Elastic Wave Velocity Measurements Research Articles

In Situ Determination of Thermoelastic Properties of Magnesite at High Pressure and Temperature With Implications to Seismic Detectability of Moderately Carbonated Lithologies in the Earth's Mantle

AbstractSubduction of carbonate‐bearing oceanic plates into Earth's interior recycles carbon from the surface to the deep mantle. The subducted carbonates can significantly affect mantle properties and dynamics. Magnesite is recognized as one of the major potential carbon hosts in the deep mantle because of its stability up to deep lower mantle conditions. However, despite many previous studies on the equation of state and elastic properties of magnesite, large discrepancies still exist for its elastic moduli and their pressure and temperature derivatives. Here we report in situ density and elastic wave velocity measurements on a natural magnesite at simultaneous high pressure‐temperature conditions up to ∼8 GPa–1073 K in a multi‐anvil apparatus using ultrasonic and synchrotron X‐ray techniques. Global fitting of the data set to finite strain equations yields KS0 = 114.0 ± 1.2 GPa, = 4.9 ± 0.3, = (−0.019 ± 0.002) GPa/K, G0 = 68.6 ± 0.4 GPa, G′ = 1.6 ± 0.1, and = (−0.018 ± 0.001) GPa/K. Compared to other major upper mantle and transition zone minerals, magnesite has intermediate VP, the lowest VS, and the lowest density. Thus, magnesite possesses higher VP/VS ratio than other mantle minerals in normal mantle regions, whereas this feature is less pronounced in subduction zone environments. Modeling of the velocity profiles of carbonated lithologies along different geotherms suggests that moderately‐enriched magnesite domains are unlikely to be detected seismically in the Earth's mantle.

Elastic wave velocity measurements of sodium aluminosilicate glass and melt at high pressure and temperature

The combination of ultrasonic technique with synchrotron X-ray diffraction and radiography in a multi-anvil apparatus was utilized to measure the elastic wave velocities of sodium aluminosilicate glass and melt with the partially depolymerized composition of Na3AlSi3O9 (NAS). The measurements were conducted at pressure and temperature of up to 7.3 GPa and at ambient temperature for glass and up to 4.3 GPa and 2120 K for melt, respectively. The compressional wave velocity (VP) of the NAS glass remained mostly constant up to 4 GPa; subsequently, it increased with increasing pressure. Additionally, the NAS glass exhibited a minimum shear wave velocity (VS) at 4–5 GPa. Alternatively, the VP of the NAS melt was smaller than that of the NAS glass, showing a velocity minimum at ∼2 GPa. The negative pressure dependence of VP of the NAS melt is completely different from the depolymerized diopside (Di) melt, which shows a monotonic increase in VP with pressure. The contrasting behavior of the NAS and Di melts is caused by the difference in their structure, characterized by their degree of polymerization. Natural magma found in the interior of the Earth, such as basalt, has a partially depolymerized composition. This study indicates that the magma can exhibit elastic properties with negative pressure dependence, similar to the NAS melt.

The development of internal pressure standards for in-house elastic wave velocity measurements in multi-anvil presses.

Ultrasonic systems are powerful tools to determine elastic wave velocities of minerals and materials at high pressure and temperature and have been extensively developed in recent decades. However, accurate measurement of sample length is required to convert travel times into wave velocities, limiting their use to synchrotron facilities or room temperature experiments in laboratories. We have made use of a close collaboration between the Bayerisches Geoinstiut and the P61B end-station beamline (PETRA III - DESY) to install ultrasonic systems and develop a novel dual travel time method for in situ pressure determination without the need for synchrotron radiation. Our method relies on the travel times of elastic waves through a reference material; it requires a thermocouple and is non-intrusive, with the reference material replacing the backing plate of the high-pressure assembly. Pressures obtained from this dual travel time method show excellent agreement with those obtained from x-ray diffraction using synchrotron radiation on standard materials. Our novel method enables in situ pressure determination at varying temperatures during in-house ultrasonic interferometry experiments. This allows us not only to determine the elastic behavior of minerals and materials but also to investigate phase diagrams, solidus, or liquidus conditions at varying pressures and temperatures during in-house experiments. During the installation of the pulse-echo ultrasonic system, we identified critical parameters for obtaining reliable data. While these requirements are well-known to experts, this study presents a comprehensive review of the different characteristics of ultrasonic systems, providing user-friendly guidelines for new users installing and operating such systems in high-pressure and high-temperature conditions.

