1 Introduction

The attenuation of seismic waves, expressed by the inverse of the quality factor (Q), is one of the important geophysical parameters characterizing the material through which seismic waves propagate. The two basic methodologies for measuring the attenuation of seismic waves are based on the use of (1) the direct waves, and (2) the coda waves. Aki (1969), Aki and Chouet ( 1975), and Sato (1977) interpreted the coda waves as single backscattered S-to-S waves from heterogeneities in the crust and upper mantle. Since then, the rate of time decay of coda-wave amplitude has been widely used for estimation of coda attenuation (Q −1C ) (Herraiz 1987). Aki (1980) first introduced the coda normalization method to estimate the frequency-dependent Q −1S . Several authors, such as Rautian and Khalturin (1978a), Aki (1980), Herrmann (1980), Roecker et al. (1982), and Campillo et al. (1985), found that Q C and the S-wave Q (Q S) estimated from direct waves or Lg waves are approximately equal. This observational result suggests that the use of coda waves is the easiest way to estimate Q S (Novelo-Casanova and Lee, 1991). On the other hand, the model of Zeng et al. (1991) predicts that the effects of intrinsic and scattering attenuation combine in a manner such that Q C should be more than Q S. However, there is still some uncertainty both about how the apparent attenuation inferred from coda waves is related to the attenuation of the direct S waves and about the relative contribution of scattering attenuation and intrinsic attenuation to the coda and S-wave attenuation (Frankel and Wennerberg, 1987; Sato, 1990; Frankel, 1991).

The tool originating from the study of coda waves is the coda normalization method, which is based on the assumption of a uniform spatial distribution of coda energy for long lapse times. The coda normalization method allows one to estimate the difference of site amplification factors as a function of frequency, to distinguish differences in source spectral characteristics, and to measure attenuation using data from only a single station (Aki, 1969, 1980; Phillips and Aki, 1986).

There are very few studies on frequency-dependent Q P, e.g., those carried out by Fedotov and Boldyrev (1969), Hough et al. (1988), and Kohketsu and Shima (1985). Yoshimoto et al. (1993) proposed a new method for simultaneous measurement of Q P and Q S by extending the conventional coda normalization method, earlier developed by Aki (1980). This method has been successfully applied further to obtain both P and S wave attenuation for a few places globally, such as Kanto, Japan by Yoshimoto et al. (1993); Western Nagano, Japan by Yoshimoto et al. (1998); South-Eastern Korea by Chung and Sato (2001); central South Korea by Kim et al. (2004); Koyna, India by Sharma et al. (2007); Bhuj, India by Padhy (2009); Cairo metropolitan area by Abdel-Fattah (2009); East-Central Iran by Ma’hood et al. (2009); Kumaun Himalaya, India by Singh et al. (2011); Kinnaur Himalaya, India by Kumar et al. (2014); and Northeast India by Padhy and Subhadra (2010). We also adapt the method of extended coda normalization.

Taylor et al. (1986) briefly defined the limitations involved with the lack of broadband data and single phase data in studying body wave attenuation characteristics. Such studies may suffer from some fundamental problems because many attenuation mechanisms are thermally activated and vary with physical properties and/or composition and will thus show variations with depth. Furthermore, some attenuation mechanisms are activated by either shear or compressional motion and therefore exhibit different frequency dependence and magnitude for P and S waves. The different frequency dependence of P and S waves therefore obliges one to study both primary and shear waves simultaneously. Here, we utilize broadband data to estimate the frequencies, where the effects due to scattering become dominant over intrinsic effects at higher frequencies (Taylor et al., 1986).

Also, regional attenuation properties are very important when comparing seismic travel-time differences (Liu et al., 1976). The importance of phase velocity dispersion arising from anelasticity has been discussed by various researchers (e.g., Lomnitz 1957; Jeffreys, 1965; Randall, 1976). Thus, the frequency dependence of seismic attenuation in the earth’s crust is crucial for correcting the velocity dispersion due to anelasticity. The attenuation properties as discussed by Karato (1993) are also very important in the interpretation of seismic tomography.

