Optimized inversion of borehole temperature data

A comparison is made between the effectiveness of the inversion of borehole temperature data (for the purpose of climate reconstruction) by the least-squares (L-2) technique and the minimization of the absolute difference between the observed and calculated data (L-1) technique. The L-1 technique is found to require approximately half the number of iterations to reach the practically achievable minimum error compared to the L-2 technique. The choice of which technique to use depends on the statistics of the difference between the observed and calculated data, and it can be advantageous to switch techniques during the inversion process. The inversion damping is also adjusted during the course of the inversion, based on the rate of change of the difference between the observed and calculated data. The aim is to get the best fit of the model to the data while minimising the model size, in the minimum number of iterations. A method of adjusting the damping to achieve this is suggested.