Wave Velocity Anisotropy Research Articles

Shear wave velocity and radial anisotropy structures beneath the central Pacific from surface wave analysis of OBS records

The central Pacific plate is an ideal area to study the dynamics of the lithosphere-asthenosphere system, as this region is far away from other dynamics systems, such as subduction zones and volcanic hotspots of mantle plumes, and has experienced simple oceanic evolution. In this study, we collect three-component continuous seismic data and differential pressure gauge data recorded by 15 broadband ocean bottom seismometers (OBSs) from the NoMelt experiment. We process continuous seismic noise data to obtain phase velocities of the fundamental (6-30 s) and first high (5-11 s) mode Rayleigh waves and fundamental mode Love waves (5-12 s). We apply a two-plane-wave method to teleseismic Rayleigh waves to obtain the fundamental mode phase velocities at 20-150 s periods, and apply high-resolution linear Radon transform to teleseismic Love waves to obtain phase velocities for the fundamental mode Love waves at 28-48 s periods. Then, we jointly invert the average phase velocities of Rayleigh and Love waves to construct 1-D isotropic shear wave velocity and radial anisotropy from the seafloor to 150 km depth beneath the NoMelt region. Our 1-D model shows a low velocity zone (LVZ) beneath a high velocity lid. By comparing our results with the predictions of partial melt models, we suggest the LVZ is attributed to the presence of a small amount of melt in the asthenosphere. Strong radial anisotropy (5-6%) is observed in the crust. But the mantle lithosphere is characterized by weak radial anisotropy (< 1%), consistent with the corner mantle flow history at the mid-ocean ridge during the formation of new oceanic plates. Strong radial anisotropy (4-5%) is observed in the asthenosphere, which is consistent with the global surface wave tomography results and numerical simulation studies, reflecting the strong shear strain of asthenosphere related to the motion of oceanic plate over the underlying asthenosphere.

Focusing Surface-Acoustic-Wave Microcavities on GaAs

Focusing microcavities for surface acoustic waves (SAWs) produce highly localized strain and piezoelectric fields that can dynamically control excitations in nanostructures. Focusing transducers (FIDTs) that generate SAW beams that match nanostructure dimensions require pattern correction due to diffraction and wave-velocity anisotropy. The anisotropy correction is normally implemented by adding a quadratic term to the dependence of the wave velocity on the propagation angle. We show that a SAW focusing to a diffraction-limited size in $\mathrm{Ga}\mathrm{As}$ requires corrections that more closely follow the group-velocity wave front, which is not a quadratic function. Optical interferometric mapping of the resultant SAW displacement field reveals tightly focused SAW beams on $\mathrm{Ga}\mathrm{As}$ with a minimal beam waist. An additional set of Gouy-phase--corrected passive fingers creates an acoustic microcavity in the focal region with a small volume and a high quality factor. Our ${\ensuremath{\lambda}}_{\mathrm{SAW}}=5.6\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}$ FIDTs are expected to scale well to the approximately 500-nm wavelength regime needed to study strong coupling between vibrations and electrons in electrostatic $\mathrm{Ga}\mathrm{As}$ quantum dots.

Delineation of Damage Zones From 3 km Downhole Geophysical Logs in the Koyna Seismogenic Zone, Western India

AbstractDelineation of subsurface faults and damage zones is a major goal of scientific drilling projects in seismically active areas. Geophysical logs acquired in a 3‐km deep scientific borehole KFD1 in the Koyna seismogenic zone, a site of recurrent reservoir triggered seismicity over the past 55 years, provide an unprecedented opportunity to investigate the rock properties and delineate the fault zones. KFD1 passed through 1,247‐m thick Deccan traps and continued for 1,767 m into the underlying granitic basement rocks that host the seismic activity in the depth range 2–10 km. We have studied the physical properties and acoustic behavior of basement granitoids from the analysis of geophysical logs from 1,500 to 3,000 m. Salient results are as follows. (1) Seven anomalous zones are identified below 2,100‐m depth based on electrical resistivity, caliper, density, neutron porosity, self‐potential, and sonic data. (2) The anomalous zones are characterized by significant shear wave velocity anisotropy (up to 25%), as revealed by cross‐dipole sonic data. (3) Dispersion analysis of dipole flexural modes confirms that the anisotropy is primarily stress induced; fast polarized shear wave azimuth (FSA) therefore indicates the orientation of maximum horizontal compressive stress SHmax. (4) Comparison of FSA with independent estimates of SHmax orientations obtained from drilling induced tensile fractures and strike of inclined fractures in the anisotropic zones shows that FSA is controlled mainly by the stress regime. Therefore, the stress rotations inferred from anisotropy analyses in the anomalous zones indicate their association with subsurface fault damage zones.

