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The problem considered was that of estimating the temperature field in a contaminated region of soil, using measurements of electrical potential and current and also of temperature, at accessible points such as the wells and electrodes and the soil surface. On the timescale considered, essentially days, the equation for the electrical potential is static. At any given time the potential $V$ satisfies the equation $\nabla \cdot (\sigma \nabla V ) = 0$. Time enters the equation only as a parameter since $\sigma$ is temperature and hence time dependent. The problem of finding $\sigma$ when both the potential $V$ and the current density $\sigma \partial{V} / \partial{n}$ are known on the boundary of the domain is a standard inverse problem of long standing. It is known that the problem is ill posed and hence that an accurate numerical solution will be difficult especially when the input data is subject to measurement errors. In this report we examine a possible method for solving the electrical inverse problem which could possibly be used in a time stepping algorithm when the conductivity changes little in each step. Since we are also able to make temperature measurements there is also the possibility of examining an inverse problem for the temperature equation. There seems to be much less literature on this problem, which in our case is essentially, a first order equation with a heat source.(We neglect thermal conductivity, which is small compared with the convection). Combining the results of both inverse problems might give a more robust method of estimating the temperature in the soil

Topics:
Materials, None/Other

Year: 2002

OAI identifier:
oai:generic.eprints.org:179/core70

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