Characteristic scale of heterogeneity of seismically active fault and its manifestation in scaling of earthquake source spectra

Previously, similarity of source spectra of Kamchatka earthquakes with respect to the common corner frequency f_c1 and the expressed deviations from similarity for the second f_c2 and the third f_c3 corner frequencies were revealed. The value of f_c3 reflects the characteristic size L_is of fault surface; correspondingly, L_is ≈ v_rT_is, where v_r is the rupture speed and T_is ≈ 1/f_c3 is characteristic time. The estimates of f_c3 are used for normalizing f_c1 and f_c2. In this way one obtains dimensionless rupture temporal parametres τ₁ and τ₂ and can further study the dependence τ₂ (τ₁). The growth of a rupture is considered as a process of aggregation of elementary fault spots of the size L_is. The dimensionless width of the random front of aggregation is on the order of τ₂. The relationship τ₂ (τ₁) approximately follows power law with exponent β. The estimates of β derived from earthquake populations of Kamchatka, USA and Central Asia (β = 0.35–0.6) agree with values expected from the known Eden’s theory of random aggregation growth and from its generalizations.     

Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis

Accurate laboratory measurement of geo-engineering properties of intact rock including uniaxial compressive strength (UCS) and modulus of elasticity (E) involves high costs and a substantial amount of time. For this reason, it is of great necessity to develop some relationships and models for estimating these parameters in rock engineering. The present study was conducted to forecast UCS and E in the sedimentary rocks using artificial neural networks (ANNs) and multivariable regression analysis (MLR). For this purpose, a total of 196 rock samples from four rock types (i.e., sandstone, conglomerate, limestone, and marl) were cored and subjected to comprehensive laboratory tests. To develop the predictive models, physical properties of studied rocks such as P wave velocity (V_p), dry density (γ_d), porosity, and water absorption (A_b) were considered as model inputs, while UCS and E were the output parameters. We evaluated the performance of MLR and ANN models by calculating correlation coefficient (R), mean absolute error (MAE), and root-mean-square error (RMSE) indices. The comparison of the obtained results revealed that ANN outperforms MLR when predicting the UCS and E.     

Effect of 2-D Random Field Discretization on Failure Probability and Failure Mechanism in Probabilistic Slope Stability

This paper investigates, using the random field theory and Monte Carlo simulation, the effects of random field discretization on failure probability, p _f, and failure mechanism of cohesive soil slope stability. The spatial sizes of the discretized elements in random field Δx, Δy in horizontal and vertical directions, respectively, are assigned a series of combinational values in order to model the discretization accuracy. The p _f of deterministic critical slip surface (DCSS) and that of the slope system both are analyzed. The numerical simulation results have demonstrated that both the ratios of Δy/λ _y (λ _y  = scale of fluctuation in vertical direction) and Δx/λ _x (λ _x  = scale of fluctuation in horizontal direction) contribute in a similar manner to the accuracy of p _f of DCSS. The effect of random field discretization on the p _f can be negligible if both the ratios of Δx/λ _x and Δy/λ _y are no greater than 0.1. The normalized discrepancy tends to increase at a linear rate with Δy/λ _y when Δx/λ _x is larger than 0.1, and vice versa for p _f of DCSS. The random field discretization tends to have more considerable influence on the p _f of DCSS than on that of the slope system. The variation of p _f versus λ _x and λ _y may exhibit opposite trends for the cases where the limit state functions of slope failure are defined on DCSS and on the slope system as well. Finally, the p _f of slope system converges in a more rapid manner to that of DCSS than the failure mechanism does to DCSS as the spatial variability of soil property grows from significant to negligible.     

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily over-consolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as half of the critical distance. This fracture criterion is known as the point method, and is part of the theory of critical distances, which is utilised in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, σ ₀, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, σ _c and σ _t. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (σ _c/σ _t = 3–50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low-confining stresses.     

Evolution of the shape parameter in the Weibull distribution for brittle rocks under uniaxial compression

Applying the statistical damage theory based on the Weibull distribution to describe rock deformation and failure processes is an important development in rock mechanics. The shape parameter of the Weibull distribution, m, determines the basic shape of the distribution curve; additionally, it also represents a physical characteristic which can be applied when constructing rock constitutive models. To study the evolution of m during rock failure when applying the Weibull distribution to rock mechanics, uniaxial cyclic loading tests of shale specimens were conducted and previous rock mechanics experiments under different temperatures and loading rates were reviewed. The results indicate that m varied with the accumulation of damage but was almost constant between the volume expansion point and the peak strength point of each specimen. Combined with previous studies about the accelerated failure behavior of rocks, we conclude that between the volume expansion point and the peak strength point, the mechanical behavior of the rock fracture process did not change significantly. Based on the characteristics of m at different damage stages during the rock failure process, ranges of m values at different damage stages are proposed. The conclusions reached in this study may be used as an important reference for theoretical research on rock mechanics.     