We have applied the single-station method based on the rate of decay of the P and S wave to the coda-wave amplitude ratio over distance for different frequencies. This method has been applied by Rautian and Khalturin (1978b), Aki (1980), and Roecker et al. (1982) to determine the attenuation of S waves for the Garm region, Tajikistan, the Kanto region, Japan, and Central Asia, respectively. Earlier studies in the Garhwal region mainly focused on attenuation of coda waves (Gupta and Kumar, 2002; Gupta et al., 1995; Mukhopadhyay et al., 2010). Here, we make an attempt to study and constrain the frequency dependence of body wave characteristics (Q P and Q S) in the Garhwal region of Northwest Himalaya.

2 Seismotectonic Settings of the Study Region

The emergence of Himalaya due to the ongoing convergence of the Indian and Eurasian Plates since 50 Myrs has accommodated nearly 2,000 km of crustal shortening in its postcollisional phase (Molnar and Tapponier, 1975). This resulted in a high level of tectonic activity developing the major tectonic boundaries striking northwest-southeast, viz. the Indus–Tsangpo suture zone (ITSZ), South Tibetan Detachment (STD), and prominent intracontinental thrust boundaries such as the Main Central Thrust (MCT), Main Boundary Thrust (MBT), and Himalayan Frontal Thrust (HFT) (Fig. 1c). All these tectonic boundaries are suggested to root into a low-angle detachment, the Main Himalayan Thrust (MHT) (Schelling and Arita, 1991; Fig. 1c). The tectonic zones characterized between these major tectonic boundaries in continuation from north to south descend from the Tethys Himalaya, Higher Himalaya, Lesser Himalaya to the Siwalik or Sub-Himalaya. The present study area, the Garhwal region, lies in the northwestern part of the Himalaya and shows development of all four tectonic zones (Fig. 1a, b). The presence of transverse tear faults along the entire Himalayan arc splits the area into different blocks along which neotectonic movement and related seismicity take place (Paul, et al., 2004). Nath et al. (2008) divided the northwest Himalaya into different active tectonic zones, where the Garhwal zone is delimited in the east and west by the Kumaun and Kinnaur active tectonic zones (Fig. 1b). These zones have experienced a number of damaging earthquakes in the past, as is evident from the recorded seismic history of this region. The Garhwal and the adjacent Kumaun region have experienced a total of 13 earthquakes with magnitude ≥6.0 recorded in the last 100 years (Rastogi, 2000). Ni and Barazangi (1984) suggested that the majority of earthquake epicenters lie just south of the surface trace of the MCT. In Garhwal Himalaya, the MCT is present at the base of the crystalline zone, inclining at a varying dip from 30° to 45° northward forming a large-scale zone of intense shearing (Gansser, 1964; Valdiya, 1980). It divides the predominantly high-grade metamorphic crystalline rocks of Higher Himalaya in the north from the low- to medium-grade unfossiliferous metasedimentary rocks of Lesser Himalaya to its south (Searle 1986). In the present study, more than 80 % of the seismic activity is observed around the surface of detachment, i.e., the MHT, which lies at about 12–15 km depth beneath Lesser and Higher Himalaya. This indicates that the MHT in most cases has been responsible for generating the Himalayan earthquakes (Pandey et al. 1999; Monsalve et al. 2006; Mahesh et al. 2013). Studying the attenuation properties of seismic waves in such a complex tectonic setting therefore provides an opportunity to augment our understanding of the medium properties.

Fig. 1
figure 1

a Tectonic map of the Garhwal–Kumaun region of northwest Himalaya, showing the major tectonic units in the region (modified after Thakur and Rawat, 1992). b Location of study area shown by square (in transparent red) in the SRTM image of India. Arrows show the direction of movement of the Indian and Eurasian Plates. Dashed rectangles show adjacent regions of Kinnaur and Kumaun Himalaya. c Simplified cross section of the Himalaya showing the main lithotectonic units: ITSZ, Indus–Tsangpo suture zone; STD, South Tibetan Detachment; MCT, Main Central Thrust; MBT, Main Boundary Thrust; HFT, Himalayan Frontal Thrust; MHT, Main Himalayan Thrust [modified after Hauck et al. (1998) and Lave and Avouac (2001)]

