Interferometry In Conjunction Research Articles

Seismic imaging of a near-vertical vein using controlled-source seismic interferometry

New methodologies for narrow-vein mining are making thin, steeply dipping mineralized veins economically viable mining targets. Drilling is the normal method for delineation and resource evaluation prior to mining. However, for the evaluation of narrow veins, significant drilling of barren rock is required. Controlled-source seismic interferometry has the potential to significantly decrease the costs of target delineation by providing high-resolution seismic images of thin, steeply dipping mineralized veins. We present a case study that employs seismic interferometry in conjunction with a walkaway vertical seismic profiling survey to image a thin (0.5–4 m), steeply dipping barite vein. The footprint of the seismic data acquisition is relatively small and compatible with operations in areas with limited access (e.g., mining camps). The technique requires some care with experimental design and data processing, but it is clearly demonstrated to produce a high-resolution seismic image. Furthermore, we demonstrate that inversion of the depth-migrated image can be used to quantify vein thickness and provide direct information for resource evaluation and reserve estimation.

Acoustic velocities, elasticity, and pressure-induced elastic softening in compressed neodymium

For the first time, the acoustic velocities and elasticity of double hexagonal close-packed neodymium (Nd) were measured at high pressure using ultrasonic interferometry in conjunction with synchrotron X-ray techniques. Both the compressional and shear wave velocities increased with an increase in pressure of up to ~5.4 GPa before they exhibited almost constant values upon further compression. This pressure-induced elastic wave velocity softening can be attributed to the structural instability in dhcp-Nd. From the current sound velocities and density data, we obtained new bulk and shear moduli as well as their pressure dependence for polycrystalline dhcp-Nd, yielding B0 = 33.2(9) GPa, G0 = 14.1(5) GPa, ∂B/∂P=3.6(4), and ∂G/∂P=1.3(2), while other elasticity-related/mechanical properties, including Young's modulus, Debye temperature, Poisson's ratio, and Grüneisen parameter, which are important parameters for the application of Nd in extreme environments, were also derived.

Thermoelastic properties of tungsten at simultaneous high pressure and temperature

The compressional (P) and shear wave velocities (S) and unit cell volumes (densities) of polycrystalline tungsten (W) have been measured simultaneously up to 10.5 GPa and 1073 K using ultrasonic interferometry in conjunction with x-ray diffraction and x-radiography techniques. Thermoelastic properties of W were derived using different methods. We obtained the isothermal bulk modulus KT0 = 310.3(1.5) GPa, its pressure derivative K′T0 = 4.4(3), its temperature derivative at constant pressure (∂KT/∂T)P=−0.0138(1)GPaK−1 and at constant volume (∂KT/∂T)V=−0.0050GPaK−1, the thermal expansion α(0, T) = 1.02(27) × 10−5 + 7.39(3.2) × 10−9 T (K−1), as well as the pressure derivative of thermal expansion (∂α/∂P)T=−1.44(1)×10−7K−1GPa−1 based on the high-temperature Birch–Murnaghan equation of state (EOS), the Vinet EOS, and thermal pressure approach. Finite strain analysis allowed us to derive the elastic properties and their pressure/temperature derivatives independent of the choice of pressure scale. A least-squares fitting yielded KS0 = 314.5(2.5) GPa, KS0′ = 4.45(9), (∂KS/∂T)P = − 0.0076(6) GPa K−1, G0 = 162.4(9) GPa, G0′ = 1.8(1), (∂G/∂T)P = − 0.0175(9) GPa K−1, and α298K=1.23×10−5K−1. Fitting current data to the Mie–Grüneisen–Debye EOS with derived θ0=383.4K yielded γ0=1.81(6)andq=0.3. The thermoelastic parameters obtained from various approaches are consistent with one another and comparable with previous results within uncertainties. Our current study provides a complete and self-consistent dataset for the thermoelastic properties of tungsten at high P–T conditions, which is important to improve the theoretical modeling of these materials under dynamic conditions.

