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.

中文翻译：

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小波在尼泊尔2015年戈尔卡地震之后在加德满都谷地地震波分析中的应用

在本文中，我们估算了尼泊尔地震（2015年4月25日）期间的地震能量，并研究了加德满都谷地的地震动时频特征。分析震源能量信号时频特性的思想是基于本文所采用的小波变换。小波变换已在压缩，时频分析，地震参数确定，气候研究等各个领域用作强大的信号分析工具。此技术特别适用于非平稳信号。众所周知，地震地震动是一个非平稳的随机过程。为了表征一个非平稳随机过程，需要数学意义上的不可测量的样本。我们在此遵循的小波变换过程有助于对地震地震动作用下的线性和非线性结构系统进行随机分析。通过与这些信号相关的小波系数来表征地震地震动的方式。连续小波变换（CWT）和离散小波变换（DWT）技术都用于研究加德满都谷地在水平和垂直方向上的地震动。这些技术有助于指出具有场地响应的长时间地面运动。我们发现，长时间的地震动具有足够的动力来破坏结构。比较水平运动和垂直运动，我们观察到大多数高振幅信号与垂直运动有关：高能量在该方向上释放。发现主要事件发生后不久，地震能量被衰减。但是阻尼的周期是不同的。这可以在DWT曲线上看到，在DWT曲线上，余震时方波小波系数很高，并且值随时间减小。换句话说，它主要与瑞利波的到来有关。我们得出的结论是，地震工程师应研究长时期的地震动，以避免在地震期间破坏结构。因此，通过使用小波技术，我们可以指定地震活动区的脆弱性和那里的局部拓扑特征。它主要与瑞利波的到来有关。我们得出的结论是，地震工程师应研究长时期的地震动，以避免在地震期间破坏结构。因此，通过使用小波技术，我们可以指定地震活动区的脆弱性和那里的局部拓扑特征。它主要与瑞利波的到来有关。我们得出的结论是，地震工程师应研究长时期的地震动，以避免在地震期间破坏结构。因此，通过使用小波技术，我们可以指定地震活动区的脆弱性和那里的局部拓扑特征。