Estimation of source and site characteristics in the North-West Himalaya and its adjoining area using generalized inversion method

. A site constraint generalized inversion technique (GINV) has been used in the present study to develop source and site spectra for the regions in and around north-west Himalaya. Database consists of 156 earthquake (EQ) records corresponding to 21 EQ events [2.5<magnitude (𝑀) <5.8], recorded at 78 recording stations. Source parameters like scalar moment ( 𝑀 0 ), corner frequency( 𝑓 𝑐 ), stress drop( ∆𝜎 ), apparent stress drop( 𝜎 𝐴 ) , and seismic energy (𝐸 𝑠 ) are computed for each EQ event by fitting the point source model to the obtained source spectra. Calculated 𝑀 0 and 𝑓 𝑐 values for all events are found in the range of 4.96 × 10 13 Nm-2.91 × 10 16 Nm and 1.50Hz-5.50Hz respectively. Further, regression analysis between the above two parameters lead to the relation: 𝑀 0 𝑓 𝑐3 = (2.09 × 10 16 Nm/s3 ) for the study area. Value of 𝐸 𝑠 computed in the study varies from 1.86 × 10 8 J-1.75 × 10 12 J. Further, value of ∆𝜎 is found varying from 0.65MPa-21.13MPa while 𝜎 𝐴 is found in the range of 0.07MPa-2.76MPa. It is observed that both ∆𝜎 and 𝜎 𝐴 approximately follow the theoretical relation as; 𝜎 𝐴 = 0.23∆𝜎 . Another outcome of the study is the site amplification curves developed based on the GINV results of horizontal and vertical components for all the recording stations. Further, site transfer function (STF) for all the recording stations characterised by the ratio of horizontal and vertical site amplification components is computed and, amplification function (A peak ) and predominant frequency (f peak ) are determined. Comparison of estimated STFs based on GINV and results of Horizontal to Vertical Spectral Ratio method (HVSR) show similarity in terms of the f peak values. using stochastic point source model and reported the value of ∆σ and 𝑓 𝑐 as 12.4MPa and 1.78Hz respectively, which are matching with the value of ∆𝜎 = 10.71MPa and 𝑓 𝑐 =2.4Hz obtained in the present work. Similarities in the results of the present study with that discussed above is encouraging considering the total independence of the methodologies used in each work including the present one.


Introduction
The north-west Himalaya and its foothills within India encompassing the states of Jammu and Kashmir, Himachal Pradesh, Uttarakhand, Punjab, Haryana and national capital of India, New Delhi is home for about 96 million people as per 2011 Census. This is one of the fastest growing regions in the entire Himalayan belt with respect to population growth due to rapid urbanization. Records of seismic activities suggest that the above area represents an active tectonic region experiencing frequent damage inducing EQs. High seismicity of this region is because of continuous subduction of the Indian plate under the Eurasian plate (Gansser 1964). Major Seismotectonic features in this region is mainly defined by three north-dipping thrusts namely; the Main Central Thrust (MCT), the Main Boundary Thrust (MBT) and the Himalayan frontal Thrust (HFT) (Valdiya, 1984). Both the MCT and the MBT are produced during the Cenozonic shortening (Valdiya 1984;Malik and Nakata 2003). The HFT is the youngest active thrust separating the Himalaya region and the Indo-Gangetic alluvial plain (Kumar et al. 2009 (Kayal, 2001) and caused huge damages to buildings in Uttarkashi district (Kumar and Mahajan, 1994). The 1999 Chamoli EQ caused landslides in Gopeshwar town, located less than 2km northwest of Chamoli city (Sarkar et al. 2001) and produced tremors in locations like Chandigarh and Delhi, located far away from the epicentre (Mundepi et al. 2010). It has to be highlighted here that IS 1893: 2016 classifies the entire north-west Himalaya region as seismic zone IV and V, indicating regions of high to very high seismic activity.
It has been widely acknowledged that ground motion at a certain site during an EQ is a collective function of site, path and source parameters (jointly referred to as EQ parameters). Site parameters accounts for the modification of incoming seismic waves characteristics (amplitude, frequency content and duration) by subsurface soil medium. Similarly, path parameters constitute geometric spreading and anelastic attenuation which account for the attenuation of seismic waves as travel away from the source through the crustal medium. On the other hand, source parameters include 0 (defined as the measure of the size of seismic disturbance), (defined as wave energy that would be released if an EQ happened in an infinite medium without energy loss) and ∆σ (defined as the measure of change in the average state of stress before and after rupture). Knowledge about region specific EQ parameters is important for seismic hazard assessment, especially those using physical models (Hassani et al. 2011). Widely used approach to estimate EQ parameters in Fourier amplitude is to apply generalized inversion (GINV) method to the recorded EQ data. GINV was introduced by Andrews, (1986) after modifying the standard spectral ratio method (Borcherdt, 1970) Table 2. In addition, Fig. 1 shows the location of the recording stations and EQs used for inversion.

