Abstract

Classical logarithmic linearization of the single backscattering model to estimate the coda Q (\( Q_{c} ) \) leads to biased results in the presence of low signal-to-noise ratio. Non-linear regression using the Levenberg–Marquardt (L–M) method has been proposed to estimate the \( Q_{c} \) in the frequency range of 3–24 Hz on local earthquakes recorded in northeast region of India. Results of both classical log-linear and non-linear approaches to the single backscattering model are compared. On datasets with good signal-to-noise ratio both the approaches lead to almost the same results. However, for datasets having low signal-to-noise ratio, we found that the log-linear technique estimates are biased. Results demonstrate that the log-linear approach overestimates the \( Q_{c} \) in comparison to the non-linear approach. Frequency dependence parameter ‘\( \eta \)’ for the L–M method is slightly higher than the conventional log-linear approach. The \( Q_{c} \) variation with lapse-time is also studied with both the approaches. The biased results of log-linear approach were observed at different frequencies at all lapse times. Significantly lower \( Q_{0} \) (1 Hz) estimates of non-linear approach indicated more heterogeneous lithosphere than the log-linear approach.

Highlights

• A novel approach to the single scattering model is proposed wherein nonlinear regression is performed to estimate coda Q_c.

• Coda attenuation and its variation with lapse time is analysed (3–24 Hz) from local earthquakes of North East India

• For datasets having a low signal-to-noise ratio the estimates of the conventional log-linear regression were biased.

• Significantly lower Q₀ estimates of the non-linear approach indicated a more heterogeneous lithosphere than a log-linear approach.

中文翻译：

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非线性回归法估算印度东北部的Coda Q

摘要

在低信噪比的情况下，单个反向散射模型的经典对数线性化以估计尾随Q（\（Q_ {c}）\）会导致结果偏差。已经提出使用Levenberg-Marquardt（LM）方法进行非线性回归来估计印度东北地区记录的3-24 Hz频率范围内的\（Q_ {c} \）。比较了单一对向散射模型的经典对数线性和非线性方法的结果。在具有良好信噪比的数据集上，两种方法得出的结果几乎相同。但是，对于具有低信噪比的数据集，我们发现对数线性技术估计存在偏差。结果表明，对数线性方法高估了\（Q_ {c} \）与非线性方法相比。LM方法的频率相关参数' \（\ eta \） '略高于常规对数线性方法。的\（Q_ {C} \）与经过时间的变化进行了研究与两个方法。在所有经过时间的不同频率下，观察到对数线性方法的偏差结果。非线性方法的\（Q_ {0} \）（1 Hz）估计值明显较低，这表明岩石对数层比对数线性方法更不均匀。

强调

• 提出了一种新的单散射模型方法，其中执行非线性回归以估计尾随Q _c。

• 印度东北部地区地震分析了尾气衰减及其随时间的变化（3–24 Hz）

• 对于信噪比低的数据集，常规对数线性回归的估计值存在偏差。

• 非线性方法的Q ₀估计值明显较低，这表明岩石对数层比对数线性方法更不均匀。