利用周遭噪訊交互關函數尾波成像台灣地殼衰減性質的側向變化

Abstract

根據前人研究顯示利用區域地震S波的尾波（coda ）可以有效地量測頻率大於1 Hz 衰減值, 通常表示為尾波的衰減因子（Qc）, 甚至區分地殼中的散射衰減因子（Qsc）和非彈性吸收衰減因子（Qi）。另外, 研究發現估計的值會與量測時所使用的窄頻濾波中心頻率以及所選取尾波的時間段和視窗長度相關。因區域地震的尾波訊號通常集中在高頻1 Hz以上，對於提供在小於1 Hz頻帶的觀測約束相當困難。近年來，隨著干涉地震學及周遭噪訊理論的發展，證實經由兩地震站所連續記錄的周遭噪訊計算交互相關函數（cross-correlation function）可求得反應兩站之間路徑底下構造的經驗格林函數（empirical Green’s function），除了最顯著的直達表面波外，隨後持續振盪的訊號則涵蓋在地球內部介質經多重散射的尾波，其能量的衰減速率同樣可用來測量該地區淺部地殼的衰減特征。 為研究台灣地殼的衰減特性，本論文沿用了Mayor等人在2016年利用地震S波尾波測量阿爾卑斯山地區衰減因子的方法。不同的是，我們提取兩兩測站所記錄的噪訊交互相關函數的尾波訊號，量測週期介於1到10秒近似反映非彈性衰減構造的吸收因子變化。得益于台灣廣而密集分佈全島，包含短週期、寬頻、以及強震型的永久地震測站網所提供2016年的連續記錄，計算任兩站間每天的交互相關函數並疊加整年得到近2000條站間距小於100公里內的經驗格林函數，作為估算尾波衰減因子的數據。透過中心週期為2, 4, 6 和8秒, 頻寬半寬度為1/3倍的中心頻率的窄頻濾波之後，選取不同尾波起始時間(tw)延遲時間長度(Lw)量測尾波能量的衰減速率以求得Qc。分析結果顯示當Lw固定時，Qc值沒有隨著不同tw而有明顯變化，也沒有呈現和站間距離的相關性。然而，如同地震尾波研究所觀察到的，噪訊提取的尾波所量測的Qc值同樣具有和Lw明顯的相關性，Qc值在選取較短的Lw時會隨著延遲時間加長而逐漸增加，當Lw增加到75~100秒長度時，Qc會趨近於一穩定的常數值，可近似吸收衰減因子值（Qi）。在選取最適當的tw和Lw值之後，透過依序移動短視窗內平滑的尾波能量取自然對數值對該視窗時間進行線性回歸計算出最吻合的直線斜率以換算Qc值。為了確保量測的可靠性，只有回歸擬合係數大於0.7以上測站對的保留進行下一步衰減構造側向變化的成像。由於路徑分佈相對均勻，我們將台灣劃分成均勻的網格，直接將求得Qc值的導數(Qc-1)均勻分佈到該測站對間路徑所經過的網格上，每一網格最終至少要有三條以上路徑通過，再將每個網格裡的所有分配到的Qc-1值取平均得到該點衰減值。結果顯示在四個頻帶都顯示出相似的側向變化，其中Qc在4 s的側向變化及覆蓋率最佳，其表面波尾波在該週期最能感應深度約3-5公里處地殼的衰減特性，最低值約50，出現在台灣西南部平原區，顯示有較高的吸收衰減，可能和覆蓋厚層的沉積物地層有關。 Qc值由西向東，即從西部麓山帶到雪山山脈和中央山脈逐漸增加，在中央山脈變質岩帶顯示較低的衰減特征，Qc值最高約120，出現在台灣中央山脈東南區域，推測台灣上部地殼的衰減特性和台灣造山運動所形成由西而東岩石變質度逐步增加有很大的關聯性。值得留意的是，目前我們主要是根據表面波不同頻率的群速度對S波速度在深度方向的敏感度對上部地殼及淺層地表Qc的衰減構造進行討論解釋，對於影響所量測尾波的衰減構造在空間的分佈變化仍需更進一步的研究。

The lapse-time dependence of the quality factor Qc measured from the S-wave coda of local earthquakes at frequencies above 1 Hz has long been proven effective to investigate separately the scattering and absorption properties of the crust. On the other hand, recent studies demonstrate that the Green’s function retrieved from the noise cross-correlation (NCF) between two stations contains a tail of multiply-scattered waves after ballistic waves like the coda of earthquakes, the decay rate of which can therefore be also exploited for mapping of subsurface attenuation structures. We follow the approach of Mayor et al. (2016) for studying the Qc variations from earthquake S-wave coda in the Alps to estimate the frequency-dependent decay rate of coda at frequencies below 1 Hz derived from the NCFs and map the lateral variations of absorption structure of the crust in Taiwan. Benefiting from the dense seismic stations distributed across Taiwan, our dataset comprises more than 2000 yearly stacked NCFs between all the available station pairs less than 100 km apart across the Taiwan island, including broad-band and short-period continuous records in 2016. The Qc is estimated from the narrow bandpass filtered coda energy centered at the periods of 2, 4, 6, and 8 s. The Qc values at certain periods determined with the fixed coda window (Lw) but different choices of coda onset time (tw) reveal no obvious trend with the inter-station distance. However, similar to the observations from the earthquake coda, the lapse-time dependence and frequency-dependence of Qc is prominently seen as Qc generally follows a transient increase with Lw at relatively short lapse times and then approaches a stabilized plateau value at Lw = 75-100 s which considered as an optimal approximation of the absorption or intrinsic attenuation quality factor Qi. After selecting proper tw and Lw to determine Qc along individual station pairs, we map the lateral variations of intrinsic attenuation by simply distributing the Qc value uniformly along the corresponding inter-station path and taking the mean values of Qc within individual 0.2*0.2 degree cells. Our results show that the Qc variation is similar in all four frequency bands while the pattern at 4s is more pronounced and the lowest (~50), implying the highest intrinsic attenuation, in the Coastal Plain of SW Taiwan covered with thick sedimentary deposits. It gradually increases toward the Western Foothills fold and thrust belt in south central Taiwan and reaches the highest (~120) in the Central Range in southeast Taiwan, which seems to be correlated with the progressive increase of the metamorphic grade in the Taiwan orogen. Further interpretation of attenuation structures based on physically-realistic coda-wave kernels are needed to reveal both lateral and depth variations of the absorption properties across complex and diverse litho-geological units in Taiwan.