ρ r | Density of crustal rocks | kg/m3 |
| G | Shear (or rigidity) modulus | Pa |
| ν | Poisson's ratio | ‐ |
| Parameters for FEM Viscoelastic Models | ||
| k | Thermal conductivity | W/(m.K) |
| C p | Specific heat capacity | J/(kg.K) |
| A D | Dorn parameter | Pa s |
| E A | Activation energy | J/mol |
| R t | Boltzmann constant | J/(mol.K) |
| T 0 | Surface temperature | K |
| T w | Magma chamber wall temperature | K |
| τ M | Characteristic Maxwell time of crustal viscoelastic relaxation | s |
| Analytical Model Parameters | ||
| ΔP i(t) | Injection pressure at inlet | Pa |
| τ P | Characteristic time of the magma propagation | s |
| t 0 | Onset time of uplift episode | s |
| t ∗ | Time when uplift rates start to decrease | s |
| β m | Compressibility of magma | Pa−1 |
| β w | Compressibility of wall rocks | Pa−1 |
| Derived Quantities | ||
| ΔP o(t) | Reservoir pressure at the conduit outlet | Pa |
| Q(t) | Volumetric flow rate | m3/s |
| q | Volumetric flux | m3/(m2.s) or m/s |
| v | Flow velocity | m/s |
| u z(t) | Vertical displacement (uplift) rate | m/s |