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3 Data

A seismic network of 10 broadband stations has been operated by Wadia Institute of Himalayan Geology (WIHG), in the Garhwal Himalaya, India, since 2007. We use waveform data from only eight stations installed in the mountainous terrain of Himalaya (Fig. 2). The other two stations, DBN and DDN, are located on thick alluvium sediments of Gangetic Plains, resulting in very high noise in the data. Therefore, we decided not to use the data from these stations in this study. The broadband stations are equipped with a Trillium 240 seismometer with high dynamic range (>138 dB) with a Taurus data acquisition system. The standard frequency bandwidth is 0.05–50 Hz, and three-component data are acquired in continuous mode at 100 samples per second for three components at each station. The data are recorded and monitored at the Central Recording Station (CRS) operating at the earthquake processing center of the Wadia Institute of Himalayan Geology (WIHG), Dehradun, India. We used 40 well-distributed local earthquakes recorded during 2007–2012 in the study region, with 2.5 ≤ M L ≤ 5 (Fig. 2). The hypocentral parameters were determined using the HYPOCENTER location program of Lienert et al. (1986) based on the crustal velocity model by Mahesh et al. (2013) and Kumar et al. (2009). The uncertainties involved in the estimation of epicenter, depth, and origin time are on the order of 0–5 km and 0–0.5 s, respectively. Here, we constrain our study to the crustal level, taking earthquakes with focal depth ≤45 km above Moho, which is nearly horizontal at 35–45 km depth beneath the Sub- and Lesser Himalaya (Caldwell et al., 2013). As mentioned in Sect. 2, the majority of the earthquakes considered in this study lie within depth of 15 km, whereas the hypocentral distance varies from 27 to 200 km.

Fig. 2
figure 2

Tectonic map of Garhwal region (modified after Thakur and Rawat, 1992) showing the earthquake events (blue filled circles). Broadband seismic station locations are shown by triangles (filled black). The tectonic boundaries are described in Fig. 1. Squares (filled red) show important localities (towns) in the study region

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The seismograms of all well-located events were visually examined for any recording problems such as high noise, missed recordings, overlapping, or early cutoff. We analyzed the local earthquake spectra of S, P, and coda-wave windows of 5-s duration where, for each event, the signal-to-noise ratio was >2 over the frequency range of 1.5–16 Hz for both P and S waves.

4 Method

The coda normalization method was first obtained by Aki (1980) to estimate frequency-dependent Q −1S . The coda normalization method was further extended by Yoshimoto et al. (1993) to estimate Q −1P . This method is termed the extended coda normalization method. In the present study, Q P and Q S values for Garhwal Himalaya region were estimated by applying the extended coda normalization method (Yoshimoto et al., 1993).

The method is based on the idea that coda waves consist of scattered S waves from random heterogeneities in the earth (Aki, 1969; Aki and Chouet, 1975; Sato, 1977). The lapse time (t C) is chosen to be >2 times the S-wave travel time (Fig. 3). For lapse times greater than twice the direct S-wave travel time, the spectral amplitude of the coda A C(f, t C) is independent of the hypocentral distance r in the regional distance range (Aki, 1980) and is given by

$$A_{\text{C}} \left( {f, t_{\text{C}} } \right) = S_{\text{S}} \left( f \right) P(f, t_{\text{C}} ) G\left( f \right) I\left( f \right),$$
(1)

where f is the frequency, S S(f) is the source spectral amplitude of S waves, P(f, t C) is the coda excitation factor, G(f) is the site amplification factor, and I(f) denotes the instrumental response. The coda excitation factor P(f, t C) represents how the spectral amplitude of coda waves decays with lapse time.

Fig. 3
figure 3

Example of a horizontal (N–S) component seismogram showing the time of arrival of P, S, and coda waves marked by down arrows. The transparent box (in blue) shows the 5 s window of P, S, and coda waves, where coda is measured at t C = 60 s from the earthquake origin time (O.T)

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Similarly, the direct body wave (P or S) spectral amplitude A i (f, r) (Yoshimoto et al., 1993) for the ith event may be written as

$$A_{i} \left( {f, r} \right) = R_{\theta \phi } S\left( f \right)r^{ - \gamma } { \exp }\left( { - \frac{\pi f}{Q\left( f \right) V}r} \right) G(f, \psi )I(f),$$
(2)

where R θ ϕ is the source radiation pattern and γ denotes the geometrical spreading exponent. The symbol Q(f) is the quality factor of the body wave, V is the average body wave velocity, and ψ represents the incidence angle of the body wave.

