Elastic Wave Speed Research Articles

Slow Earthquakes, Preseismic Velocity Changes, and the Origin of Slow Frictional Stick-Slip

Earthquakes normally occur as frictional stick-slip instabilities, resulting in catastrophic failure and seismic rupture. Tectonic faults also fail in slow earthquakes with rupture durations of months or more, yet their origin is poorly understood. Here, we present laboratory observations of repetitive, slow stick-slip in serpentinite fault zones and mechanical evidence for their origin. We document a transition from unstable to stable frictional behavior with increasing slip velocity, providing a mechanism to limit the speed of slow earthquakes. We also document reduction of P-wave speed within the active shear zone before stick-slip events. If similar mechanisms operate in nature, our results suggest that higher-resolution studies of elastic properties in tectonic fault zones may aid in the search for reliable earthquake precursors.

Orientation and rate dependence in high strain-rate compression of single-crystal silicon

High strain-rate ($\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\varepsilon}}\ensuremath{\sim}{10}^{6}\ensuremath{-}{10}^{9}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$) compression of single crystal Si reveals strong orientation- and rate-dependent precursor stresses. At these high compression rates, the peak elastic stress, ${\ensuremath{\sigma}}_{\mathrm{E}_\mathrm{Peak}}$, for Si [100], [110], and [111] exceeds twice the Hugoniot elastic limit. Near the loading surface, the rate at which Si evolves from uniaxial compression to a three-dimensional relaxed state is exponentially dependent on ${\ensuremath{\sigma}}_{\mathrm{E}_\mathrm{Peak}}$ and independent of initial crystal orientation. At later times, the high elastic wave speed results in a temporal decoupling of the elastic precursor from the main inelastic wave. A rapid high-$\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\varepsilon}}$ increase in the measured elastic stress at the onset of inelastic deformation is consistent with a transition from dislocation flow mediated by thermal activation to a phonon drag regime.

Mathematical modelling of elastoplasticity at high stress

This study describes a simple mathematical model for one-dimensional elastoplastic wave propagation in a metal in the regime where the applied stress greatly exceeds the yield stress. Attention is focused on the increasing ductility that occurs in the over-driven limit when the plastic wave speed approaches the elastic wave speed. Our model predicts that a plastic compression wave is unable to travel faster than the elastic wave speed, and instead splits into a compressive elastoplastic shock followed by a plastic expansion wave.

Acoustoelastic Lamb wave propagation in biaxially stressed plates

Acoustoelasticity, or the change in elastic wave speeds with stress, is a well-studied phenomenon for bulk waves. The effect of stress on Lamb waves is not as well understood, although it is clear that anisotropic stresses will produce anisotropy in the Lamb wave dispersion curves. Here the theory of acoustoelastic Lamb wave propagation is developed for isotropic media subjected to a biaxial, homogeneous stress field. It is shown that, as expected, dispersion curves change anisotropically for most stresses, modes, and frequencies. Interestingly, for some mode-frequency combinations, changes in phase velocity are isotropic even for a biaxial stress field. Theoretical predictions are compared to experimental results for several Lamb wave modes and frequencies for uniaxial loads applied to an aluminum plate, and the agreement is reasonably good.

The crystal fabric of ice from full‐waveform borehole sonic logging

In an ice sheet, a preferred crystal orientation fabric affects deformation rates because ice crystals are strongly anisotropic: shear along the basal plane is significantly easier than shear perpendicular to the basal plane. The effect of fabric can be as important as temperature in defining deformation rates. Fabric is typically measured using analysis of thin sections under the microscope with co‐polarized light. Due to the time‐consuming and destructive nature of these measurements, however, it is difficult to capture the spatial variation in fabric necessary for evincing ice sheet flow patterns. Because an ice crystal is similarly elastically anisotropic, the speed of elastic waves through ice can be used as a proxy for quantify anisotropy. We use borehole sonic logging measurements and thin section data from Dome C, East Antarctica to define the relations between apparent fabric and borehole measured elastic speeds (compressionalVP and vertically polarized shear VSV). These relations, valid for single maximum fabrics, allow in‐situ, depth‐continuous fabric estimates of unimodal fabric strength from borehole sonic logging. We describe the single maximum fabric usinga1: the largest eigenvalue of the second‐order orientation tensor. For ice at −16°C anda1in the 0.7‐1 range the relations areVP = 248 a13.7 + 3755 m s−1 and VSV = −210a17.3 + 1968 m s−1.

