Effective Anisotropy Parameter Research Articles

Simultaneous Bayesian inversion for effective anisotropy parameters and source locations: a physical modelling study

SUMMARY Estimating microseismic event locations is important for applications of geophysical monitoring, including hydraulic fracturing and carbon-capture and storage. Field sites for these applications are typically located in sedimentary basins that include finely stratified sediments, particularly around the target depth of the application. The fine stratification causes vertical transverse isotropy (VTI) for seismic wave propagation. In addition, such sediments often exhibit a vertically fractured rock mass that can cause horizontal transverse isotropy (HTI). Therefore, geophysical monitoring can be strongly affected by the occurrence of anisotropy caused by sets of aligned vertical fractures in finely horizontally layered media. While both HTI and VTI theories exist, a more efficient approximation to include both effects is by effective orthorhombic (ORT) models. To account for such anisotropy in microseismic monitoring, we simultaneously estimate ORT parameters, perforation shot locations, and microseismic event locations with Bayesian methods based on direct P-wave arrival times. A comparison to a HTI parametrization is carried out to examine anisotropy-model choice. The quasi-P-wave group velocities in HTI and ORT media are approximated by linearization. Anisotropy parameters are estimated with Markov chain Monte Carlo sampling that includes parallel tempering and principal-component diminishing adaptation to ensure efficient sampling of the parameter space. In contrast to deterministic inversion, our probabilistic non-linear approach includes uncertainty quantification by approximating the posterior probability density with an ensemble of model-parameter sets for effective anisotropy parameters, microseismic event locations, and horizontal locations of perforation shots. The noise standard deviation of P-arrival times is also treated as unknown. The inversion is carried out for simulated data, and for data from a physical laboratory model. In the latter case, an anisotropic layer is represented by a phenolic canvas electric material, and a star-shaped surface-receiver configuration is used to record microseismic signals. Results show that obtaining unbiased event locations requires an appropriate choice of anisotropy model and the ability to resolve anisotropy parameters. The resolution of anisotropy parameters requires significantly more data information from microseismic acquisition than required for isotropic models. Therefore, we study several acquisition scenarios for simulated and laboratory data. Assuming an HTI model in the inversion when data originate from an ORT medium causes systematic errors in event locations. However, appropriate resolution of ORT parameters requires a large acquisition aperture, an accurate perforation-shot timing, and the combination of surface acquisition with a vertical downhole array. These scenarios provide new knowledge about field requirements to produce sufficient information for the resolution of microseismic event locations in the presence of ORT effects in the data.

Subterahertz and terahertz spin and lattice dynamics of the insulating ferromagnet PbMnBO4

Orthorhombic ${\mathrm{PbMnBO}}_{4}$ is a rare example of an insulating ferromagnet in which the magnetic properties, in particular the strong magnetic anisotropy, are determined by the ${\mathrm{Mn}}^{3+}$ Jahn-Teller ion. Here, we report on the detailed investigation of magnetic excitations in the subterahertz and terahertz frequency ranges, as well as lattice excitations in the terahertz range. Using polarized azimuthally resolved Raman spectroscopy, four branches of magnetic excitations were observed and assigned to one acoustic and three optical one-magnon modes. The coupling between ferromagnetic ordering at ${T}_{C}=31\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and the Jahn-Teller distortions of $[{\mathrm{MnO}}_{6}]$ octahedra due to the spin-phonon interaction was directly observed for some specific phonon modes involved in these distortions. A spin-wave Hamiltonian was developed that allowed us to determine a unique set of exchange and effective anisotropy parameters. The intensity ratio of the anti-Stokes to Stokes acoustic magnon peaks is found to be anomalous and directly indicates the involvement of the magneto-optical parameters in the magnetic Raman scattering process.

