本研究利用濾波分析及頻譜分析等工具建立一套完整的分析方法,以探討地下水位變化對於地表高程可回復變動影響之相關性與延遲性,並可計算代表不同區域地下水位變化影響地表高程可回復變動強度的效率係數與其之間的延遲時間,而後將所建立之方法應用於濁水溪沖積扇,以彰顯所建立方法之可用性。 為瞭解沖積扇中不同區域的變化關聯性,本研究使用訊號分析方法拆解地表高程與地下水位的時間訊號,考量乾濕季降雨影響,選用一年一次的週期性訊號進行分析,將兩訊號進行正規化與疊合後,再輔以交叉相關分析以判斷其相關性及瞭解訊號間的延遲時間,最後以頻譜分析得到兩者一年一次的頻率振幅,計算將高程變動振幅除以水位變化振幅得到之比值特稱為水位效率係數,此係數較大之區域地下水位變化對地表高程可回復變動的影響強度大於此係數較小之區域。 由本研究所分析之案例結果得知,濁水溪沖積扇因乾濕季降雨補注形成的一年一次週期性地下水位變化與地表可回復變動皆呈現正相關,推斷地下水位變化引起之地下水層架構有效應力變化主控了地層的縮脹反應。扇頂區域地下水位變化與地表高程可回復變動的平均延遲時間較扇央及扇尾來得長,且地下水位變化並非瞬間引起地表高程之變動,應為地層中的壓力變化有擴散傳播的現象,影響地表高程變動需要壓力之傳遞時間,且受壓含水層中壓力傳遞速度大於非受壓含水層,影響地表高程變動所需時間較短;若比較同一站點不同深度含水層水位變化與地表高程可回復變動的延遲時間,越深層地下含水層之地下水位變化與地表高程可回復變動間的延遲時間越短,其同樣受壓力關係所影響。各區域之水位效率係數於扇頂為最小,扇尾其次,扇央最大,可知扇頂為地表高程可回復變動受地下水位變化影響最小之區域,適合規劃為地下水取用區域。
The purpose of this study is to establish an analytical method which includes filter and spectral analysis for investigating correlation between variation of groundwater level and recoverable ground fluctuation. With this analytical method we can compute efficiency coefficient and delay time of effect on recoverable ground fluctuation caused by change of groundwater level at different area. Chou-Shui River Alluvial Fan is chosen as an actual case for this analytical method. First, we use signal analysis method to separate annual periodic signal from original signal of groundwater level as well as ground elevation. And then we apply cross correlation analysis on two periodic signals for finding the correlation and delay time between these signals. At last, we can use the spectral analysis to find amplitudes of the two periodic signals and compute ratio of the two. We define this ratio as efficiency coefficient of water-level variation and with this coefficient we can understand how intensively variation of groundwater level affects recoverable ground fluctuation. From the analysis results on Chou-Shui River Alluvial Fan, the conclusion can be inferred as follows: (a) the correlation between the annual periodic variation of groundwater level and recoverable ground fluctuation is positive; (b) the average delay time is longer around Fan-top area than other areas; (c) the delay time of deeper aquifer is shorter than shallow aquifer at same station; (d) variation of groundwater level affects less to the recoverable ground fluctuation at head area where the efficiency coefficient of water-level variation is the smallest.