Development of faults as zones of deformation bands and as slip surfaces in sandstone

Three forms of fault are recognized in Entrada and Navajo Sandstones in the San Rafael Desert, southeastern Utah; deformation bands, zones of deformation bands, and slip surfaces. Small faults occur asdeformation bands, about one millimeter thick, in which pores collapse and sand grains fracture, and along which there are shear displacements on the order of a few millimeters or centimeters. Two or more deformation bands adjacent to each other, which share the same average strike and dip, form azone of deformation bands. A zone becomes thicker by addition of new bands, side by side. Displacement across a zone is the sum of displacements on each individual band. The thickest zones are about 0.5 m and total displacement across a thick zone rarely exceeds 30 cm. Finally,slip surfaces, which are through-going surfaces of discontinuity in displacement, form at either edge of zones of highly concentrated deformation bands. In contrast with individual deformation bands and zones of deformation bands, slip surfaces accommodate large displacements, on the order of several meters in the San Rafael Desert.The sequence of development is from individual deformation bands, to zones, to slip surfaces, and each type of faulting apparently is controlled by somewhat different processes. The formation of zones apparently involves strain hardening, whereas the formation of slip surfaces probably involves strain softening of crushed sandstone.     

Several effects of a baroclinic current on the cross‐stream propagation of inertial‐internal waves†

Several effects of a baroclinic current on inertial‐internal waves at constant frequency are investigated, primarily through use of the method of characteristics. The special case of waves propagating transverse to a baroclinic current is considered. When the slope of an isopycnal is of the same order of magnitude as the slope of the characteristics, appreciable asymmetries are induced in the characteristics, the phase and group velocities, and the solution itself. These asymmetric effects are especially significant for waves at the low frequency end of the passband for free waves. Also, modifications occur to the passband, resulting in anomalously high and low frequency bands. The effective local inertial frequency, σ_f = [f(f+v_x )]^1/2, separates the normal and anomalously low frequency bands. Hence, the low frequency limit of the normal frequency band increases or decreases depending upon whether the horizontal shear in the mean flow is cyclonic or anticyclonic. In the anomalous frequency bands, the slopes of both characteristics have the same sign, causing various refraction and reflection phenomena. If the absolute value of the slope, s, of an isopycnal exceeds its critical value, s_c = effective local inertial frequency/Väisälä‐Brunt frequency, the anomalously low frequency band extends to imaginary frequencies. If s ? 0, the reflection of waves from a boundary is modified, the effective wavelength is increased, and the lines of constant phase are tilted from the vertical. For the general solution, discontinuities in the first‐order partial derivatives of the velocity field occur across certain characteristics. The nonseparable normal modes do not exhibit these discontinuous derivatives, but they only satisfy one of the two pairs of kinematic boundary conditions in rectangular regions.     

Measurement of long waves at the harbor of Marina di Carrara,Italy

This paper presents the analysis of measurements of long waves at the harbor of Marina di Carrara, Italy. Nine pressure gauges (eight in the inner harbor and one outside the harbor) were used to record continuously the water surface elevation, for about 3 years; incoming short waves were measured using a directional buoy at about 500 m offshore the breakwaters. The analysis is carried out splitting the energy of the long waves into two bands, i.e., very long waves (VLW; f < 0.003 Hz) and long waves (LW; 0.003 < f < 0.030 Hz); it is found that LW energy is strongly correlated with the energy of the incoming short waves while no correlation (or very poor) is found for VLW. During energetic sea states, surface elevation spectra of VLW and LW, normalized against the wave energy of each frequency band, appear to be autosimilar; this suggests that the spectra of the incoming long waves have a mostly constant shape. Simple numerical computations of harbor resonance, carried out using a mild-slope equation linearized model, indicate that the amplification of the height of the incoming LW generated by short waves (calculated using empirical formulae from previous researches by Melito et al. 2007) inside the harbor can be reasonably predicted using such simple approach, assuming that the LW spectra are rectangular. The shape of the amplification diagram calculated by the numerical model shows reasonable (but not perfect) agreement with the shape of the normalized measured spectra inside the harbor.     

Channels for melt transport in the mantle: Numerical simulation of the formation conditions

Cracking of viscoplastic material, which cools down in the conditions of plane strain, and formation of channels through which melt is transported in the heated mantle are studied by numerical simulation. The pattern of deformations in the cooling mantle suggests that bifurcation of the deformation process leads to the formation of zones characterized by rather strong decompaction, in which plastic deformations are localized. The orientation of the zones is controlled by the preceding strain state, which binds them to the direction of the maximum initial compression. Heating and partial melting of the mantle masses perturb the stress state and also lead to the formation of the localization zones. These weakened zones may act as the channels for melt filtration in the mantle.     