Thickness effect on pinning properties for GdBa2Cu3O7-x films deposited with RF sputtering

We studied the relationship between JC and H, direction and crystallization orientation of GBCO films grown by RF sputtering with different thickness which is 0.3 um, 0.5um and 0.9um respectively. By de-convoluting the random pinning from the correlated pinning contributions, we find that all the three films exhibit a lower effective anisotropy parameter γ = 3 rather than γ = 5 in YBCO films. The thinnest film is the most anisotropic. The anisotropic scaling analysis reveals an enhanced random pinning for thick film the whole range of angles studied in the angle correlation Jc curve. The Jc-thickness dependence analysis indicates that there is a certain threshold field Hd and a certain thickness d for magnetic decoupling.

Long-range spin chirality dimer order in the Heisenberg chain with modulated Dzyaloshinskii-Moriya interactions

The ground state phase diagram of a spin $S=1/2$ $XXZ$ Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya (DM) interaction $ {\cal H}= \sum_n J\left[\left(S^x_n S^x_{n+1} +S^y_n S^y_{n+1}+\Delta S^z_n S^z_{n+1}\right)+(D_0+(-1)^n D_1)\left(S^x_n S^y_{n+1} -S^y_n S^{x}_{n+1} \right) \right] $ is studied using the continuum-limit bosonization approach and extensive density matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double frequency sine-Gordon model (DSG) where the frequences i.e. the scaling dimensions of the two competing cosine perturbation terms depend on the effective anisotropy parameter $\gamma^*=J\Delta /\sqrt{J^2+D_0^2+D_1^2}$. Exploring the ground state properties of the DSG model we have shown that the zero-temperature phase diagram contains the following four phases: (i) the ferromagnetic phase at $\gamma^*<-1$; (ii) the gapless Luttinger-liquid (LL) phase at $-1<\gamma^*< \gamma^*_{c1}=-1/\sqrt{2}$; (iii) the gapped composite (C1) phase characterized by coexistence of the long-range-ordered (LRO) dimerization pattern $\epsilon \sim (-1)^n (S_n S_{n+1})$ with the LRO alternating spin chirality pattern $\kappa \sim (-1)^{n}\left(S^{x}_{n}S^{y}_{n+1} -S^{y}_{n}S^{x}_{n+1} \right)$ at $\gamma^{\ast}_{c1}<\gamma^{\ast} <\gamma^{\ast}_{c2}$; and (iv) at $\gamma^{\ast} >\gamma^{\ast}_{c2}>1$ the gapped composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. The transition from the LL to the C1 phase at $\gamma^*_{c1}$ belongs to the Berezinskii-Kosterlitz-Thouless universality class, while the transition at $\gamma^*_{c2}$ from C1 to C2 phase is of the Ising type.

Velocity analysis with vertical seismic profile data using migration of surface-related multiples

We have developed an original method for migration velocity analysis for vertical seismic profile (VSP) data. The method is based on VSP imaging with the primary reflected data and surface-related multiples. Velocity updates are carried out by matching the images obtained by these two types of waves. To do it automatically, we have introduced an objective function of the crosscorrelation type and developed a gradient-based maximization algorithm. On synthetic walk-away VSP data sets, we found that maximization of the crosscorrelation of the images provided by the two different types of waves allowed the retrieval of the interval velocities below the borehole receivers — a problem that was considered to be challenging with a VSP acquisition. Also, the possibility of the lateral velocity gradient reconstruction was developed on a simple synthetic model. On the real walk-away VSP data set from the North Sea, we found that the method could also be used for estimation of effective anisotropy parameters below the borehole receivers. In all of our examples, the velocity model refinement based on the presented method led to significant improvements of the seismic images.

