Application of wavelet for seismic wave analysis in Kathmandu Valley after the 2015 Gorkha earthquake, Nepal

In this paper, we estimate the seismogenic energy during the Nepal Earthquake (25 April 2015) and studied the ground motion time-frequency characteristics in Kathmandu valley. The idea to analyze time-frequency characteristic of seismogenic energy signal is based on wavelet transform which we employed here. Wavelet transform has been used as a powerful signal analysis tools in various fields like compression, time-frequency analysis, earthquake parameter determination, climate studies, etc. This technique is particularly suitable for non-stationary signal. It is well recognized that the earthquake ground motion is a non-stationary random process. In order to characterize a non-stationary random process, it is required immeasurable samples in the mathematical sense. The wavelet transformation procedures that we follow here helps in random analyses of linear and non-linear structural systems, which are subjected to earthquake ground motion. The manners of seismic ground motion are characterized through wavelet coefficients associated to these signals. Both continuous wavelet transform (CWT) and discrete wavelet transform (DWT) techniques are applied to study ground motion in Kathmandu Valley in horizontal and vertical directions. These techniques help to point out the long-period ground motion with site response. We found that the long-period ground motions have enough power for structural damage. Comparing both the horizontal and the vertical motion, we observed that the most of the high amplitude signals are associated with the vertical motion: the high energy is released in that direction. It is found that the seismic energy is damped soon after the main event; however the period of damping is different. This can be seen on DWT curve where square wavelet coefficient is high at the time of aftershock and the value decrease with time. In other words, it is mostly associated with the arrival of Rayleigh waves. We concluded that long-period ground motions should be studied by earthquake engineers in order to avoid structural damage during the earthquake. Hence, by using wavelet technique we can specify the vulnerability of seismically active region and local topological features out there.