Stress wave propagation and force transmission in polymeric closed cell foams subjected to air shock loading

Polymeric foams are widely used in sandwich structures to withstand blast loadings, serving as energy dissipators and force attenuators. This study explores the mechanics involved when an air shock interacts with closed-cell polymeric foam. The authors provide a comprehensive analysis of stress wave propagation and its evolution across the foam specimen by employing ultra-high-speed imaging and digital image correlation (DIC). Measurement of elastic, plastic, and shock wave velocities inside the impacted foam was conducted. A methodology to predict elastic precursor wave velocity is proposed, that considers the foam material’s behavior at higher strain rates. The predicted values were found to be in excellent agreement with the experimentally obtained values. Furthermore, the authors investigate the force transmission through foams as a function of bulk foam density under unconfined conditions. The results reveal that under shock loading intensities where foam specimens remained in their elastic regime, a transmitted force amplification was observed relative to the input load. However, when subjected to higher-intensity shock loading, substantial foam deformation occurs during the initial propagation of the shock wave. In these cases, the transmitted force measured was found to rely on the plastic and shock waves generated within the material. Additionally, as the loading persists, the force transmissibility ratio decreases beyond the initial stress wave propagation phase, thus demonstrating the material’s suitability for blast mitigation applications.

Strong effect of liquid Fe–S on elastic wave velocity of olivine aggregate: Implication for the low velocity anomaly at the base of the lunar mantle

The origin of the seismic low velocity zone (LVZ) observed at the base of the lunar mantle is important for understanding the nature of the lunar mantle. Liquid Fe–S is considered as a possible candidate of the cause of the LVZ. However, effect of liquid Fe–S on elastic wave velocity of mantle rock has been considered to be minor, according to theoretical estimation based on the high dihedral angle of liquid Fe–S in olivine aggregate observed in previous microstructural analysis of polished sample cross sections. Here we carry out direct measurements of elastic wave velocities of liquid Fe–S-bearing olivine aggregate and report strong reduction of the elastic wave velocities in the presence of liquid Fe–S. The effects of liquid Fe–S in olivine aggregates are much more pronounced than the theoretical estimation. Three-dimensional X-ray microtomography analysis reveals that the geometry of liquid Fe–S strongly depends on the size, with larger liquid Fe–S blobs having low aspect ratios, which may predominantly affect elastic wave velocity. Since smaller spherical Fe–S blobs are much more abundant than the larger elongated blobs, conventional dihedral angle analyses based on scanning electron microscope images tend to statistically over-sample smaller blobs and under-sample larger blobs. Our results suggest that the LVZ at the base of the lunar mantle can be explained by the presence of 4.3–5.0 vol.% liquid Fe–S. The LVZ may be a hidden reservoir of highly siderophile elements (HSEs), which may explain the low abundance of HSEs in the lunar mantle compared to the Earth.

Simultaneous electrical resistivity and elastic wave velocity measurements during triaxial deformation of granite under brine-saturated conditions

We report the first experiments, where simultaneous electrical resistivity and elastic wave velocity measurements are acquired during the triaxial deformation of granite under brine-saturated conditions. Both the resistivity and elastic wave velocity increase slightly during the early stage of deformation owing to crack closure, and then decrease systematically owing to crack development as the sample approaches failure. We observe a complex relationship among the resistivity, elastic wave velocity, and porosity during deformation that is likely attributed to their different sensitivities to crack orientation, tortuosity, and connectivity. The electrical resistivity changes tend to decline as the sample approaches failure owing to the nearly complete crack connectivity, whereas the elastic wave velocities continue to decrease. These characteristic changes in resistivity and velocity at the discrete stages of deformation may provide a clue to understanding structural changes in crystalline basements that are related to crack development and fluid infiltration.Graphical

Elastic Properties of Thermally Treated Diabase and Peridotite: Implications Toward the Elastic Properties of Oceanic Lithosphere

