| Summary: | 博士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 98 === This study presents two analytical models for describing the propagation and reflection of elastic waves through a porous half-space permeated by two immiscible viscous fluids. These models are based on the poroelastic equations developed by Lo et al. (2005) for a porous medium containing two immiscible, viscous, and compressible fluids.
The first developed model depicts the propagation and attenuation of Rayleigh waves along the impermeable surface of an unsaturated poroelastic half-space. This demonstrates the existence of three modes of Rayleigh waves. These three Rayleigh waves, which are induced by the three dilatational waves (P1, P2, and P3 waves) and one shear wave (S wave) in a two-fluid saturated medium, can be expressed as the R1, R2, and R3 waves in a descending order of magnitude of phase speed. As the excitation frequency and water saturation are given, the dispersion equation of a cubic polynomial can be solved mathematically to obtain the phase speeds and attenuation coefficients of the R1, R2, and R3 waves.
Computational results demonstrate that the phase speed of the R1 wave is frequency-independent (non-dispersive) in Columbia fine sandy loam. Its value is approximately 93-95% of the shear wave speed, and nearly 28% to 49% of the P1 wave speed at frequencies of 50-200 Hz and relative water saturation ranging from 0.01 to 0.99. However, phase speeds and attenuation coefficients of the R2 and R3 waves are dispersive at the frequencies examined. The P2 and P3 waves phase speeds range 56-90% of the R2 and R3 wave speeds. The R1 wave attenuates the least while the R3 wave has the highest attenuation. Furthermore, the phase speed of the R1 wave under an impermeable surface is 1.01-1.37 times of that under a permeable boundary. Surface impermeability causes the R1 wave phase speed to match the S wave phase speed closely, compared to permeable surfaces which exhibits reduced speed at high water saturation.
In addition to the previous unsaturated case, the first model presented is extended to include a two-fluid system to investigate the impact of viscous pore-fluid mixtures on Rayleigh wave propagation and attenuation. As the seismic frequency (1-100 Hz) is stipulated, the dispersion equation is mathematically solved to determine the phase speeds and attenuation coefficients of Rayleigh waves in Lincoln sand respectively permeated by three different fluid mixtures (air-water, air-oil and oil-water). Lincoln sand is filled by two-fluid mixtures at wetting fluid saturation ranging from 1% to 99%. Computational results show that the phase speed of the R1 wave is approximately equal to 93-95% of the S wave speed in the air-water and air-oil mixtures, but the oil-water mixture is 95-96% of the S wave speed. The attenuation coefficients of the R1 wave in both air-water and air-oil systems are dependent on the difference in two fluid densities and the relative motion between the solid and fluid phases. However, the attenuation coefficient of the R1 wave in the oil-water system depends on the effective kinematic viscosity. The phase speeds of the R2 and R3 waves possess similar trends to those of the P2 and P3 waves found in Lo et al. (2005). This implies the out-of-phase motion among these three phases (solid, non-wetting, and wetting) influence the R2 wave phase speed while capillary pressure affects the R3 wave phase speed. The attenuation coefficient of the R2 wave is shown to be positively correlated to the effective dynamic viscosity similar to that of the P2 wave. The attenuation coefficient of the R3 wave in an oil-water system is highest among the three fluid mixtures, but the differences in the three two-fluid mixtures are not obvious.
The second model derived describes an incident P1 wave traveling through a traction-free porous unsaturated half-space, then four reflection waves (P1, P2, P3, S) yield due to the incident P1 wave. The amplitude ratios of the P1, P2, P3, and S waves to the incident P1 wave are derived. This model also portrays the surface displacement and stress of the solid phase during the wave reflection process. Computational results show that the reflection amplitude, surface displacement, and surface stress are functions of water saturation and angles of incidence at seismic frequency ranging from 1 Hz to 100 Hz in Lincoln sand. At normal and grazing incidence, the reflected P1 wave exists, but the reflected P2, P3, and S waves vanish during the reflection process. The reflected amplitude ratios of the P1 and S waves to the incident P1 wave are frequency-independent, while those of the P2 and P3 waves depend on excitation frequency.
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