An approximation to the transient Green's function G (x a x b, t) between points x a and x b can be estimated by taking the time derivative of the correlation function C ab(t) of records of ambient noise measured at locations x a and x b. From the general relationship between C ab(t) and G (x a x b, t) it is shown, using a stationary-phase-like argument, that in an inhomogeneous environment in the geometric limit C ab(t) consists of a superposition of signed step functions and two-sided logarithmic singularities that are delayed in time by the travel times of the rays connecting x a and x b.
ASJC Scopus subject areas
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics