地震激发地球自由振荡过程的数值模拟初步探索

地球自由振荡的固有频率与地球内部结构密切相关,研究地球自由振荡可以深入研究地球内部结构。传统的解析方法侧重于本征频率的确定,但对从地震发生到地球自由振荡被激发的全过程难以研究。从弹性波动理论基础出发,试采用谱元法结合高性能并行计算数值模拟特大地震激发的弹性波在地球内部传播过程。在不考虑地球重力情况下,对数值模拟激发地球自由振荡的结果进行功率谱密度分析,通过对谱结果的观察并与理论值进行对比分析,认识到环型振型数值模拟结果可以准确重现其长周期理论频率值,地球重力对球型振型有重要影响。探讨了是否可以通过这种方法真实重现地球自由振荡激发的过程。以期利用此方法深入探讨地球横向不均匀性对地球自由振荡的影响。     

Temperature variation of elastic constants of quartz across the α - β transition

The α − β transition of quartz was successfully observed with using a single sample by means of the rectangular parallelepiped resonance (RPR) method. An oriented rectangular parallelepiped of α-quartz single crystal was prepared and the resonant frequencies of 30–11 vibrational modes were measured from room temperature to 700°C. The softening of quartz crystal was observed as the significant reduction of resonant frequencies near the α–β transition. The present study is the first application of the RPR method to the study of phase transition. The complete set of elastic constants of α- and β-quartz were determined as a function of temperature by the least-squares inversion of the measured frequency data obtained by a single run. This is a merit yielded by the RPR method. It is shown near the α − β transition in both α- and β-quartz that the elastic parameters decrease proportionally to |T−T ₀|⁻ⁿ , where T is temperature and T ₀ is the transition temperature, 573.0°C for α-quartz and 574.3°C for β-quartz. It was also seen that linear incompressibilities K ₁ = (C ₁₁ +C ₁₂ +C ₁₃)/3 and K ₃ = (C ₃₃ +2C ₁₃)/3 decrease rapidly toward the transition, whereas, shear moduli C ₄₄, C _S1 = (C ₁₁ +C ₃₃ -2C ₁₃)/4 and C _S3 = (C ₁₁ -C ₁₂)/2 = C ₆₆ decrease only slightly. The shear modulus C _S3 = C ₆₆ increased slightly in α-quartz. The elastic properties of isotropic aggregate of quartz were calculated, and it is shown that the longitudinal wave velocity significantly decreases at the α − β transition, whereas, the shear wave velocity decreases only slightly.     

Shear wave splitting observations from the Indian shield

Measurements of shear wave splitting of the waveforms of SKS, SKKS phases recorded at all WWSSN stations (1977–1988) in the Indian shield located on diverse geotectonic units are used to retrieve the anisotropic properties of the sub-Continental lithosphere beneath these regions. The azimuth of fast polarization direction (FPD) ‘α’ and delay time ‘δt’ of the split shear waves with their uncertainties are estimated. Events well distributed in azimuth yield tightly constrained average splitting parameters of α, δt that are roughly:KOD (ENE. 0.50s); HYB (NNE, 145s); POO (N-S, 0.9s); NDI (NE, 0.95s). No consistent anisotropic direction was found at SHL, though the phenomenon of shear wave splitting was clearly observed. In order to test the utility of analog data to document such secondary effects and to authenticate our digitizing procedures, results from GEOSCOPE digital data at HYB were compared with analog data results from the same location. Presence of detectable anisotropy at all the stations is explained either in terms of past and present deformations by tectonic episodes or by plate motion related strain which forms the two end member models in interpreting the observed azimuthal anisotropy. Knowledge of surface geology and maximum horizontal compressive stress (MHS) orientations are invoked to constrain the most plausible hypothesis that explains the observed anisotropic signatures at each of these locations.     

Elastic solutions for a transversely isotropic half-space subjected to a point load

We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd.     

The role of faculae in wave-energy transfer to upper layers of the solar atmosphere: Observations

The properties of Doppler-velocity oscillations in solar faculae are analyzed at the photospheric level (based on Fe I 6569 ? and Fe I 8536 ? lines) and chromospheric level (based on Hα and Ca II 8542 ? lines) to search for upward propagating waves. The similarity of the averaged power spectra at 2.5–4 mHz is not found to be convincing proof of the presence of unidirectional wave-energy transfer from the photosphere to the chromosphere. Phase relations between the photospheric and chromospheric oscillations that are indicative of either upward or downward propagating waves are obtained for various areas in many faculae. This suggests that the wave energy of the five-minute oscillations returns to the photosphere, at least partially. The derived properties suggest that the role of faculae in the transfer of the five-minute oscillations to the chromosphere and overlying layers is not as obvious as could be expected. The relatively typical presence of low-frequency (0.5–2 mHz) oscillations in faculae and their possible important role in this energy transfer are noted.     

