Tokuo Yamamoto

Measurements of acoustic wave velocities and attenuation in marine sediments

Propagation and attenuation of acoustic waves in fluid‐saturated sediments have been studied theoretically and experimentally. In situ acoustic transmission tests in saturated beach sand show that compressional waves are dispersive within a certain frequency band where the intrinsic attenuation is maximum. This indicates that low‐frequency wave velocities in marine sediments are at least 5% to 10% less than the velocities obtained from high‐frequency measurements, and viscous damping, due to the relative motion between solid skeleton and fluid, is the main damping mechanism in the frequency range of 1–30 kHz. The agreement between the experimental results and Biot’s theory enables the remote determination of porosity and permeability of marine sediments by using measured compressional and shear wave characteristics. Approximate relations are used to determine the porosity and permeability of the marine sediments using the measured acoustic wave velocities and attenuation.

Acoustic wave propagation through porous media with arbitrary pore size distributions

In the Biot [J. Acoust. Soc. Am. 28, 168–178 (1956); 28, 179–191 (1956)] theory, the effect of frequency on the viscous forces within a porous medium is treated by replacing the kinematic viscosity ν by an oscillatory viscosity νF, in which F is a function of angular frequency ω, the kinematic viscosity ν, and the single pore size a. The mathematical expression of F for arbitrary distribution of pore sizes that can be used in the Biot theory without modification is presented. It is shown that porous media with a given permeability and porosity may be represented by an infinite number of pore size distributions. The velocities and attenuation of acoustic waves through such porous media are independent of the pore size distribution at the low‐frequency limit and at the high‐frequency limit, while they are strongly dependent on the pore size distribution in the intermediate frequency range. Comparisons between Hamilton’s [Geophysics 37, 620–646 (1972)] data of attenuation coefficient of compressional waves t...

Acoustic scattering in the ocean from velocity and density fluctuations in the sediments

According to spectral analyses of many crosswell acoustic tomograms and cores collected from ten seabed locations [Yamamoto, J. Acoust. Soc. Am. 98, 2235–2248 (1995)], the 3‐D power spectra of velocity and density fluctuations in the seabed sediments are strongly anisotropic and dipping in general. Anisotropy, dip, and spectral properties of the fluctuations vary greatly depending on the sediment type and the geographical location. Based on the Born approximation and the Wood sediment model, an analytical solution has been obtained for the acoustic wave field scattered from the velocity and density fluctuations within sediment volume having arbitrary 3‐D power spectra. Relative density fluctuations are proportional to relative velocity fluctuations in the sediment. The proportionality constant varies from over ten for soft sediments to one for dense sediments. Thus density fluctuation is the dominant mechanism for scattering from a sediment volume. The grazing angle dependence of acoustic backscattering i...

Dynamics of elastically moored floating objects

Abstract The two-dimensional problem of wave transformation by, and motions of, moored floating objects is solved numerically as a boundary value problem by direct use of Greens identity formula for a potential function. The cross-sectional shape of the floating object, the bottom configuration and the mooring arrangements may be all arbitrary. For a given incident wave, the three modes of body motion, the wave system and mooring forces are all solved at the same time. A laboratory experiment is conducted to verify the theory. Generally good agreements between the theory and experiments are obtained as long as the viscous damping due to flow separation is small. A numerical experiment indicates that a conventional sluck mooring is to worsen the wave attenuation by a floating breakwater and that a properly arranged elastic mooring can considerably improve the wave attenuation by a floating breakwater.

Wave-induced pore pressures and effective stresses in inhomogeneous seabed foundations

Abstract Stability analyses of homogeneous and inhomogeneous seabed foundations under attack by storm waves are made by calculating the wave-induced effective stresses. Wave-induced effective stress analysis of homogeneous seabed is made using the theory previously developed by the author which is based on the poro-elastic theory of Biot. Effective stresses in inhomogeneous seabeds induced by waves are calculated by approximating aa inhomogeneous bed by many layers of homogeneous soils each of which has different geotechnical soil properties. A good agreement is obtained between the theory and the pore pressure data from in situ field measurements. For a given wavelength, it is found that there exists a most unstable thickness of homogeneous seabed when the thickness is one-fifth of the wave length. As a realistic example of an inhomogeneous bed, the effective stresses in a typical seabed formation at the Mississippi Delta area of the Gulf of Mexico under the attack of design storm waves are calculated. The numerical results indicate that the storm waves induce a continuous submarine landslide which extends as deep as 9 m from the mud line. Numerical calculations also indicate that such landslides and liquefaction of seabeds can be prevented by placing a layer of concrete blocks or rubble on top of the seabeds.

