小波及灰色理論應用於地層下陷預警之研究－以濁水溪沖積扇爲例

The Application of Wavelet and Grey Theory in the Land-Subsidence Potential Analysis for the Cho-Shui River Fan

呂珍謀(Jan-Mou Leu) ； 朱木壽(Mu-Shou Chu) ； 陳厚元(Hou-Yuan Chen)

《農業工程學報》 56卷4期 (2010/12) Pp. 70-82

https://doi.org/10.29974/JTAE.201012.0006

摘要

本研究係基於各含水層地下水位和沉陷量的相關性，由地下水位站各不同時空沉陷量，利用灰關聯分析推論出關鍵地下水位站及其含水層之水位變化，再以小波分析法自地下水水位不同週期、頻率、變化幅度中，預測擬合值和奇異點的幅度大小，依其地層下陷潛勢關聯性設定警示水位，並建構灰色預測模型GM(1,1)以預測地層下陷未來發展趨勢。整體分析步驟如下：(1)篩選出關鍵地下水位站。(2)應用灰關聯分析求出關鍵含水層。(3)依據地下水位長期變動趨勢分析結果，選取多處觀測井爲指標水井。(4)以小波分析地下水位，求出局部奇異點振幅大小及時間點。(5)以灰色模型預測其地層下陷潛勢。(6)結合局部奇異值振幅及時間點等變數，藉以設定地陷潛勢預警地下水位。
本研究利用灰關聯分析，可解決地下水位站水位變化值和沉陷量關聯性離散數據問题，進而可求出關鍵沉陷含水層，配合小波分析法建構之灰色預測模型GM(1,1)，分析程序可以降低運算難度及聚焦於沉陷劇烈發生時空之關鍵影響。以濁水溪沖積扇爲例進行分析，小波分析結果顯示奇異點最大振幅發生時間點後平均2年內即發生年最大沉陷量，準確率可達85%以上，小波分析無法辨識解讀之資料點，都集中於雲林沿海地區，研判爲沿海地區潮汐或人爲開發之影響所致。

關鍵字

灰關聯分析 ； 小波分析 ； 奇異點 ； 灰色預測模型

並列摘要

This study focuses on the relationship between different layers of groundwater levels and utilize spatiotemporal related interpolate value of settlement of each groundwater station to conclude the critical groundwater station and the critical changes of water level in aquifer. I combined the variables from partial singularity amounts of amplitude of vibrations and time period to establish the potential development of subsidence in order to warn the groundwater levels earlier.
We did the following analysis: First, we selected representative groundwater stations. Second, applied to the grey relational analysis to figure out the related amount of critical aquifer. Third, we analyzed the results of long-term changing tendencies of ground water level and selected many groundwater stations. Fourth, we utilized the timing value of groundwater level of wavelet analysis and the history of movement fluctuations of ground water levels to analyze the partial singularity amounts of amplitude of vibrations and time period. Fifth, we used grey prediction model GM (1,1) to predict the potential development of land subsidence and figure out a predicted value. Sixth, we combined the reference variables from partial singularity amounts of amplitude of vibrations and time period to establish the potential development of subsidence in order to warn the groundwater levels earlier.
We can observe the singularity of the biggest amplitude time period from wavelet analysis and delay, on average, the biggest settlement amount in two years. the accuracy rate can be over 85%. The areas that can not be identified by wavelet analysis are mostly concentrated in coastal regions of Yun-Lin, which is influenced due to the tidal intrusions and artificial developments.

並列關鍵字

Grey Relational Analysis ； Wavelet Analysis ； Singularity ； Grey prediction model