GNGTS 2013 - Atti del 32° Convegno Nazionale

Fi ( ω ) is the discrete Fourier transform of the ith signal, and ak are smoothing coefficients chosen in the range 0 – 1. It is noteworthy that without smoothing cij( ω ) would be always equal to 1 (Bath, 1984). The coherence gives a measure of the signal similarity among the array stations as a function of frequency. It can be computed between two signal windows recorded at the same place but different times (time coherence), or between two signals recorded at the same time at different places (spatial coherence). In the first case the coherence measures the persistence of similarity in time, while in the second case it measures the persistence of simi- larity as the signal propagates from a place to another. The case of coherence between signals recorded at different places and different times is not of interest in seismology, and will not be deepened any more. On the contrary, we will focus our attention on the spatial coherence. Many methods of analysis are available to study the propagation properties of the seismic wavefield, in both frequency and time domain. All of them, applied to time window sliding along the signal, furnish azimuth and apparent velocity of the most coherent signal. In this work we have applied the Beam Forming method (BF) in frequency domain, and the Semblance method (Semb) in time domain. The partition of energy is evaluated in frequency domain by calculating power spectra of three component seismic signals as described by Nakahara and Margerin (2011). The energy partition ratio ( PE hr and PE ud for horizontal and vertical components) and H/V spectral ratios on coda waves are calculated on 20 s time windows starting after twice S-wave travel time and are given by: H/V = (N + E) / 2 V (4) PE hr = (N 2 + E 2 ) / (N 2 + E 2 + V 2 ) (5) PE ud = V 2 / (N 2 + E 2 + V 2 ) (6) where E , N and V are the amplitude spectra of east-west, north-south and vertical components of motion respectively. Data analysis and results. UND array was composed of 20 short period three component seismic stations installed at an average distance of about 90 m for a maximum extension of about 0.5 km (Scarpa et al. , 2004; Saccorotti et al. , 2006; Formisano et al. , 2012). The wavelength well sampled in space by the array is in the range [0.1 km, 0.5 km], which corresponds to frequency in the range 10 Hz - 50 Hz for P waves, and 5.7 Hz - 30 Hz for S waves, assuming a P wave speed of 5 km/s. Since data were acquired at 100 sps, the intrinsic high frequency limit of our signals is 40 Hz. However, many stations were affected by local sources of noise, particularly important in many cases in the band 23 Hz – 40 Hz. Therefore we trust that our data set is suitable for measuring the spatial coherence in the 5 – 23 Hz range. At lower frequency we expect the signals be more coherent as the wavelength increases, even for diffusive regime and seismic noise, because the array extension is smaller than the signal wavelength. We selected many local and regional earthquakes characterized by high signal to noise ratio (SNR). They were analyzed by applying array methods to many different frequency bands in the range 1 Hz – 20 Hz. Since the array consisted of three component stations, the array methods were applied to the three components independently. Beside the array analysis, the coherence of seismic signals among the array stations was computed on sliding window of length 10 s. Results have been plotted by colors versus time and frequency. Fig. 1 shows an example of this analysis for a regional earthquake. The spectrogram is also shown in the same picture to give a precise idea of the coda decay. The coherence is characterized by very high values (near 1) for signals at frequency lower than 1 Hz in the seismic noise and along the earthquake coda. For the P wave and its early coda the coherence takes the maximum at 64 GNGTS 2013 S essione 1.1