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It has been confirmed by comparison with particle velocities of surface waves of wave normal perpendicular to borehole axis measured by collocated seismic broadband array or borehole seismometers that high-sensitivity borehole tensor strainmeters could measure surface strain waves qualitatively. However, quantitative measurability of strain waves of wave normal being oblique to borehole axis by borehole tensor strainmeters is still a challenging problem. In this article, we introduce a scattering model of oblique-incidence seismic waves by an empty borehole to investigate the influence of incident-wave normal and polarization on theoretical-frequency-response bandwidth of borehole tensor strainmeters. Within the theoretical bandwidth of borehole tensor strainmeters, zero-frequency gains are introduced to build quantitative relation between instrumental strain waves of borehole tensor strainmeters and oblique-incidence seismic strain waves. Better understanding the influence of incident-wave normal and polarization on the relation between instrumental strain and strain components induced by the incident strain wave shows that incident-wave normal and polarization must be assessed by other instrumentation to promise quantitative measurement of incident strain waves by borehole tensor strainmeters, which would benefit in situ calibration of borehole tensor strainmeters.

It has been proven qualitatively that borehole tensor strainmeters (BTSM) could measure three surface-wave-induced strain components in the horizontal-normal plane. But strain waves are usually incident obliquely to borehole axis to induce not only horizontalnormal strain components but also the three other strain components in the plane of vertical normal, which are usually assumed to zero in conventional model of BTSM installed near the earth surface. Therefore quantitative kinematical-parameter measurement of strain waves of wave normal oblique to borehole axis by BTSM is still a challenging problem. In this paper, a scattering model of oblique-incidence seismic waves by an empty borehole is introduced to investigate instrumental responses of BTSM. Besides for the four gauges in conventional BTSM, three other gauges considering the influences of strain components in the plane of vertical normal are also introduced to build dynamic calibration matrix between instrumental and incident strains. It shows that within the effective bandwidth of BTSM, zero-frequency-gain for dynamic calibration matrix could be adopted approximately to build quantitative relation between instrumental strain waves of BTSM and oblique-incidence seismic strain waves. It is shown that the recommended gauge combinations could promise quantitative measurement of kinematic parameters of the incident strain P or S wave if high-resolution insitu calibration of BTSM has been conducted, which is important to the development of early warning system by borehole strainmeters.

Reduced graphene oxide supported titanium dioxide (GO/TiO2) heterojunction composites as highly active photocatalysts were synthesized via simple ultrasonic mixing and hydrothermal reaction using TiCl3 and GO as precursors. Their structure and morphology were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, Raman spectra, UV-vis spectroscopy, and thermogravimetic analysis. The GO/TiO2 heterojunction composites were used to degrade methyl orange (MO). The adsorption and photocatalytic degradation rate of the prepared GO/TiO2 composites increased by nearly three times compared with that of pristine TiO2 or GO, which reached up 90%, to degrade MO after 4 h, which provides a simple method to obtain photocatalytic materials.

Borehole tensor strainmeters such as the RZB tensor strainmeter, YRY tensor strainmeter, and Gladwin tensor strainmeter are highly sensitive to ground deformation over periods of minutes to months, bridging the gap in the sensitivity and frequency between Global Positioning System and seismic measurements. To discuss the possibility of quantitatively measuring seismic strain waves by borehole tensor strainmeters, a model of the scattering of plane elastic P and S waves by an empty borehole is introduced to investigate the theoretical frequency response and corresponding bandwidth of an empty borehole for borehole tensor strainmeters. The calculation of scattering waves around the empty borehole gives the changes in the diameter of the borehole. Different gauge combinations are introduced to reflect the areal strain and the maximum shear strain of the incident waves. The theoretical frequency responses for different gauge combinations are determined by the nondimensional wavenumber of the incident wave, the Poisson’s ratio of the surrounding rock, and the difference between the azimuth angle of the first gauge and the incident angle of the incident wave. Theoretical‐frequency‐response analysis of different gauge combinations for an empty borehole confirms that different gauge combinations serve as low‐pass filters. The 1% bandwidth of the gauge combinations shows that borehole tensor strainmeters could quantitatively measure seismic strain waves in the acoustic frequency range if the instrumental effective bandwidth of the gauge is sufficiently large, which will advance high‐frequency seismology and benefit in situ calibration of borehole tensor strainmeters.

