Open AccessInversion of temperature measurements in lake sediment
Author(s) -
Shen P. Y.,
Beck A. E.
Publication year - 1988
Publication title -
geophysical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0952-4592
DOI - 10.1111/j.1365-246x.1988.tb02273.x
Subject(s) - a priori and a posteriori , inversion (geology) , iterated function , thermal conductivity , inverse problem , thermal , finite element method , geology , galerkin method , heat flow , probability density function , soil science , mathematics , mathematical analysis , geomorphology , thermodynamics , physics , statistics , philosophy , epistemology , structural basin
SUMMARY The problem of determining heat flow density (HFD) from temperature data obtained in lake sediments is formulated using an iterated linear inverse theory with numerical results presented in the forms of probability density function and sensitivity coefficient. The Galerkin finite element method and a weighted finite difference scheme are used in the spatial and temporal domains respectively to allow for layered structure in the sediments and for transient disturbances arising from lake bottom temperature variation (BTV) with time. When a record of BTV is lacking, inversion of temperature data from a single probe penetration gives an unreliable estimate of HFD. This difficulty is alleviated by using multiple probe measurements which, if taken at intervals of several months, prove adequate for a reliable estimation of the HFD and the most recent part of BTV. Thermal properties of the sediments, however, must be accurately known a priori because a simultaneous estimation of HFD, BTV, and the thermal properties remains unattainable. In a practical case, HFD is usually resolved to the same extent that thermal conductivity is known a priori.