The High Frequency Decay Parameter κ ( Kappa ) in the Region of North East India

The high frequency decay parameter κ has been considered as one of the important parameters required in the simulation of earthquake strong ground motions necessary for the proper evaluation of seismic hazard of a region. The present study estimated “κ” for the highly seismic active region of North East India. The spectral analysis of 598 accelerograms of 32 earthquakes has been done using [1] approach for this purpose. The average values of “κ” have been found to be 0.049, 0.047 and 0.040 for L-, Tand V-component respectively. The distance dependence of κ is not significant in the region. The κ0 (κ at R = 0) for soft rock stations is found to be more than those of hard rock sites in consistent with other similar studies. The correlation between “κ” and earthquake magnitude at most of the stations for the region under study is not significant which indicates that κ depends on the site conditions in the region. The κ values estimated in the present study are useful for the evaluation of seismic hazard of the region.


Introduction
The spectral shape of earthquake strong ground motions plays an important role in the simulation of realistic accelerograms using different techniques.The simulated accelerograms are crucial for the proper evaluation of seismic hazard of a region.Different factors including attenuation, velocity and site conditions etc. control the spectral characteristics of the strong ground motions.It has been suggested that the spectrum of strong ground motion from earthquakes is flat above the corner frequency [2] to the maximum frequency (f max ) after which the spectrum decays fast [3].This phenomenon of high-frequency band limitation of radiated earthquake energy has been given the name "the crashing spectrum syndrome" by [4] and attributed this primarily to the local site effects.[5] suggested the source (fault nonelasticity) as cause for "f max " not the site.[6] described a site attenuation parameter "t*" in the form of exponential decay term e −πft* to the spectral attenuation of the waves.
[1] introduced a spectral decay parameter-κ (Kappa) to model the high frequency spectral attenuation.They defined the parameter "κ" as: where A 0 depends on the source, epicentral distance and other factors, f E is the frequency above which the spectral amplitude follows an exponential decay.The studies have been done to attribute the origin of "κ" to source, site and/or path attenuation.[7] and [8] have suggested that "κ" represents the near surface as well as propagation path attenuation.Some studies suggest that "κ" is source related [9] [10] [11] [12].[13] assumes "κ" as a parameter related either to source or site effects.It is considered as site parameter by [14] [15] found that "κ" was independent of earthquake size within magnitude range M < 3.5 for the events occurred in the region of Northeastern Sonora, Mexico.[16] also found no correlation between "κ" and magnitude.
In spite of the lack of agreement on the physical origin of "κ", it has been widely used in number of seismological applications like computation of site amplification factors, ground motion prediction equations [17] [18].It has become a standard parameter to constrain attenuation, peak ground acceleration and spectral shape of stochastically generated accelerograms.
In the present study, the high frequency decay parameter "κ" has been estimated at different sites and source-receiver distances for the region of North East India.The possible dependence of "κ" on distance for hard rock sites and soft soil sites has been investigated.The dependence of "κ" on earthquake size has also been examined.

Study Area and Data Used
The tectonic map of the NE India region has been shown in Figure 1.The collision of India-Eurasian plate (developed Arakan Yoma belt) and under thrusting of Indian plate below the Myanmar plate gives rise to an intricate tectonic zone in North-East Indian region [19].This region has experienced damaging earthquakes in the past including great earthquakes (1897 and 1950 Assam earthquakes), 1918 Srimangal earthquake (mb 7.6), 1930 Dhubri earthquake (M 7.1).Geologically, this region is mainly divided into five parts as eastern Himalaya, the Mishmi massif, the Indo Myanmar arc, the Brahmaputra valley, and the Shillong plateau [20].The presence of Mishmi thrust, Lohit thrust, Po Chu fault, and Tidding suture makes the tectonic of Mishmi region more complex having predominant features like Tsangpo suture, Tuting and Bame faults.The Shillong highland is represented by N-S trending Dhansiri and Kulsi faults, N-E aligned A strong motion accelerographs network has been installed in the region by Department of Earthquake Engineering, Indian Institute of Technology, Roorkee with the objectives of studying the strong ground motions characteristics for earthquake engineering purposes.The 598 accelerograms of 32 earthquakes (mb 3.9 -6.8) recorded at this network has been used in the present analysis.Figure 2 shows the locations of earthquakes and recording stations used in this study.
The lists of the earthquakes along with recording stations and geology are given in Table 1.
According to this classical method, Equation (1) can be written as: Open Journal of Earthquake Research This a linear equation between "lnA" and frequency "f".The "κ" can be estimated from the slope (m) of the line (Equation ( 2)) as: The following procedure has been adopted for the estimation of "κ": 1) First the S-wave portion of the accelerogram is selected.
2) Fourier transform of the selected wave has been obtained using FFT and plotted the same on log-linear scale i.e. with a logarithmic y-axis (amplitude) and a linear x-axis (frequency).
3) Two frequencies have been selected by visual inspection of the spectrum of S-waves: first at the start of linear downward trend in the spectrum (f1) and second at the end of linear downward trend (f2).The visual inspection of S-wave spectrum in selecting the two frequencies is preferred over the automatic procedure as f1 and f2 vary from record to record.The visual inspection avoids the biased estimates of "κ".This procedure has been used in previous studies also (e.g.[28]).4) A line has fitted between f1 and f2 in a least square sense on log-linear plot.
The slope (m) of the line gives the value of "κ" (Equation (3)).