Temperature dependence of magnetic-field angle dependent critical current density and the flux pinning in YBa2Cu3O7 thin films

The magnetic-field angle dependence of the critical current density Jc(H, θ) was measured over a wide temperature range (20–85K) in high-Jc YBa2Cu3O7 (YBCO) and DyBa2Cu3O7 (DyBCO) epitaxial films belonging to two categories. The films in the first category were prepared by thermal co-evaporation and were characterized by a high density of nanometer-sized precipitates (mostly<7nm), which act as small random (point) pins. The films in the second category were prepared by fluorine-free metalorganic deposition (FF-MOD), whose primary pinning centers were recently revealed to be dislocations (linear pins) associated with stacking faults parallel to the ab-plane. Relatively broad Jc(θ) peaks around H//ab in the shape of a stratovolcano were observed at 77–80K in the co-evaporated YBCO and DyBCO films in the first category, and the Jc(H, θ) data were scaled to be a single curve when plotted against scaled fields using an effective anisotropy parameter. However, the Jc(θ) curves became more gradual at 60–70K and the scaling behavior was broken because the radius of nano-precipitates was not sufficiently smaller than the temperature dependent Ginzburg–Landau coherence length ξ(T) at these temperatures. In contrast, sharp Jc(θ) peaks around H//ab were observed in the FF-MOD YBCO films in the second category at all temperatures in the range 20–85K. Anisotropic scaling analysis showed that the pinning was apparently due to small random pins and pins correlated with the ab-plane, and the linear pins whose radius is sufficiently smaller than ξ(T) can cause the observed Jc(H, θ). The temperature dependence of Jc due mainly to the random pinning was approximately ∼(1−T/Tc)2(1+T/Tc)2 for the FF-MOD thin films (dislocation pins), which is consistent with a simple theoretical model based on core pinning interactions. The T dependence of Jc for the co-evaporated films (nano-precipitate pins) was ∼(1−T/Tc)m (1+T/Tc)2 (m=2.1–2.6), which deviates from m=2.5 expected from the simple theoretical model because nano-precipitates are not sufficiently smaller than ξ(T) at T⩽70K.

Correlation energy, quantum phase transition, and bias potential effects in quantum Hall bilayers at ν=1

We study the correlation energy, the effective anisotropy parameter, and quantum fluctuations of the pseudospin magnetization in bilayer quantum Hall systems at total filling factor nu=1 by means of exact diagonalizations of the Hamiltonian in the spherical geometry. We compare exact diagonalization results for the ground state energy with finite-size Hartree-Fock values. In the ordered ground state phase at small layer separations the Hartree-Fock data compare reasonably with the exact results. Above the critical layer separation, however, the Hartree-Fock findings still predict an increase in the ground state energy, while the exact ground state energy is in this regime independent of the layer separation indicating the decoupling of layers and the loss of spontaneous phase coherence between them. We also find accurate values for the pseudospin anisotropy constant whose dependence of the layer separation provides another very clear indication for the strong interlayer correlations in the ordered phase and shows an inflection point at the phase boundary. Finally we discuss the possibility of interlayer correlations in biased systems even above the phase boundary for the balanced case. Certain features of our data for the pseudospin anisotropy constant as well as for quantum fluctuations of the pseudospin magnetization are not inconsistent with the occurence of this effect. However, it appears to be rather weak at least in the limit of vanishing tunneling amplitude.

Effect of the magnetic field on the c-axis resistance peak in Bi2Sr2CaCu2O8+x epitaxial films.

The measurements of the out-of-plane component of resistivity {rho}{sub {ital c}}({ital T},{ital B}) in magnetic field in high-quality epitaxial Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{ital x}} films are presented. We found that {rho}{sub {ital c}}({ital T},{ital B}) exhibits a well-pronounced peak at the edge of the superconducting transition. Magnetic field causes both a sizeable increase of the relative magnitude of the peak and a strong shift of its position to lower temperatures. We demonstrate that zero-field data and data for weak magnetic fields {ital B}{le}1 T are well described within the fluctuation theory taking into account Gaussian approximation in fluctuation behavior. Quantitative fit of the data in the framework of this theory allowed us to extract the effective anisotropy parameter, the quasiparticle relaxation time and the phase pair-breaking relaxation time. We discuss the reasons of the discrepancy between theory and experiment for stronger magnetic fields. {copyright} {ital 1996 The American Physical Society.}