Pressure-induced velocity softening in natural orthopyroxene at mantle temperature

AbstractIn this study, we have measured the compressional and shear wave velocities of (Mg1.77Fe0.22Ca0.01)Si2O6 natural orthopyroxene up to 13.5 GPa and 873 K using ultrasonic interferometry in conjunction with in situ synchrotron X-ray diffraction and imaging techniques. Previous acoustic experiments on orthoenstatite (OEn) MgSiO3 indicated that both compressional and shear velocities (VP and VS) of OEn undergo continuous velocity softening above 9 GPa at room temperature, which has been attributed to the phase transition from OEn to the metastable, high-pressure clinoenstatite HPCEn2. For the first time, our results suggest that pressure-induced velocity softening can occur in natural orthopyroxene at high-temperature conditions relevant to the Earth's cold subduction zones. Estimates of the impedance and velocity contrasts between orthopyroxene (Opx) and high-pressure clinopyroxene (HPCpx) have been calculated, and the possibility of this phase transformation being a plausible candidate for seismic X-discontinuities at depth around 250–350 km is re-evaluated.

Thermoelasticity and anomalies in the pressure dependence of phonon velocities in niobium

Compressional and shear wave velocities of polycrystalline niobium have been measured at simultaneously high pressures and temperatures up to 5.8 GPa and 1073 K, respectively, using ultrasonic interferometry in conjunction with synchrotron x-ray techniques. An anomalous pressure-induced softening behavior in the phonon velocities, probably owing to the topological change in the Fermi surface, has been observed at ∼4.8 GPa during cold compression, which is supported by the elasticity data from our first-principles calculations. In contrast, both the bulk (BS) and shear (G) moduli increase with pressures but decrease with temperatures upon compression at extreme P-T up to 5.8 GPa and 1073 K. Using finite strain equation-of-state approaches, the elasticity of bulk and shear moduli and their pressure and temperature dependences are derived from the directly measured velocities and densities, yielding BS0 = 174.9(3.2) GPa, G0 = 37.1(3) GPa, ∂BS/∂P = 3.97(9), ∂G/∂P = 0.83(5), ∂BS/∂T = −0.064(7) GPa/K, and ∂G/∂T = −0.012(3) GPa/K. On the basis of the current thermoelasticity data, Debye temperature and the high-pressure melting curve of Nb are derived. The origin of the anomalies in shear behavior at high pressure might be attributed to the progressive s-d electron-transfer-induced topological changes of the Fermi surface upon compression.

Sound velocities of aluminum‐bearing stishovite in the mantle transition zone

AbstractThe elasticity of Al‐bearing stishovite with 1.0, 3.3, and 4.5 wt % Al2O3 was investigated in the multianvil apparatus at high pressures and temperatures up to 21 GPa and 1700 K, by ultrasonic interferometry in conjunction with in situ X‐ray techniques. The moduli KS and G are found to decrease with increasing Al2O3 content, while their pressure and temperature derivatives do not change in a significant manner for 1.0 and 3.3 wt % Al2O3. The temperature derivatives for 4.5 wt % Al2O3, however, are larger, which may result from a change in the Al substitution mechanism at high Al2O3 content. It is shown that acoustic velocities of any mid‐ocean ridge basalt are lower by −0.4% than those calculated from pure stishovite data. Velocity perturbations up to −3.4% (VP) and −4.2% (VS) in subducted slabs are explained by the combination of the thermal equilibration (ΔT ~ 600 K) of the slab and Al enrichment in stishovite.

Elastic wave velocity of polycrystalline Mj80Py20 garnet to 21 GPa and 2,000 K

The elastic wave velocities of polycrystalline Mj80Py20 garnet along the majorite–pyrope system have been measured at pressures up to 21 GPa and temperatures up to 2,000 K using ultrasonic interferometry in conjunction with in situ X-ray diffraction techniques in a Kawai-type multi-anvil apparatus. The elastic moduli of Mj80Py20 garnet and their pressure and temperature derivatives are determined by a two-dimensional linear fitting of the present experimental data, yielding: K S = 161.5 (7) GPa, ∂K S/∂P = 4.42 (4), ∂K S/∂T = −0.0154 (2) GPa/K, G = 86.2 (2) GPa, ∂G/∂P = 1.28 (1), ∂G/∂T = −0.0096 (5) GPa/K. The present results together with those of the studies on the majorite–pyrope solid solutions suggest the pressure and temperature derivatives of elastic moduli are insensitive to the majorite content in the majorite–pyrope system. The velocity gradients of the majoritic garnets in the majorite–pyrope system are 3 ~ 6 times lower than those required to account for the high seismic velocity gradients observed in the mantle transition zone.

