### Abstract

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}.

Original language | English (US) |
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Journal | Journal of the Acoustical Society of America |

Volume | 130 |

Issue number | 4 |

DOIs | |

State | Published - Oct 2011 |

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### ASJC Scopus subject areas

- Acoustics and Ultrasonics
- Arts and Humanities (miscellaneous)

### Cite this

**Noise interferometry in an inhomogeneous environment in the geometric limit.** / Brown, Michael G.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Noise interferometry in an inhomogeneous environment in the geometric limit

AU - Brown, Michael G

PY - 2011/10

Y1 - 2011/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=82255193435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=82255193435&partnerID=8YFLogxK

U2 - 10.1121/1.3610260

DO - 10.1121/1.3610260

M3 - Article

VL - 130

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 4

ER -