Can unbiased source be retrieved from anisotropic waveforms by using an isotropic model of the medium?

Anisotropy is frequently present in geological structures, but usually neglected when source parameters are determined through waveform inversion. Due to the coupling of propagation and source effects in the seismic waveforms, such neglect of anisotropy will lead to an error in the retrieved source. The distortion of the mechanism of a double-couple point source located in an anisotropic medium is investigated when inverting waveforms using isotropic Green's functions. The anisotropic medium is considered to be transversely isotropic with six levels of anisotropy ranging from a fairly weak to rather strong anisotropy, up to about 24% in P waves and 11% in S waves. Inversions are based on either only direct P waves or both direct P and S waves. Two different algorithms are employed: the direct parametrization (DIRPAR, a nonlinear algorithm) and the indirect parametrization (INPAR, a hybrid scheme including linear and nonlinear steps) of the source. The orientation of the double-couple mechanism appears to be robustly retrieved. The inclination of the resulting nodal planes is very small, within 10° and 20° from the original solution, even for the highest degree of anisotropy. However, the neglect of anisotropy results in the presence of spurious isotropic and compensated linear-vector dipole (CLVD) components in the moment tensor (MT). This questions the reliability of non-double-couple components reported for numerous earthquakes.     

Ambient noise tomography with a large seismic array

The emergence of large-scale arrays of seismometers across several continents presents the opportunity to image the Earth's structure at unprecedented resolution, but methods must be developed to exploit the capabilities of these deployments. The capabilities and limitations of a method called “eikonal tomography” applied to ambient noise data are discussed here. In this method, surface wave wavefronts are tracked across an array and the gradient of the travel time field produces estimates of phase slowness and propagation direction. Application data from more than 1000 stations from EarthScope USArray in the central and western US and new Rayleigh wave isotropic and anisotropic phase velocity maps are presented together with an isotropic and azimuthally anisotropic 3D Vs model of the crust and uppermost mantle. As a ray theoretic method, eikonal tomography models bent rays but not other wavefield complexities. We present evidence, based on the systematics of an observed 1ψ component of anisotropy that we interpret as anisotropic bias caused by backscattering near an observing station, that finite frequency phenomena can be ignored in ambient noise tomography at periods shorter than ～ 40 to 50 s. At longer periods a higher order term based on wavefront amplitudes or finite frequency sensitivity kernels must be introduced if the amplitude of isotropic anomalies and the amplitude and fast-axis direction of azimuthal anisotropy are to be determined accurately.     

Molecular dynamics study of structural changes in berlinite

Fractional coordinates and anisotropic temperature factors of atoms in berlinite, AlPO₄ with the quartz topology, were successfully simulated in a molecular dynamics simulation (MDS) at high temperatures. Time-dependent and time-averaged atomic order parameters were analyzed in detail with the aid of spectral densities calculated from trajectory data. These parameters show characteristic behavior of the order-disorder regime for a structure change, where atoms spend most of the time oscillating around the ₁-sites (or ₂-sites) in the low temperature α-phase, but oscillate over both sites in the higher temperature α-phase and the β-phase. In the spectral density functions calculated for atom order parameters, a nearly zero-frequency excitation, which is accompanied by the emergence of large-scale ₁ and ₂ clusters, appears at the Γ point of the Brillouin zone below the transition point T _o, and increases in intensity up to T _o. A low-lying optic branch along Γ-M, which is strongly temperature dependent in the small q-region, is another characteristic of the spectral density functions for the β phase. The spectrum at Γ continuously reduces its frequency from 0.6 THz at temperatures far above T _o to nearly 0 THz at temperatures approaching T _o from above. The dynamical behavior in β berlinite rapidly but continuously changes from that in less oscillatory clusters in the vicinity of T _o to that in the typical β phase at temperatures departing from T _o. Received: 10 August 1998 / Revised, accepted: 18 February 1999     