The scattering model of incident seismic waves by an empty borehole has been presented to investigate the theoretical frequency response and the corresponding bandwidth of borehole tensor strainmeters. Inner-diameter changes of the stainless steel instrument casing are measured by horizontal extensometers (gauges), after the borehole tensor strainmeter is installed at a certain depth of the borehole and boned by expansive grout with the surrounding rock. There is, however, no answer for the difference between this case and the empty case. In this paper, the scattering model of incident elastic seismic waves by a two-ring borehole is introduced to investigate the influence of the expansive grout on theoretical bandwidth for the measurement of strain waves by borehole tensor strainmeters. The calculation of wave fields in the surrounding rock and the two rings by wave function expansion gives the inner-diameter changes of the stainless steel instrument casing. Several cases show that the mechanical parameters of the expansive grout have great influence on the frequency responses of borehole tensor strainmeters for different gauge combinations, but little influence on the bandwidth, which means that the high-frequency bandwidth promises the quantitative measurability of strain waves in the acoustical frequency range for borehole tensor strainmeters.

Based on the finite deformation theory of the continuum and poroelastic theory, the acoustoelastic theory for fluid-saturated porous media (FSPM) in natural and initial coordinates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre-deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitutive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.

Vibration analysis of an isotropic elastic-sphere oscillator contacting a semi-infinite cubic solid is investigated by considering dynamic deformation at the contact interface. Assuming sufficiently small oscillation amplitude of the sphere compared with the static indentation deformation, the dynamic maximum contact pressure and the variable contact radius yield a dynamic-contact pressure distribution of constant contact radius. The combination of the sphere oscillation and the solid motion at the contact interface through contact-displacement conditions gives resonance frequencies of the elastic sphere. Unlike the conventional quasi-static model, this dynamic contact model agrees well with the measurements, which will benefit the quantitative evaluation of the local Young's modulus and the orientation of micro-scaled anisotropic grains by the resonance-frequency shifts of a vibrating oscillator in resonance ultrasound microscopy and the efficient removal of micron or sub-micron particles from the substrate in the dry laser cleaning technique.

Problem statement: Resonance-type microscopies have been widely used to evaluate the nanoscaled or microscaled surface elastic propertie s of materials by the resonance-frequency shifts of an oscillator, which contacts the surface of materi als by a spherical tip. Approach: The tip-specimen contact is modeled to be a spring support, whose st iffness is given by the traditional Hertzian contac t theory. However, because of the influence of the os cillator vibration and the anisotropy in nanoscaled or microscaled region of materials, the predicted r esults from the traditional Hertzian contact theory can not coincide with the experimental observations . In order to explain this discrepancy, dynamic contact stiffness at the contact interface between a rigid sphere and a semi-infinite cubic solid is investigated. Results: An oscillating force being superposed on a biasing force excites the oscillation of the sphere contacting with the solid surface, wh ich causes the contact radius to vary with the oscillation. The assumption of sufficiently small o scillating force compared with the biasing force yields an oscillating-contact-pressure distribution of the constant contact radius and then dynamic contact stiffness. Because the oscillating-contact- pressure distribution cannot promise the uniform contact deformation, the influence of contact-displ acement conditions is discussed. Conclusion: It is shown that dynamic contact stiffness depends on the oscillating frequency and contact radius of the sphere and the solid anisotropy.

Generalized reverberation matrix (GRM) formulation is presented to investigate elastic wave propagation in a complex multilayered solid by the combination of reverberation-ray matrix (RRM) method and stiffness matrix (SM) method. RRM method formulates a reverberation matrix, which reflects the reflection or refraction of the elastic waves in the multilayered solid. However, the dimension of RRM increases as the sublayer number increases, which may result in lower calculation efficiency of the generalized rays. SM formulation yields a system matrix of the constant dimension to promise higher calculation efficiency, but it is difficult to identify the generalized rays. In order to calculate the generalized rays in the complex multi-layered solid efficiently, the RRM formulation is applied to the interested sublayer for the evaluation of the generalized rays and SM formulation to the other sublayers, to construct a generalized reverberation matrix of the constant dimension, which is independent of the sublayer number. Numerical examples show that GRM formulation has higher calculation efficiency for the generalized rays in the complex multilayered-solid configuration compared with RRM formulation.