Fractal dimension of pore space in carbonate samples from Tushka area (Egypt)

To investigate inhomogeneous and porous structures in nature, the concept of fractal dimension was established. This paper briefly introduces the definition and measurement methods of fractal dimension. Three different methods including mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and nitrogen adsorption (BET) were applied to determine the fractal dimensions of the pore space of eight carbonate rock samples taken from West Tushka area, Egypt. In the case of fractal behavior, the capillary pressure P _c and cumulative fraction V _c resulting from MICP are linearly related with a slope of D-3 in a double logarithmic plot with D being the value of fractal dimension. For NMR, the cumulative intensity fraction V _c and relaxation time T ₂ show a linear relation with a slope of 3-D in a double logarithmic plot. Fractal dimension can also be determined by the specific surface area S _por derived from nitrogen adsorption measurements and the effective hydraulic radius. The fractal dimension D shows a linear relation with the logarithm of S _por . The fractal dimension is also used in models of permeability prediction. To consider a more comprehensive data set, another 34 carbonate samples taken from the same study area were integrated in the discussion on BET method and permeability prediction. Most of the 42 rock samples show a good agreement between measured permeability and predicted permeability if the mean surface fractal dimension for each facies is used.     

Community vulnerability to hazards: introducing local expert knowledge into the equation

The accuracies of three different evolutionary artificial neural network (ANN) approaches, ANN with genetic algorithm (ANN-GA), ANN with particle swarm optimization (ANN-PSO) and ANN with imperialist competitive algorithm (ANN-ICA), were compared in estimating groundwater levels (GWL) based on precipitation, evaporation and previous GWL data. The input combinations determined using auto-, partial auto- and cross-correlation analyses and tried for each model are: (i) GWL _t?1 and GWL _t?2; (ii) GWL _t?1, GWL _t?2 and P _t ; (iii) GWL _t?1, GWL _t?2 and E _t ; (iv) GWL _t?1, GWL _t?2, P _t and E _t ; (v) GWL _t?1, GWL _t?2 and P _t?1 where GWL _t , P _t and E _t indicate the GWL, precipitation and evaporation at time t, individually. The optimal ANN-GA, ANN-PSO and ANN-ICA models were obtained by trying various control parameters. The best accuracies of the ANN-GA, ANN-PSO and ANN-ICA models were obtained from input combination (i). The mean square error accuracies of the ANN-GA and ANN-ICA models were increased by 165 and 124% using ANN-PSO model. The results indicated that the ANN-PSO model performed better than the other models in modeling monthly groundwater levels.     

Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P _f ?<?0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P _f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P _f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P _f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.     

Possible reasons for the frequency splitting of the harmonics of type II solar radio bursts

AIA/SDO data in the 193 Å channel preceding a coronal mass ejection observed at the solar limb on June 13, 2010 are used to simultaneously identify and examine two different shock fronts. The angular size of each front relative to the CME center was about 20°, and their propagation directions differed by ≈25° (≈4° in position angle). The faster front, called the blast shock, advanced the other front, called the piston shock, by R ≈ (0.02-0.03)R⊙ (R⊙ is the solar radius) and had a maximum initial speed of V_B ≈ 850 km/s (with V_P ≈ 700 km/s for the piston shock). The appearance and motion of these shocks were accompanied by a Type II radio burst observed at the fundamental frequency F and second harmonic H. Each frequency was split into two close frequencies f₁ and f₂ separated by Δf = f₂ - f₁ ? F, H. It is concluded that the observed frequency splitting Δf of the F and H components of the Type II burst could result from the simultaneous propagation of piston and blast shocks moving with different speeds in somewhat different directions displaying different coronal-plasma densities.     