Mapping Curvilinear Structures with Local Anisotropy Kriging

Interpolating geo-data with curvilinear structures using geostatistics is often disappointing. Channels, for example, become disconnected sets of lakes when interpolated from point data. In order to improve the interpolation of geological structures (e.g., curvilinear structures), we present a new form of kriging, local anisotropy kriging (LAK). Local anisotropy kriging combines a gradient algorithm from image analysis with kriging in an iterative way. After an initial standard kriging interpolation, the gradient algorithm determines the local anisotropy for each cell in the grid using a search area around the cell. Subsequently, kriging is carried out with the spatially varying anisotropy. The anisotropy calculation and subsequent kriging steps will then succeed until the result is satisfactory in the way of reproducing the curvilinear structures. Depending on the size of the search area more or less detail in the geological structures can be reproduced with LAK. Using test examples we show that LAK interpolates data with curvilinear structures more realistically than standard kriging. In a real world case, using bathymetric data of the Oosterschelde estuary, LAK also proves to be quantitatively superior to standard kriging. Absolute interpolation errors are decreased by 23%. Local anisotropy kriging only uses information from point data, which makes the method very objective, it only presents “what the data can tell.”     

Intraseasonal oscillations and interannual variability of surface winds over the Indian monsoon region

The role of intraseasonal oscillations (ISOs) in modulating synoptic and interannual variations of surface winds over the Indian monsoon region is studied using daily averaged National Centers for Environmental Prediction/National Centre for Atmospheric Research (NCEP/NCAR) reanalyses for the period 1987–1996. Two dominant ISOs are found in all years, with a period between 30–60 days and 10–20 days respectively. Although the ISOs themselves explain only about 10–25% of the daily variance, the spatial structure of variance of the ISOs is found to be nearly identical to that of high frequency activity (synoptic disturbances), indicating a significant control by the ISOs in determining the synoptic variations. Zonal and meridional propagation characteristics of the two modes and their interannual variability are studied in detail. The synoptic structure of the 30–60 day mode is similar in all years and is shown to be intimately related to the strong (‘active’) or weak (‘break’) phases of the Indian summer monsoon circulation. The peak (trough) phase of the mode in the north Bay of Bengal corresponds to the ‘active’ (‘break’) phase of monsoon strengthening (weakening) the entire large scale monsoon circulation. The ISOs modulate synoptic activity through the intensification or weakening of the large scale monsoon flow (monsoon trough). The peak wind anomalies associated with these ISOs could be as large as 30% of the seasonal mean winds in many regions. The vorticity pattern associated with the 30–60 day mode has a bi-modal meridional structure similar to the one associated with the seasonal mean winds but with a smaller meridional scale. The spatial structure of the 30–60 day mode is consistent with fluctuations of the tropical convergence zone (TCZ) between one continental and an equatorial Indian Ocean position. The 10–20 day mode has maximum amplitude in the north Bay of Bengal, where it is comparable to that of the 30–60 day mode. Elsewhere in the Indian Ocean, this mode is almost always weaker than the 30–60 day mode. In the Bay of Bengal region, the wind curl anomalies associated with the peak phases of the ISOs could be as large as 50% of the seasonal mean wind curl. Hence, ISOs in this region could drive significant ISOs in the ocean and might influence the seasonal mean currents in the Bay. On the interannual time scale, the NCEP/NCAR reanalysed wind stress is compared with the Florida State University monthly mean stress. The seasonal mean stress as well as interannual standard deviation of monthly stress from the two analyses agree well, indicating absence of any serious systematic bias in the NCEP/NCAR reanalysed winds. It is also found that the composite structure of the 30–60 day mode is strikingly similar to the dominant mode of interannual variability of the seasonal mean winds indicating a strong link between the ISOs and the seasonal mean. The ISO influences the seasonal mean and its interannual variability either through increased/decreased residence time of the TCZ in the continental position or through occurrence of stronger/weaker active/break spells. Thus, the ISOs seem to modulate all variability in this region from synoptic to interannual scales.     