The effects of source, site, and instrument can be eliminated, and data from many earthquakes can be combined to obtain a stable estimate of attenuation (Kumar et al., 2014). Due to the wide epicentral distribution of the studied earthquakes, we assume the following:

  1. 1.

    The contribution of source radiation pattern (R θ ϕ ) disappears by averaging over many different focal-plane solutions.

  2. 2.

    After normalizing, the site amplification factor G(f, ψ)/G(f) ratio becomes independent of the incidence angle (ψ) by averaging over many earthquakes.

Under these assumptions, the spectral amplitude of body waves (in this case S wave) given by Eq. 2 divided by the spectral amplitude of coda waves (Eq. 1) gives the normalized source spectral amplitude of S wave according to the following expression:

$$\ln \left[ {\frac{{A_{\text{S}} (f,r)r}}{{A_{\text{C}} (f,t_{\text{C}} )}}} \right] = - \frac{\pi f}{{Q_{\text{S}} (f)V_{\text{S}} }}r + {\text{const}}(f),$$
(3)

where Q S(f) is the quality factor of the S wave and V S is the average S wave velocity in the study region. We can estimate Q S(f) from a linear regression of ln[A S(f, r)r γ/A C(f, t)] versus the hypocentral distance r by means of the least-squares method.

Yoshimoto et al. (1993) extended the coda normalization method by assuming that the ratio of P to S wave source spectra is constant for a small range of magnitudes. The method works based on the proportionality of the coda spectral amplitude A C(f, t C) versus the source spectral amplitude of P and S waves, i.e., S P(f) and S S(f), respectively. This means that we may use the spectral amplitude of the S-coda wave for normalization of the P-wave source spectral amplitude, whence we get Eq. (4) for P wave, similar to Eq. (3).

$${ \ln }\left[ {\frac{{{A}_{\text{P}} (f ,r )r}}{{{A}_{\text{C}} (f ,t_{\text{C}} )}}} \right] = - \frac{\pi f}{{Q_{\text{P}} (f)V_{\text{P}} }}r + {\text{const(}}f ),$$
(4)

where Q P(f) is the quality factor of the P wave and V P is the average P wave velocity in the study region.

This method uses the spectral amplitude of the earthquake source normalized by the spectral amplitude of coda waves at fixed lapse time, enabling us to measure Q P and Q S, at a single station. Using Eqs. (3) and (4), we estimate the slope (m) by linear regression of a plot of the coda-normalized spectral amplitude ln[A S,P(f, r)r γ/A C(f, t)] versus the hypocentral distance (r) by means of the least-squares method, where the slopes for P \((m_{\text{P}})\) and S (\(m_{\text{S}}\)) waves are given as

$$m_{\text{P}} = - \frac{\pi f}{{Q_{\text{P}} V_{\text{P}} }},$$
(5)
$$m_{\text{S}} = - \frac{\pi f}{{Q_{\text{S}} V_{\text{S}} }}.$$
(6)

Since the ratio of P- to S-wave spectra depends on seismic moment or earthquake magnitude, it is necessary to restrict the earthquakes for analysis to a small magnitude range when we estimate Q P by using Eq. (4).

4.1 Analysis

To evaluate the frequency-dependent Q −1(P,S) , we analyzed filtered seismograms where each seismogram was digitally bandpass-filtered using a phaseless four-pole Butterworth filter with the eight passbands given in Table 1. The bandwidths were chosen to maintain relative constant bandwidth. A window length of 5 s was chosen after experimenting with various durations (Fig. 3). Each window is cosine tapered (5 %) and Fourier transformed. The coda spectral amplitude A C(f, t C) is calculated for a 5-s time window centered at fixed lapse time t C = T 0 + 60 s, where T 0 is the earthquake origin time. This is to ensure that t C is twice the S wave travel time or greater (Aki and Chouet, 1975; Rautian and Khalturin, 1978a).

Table 1 Central frequencies with their bandpass limits to filter the waveform
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From the filtered seismograms, we measured the maximum peak-to-peak amplitude of direct P and S waves. Half values of the peak-to-peak amplitudes represent A P(f, r) and A S(f, r), respectively. We used Z-component records for the P-wave analysis. Since the maximum amplitudes of S waves are nearly equal in both the N–S and E–W components, we used the N–S component for the S wave analysis (Fig. 4). We measured the coda spectral amplitude A C(f, t C) from the root-mean-squares (rms) coda amplitude (Kumar et al., 2014) of the N–S component for each frequency band. The observed values were substituted into Eqs. (3) and (4) to estimate Q P and Q S using the least-squares method.