The Effect of High Temperature on Tensile Strength and Damage Characteristics of Limestone

In this paper, the limestone specimens are heated from room temperature 25 to 800 °C in a high temperature furnace and then are subjected to Brazilian test with the AG-I250 electronic precision material testing machine. The physical properties, mechanical properties, disc failure pattern, energy absorbed per unit area and damage characteristics of disc are comprehensively investigated. The results show that: with the increase of temperature, the changing trends of tensile strength, peak strain, tensile modulus and accumulated energy absorbed per unit area of disc are similar, they are first increases, then decrease, the energy consumption index is consistent with the macroscopic damage characteristics; the value of ε_s increase first and then reduce, reaches the maximum at 600 °C. The value of n is increasing and fluctuating, but the change trend of D_c is opposite, which is decreasing and fluctuating. The slope of the damage variable-strain curves decreases first and then increases, the minimum value at 600 °C. This study is of significance to the prediction and evaluation of the stability and safety of rock mass post-high temperature.     

Cosmological tests based on the abundance of galaxy clusters

We present a new normalization for the linear density-perturbation spectrum in a multi-parameter model of the Universe. Using the differential mass function for the nearly galaxy clusters obtained from optical data, we have constructed a functional relation between the dispersion of the density contrast σ ₈ on the scale 8h ^?1 Mpc and the cosmological parameters Ω _m , Ω_Λ, h, n, f _v for each of three theoretical approximations of the mass function: Press-Schechter, Sheth-Tormen and Jenkins. An extended class of models of the Universe with general spatial curvature include four parameters for the matter components: baryons (Ω _b ), “cold” dark matter (Ω _c ), “hot” dark matter (Ω _v ), and the vacuum energy (Ω_Λ). It is shown that the most accurate normalization of the power spectrum is achieved with the Sheth-Tormen approximation.     

High-pressure displacive phase transition of a natural Mg-rich pigeonite

A high-pressure single-crystal X-ray diffraction study has been carried out on a P2₁/c natural Mg-rich pigeonite sample with composition ca. Wo₆En₇₆Fs₁₈ using a diamond anvil-cell. The unit-cell parameters were determined at 14 different pressures to 7.14 GPa. The sudden disappearance of the b-type reflections (h + k = odd) and a strong discontinuity (about 2.8%) in the unit-cell volume indicated a first-order P2₁/c–C2/c phase transition between 4.66 and 4.88 GPa. The P(V) data of the P2₁/c phase were fitted to 4.66 GPa by a third-order Birch–Murnaghan equation of state (BM3 EoS), whereas the limited number of experimental data collected within the C2/c phase between 4.88 and 7.14 GPa were fitted using the same equation of state but with K′ constrained to the value obtained for the P2₁/c fitting. The equation of state coefficients are V ₀ = 424.66(6) ų, K _T0 = 104(2) GPa and K′ = 8(1) for the P2₁/c phase, and V ₀ = 423.6(1) ų, K _T0 = 112.4(8) GPa, and K′ fixed to 8(1) for the C2/c phase. The axial moduli for a, b, and c for the P2₁/c phase were obtained using also a BM3-EoS, while for the C2/c phase only a linear calculation could be performed, and therefore the same approach was applied for comparison also to the P2₁/c phase. In general the C2/c phase exhibits axial compressibilities (β _c > β _a >> β _b) lower than those of the P2₁/c phase (β _b > β _c ≈ β _a; similar to those found in previous studies in clinopyroxenes and orthopyroxenes). The lower compressibility of the C2/c phase compared with that of the P2₁/c could be ascribed to the greater stiffness along the b direction. A previously published relationship between P _c and M2 average cation radius (i.r.) has been updated using all the literature data on P2₁/c clinopyroxene containing large cations at M2 site and our new data. The following weighted regression was obtained: P _c (GPa) = 26(4) ? 28(5) ×  i.r (Å), R ² = 0.97. This improved equation can be used to predict the critical pressure of natural P2₁/c clinopyroxene samples just knowing the composition at M2 site.     

Integration of root systems into a GIS-based slip surface model: computational experiments in a generic hillslope environment

