地震前兆引致水井水面共振之機制研究

Abstract

1999年九二一大地震發生前一天，台灣中部部分濁水溪沖積扇水井確實被觀測到地震之前兆現象，然而地震「前兆」之微小異常壓力波為何能被觀測到，吾人認為應是由於水井共振效應之放大作用所致。因此本研究期望藉由數學模式之建立分析共振現象發生之物理機制，以提供建立地震預警觀測井系統之設計參考。 本研究假設水井內部為非黏性、非旋性，且不可壓縮之均質理想流體，水井外部則為剛性結構之多孔介質流，以微小振幅波理論以及達西定律探討微小地震前兆波作用於水井之波場與物理機制。經由拘限含水層傳遞之微小前兆壓力波之波數則以Huang & Song(1993)所提出Biot(1962)第二種膨脹波波數 之表示式表示之。 本研究成功地避開直接計算之數值模擬，以理論解析方法提出合理之邊界條件，建立邊界值問題，並以正規擾動展開法(regular perturbation expansion method)及分割法(dividing method)配合正交函數之正交特性，順利解得各項合乎物理性質之解析解，且得到引發共振現象之相關參數表示式。 有別於Cooper在類似U-型管共振研究中所提出由強大壓力縱波引致水井內水體縱波共振之結果，以及傳統港池共振分析中由強大之質量通量橫波引致港池內橫波共振者，本研究得到由微小之地震前兆縱波將引致水井內橫波共振現象之結果，異於以往共振現象發生之物理機制，乃一嶄新之重大發現。 由於成功保留共振發生之相關物理參數表示式，具有對地震前兆引致水井水面共振現象解析的能力，本研究對於有關地震監測預警觀測井設計等工程應用，應能有所助益。

One day before the drastic 921-earthquake at central Taiwan in 1999, the pre-earthquake signals were observed in some water wells in Tsuo-Shui River water basin. How could the unusual tiny pressure wave of the pre-earthquake signals be observed? We believe one of the possible reasons is due to the effect of resonant amplification of wells. In this study, we expect to analyze the physical mechanism which leads the occurrence of resonant phenomenon by the construction of mathematical model. In the assumption that the water in the well is incompressible, inviscid and irrotational homogeneous ideal fluid and that outside the well is porous-media fluid with rigid structure, the small amplitude wave theory and Darcy’s law are adopted in the present study to investigate the wave field and the physical mechanism when the tiny pressure wave of the pre-earthquake signals is acting on the well. We consider the wave number of the tiny pressure wave of the pre-earthquake signals passing through confined aquifer as that of the second kind of dilational wave in Biot(1962) theory to which Huang & Song(1993) referred. The present study derives the reasonable boundary conditions, and thus constructs the boundary value problem by theoretical analytic method. Then by regular perturbation expansion method, dividing method and orthogonal condition of orthogonal functions, this study successfully solves the analytic solutions which correspond to physical phenomenon, and gets formulas of relative parameters which induce to resonance phenomenon. Instead of the result of the research similar to U-tube by Cooper(1965), longitudinal wave resonance of water in the well induced by huge longitudinal pressure wave, and that from traditional harbour resonance analysis, transverse wave resonance induced by huge transverse mass flux wave, in the study, we get a new result of resonance; i.e. resonance of transverse wave induced by tiny longitudinal pressure wave of the pre-earthquake signals. Due to the success of solving pre-earthquake signals acting on the well, the present study is helpful in analyzing well resonance and designing of observing water wells as the earthquake alert system.