Inversion of marine heat flow measurements by expansion of the   temperature decay function
  Marine heat flow data, obtained with a Lister-type probe, consists of two temperature decay curves, frictional and heat pulse decay. Both follow the same physical model of a cooling cylinder. The mathematical model describing the decays is non-linear as to the thermal sediment parameters thus a direct inversion is not possible. To overcome this difficulty, the model equations are expanded using a first-orderTaylor series. The linearised model equations are used in an iterative scheme to invert the temperature decay for undisturbed temperature and thermal conductivity of the sediment. The inversion scheme is tested first for its theoretical limitations using synthetic data. Inversion of heat flow measurements obtained during a cruise of R/V SONNE in 1996 and needle probe measurements in material of known thermal conductivity show that the algorithm is robust and gives reliable results. The programme can be obtained from the authors. 
Andreas Hartmann, Heinrich Villinger