Experimental Investigation on Mechanical and Acoustic Parameters of Different Depth Shale Under The Effect of Confining Pressure

Investigations on the effects of confining pressure and burial depth on mechanical and acoustic parameters are significant for studying the deep shale deformation, failure rule, and hydraulic fracturing. Shale specimens at six different depth levels ranging from 1535 to 1635 m have been collected from a shale gas well in southwest China. RTR-1000 rapid rock triaxial testing system has been applied to carry out the mechanical and acoustic experiments with 19 shale specimens. The experimental results revealed that the peak deviatoric stress, peak axial strain, peak volumetric strain, residual stress, and axial wave velocity are directly proportional to confining pressure and burial depth, whereas elastic modulus is not affected much by both confining pressure and burial depth and the Poisson ratio decreases with the increase of confining pressure. In the burial depth range 1535–1635 m, the variation of Poisson’s ratio is not obvious with the depth changes, and their relationship has high randomicity. The Wave velocity Anisotropy of tested shale is greatly affected by the degree of stratification development rather than the corresponding crustal stress. The coefficient of variation and the degree of stratification development are inversely proportional to burial depth. The axial wave velocity of shale is closely related to the loading process. In the compaction stage, wave velocity increases rapidly with the increase of strain. And in the elastic yielding stage, wave velocity increases slowly along with the strain build-up. This study will help to deepen the understanding of the physical and mechanical properties of Wuxi shale and guide the shale gas exploitation in China.

The impact of water on slip system activity in olivine and the formation of bimodal crystallographic preferred orientations

Crystallographic preferred orientations (CPOs) in olivine are widely used to infer the mechanisms, conditions, and kinematics of deformation of mantle rocks. Recent experiments on water-saturated olivine were the first to produce a complex CPO characterised by bimodal orientation distributions of both [100] and [001] axes and inferred to form by combined activity of (001)[100], (100)[001], and (010)[100] slip. This result potentially provides a new microstructural indicator of deformation in the presence of elevated concentrations of intracrystalline hydrous point defects and has implications for the interpretation of seismic anisotropy. Here, we document a previously unexplained natural example of this CPO type in a xenolith from Lesotho and demonstrate that it too may be explained by elevated concentrations of hydrous point defects. We test and confirm the hypothesis that combined (001)[100], (100)[001], and (010)[100] slip were responsible for formation of this CPO by (1) using high-angular resolution electron backscatter diffraction to precisely characterise the dislocation types present in both the experimental and natural samples and (2) employing visco-plastic self-consistent simulations of CPO evolution to assess the ability of these slip systems to generate the observed CPO. Finally, we utilise calculations based on effective-medium theory to predict the anisotropy of seismic wave velocities arising from the CPO of the xenolith. Maxima in S-wave velocities and anisotropy are parallel to both the shear direction and shear plane normal, whereas maxima in P-wave velocities are oblique to both, adding complexity to interpretation of deformation kinematics from seismic anisotropy.

Effective Elastic Properties of Rocks With Transversely Isotropic Background Permeated by Aligned Penny‐Shaped Cracks

