1 Introduction

The Himalayan orogeny has resulted from multiple factors, summarized as large-scale interactions between lithospheric deformation and atmospheric circulations. The Indian-Eurasian plate collision processes have yielded a diversity of geological features such as large-scale thrust, strike-slip and normal fault systems, which are exhaustively described in geological studies (Bilham et al., 1997; Burg & Chen, 1984; Burchfiel et al., 1992; Larson et al., 1999; Tapponnier et al., 1986) and regional metamorphism (Le Fort, 1996; Searle, 1991). The Himalayan orogen is supposed to have played a critical role in controlling climate change (Molnar et al., 1993). Among the most significant magmatic products resulting from the Indian-Eurasian plate collision are the High Himalayan leucogranites (HHL) formed around 25–18 Ma at about 400 MPa pressure, corresponding to a depth of 8–15 km (Le Fort et al., 1987). The present challenge is to understand the seismic attenuation beneath different seismotectonic segments augmenting the knowledge of the seismic energy budget in the study region. The Kumaun Himalaya is our study region, which is a complex seismo-tectonically active region, emplaced with major tectonic features like the Southern Tibetan Detachment (STD), Main Central Thrust (MCT), Main Boundary Thrust (MBT) and Main Frontal Thrust (MFT). Diverse models have tried to explain the evolution, tectonics and seismicity, e.g., the steady-state model (Seeber & Armbruster, 1981) and evolutionary model (Ni & Barazangi, 1984). The cause for the occurrence of small and large earthquakes is the high-strain accumulation due to Indo-Eurasian plate collision along different Himalayan frontal thrusts, within different tectonic belts such as the Lesser Himalaya (LH) and the Higher Himalaya (HH) segments. From the perspective of seismic hazard analysis, a regional seismic model is needed which facilitates quicker estimation of the ground motion intensity measures and describes the energy-attenuation process from the source region to the measurement region. This fundamentally also facilitates the knowledge of the rock properties through which the seismic waves propagate with the aid of the various measures of Q (quality factor, inverse of attenuation) (Knopoff, 1964), such as Qc (coda Q); \(Q_{\beta }\) and \(Q_{\alpha }\) (S-wave and P-wave Q) (or body wave Q). In general, the total attenuation (or Q−1) is a combination of intrinsic and scattering attenuation (Aki, 1969, 1980; Aki & Chouet, 1975). According to laboratory experiments, Vassiliou et al. (1982) have provided valuable relations between Qβ and Qα for different conditions of rock, such as: Qβ = Qα for dry rocks, Qβ ≥ Qα for partially saturated rocks and Qβ ≤ Qα for fully saturated rocks. Winkler and Nur (1982) have provided additional relations between \(\left( {\frac{{Q_{\beta } }}{{Q_{\alpha } }}} \right)\) and \(\left( {\frac{{V_{\alpha } }}{{V_{\beta } }}} \right)\)(Vα = velocity of P waves, Vβ = velocity of S waves) in characterizing the petrological properties of the upper crust. Several researchers correlate the variations of the various diagnostic parameters and frequency-dependent estimates of Q with the geology and seismotectonics of the study area (Giampiccolo et al., 2002; Jin & Aki, 1989; Matsumoto & Hasegawa, 1989; Ma & Huang, 2020; Patane et al., 1994, 2011; Rautian & Khalturin, 1978; Sato, 1982; Sharma et al., 2008; Singh & Herrmann, 1983; Tripathi et al., 2014; Yoshimoto et al., 1993).

In the Himalayas, some of the seismic attenuation (Q−1) studies in several smaller regions include Mukhopadhyay et al. (2006) in the northwestern Himalaya region, Mukhopdhyay and Sharma (2010), Mukhopadhyay et al. (2010) in Garhwal-Kumaun Himalaya, Ashish et al. (2009), Singh et al. (2012) in the Kumaun Himalaya, Tripathi et al. (2014) in Garhwal Himalaya, Mishra et al. (2020) in northwestern Himalaya and Monika et al. (2020) in Garhwal and Kumaon Himalaya. Due to the different techniques, constraints on the dataset and sampling regions, some of these studies show slightly varying results. Among the larger data set studies, Mukhopadhyay et al. (2010) investigate the seismic attenuation (Q−1 factors) using the Multiple Lapse Time Window Analysis (MLTWA) technique. In a region similar to ours, Monika et al. (2020) explores the body-wave Q−1 factors using similar methods as we used. Seismic tomography studies attempted in this region (Gupta et al., 2022; Mahesh et al., 2012) using local earthquakes relate their observed anomalous velocity variations with the possible partial melts and diverse metamorphism. Similarly, Sheehan et al. (2014) observed a zone characterized by high body wave attenuation and low \(\left( {\frac{{V_{\alpha } }}{{V_{\beta } }}} \right)\) beneath the Lesser Himalaya in Nepal.

