S-wave Energy Research Articles

Gradient principle of horizontal stress inducing rock burst in coal mine

Based on the stress distribution characteristics of rock burst multiple sites, the criterion of horizontal stress inducing layer dislocation rock burst was established. Accordingly, the influencing factors were analyzed. The analysis results indicate that the stress condition, edge of elastic zone depth, supporting strength, and the friction angle and cohesion among coal stratum, roof and floor are sensitive factors. By introducing double-couple model, the layer dislocation rock burst was explained and the energy radiation characteristics were analyzed. The SOS micro-seismic monitoring system was applied to observe the rock burst hazards about a mining face. The results show that P- and S-wave energy radiations produced by rock burst have directional characteristics. The energy radiation characteristics of the 22 rock bursts occurring on 79Z6 long-wall face are basically the same as theoretical results, that is, the ratio of S-wave energy of sensor 4 to 6 is about 1.5 and that of P-wave is smaller than 0.5. The consistency of the monitored characteristics of the energy radiation theoretically increases with the total energy increasing.

Radiative transfer of elastic waves in two-dimensional isotropic scattering media: Semi-analytical approach for isotropic source radiation

We formulate the radiative transfer of P- and S-wave energy from an isotropically radiating source in a two-dimensional infinite isotropic scattering medium. For a stable numerical calculation of seismogram envelopes, we take a semi-analytical approach: Energy densities of P and S waves are divided into three parts of the direct-wave terms, the single-scattering terms, and the multiple-scattering terms, and the first two terms and the last term are evaluated analytically and numerically, respectively. Concerning the single-scattering terms, the P- to-S and S-to-P single conversion scattering terms are expressed analytically with a complete elliptic integral of the first kind. The multiple-scattering terms are represented by a double integral with respect to frequency and wavenumber, and can be numerically evaluated by a discrete wavenumber summation and a Fast Fourier Transform. The results based on the numerical implementation are confirmed with an independent numerical calculation using the Monte Carlo method. Our formulation is also applied to consider the equilibration between P and S waves at larger lapse times. The equilibrated S-to-P energy ratio is reproduced and the equilibration time is first derived for two-dimensional cases. Our formulation will be a reference for the understanding of more complex cases.

Scalar radius of the pion and zeros in the form factor

The quadratic pion scalar radius, 〈r2〉sπ, plays an important role for present precise determinations of ππ scattering. Recently, Ynduráin, using an Omnès representation of the null isospin (I) non-strange pion scalar form factor, obtains 〈r2〉sπ=0.75±0.07fm2. This value is larger than the one calculated by solving the corresponding Muskhelishvili–Omnès equations, 〈r2〉sπ=0.61±0.04fm2. A large discrepancy between both values, given the precision, then results. We follow Ynduráin's method and show that by requiring continuity of the resulting pion scalar form factor under tiny changes in the input ππ phase shifts, the form factor obtained has a zero for some S-wave I=0T-matrices. Once this is accounted for, the resulting value is 〈r2〉sπ=0.63±0.05fm2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0ππ phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD.

Effects of source radiation patterns on the phase S670P beneath the Tonga subduction zone

SUMMARY Observations of short-period S-P converted phases from the 670 km discontinuity (S670P) provide unique constraints on the nature of the discontinuity and the seismic structure of deep subducted slabs. Because this is a subtle phase in the P codas from deep earthquakes, great care is necessary in its identification. In past work we identified S670P phases from a large number of deep events beneath Tonga primarily by showing that the arrival times for S670P had the correct dependence upon hypocentral depth. Here we offer further confirmation of our interpretation of this S-P converted phase by showing that the occurrence of the phase is a predictable consequence of the earthquake source mechanism. We show this in two ways: (1) independently determined moment tensor solutions for the earthquakes generally predict relatively high-amplitude S-P conversions where they are observed; and (2) the observed amplitudes of S670P, ScP, PP, and P arrivals vary systematically in a way which confirms that S670P, is generated with large amplitude when the S-wave energy pattern is optimal. Comparison of ScP observations with moment tensor solutions also suggests that much of the S-wave energy results from the non-double-couple or, for CMT solutions, linear vector dipole (LVD) part of the source mechanism for the northern part of the Tonga subduction zone, where we observe the strongest S670P, phases. Because these LVD components tend to be directed along fault planes inferred from deep seismicity patterns, we suggest that they may be caused by rupture propagation directivity. We conclude that the occurrence of S670P, is primarily controlled by the source radiation pattern in a way that is consistent with our previous interpretation, thus confirming that S670P, is an S-P conversion from an almost undeformed phase change boundary at about 670 km depth.

Evaporative cooling of unitary Fermi gas mixtures in optical traps

We measure the scaling laws for the number of atoms and the cloud size as a function of trap depth for evaporative cooling of a unitary Fermi gas in an optical trap. A unitary Fermi gas comprises a trapped mixture of atoms in two hyperfine states which is tuned to a collisional (Feshbach) resonance using a bias magnetic field. Near resonance, the zero energy s-wave scattering length diverges, and the s-wave scattering cross-section is limited by unitarity to be 4π/k2, where k is the relative wavevector of the colliding particles. In this case, the collision cross-section for evaporation scales inversely with the trap depth, enabling runaway evaporation under certain conditions. We demonstrate high evaporation efficiency, which is achieved by maintaining a high ratio η of trap depth to thermal energy as the trap depth is lowered. We derive and demonstrate a trap lowering curve which maintains η constant for a unitary gas. This evaporation curve yields a quantum degenerate sample from a classical gas in a fraction of a second, with only a factor of three loss in atom number.

Final state interactions in hadronicDdecays

We show that the large corrections due to final state interactions (FSI) in the D^+\to \pi^-\pi^+\pi^+, D^+_s\to \pi^-\pi^+\pi^+, and D^+\to K^-\pi^+\pi^+ decays can be accounted for by invoking scattering amplitudes in agreement with those derived from phase shifts studies. In this way, broad/overlapping resonances in S-waves are properly treated and the phase motions of the transition amplitudes are driven by the corresponding scattering matrix elements determined in many other experiments. This is an important step forward in resolving the puzzle of the FSI in these decays. We also discuss why the \sigma and \kappa resonances, hardly visible in scattering experiments, are much more prominent and clearly visible in these decays without destroying the agreement with the experimental \pi\pi and K\pi low energy S-wave phase shifts.

Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin

We obtain analytic expressions for the third-order corrections due to the strong interaction Coulomb potential to the S-wave Green function, energy levels and wave functions at the origin for arbitrary principal quantum number n. Together with the known non-Coulomb correction this results in the complete spectrum of S-states up to order α s 5 . The numerical impact of these corrections on the upsilon spectrum and the top quark pair production cross section near threshold is estimated.

Wave-energy patterns in carotid, brachial, and radial arteries: a noninvasive approach using wave-intensity analysis

The study of wave propagation at different points in the arterial circulation may provide useful information regarding ventriculoarterial interactions. We describe a number of hemodynamic parameters in the carotid, brachial, and radial arteries of normal subjects by using noninvasive techniques and wave-intensity analysis (WIA). Twenty-one normal adult subjects (14 men and 7 women, mean age 44 +/- 6 yr) underwent applanation tonometry and pulsed-wave Doppler studies of the right common carotid, brachial, and radial arteries. After ensemble averaging of the pressure and flow-velocity data, local hydraulic work was determined and a pressure-flow velocity loop was used to determine local wave speed. WIA was then applied to determine the magnitude, timings, and energies of individual waves. At all sites, forward-traveling (S) and backward-traveling (R) compression waves were observed in early systole. In mid- and late systole, forward-traveling expansion waves (X and D) were also seen. Wave speed was significantly higher in the brachial (6.97 +/- 0.58 m/s) and radial (6.78 +/- 0.62 m/s) arteries compared with the carotid artery (5.40 +/- 0.34 m/s; P < 0.05). S-wave energy was greatest in the brachial artery (993.5 +/- 87.8 mJ/m2), but R-wave energy was greatest in the radial artery (176.9 +/- 19.9 mJ/m2). X-wave energy was significantly higher in the brachial and radial arteries (176.4 +/- 32.7 and 163.2 +/- 30.5 mJ/m2, respectively) compared with the carotid artery (41.0 +/- 9.4 mJ/m2; P < 0.001). WIA illustrates important differences in wave patterns between peripheral arteries and may provide a method for understanding ventriculo-arterial interactions in the time domain.