Low frequency 1/f-like fluctuations of the AE-index as a possible manifestation of self-organized criticality in the magnetosphere

Low frequency stochastic variations of the geomagnetic AE-index characterized by 1/f^b-like power spectrum (where f is a frequency) are studied. Based on the analysis of experimental data we show that the B_z-component of IMF, velocity of solar wind plasma, and the coupling function of Akasofu are insufficient factors to explain these behaviors of the AE-index together with the 1/f^b fluctuations of geomagnetic intensity. The effect of self-organized criticality (SOC) is proposed as an internal mechanism to generate 1/f^b fluctuations in the magnetosphere. It is suggested that localized spatially current instabilities, developing in the magnetospheric tail at the initial substorm phase can be considered as SOC avalanches or dynamic clusters, superposition of which leads to the 1/f^b fluctuations of macroscopic characteristics in the system. Using the sandpile model of SOC, we undertake numerical modeling of space-localized and global disturbances of magnetospheric current layer. Qualitative conformity between the disturbed dynamics of self-organized critical state of the model and the main phases of real magnetospheric substorm development is demonstrated. It is also shown that power spectrum of sandpile model fluctuations controlled by real solar wind parameters reproduces all distinctive spectral features of the AE fluctuations.     

Elastic anisotropy due to aligned cracks in porous rock1

All theoretical expressions which relate the characteristics of saturated aligned cracks to the associated elastic anisotropy are restricted in some important way, for example to the case of stiff pore fluids, or of the absence of equant porosity, or of a moderately high frequency band. Because of these restrictions, previous theory is not suitable for application to the upper crust, where the pore fluid is brine (K_f? K₈20), the equant porosity is often substantial (φ_p > 0.1), and the frequency band is sonic to seismic. This work removes these particular restrictions, recognizing in the process an important mechanism of dispersion. A notable feature of these more general expressions is their insensitivity, at low frequency, to the aspect ratio of the cracks; only the crack density is critical. An important conclusion of this more general model is that many insights previously achieved, concerning the shear-wave splitting due to vertical aligned saturated cracks, are sustained. However, conclusions on crack orientation or crack aspect ratio, which were derived from P-wave data or from shear-wave‘critical angles’, may need to be reconsidered. Further, the non-linear coupling between pores and cracks, due to pressure equalization effects, means that the (linear) Schoenberg-Muir calculus may not be applied to such systems. The theory receives strong support from recent data by Rathore et al. on artificial samples with controlled crack geometry.     

Spectral energy contributions of quasi-periodic oscillations (2–35 days) to the variability of the f oF2

The relative contributions of quasi-periodic oscillations from 2 to 35 days to the variability of f_oF2 at middle northern latitudes between 42°N and 60°N are investigated. The f_oF2 hourly data for the whole solar cycle 21 (1976–1986) for four European ionospheric stations Rome (41.9°N, 12.5°E), Poitiers (46.5°N, 0.3°E), Kaliningrad (54.7°N, 20.6°E) and Uppsala (59.8°N, 17.6°E) are used for analysis. The relative contributions of different periodic bands due to planetary wave activity and solar flux variations are evaluated by integrated percent contributions of spectral energy for these bands. The observations suggest that a clearly expressed seasonal variation of percent contributions exists with maximum at summer solstice and minimum at winter solstice for all periodic bands. The contributions for summer increase when the latitude increases. The contributions are modulated by the solar cycle and simultaneously influenced by the long-term geomagnetic activity variations. The greater percentage of spectral energy between 2 to 35 days is contributed by the periodic bands related to the middle atmosphere planetary wave activity.     

Modified seismic design of concentrically braced frames considering flexural demand on columns

Special concentrically braced frames (SCBFs) are considered as one of the most economical and effective lateral force‐resisting systems in structures located in the regions of high seismicity. Steel braces in a braced frame undergo large axial deformations in tension and compression to dissipate the seismic energy. However, past studies have shown that SCBFs exhibit the soft‐story hinge mechanisms and unpredictable failure patterns under earthquake loading conditions. These inelastic responses along with the use of continuous structural sections as columns over consecutive floors induce flexural demand that is not considered in the current design practice. In this study, the evaluation of seismic performance of nine SCBFs designed as per the current practice has been carried out for three different story heights (i.e., three‐story, six‐story, and nine‐story) and three types of brace configurations (namely, chevron, split X, and single X). Three additional design techniques are also explored based on (i) the inclusion of column moments in the design; (ii) the theory of formation of plastic hinges; and (iii) the design of braces considering the forces computed at their post‐buckled stages. Nonlinear dynamic analyses of these study frames have been evaluated numerically using a computer software Perform‐3D for a suite of 40 ground motions representing the design basis earthquake and maximum considered earthquake hazard levels. Analyses results showed that the SCBFs designed as per the modified procedures achieved the desired performance objectives without the formation of soft‐story mechanism. Copyright © 2017 John Wiley & Sons, Ltd.     

