ISSN:
1573-8868
Keywords:
data processing
;
improperly posed problem
;
numerical analysis
;
geophysics
;
heat-flow
;
surface-temperature history
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Mathematics
Notes:
Abstract All methods proposed to date for the determination of surface temperature history from temperature profiles measured in boreholes are based on the assumption that the borehole is a hole in a semiinfinite homogeneous earth of constant diffusivity κ, and more or less ignore the fact that the mathematical formulation for this problem is improperly posed. This assumption, which frequently represents a gross oversimplification of the situation, was originally introduced as a computational expedient. We propose a computational procedure which is independent of this assumption and takes the improperly posed nature of the problem into account. The essence of the method is: (a) determine the set of borehole profiles corresponding to a given set of linearly independent surface temperature history functions, and then (b) take the coefficients of the least-squares fit of these borehole profiles to the given borehole data as the coefficients in the linear combination of surface temperature history functions which defines the required approximation to the surface temperature history. An analogous procedure can be used to determine the lower boundary condition for the heat-flow problem if the surface-temperature history is assumed to be known. Results of numerical experimentation are used to indicate the extent to which the method is viable in practice.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02111814
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