An unresolved issue in Kumaun Himalaya is the relative contributions of the Qi (quality factor corresponding to instrinsic attenuation) and Qs (quality factor corresponding to the scattering attenuation), which enhance the knowledge of crustal properties beneath Kumaun Himalaya. Scattering attenuation (Qs−1) signifies the heterogeneity of the rocks in the crust that rearranges the seismic energy without loss whereas Qi−1 characterizes the intrinsic anelasticity that changes the seismic energy into frictional heat, mostly along grain boundaries, and is closely associated with high temperature or heat flow. Thus, we envisage providing a detailed attenuation study (based on various estimates of Q−1 from various phases of the seismograms) for Kumaun Himalaya, thereby enabling the analysis of crustal rock structure for seismic hazard assessment, which will act as highly valuable inferences for both the seismologists and engineers. The single scattering model (Aki & Chouet, 1975) has been used to calculate Qc values, the coda normalization (CN) (Aki, 1980) and the extended coda normalization (ECN) methods (Yoshimoto et al., 1993) to obtain body wave Q values in the frequency range 1 to 20 Hz.

2 Seismotectonic Setting and Broadband Data Acquisition

The study region is Kumaun Himalayan region (latitude 29°N–31°N, longitude 78°E–81°E), which forms a part of the Himalayas, resulting from the underthrusting of the Indian plate with the Eurasian continental plate, after the closure of the Tethys Ocean and a following long geological evolution. The surface expression of major tectonic features of the region comprises the STD, MCT, MBT and MFT. The LH segment is structurally bounded by the MBT and MCT zone and consists of predominantly Precambrian clastic sediments. The HH segment is bounded by the lower limit of MCT zone and STD, comprising early Cambrian metasedimentary rocks. The data set consists of the broadband seismograms recorded during June 2005–June 2008 in a seismograph network operated by CSIR National Geophysical Research Institute. Figure 1 shows the seismic network along with the major tectonic features (see also Mahesh et al., 2013). Table 1 shows the details of stations considered in this study, which are segregated as per the LH and HH segments. The broadband stations are installed with Guralp CMG-3 T triaxial broadband seismometer (having a flat velocity response in 0.0083-Hz (120-s period) to 50-Hz frequency range). They are attached to 24-bit (Reftek/Trimble make) RT-130/1 digital data acquisition system and synchronized by global positioning system (GPS). The broadband stations were located on rock or stiff soil profiles and also observed to have minimum noise interference. The data were recorded at a sampling rate of 50 samples/s, and periodic maintenance was undertaken to ensure that all the stations were synchronized and operating in continuous mode.

Fig. 1
figure 1

a Tectonic map of Kumaun Himalaya shown with 32 broadband seismic stations (blue triangles). MFT Main Frontal Thrust, MBT Main Boundary Thrust, MCT Main Central Thrust, STD Southern Tibet Detachment. b The sampled study region showing the ray paths of local earthquakes (blue stars) and recording stations (red triangles) used in the estimation of seismic attenuation

Full size image
Table 1 Details of the broadband recording stations used in this study for investigating seismic attenuation, which are segregated under the Lesser Himalaya (LH) and the Higher Himalaya (HH) segments
Full size table

3 Methodology and Data Analysis

In this study, about 300 local earthquakes and corresponding digital broadband seismograms recorded at 32 seismic stations across Kumaun Himalaya were selected based on good S/N (signal to noise ratio, S/N > 2) and clear P-wave and S-wave arrivals. The magnitude of the selected local events is < 5 and focal depths < 25 km (for details, see Mahesh et al., 2012, 2013). The seismograms were Butterworth bandpass (4 pole) filtered at five central frequencies: 1.5 (1–3 Hz), 3 (2–4 Hz), 6 (4–8 Hz), 8 (6–10 Hz), 12 (8–16 Hz) and 18 (12–24 Hz). The P-wave analysis is based on vertical (Z) component seismograms, and the S-wave analysis is based on E-W (east-west) and N-S (north-south) component seismograms. Figure 2 shows the sample data processing steps and bandpass filtering on a raw seismogram for station GTH.

Fig. 2
figure 2

Original and filtered seismograms of an event recorded at GTH (Gaithi) seismic station for six central frequencies (C.F.) (1.5, 3, 6, 8, 12 and 18 Hz)