Inversion of the high-frequency source radiation of M6.8 Avachinsky Gulf, Kamchatka, earthquake using empirical and theoretical envelope Green functions

We study the generation of high-frequency S-wave energy from its source of the 1992 Avachinsky Gulf, Kamchatka, earthquake (M W = 6.8) by means of the envelope inversion method of Nakahara et al. (1998). Two versions of this technique were employed, the original version and the modified version. In the modified version, to construct the “envelope Green function” we use empirical envelope shapes, constructed by averaging data of small earthquakes from the same area, calibrated to the total energy of the theoretical envelopes. The envelope inversion procedure was applied to six mainshock records, producing estimates of spatial distribution of energy radiation in frequency bands: 1–2, 2–4, 4–8 and 8–16 Hz. In both inversions, the distribution of energy radiation shows a similar pattern: 75–90 percent of the energy was radiated soon after nucleation. Afterwards, the rupture propagated mostly in a westward direction. Similarity of both results demonstrates the robustness of the envelope inversion method. However the version of the inversion procedure that uses empirical envelopes yields more plausible characteristics of the rupture process.

Decay widths and energy shifts of ππ and πK atoms

We calculate the S-wave decay widths and energy shifts for π+π− and π±K∓ atoms in the framework of QCD + QED. The evaluation—valid at next-to-leading order in isospin symmetry breaking—is performed within a non-relativistic effective field theory. The results are of interest for future hadronic atom experiments.

Introduction to vector-processing techniques for multi-component seismic exploration

Conventional multi-component seismic analysis simply relies on appropriate component selection to provide P- and S-wave images. However, this ignores the potential cross-contamination of P-wave energy on the horizontal components, and S-wave energy on the vertical component that may occur in certain geological situations. Where wavefield cross-contamination occurs, there is potential to achieve cleaner P- and S-wave images by more fully exploiting the true vector nature of multi-component seismic data. Vector processing for exploration-scale data typically combines frequency and slowness information, together with particle motion, to distinguish different wave types. Three such multi-trace, multi-component wavefield separation schemes, termed MUSIC, IWSA and PIM, are considered here. These vector techniques all utilise a parametric approach whereby wavefield slowness and polarisation are modelled simultaneously in the frequency domain. The PIM algorithm is considered to be the most generally useful of the three algorithms. Synthetic and ocean-bottom data examples are used to demonstrate practical issues relating to the use of these vector separation schemes. In cases where there is significant cross-contamination, vector wavefield separation produces P- and S-wave records that differ significantly from the vertical and horizontal components, respectively. Where cross-contamination is less problematic, production vector processing is not warranted. In these cases, however, vector processing still provides valuable quantitative validation of the natural-separation assumption.

Crosshole seismic tomography and borehole logging for engineering site characterization in Sikeston, MO, USA

This paper presents a geophysical investigation performed in the median separating the east and west bound lanes of U.S. Highway 60, approximately 15 km west from the town of Sikeston, MO, USA. Two boreholes, drilled at depth of 45 m, approximately located 6 m from the Wahite Ditch Bridge in U.S. Highway 60, were used to carry out the geophysical tests. The objective of the survey was to obtain the density distribution of soil materials and high-resolution compressional and shear wave velocities of the shallow subsurface for computation of elastic engineering properties of the unconsolidated material interposed between the two investigated boreholes. The studied site is located in the New Madrid Seismic Zone (NMSZ), one of the major seismic source zones in the eastern United States. Although no major seismic events have occurred in the New Madrid area since the catastrophic earthquakes of 1811–1812, more intensive studies in this area are required to better understand the local soil effects and the liquefaction potential of unconsolidated earth materials on strong ground motion. Joint interpretation of borehole logs and velocity images obtained by P- and S-wave traveltime inversions outlined shallow anomalies, which were interpreted as caused by variation in relative porosity and compactness of saturated unconsolidated soil materials. In the interval between 17 and 19 m of depth, a velocity anomaly with distinct characteristics is recognized. Analysis of traveltimes of P-wave energy propagated from common source-receiver depth positions at that depth interval delineated a low velocity zone (lower than estimated P-wave velocity in water) in which propagated S-wave energy was negligible. Analysis of porosity logs did not outline any porosity anomaly for that region. The anomaly is interpreted as caused by the presence of a gas-bearing zone extending for 1.5 m (+0.76 m from the top and the bottom of the depth interval), through which propagation of shear energy was almost prevented and compressional energy traveled a very low speed. Relative lower values of shear modulus were computed for the gas-bearing zone; the same depth interval also exhibited relative lower values of bulk modulus, relative higher values of compressibility and relative high porosity. However, the low velocity anomaly is not caused by relative increased porosity but rather to replacement of water by gas in the pore volumes of this zone. The presence of a shallow thin gas-bearing zone is interpreted as hazardous in the occurrence of strong motion in the New Madrid Seismic Zone. Shallow water table, as detected by seismic and log measurements in the area, increases the risk of liquefaction of the sampled soil under strong ground motions.

