Effects of cation disordering in a natural MgAl2O4 spinel observed by rectangular parallelepiped ultrasonic resonance and Raman measurements

At moderate temperatures, the elastic properties of natural MgAl₂O₄ spinel differ in several significant ways from properties of synthetic spinels. Below 1000 K, the ultrasonic resonant frequencies of an ordered natural spinel change significantly after heat treatment; at higher temperatures, both types of spinels have similar resonant responses. The temperature derivatives of the elastic constants of an ordered spinel also differ from those of disordered spinels at moderate temperatures; again, at higher temperatures, both types of spinels have similar behaviors. The Raman spectra also differ below 1000 K for ordered natural and disordered spinels and are similar at higher temperatures and after cooling to ambient temperature. We associate these changes in ultrasonic resonance and Raman spectra of spinel with cation disordering at high temperature which may be quenched by cooling. We deduce estimates of the inversion parameter from the relative intensities of the two A_1g Raman modes in very good agreement with estimates made from other measurements. We find thatC ₁₁ andC ₁₂ decrease by 4 and 8%, respectively, with 20% inversion in spinel;C ₄₄ is less sensitive to cation order. These results imply that previous measurements of the adiabatic elastic constants of spinels at ambient conditions have been affected by the state of cation disorder of the specimen.     

Influence of viscosity on the phase of earth tides

The effect of viscosity on the phase of earth tides is computed. Computations are based on the general theory of the effect of viscosity of the mantle considered as a Maxwell body as it has been elaborated by Molodensky (1963). The problem is solved by the method of variation of constants, starting from the solution for the case of an ideally elastic, spherically symmetrical globe. The computations presented here cover the cases of the earth models B₁ and B₂ of Bullen and Haddon (1967). Love numbers k, l, h were computed for tides of second and third order, and values of phase delay due to viscosity were computed for tides of second order.     

In-situ fluid-pressure measurements for earthquake prediction: An example from a deep well at Hi Vista,California

Short-term earthquake prediction requires sensitive instruments for measuring the small anomalous changes in stress and strain that precede earthquakes. Instruments installed at or near the surface have proven too noisy for measuring anomalies of the size expected to occur, and it is now recognized that even to have the possibility of a reliable earthquake-prediction system will require instruments installed in drill holes at depths sufficient to reduce the background noise to a level below that of the expected premonitory signals. We are conducting experiments to determine the maximum signal-to-noise improvement that can be obtained in drill holes. In a 592 m well in the Mojave Desert near Hi Vista, California, we measured water-level changes with amplitudes greater than 10 cm, induced by earth tides. By removing the effects of barometric pressure and the stress related to earth tides, we have achieved a sensitivity to volumetric strain rates of 10^–9 to 10^–10 per day. Further improvement may be possible, and it appears that a successful earthquake-prediction capability may be achieved with an array of instruments installed in drill holes at depths of about 1 km, assuming that the premonitory strain signals are, in fact, present.     

Measurements of tidal gravity and load deformations on Unst (Shetlands)

Summary The tidal gravimetric factor due to the elastic yielding of the Earth has been determined by gravimetric measurements on Unst (Shetland Islands), extending over the time of one month. Its corrected value isG=1.205±0.03. The influence of applying different methods of harmonic analysis, and the effects of ambient temperature and pressures and of the sea tides on the gravimetric results are discussed. No significant difference inG for semi-diurnal and diurnal tides remains after the necessary corrections have been made. The amplitude of the semidiurnal load depression is about 2 cm and it is shown that the more distant North Atlantic tides have a greater effect than the regional tides near the Shetlands. An approximate calculation gives 4.3×10¹¹ CGS-units as the mean rigidity of the part of the Earth's crust yielding to the maritime loading differences in this region.     

Properties of a nonlinear solar dynamo model

Abstract

A simple nonlinear model is developed for the solar dynamo, in which the real convective spherical shell is approximated by a thin flat slab, and only the back-reaction of the field B on the helicity is taken into account by choosing the simple law α = α(1-ζB ²), where α and ζ are constants, to represent the decrease in generation coefficient ζ with increasing field strength. Analytic expressions are obtained for the amplitude of the field oscillation and its period, T, as functions of the deviation d - d_CT of a dynamo number d from its critical value d_cr for regeneration. A symmetry is found for the case of oscillations of small constant amplitude: B(t+½T)= -B(t). A Landau equation is obtained that describes the transition to such oscillations.     