Elasticity and sound velocities of polycrystalline grossular garnet (Ca3Al2Si3O12) at simultaneous high pressures and high temperatures

The elastic wave velocities of a dense polycrystalline specimen (99.7% of theoretical density) of synthetic grossular garnet (Ca3Al2Si3O12) were measured to pressures of ∼10GPa and temperatures of 1000K by transfer-function ultrasonic interferometry in conjunction with energy-dispersive synchrotron X-radiation in a deformation DIA-type cubic-anvil apparatus. The calculated elastic bulk (Ks) and shear (G) moduli data were fitted to functions of Eulerian strain to 3rd order, yielding the zero-pressure values [Ks=171.2 (8)GPa; G=107.4 (2)GPa] and their pressure derivatives [(∂Ks/∂P)T=4.47 (2); (∂G/∂P)T=1.29 (5)]. The temperature dependences of the elastic moduli obtained from linear regression of entire P–T–Ks and P–T–G data are: (∂Ks/∂T)P=−1.38 (3)×10−2 GPa/K and (∂G/∂T)P=−1.28 (2)×10−2GPa/K. These results together with those from previous studies for garnets with varying compositions suggest that most of the thermo-elastic properties of garnet are insensitive to grossular content, with the exception of the shear modulus, which significantly depends on the calcium content.

Studies on Digital Shearography for Testing of Aircraft Composite Structures and Honeycomb-Based Specimen

This paper reviews shearography and its applications for testing of aircraft composite structures and honeycomb-based specimen. Shearography is a laser-based interferometry in conjunction with the digital imaging processing technique for full-field measurement of surface deformation. It reveals defects in an object by looking for defect-induced deformation anomalies. It does not require special vibration isolation, and with the development of a small and mobile measuring device (portable inspection system), it can be employed easily in field/factory environments.

Density and elasticity of Zr 46Cu 37.6Ag 8.4Al 8 bulk metallic glass at high pressure

Compressional and shear wave velocities of Zr46Cu37.6Ag8.4Al8 bulk metallic glass (BMG) have been measured up to 6.3 GPa at room temperature using ultrasonic interferometry in conjunction with synchrotron X-radiography. The densities at high pressures are uniquely determined using the measured velocities. The experimental results for the elastic moduli of Zr46Cu37.6Ag8.4Al8 show a reasonable agreement with the Voigt–Reuss–Hill approximation of the element metal phases, indicating that the elastic properties of the BMG have a close correlation with its constituent components.

Experimental and theoretical studies on the elasticity of molybdenum to 12 GPa

Experiments have been conducted to measure compressional (VP) and shear wave (VS) velocities as well as unit-cell volumes (densities) of molybdenum to 12.0 GPa at room temperature using ultrasonic interferometry in conjunction with synchrotron x-radiation. Both VP and VS as well as the adiabatic bulk (KS) and shear (G) moduli exhibit monotonic increase with increasing pressure. A finite strain equation of state analysis of the directly measured velocities and densities yields KS0=260.7(5) GPa, G0=125.1(2) GPa, KS0′=4.7(1), and G0′=1.5(1) for the elastic bulk and shear moduli and their pressure derivatives at ambient conditions. Complimentary to the experimental data, VP and VS as well as the elastic bulk and shear moduli were also computed using density functional theory (DFT) at pressures comparable to the current experiment. Comparing with experimental results, the velocities and elastic moduli from DFT calculations exhibit close agreement with the current experimental data both in their values as well as in their pressure dependence.

Elasticity of amorphous zirconium tungstate at high pressure

Compressional (VP) and shear wave (VS) velocities of the amorphous phase of ZrW2O8 have been measured up to 10.4 GPa at room temperature using ultrasonic interferometry in conjunction with synchrotron x radiation. The pressure-density relation is determined using the measured velocities. Both VP and VS, as well as the adiabatic bulk and shear moduli, exhibit monotonic increase with increasing pressure. The pressure derivatives of the bulk and shear moduli are determined to be KS0′=7.3(1) and G0′=1.8(1), with bulk and shear moduli KS0=61.7(5) GPa and G0=35.0(2) GPa. Comparing with the α phase, VP, VS, KS0, E, Θac, and σ of the amorphous phase decrease by 14.8%, 10.0%, 17.2%, 2.9%, 1.2%, and 15.5%, along with 28% and 3.2% increase in density and shear modulus, respectively.