Full size image

In the first part, Qc values are estimated, assuming the single backscattering model proposed by Aki and Chouet (1975). In this model, the outgoing body waves are scattered only once before reaching the recording station. The coda waves as seen in the decreasing tail portion of a seismogram, are interpreted as backscattered body waves generated by multiple small-scale heterogeneities existing in the crust and upper mantle. Using the Aki (1980) model, the coda amplitude in a seismogram, as a function of central frequency, f, in a certain narrow bandwidth, and the lapse time, t, which is measured from the origin time of the earthquake, can be expressed as:

$$A_{c} \left( {f,t} \right) = S\left( f \right)t^{ - \gamma } e^{{\frac{ - \pi ft}{{Q_{c} }}}} ,$$
(1)

where S(f) is the source function at frequency f. Here, factor γ is the geometrical spreading factor, and Qc is the apparent quality factor of the coda waves associated with the attenuation in the medium. Considering γ = 1, representative of scattered body waves, the above Eq. (1) can be re-written as

$$\ln \left[ {A_{c} \left( {f,t} \right)t} \right] = \ln S\left( f \right) - \left( {\frac{\pi f}{{Q_{c} }}} \right)t$$
(2)

The above linear Eq. (2) has a slope − πf/Qc, from which Qc can be estimated.

The coda spectral amplitude, AC(f,tC), is derived from the root mean square (r.m.s) amplitude for the time window of 5 s for different lapse times. A sliding time window (or moving average) of size 250 data samples (corresponding to 5 s) is used and then advanced through the window lengths from 20 to 50 s corresponding to different lapse times. Figures 2 and 3 show the example steps in data processing for Qc estimation for the seismic station GTH.

Fig. 3
figure 3

Variation of \(\ln \left[ {A_{c} \left( {f,t} \right)t} \right]\) with lapse time t at the six central frequencies for the seismograms as shown in Fig. 2

Full size image

In the second part, the coda normalization (CN) method introduced by Aki (1980) and modified as extended coda normalization (ECN) method, by Yoshimoto et al. (1993) is used to compute Qβ, Qα. The CN method is suggested as a single-station method to normalize the spectral amplitude of the earthquake source by that of the coda waves at fixed lapse time, which is done here by comparing S wave (or P wave) and coda wave amplitudes of events at different hypocentral distances, followed by the division of the amplitude of direct S-wave by the coda amplitude measured at fixed lapse times tc.

The spectral amplitude of the direct S wave, As(f,r), is expressed as

$$A_{s} \left( {f,r} \right) = R_{\theta \emptyset } I\left( f \right)S_{s } \left( f \right)G\left( f \right)r^{ - \gamma } e^{{\left[ {\frac{ - \pi fr}{{Q_{\beta } \left( f \right)V_{\beta } }}} \right]}} ,$$
(3)

where Rθϕ is the source radiation pattern, γ is the geometrical spreading exponent, Qβ(f) is the S wave quality factor, and Vβ is the average S wave velocity.

For lapse times greater than roughly twice the direct S-wave travel time, and considering the effects of factors like the coda excitation factor P(f, tc), source spectral amplitude of S waves Ss(f), site effect G(f) and the recording instrumental response I(f), the spectral amplitude of the coda wave is expressed as

$$A_{c} \left( {f, t_{c} } \right) = S_{s } \left( f \right)P\left( {f,t_{c} } \right)G\left( f \right)I\left( f \right).$$
(4)

After dividing Eq. (3) by Eq. (4), and taking the natural logarithm, we get the equation for attenuation of the direct S waves as

$$\left[ {ln\left( {\frac{{A_{s} \left( {f,r} \right)r^{\gamma } }}{{A_{c} \left( {f, t_{c} } \right)}}} \right)} \right] = \frac{ - \pi f}{{Q_{\beta } \left( f \right)V_{\beta} }}r + {\text{constant}}\left( f \right).$$
(5)

In the above Eq. (5), division by the coda amplitudes is presumed to remove the site effects so that amplitudes from different stations can be compared. Another assumption is that averaging over a number of S waves from events at different azimuths diminishes the effect of the radiation pattern, Rθϕ. Here, Qβ can be computed from the linear regression of \(\left[ {ln\left( {\frac{{A_{s} \left( {f,r} \right)r^{\gamma } }}{{A_{c} \left( {f, t_{c} } \right)}}} \right)} \right]\) versus hypocentral distance and r by means of least squares method.

The same methodology as used in the CN method is extended to P-wave ECN method as proposed by Yoshimoto et al. (1993) for direct P wave. The ECN method stands on the assumption that earthquakes within a small magnitude range (in this study, M < 5) have the same spectral ratio of P to S wave radiation within a narrow frequency range and existence of a proportionality among the coda spectral amplitude, Ac, the source spectral amplitude of S waves, SS, and the source spectral amplitude of P waves, SP, as follows:

$$A_{c} \left( {f, t_{c} } \right) \propto S_{s } \left( f \right) \propto S_{P } \left( f \right),$$
(6)

which implies that we can use the spectral amplitude of the S-wave coda for the normalization of P-wave spectral amplitude. Using Yoshimoto et al. (1993), a similar equation for P waves is expressed as

$$\left[ {{\text{ln}}\left( {\frac{{A_{p} \left( {f,r} \right)r^{\gamma } }}{{A_{c} \left( {f, t_{c} } \right)}}} \right)} \right] = \frac{ - \pi f}{{Q_{\alpha } \left( f \right)V_{\alpha } }}r + {\text{constant}}\left( f \right),$$
(7)

where Vα is the average P wave velocity. Qα (for P waves) is obtained from the linear least squares regression of \(\left[ {{\text{ln}}\left( {\frac{{A_{p} \left( {f,r} \right)r^{\gamma } }}{{A_{c} \left( {f, t_{c} } \right)}}} \right)} \right]\) versus hypocentral distance, r.

