Youcef Bouzidi

A large ultrasonic bounded acoustic pulse transducer for acoustic transmission goniometry : Modeling and calibration

A large, flat ultrasonic transmitter and a small receiver are developed for studies of material properties in acoustic transmission goniometry. While the character of the wave field produced by the transmitter can be considered as a plane wave as observed by the receiver, diffraction effects are noticeable near critical angles and result in the appearance of weak but detectable arrivals. Transmitted ultrasonic waveforms are acquired in one elastic silicate glass and two visco-elastic acrylic glass sample plates as a function of the angle of incidence. Phase velocities are determined from modeling of the shape of curves of the observed arrival times versus angle of incidence. The waveform observations are modeled using a phase propagation technique that incorporates full wave behavior including attenuation. Subtle diffraction effects are captured in addition to the main bounded pulse propagation. The full propagation modeling allows for various arrivals to be unambiguously interpreted. The results of the plane wave solution are close to the full wave propagation modeling without any corrections to the observed wave field. This is an advantage as it places confidence that later analyses can use simpler plane wave solutions without the need for additional diffraction corrections. A further advantage is that the uniform bounded acoustic pulse allows for the detection of weak arrivals such as a low energy edge diffraction observed in our experiments.

Quantitative modeling of reflected ultrasonic bounded beams and a new estimate of the Schoch shift

The wavefields of bounded acoustic beams and pulses reflected from water-loaded plates are fully modeled with the phase advance technique. The wavefield produced at the source is propagated at any incidence angle using phaseshift modeling that incorporates the full analytic solution for the acoustic reflectivity at the interface. This approach provides for the ready visualization of both the stationary monofrequency beam wavefield and animation of the temporally bounded pulse. The model images are reminiscent of the classic Schlieren photographs that first illustrated the nonspecular behavior of the reflected beams incident near critical angles. Various phenomena such as the lateral displacement and the null zone at the Rayleigh critical angle are recreated. A new approximation for this shift agrees well with that of the peak energy of the reflected beam. Similar effects are observed during the reflection of a bounded pulse. Although more computationally costly than existing analytic approximations, the phase advance technique can facilitate the interpretation of reflectivity measurements obtained in laboratory experiments. In particular, the full visualization allows for a better understanding of the behavior of reflected waves at any angle of incidence.

Acoustic reflectivity goniometry of bounded ultrasonic pulses: Experimental verification of numerical models

The angle of incidence reflectivity of a bounded acoustic pulse from water loaded elastic solids is tested using an experimental configuration with a large transmitter and a small pointlike receiver. The experimental response, affected by well-known nonspecular effects near critical angles, is modeled fully by propagation of the full bounded pulse using a phase advance technique. This allows for visualization of the evolution of the bounded pulse with time and upon reflection. The modeled and the observed reflectivities and phase rotations, as measured along the specular path, agree well with observations even at post Rayleigh critical angles of incidence. Moreover, small amplitude deviations are accurately reproduced. The longitudinal and Rayleigh critical angles are obtained from the observed reflectivity curves and used to calculate the material elastic wave speeds, which are in good agreement with those measured directly. The density is also obtained by inversion of portions of the reflectivity curves...

Numerical Models of Converted Slow P-wave Modes in Porous Media

Biot theory has predicted a second P-wave that can propagate in a fluid saturated porous material. This wave can be regarded as a propagating wave predominantly through the fluid saturating the medium. For this wave, the fluid moves opposite to the solid and is highly attenuated. Consequently, it is hard to detect and has only been observed in laboratory experiments so far. Several boundary conditions for the reflection and transmission of plane waves at plane interfaces separating media involving porous rocks have been proposed since the Biot theory was introduced in the 1950’s. However there is a controversy on which set of boundary conditions should be employed for such media. Only experimental tests can warrant a definitive answer to this controversy. In this contribution, forward numerical models for the reflection-transmission in porous media will be presented at both high and low frequencies. These models are based on wave propagation using Biot theory and various sets of boundary conditions. Converted waves from and to a slow P-wave mode will be given a particular attention. Models, obtained at an interface between a water-saturated porous rock and water using the open boundary conditions, show converted slow P-waves with moderate amplitudes. However models derived from boundary conditions that restrict relative fluid movement with respect to the solid, such as those used in the case of a porous-solid interface, lead to weak converted slow P-waves. This confirms that the slow P-wave is predominantly a flow process. However, recent reflectivity experiments from a porous-solid interface exhibit converted slow P-waves with significant amplitudes that cannot be explained by the closed boundary conditions. The modeling also shows that the slow P-wave can convert to both a fast P-wave and to an S-wave (or vice versa) with relatively significant amount of energy when the relative fluid-solid motion is not restricted at the interface.

Laboratory calibration of amplitude variation with angle using an acoustic goniometer

Summary A variety of approximations to Zoeppritz’s equations, describing the variation in reflectivity with angle of incidence from the interface between two elastic media, are employed in AVO impedance inversions. However, Zoeppritz’s equations describe the variation in reflectivity with angle of incidence from the interface between two nonporous, perfectly elastic media; and while this is probably adequate it is important to further study reflectivity from fluid-filled porous materials. Here, initial results from new method for experimentally measuring Amplitude Variations with Angle (AVA) in complex materials is described. Samples are placed precisely on an acoustic goniometer placed in a large water filled tank. Experimental difficulties are reduced by employing a specially designed transducer that produces plane wave flat over a 5 cm by 3 cm area and stable to at least 37 cm of propagation distance. Reflected signals are detected with small hydrophone. Amplitudes observed in reflectivity calibration tests on glass and copper samples agree very well with theoretical models for both with maxima seen at both the P-wave and S-wave critical angles indicating that the system will work well for more difficult studies over porous media. However, a more substantial drop in amplitude is seen at the Rayleigh angle, i.e. the angle of incidence at which the incoming ray is critically refracted with respect to the pseudo-Rayleigh interfacial wave between the water and the material. This effect is not predicted by the Zoeppritz based formulations but is well known in the acoustics community. The Rayleigh angle may be used to obtain additional information about the medium. Further, this Rayleigh angle has the potential to be produced at the boundary between two solid media such that AVO observations and inversions may be biased.