Data processing
For inversion analysis, EQ records are subjected to baseline correction with a 5% cosine taper followed by bandpass Butterworth filter in the frequency range of 0.25Hz and 15Hz. Further, S wave part of each accelerogram is selected as the time windows beginning from 0.5s before the starting of the S wave and ending when 90% of the total energy of the EQ record is reached (Bindi et al. 2009). In addition, the time windows for EQ records vary from 4 to 15s. The maximum window length is restricted to 15s in order to avoid records having too much Coda wave energy (following Oth et al. 2008). Further, the Fourier amplitude spectra (FAS) are calculated for S wave portion of the EQ record. Obtained FAS is then smoothened as per Konno and Ohmachi (1999) algorithm with a smoothing parameter b = 20. Further, source and site spectra are generated simultaneously using an inversion procedure as discussed in Section 3.

Generalized Inversion Method
The smoothened FAS, ( , ) at a recording station , from source with and hypocentral distance can be expressed in frequency domain ( ) following Castro, (1990) as; Here, ( ) , ( , ) and ( ) denote the source spectrum, path attenuation component and site term respectively. Later, the path attenuation component is removed from ( ) in accordance with Andrews (1986) as; The value of ( , ) includes the effects of anelasticity of heterogeneous media and geometric spreading, which as per Castro, (1990) can be determined using the following expression; In eq. 3, ( ) is the quality factor for S wave and β is the average shear wave velocity of the crustal medium for the region considered as 3.5km/s as per Mukhopadhyay and Kayal, (2003). Value of = 105 0.94 as given by Harinarayan and Kumar, (2018c) for the region in and around the north-west Himalaya is used in this work. Eq. 2 is linearized by taking natural logarithms as follows; According to Andrews, (1986), an undetermined degree of freedom between source and site term exists in eq. 4 that can be resolved by using constrained site spectral function in the inversion (Castro et al. 1990

Result
Earlier discussed source and site spectrum are estimated here using the inversion procedure discussed in the preceding section. Results of the inversion are discussed below.

Source Parameters
The source spectrum, ( ) of all the 21 EQ events obtained from inversion is shown in Fig. 3 (indicated by dashed line). In order to estimate source parameters, each source spectrum is compared and fitted to point source model of Brune, (1970) as discussed below; The obtained source spectra, ( ) of the ℎ EQ event, from the inversion is expressed as (Brune, 1970); 0 of 21 EQ events, based on ( ) , obtained in inversion, is computed using eq. 6 as shown in Fig. 3. Further, 0 of each EQ event is compared and fitted to the theoretical model given in eq. 7 (after Brune, 1970) in order to estimate source parameters.
A nonlinear least square approach (similar to Bindi et al. 2009) is adopted here to determine the values of 0 , and ϓ for each EQ event, based on 0 values in eq. 7. The values of 0 , and ϓ obtained in the present study are tabulated in Table 2 In eq. 12, is the rigidity modulus estimated using the formula: = 2 . Calculated values of σ are tabulated in Table 2 Column 13. It can be seen from the Table 2, column 13 that the estimated σ in the present study is in the range of 0.07MPa to 2.76MPa, with an average of 0.81MPa for 21 events. Fig. 4 shows a comparison of σ A , ∆σ and the theoretical line, σ A = 0.23 ∆σ given by Kikuchi and Fukao, (1988) represented by a solid line. It can be seen from Fig. 4 that the relation between estimated σ and ∆σ in the present study is consistent with the theoretical relation.