Ultrasonic Velocities, Acoustic Emission Characteristics and Crack Damage of Basalt and Granite

Acoustic emissions (AE), compressional (P), shear (S) wave velocities, and volumetric strain of Etna basalt and Aue granite were measured simultaneously during triaxial compression tests. Deformation-induced AE activity and velocity changes were monitored using twelve P-wave sensors and eight orthogonally polarized S-wave piezoelectric sensors; volumetric strain was measured using two pairs of orthogonal strain gages glued directly to the rock surface. P-wave velocity in basalt is about 3 km/s at atmospheric pressure, but increases by > 50% when the hydrostatic pressure is increased to 120 MPa. In granite samples initial P-wave velocity is 5 km/s and increases with pressure by < 20%. The pressure-induced changes of elastic wave speed indicate dominantly compliant low-aspect ratio pores in both materials, in addition Etna basalt also contains high-aspect ratio voids. In triaxial loading, stress-induced anisotropy of P-wave velocities was significantly higher for basalt than for granite, with vertical velocity components being faster than horizontal velocities. However, with increasing axial load, horizontal velocities show a small increase for basalt but a significant decrease for granite. Using first motion polarity we determined AE source types generated during triaxial loading of the samples. With increasing differential stress AE activity in granite and basalt increased with a significant contribution of tensile events. Close to failure the relative contribution of tensile events and horizontal wave velocities decreased significantly. A concomitant increase of double-couple events indicating shear, suggests shear cracks linking previously formed tensile cracks.     

Quasi-Static Strain and Stress Fields due to a Moment Tensor in Elastic–Viscoelastic Layered Half-Space

We derived explicit expressions in the time domain for 3-D quasi-static strain and stress fields, due to a point moment tensor source in an elastic surface layer overlying viscoelastic half-space under gravity. The expressions of strain in the elastic surface layer were directly obtained from the expressions of displacement in our previous paper. The conversion of strain into stress is easy, because the stress–strain relation of elastic material is linear. In the viscoelastic substratum, the expressions of strain were obtained by applying the correspondence principle of linear viscoelasticity to the associated elastic solution. The strain–stress conversion is not straightforward, as the stress–strain relation of viscoelastic material is usually given in a differential form. To convert strain into stress, we used an integral form of the stress–strain relation instead of the usual differential form. The expressions give the responses of elastic half-space at \( t = 0 \) , and the responses of an elastic plate floating on non-viscous liquid at \( t = \infty \) . The moment tensor is rationally decomposed into the three independent force systems, corresponding to isotropic expansion, shear faulting and crack opening, and so the expressions include the strain and stress fields for these force systems as special cases. As the first numerical example, we computed the temporal changes in strain and stress fields after the sudden opening of an infinitely long vertical crack cutting the elastic surface layer. Here, we observe that the stress changes caused by the sudden crack opening gradually decay with time and vanish at \( t = \infty \) everywhere. After the completion of stress relaxation, a characteristic pattern of shear strain remains in the viscoelastic substratum. Since the strain and stress fields at \( t = \infty \) can be read as the strain- and stress-rate fields caused by steady crack opening, respectively, this numerical example demonstrates the realization of a steady stress state supported by steady viscous flow in the asthenosphere, associated with steady seafloor spreading at mid-ocean ridges. For the second numerical example, we computed the temporal changes in strain and stress fields after the 2011 Tohoku-oki mega-thrust earthquake, which occurred at the North American-Pacific plate interface. In this numerical example, the stress changes caused by coseismic fault slip vanish at \( t = \infty \) in the viscoelastic substratum, but remain in the elastic surface layer. The coseismic stress changes (and also strain changes) in the elastic surface layer diffuse away from the source region with time, due to gradual stress relaxation in the viscoelastic substratum.     

Elastk-plastic dynamic analysis of structures using known elastic solutions

A numerical method is shown to analyse the dynamic elastic-plastic responses of those structures with known elastic solutions. The displacement at one point at time t caused by a unit load applied at another point at zero time, called dynamic influence coefficient, is calculated from the known elastic solutions. Incremental plastic strain is accounted for by a set of additional incremental loads, so the stiffness matrix and the eigenvectors do not vary with time. From the incremental load including that caused by the incremental plastic strain, the displacement vs. time of the structure is obtained. This method is applied to simply supported beams with bilinear stress-strain relations with different strain-hardening rates and to a simply supported elastic-ideally plastic rectangular plate. This procedure can be extended to structures with no available known analytical elastic solutions. For these structures, the elastic solutions can be obtained by the finite element method.     

