Estimation of Coda Q for northeast India using nonlinear regression

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.