223 nm photodissociation of OCS. Two components in S(1D2) and S(3P2) channels

The speed and angular distributions of S(1D2 and 3P2) atoms produced by 223 nm photodissociation of OCS have been measured by a two-dimensional ion imaging method. The S(1D2) and S(3P2) distributions exhibited similar features; the speed distributions consist of two Gaussian components, and the effective anisotropy parameters (βeff) for the fast and slow components are about 0.1 and 1.0. The result suggests that the triplet products are produced by intersystem crossing following singlet-singlet optical transition(s).

223 nm photodissociation of OCS. Two components in S( 1D 2) and S( 3P 2) channels

The speed and angular distributions of S( 1D 2 and 3P 2) atoms produced by 223 nm photodissociation of OCS have been measured by a two-dimensional ion imaging method. The S( 1D 2) and S( 3P 2) distributions exhibited similar features; the speed distributions consist of two Gaussian components, and the effective anisotropy parameters ( β eff) for the fast and slow components are about 0.1 and 1.0. The result suggests that the triplet products are produced by intersystem crossing following singlet-singlet optical transition(s).

Photodissociation of the CHFCl2 and CHCl3 molecules and the CHCl2 radical in a beam at 193 nm

Abstract The collision-free photodissociation of CHFCl 2 and CHCl 3 at 193 nm has been studied by photofragment translational spectroscopy. In both systems the primary dissociation proceeds: exclusively via the rupture of a CCl bond. The broad and unstructured UV spectra of the parent molecules and the rather high kinetic energy release ∼45% of the available energy) in conjunction with the narrow translational energy distributions of the fragments are consistent with the CCl bond fission being a direct dissociation process. The photofragment angular distributions are characterized by anisotropy parameter β=0.5±0.1 (CHFCl 2 ) and β=0.0±0.1 (CHCl 3 ). Therefore, the photolysis of CHFCl2 involves an electronic transition polarised parallel to the line connecting the two Cl atoms. In the case of CHCl3, the nearly isotropic fragment recoil is attributed to the excitation of overlapping transitions of A 1 ←A 1 and E←A 1 type, respectively, hence leading to an effective anisotropy parameter β eff = aβ A1 + bβ E ∼0. The CHCl 2 radical produced in the primary reaction CHCl 3 + h ν→ CHCl 2 + Cl can absorb a further photon and is then selectively dissociated by molecular elimination of HCl according to CHCl 2 + h ν→CCl + HCl

Velocity relaxation of S(1D) by rare gases measured by Doppler spectroscopy

Velocity relaxation of S(1D) by He, Ar, and Xe has been monitored by measuring the Doppler profile of the S(1D) for variable collision partner pressures at a fixed time delay following creation of S(1D) by pulsed laser photolysis of OCS at 222 nm. The nascent S(1D) has a mean speed about three times that at room temperature and an effective anisotropy parameter of β=0.5. A calculation assuming elastic hard-sphere collisions is performed to model the process. The data are in qualitative agreement with the model in that the angular distribution relaxes more rapidly with collision number as the mass ratio between the collision partner and sulfur approaches infinity, whereas the speed distribution relaxes more rapidly as the mass ratio approaches one. Helium behaves as predicted by the hard-sphere model with a collision cross section of σcol=26±2 Å2. However, the cross sections for argon and xenon are found to depend on the collision energy. The dependence allows an estimation of the following Lennard-Jones parameters: for argon σ=3.6±0.5 Å and ε=2.5±0.5 kJ/mol; for xenon σ=3.9±0.5 Å and ε=3.9±0.8 kJ/mol.

