Accurate time-frequency-wavenumber analysis to study coda waves

An accurate method is developed to characterize the seismic coda phases recorded by small-aperture arrays. The coda is modelled as a superposition of several interfering wavelets identified by their arrival time, frequency content, backazimuth and apparent velocity of propagation. The wavelets are caused by the diffraction and refraction of the direct wavefield by heterogeneities of the propagation medium. The deterministic modelling is different from the statistical one generally used to retrieve mean parameters of the medium. As the complexity of the medium increases, separation of interfering wavelets needs an accurate time-frequency-wavenumber decomposition method that consists of detection and characterization of the different coherent wavelets propagating through the array. Detection is realized by mean time-frequency decomposition, based on the ridges algorithm. The MUltiple SIgnal Classification (MUSIC) algorithm, allowing a higher separation of simultaneous wavelets in the wavenumber domain, is then used to characterize the propagation parameters of the detected components. An optimal use of the MUSIC algorithm assumes the knowledge of the number of sources that simultaneously propagate through the array. The new iterative technique presented here allows the automatic determination of this number of sources. This methodology is applied to synthetic signals simulated in a heterogeneous medium. Results obtained show that: (i) the diffracted wavefield may be more energetic than the primary direct one and (ii) the relative energy diffracted by each heterogeneity is strongly dependent on the location of the array within the medium. The well-controlled results obtained for the synthetic examples allow interpretations of the observations made during the Annot experiment in the southern French Alps in 1998, where four small-aperture arrays were deployed, with small distances between each array ( 10 km). The time-azimuth-velocity evolutions determined for the earthquakes recorded during this experiment are used to characterize the heterogeneous structures of the medium.