AbstractSeismic characterization of fractures is of great importance in many disciplines, for which rock physics models provide the basis to link fracture properties to seismic attributes. However, to date, most rock physics models neglect the background anisotropy that may exist in many fractured formations. Hence, in this work, we developed a theoretical model for rock effective elastic properties with penny‐shaped cracks embedded in the transversely isotropic (TI) background medium. We first derived analytical solutions for the case with dry or fluid‐filled penny‐shaped cracks parallel to the isotropic plane of TI background medium. Further, the results were extended to the case with cracks inclined to the isotropic plane with any angles. We then studied, based on the developed theoretical model, two tight sand samples with TI and isotropic background, respectively, to illustrate effects of background anisotropy on effective elastic properties of fractured rocks. The results show that the background anisotropy has significant influence on P and S wave velocity anisotropy, as well as on shear wave splitting. The background anisotropy can either increase or decrease P and SH wave velocity anisotropy depending on crack inclination angles, whereas it has relatively small influence on SV wave velocity anisotropy. To further illustrate the important effects of background anisotropy, we compared theoretical predictions to ultrasonic measurements on a synthetic fractured sandstone sample with TI background medium. The results show notable improvement of the agreement between theoretical predictions and experimental results after considering background anisotropy.

Anisotropy of Stable Single Domain Ferrimagnetic Particles in a Rock Sample from Gyroremanent Magnetization and Comparison with Other Anisotropy Methods

The orientation of stable single domain (SSD) ferrimagnetic particles in an igneous rock sample was determined by a sensitive technique utilizing gyroremanent magnetization (GRM). Components of GRM were measured in the sample upon exposure to an alternating field (AF) at various orientations in 3 orthogonal planes. The major components of GRM exhibited a sin(2θ) dependence on AF orientation in the respective perpendicular planes. This was in accordance with theory [1] and contrary to some previously reported experimental results on magnetic recording tape, which produced a distorted sin(2θ) dependence of the GRM [1]. The explanation is likely due to the SSD ferrimagnetic particles in the rock sample being more dispersed (less interacting) compared to the highly interacting SSD particles in the magnetic tape sample of the previous study. The GRM results were consistent with another remanence anisotropy method, anisotropy of isothermal remanent magnetization (AIRM). This method again measures the anisotropy of the remanence carrying ferrimagnetic particles, but the IRM is also acquired by larger multidomain (MD) particles as well as by the SSD particles. The results were also consistent with the visible rock anisotropy (petrofabric), the anisotropy of magnetic susceptibility (AMS), and the shear wave velocity anisotropy. A comparison of all the methods demonstrated that the fine SSD particles, which make up only a small proportion of the rock, were aligned in quite a similar orientation to that of the main rock forming minerals that constituted the bulk of the sample.

Imaging the Eastern Trans‐Mexican Volcanic Belt With Ambient Seismic Noise: Evidence for a Slab Tear

AbstractThe eastern sector of the Trans‐Mexican Volcanic Belt (TMVB) is an enigmatic narrow zone that lies just above where the Cocos plate displays a sharp transition in dipping angle in central Mexico. Current plate models indicate that the transition from flat to steeper subduction is continuous through this region, but the abrupt end of the TMVB suggests that the difference in subduction styles is more likely to be accommodated by a slab tear. Based on a high‐resolution shear wave velocity and radial anisotropy model of the region, we argue that a slab tear within South Cocos can explain the abrupt end of the TMVB. We also quantify the azimuthal anisotropy beneath each seismic station and present a well‐defined flow pattern that shows how mantle material is being displaced from beneath the slab to the mantle wedge through the tear in the subducted Cocos plate. We suggest that the toroidal mantle flow formed around the slab edges is responsible for the existence of the volcanic gap in central Mexico. Moreover, we propose that the temperature increase caused by the influx of hot, less dense mantle material flowing through the tear to the Veracruz area may have significant implications for the thermomechanical state of the subducted slab and explain why the intermediate‐depth seismicity ends suddenly at the southern boundary of the Veracruz basin. The composite mantle flow formed by the movement of mantle material through the slab tears in western and southern Mexico may be allowing the Cocos plate to roll back in segments.

Development and Recovery of Stress‐Induced Elastic Anisotropy During Cyclic Loading Experiment on Westerly Granite

AbstractIn the upper crust, where brittle deformation mechanisms dominate, the development of crack networks subject to anisotropic stress fields generates stress‐induced elastic anisotropy. Here a rock specimen of Westerly granite was submitted to differential stress cycles (i.e., loading and unloading) of increasing amplitudes, up to failure and under upper crustal conditions. Combined records of strains, acoustic emissions, and P and S elastic wave anisotropies demonstrate that increasing differential stress promotes crack opening, sliding, and propagation subparallel to the main compressive stress orientation. However, the significant elastic anisotropies observed during loading (≥20%) almost vanish upon stress removal, demonstrating that in the absence of stress, crack‐related elastic anisotropy remains limited (≤10%). As a consequence, (i) crack‐related elastic anisotropies measured in the crust will likely be a strong function of the level of differential stress, and consequently (ii) continuous monitoring of elastic wave velocity anisotropy along faults could shed light on the mechanism of stress accumulation during interseismic loading.

