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P>Computing the magnitude of an earthquake requires correcting for the propagation effects from the source to the receivers. This is often accomplished by performing numerical simulations using a suitable Earth model. In this work, the energy magnitude M(e) is considered and its determination is performed using theoretical spectral amplitude decay functions over teleseismic distances based on the global Earth model AK135Q. Since the high frequency part (above the corner frequency) of the source spectrum has to be considered in computing M(e), the influence of propagation and site effects may not be negligible and they could bias the single station M(e) estimations. Therefore, in this study we assess the inter- and intrastation distributions of errors by considering the M(e) residuals computed for a large data set of earthquakes recorded at teleseismic distances by seismic stations deployed worldwide. To separate the inter- and intrastation contribution of errors, we apply a maximum likelihood approach to the M(e) residuals. We show that the interstation errors (describing a sort of site effect for a station) are within +/- 0.2 magnitude units for most stations and their spatial distribution reflects the expected lateral variation affecting the velocity and attenuation of the Earth's structure in the uppermost layers, not accounted for by the 1-D AK135Q model. The variance of the intrastation error distribution (describing the record-to-record component of variability) is larger than the interstation one (0.240 against 0.159), and the spatial distribution of the errors is not random but shows specific patterns depending on the source-to-station paths. The set of coefficients empirically determined may be used in the future to account for the heterogeneities of the real Earth not considered in the theoretical calculations of the spectral amplitude decay functions used to correct the recorded data for propagation effects.
In this work, we analyse continuous measurements of microseisms to assess the reliability of the fundamental resonance frequency estimated by means of the horizontal-to-vertical (H/V) spectral ratio within the 0.1-1 Hz frequency range, using short-period sensors (natural period of 1 s). We apply the H/V technique to recordings of stations installed in two alluvial basins with different sedimentary cover thicknesses-the Lower Rhine Embayment (Germany) and the Gubbio Plain (Central Italy). The spectral ratios are estimated over the time-frequency domain, and we discuss the reliability of the results considering both the variability of the microseism activity and the amplitude of the instrumental noise. We show that microseisms measured by short period sensors allow the retrieval of fundamental resonance frequencies greater than about 0.1-0.2 Hz, with this lower frequency bound depending on the relative amplitude of the microseism signal and the self-noise of the instruments. In particular, we show an example where the considered short-period sensor is connected to instruments characterized by an instrumental noise level which allows detecting only fundamental frequencies greater than about 0.4 Hz. Since the frequency at which the peak of the H/V spectral ratio is biased depends upon the seismic signal-to-instrument noise ratio, the power spectral amplitude of instrumental self- noise should be always considered when interpreting the frequency of the peak as the fundamental resonance frequency of the investigated site.