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.

$\bf{Highlights}$

$\bullet$ A novel approach to the single scattering model is proposed wherein nonlinear regression is performed to estimate coda $Q_{c}$.

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

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

$\bullet$ Significantly lower $Q_{0}$ estimates of the non-linear approach indicated a more heterogeneous lithosphere than a log-linear approach.