AbstractSupported by laboratory experimental results, the reduction in elastic thickness () and flexural rigidity () at trench outer rise, which enables bending, is attributed to damage. A series of laboratory experiments were performed on intact and thermally treated diabase and peridotite (400°C–800°C) under increasing confining pressures (3–200 MPa) at room temperature. Simultaneous porosity and elastic wave velocity (P and S) measurements were obtained under dry and fluid saturated conditions. The velocity and porosity inversions indicated a significant variation in crack properties (crack density, aspect ratio) and reduction in Young's modulus, of thermally treated samples in comparison to the intact samples. Hence the experimental results suggested weakening in elastic properties of a damaged oceanic lithosphere. Subsequently created lithospheric strength profiles showed a strength reduction in wet models in comparison to dry models. Under the assumption of different cooling models, the aging of the plate resulted in an increase in strength with deeper neutral zones. The outcome of the strength profiles was utilized to estimate and , which are also dependent on the elasticity of the lithosphere. The results showed a reduction in with increasing damage and suggest that the bending at the subduction zone is facilitated by weakened elastic properties of a damaged lithosphere. While most of the geophysical observations of were able to be constrained by the proposed damaged models, some shallow observations indicated enhanced damage triggered either by increased depth to brittle‐ductile transition or by large bending related faulting events.

Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice

An optimization problem is proposed for inferring physical properties of polycrystals given ultrasonic (elastic) wave velocity measurements, made across multiple sample orientations. The feasibility of the method is demonstrated by inferring both the effective grain elastic parameters and the grain c -axis orientation distribution function (ODF) of ice-core samples from Priestley glacier, Antarctica. The method relies on expanding the ODF in terms of a spherical harmonic series, which allows for a non-parametric estimation of the sample ODF. Moreover, any linear combination of the Voigt (strain) and Reuss (stress) homogenization scheme is allowed, although for glacier ice, the exact choice is found to matter little for bulk elastic behaviour, and thus for inferred physical properties, too. Finally, the accuracy of the inferred grain elastic parameters is discussed, including the well-posedness and shortcomings of the inverse problem, relevant for future adoptions in glaciology, geology and elsewhere.

Correlation of Dynamic and Static Young’s Modulus for Limestone

The application of rock mechanics in the area of geotechnical engineering is important especially, in describing the strength of rock material for essessing the stability of excavations, foundations and slopes in rock. In this study, the characterization of the rock material was investigated through the Young’s modulus parameter, which describes the relationship between the stress applied to the rock material and the resulting strain. For an elastic and homogeneous solid, the measurement of Young’s modulus can be determined either from the static or dynamic measurements. Numerous studies outline the differences between the Young’s modulus obtained from static and dynamic measurement in the laboratory. Comparatively, the measurement using static methods are more direct and realistic, as it describes the behaviour of rock deformation until failure occurs. The dynamic methods are more versatile and continuous, as they rely solely on the measurement of elastic wave velocities. However, one of the most notable disadvantages of rock material characterization by means of dynamic methods is that it overestimates the failure of rock material when compared to its actual value. With this in mind, the aim of this study is to obtain the measurements of Young’s modulus using both the static and dynamic methods. Based on the comparison made, an empirical equation of Est = 0.9264 (Edy) + 0.4976 with coefficient of determination, R2 of 0.8 is obtained for estimating the static Young’s modulus for limestone. The equation is applicable in situation where static measurement could not be carried out, and also serves as reliable estimation of Young’s modulus from dynamic measurement.

Reassessment of a bond correction method for in situ ultrasonic interferometry on elastic wave velocity measurement under high pressure and high temperature

ABSTRACT A new bond correction method for simultaneous elastic wave velocity measurement of in situ synchrotron X-ray technique and ultrasonic interferometry combined with a Kawai type multi-anvil apparatus is developed to measure elastic wave velocity precisely. The new method was validated using data from the literature and new elastic constant data of gold obtained under high pressure and high-temperature conditions. Elastic wave velocities corrected using the new method show lower values than those obtained without bond correction and using the conventional method, which show good agreement with datasets by in situ Brillouin scattering measurement and ab initio calculation. When the sample length is 1 mm under ambient conditions, the corrected V P and V S became 3.7% and 1.6% lower, respectively, than values obtained without bond correction under 12 GPa and 900 K. Results show that correcting the bond effect is extremely important, especially when the sample length is less than 1 mm.