Root systems of trees reinforce the underlying soil in hillslope environments and therefore potentially increase slope stability. So far, the influence of root systems is disregarded in Geographic Information System (GIS) models that calculate slope stability along distinct failure plane. In this study, we analyse the impact of different root system compositions and densities on slope stability conditions computed by a GIS-based slip surface model. We apply the 2.5D slip surface model r.slope.stability to 23 root system scenarios imposed on pyramidoid-shaped elements of a generic landscape. Shallow, taproot and mixed root systems are approximated by paraboloids and different stand and patch densities are considered. The slope failure probability (P_f) is derived for each raster cell of the generic landscape, considering the reinforcement through root cohesion. Average and standard deviation of P_f are analysed for each scenario. As expected, the r.slope.stability yields the highest values of P_f for the scenario without roots. In contrast, homogeneous stands with taproot or mixed root systems yield the lowest values of P_f. P_f generally decreases with increasing stand density, whereby stand density appears to exert a more pronounced influence on P_f than patch density. For patchy stands, P_f increases with a decreasing size of the tested slip surfaces. The patterns yielded by the computational experiments are largely in line with the results of previous studies. This approach provides an innovative and simple strategy to approximate the additional cohesion supplied by root systems and thereby considers various compositions of forest stands in 2.5D slip surface models. Our findings will be useful for developing strategies towards appropriately parameterising root reinforcement in real-world slope stability modelling campaigns.     

On the correlation between spectra of solar microwave bursts and proton fluxes near the Earth

Studies of the extreme solar proton event of January 20, 2005 intensified the contest over of a long-standing problem: are solar cosmic rays arriving at the Earth accelerated by solar flares or by shocks preceding rapidly moving coronal mass ejections? Among the most important questions is the relationship between the energy spectra of the solar cosmic rays and the frequency spectra of flare microwave bursts. Some studies of previous solar-activity cycles have shown that such a relationship does exist, in particular, for protons with energies of tens of MeV. The present work analyzes this relation using data for 1987–2008. For flare events observed in the western half of the disk, there is a significant correlation between the index δ, which is equivalent to the power-law index of the integrated energy spectrum of 10–100 MeV protons detected near the Earth’s orbit, and radio burst parameters such as a ratio of peak fluxes S at two frequencies (for example, at 9 and 15 GHz) and a microwave peak frequency f _m . Proton fluxes with hard (flat) energy spectra (δ ≤ 1.5) correspond to hard microwave frequency spectra (S ₉/S ₁₅ ≤ 1 and f _m ≥ 15 GHz), while flares with soft radio spectra (S ₉/S ₁₅ ≥ 1.5 and f _m ≤ 5 GHz) result in proton fluxes with soft (steep) energy spectra (δ ≥ 1.5–2). It is also shown that powerful high-frequency bursts with the hardest radio spectra (f _m ≈ 30 GHz) can point at acceleration of significant proton fluxes in flares occurring in strong magnetic fields. These results argue that solar cosmic rays (or at least their initial impulses) are mainly accelerated in flares associated with impulsive and post-eruptive energy release, rather than in shocks driven by coronal mass ejections.     

Effect of foliation orientation on the P- and S-wave velocity anisotropies and dynamic elastic constants of the quartz-micaschists metamorphic rocks,Angouran mine,Iran

Laboratory measurements are required to study geophysical properties of the subsurface because of lacking direct observation of Earth’s crust. In this research, compressional (P) and shear (S) wave velocity measurements have been conducted on cylindrical specimens of Quartz-micaschist cored using rock blocks taken from the zinc and lead Angouran mine, Zanjan, northwest of Iran. Cylindrical rock specimens were prepared from the blocks by coring in 0°, 30°, 45°, 60°, and 90° into the foliation direction. P- and S-wave velocities were measured along the cylindrical specimens with different foliation orientations. Percent variations of the P- and S-wave velocities (Thomsen’s anisotropic parameters ε and γ) and constant dynamic modulus of test results have been determined. Percent variations of the P-wave velocity (ε) increase with an increase of the foliation angle with respect to the propagating waves direction by a parabolic function as it shows P-wave velocity differences up to a maximum value of 50 %. Thomsen’s anisotropic parameter of γ has also the same function with the foliation angle. Meanwhile, foliation orientation has a much greater influence on ε than γ for foliation angle from 45° to 90° as \( \frac{\varepsilon }{\gamma } \) ratio increases with an increase of foliation angle. Values of dynamic elastic modulus (E), Poisson’s ratio (ν), shear modulus (μ), bulk modulus (K), and Lamé’s constant (λ) increase with the increase of foliation angle with the parabolic function. The results show that dynamic elastic modulus, Poisson’s ratio, shear modulus, bulk modulus, and Lamé’s constant have anisotropic behavior in relation with the foliation orientation.     