It is also observed that the CN and ECN methods are effective techniques for combining amplitudes from different earthquakes and stations of a sub-region on the same plot to assess the average attenuation characteristics of that sub-region by estimating the Qβ and Qα, respectively, from slopes using Eqs. (5) and (7). In this paper, we report direct body wave Q values determined after fixing the geometrical spreading as r−1 (with γ = 1) and letting Q vary with frequency so that these estimates can be comparable to other studies that use frequency-dependent Q estimates.

The scatterers accountable for the generation of coda waves are largely assumed to be distributed over the surface area of an ellipsoid (Pulli, 1984; Sato, 1978) and can be computed from relations such as

$$\frac{{X^{2} }}{{\left( \frac{vt}{2} \right)^{2} }} + \frac{{Y^{2} }}{{\left( {\frac{vt}{2} - r} \right)^{2} }} = 1,$$
(8)

where X and Y denote the major and minor axes of the ellipsoid; r is the distance between the earthquake source and the recording station; v and t represent the velocity of S wave (3.4 km/s; Mahesh et al., 2013) and lapse time (40 s), respectively. As per Aki and Chouet (1975), if r equals zero, then the Eq. (8) represents the circular area of radius vt/2, i.e., 68 km and a circular area (of scatterers) of 14,519 km2.

The third part of the computation consists of the extraction of the quality factors corresponding to intrinsic and scattering attenuation, namely, Qi and Qs. In recent years, several researchers have attempted to separate the contribution of intrinsic and scattering attenuation. According to Zeng et al.(1991) and Wennerberg (1993), Qi and Qs can be estimated from Qc and Qβ as

$$Q_{{\text{c}}}^{ - 1} = Q_{{\text{i}}}^{ - 1} + \frac{{\left\{ {1 - 2\delta \left( \tau \right)} \right\}}}{{Q_{s} }},$$
(9)

where

$$\delta \left( \tau \right) = \frac{0.72}{{\left( {4.44 + 0.738\tau } \right)}} - 0.5,$$
(10)
$$\tau = \frac{\omega t}{{Q_{{\text{s}}} }},$$
(11)

and ω and t are the angular frequency and the lapse time respectively.

If Qd describes the total quality factor for direct S waves, it can be expressed as the sum of inverse of intrinsic and scattering attenuation, as

$$\frac{1}{{Q_{{\text{d}}} }} = \frac{1}{{Q_{{\text{i}}} }} + \frac{1}{{Q_{{\text{s}}} }}.$$
(12)

From which Qs and Qi are derived as follows (Wennerberg, 1993):

$$\frac{1}{{Q_{{\text{s}}} }} = \left\{ {\frac{1}{2\delta \left( \tau \right)}} \right\}\left\{ {\frac{1}{{Q_{{\text{d}}} }} - \frac{1}{{Q_{{\text{c}}} \left( \tau \right)}}} \right\},$$
(13)
$$\frac{1}{{Q_{{\text{i}}} }} = \left\{ {\frac{1}{2\delta \left( \tau \right)}} \right\}\left\{ {\frac{1}{{Q_{{\text{c}}} \left( \tau \right)}} + \frac{{\left[ {2\delta \left( \tau \right) - 1} \right]}}{{Q_{{\text{d}}} }}} \right\}.$$
(14)

Considering Eqs. (8) to (14), Qs is obtained from the positive root of the quadratic equation:

$$4.44\left( { \frac{1}{{Q_{{\text{d}}} }} - \frac{1}{{Q_{{\text{c}}} }}} \right)Q_{{\text{s}}}^{2} + \left[ {0.738\left( {\frac{1}{{Q_{{\text{d}}} }} - \frac{1}{{Q_{{\text{c}}} }}} \right)\omega t - 5.88} \right]Q_{{\text{s}}} - 0.738\omega t = 0,$$
(15)

and Qi is similarly obtained from the positive value of Qs as:

$$Q_{{\text{i}}} = Q_{{\text{d}}} \left( {\frac{{Q_{{\text{s}}} }}{{Q_{{\text{s}}} - Q_{{\text{d}}} }}} \right).$$
(16)

The root mean square (rms) amplitudes of the coda waves were determined for each waveform in each frequency band, with the window lengths at 5 s. Figures 2 and 3 show the example steps in data processing for Qc estimation for the seismic station GTH.