Fig. 4
figure 4

Comparison between the velocity spectra of the north component to the east for a single earthquake at eight stations considered in the present study

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The average velocities V P (6.4 km/s) and V S (3.7 km/s) of the lithosphere were taken from the velocity model given by Mahesh et al. (2013) and Kumar et al. (2009). The structure of the lithosphere beneath the Garhwal Himalaya is very complex, where the Indian Plate interacts with the Tibetan Plate. In these regions, geometrical spreading plays an important role as it affects the decay rate of the seismic wave amplitude (Yoshimoto et al., 1993).

Studying the attenuation properties of S wave in New York State and South Africa, Frankel et al. (1990) reported that Q −1S does not depend on frequency after changing the value of the geometrical spreading exponent (γ) from 0.7 to 1.3. In contrast to those results, Yoshimoto (1993) in a similar attempt for Kanto region reported that the Q −1 values in each frequency band did not change significantly with variation of gamma to 0.75, 1, and 1.25, but the frequency dependence becomes smaller for larger γ. He also explained that the value of γ is 1 for earthquakes with hypocentral depth deeper than the Moho, whereas in case of crustal earthquakes, reflections from the Conrad and/or Moho discontinuity may change the value of γ from 1. However, from their study, the expected apparent trends from the effect of reflections were not found to be satisfactory. Therefore, we take a geometrical spreading exponent γ = 1 in our study region. This gives an inverse power law with hypocentral distance of r −1, which is generally accepted and commonly used for estimation of direct body wave attenuation in the crust (Chin and Aki 1991; Ishida, 1992; Yoshimoto et al., 1993; Singh et al., 2012, Kumar et al., 2014). The coda-normalized amplitude of P and S waves are plotted against hypocentral distance for each station at each frequency band in Fig. 5. To minimize the sum of the absolute deviations of the differences between the data and the data estimated by the model, we applied least-squares fitting as shown in Fig. 5. The slopes in Eqs. (5) and (6) were then used to estimate the quality factor (Q) of P and S waves.

Fig. 5
figure 5figure 5

Coda-normalized peak amplitude decay of P waves (blue circles) and S waves (black circles) with hypocentral distance for stations a ABI, b CKA, and c GKD, at different central frequencies (Table 1). Solid lines indicate least-squares fits for the whole earthquakes for P and S waves, respectively

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5 Results and Discussion

By using the extended coda normalization method given by Yoshimoto et al. (1993), we calculated Q P and Q S for the study region. We found that both quality factors for P (Q P) and S (Q S) depend strongly on frequency (Fig. 6), increasing from about Q P = 88 and Q S = 202 at 1.5 Hz to Q P = 773 and Q S = 1,512 at 16 Hz. The slopes of the best fit lines as indicated in Fig. 5 were used to estimate Q P and Q S for each station using the relations in Eqs. (3, 4) (Table 2). The values of Q P and Q S obtained for each station against frequency were averaged to estimate the Q P and Q S for the Garhwal region (Table 3). The frequency-dependent relations, fitted by a power law, take the form Q = Q 0 f n (where Q 0 is Q at 1 Hz and n is the frequency relation parameter) as shown in Fig. 6 and Table 3. The standard errors represented by the vertical error bars for Q P and Q S are much smaller at low than higher frequencies (Fig. 6). The following power laws were estimated for Garhwal Himalaya region based on the above analysis:

Fig. 6
figure 6

Plots of mean value of Q P and Q S against frequency, for the whole Garhwal Himalaya. A power law of the form Q = Q 0 f n is fitted. Vertical lines are standard error bars

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Table 2 Frequency-dependent values of Q P and Q S for eight stations in Garhwal Himalaya
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Table 3 Average values of Q P and Q S along with their standard deviations at different central frequencies
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  1. (i)

    Q P = 56 ± 8f 0.91±0.002.

  2. (ii)

    Q S = 151 ± 8f 0.84±0.002.

