Based on the fact that the Hankel matrix representing clean seismic data is low rank, low-rank approximation methods have been widely utilized for removing noise from seismic data. A common strategy for real seismic data is to perform the low-rank approximations for small local windows where the events can be approximately viewed as linear. This raises a fundamental question of selecting an optimal rank that best captures the number of events for each local window. Gavish and Donoho proposed a method to select the rank when the noise is independent and identically distributed. Gaussian matrix by analysing the statistical performance of the singular values of the Gaussian matrices. However, such statistical performance is not available for noisy Hankel matrices. In this paper, we adopt the same strategy and propose a rule that computes the number of singular values exceed the median singular value by a multiplicative factor. We suggest a multiplicative factor of 3 based on simulations which mimic the theories underlying Gavish and Donoho in the independent and identically distributed Gaussian setting. The proposed optimal rank selection rule can be incorporated into the classical low-rank approximation method and many other recently developed methods such as those by shrinking the singular values. The low-rank approximation methods with optimally selected rank rule can automatically suppress most of the noise while preserving the main features of the seismic data in each window. Experiments on both synthetic and field seismic data demonstrate the superior performance of the proposed rank selection rule for seismic data denoising. 相似文献
A previous analysis [Improta, L., G. Di Giulio, and A. Rovelli (2005). Variations of local seismic response in Benevento (Southern Italy) using earthquakes and ambient noise recordings, J. Seism. 9, 191–210.] of small magnitude earthquakes recorded at 12 sites within the city of Benevento has stressed the significant role played by near-surface geology in causing variability of the ground motion. In this paper, we extend the study of the seismic response from 12 sites to the entire urban area. Based on inferences from the comparison at the 12 sites between earthquake and ambient vibration results, we have collected ambient noise at about 100 sites within the city, intensifying measurements across the main shallow geological variations. We use borehole data to interpret ambient noise H/V spectral ratios in terms of near-surface geology comparing H/V curves to theoretical transfer functions of 1D models along five well-constrained profiles.
On the basis of geological, geotechnical, and seismic data, we identify three main typologies of seismic response in the city. Each type of response is associated to zones sharing common soil conditions and similar soil classes according to building codes for seismic design. Moreover, we find that the spatial variation of the seismic response in the ancient town area is consistent with the damage pattern produced by a very destructive, well-documented historical earthquake that struck the city in 1688, causing MCS intensity of IX–X in Benevento.
Finally, we use ground motions recorded during the experiment by Improta et al. [Improta, L., G. Di Giulio, and A. Rovelli (2005). Variations of local seismic response in Benevento (Southern Italy) using earthquakes and ambient noise recordings, J. Seism. 9, 191–210.] to generate synthetic seismograms of moderate to strong (Mw 5.7, Molise 2002 and Ms 6.9, 1980 Irpinia) earthquakes. We calibrate the random summation technique by Ordaz et al. [Ordaz, M., J. Arboleda, and S.K. Singh (1995). A scheme of random summation of an Empirical Green's Function to estimate ground motions for future large earthquakes, Bull. Seism. Soc. Am. 85, 1635–1647.] using recordings of these earthquakes available in Benevento. After a satisfactory fit between observed and synthetic seismograms, we compute response spectra at different sites and speculate on effects of the geology class at large level of shaking, including soil nonlinearity. We find that large discrepancies from design spectra prescribed by seismic codes can occur for a wide sector of Benevento, especially for periods < 0.5 s. 相似文献
Simulation technique for whistler mode signal propagating through inhomogeneous plasma using WKB approximation has been developed (Singh, K., Singh, R.P., Ferencz, O.E., 2004. Simulation of whistler mode propagation for low latitude stations. Earth Planet Space 56, 979-987). In the present paper, we have used it for the analysis of recorded signals at low latitudes and estimated the nose frequency, which is not observed on the dynamic spectra. At low latitudes nose frequency is ∼100 kHz or more and therefore it is absent in the dynamic spectra due to attenuation of the signal at higher frequencies. The importance of nose frequency is in determining the exact path of propagation, which is required in probing of ambient medium. It is shown that the method permits to study the nose frequency variation, it can be used to deduce physical parameters as the global electric field. A case study permits to get a reasonable value of the electric field, which up to now could not be done at very low latitude. 相似文献