Correlating failure strength with wave velocities for cemented sands from the particle-level analysis

Measurement of elastic wave velocities allows engineers to effectively characterize and monitor the stiffness and strength development of the cemented soils. Several correlations between elastic wave velocity and strength, as well as correlations between small-strain modulus and strength, have been proposed for different materials. However, since the physical justification of the stiffness-strength correlation is not fully understood, criticisms and diverse views still exist. This study derived the analytical correlation between the elastic wave velocity (or small-strain stiffness) and the unconfined compressive strength of cemented soil, based on a simple cubic packing of coated equal-sized spheres. The analytical derivation suggested a one-parameter power function between the strength and the wave velocity or stiffness, with the power index of 4 and 2 for wave velocity and stiffness, respectively. To verify the derived correlation model, a first-hand laboratory database was used. Factors affecting the correlations are also discussed.

Effects of Alteration and Cracks on the Seismic Velocity Structure of Oceanic Lithosphere Inferred From Ultrasonic Measurements of Mafic and Ultramafic Samples Collected by the Oman Drilling Project

AbstractSeismic velocity structures of the oceanic lithosphere are variable due to the variation of alteration and heterogeneities in porosity. In order to interpret geophysically determined velocity structures, it is necessary to understand how the seismic velocity of the oceanic lithosphere is affected by alteration and porosity. We conducted petrological analysis and elastic wave velocity measurements at 200 MPa on mafic and ultramafic rocks drilled from the Samail ophiolite. The elastic wave velocity calculated from the mineral abundances of the ultramafic rocks was sensitive to serpentinization, whereas that of the mafic rocks was nearly independent of the alteration, suggesting that velocity changes with depth in the oceanic crust are mainly due to porosity reduction. Based on the effective medium theory and pressure dependence of the experimentally determined velocity, the change in the porosity was estimated to be 0.04%–0.42% at 200 MPa, indicating porosity reduction by the increase of lithostatic pressure in the oceanic crust in the fast‐spreading system such as the Pacific plate. We estimated the degree of hydration in the mantle to account for the geophysical observations based on the laboratory experiments. Both the crustal porosity and mantle serpentinization increase towards the trench due to fracture related plate bending, indicating extensive hydration of the oceanic lithosphere close to the trench. From these estimates, water contents in the oceanic lithosphere were calculated to be as high as 3 wt.% in the shallow crust and 6 wt.% in the upper most mantle, which is significant for water transport into Earth's interior.

Pressure, temperature and lithological dependence of seismic and magnetic susceptibility anisotropy in amphibolites and gneisses from the central Scandinavian Caledonides

As a petrofabric indicator, anisotropy of magnetic susceptibility (AMS) can potentially be used to infer seismic properties of rocks, and in particular seismic anisotropy. To evaluate the link between AMS and seismic anisotropy we present laboratory measurements of elastic wave velocities and anisotropy of magnetic susceptibility (AMS) for eight samples from the deep drilling investigation forming a part of the Collisional Orogeny in the Scandinavian Caledonides (COSC) project. The samples consist of a representative suite of mid crustal, deformed rock types, namely felsic and biotite-rich gneisses, and amphibolites (mafic gneisses). Compressional (P) and shear (S) waves were measured at confining pressures from room pressure to 600 MPa and temperature from room condition to 600 °C. Seismic anisotropy changes with increasing temperature and pressure, where the effect of pressure is more significant than temperature. Increasing pressure, considering the range of samples, results in an increase in mean wave speed values from 4.52 to 7.86 km/s for P waves and from 2.75 to 4.09 km/s for S waves. Biotite gneiss and amphibolite exhibit the highest anisotropy with P wave anisotropy (AVp) in the ranges of ~9% to ~20%, and maximum S- wave anisotropy exceeds 10%. In contrast, Felsic gneisses are significantly less anisotropic, with AVp of <7% and AVs of <6%. Up to 20% anisotropy may be generated by microcracks at 600 MPa and 600 °C, which is likely originating from thermal expansion of anisotropic minerals. An agreement is found between AMS and seismic anisotropy, although this is only a case if mean magnetic susceptibility (kmean) ranges between ~1 × 10−5 to ~1 × 10−3 [SI]. Such kmean values are common in rocks dominated by paramagnetic matrix minerals. Based on our results we propose that such samples are the most likely to be useful for the prediction of seismic anisotropy based on their AMS.