Compared with Q P, the Q S values are found to be high for a given frequency range. The ratio Q S/Q P > 1 indicates the presence of scatterers in the medium (Hough and Anderson, 1988). Also, a high value of Q S/Q P is expected in regions partially saturated with fluids (Toksoz et al. 1979; De Lorenzo et al. 2013; Hauksson and Shearer 2006). Earlier results from various studies show that such low Q P and Q S values characterize and correspond to those of seismically active areas in the world rather than stable areas (Sato and Fehler, 1998). A comparative study of Q C relationships for different seismically active regions was discussed by Joshi (2006), suggesting low Q 0 and high n values for these regions. The results obtained for Q P(f) and Q S(f) in the present study show good agreement with other studies, with low Q 0 (<200) and high n (>0.8) values, which are characteristic of tectonically and seismically active regions (Kumar et al., 2005; Joshi, 2006). The power law defining the frequency dependence of Q P and Q S is characterized by high n = 0.91 and n = 0.84, respectively. The quality factor for P wave is less than that for S wave over the entire frequency range.

The frequency-dependent nature of attenuation, manifesting less pronounced attenuation at high compared with lower frequencies, characterizes the presence of complex structures in tectonically active zones (Padhy and Subhadra, 2010). Such frequency-dependent relations for the region of Garhwal Himalaya could possibly be explained by the tectonics, being attributed to the ongoing underthrusting of the Indian Plate beneath the Eurasian Plate along the whole Himalayan range with differential rates (Molnar and Tapponnier, 1975; Nandy and Dasgupta, 1991).

The study of scattering and intrinsic attenuation for Garhwal and Kumaun region by Mukhopadhyay et al. (2010) suggests that scattering attenuation primarily contributes to seismic wave attenuation, with much higher values compared with intrinsic attenuation at frequency of around 1 Hz. A strong frequency dependence of attenuation due to scattering is observed when the heterogeneities responsible for scattering are of sizes comparable to the lowest frequency analyzed (e.g., Tuvè et al., 2006; Giampiccolo et al., 2006; Akinci and Eydŏgan, 2000; Canas et al.,1998; Akinci et al., 1995; Mayeda et al., 1992). This can be inferred as an indirect indicator of macroscale earth heterogeneity (Leary, 1995). According to Mukhopadhyay et al. (2010), the values of attenuation due to scattering for Garhwal–Kumaun region lie approximately in the middle of all other global values. This is supported by the results obtained in this study and by comparing these results with other regional and global studies (in Sects. 5.1, 5.2, and 5.3).

The seismic attenuation study carried out by Ashish et al. (2009) in the Garhwal region through analysis of Lg waveforms from regional earthquakes indicates high attenuation below the Higher Himalaya compared with that under the Lesser Himalaya. They suggested that the high attenuation is due to the low viscosity and partial melt beneath the Higher Himalayan crust. The present study was constrained along the MCT and to its south, covering a very small part of Higher Himalaya (Fig. 2). The low values of Q P in comparison with Q S (Table 3) for the given frequency range indicate high attenuation of P waves. This suggests that the attenuation in the region could not be influenced by low-viscosity material or the partial melt, as the effect of fluid or melt fraction in the crust shows dominance in attenuation (1/Q) of S-wave velocity (Mitchell, 1995). Additionally, another reason for the high attenuation may be the occurrence of graphite-rich layers along the metasedimentary sequences of Indian Lesser Himalaya (Rawat et al., 2011) and in the Higher Himalayan Crystallines along the zone of MCT (Sachan et al., 2001). Graphite in the form of fault gouges along the fault zone acts as a lubricating agent which can effectively reduce fault strength and work as a weakening agent (Oohashi et al., 2013). According to Oohashi et al. (2013), fault weakening by graphite may also be important at depths where other fault lubricants such as hydrated clay minerals become unstable. In the shallow parts, graphite-bearing fault zones may weaken mature faults more significantly.

Also, the high b-value in the Garhwal Himalaya, explicitly for Uttarkashi (Kayal et al., 1996) and Chamoli area (Kayal et al., 2001), possibly accounts for higher heterogeneity. A high b-value may also indicate the presence of low-strength rocks in the crust that invariably undergo brittle failure at lower stress level, resulting in high seismicity (Wason et al., 2002; Lowrie, 1997; Khan, 2003). These arguments might explain the high seismicity and high attenuation indicating the high heterogeneities observed in the crust of Garhwal Himalaya.