Understanding progressive rock failure and associated seismicity using ultrasonic tomography and numerical simulation

Monitoring the stability of underground rock excavation zones, such as tunnels and underground mines, is critical to their operational safety. The stability of these structures is related to the stress redistribution introduced by the excavation process and disturbance during the operation. Therefore, the characteristics of progressive rock failure behaviour at different stress conditions must be investigated. In this study, we address this problem using a laboratory experiment, coupled with ultrasonic tomography (UT) and numerical simulation. A time-lapse two-dimensional (2D) UT observation was conducted on a granite slab under uniaxial compression. This test was then reproduced numerically by the combined finite-discrete element method (FDEM). This innovative combination of technologies depicted the entire deformation and failure processes at macroscopic and microscopic scales. Quantitative assessments of the results suggested six precursory behaviours indicating the catastrophic failure of the rock: (1) decrease of the average wave velocity perpendicular to the loading direction, (2) increase of the heterogeneity and anisotropy of wave velocity, (3) exponential increase of seismic rate, (4) spatial localization of damage onto the failure plane, (5) increase of the dominance of shear failure, and (6) slight recovery of b-value, followed by a significant drop. An integrated monitoring and analysis of these indicators, accompanied by carefully calibrated numerical simulations, may provide vital information regarding the stability of underground structures.

Nondestructive ultrasonic evaluation of additively manufactured AlSi10Mg samples

Pulse-echo ultrasonic method was carried out to investigate possible anisotropy in selective laser melting additively manufactured (AM) AlSi10Mg samples. Three types of ultrasonic analyses were employed: time of flight (TOF) sound velocity measurement, frequency depended attenuation and exponential fitted attenuation. Analysis of the transverse waves TOF sound velocity as a function the oscillation angle relative to the build direction reveals that the AM AlSi10Mg material has anisotropy in both transverse wave velocity and attenuation with respect to the build direction. Such an anisotropy is with symmetry around the build direction. Three transverse wave velocity zones were identified, low-velocity zone, where the transverse oscillation direction perpendicular to the build direction, high-velocity zone where the transverse oscillation direction parallel to the build direction and a transition zone. This behavior held even after heat treatments. The transverse velocity and the frequency depended attenuation seems to be sensitive tools that enable detection of subtle changes in AM products.

Electronic structure, elasticity, Debye temperature and anisotropy of cubic WO3 from first-principles calculation.

The electron structure, elastic constant, Debye temperature and anisotropy of elastic wave velocity for cubic WO3 are studied using CASTEP based on density functional theory. The optimized structure is consistent with previous work and the band gap is obtained by computing the electronic structure; the top of the valence band is not at the same point as the bottom of the conduction band, which is an indirect band-gap oxide. Electronic properties are studied from the calculation of band structure, densities of states and charge densities. The bulk and shear moduli, Young's modulus, hardness and Poisson's ratio for WO3 are studied by the elastic constants. We calculated acoustic wave velocities in different directions and estimated the Debye temperature from the acoustic velocity. The anisotropy of WO3 was analysed from the point of view of a pure wave and quasi wave.

