Minimum Relative Entropy: Theory and application to surface temperature reconstruction from borehole temperature measurements

In this paper we extend the minimum relative entropy (MRE) method to recons truct ground surface temperature changes (GST) from borehole temperature me asurements (BHT). The application of MRE to recovering GST is promising and provides an alternative to other inverse methods in geophysics. The relati ve entropy formulation provides the advantage of allowing for a prior bias in the estimated pdf and 'hard' bounds if desired. Test cases showed good r ecoveries of the GST. The method was utilized in recovering GST from two da ta sets in Canada. The Lac Dufault data gave very consistent results for di fferent choices of a priori information and bounds. The Mariner results wer e not as good quality This method has only recovered past ground surface te mperatures, which does not directly provide information regarding climate c hange. However, results contained herein show fairly uniform temperatures u ntil the past 100 to 500 years and in more recent times about a 4 degrees C rise in temperature, consistent with previous published results.