Processes of magma ascent from source to surface are considered as
bulk behavior averaged over geological time. Assuming that magma
ascent can be approximated by the flow of a viscous fluid within a
homogeneous porous medium (Bonafede and Boschi, 1992), it can be
modeled following the ergodic hypothesis using Darcy’s law.
Different conductivities (isotropic, anisotropic, not homogeneous,
time dependent) are used to simulate multiple pathways due to the
presence of fractures, varying lithology, thermal state, and/or
regional stresses. Conductivity can also be dependent on the flow
itself to simulate the evolution of the volcanic system through
development of magma focusing.
The volumetric flow can be directly compared with the probability distribution at the surface. This model allows to have a continuous description of magma migration in order to validate outputs of the two other tasks (statistical models). That way, we can explore the physical processes that may give rise to heterogeneous flux in numerical models and relate these processes to observed vent distribution and volume flux at the surface
We believe that in distributed fields, low conductivity of the crust and low productivity of the source do not allow magma focusing. Consequently, the field develops in size because volcanic activity migrates spatially and never occurs from the same vent over long-time intervals.
In contrast, central-vent dominated systems, characterized by frequent eruptions generally from vents on the upper flanks of a polygenetic edifice, are related to a crust high conductivity is the reason why magma flux is focused and creates a silicic reservoir impermeable to basaltic magmas that erupt laterally.