隨 著 爆 發 性 噴 發 造 成 的 火 山 震 顫 是 無 所 不 在 的 ， 而 在 印 尼 東 爪 哇 Semeru 火 山 也 發 現 一 樣 的 訊 號 。 為 了 探 究 顫 動 的 非 線 性 動 力 學 性 質 分 ， 本 研 究 使 用 非 線 性 動 力 學 方 法 分 析從2009 年11 月 22 日 到 12 月 31 日 的 二 十 五 筆 火 山 地 震 數 據 。 由 Takens 的 延 遲 嵌 入 理 論 說 明 了 原 始 地 震 波 形 的 非 線 性 系 統 的 行 為 演 變 描 述 相 空 間 被 重 新 建 構 。 在 給 定 7 – 11 秒 的 延 遲 時 間 範 圍 內 ， 重 建 的 延 遲 時 間 被 選 擇 用 來 檢 查 相 關 函 數 和 平 均 相 互 信 息 。 假 近 鄰 法 應 用 於 時 間 數 據 設 置 ， 在 5 – 7秒 之 間 產 生 足 夠 的 嵌 入 維 度 。 在 鄰 近 軌 道 的 那 些 混 亂 狀 態 標 誌 的 指 數 歧 異 度 可 以 利 用 最 大 Lyapunov 指 數（ MLE ） 被 量 化 。 MLE 被 用 來 檢 測 在 震 顫 信 號 上 數 量 的 泛 音 及 時 間 的 函 數 變 化 。 這 意 味 著 ，震 顫 源 在 幾 個 泛 音 頻 率 的 準 週 期 狀 態 及 小 的 MLEs (~ 0.013) 和 一 個 有 著 更 多 泛 音 的 混 亂 的 狀 態 及 較 大 的 MLEs (up to 0.039) 之 間 波 動 著 。 吸 引 維 度 的 估 計 是 使 用 由 Grassberg Procaccia 所 提 出 的 相 關 演 算 法 來 完 成 的 。相 關 維 度 的 事 件 等 於 或 小 於 2 時 ， 有 可 能 作 為 在 相 空 間 中 的 吸 引 環 面 ， 然 而 對 於 相 關 維 度 事 件 大 於 2 的 情 況 中 ， 軌 跡 不 會 靠 近 圓 環 ， 因 此 ， 對 於 一 些 沿 著 圓 環 的 隨 意 較 大 的 資 料 數 據 ， 就 可 以 探 究 較 大 面 積 的 相 空 間 。 實 體 觀 測 說 明 微 震 源 涉 及 氣 體 從 噴 泉 堵 塞 物 從 一 個 或 多 個 裂 隙 中 溢 出 。 在 測 定 震 顫 特 徵 上 ， 堵 塞 物 的 性 質 扮 演 了 一 個 非 常 重 要 的 角 色。

Volcanic tremor that follows explosive eruptions is an ubiquitous signal found in several volcanoes and also found at Semeru volcano, East Java, Indonesia. Twenty five episodes of volcanic tremor data from 22 November – 31 December 2009 have been analyzed using methods from the discipline of nonlinear dynamics in order to investigate their nonlinear dynamical properties. The phase space which describes the evolution of the behavior of nonlinear system was reconstructed from the original tremor seismograms using the delay embedding theorem suggest by Takens. The delay time used for reconstruction was selected after examining the autocorrelation function and average mutual information giving delay time in the range of 7-11. The false nearest neighbor method was applied to time data set yielding sufficient embedding dimension between 5-7. Exponential divergence of nearby orbits is the hallmark of chaotic behavior and was quantified by the maximal Lyapunov exponent (MLE). MLEs were found to vary as a function of the number of overtones in tremor signal and as a function of time. This implies that the tremor source fluctuates between a quasi-periodic state with few overtone frequencies and small MLEs (~0.013) and a chaotic one with more overtones and larger MLEs (up to 0.039). Estimation of attractor dimension was done using the correlation algorithm suggested by Grassberg and Procaccia. The events with the correlation dimension equal to or less than 2 likely have a torus as an attractor in the phase space. For events that have correlation dimension larger than 2, the trajectory is not bounded close to the torus and therefore it can explore a larger area of the phase space. No correlation dimension for some events can be explained due to dynamical correlations that persist for arbitrarily large data sets along a torus. Physical observations indicate that the tremor source involved gas escaping from the plug of conduit through one or more fractures. The properties of the plug probably played a very important role in determining the characteristics of the tremor signal.

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