Coordinated Simultaneous Freja Satellite and Niemegk Observatory ULF Measurements

The standard FFT analysis was applied to thirteen pulsation events selected from the March–April 1993 simultaneous measurements in space (Freja satellite) and on the ground (Niemegk Observatory). The spectral processing of the six-minute sections of record in two coordinate components perpendicular to the magnetic field lines had two principal subjects in view: a) Frequency-amplitude satellite-ground relations. The average values of smoothed spectral amplitude transmission coefficients in the total Pc4-3 and, separately, in Pc4 and Pc3 bands were 0.60, 0.48 and 0.70, respectively. The maximum values were observed within the Pc3 band, near f 30 mHz. b) Estimation of frequency bands of field line resonances (FLRs) recorded on Freja. Freja's motion in a broad latitude range (±5° around Niemegk) during the measurements enabled two frequency bands of FLRs with a width of 10's of mHz to be identified on Freja. The weighted frequencies of the FLRs bands on Freja were f _wA 36 mHz and f _wB 18 mHz with fine structure separations of about 5 mHz and 4 mHz, respectively. The second band with f _wB 18 mHz was mostly not observed at Niemegk, and this could be the consequence of the satellite moving partly through regions of L greater than that of Niemegk.     

Mechanisms to limit higher mode effects in a controlled rocking steel frame. 1: Concept,modelling, and low‐amplitude shake table testing

Controlled rocking steel frames have been proposed as an efficient way to avoid the structural damage and residual deformations that are expected in conventional seismic force resisting systems. Although the base rocking response is intended to limit the force demands, higher mode effects can amplify member design forces, reducing the viability of the system. This paper suggests that seismic forces may be limited more effectively by providing multiple force‐limiting mechanisms. Two techniques are proposed: detailing one or more rocking joints above the base rocking joint and providing a self‐centring energy dissipative (SCED) brace at one or more levels. These concepts are applied to the design of an eight‐storey prototype structure and a shake table model at 30% scale. A simple numerical model that was used as a design tool is in good agreement with frequency characterization and low‐amplitude seismic tests of the shake table model, particularly when multiple force‐limiting mechanisms are active. These results suggest that the proposed mechanisms can enable better capacity design by reducing the variability of peak seismic force demands without causing excessive displacements. Similar results are expected for other systems that rely on a single location of concentrated nonlinearity to limit peak seismic loads. Copyright © 2012 John Wiley & Sons, Ltd.     

Characterization of volcanic thermal anomalies by means of sub-pixel temperature distribution analysis

The simultaneous solution of the Planck equation (involving the widely used “dual-band” technique) using two shortwave infrared (SWIR) bands allows for an estimate of the fractional area of the hottest part of an active lava flow (f _h) and the background temperature of the cooler crust (T _c). The use of a high spectral and spatial resolution imaging spectrometer with a wide dynamic range of 15 bits (DAIS 7915) in the wavelength range from 0.501 to 12.67 μm resulted in the identification of crustal temperature and fractional areas for an intra-crater hot spot at Mount Etna, Italy. This study indicates the existence of a relationship between these T _c and f _h extracted from DAIS and Landsat TM data. When the dual band equation system is performed on a lava flow, a logarithmic distribution is obtained from a plot of the fractional area of the hottest temperature vs. the temperature of the cooler crust. An entirely different distribution is obtained over active degassing vents, where increases in T _c occur without any increase in f _h. This result indicates that we can use scatter plots of T _c vs. fh to discriminate between different types of volcanic activity, in this case between degassing vents and lava flows, using satellite thermal data.     

Frequency band of mirroring and bands of increased transmissivity of ULF waves through the ionosphere

Summary Using methods of numerical modelling of the propagation of ULF waves through the ionosphere, the characteristics of the vertical flux of electromagnetic energy are analysed in the ULF range — at the outer boundary of the modelled ionosphere (altitude 1000 km) the reflexibility and penetrability of the energy, at the Earth's surface the transmissivity of the energy. The existence of two frequency bands is proved within the ULF range with different forms of ionospheric wave filtration: a) The band of extremely low frequencies, f<0.1–0.2 Hz (pc3–5 and Pc2 pulsation ranges) with a mirroring effect of the ionosphere-Earth system, but with small absorption; b) the band f>0.2 Hz (the Pc1 range) with increased absorption, but with resonance windows and wave emissions with a very well defined frequency structure.     