Static and dynamic elastic moduli of organic-rich chalk

The elastic moduli and anisotropy of organic-rich rocks are of great importance to geoengineering and geoprospecting of oil and gas reservoirs. In this paper, we probe into the static and dynamic moduli of the Ghareb–Mishash chalk through laboratory measurements and new analytical approaches. We define a new anisotropy parameter, ‘hydrostatic strain ratio’ (Ω), which describes the differential contraction of anisotropic rocks consequent to hydrostatic compression. Ω depends on the C₁₁, C₁₂, C₁₃ and C₃₃ stiffness constants of a transversely isotropic material, and therefore enables a unique insight into the anisotropic behaviour of TI rocks. Ω proves more sensitive to anisotropy within the weak anisotropy range, when compared with Thomsen's ε and γ parameters. We use Ω to derive static moduli from triaxial compression tests performed on a single specimen. This is done by novel employment of a hydrostatic-deviatoric combination for transversely isotropic elastic stiffnesses. Dynamic moduli are obtained from acoustic velocities measurements. We find that the bedding-normal velocities are described well by defining kerogen as the load-supporting matrix in a Hashin–Shtrikman model (‘Hashin–Shtrikman (HS) kerogen’). The dynamic moduli of the Ghareb–Mishash chalk in dry conditions are significantly higher than the static moduli. The dynamic/static moduli ratio decreases from ∼4 to ∼2 with increasing kerogen content. Both the static and dynamic moduli decrease significantly with increasing porosity and kerogen content. The effect of porosity on them is two times stronger than the effect of kerogen.     

Lunar perturbations in geomagnetic field and in the characteristics ofF-region over huancayo

Summary The lunar daily (L) and lunar monthly (M) variations in horizontal magnetic field (H), maximum electron density (N _max ), height of peak ionisation (h _max ), semi-thickness (y _m ) of theF ₂ layer and total electron content (N _t ) at Huancayo for the period January 1960 to December 1961 are described. The lunar tidal variations inh _max follow sympathetically the variations inH such that an increase of magnetic field causes the raising of height of peak ionisation. Lunar tides inN _max are opposite in phase to that ofh _max with a delay of about 1–2 hours, suggesting that an increase of height causes a decrease in maximum electron density. The lunar tides in semi-thickness are very similar in phase to that inh _max . The lunar tidal effects in any of the parameters are largest inD-months and least inJ-months. The amplitude of lunar tides in maximum electron density seems to increase with increasing height whereas the phase seems to be constant with height. It is concluded that lunar tides in the ionospheric parameters at magnetic equator are greatly controlled by the corresponding geomagnetic variations.Presented at the Third International Symposium on Equatorial Aeronomy, Ahmedabad, 3–10 February 1969.     

双轴压力下岩样自电位变化实验的新结果

利用伺服控制双轴加载系统,采用阵列式布局的应变、自电位测量方法,对岩石样品弹性变形阶段和破坏过程中的应变和自电位进行了实验研究. 结果表明,在突然加卸载、黏滑和岩样破裂几种特定情况下,自电位和应变场均出现了互相关联的脉冲状突然变化,且具有相当大的空间展布. 尽管有时应力σ值相当高,但当应力变化率γ= dσ/ dt为零（恒载）且保持正、负常数（匀速加、卸载）时,自电位始终没有异常出现. 反之,无论γ的增量Δγ为正值或负值,当γ突变,即对样品进行突然加卸载的时刻则出现了脉冲状自电位信号ΔV,Δγ的正或负对ΔV的影响是相反的. 分析表明,应力突变时ΔV与Δγ的异常幅度成正比. 应力突变和岩石破裂过程中自电位明显的时空变化意味着,孕震区附近如果自电位有突变,就有可能观测到相关的自电位前兆和同震变化, 并可能出现同步的应变变化,这给地震的自电位和应变前兆方法提供了实验证据.     

Tides off‐shore: Transition from California coastal to deep‐sea waters‡

Abstract

Tidal pressures and currents were measured with self‐contained capsules dropped to the sea floor for one month at distances of 175, 190, and 500 nautical miles from San Diego. These observations, together with a one‐week bottom pressure record by Filloux at 750 n miles, and three half‐week bottom current records by Isaacs et al, at intermediary distances, were analyzed for tidal components by cross‐correlation with a noise‐free reference time series. (For short records this method has some merit over classical tide analysis.) It was found that the tide decays seaward to e^‐1 times the coastal amplitude over a distance of order 1000 km for the semidiurnal species, slower for the diurnal species. Tidal currents turn counterclockwise, and are polarized with maximum flow parrallel to shore in the direction of tidal propagation (320°T) at local high tide. The current amplitude is roughly 2 cm/sec for the semidiurnal component, 1 cm/sec for the diurnal component. Superimposed baroclinic tidal currents lead to poor signal: noise ratios (between 1:1 and 10:1) for the barotropic currents. In contrast, the ratio is typically 1000:1 for the bottom pressures and generally exceeds that for coastal tide stations of comparable duration. Published I.H.B. tidal constants for exposed California coastal stations indicate “upshore” (towards 320°T) propagation at 140 m/sec for semidiurnal tides. 214 m/sec for diurnal tides.