The role of Biot slow waves in electroseismic wave phenomena.

The electromagnetic fields that are generated as a spherical seismic wave (either P or S) traverses an interface separating two porous materials are numerically modeled both with and without the generation of Biot slow waves at the interface. In the case of an incident fast-P wave, the predicted electric-field amplitudes when slow waves are neglected can easily be off by as much as an order of magnitude. In the case of an incident S wave, the error is much smaller (typically on the order of 10% or less) because not much S-wave energy gets converted into slow waves. In neglecting the slow waves, only six plane waves (reflected and transmitted fast-P, S, and EM waves) are available with which to match the eight continuity conditions that hold at each interface. This overdetermined problem is solved by placing weights on the eight continuity conditions so that those conditions that are most important for obtaining the proper response are emphasized. It is demonstrated that when slow waves are neglected, it is best to also neglect the continuity of the Darcy flow and fluid pressure across an interface. The principal conclusion of this work is that to properly model the electromagnetic (EM) fields generated at an interface by an incident seismic wave, the full Biot theory that allows for generation of slow waves must be employed.

Regional phases in continental and oceanic environments

SUMMARY The very different crustal thicknesses between continental and oceanic crust lead to the establishment of distinct styles of regional seismic wavefield. Observations and numerical simulations of events near subduction zones in Japan allow a direct comparison of seismic wave propagation in oceanic and continental structures. The thick zone of lower seismic velocities in the continental crust acts to trap S-wave energy in particular and generates crustally guided phases such as Pg, Lg. In the oceanic environment there is no efficient S-wave trapping and crustal energy progressively leaks into the mantle. Reverberations in the crust and the water above help to sustain the amplitude of the mantle arrivals Pn, Sn to large distances.

Logarithmic corrections in m 1/m 2 to the fine shift of the S-wave energy levels in the muonium atom

A α 5 μ 3 (m 1 m 2)−1 (m 1/m 2)ln(m 1/m 2) correction stemming from a consecutive exchange of a Coulomb and a transverse photon between the muon and the electron of the muonium atom is revealed and calculated (μ is the reduced mass of the system). Additional contributions of order α 6 μ 3 (m 1 m 2)−1ln(m 1/m 2) due to one-photon exchange in the muonium atom are taken into account.

Critical fields and specific heat ofLuNi2B2C

We have measured the upper critical magnetic field, lower critical magnetic field, and low-temperature specific heat of ${\mathrm{LuNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}.$ Our upper critical-field measurements above $\ensuremath{\sim}2\mathrm{K}$ are consistent with earlier measurements by other groups. The upper critical field exhibits a finite slope as $\stackrel{\ensuremath{\rightarrow}}{T}0,$ and we discuss possible origins of this very unusual behavior. We observe a linear temperature dependence for the lower critical field of our single-crystal sample, a temperature dependence that disagrees with earlier measurements on polycrystals and suggests that the lower critical field may be anisotropic. The Sommerfeld coefficient increases with magnetic field as ${H}^{\ensuremath{\epsilon}}$ with $\ensuremath{\epsilon}=0.63\ifmmode\pm\else\textpm\fi{}0.12$ in qualitative agreement with earlier work. The temperature dependence of the zero-field electronic specific heat is exponential well below ${T}_{c}.$ We discuss our results in light of recent proposals of both anisotropic s-wave and d-wave superconductivity for ${\mathrm{LuNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}.$ Our data seem most consistent with strong-coupling superconductivity and a weakly anisotropic s-wave energy gap.

