Surface temperature determination from Borehole measurements: Regularization and error estimates
نویسندگان
چکیده
منابع مشابه
Surface Temperature Determination from Borehole Measurements : Regularization and Error Estimates
The authors consider the problem of determining the temperature distribution u(x, t) on the half-line x 0, > 0, from measurements at an interior point, for all > 0. As is well-known, this is an ill-posed problem Using the Tikhonov method, the authors give a regularized solution, and assuming the (unknown) exact solution is in H(R),a > 0 They give an error estimate of the order for e 0, where e ...
متن کاملImpact of borehole depths on reconstructed estimates of ground surface temperature histories and energy storage
Estimates of ground surface temperature changes and continental energy storage from geothermal data have become well-accepted indicators of climatic changes. These estimates are independent contributions to the ensemble of paleoclimatic reconstructions and have been used for the validation of general circulation models, and as a component of the energy budget accounting of the global climate sy...
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Modelling of surface temperature change effect on temperature vs. depth and temperature-depth logs in Western Canada Sedimentary Basin show that SAT (surface air temperature) forcing is the main driving factor for the underground temperature changes diffusing with depth. It supports the validity of the basic hypothesis of borehole temperature paleoclimatology, namely that the ground surface tem...
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We consider the problem of finding the initial temperature, from the final temperature, in the nonhomogeneous heat equation ut − uxx = f(x, t), (x, t) ∈ (0, π)× (0, T ), u(0, t) = u(π, t) = 0, (x, t) ∈ (0, π)× (0, T ). This problem is known as the backward heat problem and is severely ill-posed. Our goal is to present a simple and convenient regularization method, and sharp error estimates for ...
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In this paper, the Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a new regularization method to solve it based on the solution given by the method of separation of variables. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effectiveness ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1995
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171295000755