The Evolution of Cracks in Maluanshan Granite Subjected to Different Temperature Processing

The understanding of the change in the physical and mechanical properties of rock before and after heating is of great significance for the site selection of mattamore and the exploitation of geothermal resources. It is known that before and after heating, the changes in wave velocity, wave velocity anisotropy and permeability of rock are due to the evolution of cracks in the rock. In this study, the wave velocity and permeability of granite specimen from the Maluanshan tunnel in Shenzhen, China, were measured after high-temperature processing at atmospheric pressure. The effects of temperature on the properties of rock based on the acoustics and permeability were measured and analyzed. The evolution of the cracks in Maluanshan granite was inverted through the change rule of the cracks, wave velocity anisotropy and permeability with temperature. The main conclusions were as follows: (1) Both granite P and S wave velocities decreased with the increasing temperature, and the thermal cracking occurred in four stages: between 50 and 250 °C, the crack stabilization development stage was in effect; between 250 and 300 °C, an accelerated development stage of the cracks existed; between 300 and 350 °C, a shift stage for the cracks was entered; and finally, from 350 to 700 °C, the cracks continued into a further development stage; (2) The coefficient of variation could be used to reflect the structural feature change of the rocks in the study of the wave velocity anisotropy. The structures of cracks were observed to change before and after 300 °C. (3) The Maluanshan granite permeability increases with the increasing processing temperature. It was observed that the higher the processing temperature, the larger the increase in the permeability rate. A porosity function was used as a variable to analyze the relationship between the porosity function and permeability as follows: from 50 to 200 °C, the permeability was determined by the microcracks; 200–400 °C was the transition stage; and between 400 and 700 °C, the permeability was determined by the macrocracks.

Classification and assessment of rock mass parameters in Choghart iron mine using P-wave velocity

Engineering rock mass classification, based on empirical relations between rock mass parameters and engineering applications, is commonly used in rock engineering and forms the basis for designing rock structures. The basic data required may be obtained from visual observation and laboratory or field tests. However, owing to the discontinuous and variable nature of rock masses, it is difficult for rock engineers to directly obtain the specific design parameters needed. As an alternative, the use of geophysical methods in geomechanics such as seismography may largely address this problem. In this study, 25 seismic profiles with the total length of 543 m have been scanned to determine the geomechanical properties of the rock mass in blocks I, III and IV-2 of the Choghart iron mine. Moreover, rock joint measurements and sampling for laboratory tests were conducted. The results show that the rock mass rating (RMR) and Q values have a close relation with P-wave velocity parameters, including P-wave velocity in field (VPF), P-wave velocity in the laboratory (VPL) and the ratio of VPF to VPL (i.e. KP = VPF/VPL). However, Q value, totally, has greater correlation coefficient and less error than the RMR. In addition, rock mass parameters including rock quality designation (RQD), uniaxial compressive strength (UCS), joint roughness coefficient (JRC) and Schmidt number (RN) show close relationship with P-wave velocity. An equation based on these parameters was obtained to estimate the P-wave velocity in the rock mass with a correlation coefficient of 91%. The velocities in two orthogonal directions and the results of joint study show that the wave velocity anisotropy in rock mass may be used as an efficient tool to assess the strong and weak directions in rock mass.

Anatomy of the Colima volcano magmatic system, Mexico

Colima volcano is one of the most active volcanoes in continental north America. It is located within the Colima graben on the western part of the Colima rift zone. Although extensively studied, the internal structure and deep magmatic system remains unknown. This research gives new clues to understand how and where magmas are produced and stored at depth. Using ambient seismic noise, we jointly invert for Rayleigh and Love wave dispersion curves for both phase and group velocity, which is applied for the first time in a volcanic environment. We invert for both the shear wave velocity and radial anisotropy. The 3D high resolution shear wave velocity model shows a deep, large and well-delineated elliptic-shape magmatic reservoir below the Colima volcano complex at a depth of about 15 km. On the other hand, the radial anisotropy model shows a significant negative feature (i.e., VSV>VSH) revealed from ≥35 km depth until the top of the magma reservoir at about 12 km depth. The latter suggests the presence of numerous vertical fractures where fluids, rooting from a well-known mantle window, can easily migrate upward and then accumulate in the magma reservoir. Furthermore, the convergence of both a low velocity zone and a negative anisotropy suggests that the magma is mainly stored in conduits or inter-fingered dykes as opposed to horizontally stratified magma reservoir.

