Revising the method proposed by Vasco et al., we developed a new method for more accurately estimating groundwater flow by an inverse analysis of tilt data on the surface. The features of this method are that 1) a region (V) where groundwater flow occurs is divided into elements in which the volume change in groundwater per unit volume of rock (Δν) and the Skempton coefficient B are assumed to vary in a linear or quadratic manner with the coordinates, that 2) the values of Δν are set to zero at the boundaries of the region V and that 3) as constraining conditions which are weighed and added to a squared error in tilt, the sum of squared second derivatives of Δν are used. We call the method using linear interpolation Inversion-1 and that using quadratic interpolation Inversion-2.
First, analyses by these methods were conducted for two flow models of water injection to know the applicability of the methods. It was shown that both Inversion-1 and Inversion-2 can evaluate the volume change in groundwater much more accurately than the method by Vasco et al. when Δν varies relatively gently with the distance from the injection point (Model 1). However, when Δν varies steeply with the distance from the injection point (Model 2), either Inversion-1 or Inversion-2 cannot produce good results. This was considered to be caused by the fact that the measured data are much fewer than Δν to be determined. Furthermore, the effect of the size of the region V on the estimation of Δν was analyzed since it is usually difficult to accurately estimate the size of a region where water flow occurs. The results showed that the effect of the size of the region V is relatively small for both Inversion-1 and Inversion-2 unless the size is much smaller than the real one and that Inversion-2 produces a smaller error than Inversion-1. Thus, it can be said that it is better to perform an analysis by Inversion-2 with a large size of the region V in the beginning.