4 Results and Discussion

The computations and the corresponding seismic attenuation models are separately shown below for Qc, Qβ, Qα, Qi and Qs.

4.1 Seismic Attenuation Model from Q c

As shown in Figs. 2 and 3, the outline of the estimation of Qc is depicted for the representative seismic station GTH. The average Qc values were obtained after averaging all the individual Qc values. The estimates of Q0 and n along with 1σ (standard deviation) for different stations and different lapse times are shown in Table 2. In Table 3, we show the estimated values of the quality factors Qc for each lapse time window (LTW) and at different (six) central frequencies (CFs). The frequency-dependent Qc(f) for the entire region is also shown.

Table 2 Estimated values of the coda quality factors Q (at 1 Hz) and exponent of frequency dependence ‘n’ along with corresponding ± 1 standard deviation (1σ) for different lapse time windows (LTWs)
Full size table
Table 3 Estimated values of the quality factors Qc for each lapse time window (LTW) and at six central frequencies (CFs). The frequency-dependent Qc (f) for the entire region is also shown
Full size table

Figure 4 shows the variation of Q0 (Q at 1 Hz) and n (frequency-dependence coefficient) with lapse time windows from 20 to 50 s in Kumaun Himalaya. Q0 increases in general with lapse times, whereas the values of n decrease. This is interpreted as the frequency-dependent nature of the attenuation mechanism in the tectonically active Kumaun Himalaya. The reason for different estimates of Qc for short and longer lapse times can be explained by the different volumes of ellipsoidal region mapped and with decreasing heterogeneity in the crust (Akinci et al., 1995; Ibanez et al., 1990; Roecker et al., 1982). The frequency-dependent coda-wave attenuation (Qc−1) in Kumaun Himalaya is evident in Figs. 3, 4 and Table 3. Several studies (Aki, 1980; Pulli & Aki, 1981; Roecker et al., 1982) have reported a correlation between n and tectonic activity.

Fig. 4
figure 4

Average values of Q0 (left side) and n (right side) as functions of lapse time window (LTW). Standard deviations (± 1σ) are shown as error bars

Full size image

4.2 Seismic Attenuation Model from Body Waves

Table 4 shows the estimated values of the body wave quality factors Qβ, Qα at six central frequencies (CFs; 1.5, 3, 6, 8, 12 and 18 Hz). The frequency-dependent Qβ(f) and Qα(f) for the entire region are also shown.

Table 4 Estimated values of the body wave quality factors Qβ, Qα at the six central frequencies (CFs). The frequency-dependent Qβ(f) and Qα(f) for the entire region are also shown
Full size table

For estimation of Qβ, the plots of \(\left[ {{\text{ln}}\left( {\frac{{A_{\beta } \left( {f,r} \right)r^{\gamma } }}{{A_{{\text{c}}} \left( {f, t_{{\text{c}}} } \right)}}} \right)} \right]\) versus hypocentral distance, r (at γ = 1), for the different central frequencies were plotted for different events and stations (see Akinci and Eyidogan, 1996; Frankel, 1991) as shown in Fig. 5. Using the ECN method, as described in the previous section, for estimation of Qα, the plots of \(\left[ {{\text{ln}}\left( {\frac{{A_{\alpha } \left( {f,r} \right)r^{\gamma } }}{{A_{{\text{c}}} \left( {f, t_{{\text{c}}} } \right)}}} \right)} \right]\) versus hypocentral distance, r, for the different central frequencies were plotted for different events and stations, as shown in Fig. 6. In both Figs. 5 and 6, the regression lines from the least-squares estimate are shown in red color. The values of Qβ and Qα obtained from slopes of the least-squares fits are shown for each central frequency. The linear least squares regression provides the average values of the quality factor.

Fig. 5
figure 5

Coda normalized peak amplitude decay of S waves with hypocentral distance at six central frequencies (1.5, 3, 6, 8, 12 and 18 Hz). The regression lines from the least-squares estimate are shown in red color. The values of Qβ obtained from slopes of the least-squares fits are shown for each central frequency

Full size image
Fig. 6
figure 6

Coda normalized peak amplitude decay of P waves with hypocentral distance at six central frequencies (1.5, 3, 6, 8, 12 and 18 Hz). The regression lines from the least-squares estimate are shown in blue color. The values of Qα obtained from slopes of the least-squares fits are shown for each central frequency