Closure to “Discussion of ‘Measurement of Stiffness Anisotropy in Kaolinite Using Bender Element Tests in a Floating Wall Consolidometer’ by X. Kang, G.-C. Kang, and B. Bate” by Coffman, Salazar and Zhao

Abstract The authors appreciate the interest of the discussers in this paper. The main arguments of the discussers were: (1) comparing the back-pressure saturated, constant-rate-of-strain consolidation device that incorporated bender elements (BP-CRS-BE device) developed by the discussers to the floating wall consolidometer based bender element testing system in the original paper (Kang, X., Kang, G.-C., and Bate, B., 2014, “Shear Wave Velocity Anisotropy of Kaolinite Using a Floating Wall Consolidometer-Type Bender Element Testing System,” Geotech. Test. J., Vol. 37, No. 5, pp. 869–883. [DOI: 10.1520/GTJ20120205]); (2) requesting the quantification of both the system lag and the machine deflection; (3) suggesting the authors use cross correlation method to determine the first arrival time because Vs values obtained by time domain method are “only approximate,” while the latter was the only method used by the discussers in their referenced work (Salazar, S. E. and Coffman, R. A., 2014, “Design and Fabrication of End Platens for Acquisition of Small-Strain Piezoelectric Measurements during Large-Strain Triaxial Extension and Triaxial Compression Testing,” Geotech. Test. J., Vol. 43, No. 2. pp. 1–11. [DOI: 10.1520/GTJ20140057]); and (4) making misleading arguments regarding the compression and shear waves measurements. In this closure, the authors first briefly compared the BP-CRS-BE device to the floating wall consolidometer based bender element testing system, and pointed out that (1) the well-documented wavelength ratio (Rd ratio) consideration in designing a bender element device and the seemingly unsatisfaction of such consideration in the BP-CRS-BE device, and that (2) both the lack of details in B-value checking to examine saturation and the lack of shear wave velocity resulted from the BP-CRS-BE device to substantiate the arguments of the discussers. Then the authors provided the requested quantifications of both system lag and machine deflection to address some postulations by the discussers. The authors disagreed with Arguments 3 and 4 made by the discussers, and respond accordingly.

Imaging the lithospheric structure beneath the Indian continent

AbstractWe present a high‐resolution 3‐D lithospheric model of the Indian plate region down to 300 km depth, obtained by inverting a new massive database of surface wave observations, using classical tomographic methods. Data are collected from more than 550 seismic broadband stations spanning the Indian subcontinent and surrounding regions. The Rayleigh wave dispersion measurements along ~14,000 paths are made in a broad frequency range (16–250 s). Our regionalized surface wave (group and phase) dispersion data are inverted at depth in two steps: first an isotropic inversion and next an anisotropic inversion of the phase velocity including the SV wave velocity and azimuthal anisotropy, based on the perturbation theory. We are able to recover most of the known geological structures in the region, such as the slow velocities associated with the thick crust in the Himalaya and Tibetan plateau and the fast velocities associated with the Indian Precambrian shield. Our estimates of the depth to the Lithosphere‐Asthenosphere boundary (LAB) derived from seismic velocity Vsv reductions at depth reveal large variations (120–250 km) beneath the different cratonic blocks. The lithospheric thickness is ~120 km in the eastern Dharwar, ~160 km in the western Dharwar, ~140–200 km in Bastar, and ~160–200 km in the Singhbhum Craton. The thickest (200–250 km) cratonic roots are present beneath central India. A low velocity layer associated with the midlithospheric discontinuity is present when the root of the lithosphere is deep.

The observation of AE events under uniaxial compression and the quantitative relationship between the anisotropy index and the main failure plane

