Acoustic Properties Of Gas-bearing Marine Sediments

As an important parameter of sonar equation,transmission loss is determined by marine environment.Marine sediment is an important boundary that influences sound propagation in the ocean.Sound speed and attenuation in sediment have an important effect on the transmission loss of the sound field.However,the presence of gas can significantly alter the sound speed and attenuation in marine sediment,thereby affecting sound propagation in the ocean.The volume vibrations of bubbles in pore water is intergrated into the continuity equation of pore-fluid filtration on the basis of Biot model for saturated marine sediment,so as to obtain the continuity equation of pore-fluid filtration with bubble volume vibration.On this basis,combining the equations of motion and constitutive relations of the porous medium,a new displacement vector wave equation of porous medium under the influence of bubble is derived.A predictive model for sound speed and attenuation in gassy sediment of type I(interstitial bubbles)and type III(sediment-displacing bubbles)is obtained by introducing the linear approximate solution of bubble pulsation in water and visco-elastic medium under the assumption of small acoustic disturbances.Sound speed and attenuation in gassy sediment show three distinct zones of frequency-dependent behavior.For frequencies below resonance,bubbles vibrate with low-frequency sound wave and the compressibility of marine sediments significantly reduced due to the presence of gas bubbles.Although the density of sediments that contains only a small amount of gas remains unchanged,the sound speed of which is significantly reduced and its coefficient of attenuation is higher than that in gas-free sediments because of the additional dissipation mechanisms due to bubble pulsation.Near the resonance frequency of air bubble,a transition zone is observed,where phase velocity of sound speed dramatically increases.At the resonance frequency,gassy sediment will be highly dispersive and attenuation is highest,similar to the properties of bubble liquids.Above the resonance frequency,the bubbles will be hardly vibrate following the sound frequency,and the compressibility effect of bubble presence is very small,the sound speed remains almost the same as gas-free sediment,but the coefficient of attenuation is higher than that in gas-free sediment and gradually increases with frequency.The acoustic model developed in this thesis can predict sound speed and attenuation for two kinds of compressional waves and one shear wave.The current model combines the dispersion regimes associated with bubble pulsation and the relative motion between pore water and solid framework.Moreover,this model can be used through a fully acoustic inversion to estimate the size distribution of gas bubble.The acoustic reflection coefficient at the water/gassy sediment interface is derived based on the current model for gassy sediments.The effect of bubbles on the reflection coefficient is analyzed through numerical calculation.For wave frequency near the bubble resonance frequency,bubble resonance cause high scattering and high attenuation,which lead to a high reflection coefficient and a poor acoustic penetration at the water/gassy sediment interface.Since that the modulus of frame is smaller than the modulus of grain and fluid,in this thesis,the effective density fluid approximation is applied to current acoustic model for gassy sediments,and perturbation theory had been used to the corrected effective density fluid model for gassy sediment.Moreover,the analytical expression of the equivalent wave number of gassy sediment is derived for non-uniform distribution of gas bubble,and the effect of non-uniform distribution of air bubbles on sound propagation is analyzed.Notably,acoustic scattering caused by the random distribution of bubbles leads to an additional resonance peak at frequency higher than the resonance frequency.In this thesis,an acoustic inversion method is proposed based on spline B and the corrected effective density fluid model,for the inversion of bubble size distribution in marine sediment.This method transforms the integral equation into a system of linear equations,which significantly simplifies the computational complexity.This inversion method can be used when the sound speed and attenuation of the sediment will be known within a certain frequency band.However,if only the data about coefficient of attenuation will be available,the method will be inapplicable.Therefore,in this thesis an alternative inversion method based on modified Gaussian function had been introduced,and this method had been applied for the inversion of attenuation data of gassy sediment over frequency range 500 Hz to 3,000 Hz in laboratory,the measured data is agree with the inversion result.Three experiments,i.e.,water tank,pool,and sea experiments,were conducted to verify the acoustic model for gassy sediment.In laboratory,the attenuation coefficients of sediment that contains different gas contents are measured over frequency range of 50 kHz to 170 kHz by injecting air bubbles into saturated sediments.The measured coefficients of attenuation show significant fluctuation near the frequency of 80 kHz due to resonance of air bubbles.Although none of the corresponding gas bubbles resonates at frequency higher than 100 kHz,the coefficient of attenuation still increases with frequency,which is consistent with the results predicted by the current model for frequency above resonance.After several times of bubble injection,gas content in sediment increases,and leads increasing of coefficient of attenuation.From the pool experiment,four resonance peaks were observed at frequency band 500-3,000 Hz due to the resonance of different bubble sizes.Method of using several modified Gaussian functions was applied to determine the bubble size distribution using measured attenuation data,and the suitable bubble size distribution is obtained.Gas bubbles with radius of 1 mm to 4 mm will dominate attenuation at these four resonance peaks.The change in measured coefficient of attenuation during the sea experiment in situ shows that the resonance of bubbles will change with the change of hydrostatic pressure,which leads to a shift about peak frequency of attenuation.