David M. F. Chapman

Dispersion of interface waves in sediments with power-law shear speed profiles. II. Experimental observations and seismo-acoustic inversions

The propagation of seismic interface waves is investigated in soft marine sediments in which the density is constant, the shear modulus is small, and the profile of shear speed c(s) versus depth z is of the power-law form c(s) (z) = c0z(v), in which c0 and v are constants (0< v < 1). Both the phase speed V and the group speed U of interface waves scale with frequency as f(v/(v -1)) and they obey the simple relation U= (1 - v) V. These relations are derived in a simple way using ray theory and the WKB method; a companion paper [O. A. Godin and D. M. F. Chapman, J. Acoust. Soc. Am. 110, 1890 (2001)] rigorously derives the same result from the solutions to the equations of motion. The frequency scaling is shown to exist in experimental data sets of interface wave phase speed and group speed. Approximate analytical formulas for the dispersion relations (phase and group speed versus frequency) enable direct inversion of the profile parameters c0 and v from the experimental data. In cases for which there is multi-mode dispersion data, the water-sediment density ratio can be determined as well. The theory applies to vertically polarized (P-SV) modes as well as to horizontally polarized (SH) modes (that is, Love waves).

Low‐frequency acoustic propagation loss in shallow water over hard‐rock seabeds covered by a thin layer of elastic–solid sediment

Shallow‐water seabeds are often varied and complex, and are known to have a strong effect on acoustic propagation. Some of these seabeds can be modeled successfully as fluid or solid half‐spaces. However, unexpectedly high propagation loss with respect to these models has been measured in several regions with rough, partially exposed, hard‐rock seabeds. It is shown that the high propagation loss in these areas can be modeled successfully by introducing a thin layer of elastic–solid sediment over the hard‐rock substrate. Propagation loss predictions using the safari fast‐field program exhibit bands of high loss at regularly spaced frequencies. Normal‐mode calculations show resonance phenomena, with large peaks in the modal attenuation coefficients at these same frequencies, and with rapid changes in the mode wavenumbers. Bottom reflection loss calculations indicate that the high propagation loss is due to absorption of shear waves in the sediment layer.

Shear-speed gradients and ocean seismo-acoustic noise resonances

Measurements of infrasonic seismo-acoustic ambient noise using an ocean bottom seismometer in shallow water have uncovered an unusual phenomenon: the noise spectrum of the horizontal component of seabed velocity shows several prominent peaks in the frequency range 0–8 Hz, whereas the noise spectra of both the acoustic pressure and the vertical component of seabed velocity show very weak or nonexistent features at the same frequencies. This structure is interpreted theoretically as resonances of shear waves of vertical polarization in the upper sediment layer, excited by the diffuse infrasonic sound field in the water. Independent interface wave dispersion studies at the site have revealed an approximate power-law profile of shear speed versus depth, having the form c(z)=c0zν, with c0=21.5 and ν=0.60 (SI units). The theoretical development concentrates on exact analytic solutions for the resonance frequencies and wave field for power-law profiles and on the WKB and more advanced asymptotic solutions in the...

The group velocity of normal modes

A simple, general formula for normal mode group velocities provides an intuitive grasp of the factors influencing group velocity, especially for shallow water environments associated with strong seabed interaction. This is demonstrated using some hypothetical shallow water environments, and by comparing mode shapes at different frequencies. The formula is especially convenient to implement in normal mode computer codes which already perform similar calculations for mode normalization and attenuation coefficients. Using the WKB approximation to the normal mode functions, the formula is identified with the average horizontal speed of the ray equivalent to the mode. For a shallow water environment with bottom interaction, the group velocity formula is shown to include the beam and the time displacement effects of modified ray theory. This result strenghthens the ray/mode analogy which is used in analyzing ocean acoustics problems.

Underwater acoustic ambient noise levels on the eastern Canadian continental shelf

This paper reports the analysis of shallow‐water ambient noise levels collected by Defence Research Establishment Atlantic during 14 cruises over the period 1972 to 1985. A weighted average is formed to de‐bias the samples, with the aim of answering the question: ‘‘If one were to pick a site randomly on the eastern Canadian continental shelf at a random time, and perform an ambient noise measurement, what would be the expected noise level?’’ The samples are also grouped according to whether they were taken on the Scotian Shelf, the Grand Banks, or the Flemish Cap, and according to season. The frequency range covered is 30 to 900 Hz. The weighted mean and standard deviation of the noise levels are presented, as well as the correlation coefficient between the noise levels and wind speed. The results show that the eastern Canadian continental shelf as a whole presents levels that are characteristic of areas with high shipping density and good acoustic propagation, with the Scotian Shelf showing generally hig...