Elasticity of (Mg 0.87Fe 0.13) 2SiO 4 wadsleyite to 12 GPa and 1073 K

Elasticity of (Mg 0.87Fe 0.13) 2SiO 4 wadsleyite has been measured at simultaneous high pressure and high temperature to 12 GPa and 1073 K using ultrasonic interferometry in conjunction with synchrotron X-radiation. The elastic moduli and their pressure and temperature derivatives are precisely determined using pressure-standard-free third-order and fourth-order finite strain equations. Combined with previous thermoelastic data on olivine, the density, velocity and acoustic impedance contrasts between α- and β-(Mg 0.9Fe 0.1) 2SiO 4 at 410-km depth are calculated along a 1673 K adiabatic geotherm. Both the third- and fourth-order finite strain equation fitting results give estimation of ∼33–58% olivine content in the upper mantle to account for a seismic discontinuity of ∼5% velocity jumps, and 8.5% ( P wave) and 11.1% ( S wave) impedance jumps at 410 km depth.

Simultaneous ultrasonic and synchrotron x-ray studies on pressure induced α-ω phase transition in zirconium

Compressional and shear wave velocities as well as unit-cell volumes across the α-ω transition of Zr have been measured up to 10.5 GPa at room temperature using ultrasonic interferometry in conjunction with synchrotron x radiation. In the pressure range of 5.0 to 6.2 GPa, a mixture of α and ω phase is clearly identified and the α phase is completely transformed to ω phase at 6.8 GPa. The measured velocity jumps across the α-ω transition are 9.6% and 13.1% for P and S waves, respectively. Negative pressure dependence for the shear modulus of α-Zr has been found at pressures from 1.4 to 2.9 GPa, which may be ascribed to the shear instability of the α phase prior to transition. According to velocity data, the onset pressure of the α-ω transition is determined to be ∼4.0 GPa.

Elasticity ofω-phase zirconium

Compressional $({V}_{P})$ and shear wave $({V}_{S})$ velocities as well as unit-cell volumes of the $\ensuremath{\omega}$ phase of Zr have been measured at high pressure $(6.9--10.9\phantom{\rule{0.3em}{0ex}}\mathrm{GPa})$ at room temperature using ultrasonic interferometry in conjunction with synchrotron x radiation. Both ${V}_{P}$ and ${V}_{S}$ as well as the adiabatic bulk $({K}_{S})$ and shear $(G)$ moduli exhibit monotonic increase with increasing pressure. Using a finite strain equation of state approach, the elastic bulk and shear moduli and their pressure derivatives are derived from the directly measured velocities and densities, yielding ${K}_{S0}=104.0\phantom{\rule{0.3em}{0ex}}(16)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${G}_{0}=45.1\phantom{\rule{0.3em}{0ex}}(9)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${K}_{S0}^{\ensuremath{'}}=2.8$ (2), and ${G}_{0}^{\ensuremath{'}}=0.6$ (1) independent of pressure calibration. The low pressure dependence of ${K}_{S0}$ and ${G}_{0}$ may be attributed to the pressure-induced progressive $s\text{\ensuremath{-}}d$ electron transfer in the $\ensuremath{\omega}\text{\ensuremath{-}}\mathrm{Zr}$ as suggested by previous Raman studies as well as static compressions at high pressure.

Indoor seismology by probing the Earth's interior by using sound velocity measurements at high pressures and temperatures

The adiabatic bulk (K(S)) and shear (G) moduli of mantle materials at high pressure and temperature can be obtained directly by measuring compressional and shear wave velocities in the laboratory with experimental techniques based on physical acoustics. We present the application of the current state-of-the-art experimental techniques by using ultrasonic interferometry in conjunction with synchrotron x radiation to study the elasticity of olivine and pyroxenes and their high-pressure phases. By using these updated thermoelasticity data for these phases, velocity and density profiles for a pyrolite model are constructed and compared with radial seismic models. We conclude that pyrolite provides an adequate explanation of the major seismic discontinuities at 410- and 660-km depths, the gradient in the transition zone, as well as the velocities in the lower mantle, if the uncertainties in the modeling and the variations in different seismic models are considered. The characteristics of the seismic scaling factors in response to thermal anomalies suggest that anticorrelations between bulk sound and shear wave velocities, as well as the large positive density anomalies observed in the lower mantle, cannot be explained fully without invoking chemical variations.