Energy of acoustic signals in a borehole

In the present article, the dependencies of the acoustic signal total energy and the energies of the wave packets of different types of the waves on the elastic parameters and permeability of rocks have been studied. We have considered traditional logging tools containing acoustical monopole source. Calculations were performed in a frequency range of dozens of kilohertz, typical for acoustic well logging. It was shown that in a typical high-velocity formation (v_s > v_f, where v_s and v_f are the velocities of the shear wave in the rock and of the compressional wave in the borehole fluid, respectively), the pseudo-Rayleigh waves, whose elastic properties depend mainly on the shear modulus of the rock, contributed significant energy to the total signal energy in the borehole. The energies of different wave packets depend on the permeability in different ways. The greatest sensitivity to permeability change has been shown by the acoustic signal total energy and the energy of the low-velocity part of the pseudo-Rayleigh wave packet. The theoretical analysis was illustrated by real sonic log data.     

Failure Mode and Spatial Distribution of Damage in Rothbach Sandstone in the Brittle-ductile Transition

— To elucidate the spatial complexity of damage and evolution of localized failure in the transitional regime from brittle faulting to cataclastic ductile flow in a porous sandstone, we performed a series of triaxial compression experiments on Rothbach sandstone (20% porosity). Quantitative microstructural analysis and X-ray computed tomography (CT) imaging were conducted on deformed samples. Localized failure was observed in samples at effective pressures ranging from 5 MPa to 130 MPa. In the brittle faulting regime, dilating shear bands were observed. The CT images and stereological measurements reveal the geometric complexity and spatial heterogeneity of damage in the failed samples. In the transitional regime (at effective pressures between 45 MPa and 130 MPa), compacting shear bands at high angles and compaction bands perpendicular to the maximum compression direction were observed. The laboratory results suggest that these complex localized features can be pervasive in sandstone formations, not just limited to the very porous aeolian sandstone in which they were first documented. The microstructural observations are in qualitative agreement with theoretical predictions of bifurcation analyses, except for the occurrence of compaction bands in the sample deformed at effective pressure of 130 MPa. The bifurcation analysis with the constitutive model used in this paper is nonadequate to predict compaction band formation, may be due to the neglect of bedding anisotropy of the rock and multiple yield mechanisms in the constitutive model.     

Dependence of the energy released during earthquake on ambient shear stress

Starting with dislocation model, using the result of the fracture mechanics: the slip displacement at the crack tip is proportional to the length of the crack and the applied ambient shear stressτ ₀ ² , we consider the dislocation in the earthquake to be the slip displacement at the crack tip and have obtained the analysis expresses of displacement and velocity pulse for the circular crack and have calculated the seismic wave energy radiated by earthquake. The seismic wave energyE ∞M ₀ τ ₀ ² f(v) _r , i. e.E is proportional to the seismic momentM ₀ and the square of the ambient shear stressτ ₀ ² and increases with the rupture velocityv _r . In frequency domain, integrating the square of source velocity spectrum derived from our the scaling law model, we have also obtained the seismic wave energyE released by earthquake and earthquake radiated effficiencyη.E ∞M ₀ τ ₀ ² also. If takingτ ₀ = 10.0 MPa, E=4.79M ₀. This result is consistent with the estimate by Vassiliou and Kanamori (1982). Theη=5.26%. The distribution of the seismic wave energy is that most of the energy contains in the frequency range between the first corner frequencyf _c1 and thirdf _c3, amount to 92.3% the energy in the rangef<f _c1 is about 3.85% and 3.85% whenf>f _c3. Thef _c3 is about 8Hz forM ⩾ 6, thus most of radiated energy is below 2Hz. This phenomenon had been verified by Vassiliou Kanamori. Previous results show the energy radiated by earthquake to be strongly dependent on ambient shear stress. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 146–152, 1993. This work was supported by the Deutsche Forschungsgemeinschaft, Bonn, F. R. Germany. The support is grateful acknowledged. The authors are also grateful to Professor Klussmann and Mr. Hasthoff for their lots of help.     

