Uncertainty evaluation with increasing borehole drilling in subsurface hydrogeological explorations

Quantities of drilling boreholes have been a difficult subject for field investigators in such as subsurface hydrogeological explorations. This problem becomes a bigger in heterogeneous formations or rock masses so we need to develop quantitative criteria for evaluating uncertainties during borehole investigations.To test an uncertainty reduction with increasing boreholes, we prepared a simple hydrogeological model and virtual hydraulic tests were carried out by using this model. The model consists of 125,000 elements of which hydraulic conductivities are generated randomly from the log-normal distribution in a 2-kilometer cube. Uncertainties were calculated by the difference of head distributions between the original model and the inchoate models made by virtual hydraulic test one by one.The results show the level and the variance of uncertainty are strongly correlated to the average and variance of the hydraulic conductivities. This kind of trends also could be seen in the actual field data obtained from the deep borehole investigations in Horonobe Town, northern Hokkaido, Japan. Here, a new approach using fractional bias (FB) and normalized mean square error (NMSE) for evaluating uncertainty characteristics will be introduced and the possibility of use as an indicator for decision making (i.e. to stop borehole drilling or to continue borehole drilling) in field investigations will be discussed.