Results and Discussion
The values of "κ" have been estimated for the three components (N-S, E-W and Z) of the recorded accelerograms using the procedure described above.Figure 3 shows the log-linear plots along with the best fitted lines for some of the records.Figure 3.The log-linear plots for estimating "κ" along with the best fitted lines for some of the records.
It has been found that f1 lies in the range 2-13 Hz while f2 is in the range 20 -28 Hz.The estimated values of "κ" corresponding to three components for the earthquakes and recording stations are given in Table 2 along with the site geology.The standard deviations are also given in the table.The average values of "κ" has been found to be 0.049 (L-component), 0.047 (T-component) and 0.040 (V-component).A comparison between the κ values obtained from horizontal and vertical components is shown in Figure 4.The values are found to be similar for most of the events.The vertical estimates are smaller than those of horizontal estimates.This has been observed in other studies [28] [30].The values obtained in the present study have been compared with those of other regions of the world in Table 3.The estimates are found to be consistent.
The distance dependence of κ has been analyzed using the following linear model [1]: where κ 0 is the value of κ at distance R = 0.This model has been used in many studies due to its simplicity of formulation (e.g.[1]; [28]; [31]).κ 0 is believed to be station-dependent and may be related to the near surface attenuation.The distance dependence of κ estimated from horizontal and vertical components is

For horizontal component
We note that distance dependence for both the components is not significant.
The values of κ 0 as 0.041 (horizontal component) and 0.037 (vertical component) represent the overall value for the region.The difference in these two values indicates that site response is different for different components as has been observed in site amplification studies.The estimate of κ 0 (vertical) is useful along with H/V ratio for the first order estimation of site effect where site-specific borehole data is not available as suggested by [30].The κ 0 for soft rock stations is found to be more than those of hard rock sites.The ratio of κ 0 for soft rock to hard rock is equal to 1.09.Similar observations have been found to be in different studies for other regions.[28] found that kappa depends on both local geology (Soil or Rock) and source to site distance in France.They have estimated κ 0 (soil) = 0.0270 and κ 0 (rock) = 0.0207.[32] has found κ 0 for soil as 0.036 and κ 0 for rock as 0.030 for Southern California.[33] has estimated κ 0 values varying in the range 0.032 -0.097 at surface and in the range 0.012 -0.078 in borehole (may be considered as hard rock site) for Taiwan region.[31] has found κ = 0.016 for hard rock site and 0.0201 for soft   formations as suggested by [33].
The dependence of kappa values on earthquake size has been examined by plotting the estimated κ values with earthquake magnitudes for the stations where sufficient number of earthquake have been recorded.Figure 8(a)-(c) show such plots for some of the stations.We note that there is a scatter and the correlation between "κ" and magnitude at most of the stations for the region under study is not significant.This suggests that that "κ" is not related to source effect for NE Himalaya region.[31] has reported similar property of κ for smaller magnitude earthquakes occurred in Kachchh region of Gujarat, India.The analysis in the present study indicates that kappa for NE region is related with the high frequency attenuation in the top surface layer.One of the scientific discussions about κ is whether it is due to source effect or site effect or both.The different studies show different results for different regions of the world.The present study based on the available data found that κ is related to site effect in NE region.This is empirical inference drawn on the basis of recorded waveforms in the region.The same may be validated with more data whenever available.

Conclusions
The average value of κ estimated from the spectral analysis of horizontal components of 598 accelerograms for NE India region has been found to be in the range 0.047 -0.049 and 0.040 for vertical component.The distance dependence of κ is not significant.The κ 0 (soft site)/κ 0 (rock site) ratio is found to be 1.09.The analysis shows that κ is not dependent on the magnitude but dependent on site-condition in the region for the range of magnitudes studies here.The study presents the κ model for NE India region which is first study of its kind in the region.The inferences drawn about κ in the NE region are based on the data available for the analysis.The same may be validated further as and when more data is available.With more data, the spatial distribution may also be investigated in the region.The other methods reported in the literature may also be applied to estimate κ in the region.The estimated values of κ are useful in the studies of Ground Motion Prediction Equations (GMPE) as well as for the simulation of earthquake strong ground motions in the seismically active NE region.Thus this study is important for bearing on the seismic hazard studies of the region.

Figure 1 .
Figure 1.Seismicity along with tectonics of the North-East Region, India.

Figure 2 .
Figure 2. Location of earthquakes and recording stations used in present study.
shown in Figure5(a) and Figure5 (b).The fitted linear model gives the regres-

Figure 6 (
Figure 6(a) and Figure 6(b) show the distance dependence of κ on hard rock sites and soft soil sites separately.The linear fit gives the following relations: 0.034 0.0000158 к R = + For hard rock sites

Figure 4 .
Figure 4.A comparison between the κ values obtained from horizontal and vertical components.

Figure 7 .
Figure 7. Distance dependence of κ for individual station where sufficient numbers of earthquake have been recorded.

Figure 8 .
Figure 8. Magnitude dependency of kappa at some of the stations.

Table 1 .
List of Earthquakes along with recording stations used to compute κ and Ns is number of stations.

Table 2 .
The estimated values of κ for the three components of earthquakes along with recording stations with site geology.

Table 3 .
Comparison of kappa value estimated in present study with those of different regions of world.