On stress-dependent elastic moduli and wave speeds

On the basis of the general nonlinear theory of a hyperelastic material with initial stress, initially without consideration of the origin of the initial stress, we determine explicit expressions for the stress-dependent tensor of incremental elastic moduli. In considering three special cases of initial stress within the general framework, namely hydrostatic stress, uniaxial stress and planar shear stress, we then elucidate in general form the dependence of various elastic moduli on the initial stress. In each case the effect of initial stress on the wave speed of homogeneous plane waves is studied and it is shown how various special theories from the earlier literature fit within the general framework. We then consider the situation in which the initial stress is a pre-stress associated with a finite deformation and, in particular, we discuss the specialization to the second-order theory of elasticity and highlight connections between several classical approaches to the topic, again with special reference to the influence of higher-order terms on the speed of homogeneous plane waves. Some discrepancies arising in the earlier literature are noted.

Elastic waves and damage quantification in brittle material with evolving damage

This paper presents an analysis of the elastic wave propagation in brittle materials containing a distribution of microcracks. The crack-size distribution is assumed to be isotropic and exponential. The evolution of the mean crack size is described by a rate-dependent damage model based on the mechanics of microcracks. The analysis shows that the elastic wave speeds of a brittle material are sensitive to the change in the mean size of the distributed cracks in the material. The dependence of the wave speeds on the applied strain can also be used to validate the damage model. An example of a brittle ceramic under uniaxial-strain tension is presented to show quantitatively the changes in the longitudinal and shear wave speeds as functions of the applied strain. Explicit relations between the wave speeds and the mean crack size in the material are given.

Elastic Waves of Anisotropic Saturated Porous Solids with Thermal Effect

The motion equations of anisotropic media, coupled to the mass conservation and thermo-equilibrium equations of fluid, are studied here based on the standard space of physical presentation for consolidation of anisotropic saturated soils, in which a new compressible thermo-elastic model is induced. A set of uncoupled equation of elastic waves in anisotropic saturated solids is deduced. The results show that the elastic waves and speeds of elastic waves is affected by both anisotropic subspaces of solids and thermal and compressive coupling coefficients between fluid and solid. Based on these laws, we discuss the elastic wave behaviour for isotropic solids.

Research on Tomography by Using Seismic Reflection Wave in Laneway

As a necessary step and an integral part of works in laneway, the geological prediction is an important means of reducing disaster losses and geological disasters in the works in laneway. This paper mainly discusses tunnel reflection tomography by using seismic reflection wave in laneway. The speed of elastic wave in front of tunnel face and the three-dimensional images can be figured out when the detector check the reflection of elastic wave from the focal points on the tunnel face. The location, size and depth of cave can be ascertained. According to the forecasts of laneway works in the Iron Mine Xishimen, tunnel reflection tomography by using seismic reflection wave can well forecast engineering geology and hydro-geological conditions in front of tunnel face. It will help to supply positive guidance for working plan and construction measures in laneway. Therefore, the construction safety and speed can be ensured, helping to lead to great practical significance and significant economic benefits.

Thermal Effect on Elastic Waves of Anisotropic Saturated Porous Solid

The motion equations of anisotropic media, coupled to the mass conservation and thermoequilibrium equations of fluid, are studied here based on the standard space of physical presentation for thermoelastic dynamics of anisotropic saturated porous solids. By introducing a new compressible thermo‐elastic model, a set of uncoupled equations of elastic waves are deduced. The results show that the elastic waves and speeds of elastic waves are affected by both anisotropic subspaces of solids and thermal and compressive coupling coefficients between fluid and solid. Based on these laws, we discuss the propagation behaviour of elastic waves for various anisotropic solids.

OS11F060 Detection of Internal Defects in Concrete Structures by Analyzing Elastic Wave Propagation

Though the impact echo method is commonly used for thickness measurement of plate concrete structures, the method to detect the internal defects in concrete structures is still not clearly established. Basically the impact echo technology is used to obtain the resonant frequency of flutter echo between the measuring surface and the opposite surface of a concrete plate. The thickness can be calculated by dividing the elastic wave speed of the concrete by twice the measured dominant frequency. By this method, if the thickness of the plate is known, the wave speed of the flutter echo can be calculated. We found out that the travel path condition of the wave affect the wave speed. The wave speed is almost always reduced if there is defected area on the path. In case the cross section of defect is circular, higher harmonic frequencies are generated near the direct top surface of the defected areas. From these observations, distribution of the flutter echo's wave speed on the measuring plane shows the location of the projection area of the defect. The results of the experiments using concrete plate with voids show that the location of the voids are indicated by the area where the wave speeds of the flutter echo are slower than the areas with no voids. Also the method and the results for location detection and degree of filling of the actual PC bridge sheaths are shown in this paper.

