傾斜計を用いた地下水流動評価法の開発とモデル解析 Development of a Method for Estimating Groundwater Flow by Titltmeters and Model Analysis
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 (Δ<I>ν</I>) and the Skempton coefficient <I>B</I> are assumed to vary in a linear or quadratic manner with the coordinates, that 2) the values of Δ<I>ν</I> 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 Δ<I>ν</I> are used. We call the method using linear interpolation Inversion-1 and that using quadratic interpolation Inversion-2.<BR>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 Δ<I>ν</I> varies relatively gently with the distance from the injection point (Model 1). However, when Δ<I>ν</I> 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 Δ<I>ν</I> to be determined. Furthermore, the effect of the size of the region V on the estimation of Δ<I>ν</I> 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.
- Journal of MMIJ : journal of the Mining and Materials Processing Institute of Japan
Journal of MMIJ : journal of the Mining and Materials Processing Institute of Japan 123(1), 17-25, 2007-01-25
The Mining and Materials Processing Institute of Japan