Resolution of ground temperature histories inverted from borehole temperature data

Inversion methods have been used to determine ground temperature history from borehole temperature data. This paper examines the resolution of an inversion method based on singular value decomposition. The method includes in the constraints the rate of change of subsurface if available. The response of the Earth to a unit pulselike change in surface temperature and the model resolution were calculated to determine the details of ground temperature variations obtainable from geothermal data. The model parameters estimated by the inversion correspond to averages over time intervals of increasing length with time. For a unit impulse temperature change occurring at time t before present, the estimated ground temperature history shows the event “spread” over at least 60% the time of occurrence. In practice, the resolution is not improved by increasing the sampling frequency of the data. Likewise, the simultaneous inversion of the temperature profile and of its time derivative does not significantly improve the resolution. Selection of a particular parametrization may improve resolution of the chosen parameters, but not the actual resolution since the parameters represent longer time averages. Temperature data from the Minchin Lake borehole in western Ontario, which was logged twice over 15 years, have been inverted to illustrate these conclusions.