OS11-1-4 Detection of Internal Defects in Concrete Structures by Analyzing Elastic Wave Propagation

Though the impact echo method is commonly used for thickness measurement of plate concrete structures, the method to detect the internal defects in concrete structures is still not clearly established. Basically the impact echo technology is used to obtain the resonant frequency of flutter echo between the measuring surface and the opposite surface of a concrete plate. Abstract The thickness can be calculated by dividing the elastic wave speed of the concrete by twice the measured dominant frequency. By this method, if the thickness of the plate is known, the wave speed of the flutter echo can be calculated. We found out that the travel path condition of the wave affect the wave speed. The wave speed is almost always reduced if there is defected area on the path. In case the cross section of defect is circular, higher harmonic frequencies are generated near the direct top surface of the defected areas. From these observations, distribution of the flutter echo's wave speed on the measuring plane shows the location of the projection area of the defect. The results of the experiments using concrete plate with voids show that the location of the voids are indicated by the area where the wave speeds of the flutter echo are slower than the areas with no voids. Also the method and the results for location detection and degree of filling of the actual PC bridge sheaths are shown in this paper.

A time-discrete model for dynamic fracture based on crack regularization

We propose a discrete time model for dynamic fracture based on crack regularization. The advantages of our approach are threefold: first, our regularization of the crack set has been rigorously shown to converge to the correct sharp-interface energy Ambrosio and Tortorelli (Comm. Pure Appl. Math., 43(8): 999–1036 (1990); Boll. Un. Mat. Ital. B (7), 6(1):105–123, 1992); second, our condition for crack growth, based on Griffith’s criterion, matches that of quasi-static settings Bourdin (Interfaces Free Bound 9(3): 411–430, 2007) where Griffith originally stated his criterion; third, solutions to our model converge, as the time-step tends to zero, to solutions of the correct continuous time model Larsen (Math Models Methods Appl Sci 20:1021–1048, 2010). Furthermore, in implementing this model, we naturally recover several features, such as the elastic wave speed as an upper bound on crack speed, and crack branching for sufficiently rapid boundary displacements. We conclude by comparing our approach to so-called “phase-field” ones. In particular, we explain why phase-field approaches are good for approximating free boundaries, but not the free discontinuity sets that model fracture.

An improved algorithm for detecting point of impact in anisotropic inhomogeneous plates

Conventional triangulation techniques fail to correctly predict the acoustic source location in anisotropic plates due to the direction dependent nature of the elastic wave speeds. To overcome this problem, Kundu et al. [1] proposed an alternative method for acoustic source prediction based on optimizing an objective function. They defined an objective function that uses the time of flight information of the acoustic waves to the passive transducers attached to the plate and the wave propagation direction ( θ) from the source point to the receiving sensors. Some weaknesses of the original algorithm proposed in Ref. [1] were later overcome by developing a modified objective function [2]. A new objective function is introduced here to further simplify the optimization procedure and improve the computational efficiency. A new algorithm for source location is also introduced here to increase the source location accuracy. The performance of the objective function and source location algorithm were experimentally verified on a homogeneous anisotropic plate and a non-homogeneous anisotropic plate with a doubler patch. Results from these experiments indicate that the new objective function and source location algorithm have improved performance when compared with those discussed in Refs. [1,2].

A fully dynamic theory of piezoelectromagnetic waves

The Maxwell’s equations, coupled to the mechanical equations of motion, are studied here based on the standard spaces of the physical presentation. The complete set of uncoupled and fully dynamic equations of waves in anisotropic piezomagnetic media is deduced, in which the equations of electromagnetic waves and elastic ones are both of order 4. The results show that the number of electromagnetic and elastic waves is determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behavior of piezoelectromagnetic waves in the piezomagnetic material of class 6mm; the electromagnetic waves with the speed of elastic waves and elastic waves with the speed of electromagnetic waves are obtained.

Asymptotic behavior of reflection of discontinuities in thermoelasticity with second sound in one space variable

This paper is devoted to the study of asymptotic behavior in the propagation and reflection of discontinuous solutions to linear and semilinear thermoelastic equations with second sound in one space variable. When the relaxation parameter goes to zero, we obtain that the jump of temperature vanishes while jumps of elastic waves and heat flux are propagated and reflected with the elastic speeds. Furthermore, it is observed that these jumps decay exponentially when the time goes to infinity, and the decay rates not only depend on the growth rate of the nonlinear source terms and heat conduction coefficient, but also depend on the change rates of speeds of elastic waves.

