Article,
Accurate time-frequency-wavenumber analysis to study coda waves
Geophysical Journal International, 158 (2): 577--591 (August 2004)
DOI: 10.1111/j.1365-246X.2004.02211.x
Abstract
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.