Lithospheric structure beneath the East China Sea revealed by Rayleigh-wave phase velocities

We explore the variations of Rayleigh-wave phase-velocity beneath the East China Sea in a broad period range (5–200 s). Rayleigh-wave dispersion curves are measured by the two-station technique for a total of 373 interstation paths using vertical-component broad-band waveforms at 32 seismic stations around the East China Sea from 6891 global earthquakes.The resulting maps of Rayleigh-wave phase velocity and azimuthal anisotropy provide a high resolution model of the lithospheric mantle beneath the East China Sea. The model exhibits four regions with different isotropic and anisotropic patterns: the Bohai Sea, belonging to the North China Craton, displays a continental signature with fast velocities at short periods; the Yellow Sea, very stable unit associated with low deformation, exhibits fast velocities and limited anisotropy; the southern part of the East China Sea, with high deformation and many fractures and faults, is related to slow velocities and high anisotropic signature; and the Ryukyu Trench shows high-velocity perturbations and slab parallel anisotropy.     

Thermal expansion of new arsenate minerals,bradaczekite, NaCu<Subscript>4</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>, and urusovite,Cu(AsAlO<Subscript>5</Subscript>)

Thermal behavior of two new exhalation copper-bearing minerals, bradaczekite and urusovite, from the Great Tolbachik Fissure Eruption (1975–1976, Kamchatka Peninsula, Russia) has been studied by X-ray thermal analysis within the range 20–700°C in air. The following major values of the thermal expansion tensor have been calculated for urusovite: α₁₁ = 10, α₂₂ = α_b = 7, α₃₃ = 4, α_V = 21 × 10⁻⁶°C⁻¹, μ = c∧α₃₃ = 49° and bradaczekite: α_11aver = 23, α₂₂ = 8, α_33aver = 6 × 10⁻⁶°C⁻¹, μ(c∧α₃₃) = 73°. The sharp anisotropy of thermal deformations of these minerals, absences of phase transitions, and stability of the minerals in the selected temperature range corresponding to conditions of their formation and alteration during the posteruption period of the volcanic activity are established.     

Thermal instability of the fluid column in a borehole: application to the Yaxcopoil hole (Mexico)

Observational evidence proved that even when a borehole is in “fully” stabilized conditions, temperature data may exhibit certain unrest resembling irregular oscillations in the order of hundredths or (in the extreme case) even tenths of degree. Temperature was monitored in complicated hydrogeological conditions in the Yaxcopoil-1 hole (Chicxulub impact structure, Mexico). Two experiments are reported: (a) 20-day monitoring when a logger was located in the center of the high temperature gradient anomaly produced by the cold wave slowly propagating downwards and (b) simultaneous three-loggers 18-day monitoring with loggers located above, in and below the anomaly. All observed temperature–time series displayed intermittent oscillations of temperature with sharp gradients and large fluctuations over all observed time scales. While the “upper” and “lower” records revealed quasi-periodic temperature variations, the “central” record shows fast temperature oscillations with strong up-and-down reversals, all with amplitudes up to a few tenths of degree. The observed temperature–time series were processed by recurrence and recurrence interval quantification as well as by spectral analyses. It is shown that fluid in a borehole, subject to thermal gradient, is stable, as far as the gradient remains below a certain critical value. At higher Rayleigh numbers, the periodic character of oscillations typical for “quiescent” regime is superseded by stochastic features. This “oscillatory” convection occurs due to instability of the horizontal boundary layers. In the specific case of the Yaxcopoil hole, the time series above and below the cold wave (characterized by relatively lower temperature gradients between 20 and 50 mK/m) contain a clear low frequency component produced by tidal forcing. This component dominates over the high frequency domain (periods from 10–15 to 1 min), which exhibit a scaling behavior. This pattern conspicuously changes in the center part of the cold wave, where the local temperature gradient exceeds 200 mK/m and where tidal forcing composes only ~3% of the signal.     

New thermoelastic parameters of natural <Emphasis Type="Italic">C</Emphasis>2/<Emphasis Type="Italic">c</Emphasis> omphacite

The compressibility at room temperature and the thermal expansion at room pressure of two disordered crystals (space group C2/c) obtained by annealing a natural omphacite sample (space group P2/n) of composition close to Jd₅₆Di₄₄ and Jd₅₅Di₄₅, respectively, have been studied by single-crystal X-ray diffraction. Using a Birch–Murnaghan equation of state truncated at the third order [BM3-EoS], we have obtained the following coefficients: V ₀ = 421.04(7) Å³, K _T0 = 119(2) GPa, K′ = 5.7(6). A parameterized form of the BM3 EoS was used to determine the axial moduli of a, b and c. The anisotropy scheme is β _c  ≤ β _a  ≤ β _b , with an anisotropy ratio 1.05:1.00:1.07. A fitting of the lattice variation as a function of temperature, allowing for linear dependency of the thermal expansion coefficient on the temperature, yielded α_V(1bar,303K) = 2.64(2) × 10⁻⁵ K⁻¹ and an axial thermal expansion anisotropy of α _b  ≫ α _a  > α _c . Comparison of our results with available data on compressibility and thermal expansion shows that while a reasonable ideal behaviour can be proposed for the compressibility of clinopyroxenes in the jadeite–diopside binary join [K _T0 as a function of Jd molar %: K _T0 = 106(1) GPa + 0.28(2) × Jd_(mol%)], the available data have not sufficient quality to extract the behaviour of thermal expansion for the same binary join in terms of composition.     

Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

Elastic solutions for a transversely isotropic half-space subjected to buried asymmetric-loads

Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

Long-period oscillations of the solar microwave emission

Modulations of the microwave emission of the Sun at 11.7 GHz have been studied using more than 40 events observed in 2001 at the Mets?hovi Radio Observatory. In nearly all the observed events, low-frequency modulations with periods of 3–90 min were detected. As a rule, simultaneous modulation of the emission at several frequencies was observed. One possible origin of such modulations with periods 5–10 min is parametric resonance arising in coronal magnetic loops as a result of interactions with the 5-min photospheric oscillations, while the long-period modulations could be a manifestation of sunspot oscillations. Torsional (ϑ-mode) and radial (r-mode) oscillations have such periods. The frequency of occurrence of oscillations with the determined periods is considered, and a lower limit for the brightness temperature of the oscillations is estimated.     

Strength Anisotropy of Compacted Decomposed Granite Soils

In order to investigate the strength and deformation anisotropy of compacted decomposed granite soils, a series of drained triaxial compression tests was performed on unsaturated and saturated decomposed granite soils. The specimens were subjected to compression tests such that the angle δ of the direction of the major principal stress, σ ₁, during triaxial compression relative to the compaction plane (bedding plane) varies, with δ = 0°, 45° and 90°. Test results indicated that the compressive strain of the specimens subjected to isotropic consolidation was influenced strongly by the angle δ. In addition, the effect of the angle δ on the triaxial compressive strength and deformation was more evident in unsaturated specimens than in saturated specimens. Based on the test results, a procedure which can be used to estimate the shear strength of unsaturated soils taking into account various angles δ was proposed.     

Thermal expansion and decomposition of jarosite: a high-temperature neutron diffraction study

The structure of deuterated jarosite, KFe₃(SO₄)₂(OD)₆, was investigated using time-of-flight neutron diffraction up to its dehydroxylation temperature. Rietveld analysis reveals that with increasing temperature, its c dimension expands at a rate ~10 times greater than that for a. This anisotropy of thermal expansion is due to rapid increase in the thickness of the (001) sheet of [Fe(O,OH)₆] octahedra and [SO₄] tetrahedra with increasing temperature. Fitting of the measured cell volumes yields a coefficient of thermal expansion, α = α₀ + α₁ T, where α₀ = 1.01 × 10⁻⁴ K⁻¹ and α₁ = −1.15 × 10⁻⁷ K⁻². On heating, the hydrogen bonds, O1···D–O3, through which the (001) octahedral–tetrahedral sheets are held together, become weakened, as reflected by an increase in the D···O1 distance and a concomitant decrease in the O3–D distance with increasing temperature. On further heating to 575 K, jarosite starts to decompose into nanocrystalline yavapaiite and hematite (as well as water vapor), a direct result of the breaking of the hydrogen bonds that hold the jarosite structure together.     

Magnetic-field structure in the accretion disks of semi-detached binary systems

The results of three-dimensional MHD numerical simulations are used to investigate the characteristic properties of the magnetic-field structures in the accretion disks of semi-detached binary systems. It is assumed that the intrinsic magnetic field of the accretor star is dipolar. Turbulent diffusion of the magnetic field in the disk is taken into account. The SS Cyg system is considered as an example. The results of the numerical simulations show the intense generation of a predominantly toroidal magnetic field in the accretion disk. Magnetic zones with well defined structures for the toroidal magnetic field form in the disk, which are separated by current sheets in which there ismagnetic reconnection and current dissipation. Possible observational manifestations of such structures are discussed. It is shown that the interaction of a spiral precessional wave with the accretor’s magnetosphere could lead to quasi-periodic oscillations of the accretion rate.