To interpret these diverse observations, we have computed the dispersion laws for all possible rotationally‐gravitationally trapped waves against a straight coast with shelf. Trapped solutions are conveniently portrayed in terms of a parameter μ such that ? = sin μ = iu/v and f = ‐ cos μ = η/v define the ellipticity and impedance of the wave motion, η, u and v being off‐shelf dimensionless elevation, normal‐to‐shore and longshore components of velocity, respectively. We then attempt to fit the observations by a superposition of the possible wave classes, all of the same tidal frequency: (a) a free Kelvin‐like edge wave with small μ (mostly trapped by rotation, but somewhat slowed by the shelf); (6) a free Poincare‐like leaky wave; and (c) a forced wave (the distortion of the sea bottom by the tide producing forces plays a significant role). The mod el can account for the main features of the observed tidal heights, and gives relative amplitudes at the coast of 54:16:4 cm for components a:b:c in the case of the semidiurnal tides, 21:24:9 cm for the diurnal tides. The results place a semidiurnal amphidrome about midway between San Diego and Hawaii. Tidal currents are not well fitted by the model, and there are problems associated with the separation of barotropic and baroclinic modes, and with the benthic boundary layer. Coastal energy dissipation is small in the sea under investigation, but a “ capacitive “ phase delay appears to be associated with Northern California harbors and inland waters.     

全球Schwiderski海潮模型M2分波在中国大陆产生的应变负荷潮

本文利用计算应变负荷潮的积分Green函数方法,计算了全球Schwiderski海潮模型M₂分波在中国大陆产生的应变负荷潮.根据负荷潮的分布特点,中国大陆大致可以分成以东经100°为界的东、西两个区域.在东区,负荷潮主要受太平洋海潮的控制;在西部内陆地区,除太平洋海潮外,它们还明显地受印度洋海潮的影响.根据本文计算结果绘制的M₂分波应变负荷潮在中国大陆的地理分布图,为如何正确考虑M₂分波负荷潮对应变固体潮观测结果的影响提供了重要的参考资料.     

Possible strain events reflected in water levels in wells along San Jacinto fault zone,southern California

Water levels have been monitored in wells along the San Jacinto fault zone since 1977. The three largest earthquakes to occur within 30 km of the segment of the San Jacinto fault zone being monitored with continuous recorders showed magnitudesM of 4.5, 4.8, and 5.5. Two wells in Borrego Valley, 31 to 32 km southeast of theM=5.5 earthquake on 25 February 1980, showed anomalous spikes recording a probable strain event 88 hours before the earthquake. Two other wells 12 km northwest of the epicenter showed no water-level anomalies. No water-level anomalies preceded theM=4.8 earthquake near Anza on 15 June 1982. Anomalous water-level fluctuations occurred in a well near Ocotillo Wells, 13 km northeast of theM=4.5 earthquake on 22 March 1982, 19 to 23 days prior to the earthquake. Similar fluctuations in other wells have not been followed by sizable earthquakes. A simultaneous drop in water level occurred in four wells on 8 September 1982; this possible strain event was not associated with a sizable earthquake. The presumed strain events occur only in wells that show earth tides and may have been the result of creep on strands of the San Jacinto fault zone. Although water-level anomalies have occurred in only one or two wells prior to two out of three moderate (M=4.5–5.5) earthquakes, the simultaneous drop in water level on 8 September 1982 and the spikes in two wells before theM=5.5 earthquake on 25 February 1980 suggest that wells responsive to earth tides may detect strain events.     

Spatial Scaling of Effective Modulus and Correlation of Deformation Near the Critical Point of Fracturing

Many observations point to the lithosphere being metastable and close to a critical mechanical point. Exercises in modelling deformation, past or present, across subsurface reservoirs need to take account of this criticality in an efficient way. Using a renormalization technique, the spatial scaling of effective elastic modulus is derived for 2-D and 3-D bodies close to the critical point of through-going fracturing. The resulting exponent, d_μ, of spatial scaling of effective modulus with size, , takes the values ~ −2.5 and −4.2 in two- and three-dimensional space, respectively. The exponents are compatible with those for scaling of effective modulus with fracture density near the percolation threshold determined by other workers from numerical experiments; the high absolute values are also approximately consistent with empirical data from a) fluctuations in depth of a seismic surface; b) `1/k' scaling of heterogeneities observed in one-dimensional well-log samples; c) spatial correlation of slip displacements induced by water injection. The effective modulus scaling modifies the spatial correlation of components of displacement or strain for a domain close to the critical point of fracturing. This correlation function has been used to geostatistically interpolate components of the strain tensor across subsurface reservoirs with the prime purpose of predicting fracture densities between drilled wells. Simulations of strain distributions appear realistic and can be conditioned to surface depths and observations at wells of fracture-related information such as densities and orientations, welltest permeabilities, changes in well-test permeabilities, etc.     