Compressibility of Sands of Various Geologic Origins at Pre-crushing Stress Levels

This study quantifies the influence of various intrinsic soil properties including particle roundness, R, sphericity, S, 50% size by weight, D ₅₀, coefficient of uniformity, C _u, and the state property of relative density, D _r, on the compression and recompression indices, C _c and C _r, of sands of various geologic origins at pre-crushing stress levels. Twenty-four sands exhibiting a wide range of particle shapes, gradations, and geologic origins were collected for the study. The particle shapes were determined using a computational geometry algorithm which allows characterization of a statistically large number of particles in specimens. One dimensional oedometer tests were performed on the soils. The new data was augmented with many previously published results. Through statistical analyses, simple functional relationships are developed for C _c and C _r. In both cases, the models utilized only R and D _r since other intrinsic properties proved to have lesser direct influence on the compression indices. However, previous studies showed that the contributions of S and C _u are felt through their effects on index packing void ratios and thus on D _r. The accuracy of the models was confirmed by comparison of predicted and observed C _c and C _r values.     

Optimal choice of the softening length and time step in <Emphasis Type="Italic">N</Emphasis>-body simulations

A criterion for the choice of optimal softening length ε for the potential and the choice of time step dt for N-body simulations of a collisionless stellar system is analyzed. Plummer and Hernquist spheres are used as models to analyze how changes in various parameters of an initially equilibrium stable model depend on ε and dt. These dependences are used to derive a criterion for choosing ε and dt. The resulting criterion is compared to Merritt’s criterion for choosing the softening length, which is based on minimizing the mean irregular force acting on a particle with unit mass. Our criterion for choosing ε and dt indicate that ε must be a factor of 1.5–2 smaller than the mean distance between particles in the densest regions to be resolved. The time step must always be adjusted to the chosen ε (the particle must, on average, travel a distance smaller than 0.5 ε during one time step). An algorithm for solving N-body problems with adaptive variations of the softening length is discussed in connection with the task of choosing ε, but is found not to be promising.     

Determination of the thermodynamic properties of compounds in the Ag-Au-Se and Ag-Au-Te systems by the EMF method

The standard thermodynamic properties (Δ_f G°, S°, Δ_f H°) of the following synthetic minerals and compounds in the Ag-Au-Se and Ag-Au-Te systems were determined by the EMF method: β-Ag₂Se (low-temperature naumannite), α-Ag₂Se (high-temperature naumannite), Ag₃AuSe₂ (fischesserite), AuSe, Ag₅Te₃ (stützite), Ag₂ Te (hessite), and Ag₃AuTe₂ (petzite). All minerals and compounds were produced by solid-phase synthesis from elements or electrum of the given composition in evacuated ampoules made of quartz glass. The phases were verified by X-ray diffraction analysis, microscopically in reflected light, and with an electron microprobe. The absence of the ternary compound AgAuSe in the Ag-Au-Se system was confirmed by solid-phase annealing. On the basis of experimental data on the electromotive force E versus temperature, the equations E(T) were calculated, from which the temperature-dependent relationships of the Gibbs energy in the relevant reactions and the standard thermodynamic functions of compounds within the range 300–502 K were obtained.     

Coda <Emphasis Type="Italic">Q</Emphasis> in Qeshm Island,south of Iran,using aftershocks of the Qeshm earthquake of November 27, 2005

Coda wave attenuation is estimated for Qeshm Island which is located in the southeastern part of Zagros. For this purpose, the aftershocks of Qeshm earthquake in November 27, 2005, recorded within an epicentral distance less than 100 km, have been used. More than 829 earthquakes were recorded by a local temporary network consisting of 16 short period stations installed after a week after the main shock for ～10 weeks. The coda quality factor, Q _c, was estimated using the single-backscattering model in frequency bands of 0.5–24 Hz. In this research, lateral and vertical variations of coda Q in Qeshm Island are explored. In Qeshm Island, absence of significant lateral variation of coda Q is observed. To investigate the attenuation variation with depth, the coda Q value was calculated for coda time windows with different lengths (5, 10, 15, 20, 25, and 30 s). It is observed that coda Q increases with depth. However, in our study area, the rate of increase of coda Q with depth is not uniform. Beneath Qeshm Island, the rate of increase of coda Q is greater at depths less than ～40 km compared with those of larger depths. This is indicating the existence of a low attenuation anomalous structure under the ～40-km depth which may be correlated with the Moho depth in this region. The average frequency relation for this region is Q _c = 36 ± 1.2f ^{0.94 ± 0.039} at a 5 s-lapse time window length and Q _c = 110 ± 1.8f ^{0.88 ± 0.09} at a 30-s lapse time window length.