Heat flow in random medium: First order theory

Summary Steady state heat flow in a weakly random semi-infinite medium is considered from a geophysical point of view. The principal finding of the present investigation is that the variance of thermal gradient (vertical) is several times larger than the variance of thermal conductivity. The variance of the thermal gradient decreases with increasing depth of measurement but approaches a certain constant value, which depends upon the spectral characteristics of thermal conductivity. The variance of heat flow is generally lower ( 10%) than the variance of the thermal gradient, but it behaves similarly. The dip of the medium (assuming it to be randomly layered) significantly affects the variance of the thermal gradient. The variance is miniumum for an intermediate dip.