Thermal and Dynamic Properties of Volcanic Lava Inferred from Measurements on its Surface

Abstract:

Modern remote sensing technologies allow for detecting the absolute temperature at the surface of volcanic lava, and the heat flow could be then inferred from the Stefan-Boltzmann law. Is it possible to use these surface thermal data to constrain the thermal and dynamic conditions inside the lava? We propose a quantitative approach to reconstruct temperature and velocity in the steady-state volcanic lava flow from thermal observations at its surface. This problem is reduced to a combination of the direct and inverse problems of mass- and heat transport. Namely, using known conditions at the lava surface we determine the missing condition at the bottom of lava (the inverse problem) and then search for the physical properties of lava – temperature and flow velocity – inside the lava (the direct problem). Assuming that the lava rheology and the thermal conductivity are temperature-dependent, we determine the flow characteristics in the model domain using an adjoint method. We show that in the case of smooth input data (observations) the lava temperature and the flow velocity can be reconstructed with a high accuracy. The noise imposed on the smooth input data results in a less accurate solution, but still acceptable below some noise level.