P- and S-wave characterization of near‐surface reflectivity from glacial tills using vertical seismic profiles

Fundamental reflectivity properties are established within the glacial deposits of central Saskatchewan, Canada. Multicomponent vertical seismic profile (VSP) data collected in three shallow boreholes are used to obtain detailed acoustic property information within the first 80 m of the near‐surface strata. The integration of both P- and S-wave VSP data, in conjunction with other borehole geophysics, provided a unique opportunity to obtain in‐situ seismic reflection response properties in layered clay and sand tills. P- and S-wave interval velocity profiles, in conjunction with P- and S-wave VSP reflectivities are analyzed to provide insight into seismic wavefield behavior within ∼80 m of the surface. In general, shear wave energy identifies more reflective intervals than the P-wave energy because of better vertical resolution for S-wave energy (0.75 m) compared to P-wave energy (2.3 m) based on quarter wavelength criterion. For these saturated, unconsolidated glacial deposits, more details about the lithologic constituents and in‐situ porosity are detectable from the S-wave reflectivity, but P-wave reflections provide a good technique for mapping the bulk changes. The principal cause of seismic reflectivity is the presence and/or amount of sand, and the degree of fluid‐filled porosity within the investigated formations.

Threshold resonances in a double well system

It is shown that the resonance reported by Szmytkowski and Szmytkowski [Phys. Lett. A 235 (1997) 217] is not a proximity resonance as defined by Heller [Phys. Rev. Lett. 77 (1996) 4122]. Rather, it can be related to a threshold resonance connected to the antisymmetric bound state of the two wells, which enters the continuum when the wells are one scattering length apart. In addition, a surprising disappearance of the low energy s-wave cross section of two nearby wells is discussed.

Positronium–hydrogen-atom scattering in a five-state model

The scattering of orthopositronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for $\mathrm{Ps}(1s)\mathrm{H}(2s,2p)$ and $\mathrm{Ps}(2s,2p)\mathrm{H}(1s)$ excitations using a recently proposed electron-exchange model potential. The higher $(ng~3)$ excitations and ionization of the Ps atom are calculated using the first Born approximation. Calculations are reported of scattering lengths, phase shifts, elastic, Ps and H excitation, and total cross sections. Remarkable correlations are observed between the S-wave Ps-H binding energy and the singlet scattering length, effective range, and resonance energy obtained in various model calculations. These correlations suggest that if a Ps-H dynamical model yields the correct result for one of these four observables, it is expected to lead to the correct result for the other three. The present model, which is constructed so as to reproduce the Ps-H resonance at 4.01 eV, automatically yields a Ps-H bound state at $\ensuremath{-}1.05$ eV that compares well with the accurate value of $\ensuremath{-}1.067$ eV. The model leads to a singlet scattering length of ${3.72a}_{0}$ and effective range of ${1.67a}_{0},$ whereas the correlations suggest the precise values of ${3.50a}_{0}$ and ${1.65a}_{0}$ for these observables, respectively.

Spatial distribution of high-frequency energy radiation on the fault of the 1995 Hyogo-Ken Nanbu, Japan, earthquake (MW6.9) on the basis of the seismogram envelope inversion

AbstractWe studied the generation and propagation of high-frequency (above 1 Hz) S-wave energy from the 1995 Hyogo-Ken Nanbu (Kobe), Japan, earthquake (MW 6.9) by analyzing seismogram envelopes of the mainshock and aftershocks. We first investigated the propagation characteristics of high-frequency S-wave energy in the heterogeneous lithosphere around the source region. By applying the multiple lapse time window analysis method to aftershock records, we estimated two parameters that quantitatively characterize the heterogeneity of the medium: the total scattering coefficient and the intrinsic absorption of the medium for S waves. Observed envelopes of aftershocks were well reproduced by the envelope Green functions synthesized based on the radiative transfer theory with the obtained parameters. Next, we applied the envelope inversion method to 13 strong-motion records of the mainshock. We divided the mainshock fault plane of 49 × 21 km into 21 subfaults of 7 × 7 km square and estimated the spatial distribution of the high-frequency energy radiation on that plane. The average constant rupture velocity and the duration of energy radiation for each subfault were determined by grid searching to be 3.0 km/sec and 5.0 sec, respectively. Energy radiated from the whole fault plane was estimated as 4.9 × 1014 J for 1 to 2 Hz, 3.3 × 1014 J for 2 to 4 Hz, 1.5 × 1014 J for 4 to 8 Hz, 8.9 × 1012 J for 8 to 16 Hz, and 9.8 × 1014 J in all four frequency bands. We found that strong energy was mainly radiated from three regions on the mainshock fault plane: around the initial rupture point, near the surface at Awaji Island, and a shallow portion beneath Kobe. We interpret that energetic portions were associated with rupture acceleration, a fault surface break, and rupture termination, respectively.