Abstract
Under study is the problem of estimation of the terrestrial heat flow from the temperature measurements in the bottom sediments. The problem is divided into the two subproblems: first, we solve the one-dimensional inverse problem of estimating the heat conductivity λ and, second, compute the heat flow value by solving the direct stationary problem using the just-found value of λ. We develop a sweep method for solving the direct problem which differs from the standard. An optimization approach is used for solving the inverse problem, and the explicit formulas are obtained for computing the gradient of the error functional. We analyze the factors that cause errors in estimating the heat flow. We show that the main contribution to the errors is given by the presence of harmonics with the periods exceeding the temperature monitoring time interval. We show that if the parameters of the harmonics are known then we can calculate some corrections for the obtained value of the heat flow. The results were applied to the data of temperature measurements carried out at the bottom of Lake Teletskoye from June of 2008 to September of 2010. For finding the long- period harmonics, we use the meteorological data about the bottom water temperature from 1968 to 2011. This allowed us to estimate the heat flow through the bottom of Lake Teletskoye as well as the thermal diffusivity in the upper layer of the sediments.
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