## Heat transfer from a convecting crystallizing, replenished magmatic sill and its link to seafloor hydrothermal heat output

##### Abstract

Hydrothermal systems at oceanic spreading centers play an important role in the composition of seawater, the formation of ore deposits, the support of microbial and macrofaunal ecosystems, and even for the development of life on early earth. These circulation systems are driven by heat transport from the underlying magma chamber, where latent heat of crystallization and sensible heat from cooling are transferred by vigorous, high Rayleigh number convection through a thin conductive boundary layer.
The traditional study of magmatic-hydrothermal systems is primarily based on the time-series observation, which takes the form of repeat visits, continuous offline monitoring by autonomous instruments, or continuous online monitoring by instruments with satellite or cable links to shore. Although a number of studies have deployed autonomous monitoring instruments at vents and around mid-ocean ridges to investigate geophysical and hydrothermal processes, the data are still rather limited and a comprehensive understanding of magma-hydrothermal processes at oceanic spreading centers is lacking. Numerical modeling needs to be employed to elucidate the dynamic behavior of magmatic hydrothermal systems and for testing completing hypotheses in these complex, data-poor environments.
In this dissertation, I develop a mathematical framework for investigating heat transport from a vigorously convecting, crystallizing, cooling, and replenished magma chamber to an overlying hydrothermal system at an oceanic spreading center. The resulting equations are solved numerically using MATLAB. The simulations proceed step-by-step to investigate several different aspects of the system.
First, I consider a hydrothermal system driven by convection, cooling and crystallization in a ~ 100 m thick basaltic magma sill representing an axial magma chamber (AMC) at an oceanic spreading center. I investigate two different crystallization scenarios, crystal-suspended and crystal-settling, and consider both un-replenished and replenished AMCs. In cases without magma replenishment, the simulation results for crystals-suspended models show that heat output and the hydrothermal temperature decrease rapidly and crystallinity reaches 60% in less than ten years. In crystals-settling models, magma convection may last for decades, but decreasing heat output and hydrothermal temperatures still occur on decadal timescales. When magma replenishment is included, the magmatic heat flux approaches steady state on decadal timescales, while the magma body grows to double its original size. The rate of magma replenishment needed ranges between 5 x 10⁵ and 5 x 10⁶ m³/yr, which is somewhat faster than required for seafloor spreading, but less than fluxes to some terrestrial and subseafloor volcanoes on similar timescales. The heat output from a convecting, crystallizing, replenished magma body that is needed to drive observed high-temperature hydrothermal systems is consistent, with gabbro glacier models of crustal production at mid-ocean ridges.
Secondly, I study the heat transfer model from a parametric perspective and examine the effects of both initial magma chamber thickness and magma replenishment rate on the hydrothermal heat output. The initial rate of convective heat transfer is independent of the initial sill thickness; but without magma replenishment, the rate of decay of the heat output varies linearly with thickness, resulting in short convective lifetimes and decaying hydrothermal temperatures for sills up to ~ 100m thick. When magma replenishment is included in crystals settling scenarios at constant or exponentially decreasing rates of ~ 10⁻⁸ m/s to the base of the sill, growth of the sill results in stabilized heat output and hydrothermal temperature on decadal timescales and a relatively constant to increasing thickness of the liquid layer. Sills initially ~ 10 m thick can grow, in principal, to ~ 10 times their initial size with stable heat output and a final melt thickness less than 100m. Seismic data provides evidence of AMC thickness, but it can not discriminate whether it denotes initial magma thickness or is a result of replenishment. These results suggest that magma replenishment might not be seismically detectable on decadal time scales. Periodic replenishment may also result in quasi-stable heat output, but the magnitude of the heat output may vary considerably in crystals suspended models at low frequencies; compared to crystals settling models. In these models the direct coupling between magmatic and hydrothermal heat output suggests that heat output fluctuations might be recorded in hydrothermal vents; but if damping effects of the basal conductive boundary layer and the upflow zone are taken into account, it seems unlikely that heat output fluctuations on a time scale of years would be recorded in hydrothermal vent temperatures or heat output.
Thirdly, I extend the work to the binary system motivated by the fact that the real magmas are multi-component fluids. I focus on the extensively studied binary system, diopside-anorthite (Di-An), and investigate the effects of convection of a two-component magma system on the hydrothermal circulation system through the dynamic modeling of both temperature and heat output. I model the melt temperature and viscosity as a function of Di concentration, and incorporate these relations in the modeling of the heat flux. Simulations comparing the effects of different initial Di concentrations indicate that magmas with higher initial Di concentrations convect more vigorously, which results in faster heat transfer, more rapid removal of Di from the melt and growth of crystals on the floor. With magma replenishment, I assume that the magma chamber grows either horizontally or vertically. In either case magma replenishment at a constant rate of ~ 10⁻⁸ m³/a can maintain relatively stable heat output of 10⁷-10⁹ Watts and reasonable hydrothermal vent temperatures for decades. The final stabilized heat flux increases with increasing Di content of the added magma. Periodic replenishment with a 10 year period results in temperature perturbations within the magma that also increase as a function of increasing Di. With the simple magma model used here, one can not discern conclusively whether the decrease in magma temperature between the 1991/1992 and the 2005/2006 eruptions at EPR 9°50'N involved replenishment with more or less evolved magmas.
Fourthly, I investigate a high-silica magma chamber as the hydrothermal circulation driver. I construct viscosity models for andesite and dacite melts as a function of temperature and water content and incorporate these expressions into a numerical model of thermal convective heat transport from a high Rayleigh number, well-mixed, crystallizing and replenished magma sill beneath a hydrothermal circulation system. Simulations comparing the time dependent heat flux from basalt, 0.1wt.% andesite, 3wt.% andesite, and 4wt.% dacite, indicate that higher viscosity magmas convect less vigorously, which results not only in lower heat transport and hydrothermal vent temperatures, but also in a lower decay rate of the vent temperature. Though somewhat colder, hydrothermal systems driven by unreplenished high-silica melts tend to have a longer lifetime than those driven by basalts, assuming a heat output cutoff of 10⁷ Watts. As in the basaltic case, magma replenishment at a rate of ~ 3 x 10⁵ - 3 x 10⁶ m³/a can maintain relatively stable heat output of 10⁷-10⁹ Watts and hydrothermal vent temperatures for decades. Idealized models of porous flow through the lower crust suggest such replenishment rates are not likely to occur, especially for high-viscosity magmas such as andesite and dacite. Long term stability of hydrothermal systems driven by these magmas requires an alternate means of magma replenishment.
Finally, the dissertation concludes by discussing some avenues for future work. Most important of these are to: (1) couple magma convection with more realistic hydrothermal models and (2) link magma chamber processes to better physical models of replenishment and eruption.