The traditional acoustic attenuation coefficient is derived from an analogy of the attenuation of an electromagnetic wave propagating inside a non-ideal medium, featuring only the attenuation of wave propagation. Nonetheless, the particles inside viscous solids have mass, vibrating energy, viscosity, and inertia of motion, and they go through transient and damping attenuation processes. Based on the long-wavelength approximation, in this paper, we use the energy conservation law to analyze the effect of the viscosity of the medium on acoustic attenuation. We derive the acoustic attenuation coefficient by combinations of the dynamical equation of a solid in an acoustic field with conventional longitudinal wave propagation under a spring oscillator model. Considering the attenuation of propagating waves and the damping attenuation of particle vibration, we develop a frequency dispersion relation of phase velocity for the longitudinal wave propagating inside viscous solid media. We find that the acoustic impulse response and vibrational system function depends on the physical properties of the viscous solid media and their internal structure. Combined with system function, the impulse response can be an excellent tool to invert the physical properties of solids and their internal structures. We select a well-known rock sample for analysis, calculate the impulse response and vibrational system function, and reveal new physical insight into creating acoustic attenuation and frequency dispersion of phase velocity. The results showed that the newly developed acoustic attenuation coefficients enjoy a substantial improvement over the conventional acoustic attenuation coefficients reported in the literature, which is essential for industrial applications; so are the dispersion characteristics.

We report on a transient response model of thin cylindrical piezoelectric transducers used in the petroleum logging tools, parallel to a recently established transient response model of thin spherical-shell transducers. Established on a series of parallel-connected equivalent-circuits, this model provides insightful information on the physical characteristics of the thin cylindrical piezoelectric transducers, i.e., the transient response, center-frequency, and directivity of the transducer. We have developed a measurement system corresponding to the new model to provide a state-of-the-art comparison between theory and experiment. We found that the measured results were in good agreement with those of theoretical calculations.

Geoacoustic exploration is a rapidly evolving field investigating underground rock formations and sediment environments through acoustic waves. In this paper, we present a review of recent research progress, focusing on newly discovered physical phenomena, such as the reflection and refraction of acoustic waves at the interface between anisotropic rocks and between liquid and solid, the characteristics of electric-acoustic (and acoustic-electric) conversion of piezoelectric transducers, the physical mechanism of acoustic wave propagation in viscous media, and the generation of intrinsic noise. We developed new physical models, introduced a parallel transmission network describing piezoelectric transducers for electric-acoustic (and acoustic-electric) energy transfer, and derived new formulations and algorithms associated with the latest model. We will discuss the potential of abnormal incidence angle, acoustic attenuation, and acoustic Goos-Hänchen effect and propose a method of inversion of formation reflection coefficient using logging and seismic data acquired from anisotropic rocks with dip angle. We will also discuss the physical mechanism and potential applications of the intrinsic noise generated inside viscous solid media. Finally, we introduce a parallel/series lumped vibrational transmission network, explain the acoustic measurement process, and discuss applications of the Kaiser effect in petroleum engineering.

We report a newly discovered anomalous incident-angle of an elastically refracted P-wave, arising from a P-wave impinging on an interface between two VTI media with strong anisotropy. This anomalous incident-angle is found to be located in the post-critical incident-angle region corresponding to a refracted P-wave. Invoking Snell’s law for a refracted P-wave provides two distinctive solutions before and after the anomalous incident-angle. For an inhomogeneously refracted and elliptically polarized P-wave at the anomalous incident-angle, its rotational direction experiences an acute variation, from left-hand elliptical to right-hand elliptical polarization. The new findings provide us an enhanced understanding of acoustical-wave scattering and lead potentially to widespread and novel applications.

In this paper, we report a new model in analysis of spherical thin-shell piezoelectric transducers for transient response, based on Fourier transform and the principle of linear superposition. We show that a circuit-network, a combination of a series of parallel-connected equivalent-circuits, can be used in description of a spherical thin-shell piezoelectric transducer. When excited by a signal with multiple frequency components, each circuit would have a distinctive radiation resistance and a radiation mass, arising from an individual frequency component. Each frequency component would act independently on the electric/mechanic-terminals. A cumulative signal-output from the mechanic/electric-terminals is measured as the overall acoustic/electric output. As a prototype example in testing the new model, we have designed two spherical shin-shell transducers, applied a gated sine electric-signal as the initial excitation, and recorded the experimental information. The transient response and the output signals are calculated based on the new model. The results of calculation are in good agreement with that of experimental observation.