Photofragmentation dynamics of H 2O 2 at 193 nm

The photofragmentation dynamics of H 2O 2 at 193 nm have been analyzed by probing the OH products by Doppler spectroscopy using laser-induced fluorescence. The excess energy ( E av = 417 kJ mol ) appears mostly as trandational motion of the fragments with f t = 0.84. No vibrational excitation was observed ( f v < 0.003). The rotational state distribution is strongly inverted, peaking for N = 12 which results f r = 0.16. Our results indicate that previously published rotational state distributions are not nascent in character, but are perturbed by rotational relaxation. Individual fragment recoil velocities obtained from Doppler lineshapes are v = 4950 m s −1 [OH( N = 4)] and v = 4550 m s −1 [OH( N = 10)]. The effective anisotropy parameter β eff is slightly negative at high N (β eff =0.35 at N = 10).

Experimental total collision cross sections in the glory region for atom-molecule systems

In a crossed supersonic beam apparatus measurements have been performed on the total cross section as a function of velocity in the thermal range for the systems O 2-Ar; O 2-Kr; N 2-Ar and NO-Ar. The anisotropy of the interaction effects the glory structure in the total cross section through a shift in the position of the glories and a quenching of the amplitudes. The analysis of the data is performed within the framework of the infinite order sudden approximation. An analytical expression for the shift function and the quenching function is derived. Assuming a P 2-type anisotropy in the potential the value of the effective anisotropy parameter is determined together with the earlier introduced quantities related to the spherical part of the potentials. The various potentials proposed in the literature for the presently investigated systems are tested accordingly.

Spin-Wave Excitations in Ho0.5Er0.5

The propagation of spin waves in the conical and spiral magnetic phases of the alloy Ho0.5Er0.5 has been studied by neutron inelastic scattering. The spin-wave energies are comparable with those observed in Ho and Er. The spin-wave dispersion curves at 4.2°K were analyzed in terms of the Fourier transformed exchange energy, J(q) - J(0), and an effective anisotropy parameter. The linewidths and energies of certain spin-wave modes were studied as a function of temperature. As the temperature was raised the spin-wave energies decreased. The linewidth of the distribution at Q = (0, 0, 2π/c) increased sharply on raising the temperature toward the cone-to-spiral transition. No broadening was observed for the mode of the same wave vector in Ho over the same temperature range.

Many-Valley Dipole Scattering of Electrons in Germanium and Silicon

The theory of dipole scattering is developed for germanium and silicon, whose conduction-band structure can be described by a simple many-valley model. A formalism is used which employs a linear approximation to the distribution function, and is due to Herring and Vogt. It is shown that, in the approximation, an alternative approach due to Samoilovich et al. gives an identical result. The relaxation-time ratio $\frac{{\ensuremath{\tau}}_{\ensuremath{\parallel}}}{{\ensuremath{\tau}}_{\ensuremath{\perp}}}$ is computed as a function of energy and it is shown analytically that, as $E\ensuremath{\rightarrow}\ensuremath{\infty}$, $\frac{{\ensuremath{\tau}}_{\ensuremath{\parallel}}}{{\ensuremath{\tau}}_{\ensuremath{\perp}}}\ensuremath{\rightarrow}3.69$. This is approximately the square root of the corresponding result for point ions. Thus the scattering due to dipoles is less sensitive to the anistropy of the energy surfaces than in the point-ion case. This can be explained by considering the form of the cross sections presented by each type of scattering center. Finally, some numerical work on the mobility and the effective anisotropy parameter is presented.

Ionized Impurity Scattering in n-Type Germanium and n-Type Silicon

The relaxation time tensor components for ionized impurity scattering in semiconductors with ellipsoidal energy surfaces are derived on the basis of the Herring-Vogt formalism. Numerical evaluation is performed for n -type germanium and n -type silicon. It is found that the anisotropy of ionized impurity scattering is dependent on energy. The mobility and the effective anisotropy parameter K =µ ⊥ /µ || for n -Ge are evaluated by using the calculated relaxation times for ionized impurity scattering and the experimentally determined lattice scattering mobility. Fair agreement between theory and experiment is obtained at liquid nitrogen temperature for carrier concentrations smaller than 10 17 /cm 3 .