Comparison with Existing Literatures
There are limited studies available where source parameters for EQs in the north-west Himalaya were determined  Table 2]. These findings are close to the values of ∆σ =0.9MPa, =2.3Hz and =550.8m, obtained in the present study (see Fig. 5a). In another study, Kumar et al. (2016), based on Spectral analysis using grid search technique reported values of ∆σ as 4.16Mpa and 3.6Mpa for 2009 January EQ [event no. 3, Table 2] and 2008 September EQ [event no. 4, Table 2] respectively. It has to be highlighted here that above values by Kumar et al. (2016) are close with ∆σ of 8.6MPa and 1.6MPa respectively, obtained for the same events, in present study (see Fig. 5b 12, Table 2] using stochastic point source model and reported the value of ∆σ and as 12.4MPa and 1.78Hz respectively, which are matching with the value of ∆ = 10.71MPa and =2.4Hz obtained in the present work.
Similarities in the results of the present study with that discussed above is encouraging considering the total independence of the methodologies used in each work including the present one.

Empirical correlations
To understand the relation between 0 and in the north-west Himalaya, 0 is plotted against in logarithmic units (similar to Aki, 1967) and the regression yields the following expression: Eq. 13 indicates that with increase in 0 decreases. According to Aki, (1967), follows the scaling law: Plot for eq. 14 is indicated by solid line in Fig. 6. Eq. 14 is rewritten as:  The variation of ∆σ with 0 , shown in Fig. 8 illustrate that ∆σ do not exhibit significant variation with 0 .
Similarly Fig. 9 shows lack of dependence of ∆σ with . The significant lack of dependence of ∆σ with 0 , and along with the cube root scaling of (in eq. 13) collectively indicates that the EQs in the north-west Himalaya follow the self-similarity process. A similar observation is reported by Kumar et al. (2016) for EQs (3.4<mb <5.8) in the north-west Himalaya.  Table 1, Columns 5 and 6 respectively. Maximum value of fpeak of 6Hz is observed for the recording station JAFR with Apeak of 2.
Maximum value of Apeak of 6.9 for UDH recording station is observed at 2.7Hz. Range of Apeak varies between 2 and 6.9, while the range of fpeak varies between 0.7Hz and 6Hz. In addition to site class given by Chopra et al. (2018), the possible range of fpeak (see Table 3), estimated from the range of period (Tg) as given by Di'Alessandro et al. (2012), for each site class, is also presented in column 10,  2018), is also presented in Fig. 11(a-d). In can be clearly observed from Fig. 11(a-d) that fpeak values based on each of the three curves, for each of the recording stations considered, are closely matching.  Site Description CL-I fpeak >5 Hz CL-II 2.5 Hz ≤ fpeak ≤ 5 Hz CL-III 1.66Hz ≤ fpeak ≤ 2.5 Hz CL-IV fpeak < 1.66 Hz CL-V fpeak not identifiable/flat H/V CL-VI Broad amplification/multiple peaks above 5 Hz CL-VII fpeak not identifiable/multiple peaks over period range

Conclusion
In the present study, 156 EQ records from regions in and around the north-west Himalaya are processed and analysed for separating source and site spectra using GINV method. Obtained source spectra is fitted to the theoretical source model to get 0 and . Furthermore, ∆ , and are also calculated for the above events.
Based on these findings, correlations between the estimated source parameters are proposed leading to the following conclusions; 1. Within the range 4.96 × 10 13 Nm < 0 < 2.91 × 10 16 Nm, 0 is approximately proportional to −3 , with In addition, STF curves developed based on the results of GINV for horizontal and vertical components shows clear and distinct peak for majority of the recording stations. Values of fpeak and Apeak obtained from the STF curves are in the range of 0.7 to 6Hz and 2 to 6.9 respectively. STF curves from GINV method is compared with HVSR estimates. Comparison between the two methods shows similarities in terms of the general shape and values of fpeak and are found matching with the existing literature.