In addition to the above facts, P waves above geothermal systems exhibit anomalously high seismic attenuation (Young and Ward, 1980). The ubiquitous presence of hot springs along the MCT zone in Garhwal and Kumaun Himalaya (Valdiya, 1980) and in the Nepal Himalaya (Derry et al. 2009; Bhattarai, 1980) testifies to the high level of hydrothermal fluids channeled upwards along the MCT zone (Searle et al., 2008), suggesting high saturation zone around the MCT, and this also explains the high attenuation in the crust of Garhwal Himalaya.

5.1 Comparison of Q S and Q C in Garhwal Himalaya

Similarity in the frequency dependence of the Q S and Q C values has been reported from different regions (e.g., Aki, 1980; Roecker et al., 1982; Rovelli et al. 1988; Kvamme and Havskov, 1989). This supports the concept that coda waves are composed of S waves (Aki, 1992) and that the attenuation mechanism for coda waves is similar to that of direct S waves (Aki, 1980). However, as discussed in Sect. 1, some uncertainty still remains regarding how the apparent attenuation inferred from coda waves is related to the attenuation of direct S waves. The coda attenuation parameter in the Indian lithosphere has been estimated by various workers (Gupta et al., 1995, 1998; Mandal and Rastogi, 1998; Mandal et al., 2001, 2004; Tripathi and Ugalde, 2004; Kumar et al., 2005; Mukhopadhyay et al., 2006). In parts of northwest Himalaya, mainly in Garhwal Himalaya, the S-wave coda attenuation (Q −1C ) has been extensively studied (Gupta et al., 1995; Mukhopadhyay et al., 2010). The Q S relation obtained in the present study can be compared with the frequency-dependent Q C given by Gupta et al. (1995) and Mukhopadhyay et al. (2010) for the same region (Fig. 7).

Fig. 7
figure 7

Comparison between Q S and Q C against frequency in Garhwal Himalaya

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This shows similarity between the frequency-dependent Q S and Q C in Garhwal Himalaya, supporting the concept and mechanism that coda waves are similar to direct S waves (Aki, 1992, 1980). However, results for the higher frequencies (>8 Hz) show Q C > Q S (Fig. 7). Such deviation of Q S above 8 Hz has also been reported for the Chamoli region in the Garhwal Himalaya by Sharma et al. (2009), suggesting the dominance of scattering attenuation in the region Sharma et al. (2009). The dominant scattering effects in the crust of Garhwal Himalaya are also discussed in Sects. 5 and 5.3.

5.2 Comparison of Regional and Global Attenuation Characteristics

The results obtained for Q P and Q S for the Garhwal Himalaya, India (Fig. 5) are compared here with those reported from several studies globally (Fig. 8a, b). The low values of Q P and Q S indicate the region to be seismically active, whereas stable regions show high values of Q P and Q S (Sharma et al., 2007; Yoshimoto et al., 1993; Singh et al., 2012; Kumar et al., 2014; Kim et al., 2004; Kvamme and Havskov, 1989). Figure 8a, b shows a global comparison plot of Q P and Q S for the Garhwal Himalaya, indicating the study region to be among the seismically active regions in the world. The values obtained in this study for the frequency-dependent Q P(f) shows similarity with the neighboring areas of Kinnaur and Kumaun Himalaya (Fig. 8a). The comparison of Q P at low frequencies shows slightly higher values for Garhwal region, whereas with increasing frequency the value decreases, indicating higher attenuation at high frequencies with respect to both adjoining regions.

Fig. 8
figure 8

Comparison of a Q P and b Q S values of this study with regions of different tectonic settings of the world. The compared relations for Q (P,S) versus frequency are as follows: Kanto, Japan (Yoshimoto et al. 1993); East-Central Iran (Ma’hood et al., 2009); Kumaun Himalaya (Singh et al., 2012); Northeast India (Padhy and Subhadra, 2010); Kachchh, India (Chopra et al., 2011); Saurashtra Region (Chopra et al., 2011); Mainland Gujarat, India (Chopra et al., 2011); Kinnaur Himalaya, India (Kumar et al., 2014); Garhwal region, India (Joshi, 2006); Oaxaca, Mexico (Castro and Munguia, 1993); Northwestern Turkey (Bindi et al., 2006); Chamoli region, India (Sharma et al., 2007); Northern Greece (Hatzidimitriou, 1995)

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The results obtained in this study using broadband seismograms for frequency-dependent shear wave Q S(f) in the Garhwal region can also be compared with the results obtained from strong motion seismograms by Joshi (2006), for the same region. The study by Joshi (2006) provides the relation Q S = 112f 0.97, using the least-squares inversion technique. The Q S values obtained from the present work are in good agreement for all the frequency ranges, moreover following the same trend (Fig. 8b).

