Fractional Brownian Motion in Seismic Noise

Here, we present a preliminary study of the statistical features of the seismic noise in the frequency range from 1 Hz to 40 Hz. In detail, we have investigated the 3-d average squared soil displacement r² and the distribution function of the displacement fluctuations in different geological sites. The anomalous scaling of the squared displacement r²~= t^α with 1.5 <= α <= 2, and the Gaussian shape of the fluctuation distribution function suggest that seismic noise, when studied in the limit of ground shaking, is consistent with a persistent fractional browian motion (FBM) characterized by a Hurst exponent H > 1/2. A brief discussion of our results in connection with seismic radiation transport in heterogeneous geological media is also given.