Compressional and shear-wave velocities of the polycrystallineCaGeO3perovskite to10GPa

Compressional and shear-wave velocities and unit-cell volumes of orthorhombic $\mathrm{Ca}\mathrm{Ge}{\mathrm{O}}_{3}$ perovskite have been measured up to $10\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ at ambient temperature using ultrasonic interferometry in conjunction with synchrotron x radiation. Fitting all velocity and unit-cell volume data to finite-strain equations yields the zero-pressure adiabatic bulk and shear moduli and their pressure derivatives ${K}_{S0}=194.6$ $(11)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${G}_{0}=109.5$ $(5)\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, $K_{S0}{}^{\ensuremath{'}}=6.4$ (2), $G_{0}{}^{\ensuremath{'}}=1.7$ (1), with an rms misfit of $0.009\phantom{\rule{0.3em}{0ex}}\mathrm{km}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. From the data in the current study, we have observed no discontinuities or elasticity softening for either the bulk or shear moduli up to the peak pressure of $10\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$.

Ultrasonic observations of elasticity changes across phase transformations in MgSiO3 pyroxenes

Using ultrasonic interferometry in conjunction with synchrotron X-radiation techniques in a high-pressure, multi-anvil apparatus, the elastic behavior of MgSiO3 pyroxene has been continuously monitored as the specimens undergo phase transformations from the orthoenstatite (OEN) to the high-pressure clinoenstatite phase (HP-CEN) and from HP-CEN to the low-pressure clinoenstatite phase (LP-CEN). In the former case, elastic softening and amplitude attenuation is observed for both compresssional (P) and shear (S) waves when the pressure exceeds 9 GPa at room temperature, which we suggest is associated with a transition to a metastable phase intermediate between OEN and HP-CEN. In the latter case, both P and S wave velocities decrease rapidly as the back-transformation from HP-CEN to LP-CEN occurs on decrease of pressure below 4 GPa at room temperature; this is accompanied by an increase in attenuation of the P waves in the specimen, but not the S waves.

Elasticity of San Carlos olivine to 8 GPa and 1073 K

Elasticity of San Carlos olivine, (Mg0.9, Fe0.1)2SiO4, has been measured at simultaneous high pressure and high temperature to 8.2 GPa and 1073 K using ultrasonic interferometry in conjunction with synchrotron X‐radiation. The elastic moduli and their pressure and temperature derivatives are precisely determined using a pressure standard free fit using third‐order finite strain equations to the velocity and unit cell volume data in the entire pressure and temperature range, yielding KS0 = 130.3(4) GPa, G0 = 77.4(2) GPa, K′S0 = 4.61(11), G′0 = 1.61(4), ∂KS/∂T = −0.0164(5) GPa/K, and ∂G/∂T = −0.0130(3) GPa/K. Combined with previous thermoelastic data on wadsleyite, the velocity contrasts between α‐ and β‐(Mg, Fe)2SiO4 at 410‐km depth are calculated along a 1673 K adiabatic geotherm with plausible iron partition between the two phases. The fraction of olivine consistent with a ∼5% seismic discontinuity in an anhydrous mantle is constrained to be less than ∼50% with the possibility that a hydrous or a cooler mantle increases the olivine content towards pyrolitic composition.

Pressure and temperature dependence of elastic wave velocity of MgSiO 3 perovskite and the composition of the lower mantle

Simultaneous measurements of compressional ( P) and shear ( S) wave velocities and unit cell volume (density) have been conducted on MgSiO 3 perovskite to 9.2 GPa and 873 K using ultrasonic interferometry in conjunction with X-ray diffraction. Finite strain analysis of current data allowed us to determine the elastic moduli and their pressure derivatives independent of the pressure measurement. The results are K S = 253(2) GPa, G = 173(1) GPa, ∂ K S / ∂P = 4.4(1) and ∂G/ ∂P = 2.0(1). The temperature derivatives of the bulk and shear moduli were tightly constrained from acoustic velocity measurements, yielding ∂ K S /∂ T = −0.021(2) GPa/K and ∂ G/∂ T = −0.028(2) GPa/K. P and S wave velocities and density profiles for a pyrolite compositional model consisting of magnesium silicate perovskite and magnesiowustite are calculated at lower mantle depths along a 1600 K adiabatic geotherm, the results agree with those of seismic model PREM within 0.5, 0.5 and 0.3%, respectively, from 800 to ∼2600 km. The effect of Fe and Mg partitioning between magnesium silicate perovskite and magnesiowustite on the calculated velocities and density is negligibly small compared to the effects of composition and temperature. Simultaneous constraints from P and S wave velocities and density support for a homogeneous lower mantle with pyrolitic composition.