The regional comparison of Q S(f) indicates that the shear wave attenuation is lowest in the Kumaun region, moderate in the Garhwal region, and highest in the Kinnaur region for all frequency ranges (Fig. 8b). This indicates a variation in lateral heterogeneity from eastern to western parts of the northwest Himalaya. Such variations in lateral heterogeneity may occur due to the presence of low-viscosity and partial melt material within the crust (Ashish et al., 2009).

5.3 Comparison of Global Q S/Q P ratio

The ratio Q S/Q P was originally derived from a theoretical consideration which accounts for attenuation of low-frequency seismic waves of ≤0.1 Hz (Anderson et al., 1965), whereas for high frequencies it is significantly larger than 4/9 (Yoshimoto et al., 1993). The obtained Q S/Q P > 1 has also been observed in the upper crust of many other regions with a high degree of lateral heterogeneity (Bianco et al., 1999; Sato and Fehler, 1998). The ratio Q S/Q P does not depend on distance, suggesting a higher homogeneity of the properties that control this ratio (Bindi et al., 2006). In the present analysis, we find that P waves are attenuated more strongly than S waves (Q S/Q P > 1) for the entire frequency range (Fig. 9; Table 3). Sharma et al. (2009) calculated the ratio Q S/Q P > 1 for the Chamoli region in Garhwal Himalaya and inferred scattering to be a dominant phenomenon in seismic wave attenuation. They also validated the dominance of scattering by comparing the attenuation relation for S waves with that of coda waves obtained by Mandal et al. (2001), showing Q C > Q S for higher frequencies (>8 Hz). Similar results are obtained in this study, where we find the Q c obtained by Gupta et al. (1995) and Mukhopadhyay et al. (2010) is high for the higher frequencies (>8 Hz) (Fig. 7). The curve for Q S/Q P for the study region indicates that the study region lies in a zone of seismically very unstable regions of the world (Fig. 9).

Fig. 9
figure 9

Global comparison plot of Q S/Q P for Garhwal Himalaya for the entire frequency range

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A high degree of structural heterogeneities is expected in the crust of Garhwal Himalaya, as revealed by studying the lapse time dependence of the coda Q in the Garhwal region (Mukhopadhyay et al., 2008) with a high degree of lateral heterogeneity on the basis of tomographic analysis (Mukhopadhyay and Sharma, 2010). In the vicinity, the Kumaun region is more heterogeneous and less stable compared with the Garhwal Himalaya (Paul et al., 2003; Singh et al., 2012).

6 Conclusions

We applied the extended coda normalization method to investigate attenuation of P and S waves in the crust beneath the Garhwal Himalaya region, by analyzing seismograms of 40 local earthquakes. The frequency-dependent Q P and Q S in the lithosphere beneath the Garhwal region were obtained as 56 ± 8f 0.91±0.002 and 151 ± 8f 0.84 ± 0.002 in the frequency range of 1.5–16 Hz. The estimated Q P and Q S are found to be strongly frequency dependent, proportional to f 0.91 and f 0.84, respectively. The low values of frequency-dependent Q S(f) and Q P(f) and high values of the frequency relation parameter n for the study area indicate that the region lies in a tectonically active area of the world. It has also been observed that at higher frequencies the attenuation is low. The frequency dependence of shear wave is very similar to the frequency dependence of the coda Q for the Garhwal Himalaya, substantiating the fact that coda waves are composed of S waves and the attenuation mechanism for both waves is similar in the region. Above 8 Hz, the comparison shows Q C > Q S, indicating dominance of scattering attenuation in the region.

Also, the high value of Q S/Q P > 1 and the strong frequency dependence of Q suggest that scattering may be one of the important factors contributing to attenuation of body waves in the Garhwal Himalaya. The results obtained here will help to constrain the frequency dependence of seismic attenuation in the earth’s crust, which is crucial to further correct the velocity dispersion due to attenuation in the region.