All-optical noncontact phase-domain photoacoustic elastography.

Mechanical properties such as elasticity are important indicators of tissue functions that can be used for clinical diagnosis and disease monitoring. However, most current elastography techniques are limited in their ability to distinguish localized microstructural mechanical variations due to employing elastic wave velocity measurement. In addition, their contact-based measurement manner is not favored and may even be prohibited in many applications. In this Letter, we propose all-optical noncontact phase-domain photoacoustic elastography (NPD-PAE), leveraging the temporal response characteristics of laser-induced thermoelastic displacement using optical interferometric detection to calculate the elastic modulus. The all-optical pump-probe method allows the capture of the initial displacement profiles generated at the origin, thus enabling the extraction of in situ elasticity. The feasibility of the method was verified using a tissue-mimicking phantom. The capability to map the mechanical contrast was demonstrated on an ex vivo biological tissue. NPD-PAE opens a new avenue for development of a noncontact elastography technique, holding great potential in the biomedical field and materials science.

Tensile strength and elastic properties of fine-grained ice aggregates: Implications for crater formation on small icy bodies

The mechanical and elastic properties of ice aggregates are important in the physics of avalanches and crater formation on icy bodies, such as icy satellites and cometary nuclei. Here we conducted uniaxial tensile tests and elastic-wave velocity measurements on artificial fine-grained ice aggregates (snow) to infer the potential for crater formation on small icy bodies. The uniaxial tensile tests on the artificial snow with filling factors (f) in the 0.30–0.59 range at −15 °C demonstrate that the tensile strength (Yt) depends on its filling factor; we obtained the empirical equation Yt=103.5f3.5 (in kPa) based on our results, which is consistent with the upper limit of natural snow’s tensile strength. The compressional- and shear-wave velocities of artificial snow with f≥ 0.4 were measured via the ultrasonic pulse velocity method. The elastic-wave velocities decrease linearly with decreasing f values. Our calculations for the Young’s moduli of the artificial snow from the elastic-wave velocity measurements are 10–40 times higher than those from the tensile tests, which indicate the rate-dependent properties of the fine-grained ice aggregates. We propose a tensile strength estimation of a cometary surface via an artificial impact based on our results and a crater-scaling law in the strength-dominated regime.

Role of Ultrasound Elastography in Patient Selection for Prostatic Artery Embolization

PurposeTo determine the effects of prostatic artery embolization (PAE) on prostate elasticity as assessed using ultrasound elastography (US-E) and to describe baseline US-E's potential role in patient selection. Materials and MethodsThis was a prospective investigation that included 20 patients undergoing PAE to treat lower urinary tract symptoms attributed to benign prostatic hyperplasia (BPH). US-E with measurement of the prostatic elastic modulus (EM) and shear wave velocity (SWV) was performed before PAE and at 1-month follow-up. Baseline, 3-month, and 1-year follow-up evaluations included prostate-specific antigen, uroflowmetry, pelvic magnetic resonance imaging, and clinical assessment using the International Prostate Symptom Score (IPSS) and quality of life (QoL) metrics. ResultsSeventeen patients entered statistical analysis. US-E showed a significant reduction in mean prostatic EM (34.4 kPa vs 46.3 kPa, −24.7%, P < .0001) and SWV (3.55 m/s vs 4.46 m/s, −20.0%, P < .0001) after PAE. There were moderate positive correlations between baseline EM and 1-year IPSS (R = 0.62, P = .007) and between baseline SWV and 1-year IPSS (R = 0.68, P = .002). Baseline SWV ≥ 5.59 m/s and baseline EM ≥ 50.14 kPa were associated with suboptimal IPSS and QoL outcomes after PAE with high degrees of sensitivity (100%) and specificity (69-100%). ConclusionsPAE led to a positive effect on the BPH dynamic component related to prostatic elasticity. There was a moderate positive correlation between baseline prostatic elastographic parameters and 12-month IPSS. Measurement of baseline elastographic characteristics may become useful for the evaluation and selection of patients for PAE.

