We herein present new frequency-dependent coda-\(Q\,\,(Q_\mathrm{c})\) relations (\(Q_\mathrm{c} =Q_{\text {0}}f ^{n})\) (frequency ranges between 2 and 18 Hz) for three regions of the eastern Indian craton (EIC), viz., the Singhbhum Odisha craton (SOC) and the Eastern Ghat mobile belt (EGMB), comprising the Mahanadi basin and the Chotanagpur granitic gneissic terrain (CGGT). The frequency-dependent coda-\(Q_\mathrm{c}\) relations are obtained through the single backscattering model for coda waves (\(Q_\mathrm{c})\) of local earthquakes which are recorded on 15 three-component broadband seismograph stations in the regions. In this work, we pay special attention to test the lapse time (\(t_\mathrm{L})\) dependency of coda-Q (\(Q_\mathrm{c})\) estimates for the three regions. Lapse time signifies the sample area of the coda wave of the study region. Generally, the sample area increases with lapse time. To test the lapse time (\(t_\mathrm{L})\) dependency, nine different lapse time windows (\(t_\mathrm{L})\) from 10 to 90 s with 10 s interval are considered. On the ground of estimated poor correlation coefficients, only six lapse time windows (\(t_\mathrm{L})\) from 40 to 90 s with 10 s interval are considered. Our results suggest more heterogeneity in EGMB than that of the SOC and CGGT region. Estimates of \(Q_{\text {0}}\) and n for the three regions of EIC (SOC, EGMB and CGGT) are found to be consistent with the results of \(Q_{\text {0}}\) and n for mildly active less heterogeneous seismic zones in different parts of the world. By assuming entirely intrinsic attenuation characteristics, actual hazard parameters, i.e., extinction distance and anelastic attenuation coefficients are also computed for the three regions. The extinction distance (\(L_\mathrm{e})\) provides an idea of the distribution of scatterers in the lithosphere and anelastic attenuation coefficients signify the anelasticity of the medium, i.e., fluid movement and grain distribution. The estimate of extinction distance and attenuation coefficients suggests that for all three study regions, the upper mantle is relatively less heterogeneous and attenuation below 110–126 km depth is also comparatively lower. Coda Q indicates the degree of fracture and heterogeneity in the lithosphere related to seismicity. A higher estimate of \(Q_{\text {0}}\) values in the Archaean SOC region and the Proterozoic CGGT region is found when compared with that of the sedimentary-rich EGMB. It can be inferred that seismically less active cratons in general comprise high \(Q_{\text {0}}\) values, whereas the sedimentary-rich EGMB is more attenuative, characterised by a low coda \(Q_{\text {0}}\) value. Moreover, it is found that the estimated \(Q_{\text {0}}\) values for CGGT region are a little bit higher than that for the SOC region. This can be explained as a comparatively less disturbed and less heterogonous land mass that is present in the CGGT region as compared to the SOC region, which comprises different minerals, ore bodies, fault scarps and shear zones. The developed \(Q_\mathrm{c}\) relation for the EIC region could be useful for the study of hazards and ground motion prediction.
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