We present a hybrid method for the evaluation of transient elastic-wave propagation in a multilayered solid, integrating reverberation matrix method with the theory of generalized rays. Adopting reverberation matrix formulation, Laplace–Fourier domain solutions of elastic waves in the multilayered solid are expanded into the sum of a series of generalized-ray group integrals. Each generalized-ray group integral containing Kth power of reverberation matrix R represents the set of K-times reflections and refractions of source waves arriving at receivers in the multilayered solid, which was computed by fast inverse Laplace transform (FILT) and fast Fourier transform (FFT) algorithms. However, the calculation burden and low precision of FILT–FFT algorithm limit the application of reverberation matrix method. In this paper, we expand each of generalized-ray group integrals into the sum of a series of generalized-ray integrals, each of which is accurately evaluated by Cagniard–De Hoop method in the theory of generalized ray. The numerical examples demonstrate that the proposed method makes it possible to calculate the early-time transient response in the complex multilayered-solid configuration efficiently.

Dynamic contact stiffness at the interface between a vibrating rigid sphere and a semi-infinite transversely isotropic viscoelastic solid is investigated. An oscillating force super-imposed onto a static compressive force in the vertical direction excites the vibration of a rigid sphere, which causes variable contact radius and contact pressure distribution in the contact region. The assumption of a sufficiently small oscillating force yields a dynamic contact-pressure distribution of a constant contact radius, which gives dynamic contact stiffness at the interface between the rigid sphere and the semi-infinite solid. Numerical calculations show the influence of vibration frequency of the sphere, and elastic constants of the transversely isotropic solid on dynamic contact stiffness, which benefits quantitative evaluation of elastic constants and orientation of single hexagonal grains by resonance-frequency shifts of the oscillator in resonance ultrasound microscopy.

This paper considers the problem of estimation for binomial proportions of sensitive or stigmatizing attributes in the population of interest. Randomized response techniques are suggested for protecting the privacy of respondents and reducing the response bias while eliciting information on sensitive attributes. In many sensitive question surveys, the same population is often sampled repeatedly on each occasion. In this paper, we apply successive sampling scheme to improve the estimation of the sensitive proportion on current occasion.

Vibration of a rigid sphere contacting a semi-infinite viscoelastic solid is studied theoretically. The rigid sphere is subjected to an oscillating force while being compressed in the vertical direction by a static force. The contact-pressure distribution and contact radius at the interface vary with the oscillation. Assuming sufficiently small oscillating force, we derive the dynamic-contact-pressure distribution with the constant contact radius, which establishes dynamic contact stiffness between the sphere and the viscoelastic solid. Numerical calculations show the influence of vibration frequency, contact radius, Poisson's ratio, and the damping characteristic of the solid.

Tian J., Ogi H., Tada T., et al. "Local surface elastic constants by resonant-ultrasound microscopy", Journal of Applied Physics, 96(1), 133-137 (2004) https://doi.org/10.1063/1.1755432., The resonant-ultrasound microscopy is discussed for measuring elastic-constant distribution over a solid's surface. An oscillating electric field is applied to a rectangular-parallelepiped oscillator of langasite crystal by a sorrounding solenoid coil. This generates and detects the vibrations of the crystal without electrodes and wires. An accurate resonance-frequency measurement is provided by the isolated langasite crystal.

Tian J., Ogi H., Hirao M. "Vibration analysis of an elastic-sphere oscillator contacting semi-infinite viscoelastic solids in resonant ultrasound microscopy", Journal of Applied Physics, 95(12), 8366-8375 (2004) https://doi.org/10.1063/1.1737472., Resonant-ultrasound microscopy evaluates local Young’s modulus of materials by the resonant-frequency shift of a vibrating oscillator. This study presents a dynamic-contact model to analyze free vibrations of an isotropic elastic-sphere oscillator contacting two semi-infinite viscoelastic solids, which sandwich the sphere. Assuming frictionless contacts and smaller vibrational amplitude, dynamic-contact pressure distributions are obtained with the linearized maximum contact pressure and contact radius. Combining the sphere oscillation and the solid motions through contact-displacement boundary conditions, resonant frequencies of the elastic sphere are obtained. Unlike the quasistatic model, this dynamic model agrees well with the measurements.