Full size image

4.3 Intrinsic (Q i −1) and Scattering Attenuation (Q s −1)

The knowledge of the proportionate contributions of intrinsic attenuation (Qi−1) and scattering attenuation (Qs−1) to the total attenuation is quite useful to interpret the mechanism of seismic wave energy dissipation. The contributions of scattering and intrinsic attenuation are extracted using Wennerberg’s (1993) formulation, using the independent estimates of Qc (a lapse time of 40 s) and Qβ. The estimated values of Qi and Qs at six central frequencies are shown in Table 5. Similarly, Table 6 shows the frequency-dependence relations for Qs and Qi. The estimated values of Qi and Qs indicate an increase with frequency. As shown in Fig. 7, the relations obtained by using least-squares regression analysis are Qi = (231 ± 0.2)f(0.77 ± 0.01) and Qs  = (67 ± 0.5)f(0.99 ± 0.07). This study shows that the intrinsic attenuation (Qi−1) is less dominant over scattering attenuation (Qs−1) in the frequency range 1.0–20 Hz. As mentioned earlier, dominant scattering attenuation parameter (Qs−1) describes the crustal inhomogeneity in the study region due to a multitude of cracks and pores. For comparative analysis of different tectonic regions, such as LH and HH segments, within our study region, we perform comparative analysis as described in subsequent sections below and as depicted in Fig. 8a–d.

Table 5 Separation of Qc (at LTW = 40 s) in terms of Qs and Qi using Qβ by Wennerberg formulations
Full size table
Table 6 Frequency-dependence relations for scattering factor, Qs and intrinsic factor, Qi
Full size table
Fig. 7
figure 7

Variation of Qc−1, Qβ−1, Qα−1, Qsc−1 and Qi−1 with frequency (Hz) for the Kumaun Himalaya in this study

Full size image
Fig. 8
figure 8figure 8figure 8figure 8

a Coda normalized peak amplitude decay of S waves with hypocentral distance at the six central frequencies for stations in Lower Himalaya (LH) segment. The regression lines from the least-squares estimate are shown in red color. The values of Qβ obtained from slopes of the least-squares fits are shown for each central frequency, and the frequency-dependent power law is shown in red. b Coda normalized peak amplitude decay of P waves with hypocentral distance at the six central frequencies for stations in LH segment. The regression lines from the least-squares estimate are shown in blue color. The values of Qα obtained from slopes of the least-squares fits are shown for each central frequency, and the frequency-dependent power law is shown in blue. c Coda normalized peak amplitude decay of S waves with hypocentral distance at the six central frequencies for stations in Higher Himalaya (HH) segment. The regression lines from the least-squares estimate are shown in red color. The values of Qβ obtained from slopes of the least-squares fits are shown for each central frequency, and the frequency-dependent power law is shown in red. d Coda normalized peak amplitude decay of P waves with hypocentral distance at the six central frequencies for stations in HH segment. The regression lines from the least-squares estimate are shown in blue color. The values of Qα obtained from slopes of the least-squares fits are shown for each central frequency, and the frequency-dependent power law is shown in blue

Full size image

To understand the relation between Qc−1 and Qi−1 for the whole region to obtain a broader sense, we observe from Fig. 7 that Qc−1 is close to Qi−1. These observations are in good agreement with other worldwide studies carried out in tectonic regions (Akinci et al., 1995; Bianco et al., 2002; Frankel & Wennerberg, 1987). In this way, Fig. 9 shows the relation between Qc−1 vs. frequency (Hz) of this study compared to other studies. We provide comparisons with Qc−1 studies, such as Paul et al. (2003) (Kumaun Himalaya); Kumar et al. (2005) (northwest Himalaya, India); Mukhopadhyay et al. (2006) (western Himalaya, India); Sharma et al. (2008) (Kachch, India); Mukhopadhay et al. (2010) (Garhwal-Kumaun Himalaya); Hazarika et al. (2013) (Sikkim Himalaya, India); Mishra et al. (2020) (northwest Himalaya, India); Padhy et al. (2011) (Andaman, India). Similarly, Figs. 10, 11 and 12 show the essential relations between Qβ−1, Qα−1 with frequency (Hz) and between Qβ and Qα for this study and compared to other studies. We compare with studies such as Yoshimoto et al. (1993) (in Kanto region, Japan); Chung and Sato (2001) (in southeastern Korea); Sharma et al. (2008) (in Kachch, India); Padhy et al. (2011) (in Bhuj, India); Singh et al. (2012) (in Kumaun Himalaya); Hazarika et al. (2013) (in Sikkim Himalaya, India); Tripathi et al. (2014) (in Garhwal Himalaya, India); Monika et al. (2020) (in Kumaun Himalaya); Ma and Huang (2020) (in Central and Western Tien Shan); Castro et al. (2021) (in Central Apennines, Italy). We observe that the ratio Qα−1/Qβ−1 > 1 for the entire frequency range considered. So, in the broader sense, these observations are in agreement with the above studies and with earlier works (such as Canas et al., 1998; Del Pezzo et al., 1995; Giampiccolo et al., 2004; Rautian & Khalturin, 1978). Now, we discuss the observations regarding the two considered tectonic segments in the study region.