On the response of a Coulomb‐damped poroelastic bed to water waves

Abstract The problem of forced vibration of a slightly inelastic porous bed by water waves is treated analytically on the basis of a linearized expression of the nonlinear damping term for the grain‐to‐grain friction in bed soils and the linear theory by Biot (1962a [Jour. Appl. Physics, 33:1482–1498]) on the elastic wave propagation in porous media. A dispersion relation of water waves is obtained as a function of wave frequency, water depth, permeability, Poissons ratio, rigidity, and specific loss of bed soil. Three types of elastic waves are induced in a bed by water waves: a shear wave and a compressional wave in the skeletal frame of soil, and a compressional wave in the pore fluid. The compressional wave, due to the motion of the pore fluid relative to the skeletal frame of soil, is highly damped by the viscosity of pore fluid and only a short range effect near the boundaries of discontinuity, such as a sea‐seabed interface. The seabed response to water waves is characterized by the two Mach numbe...

Summary of marine sedimentary shear modulus and acoustic speed profile results using a gravity wave inversion technique

Experimental techniques and inverse methods have been established to extract marine sediment shear modulus with depth profiles from measurements of wave‐induced seabed motion on the shallow continental shelf. Seabed sediments are modeled as a quasistatic, incompressible, layered elastic medium in response to wave‐induced pressures. An iterative eigenvalue expansion technique is used to extract the inverse. Under typical continental shelf conditions, this inversion method is found to have a depth resolution limit of approximately 3 m, with a maximum penetration of 200 m. Using semiempirical sediment models, it is possible to deduce sediment porosity, bulk density, and shear and compressional wave speeds from the shear modulus profile. One representative result from the New Jersey Shelf is examined in detail, and favorably compared with independent sediment profiling methods. A summary of experimentally determined sediment profiles from four other sites on the Eastern U.S. continental shelf is given.

Synthetic seismograms for marine sediments and determination of porosity and permeability

We present numerical simulations of vertical seismic profiles (VSPs) of marine sediments. The theoretical seismograms, which are computed for vertically incident waves in flat layered poroelastic media, include the effects of dispersion and attenuation predicted by Biot theory. According to Biot theory, fast and slow compressional waves are excited and there is mode conversion at the interfaces. We include this effect in the calculation of reflection and transmission coefficients as an energy‐loss mechanism through the slow compressional waves. Finally, we examine the spectral ratio method for determining porosity and permeability from synthetic seismogram data. Analytical expressions for the velocity and specific attenuation are found based on the weak‐frame approximation. Once the frequency‐dependent velocity and specific attenuation are calculated, the porosity and permeability of marine sediments can be determined by using the proposed weak‐frame approximations. Spectral ratio calculations on syntheti...

Gravity waves and acoustic waves generated by submarine earthquakes

Abstract The time harmonic problem of the propagation of gravity waves and acoustic waves in the ocean by vertical oscillation of a block of ocean floor is treated analytically. It is found that the evanescent modes of gravity waves change into the propagating modes of acoustic waves at frequencies above the cut-off frequencies. Therefore, the common assumption of an incompressible ocean water invites serious errors in the pressures and the tsunami waves near the source. From the propagating acoustic wave spectra, it is shown that the size and the amplitude of the oscillating source can be determined far in advance of tsunami arrival.

Experimental investigation of sediment effect on acoustic wave propagation in the shallow ocean

In shallow water the sediment layers have very strong effects on the propagation of acoustic waves. An effort to study the effects of the sediment has been made using 50‐ to 600‐Hz continuous wave acoustic propagation data taken by Carey [‘‘Experimental verification and application of bottom shear modulus profile (BSMP) method,’’ Oceans ’91 Proceedings (1991)] at the Atlantic margin coring project (AMCOR) borehole 6010 off the coast of New Jersey combined with sediment properties measured at that site by Yamamoto et al. of the University of Miami Geoacoustic Laboratory using the bottom shear modulus profiler (BSMP) method. Excellent agreement was found between the model and data indicating the acceptability of BSMP sediment values as input for acoustic propagation studies. The introduction of shear or tangential stresses in the model was found to have no effect upon which modes propagated but only on their modal intensity. The higher the order of the mode the greater the penetration in the seafloor and th...