Gas Void Fraction Estimation in Gassy Sand Sediment with Difference Frequency Wave Method

Nonlinearity parameter can be used for the estimation of the gas void fraction in gassy sand sediment. If two primary acoustic waves of different frequencies are incident on gassy sediment, nonlinear acoustic waves can be strongly generated at the difference frequency of the primary frequencies. Nonlinearity parameter of gassy sediment is related to the gas void fraction provided the primary frequencies are lower than bubble resonance frequencies. In the present study, the difference frequency wave was employed to estimate nonlinearity parameter of gassy sand sediment under laboratory conditions. Nonlinearity parameter in gassy sand sediment was e =2.54·10. Then, the estimated gas void fraction in gassy sand sediment was ß =7.98·10. This value well agreed with that estimated from the sound speed variation. This study suggests that the difference frequency acoustic wave method seems very feasible to estimate the void fraction in gassy sand sediment. INTRODUCTION The porous media, such as soils, rocks, and sediments, exhibit high nonlinearity in comparison with the nonporous media [1, 2]. The nonlinearity of the sediments can play an important role for oil field prospecting and ecological monitoring in the ocean. Most of the sediments in the ocean contain a lot of bubbles, which show very sensitive nonlinear responses for acoustic waves. Therefore, nonlinear acoustic responses of the bubbles can be usefully utilized for estimation of the gas void fraction in gassy sediment [3]. In this study, the nonlinear generation of difference frequency acoustic waves in gassy sand sediment under laboratory conditions was investigated. The nonlinearity parameter of the sediment was evaluated by using a theory of the parametric acoustic array for difference frequency acoustic wave. Gas void fraction of the sediment was estimated from the evaluated nonlinearity parameter. It was also compared with that estimated from the sound speed variation in the sediment. THEORY If we consider that two primary acoustic waves are incident on a sediment layer with thickness l in water as shown in Fig.1(a), the nonlinear acoustic wave at the difference frequency can be generated in the layer. The acoustic pressure fields of two primary acoustic waves in the sediment layer located at far distance H can be expressed as follows: 2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 ( ( ') / ) exp{ ( )}exp[ { ( / 2 )}] f s w P A TR D H z H j t k z H θ α ω ρ⊥ = − − − + , (Eq.1) 1,2 A are pressure amplitudes of two primary waves at the piston source, 1,2 ( ') D θ and 2 1,2 1,2 / f w R a π λ = are the beam directivity functions and the Rayleigh distance for primary frequencies at the piston source in water, 2 /( ) s s s s w w T c c c ρ ρ ρ = + is the transmission coefficient of the primary acoustic wave from water into the sediment layer. Then, the backscattered difference frequency wave field from the layer can be given in forms of