Simultaneous inversion of borehole temperature data for determination of ground surface temperature history

Recent variations of the ground surface temperature, recorded in the Earth's subsurface, can be inverted from borehole temperature data, The resolution of the inversion of borehole temperature logs is poor, even when the noise level is low. This report concerns the potential improvement in the resolution of ground surface temperature history when temperature logs from several boreholes are inverted simultaneously. For an inversion algorithm based on singular value decomposition, the singular values obtained for simultaneous inversion of several boreholes do not decrease as rapidly as the singular values for a single borehole. With the same value of the cut-off or of the damping parameter, more eigenvectors remain in the solution and give higher resolution for several boreholes than for one. Tests conducted with synthetic data for 15 boreholes show that the improvement in resolution is real but not spectacular. These tests indicate that borehole temperature logs should have approximately the same sampling interval. Temperature profiles over different depth ranges can be inverted if the reference heat flows and ground temperatures are included in the parameters determined by the inversion. Tests also show that no consistent ground-temperature history (GTH) is obtained when inverting data from boreholes that have experienced different surface-temperature variations. Simultaneous inversion can be applied to: (1) obtain a local GTH for a single site with several boreholes having identical surface conditions, or (2) obtain regional averages with data from different sites that have experienced the same variations in ground temperature. Temperature profiles measured in four boreholes near Belleterre, in eastern Canada, appear to have recorded the same perturbation. Inversion of the temperature data from individual boreholes yields similar, but not identical, GTHs. The GTH obtained by simultaneous inversion of these four boreholes indicates a cool period, with minimum temperatures at ca. 1800 AD, followed by warming above the reference level. It is consistent with other analyses indicating recent warming in eastern Canada.