Experimental study of the elasticity of single crystalline calcite under high pressure (the calcite I—calcite II transition at 14.6 kbar)

The length variations and the ultrasonic wave velocities were measured along principal single crystal calcite axes under high pressure.We have observed that six independent elastic constants undergo drastic changes at the calcite I—calcite II transition point at 14.6 kbar. Furthermore, we have determinated the length and volumetric variations in the phases I and II and during the I–II transition.These results allow us to deduce the following important points: influence of the planar CO₃ groups on the strong linear compressibility anisotropy in phase I; reciprocal relation between the decrease of elastic constants at the transition point and the anomaly of compressibility of the calcite II; compatibility of our data with the monoclinic structure of calcite II.     

A statistical review of mudrock elastic anisotropy

Mudrocks, defined to be fine‐grained siliclastic sedimentary rocks such as siltstones, claystones, mudstones and shales, are often anisotropic due to lamination and microscopic alignments of clay platelets. The resulting elastic anisotropy is often non‐negligible for many applications in the earth sciences such as wellbore stability, well stimulation and seismic imaging. Anisotropic elastic properties reported in the open literature have been compiled and statistically analysed. Correlations between elastic parameters are observed, which will be useful in the typical case that limited information on a rock's elastic properties is known. For example, it is observed that the highest degree of correlation is between the horizontal elastic stiffnesses C₁₁ and C₆₆. The results of statistical analysis are generally consistent with prior observations. In particular, it is observed that Thomsen's ? and γ parameters are almost always positive, Thomsen's ? and γ parameters are well correlated, Thomsen's δ is most frequently small and Thomsen's ? is generally larger than Thomsen's δ. These observations suggest that the typical range for the elastic properties of mudrocks span a sub‐space less than the five elastic constants required to fully define a Vertical Transversel Isotropic medium. Principal component analysis confirms this and that four principal components can be used to span the space of observed elastic parameters.     

Assessing baseflow index vulnerability to variation in dry spell length for a range of catchment and climate properties

Baseflow index (BFI) prediction in ungauged basins has largely been based on the use of catchment physiographic attributes as dominant variables. In a context where changes in climate are increasingly evident, it is also important to study how the slow component of flow is potentially affected by climate. The aim of this study was to illustrate the impact of climate variability on the baseflow process based on analysis of daily rainfall characteristics and hydrological modelling simulation exercises validated with observed data. Ten catchments were analysed that span southern to northern Europe and range from arid Mediterranean to maritime temperate climate conditions. Additionally, more than 2,000 virtual catchments were modelled that cover an extended gradient of physiographic and climate properties. The relative amounts of baseflow were summarized by the BFI. The catchment slow response delay time (Ks) was assumed to be a measure of catchment effects, and the impact of climate properties was investigated with the dry spell length (d). Well‐drained and poorly‐drained groups were identified based on Ks and d, and their response to an increase or decrease in dry spell length was analysed. Overall, for either well‐ or poorly‐drained groups, an extension in dry spell length appeared to have minor effects on the baseflow compared with a decrease in dry spell length. Under the same dry spell variation, the BFI vulnerability appeared higher for catchments characterized by large initial d values in combination with poorly‐drained systems, but attributing an equal weight to the variations in d both in the case of dry and wet initial conditions, it is in the end concluded that the BFI vulnerability appears higher for systems laying in the transition zone between well‐ and poorly‐drained systems.     

2011-2014年康定周边地形变场变化与芦山7.0级地震及康定两次中强地震的关系研究

收集康定地震区及周边（99.6°~105.2°E,27.8°~33.0°N范围内）连续GPS观测站的资料求解站速度场,采用刚性-线弹性运动方程计算方法,拟合计算得到研究区域规格网格点（0.4°×0.4°）的速度值和主应变率值。基于该结果分析研究区内的运动特征和应变场变化情况,并讨论其与地震孕育发生的关系。分析结果表明,芦山7.0级地震发生前研究区呈现应变能量积累态势,而地震之后研究区呈应变能量释放调整态势,2014年康定地震的发生就是该区构造运动调整下的产物。