Tian J., Ogi H., Tada T., et al. "Young's modulus mapping on SCS-6 SiCf/Ti-6Al-4V composite by electromagnetic-resonance-ultrasound microscopy", Journal of Applied Physics, 94(10), 6472-6476 (2003) https://doi.org/10.1063/1.1623611., Electromagnetic-resonance-ultrasound microscopy was applied to visualize Young’s-modulus distribution in SCS-6 SiC fiber/Ti-6Al-4V composite. Resonance of a piezoelectric langasite (La3Ga5SiO14) crystal is excited and detected by a surrounding solenoid coil without any contact between them. Point contact with the specimen causes a shift in resonance frequency of the order of 10−4,depending on the local elastic stiffness of the contacting material. Two-dimensional stepping on the specimen surface provides the image of Young’s-modulus distribution. Calibration measurements based on contact theory allow determination of Young’s moduli of the carbon core (150 GPa), SiC sheaths (180–505 GPa), and Ti-6Al-4V matrix (90 GPa). The radial variation of Young’s modulus depicts the concentric multi-phase layers in an SCS-6 fiber.

The incremental acoustoelastic equations for fluid-saturated porous media (FSPM) under the large static pre-deformation are derived in this paper by incremental loading method based on classic acoustoelastic theory of FSPM, which provides quantitative acoustoelastic relation of FSPM with arbitrary constitutive equation. Isotropic FSPM with third-order constitutive equation are taken as an example to give the relation between wave velocity and confining pressure and discuss the effect of loading step on acoustoelastic relations of isotropic FSPM under closed-pore jacketed condition and opened-pore jacketed condition.

Acoustoelastic theory for a dissipative fluid-saturated porous rock (FSPR) is investigated based on the finite deformation theory of the continuum and poroelastic theory. The assumption of a small dynamic motion superimposed on a largely static pre-deformation of the FSPR yields natural, initial, and final configurations. The consideration of homogeneous pre-deformation, dissipation induced by the Poiseuille-type fluid-solid relative motion, the plane harmonic form of the small dynamic motion according to the constitutive relations and equations of motion of the dissipative FSPR gives acoustoelastic equations, which provide the analytical formulations for the relation of the velocities of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with the solid-skeleton stresses and the fluid pore-pressure. Taking a rock under open-pore jacketed condition as an example, the detailed discussions about the characteristic of wave dispersion and attenuation for the shear waves are shown that the characteristic of wave dispersion and attenuation for the dissipative FSPR is usually influenced by the pre-deformation. The pre-deformation has little effect on the characteristic of wave dispersion and attenuation for dissipative FSPR only when the components of the applied initial principal stresses are equal.

Ogi H., Tian J., Tada T., et al. "Elastic-stiffness mapping by resonance-ultrasound microscopy with isolated piezoelectric oscillator", Applied Physics Letters, 83(3), 464 (2003) https://doi.org/10.1063/1.1593819., A resonance-ultrasound microscopy has been developed for mapping a material’s elastic constant in a localized surface region. It detects the effective elastic modulus through a resonance frequency of free vibrations of a solid probe touching the specimen via a small tungsten-carbide bearing. Langasite (La3Ga5SiO14) crystal is used as a probe because of the low sensitivity of its elastic constants to temperature and its high piezoelectric coefficients. The vibration of the probe is excited and detected with a surrounding solenoid coil. This noncontacting acoustic coupling isolates the probe vibration and measures the resonance frequency with an accuracy better than one part in 105. This microscopic method is applied to a composite material consisting of silicon-carbide (SiC) fibers in titanium-alloy matrix. The stiffness distribution inside a single fiber was determined.

