Surface heat flux histories from inversion of geothermal data: Energy balance at the Earth's surface

Past changes in the Earth's surface energy balance propagate into the subsu rface and appear as perturbations of the subsurface thermal regime. This pa per presents a singular value decomposition inversion method used to recons truct surface heat flux histories (SHFH) from the heat flux anomalies detec ted in the shallow subsurface. Synthetic tests were used to assess the robu stness of the inversion procedure. It was found that data noise can have a significant effect on the stability of the SHFH inferred from inversion. Th is translates in SHFHs having lower temporal resolution than ground surface temperature histories (GSTHs) obtained from the same data, but the long-te rm trends are robust. Results are encouraging for temperature data noise le vels typically encountered in field measurements. Synthetic data tests yiel d results in agreement with analytical expressions derived from GSTHs for t he same parameterization. Temperature-depth profiles from Canada's geotherm al database were used to illustrate the inversion procedure, Individual tem perature profile inversions are shown as examples. All 112 temperature logs in the database were used to obtain a mean heat flux history for the regio n. Results indicate that the ground heat flux has increased an average of 2 4 mW m(-2) over the last 200 years in Canada. Application of this method to the existing global geothermal data base should allow for a quantification of the global energy balance at the Earth's surface for the past few centu ries and may be useful for land surface models.