Fig. 9
figure 9

Comparison of Qc−1 with frequency (Hz) of our study with other studies

Full size image
Fig. 10
figure 10

Comparison of Qβ−1 of our study with other studies in India and other parts of the world

Full size image
Fig. 11
figure 11

Comparison of Qα−1 with frequency (Hz) of our study with other studies in India and other parts of the world

Full size image
Fig. 12
figure 12

Comparison of variation of Qβ, Qα \({\text{and evaluation of the }}\left( {\frac{{Q_{\beta } }}{{Q_{\alpha } }}} \right)\) ratio obtained in this study and as reported by other studies in India and other parts of the world

Full size image

5 Observed Patterns Among LH and HH Segments

We provide a more refined perspective of the body wave attenuation characteristics across the LH and HH segments, which has a wider implication for structure and geotechnical analysis. We show the estimations for Qβ, Qα for the LH and HH segments in Fig. 8a–d and Table 7. We observe that the LH segment has higher values Qβ, Qα at each of the six frequencies and at 1 Hz (Q0). The higher values of Qβ, Qα (implying lower attenuation, Qβ−1, Qα−1) beneath the crust in the LH segment (as compared to HH segment) might be correlated to the underthrusting Indian Plate, leading to the fractures, brittle conditions and earthquake ruptures in the crust and uppermost mantle. It is also possible that the diversified geological features and/or varying fluid content in LH may give rise to lower attenuation, Qβ−1, Qα−1 (compared to HH segment). Thus, the LH seems to be differentiated from the HH segments in terms of higher extent of fractures and fluids/partial-melts.

Table 7 Estimated values of the body wave quality factors Qβ, Qα at six central frequencies (CFs) and frequency-dependent Qβ(f), Qα(f) for the LH and HH segments
Full size table

6 Geological Implications

In line with the above observations of Qα−1/Qβ−1 > 1, and the predominance of (Qs−1) over (Qi−1), our investigation seems to indicate the presence of heterogeneities in the form of cracks and pores, possibly related to the multi-scale deformation of the Indian lithosphere. Figure 13 shows the variations of (Qi−1), which are compared with other studies, such as, Sharma et al. (2008) (in Kachch, India); Padhy and Subhadra (2013) (in northeast India); Mukhopadhyay et al. (2010) (in Garhwal-Kumaun Himalaya); Hazarika et al. (2013) (in Sikkim Himalaya, India); Del Pezzo et al. (2019) (in Peloritani Mountains, Italy); Akinci et al. (2020) (in Central Apennines, Italy). The variations of (Qs−1) are shown in Fig. 14, along with comparisons with other studies, as mentioned above. Similarly, Fig. 15 shows the variation of the Qi−1 and Qs−1 in this study, along with comparisons with above-mentioned studies. Mukhopadhyay et al. (2010) sampled a similar region and have suggested the dominance of scattering attenuation (Qs−1) over intrinsic attenuation (Qi−1). Similar to their results, we also observe that the frequency-dependence parameter ‘n’ of (Qs−1) is larger than that of (Qi−1), further strengthening the argument and evidence of large-scale heterogeneities. Del-Pezzo et al. (2019) (Peloritani Mountains, Italy) show that scattering attenuation is dominant in the active Peloritani mountains (Italy) below 6 Hz. Similarly, Akinci et al. (2020) indicate similar scattering attenuation (Qs−1) as obtained in our study region.

Fig. 13
figure 13

Comparison of Qi−1 with frequency (Hz) of this study and other studies in India and other parts of the world

Full size image
Fig. 14
figure 14

Comparison of Qs−1 with frequency (Hz) of this study and other studies in India and other parts of the world

Full size image
Fig. 15
figure 15

Comparison of Qi and Qs in this study with other studies in India and other parts of the world

Full size image

On the whole, the substantial frequency dependence of the different attenuation quality factors suggests an essentially heterogeneous crust in the Kumaun Himalaya. The present study shows that Qc−1 <  Qβ−1, but Qc−1 is close to Qi−1 (Fig. 7). The study by Shang and Gao (1988) shows that in a highly heterogeneous and scattering medium, the coda attenuation (Qc−1) is identical to (Qi−1). Our results and observations endorse similar findings.

This study also seems to support Zeng’s (1991) radiative transfer theory that Qi−1 and Qs−1 combine in such a way that Qc−1 <  Qβ−1.