Tomographic image of the crust and upper mantle beneath the western Tien Shan from the MANAS broadband deployment: Possible evidence for lithospheric delamination

We combine teleseismic P arrival times from the recent MANAS deployment of broadband sensors with P and S arrival times from local events recorded by the GENGHIS deployment and analog observations from the Kyrgyz Institute of Seismology to generate a high resolution (~ 20 km) image of elastic wavespeeds in the crust and upper mantle beneath the western Tien Shan. The total data set consists of 29,006 P and 21,491 S arrivals from 2176 local events recorded at 144 stations along with 5202 P arrivals from 263 teleseismic events recorded at 40 stations. The most significant feature in our image of the mantle beneath the Tien Shan is a pair of large, elongated high wavespeed regions dipping in opposite directions from the near surface to depths of at least 400 km. These regions appear to be continuous and extend upwards to bounding range fronts where the Tarim Basin is being overthrust by the Kokshal range on the south side, and the Kazach shield underthrusts the Kyrgyz range on the north side. While it is tempting to interpret these high wavespeed anomalies as evidence for contemporary subduction of continental lithosphere, such a scenario is difficult to reconcile with both the timing of the orogen and the size of the wavespeed anomaly. We suggest instead that they represent downwelling side-limbs of a lithospheric delamination beneath the central part of the Tien Shan, possibly by siphoning of the bordering continental lithosphere as the central part descends.

Temperature variation of Young’s modulus and elastic wave speed in a mixture of solid‐particles in liquid.

The variation of ultrasonic wave speed in the solid‐liquid mixtures as a function of temperature is studied. The goal of this investigation is to determine temperature dependence of the elastic moduli of materials consisting of different size solid particles. The elastic wave speed in solids is assumed to be proportional to the square root of Young’s modulus of the material. Elastic wave speed in the material is related to the variation of Young’s modulus of the solid constituents. Also considered are temperature dependence of the wave attenuation, by scattering and absorption, and the effects of phonon modes, their amplitude and frequency, on the elastic moduli and wave dispersion in the material. Previous experimental data have shown a decrease in elastic moduli at the contact points of solid particles with increase in elastic wave frequency. Findings on the variations of elastic wave speed in solids with temperature and frequency are compared to analyze any similarity between the effect of wave frequen...

Correction to “Elastic wave speeds and moduli in polycrystalline ice Ih, sI methane hydrate, and sII methane‐ethane hydrate”

F(T,P) = aT + bP + c a b c Uncertainty Vp (m s ) 2.67 ± 0.05 0.2 ± 0.08 3864 ± 2 ±1.5 Vs (m s ) 1.244 ± 0.005 0.198 ± 0.007 1942.4 ± 0.2 ±1.5 n (2.0 ± 0.6) 10 5 (6.8 ± 0.9) 10 5 0.3310 ± 0.0002 ±3 M (GPa) (2.15 ± 0.04) 10 2 (4.02 ± 0.03) 10 3 13.69 ± 0.02 ±4 G (GPa) (5.03 ± 0.02) 10 3 (3.0 ± 0.2) 10 4 3.459 ± 0.0007 ±4 K (GPa) (1.48 ± 0.04) 10 2 (3.4 ± 0.5) 10 3 9.07 ± 0.02 ±6 Vp, compressional wave speeds; Vs, shear wave speeds; n, Poisson’s ratio; M, dynamic compressional wave; G, shear moduli; and K, bulk moduli; temperature of 20 to 5 C; and piston pressure of 22.4 to 32.8 MPa. Calculated density range was 0.920 to 0.923 g cm . Units for a are the units of the property being fit divided by C. Units for b are those of the property being fit divided by MPa. Units for c are those of the property being fit. Uncertainty is given as a percentage of the property being fit.

Elastic wave speeds and moduli in polycrystalline ice Ih, sI methane hydrate, and sII methane‐ethane hydrate

We used ultrasonic pulse transmission to measure compressional, P, and shear, S, wave speeds in laboratory‐formed polycrystalline ice Ih, sI methane hydrate, and sII methane‐ethane hydrate. From the wave speed's linear dependence on temperature and pressure and from the sample's calculated density, we derived expressions for bulk, shear, and compressional wave moduli and Poisson's ratio from −20 to −5°C and 22.4 to 32.8 MPa for ice Ih, −20 to 15°C and 30.5 to 97.7 MPa for sI methane hydrate, and −20 to 10°C and 30.5 to 91.6 MPa for sII methane‐ethane hydrate. All three materials had comparable P and S wave speeds and decreasing shear wave speeds with increasing applied pressure. Each material also showed evidence of rapid intergranular bonding, with a corresponding increase in wave speed, in response to pauses in sample deformation. There were also key differences. Resistance to uniaxial compaction, indicated by the pressure required to compact initially porous samples, was significantly lower for ice Ih than for either hydrate. The ice Ih shear modulus decreased with increasing pressure, in contrast to the increase measured in both hydrates.