DETERMINATION OF THE DELAY TIMES BETWEEN TWO OR MORE INTERFERED BODY WAVE TRAINS USING BY SPECTRAL TECHNIQUES

Study comprises that using of the some spectral techniques for defining of the delay times of interfered waves, investigating their solution power of these techniques on both synthetic and real data. First of all, theoretical model consisting of more than one signals are evaluated and the spectral methods are tested to determine the delay times. Then these methods are applied to the vertical component seismograms of teleseismic events and also some more regional events occurred in a Mediterranean Sea to determine delays between seismic phases (e.g. pP, sP and PcP phases).

In order to represent seismic phases in our model we use some specific functions (berlage function, etc). For different delay times, cepstral techniques, autocorrelation function and spectral nulls are used on the models. Phase differences between the components of the model are also tested as well as delay times.

Cepstral techniques are used to detect echoes in a signal simple Fourier transform processing methods. They offer natural nonparametric means for estimating general echo patterns in single series. They have been used in as well as in applications to diverse fields such as speech analysis, image processing and radar. The cepstrum is defined as the Fourier transform of log of the spectrum of a time-domain signal and is designed to take advantage of the periodicity that occurs in the power spectrum when echoes are present in the original signal. In principle, the cepstrum can be used to detect the periodicity in the seismic spectrum that is due to the interference of the direct (P) and depth (pP and/or sP) phases. This periodicity is directly related to the depth phase delay time which is in turn directly related to focal depth.

Synthetic teleseismic seismograms are constructed by using berlage function as main seismic phase and its echoes. We use the models with one and two echoes with or without noise. We also investigate phase differences between main wavelet and its echoes by the using spectral techniques.

The results obtained from this study were compared to IASP91 model and tested its reliabilities. On the real data after the effective data processing it is seen that delay times between interfered body wave trains were achieved almost equal to the IASP91 global 1-D model. Cepstral techniques are very efficient to determine arrival times and amplitudes of the wavelet and its echoes. Cepstral – F statistic method also improves the results in case of local network data that an event recorded at various stations in the seismic network.