HR: 08:30h
AN: S31A-01 INVITED     [Abstracts]
TI: Diffuse Field Correlations in Open Systems
AU: * Weaver, R L
EM: r-weaver@uiuc.edu
AF: Department of Theoretical and Applied Mechanics, University of Illinois, 104 So Wright Street, Urbana, IL 61801 United States
AB: Recent theoretical progress in understanding diffuse field correlations is reviewed with a view towards applications in seismology. As is now well known, an identity between diffuse field correlations and the Green function follows from a definition of a diffuse field as an uncorrelated smooth superposition of normal modes. Such a definition is, however, inapplicable in most open structures, the earth in particular. A preferable definition might be that of room acoustics: a diffuse field is an uncorrelated isotropic superposition of plane waves, but this is inapplicable to heterogeneous structures or near boundaries. It is shown here that an alternative definition, of a locally diffuse field, applies to open heterogeneous structures like the earth. The field is taken to be one in equilibrium with an incident field consisting of an uncorrelated isotropic superposition of incident plane waves. This definition is applicable to both heterogeneous and open systems. It is shown, using a reciprocity argument, to lead to the familiar identity between the diffuse field's correlations and the local Green's function of the structure including all local reflections and scatterings. Applications of these ideas to Seismology have successfully recovered the ballistic surface wave part of the Green function. Other parts of the Green function have not been retrieved. One presumes their amplitudes lie below the remaining fluctuations in the correlograms, but theory has so far not addressed the issue. Here we take a model of diffuse fields in open structures as that resulting from a Gaussian random distribution of sources spread over all space. It is found that this model lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green function. The model indicates that such conformation is strongest at low frequencies. Ray arrivals are detectable only if sufficient data has been collected; the amount of data needed scales with the square of the frequency, and for surface (bulk) waves with the (square of the) source-receiver separation. Thus, long distance high frequency rays will be most difficult to retrieve. The result is consistent with seismological examples.
UR: http://www.tam.uiuc.edu/faculty/weaver/publications/OpenFlucts.pdf
DE: 0910 Data processing
SC: Seismology [S]
MN: 2005 Joint Assembly