Determination of P and S Phase Using Maximum Overlap of Discrete Wavelet Transform (A Case Study on 2017 Sarpol-e Zahab Earthquake)

Automatic seismic phase picking algorithms are one of the current research topics and have special significance in seismic data processing requirements. One of the most fundamental tasks in seismology is the identification arrival time of seismic phases such as the compressional or P-wave, transversal or S-wave, Rayleigh-wave, Love-wave, reflected and refracted wave from boundary layers must be identified. Seismic phase arrival time identification enables scientists to derive important geophysical and seismological information, such as the geotectonic settings, structure of the earth’s interior, seismicity of an area and seismic hazard assessment. Traditionally, these quantities were measured manually by human experts, but as seismic networks have grown worldwide, such tasks have been increasingly taken up by automated algorithms. because seismic network or even a single station operating continuously at high sampling frequency produces an enormous amount of data, processing of such a volume of waveforms manually is very time-consuming and requires considerable manpower. In addition, due to human error, incorrect detection of the phase can affect future studies. Therefore, it is needed to an alternative more efficient, faster, and accurate method that reduces the human, financial and time costs and also decreases the probability of errors. Hence, in recent decades, significant efforts have been made to develop automatic phase picking methods.
 Wavelet transform is a tool in the analysis of nonstationary signals such as the seismic signal. This is due to the ability of the wavelet transform to resolve features at various scales [1]. In particular, there are two types of wavelet transforms, orthogonal as discrete wavelet transform (DWT) and non-orthogonal as maximal overlap discrete wavelet transform (MODWT). DWT is useful in decomposing time series data into an orthogonal set of components with different frequencies. Whereas MODWT is a variant of DWT that can handle any sample size. The smooth and detail coefficients of MODWT multiresolution analysis are associated with zero phase filters and produces a more asymptotically efficient wavelet variance estimator than the DWT [2]. Working in the wavelet domain allows multiresolution analysis of the waveform, and provides the means to distinguish the phase arrival from random or systematic noise. In this work, we take advantage of the wavelet transform properties and define characteristic functions to detect P- and S-wave arrivals. The version of the maximum overlap discrete wavelet transform (MODWT) is used to determine and picking the arrival time of the P and S phases. The methodology of this study is divided into two parts: the first part is about the determination of the P arrival time obtained by processing the stacked envelop of the wavelet transform coefficients. The second part is determining the S arrival time, the automatic S-phase detection algorithm that we present in this paper is a combination of wavelet transform (WT) and AR model. The estimation of arrival time of the S wave is done in two steps. At first, an initial estimation of arrival time is calculated using the MODWT transform. In the next step, the final estimation of the S wave arrival time is calculated using an AR model.
Method is tested on a significant number of Kermanshah cluster earthquakes. The results of automatic phase picker algorithm in this study have been compared with the STA/LTA method to assess the accuracy.