Equipartition Assessment Using one Station

The elastodynamic Green function can be retrieved from averaging cross correlations of recorded motions within a equipartitioned diffuse seismic field. If only one station is available the autocorrelation allows computing the kinetic energy density and its average is proportional to the imaginary part of the Green function trace at the source. The sum of average energy densities for each degree of freedom (1, 2 and 3) equals the sum of energy densities associated to the various wave types (e.g. P, SV, and SH). For a full elastic space , energy densities fulfill: E1+E2+E3 = EP+ES and equipartition implies that energy is shared in fixed proportions. By means of carefully designed experiments (Hennino et al., 2001), the elastic energy components are separated in both dilatational and shear waves to compute spatial derivatives from small array recordings. It was found that coda waves display elastic equipartition as predicted by theory. Alternatively, here we explore the use of the degrees of freedom of a 3D system to assess the equipartitioned nature of the seismic field using only one station. In the full space case the energies related to each orthogonal direction are equal, therefore each direction shares one third of total available energy density. We used the same data set gathered by Hennino et al. at Chilpancingo, Mexico. Twelve earthquakes were recorded at the four stations of a small array. For each component we calculate the Hilbert envelope. An estimate of the component energies is obtained as fraction of the total energy. For a smoothed running average of fifteen seconds the fraction has a mean close to approximately 0.33, at several portions of records. These preliminary results suggest that equipartition in the Maxwell sense is displayed not only by the coda but by the pre-event noise as well. Another set of data was analyzed. A series of records were obtained at four stations in deep sites in the Tautona and Mponeng gold mines, South Africa. The depth of the recordings ranges from 2 to 3.5 km and the records show some small earthquakes (M=2) and noise as well. A preliminary analysis suggests that the coda exhibits clear elastic equipartition in the frequency band 10 - 30 Hz. Although in some cases the pre- event noise shows equipartition. This feature is not ubiquitous. Our results from analysis of recorded data in Chilpancingo, Mexico, and Tautona Mine, South Africa suggest that equipartition, and thus the diffuse nature of a seismic field, can be estimated using only one station. Acknowledgements. Partial supports from DGAPA-UNAM, Project IN114706, Mexico; and from project DyETI of INSU-CNRS, France are greatly appreciated.