Continuous Wavelet Decomposition Algorithms for Automatic Detection of Compressional‐ and Shear‐Wave Arrival Times

Abstract

Abstract The determination of P ‐ and S ‐wave arrival times is important for a variety of seismological applications including earthquake detection and seismic tomography. The method is based on the continuous wavelet transform of the waveforms. Unlike Fourier transform, the basis functions are localized in time and frequency, therefore, wavelet transform is suitable for analysis of nonstationary signals. For detecting the P ‐wave arrival, the wavelet coefficients are calculated using the vertical component of the seismogram. In the case of the S ‐wave arrival, we take advantage of the polarization of the shear waves, and cross examine the wavelet coefficients from two horizontal recordings. In addition, shear‐wave splitting, the time delay of polarized S waves, can be measured using real and imaginary wavelets. Because these steps can be automated, application of the technique can easily generate a large database of shear‐wave splitting measurements for studies of anisotropy.