• Guided waves;
  • Site effects;
  • Statistical seismology;
  • Wave scattering and diffraction


We have studied the partition of shear, compressional and kinetic energies in the coda of 10 earthquakes recorded on a dense array, located at Pinyon Flats Observatory (PFO), California. Deformation energies are estimated by measuring finite differences of the wavefield components. We have thoroughly studied the validity and stability of this technique for the PFO data and obtained reliable measurements in the 5–7 Hz frequency band. We observe a clear stabilization of the ratio between shear and compressional energies (WS/WP) in the coda, with similar values for all 10 earthquakes under study. We interpret this observation as a signature of equipartition. The average WS/WP ratio is about 2.8, which is smaller by a factor 2.5 than the expected value, around 7.2, for equipartitioned elastic waves at the surface of a homogeneous Poisson half-space. The ratio between the vertical and horizontal kinetic energies (V2/H2) also exhibits stabilization in the coda and can be measured from 5 to 25 Hz. The V2/H2 ratio shows an abrupt transition from 0.1 in the 5–10 Hz band, to about 0.8 in the 15–25 Hz band. These measured values are again in sharp contrast with the theoretical prediction, around 0.56, for equipartitioned elastic waves at the surface of a Poisson half-space. To explain these observations, we have developed a theory of equipartition in a layered elastic half-space. Using a rigorous spectral decomposition of the elastic wave equation, we define equipartition as a white noise distributed over the complete set of eigenfunctions. This definition is shown to agree with the standard physical concepts in canonical cases. The theory predicts that close to the resonance frequency of a low-velocity layer, the ratio between the shear and compressional energies strongly decreases. Using a detailed model of the subsurface at PFO, this counter-intuitive result is found to be in good qualitative and quantitative agreement with the observations. Near the resonance frequency of the low-velocity structure, the drop of the energy ratios WS/WP and V2/H2 is controlled by the change of ellipticity of the Rayleigh wave and the large contribution of the fundamental Love mode. At higher frequencies, the interplay between Rayleigh and Love modes trapped in shallow low-velocity layers is responsible for the abrupt increase of the kinetic energy ratio V2/H2. Our study demonstrates that the partition of energy in the seismic coda contains information on the local geological structure.