Use of Modified Tikhonov Regularization in Analysis of Ground Surface Temperature Variations

Abstract

Inversion techniques employed in geothermal studies of ground surface temperature (GST) changes are known to have problems of instability and non-uniqueness in numerical solutions. In the present work it is pointed out that some of these difficulties can be overcome through the use of a method based on Tikhonov regularization of order one which imposes smoothing of main parameters. A major disadvantage of this approach is obliteration of weak thermal signals usually present at larger depths at the expense of strong ones present at relatively shallow depths. In the present work we consider a convenient way of minimizing this problem using a method based on Tikhonov regularization of order one. In this approach residuals of observational data are minimized by imposing constraints on the variations of smoothing parameters, that is controlled by the magnitude of regularization coefficients. This is accomplished in two stages of inversion. In the first stage we seek an estimation of the dates of climate events derived from results of temperature logs. Inversion of the second stage allows estimation of the magnitudes of GST variations that are compatible with the ages of climate events of the first stage. The advantage is in finding better solutions without introducing other artefacts on the climate history. Such two-stage Tikhonov regularization procedures has been employed for extracting complementary information on GST history in continental regions of Brazil. The results reveal that the main warming event of the last century has been preceded by several secondary events during the time period of 1400 to the 2000 A.D.