Modeling diffusion in 1D within melt embayments: correcting for 3D geometry

Abstract:

The rate at which magma decompresses as it travels from depth to the Earth’s surface exerts a first-order control on how explosively a volcano erupts. Fast decompression rates tend to result in high intensity, explosive eruptions whereas slow decompression rates tend to result in low intensity, effusive eruptions. This relationship is due to the dependence of gas exsolution efficiency on decompression rate. Dissolved volatiles in magma, such as H₂O and CO₂, exsolve into a separate vapor phase as confining pressure decreases; the rate at which confining pressure decreases controls the amount of gas overpressure that develops within the system. Thus, determining decompression rate is a critical goal for understanding drivers of volcanic eruptions; however, it is a difficult parameter to constrain. A recently developed technique that is gaining more use leverages concentration gradients that develop during decompression within pockets of melt partially trapped in crystals. These melt pockets, which are known as melt embayments, never fully close off from the host melt, which allows diffusive exchange of volatiles with the host melt during decompression. Diffusion modeling can then be used to calculate the time needed to produce measured volatile concentration gradients. This technique has not been previously examined to determine the uncertainties and errors associated with the current implementation.

We conducted a series of numerical models to test the error associated with using 1D diffusion models to represent diffusion within complex, 3D embayments. Our suite of models varied key geometrical factors, such as degree of constriction at the embayment mouth and the length of the constriction relative to the total embayment length. These parameters were used to create simple equations that correct for discrepancies in imposed 3D decompression rates and modeled 1D rates, applicable to a broad range of geometries, decompression rates, compositions, and diffusing species.