Also, the ratio, (Qα−1/Qβ−1) (> 1 in our study; as in Fig. 12), indicates a high degree of heterogeneity of the rocks in the crust beneath Kumaun Himalaya. In our study region, the P-wave attenuation seems to be more than S-waves. The ratio, Qα−1/Qβ−1, in our study varies between 1.7 and 2.2. Earlier studies like Yoshimoto et al. (1993) and Rautian and Khalturin (1978) found that the ratio, Qα−1/Qβ−1, is close to the ratio, Vα/Vβ (~ 1.73) (Vα is the P-wave velocity; Vβ is the S-wave velocity) value for crustal rocks in their study regions. As per Winkler and Nur (1982) (see Fig. 5 of this reference), Qα−1/Qβ−1 ratio is between 1.5 and 2, and Vα/Vβ varies between 1.5 and 1.75 for partially saturated (~ 90%) rocks. A high Vα/Vβ ratio possibly indicates a fluid or melt state in rocks as indicated in tomographic studies (Mahesh et al., 2012). The presence and release of fluids cause permeation upwards into the brittle part of the crust, thereby reducing the fault zone friction and leading to the generation of crustal earthquakes. According to a recent tomography study by the authors (Gupta et al., 2022), the small-, moderate- and strong-magnitude earthquakes are largely restricted to the fluid-trapped portions and quartz-rich rocks in the upper crust, seemingly with a geometrical alignment of the crustal lithology. The studies conducted in similar regions (such as in Mishra et al., 2020; Monika et al. 2020; Singh et al., 2012; Tripathi et al., 2014) and other heterogenous and active regions (such as Kanto region, Japan, Yoshimoto et al., 1993; Central-East Iran, Mahood et al., 2009; Bhuj region, India, Padhy et al., 2011) indicate a prominent observation of Qα−1/Qβ−1 > 1. From a perspective of seismic hazard, recent studies in east Asia have investigated the spatial and temporal variations in the crust from shallow earthquakes to understand the cyclic behavior of the occurrence of cracks and their healing (Iqbal et al., 2021). They conclude that the estimates of scattering attenuation (Qs−1), before and after occurrence of events, are powerful means to assess the variations in crustal inhomogeneity due to cracks. Thus, the seismicity in Kumaun Himalaya may enhance the crustal inhomogeneity, thereby presenting a predominantly scattering attenuation model.

In other tectonic domains with intrinsic attenuation (Qi−1), the role of increased temperature is often suggested in grain boundary sliding beneath the crust, having temperatures > 900 °C. The increased temperature then becomes the primary controlling factor in attenuation (Mitchell, 1995) as the deformation behavior is altered from elastic to anelastic to viscous (Jackson et al., 2002). The hydrothermal reactions cause fluids to rise upward through cracks while allowing them to reside predominantly in the upper crust. Furthermore, the cracks filled with liquids, as aforementioned, affect the attenuation mechanism related to P and S waves. Ashish et al. (2009) have suggested the existence of Miocene leucogranite plutons, a magmatic byproduct resulting from the Indo-Asian collision.

In general, our results provide a first-order characterization of the nature of the crustal rocks and seismic attenuation and are seen to match well with other active regions. Our results show that the LH and HH segments are well differentiated in terms of rock lithology and the scattering attenuation is the dominant mechanism of seismic attenuation in the whole study region. We note that model assumptions might result in simplification of a complex structure, as observed by various researchers. We believe that this study of seismic attenuation in such a complex region can add information which are playing a fundamental role in active tectonic settings. A comparative analysis of different modeling techniques may bring out deeper insights, which may be explored in future studies.

7 Conclusions

Seismic wave attenuation in the Kumaun Himalaya has been estimated using body and coda waves at 1–20 Hz using about 300 local events. Seismic attenuation is analyzed for the entire study region and distinct tectonic belts such as the Lesser Himalaya (LH) and the Higher Himalaya (HH) segments. Coda wave attenuation (Qc−1) and body wave attenuation [Qα−1 (P-wave), Qβ−1 (S-wave)] were estimated using single isotropic-scattering model and extended coda-normalization method, respectively. The estimated attenuation mechanisms show a strong dependence on frequency, expressed as power laws (Qc = Q0fn). From our Qc analysis, Q0 and n vary as 320 and 0.78 for lapse time window 20 s to 656 and 0.55 at lapse time window 50 s. The body waves Q are expressed as Qα = (36.28 ± 0.05)f(0.85±0.01) and Qβ = (50.58 ± 0.15)f(0.94±0.01). We observe that the ratio Qα−1/Qβ−1 is larger than unity for the whole frequency range, which is interpreted as the effect of seismically active regions and heterogeneous crustal regimes. The heterogeneities, however, may be varied and the result of fractures and the presence of pore fluids or partial melts in the upper crust. Additionally, we show that the Lesser Himalaya (LH) and the Higher Himalaya (HH) segments are characterized by differentiated rock lithology, with possible roles of underthrusting and deformation. Apart from that, the extracted intrinsic absorption (Qi−1) and scattering (Qs−1) attenuation indicate the dominance of scattering attenuation (Qs−1). The results also show that (1) Qc−1 is less than Qβ−1; (2) the ratio (Qα−1/Qβ−1) lies between 1.7 and 2.25, indicating the presence of partially saturated rocks in the crust beneath Kumaun Himalaya. The LH and HH tectonic segments imply divergent geology, indicate varying attenuative characteristics, and have a significant role in seismic hazard analysis in Kumaun Himalaya.