Quantitative reconstruction of thermal and dynamic characteristics of lava flow from surface thermal measurements

Abstract

We study a model of lava flow to determine its thermal and dynamic characteristics from thermal measurements of the lava at its surface. Mathematically this problem is reduced to solving an inverse boundary problem. Namely, using known conditions at one part of the model boundary we determine the missing condition at the remaining part of the boundary. We develop a numerical approach to the mathematical problem in the case of steady-state flow. Assuming that the temperature and the heat flow are prescribed at the upper surface of the model domain, we determine the flow characteristics in the entire model domain using a variational (adjoint) method. We have performed computations of model examples and showed that in the case of smooth input data the lava temperature and the flow velocity can be reconstructed with a high accuracy. As expected, a noise imposed on the smooth input data results in a less accurate solution, but still acceptable below some noise level. Also we analyse the influence of optimization methods on the solution convergence rate. The proposed method for reconstruction of physical parameters of lava flows can also be applied to other problems in geophysical fluid flows.

Geohazard research, modeling, and assessment for disaster risk reduction

“…Combined with pattern recognition techniques developed for identification of zones prone to earthquakes [Gvishiani et al, 2013;Soloviev et al, 2014], earthquake simulators may forecast the place of large events with higher accuracy. Similarly, advanced modeling of lava flows Korotkii et al, 2016] allows to trace different ways of lava extent enhancing hazard assessment. Meanwhile with time it was recognized that there are much more challenging problems including concatenated hazards and risk analysis including many components leading to a disaster.…”

“…Meanwhile the temperature and flow rate inside the lava flow are unknown, and very difficult to determine after a solidification of its uppermost part and development of a crust. Ismail-Zadeh et al [2016] and Korotkii et al [2016] proposed a new quantitative approach to determine thermal and dynamic characteristics of a lava flow from thermal measurements at its surface. This approach is based on a determination of the optimal temperature at the lower boundary of lava flow from the known heat flow at the lava's upper surface, and on a subsequent determination of the temperature and flow rates inside the lava.…”

“…Mathematically this approach leads to solving an inverse boundary problem using a variational (adjoint) method. Korotkii et al [2016] showed that in the case of smoothed measured data the lava temperature and its flow velocity can be reconstructed with a high accuracy, but noisy data degrade the accuracy of the solution.…”

International Union of Geodesy and Geophysics (IUGG)—Integrating Natural Hazard Science with Disaster Risk Reduction Policy

“…Also the union encourages analysis, modeling, and risk assessments related to natural hazards including landslides, lahars, lava, and debris flows, avalanches and rock falls (e.g. Crutchley et al 2013;Edwards et al 2014;Korotkii et al 2016).…”

Recovery of Flow Parameters of Viscous Heat-Conducting Fluid by Some Changes at Its Surface

“…Обратные задачи восстановления тепловых режимов в геофизических процессах составляют новое направление в моделировании различных технологических и природных процессов (см., например, [4][5][6][7][8][9]). Необходимо отметить большой интерес к решению подобных задач среди специалистов в области моделирования геодинамических процессов, процессов химического синтеза и многих других отраслей знаний [7][8][9]. Этому способствует совершенствование методов обработки данных и накопление статистической информации о природном процессе или явлении.…”