Different matrix formulations have been developed to investigate the elastic-wave propagation in a multilayered solid, which have been widely used in the fields of seismology, ocean acoustics(Pao et al., 2000), and non-destructive evaluation (Lowe, 1995), etc. Transfer matrix (TM) method (Haskell, 1953; Thomson, 1950), as one of the most important matrix formulations, yields a simple configuration and efficient computational ability to facilitate its wide application in many research fields. Stiffness matrix (SM) method (Rokhlin & Wang, 2002; Wang & Rokhlin, 2001) has been proposed to resolve the inherent computational instability for the large product of frequency and thickness in TM method. The SM formulation utilizes the stiffness matrix of each sublayer in a recursive algorithm to obtain the stacked stiffness matrix for the multilayered solid. However, the SM formulation is difficult to identify the generalized-ray propagation in the multilayered solid. In order to evaluate the transient wave propagation in the multilayered solid, Su, Tian, and Pao (Su et al., 2002; Tian & Xie, 2009; Tian et al., 2006) presented reverberation-ray matrix (RRM) formulation. Introducing the local scattering relations at interfaces and the phase relations in sublayers, a system of equations is formulated by a reverberation matrix R , which can be automatically represented as a series of generalized ray group integrals according to the times of reflections and refractions of generalized rays at interfaces. Each generalized ray group integral containing k R represents the set of K times reflections and transmissions of source waves arriving at receivers in the multilayered solid, which is very suitable to automatic computer programming for the simple multilayered-solid configuration. However, the dimension of the reverberation matrix will increase as the number of the sublayers increases, which may yield the lower calculation efficiency of the generalized-ray groups in the complex multilayered solid(Tian & Xie, 2009). In order to increase the calculation efficiency of the generalized-ray groups, Tian presented the reverberation-transfer matrix (RTM) and generalized reverberation matrix (GRM) formulations, respectively. In RTM formulation, RRM formulation is applied to the interested sublayer for the evaluation of the generalized rays and TM formulation to the other sublayers, to construct a RTM of the constant dimension, which is independent of the sublayer number. However, the RTM suffers from the inherent numerical instabilities particularly when the layer thickness becomes large and/ or the frequency is high. GRM

We present a hybrid method for transient elastic‐wave propagation in a multilayered solid, integrating reverberation matrix method with the theory of generalized rays. Adopting reverberation matrix formulation, Laplace‐domain solutions of elastic waves in the multilayered solid are expanded into the sum of a series of ray group integrals. Each ray group integral containing Kth power of reverberation matrix R represents the set of K times reflections and transmissions of source waves arriving at receivers in the multilayered solid, which was solved by Fast Inverse Laplace transform (FILT) algorithm. However, the calculation burden and low precision of FILT algorithm limit the further application of reverberation matrix method. In this paper, we expand each of ray group integrals into the sum of a series of generalized ray integrals, each of which is exactly evaluated by Cagniard‐De Hoop method in the theory of generalized ray. The numerical example demonstrates that the hybrid method makes it possible to c...

Jiayong Tian, Hirotsugu Ogi, Toyokazu Tada, and Masahiko Hirao. Vibration analysis on electromagnetic-resonance-ultrasound microscopy (ERUM) for determining localized elastic constants of solids. Journal of the Acoustical Society of America, 2004, 115(2), 630. https://doi.org/10.1121/1.1642618., In this paper we present a new acoustic-resonance microscopy, Electromagnetic-Resonance-Ultrasound Microscopy (ERUM), to measure the localized elastic stiffness of a solid material. It visualizes the resonance-frequency shift of vibrating piezoelectric crystal (langasite, La₃Ga₅SiO₁₄) excited by an electric field from a solenoid coil. The acoustic coupling is made only at the tip of the crystal touching the specimen surface. Being based on the calibration for the specimen's effective stiffness, the local elasticity is determined from the resonance frequencies of the crystal with the Rayleigh-Ritz method. An approximate model for the specimen's effective stiffness predicts the shift of resonance frequencies, for which the conventional Hertz-contact model is improved. As an illustrating example, the mapping of Young's modulus of a duplex stainless steel is presented, which shows good agreement with the existing study.

Tian J., Ogi H., Hirao M. "Effect of elastic anisotropy on contact stiffness in resonance ultrasound microscopy", Applied Physics Letters, 87(20), 204107 (2005) https://doi.org/10.1063/1.2131201., The classical Hertzian-contact theory for an isotropic material has been adopted to simplify quantitative evaluation of local elastic modulus by resonance-ultrasound microscopy (RUM). However, the validity of this simplified model must be confirmed because most materials show elastic anisotropy in small regions. This study investigates the influence of the elastic anisotropy of the tip and the specimen on the determination of the local elastic modulus in RUM by introducing the Hertzian-contact stiffness for orthorhombic materials. Numerical results reveal that specimen anisotropy significantly affects the contact stiffness and the quantitative evaluation of local elastic modulus even for specimens with weak anisotropy when we consider the anisotropy of the oscillator tip in RUM. © 2005 American Institute of Physics.