Sound Velocity of MgSiO3 Majorite Garnet up to 18 GPa and 2000 K

AbstractMgSiO3 majorite is the most significant endmember of the Al‐deficient majorite garnets that form at depths higher than ∼400 km, in the mantle transition zone (MTZ). Here, we report elastic wave velocity measurements on polycrystalline MgSiO3 majorite samples, up to 18.4 GPa and 2000 K by ultrasonic interferometry techniques combined with in situ X‐ray diffraction measurements in a multianvil apparatus. Our data show MgSiO3 majorite has the lowest elastic moduli among silicate garnet endmembers, under the pressure and temperature conditions of the MTZ. These new data combined with those of other garnet endmembers allowed to estimate VP and VS of majorite with compositions relevant to the MTZ. The results suggest that variation of MgSiO3 component in garnet may play a role for interpreting seismic gradients atop the 410‐km discontinuity while below ∼520 km, the velocity contrasts hold too low values to explain the discrepancy between mineral physics data and seismological observations.

Continuous measurement of ultrasonic elastic wave velocities, X-ray radiography and X-ray diffraction of Zr50Cu40Al10 metallic glass at high pressure and high temperature conditions

ABSTRACT A new experimental setup to continuously and automatically measure ultrasonic elastic wave velocities, X-ray radiography, and X-ray diffraction in large volume press is developed to explore structural change of amorphous materials at in situ high pressure and high temperature conditions. A continuous measurement for Zr50Cu40Al10 metallic glass is carried out during the heating process from 304 to 1102 K under high pressure conditions of 6.8–8.6 GPa. The sample length, elastic wave velocities, and Poisson’s ratio show marked changes at 611, 745, 825, and 874 K, which are interpreted as glass transition temperature (Tg ) at 611 K, two polyamorphic structural changes at 745 and 825 K, and crystallization above 874 K, respectively. We find that the 1.2Tg temperature (733 K at ∼8 GPa), where simulations study predicted occurrence of thermal rejuvenation, corresponds to the temperature of the polyamorphic structural change (745 K) in Zr50Cu40Al10 metallic glass.

Porosity dependence of elastic moduli of snow and firn

AbstractMeasurements of elastic wave velocities enable non-destructive estimation of the mechanical properties, elastic moduli and density of snow and firn. The variation of elastic moduli with porosity in dry snow and firn is modeled using a differential effective medium scheme modified to account for the critical porosity above which the bulk and shear moduli of the ice frame vanish. A comparison of predicted and measured elastic moduli indicates that the shear modulus of ice in snow is lower than that computed from single crystal elastic stiffnesses of ice. This may indicate that the bonds between snow particles are more deformable under shear than under compression. A partial alignment of ice crystals also may contribute. Good agreement between elastic stiffnesses of the ice frame obtained from elastic wave velocity measurements and the predictions of the theory is observed. The approach is simple and compact, and does not require the use of empirical fits to the data. Owing to its simplicity, this model may prove useful in a variety of potential applications such as construction on snow, interpretation of seismic measurements to monitor and locate avalanches and estimation of density within compacting snow deposited on glaciers and ice sheets.

Analysis of shale property changes after geochemical interaction under CO2 sequestration conditions

This study implements a supercritical CO2 (scCO2) sequestration environment in a laboratory and investigates the geochemical effects of scCO2 on the properties of rock specimens. Shale specimens constituting caprock were kept in a laboratory reactor chamber with scCO2 for 63 days. Chemical interaction between rock surface and the scCO2 was then induced, and the changes in the properties were inspected before and after the reaction through various tests. The non-destructive tests comprised measurement of elastic wave velocity, shore hardness followed by investigation using the inductively coupled plasma mass spectrometer, and scanning probe microscope. The destructive tests include uniaxial compressive strength, Brazilian tensile strength, and X-ray fluorescence tests. Results show that mechanical properties are significantly weakened when shale specimens are exposed to both scCO2 and brine. The specimens reacting with only scCO2 induced a self-healing effect by precipitation of secondary sediments, becoming a more intact rock with increased strength and elastic modulus. The results denote that the geochemical alteration of shale occurs in a short time and are highly dependent on the reaction conditions. These results provide fundamental information for the stability of CO2 storage sites regarding the physical and chemical reactions between rocks under geological sequestration conditions.