The normal-mode theory of air-to-water sound transmission in the ocean

The normal‐mode theory is presented for the transmission of sound from a stationary source in a homogeneous, stationary, air layer into an arbitrarily stratified ocean. Transmission loss calculations are performed for a Pekeris‐type shallow‐water environment consisting of an isospeed water layer over a uniform elastic solid seabed. Notable features of the results are: the sensitivity of transmission loss to bottom type, the weak dependence of incoherent transmission loss upon source height, and a 25 log r range dependence of average transmission loss in the mode‐stripping region. Finally, some approximate intensity‐range relations are proposed for shallow‐water propagation.

The effective depth of a Pekeris ocean waveguide, including shear wave effects

Weston’s [J. Acoust. Soc. Am. 32, 647–654 (1960)] concept of the effective depth of a Pekeris‐type shallow water waveguide has been extended to admit seabeds that support shear waves. The amended effective depth formula leads to estimates of normal mode phase speeds that are surprisingly accurate, without numerical iteration. Results for six hypothetical, though realistic, bottom types are compared with an ‘‘exact’’ normal mode model that includes shear wave effects and another normal mode model that does not.

A simple shallow water propagation model including shear wave effects

The Perkeris model has proved to be very useful in describing some features of acoustic propagation in shallow water, and as a simple test of ideas in normal mode theory. The basic model consists of a homogeneous layer of fluid overlying an infinite homogeneous fluid half‐space of greater sound speed. Here we extend the Pekeris model to handle the case of a fluid overlying an elastic basement in which the shear speed is less than the (compressional) speed of sound in the fluid. This gives rise to leaky modes in which both the mode eigenfunctions and eigenvalues are complex. The model predictions are compared to some measured propagation losses for a shallow water site overlying a chalk bottom, where shear‐wave conversion at the water‐chalk interface causes large losses. The predictions of the simple model explain the very high losses measured at frequencies less than 200 Hz. At higher frequencies the sound speed profile and a thin sediment layer become important, but then an all‐fluid normal mode model is...

Quantifying the interaction of an ocean bottom seismometer with the seabed

A theory is presented for the coupling between an ocean bottom seismometer (OBS), the sediments upon which it rests, and the surrounding water. Assuming that rotational and tilt effects are negligible (or have been made negligible through instrument design), the response of the OBS to forced harmonic motion is considered in both horizontal and vertical directions. Under these conditions it is concluded that the measured ratio of velocities when the OBS is on the seabed and when it is freely suspended in water (for an identical force) completely characterizes the OBS/seabed interaction. This enables the velocity transfer functions to be directly calculated without recourse to a detailed model of sediment/structure interaction. An OBS was designed and constructed with good coupling to seabed motion and reduction of rocking effects as principal design criteria, including an onboard shaker to conduct in situ coupling experiments. The amplitude and phase of coupling data collected on a clay seabed provide transfer functions due to horizontal and vertical seabed motion and horizontal water motion. In addition, a simple mass-spring-dashpot model of OBS/seabed interaction permits the analysis of amplitude-only coupling data. Good vertical coupling can be achieved over a wide bandwidth by designing the sensor package to have a large hydrodynamic added mass in the vertical. Good coupling to horizontal seabed motion is more difficult to achieve but is possible within a limited bandwidth, even on very soft seabeds. Finally, an example of seismoacoustic noise is presented. Hydrophone signals are compared with horizontal geophone signals received from sources within the ocean and within the seabed, and the differences are explained in terms of the coupling transfer functions.

A coherent ray model of plane‐wave reflection from a thin sediment layer

Plane‐wave reflection from a thin, elastic solid sediment layer over a hard basement is modeled by a simple ray model that includes only two ray families: a family of compressional waves that transit the sediment layer any number of times before returning to the water; and a similar family that includes doubly converted compressional waves. (The latter are compressional waves that are converted to shear waves at the basement, make one or more round‐trip transits of the sediment layer, and are converted back into compressional waves at the basement.) The theory is applied to homogenous sediment layers with low shear speeds, and it provides valuable insight into the physical processes governing reflection from several seabed environments of interest. The coherent sum of all the rays belonging to these families leads to a closed‐form expression for the overall reflection coefficient that includes several characteristic features also simulated by full wave‐theoretical numerical models, such as bottom‐loss res...