Ground-Motion Scaling in the Western Alps

In order to empirically obtain the scaling relationships for the high-frequency ground motion in the Western Alps (NW Italy), regressions are carried out on more than 7500 seismograms from 957 regional earthquakes. The waveforms were selected from the database of 6 three-component stations of the RSNI (Regional Seismic network of Northwestern Italy). The events, M _W ranging between 1.2 and 4.8, were recorded within a hypocentral distance of 200 km during the time period: 1996–2001. The peak ground velocities are measured in selected narrow-frequency bands, between 0.5 and 14 Hz. Results are presented in terms of a regional attenuation function for the vertical ground motion, a set of vertical excitation terms at the reference station STV2 (hard-rock), and a set of site terms (vertical and horizontal), all relative to the vertical component of station STV2.The regional propagation of the ground motion is modeled after quantifying the expected duration of the seismic motion as a function of frequency and hypocentral distance. A simple functional form is used to take into account both the geometrical and the anelastic attenuation: a multi-variable grid search yielded a quality factor Q(f) = 310f ^0.20, together with a quadri-linear geometrical spreading at low frequency. A simpler, bi-linear geometrical spreading seems to be more appropriate at higher frequencies (f > 1.0 Hz). Excitation terms are matched by using a Brune spectral model with variable, magnitude-dependent stress drop: at M _w 4.8, we used Δσ = 50 MPa. A regional distance-independent attenuation parameter is obtained (κ₀ = 0.012 s) by modelling the average spectral decay at high frequency of small earthquakes.In order to predict the absolute levels of ground shaking in the region, the excitation/attenuation model is used through the Random Vibration Theory (RVT) with a stochastic point-source model. The expected peak-ground accelerations (PGA) are compared with the ones derived by Ambraseys et al. (1996) for the Mediterranean region and by Sabetta and Pugliese (1996) for the Italian territory.     

Estimation of frequency dependent coda wave attenuation structure at the vicinity of Cairo Metropolitan Area

Estimation of seismic wave attenuation in the shallow crust in terms of coda wave Q structure previously investigated in the vicinity of Cairo Metropolitan Area was improved using seismograms of local earthquakes recorded by the Egyptian National Seismic Network. The seismic wave attenuation was measured from the time decay of coda wave amplitudes on narrow bandpass filtered seismograms based on the single scattering theory. The frequency bands of interest are from 1.5 to 18 Hz. In general, the values obtained for various events recorded at El-Fayoum and Wadi Hagul stations are very similar for all frequency bands. A regional attenuation law Q _c = 85.66 f ^0.79 was obtained.     

Frequency‐space wavefield extrapolation using infinite impulse response digital filters: is it feasible?

The purpose of this paper is to study the possibility of performing practically stable and efficient frequency‐space (f?x) wavefield extrapolation for the application of seismic imaging and datuming via infinite impulse response (IIR) filters. The model reduction control theory was adopted to design such IIR f?x extrapolation filters. The model reduction theory reduces the order of a given order system which, in this case, involves reducing a finite impulse response (FIR) f?x extrapolation filter system into an IIR f?x extrapolation filter system. This theory relies on decomposing the states of the given filter system into strong and weakly coupled sub‐systems, and then eliminating the weakly coupled states via singular value decomposition of the Hankel and the impulse response Gramian matrices. Simulation results indicate that IIR f?x filters can be obtained, which are stable from an IIR filter design point of view. Simulations also indicate that stable seismic impulse responses and synthetics can be obtained with a reduced system model order and, hence, less computational efforts with respect to the number of complex multiplications and additions per output sample. It is hoped that this study will open new possibilities for researchers to reconsider designing IIR f?x explicit depth extrapolation filters due to their expected computational savings and wavenumber response accuracy, when compared to the FIR f?x explicit depth extrapolation filters.     

Persistence of Planetary Waves in the Lower Ionosphere

The transient planetary waves in the atmosphere and ionosphere seem to occur in the form of bursts of a couple of waves with limited persistence. To study persistence of planetary wave events in the lower ionosphere, data from two radio paths from Central Europe are used, Luxembourg – Panská Ves (f = 6.09 MHz, f _eq = 2.1-2.2 MHz) and Deutschlandfunk – Panská Ves (f = 1539 kHz, f _eq = 650-700 kHz). The absorption along the former radio paths is formed very predominantly at altitudes of about 90-100 km, whereas the latter absorption is formed mostly at altitudes of about 85-90 km. The persistence of planetary wave type oscillations is studied in three period bands centred at 5, 10 and 16 days. Waves with period T near 5 days reveal a typical persistence of wave events around 5 cycles. Waves with T = 10 days are less persistent with a typical persistence of 3-4 cycles. The typical persistence of waves T = 16 days is no more than 3 cycles. In terms of number of cycles, the persistence of oscillations evidently decreases with increasing period. On the other hand, in terms of number of days, the persistence seems rather to increase with increasing period.