### Abstract

A pulse propagates normally through a stratified medium. It is known from numerical experiments and heuristic arguments that under certain circumstances, including those arising in seismic exploration, the shape and precise travel time of the forward propagating pulse as it travels over large distances depends to a good approximation only upon the autocorrelation function of the medium properties. The expression for this dependence is surprisingly simple and is known as the O'Doherty-Anstey approximation after the authors who first derived it in 1971. We give a theoretical estimate of the error committed in making this approximation. The analysis proceeds by first obtaining a closed equation governing the evolution of the propagation mode of interest. There is an interesting interplay of frequency- and time-domain considerations. Thus the error is frequency dependent, but depends also on the length of time for which the signal is to be computed. In contrast to earlier related work we give a rigorous error estimate, which is derived in a deterministic context, without the use of small or large parameters. Some previous results involving limits as small parameters tend to zero are recovered by application of our general estimate.

Original language | English (US) |
---|---|

Pages (from-to) | 357-373 |

Number of pages | 17 |

Journal | Wave Motion |

Volume | 21 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1995 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Wave Motion*,

*21*(4), 357-373. https://doi.org/10.1016/0165-2125(95)00008-7

}

*Wave Motion*, vol. 21, no. 4, pp. 357-373. https://doi.org/10.1016/0165-2125(95)00008-7

**The accuracy of the O'Doherty-Anstey approximation for wave propagation in highly disordered stratified media.** / Berlyand, Leonid V.; Burridge, Robert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The accuracy of the O'Doherty-Anstey approximation for wave propagation in highly disordered stratified media

AU - Berlyand, Leonid V.

AU - Burridge, Robert

PY - 1995/1/1

Y1 - 1995/1/1

N2 - A pulse propagates normally through a stratified medium. It is known from numerical experiments and heuristic arguments that under certain circumstances, including those arising in seismic exploration, the shape and precise travel time of the forward propagating pulse as it travels over large distances depends to a good approximation only upon the autocorrelation function of the medium properties. The expression for this dependence is surprisingly simple and is known as the O'Doherty-Anstey approximation after the authors who first derived it in 1971. We give a theoretical estimate of the error committed in making this approximation. The analysis proceeds by first obtaining a closed equation governing the evolution of the propagation mode of interest. There is an interesting interplay of frequency- and time-domain considerations. Thus the error is frequency dependent, but depends also on the length of time for which the signal is to be computed. In contrast to earlier related work we give a rigorous error estimate, which is derived in a deterministic context, without the use of small or large parameters. Some previous results involving limits as small parameters tend to zero are recovered by application of our general estimate.

AB - A pulse propagates normally through a stratified medium. It is known from numerical experiments and heuristic arguments that under certain circumstances, including those arising in seismic exploration, the shape and precise travel time of the forward propagating pulse as it travels over large distances depends to a good approximation only upon the autocorrelation function of the medium properties. The expression for this dependence is surprisingly simple and is known as the O'Doherty-Anstey approximation after the authors who first derived it in 1971. We give a theoretical estimate of the error committed in making this approximation. The analysis proceeds by first obtaining a closed equation governing the evolution of the propagation mode of interest. There is an interesting interplay of frequency- and time-domain considerations. Thus the error is frequency dependent, but depends also on the length of time for which the signal is to be computed. In contrast to earlier related work we give a rigorous error estimate, which is derived in a deterministic context, without the use of small or large parameters. Some previous results involving limits as small parameters tend to zero are recovered by application of our general estimate.

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U2 - 10.1016/0165-2125(95)00008-7

DO - 10.1016/0165-2125(95)00008-7

M3 - Article

VL - 21

SP - 357

EP - 373

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

IS - 4

ER -