Patent Document ID: 20040220740
Application ID: 10813437
Patent Flag: 0

Claim One:
1. A method for obtaining closed form expressions for subsurface temperature depth distribution along with its error bounds, the method comprising using a stochastic heat conduction equation incorporating random thermal conductivity to obtain a mean and variance in temperature fields for a set of boundary conditions: the equation consisting of 19 &dd; &dd; z &it; { ( K _ + K ′ &af; ( z ) ) &it; &dd; T &dd; z } = - A &af; ( z ) ( 1 ) where T is the temperature (° C.) A(z) is the radiogenic heat source (&mgr;W /m 3 ), K(z)&equals;{overscore (K)}&plus;K′(z) is the thermal conductivity (W/m ° C.) which is expressed as a sum of a deterministic component and a random component K′(z) is the random component with mean zero and a Gaussian colored noise correlation structure represented by E ( K′ ( z ))&equals;0  (2) E ( K′ ( z 1 ) K′ ( z 2 ))&equals;&sgr; K 2 e −&rgr;&verbar;z 1 −z 2 &verbar; (3) where &sgr; K 2 is the variance is thermal conductivity (W/m ° C.) 2 &rgr;is the correlation decay parameter m −1 (or 1/&rgr; is the correlation length scale) and z 1 and Z 2 are the depths (m)