In this paper, the P-wave velocities in different directions of sandstone samples under uniaxial compression are measured. The results indicate that the changes in the P-wave velocity in different directions are almost the same. In the initial stage of loading, the P-wave velocity exhibits a rising trend due to compaction and closure of preexisting fissures. As the stress increase, preexisting fissures are closed but induced fractures are not yet generated. The sandstone samples become denser and more uniform. The P-wave velocity remains in a steady state at a high level. In the late stage of loading, the P-wave velocity drops significantly due to the expansion and breakthrough of induced fractures. The P-wave velocity anisotropy index ε is analyzed during the process of loading. It can be observed that the change in the degree of wave velocity anisotropy can be divided into three stages: the AB stage, the BC stage and the CD stage, with a changing trend from decline to incline. In the initial stage of loading, the preexisting fissures have a randomized distribution, and the change is large-scale and uniform. The difference in each spatial point decreases gradually, and synchronization increases gradually. Thus, the P-wave velocity anisotropy declines. As the stress increases gradually, with the expansion and breakthrough of induced fractures, the difference in each spatial point increases. Before failure of rock samples, the violent change region of the rock samples' internal structure is focused on a narrow two-dimensional zone, and the rock samples' structural change is obviously local. Therefore, the degree of velocity anisotropy rises after declining, and it also has good corresponding relation among the AE count, the location of AE events and the degree of wave velocity anisotropy. The projection plane of the main fracture plane on the axis plane is recorded as M plane. Based on the AFF equation, for the CD stage, we analyze the quantitative relationship between the velocity anisotropy index ε and angle θ, which is the difference between the angle of the M plane and the X plane and the angle of the M plane and the Y plane from the theoretical point. The results indicate that 1ε and cotθ2 have good negative linear relationship that can be expressed as cotθ2=a∗1ε+b. According to experimental data, the linear fit of 1ε and cotθ2 is found, obtaining cotθ2=−0.04721ε+0.03, with a linear fit index of 0.908. From an experimental point of view, the linear relationship between 1ε and cotθ2 is verified. Through this research, we propose a new method for quantitatively predicting the main fracture occurrence position by P-wave velocity anisotropy. This work has an important significance for understanding buckling failure of rocks.

Radial anisotropy beneath northeast T ibet, implications for lithosphere deformation at a restraining bend in the K unlun fault and its vicinity

Three-dimensional shear wave velocity and radial anisotropy models of the crust and upper mantle beneath the NE Tibetan plateau are constructed from new measurements of Love wave dispersions (20–77s) and previously obtained Rayleigh wave dispersions (20–87s) using a two-plane-wave method. The mid-lower crust is characterized with positive anisotropy (VSH > VSV) with large strength beneath the Qinling and Qilian Mountains and small values beneath the Anyemaqen Mountain. The large positive anisotropy can be explained by horizontal alignment of anisotropic minerals in the mid-lower crust due to crustal flow. The mantle lithosphere above 90 km is largely isotropic while weak positive anisotropy appears beneath 90 km, which probably marks the lithosphere-asthenosphere boundary (LAB). A low shear wave velocity anomaly and relatively negative radial anisotropy are imaged in the entire lithosphere beneath the restraining bend in the eastern Kunlun fault, consistent with a weak lithosphere experiencing vertical thickening under horizontal compression. The asthenosphere at the restraining bend is characterized by significant low velocity and positive radial anisotropy, reflecting that the asthenosphere here is probably hotter, has more melts, and deforms more easily than the surrounding region. We propose that the lithosphere at the restraining bend was vertically thickened and subsequently delaminated locally, and induced asthenosphere upwelling. This model explains the observations of velocity and anisotropy anomalies in the lithosphere and asthenosphere as well as geological observations of rapid rock uplift at the restraining bend of the Kunlun fault.

An ultrasonic through-transmission technique for monitoring the setting of injectable calcium phosphate cement

An ultrasound through-transmission method to monitor the setting process of injectable calcium phosphate bone cements in body fluids is presented. This method can be used to determine the acoustic properties of the bone cement as it sets, which are linked to its material properties and provide some information about changes occurring within the cement. The development of the methodology of ultrasonic testing and execution of velocity measurements of the longitudinal and transverse waves using the through-transmission method made it possible to determine the material constants of samples during the setting and hardening process of an injectable cement paste in physiological fluids (i.e. the Young's modulus (E), the Poisson ratio (ν) and the shear modulus (G)), and to determine the degree of anisotropy of wave velocity in the samples. A strong advantage of the proposed method is that it is non-destructive, and the same sample can be used to monitor the whole process of the cement setting. The testing was performed on premixed and injectable calcium phosphate (CPC)/chitosan blend, where glycerol was used as a liquid phase. Comparisons between ultrasonic velocity and empirical tests such as compressive strength, porosity measurement, FTIR, SEM and XRD analysis at different days of immersion in Ringer's solutions showed that the ultrasonic velocity can be very useful to provide in situ information about changes occurring within the cement.