Cross-axis sensitivity of accelerographs with pendulum like transducers—mathematical model and the inverse problem

A mathematical model for a three-component accelerograph is presented that accounts for the effects of transducer misalignment and cross-axis sensitivity. The former refers to departures in the alignment of the transducer penduli (typically of the order of few degrees) from an ideal orthogonal system, and the latter to a transducer recording components of motion in directions other than its principal sensitivity axis. Transducer misalignment magnifies the effects of cross-axis sensitivity. These effects are significant only for large amplitude recordings (peak acceleration close to 1g), for example in the near-field of the 1994 Northridge, California, earthquake. The misalignment angles and the angular amplification constant can be determined by a static tilt test, performed in the field, and solving a generalized inverse problem. This paper presents an algorithm for solution of this inverse problem on a routine basis. Practical implementation of the algorithm and results for 76 instruments of the Los Angeles Strong Motion Array are presented in a separate paper. © 1998 John Wiley & Sons, Ltd.     

Velocity sensitivity in transversely isotropic media1

We consider the problem of determining and predicting how the wave speeds in particular directions for a transversely isotropic (TI) medium depend on particular combinations of the density-normalized moduli A_ij. The expressions for the q^P and q^SV velocities are known to depend on four moduli. Normally, we can only determine three independent parameters from q^P data, or two from q^SZ data, as the others have much lower sensitivity. The resolvable parameters are conveniently described by axial and off-axis parameters: for q^P rays, P_0°= A₁₁, P_90°= A₃₃ and P_45°=(A₁₁+ A₃₃)/4 + (A₁₃+2A₅₅)/2; and for q^SV rays, S_0°= S_90°=A₅₅ and S 45°= (A₁₁+ A ₃₃)/4- A₁₃/2. These parameters control the magnitude of the squared-velocities on the axes and at approximately 45°. For an arbitrary TI medium, if the medium is perturbed in a way that preserves a particular parameter, then slowness points in the associated direction and mode witl be approximately preserved in the new medium. we refer to these parameters as ‘push-pins’, i.e. if a parameter is fixed, the associated part of the slowness surface is pinned in place. Because, these five push-pins only contain four independent moduli, we can only fix at most three push-pins. Perturbing one of the other parameters inevitably perturbs the other. Numerical results illustrating the linkage between two push-pins, when three are fixed, are presented. So-called anomalous TI media occur when the roles of the q^P and q^SV waves are reversed: in some directions the faster ray has transverse polarization. That, in turn, requires anomalous velocities at the push-pins, i.e. S_0° > P_0°, S_45° > P_45° and/or S_90° > P_90° (equivalent to the usual anomalous conditions A₁₁ < A₅₅, < 0 and/or A₃₃ < A⁵⁵). In the Appendix, we confirm that anomalous sensitivities of the velocities at the five push-pins only occur in such media, although the push-pins still apply if interpreted appropriately. Truly anomalous sensitivities, in which push-pins play no role, only occur in media near the boundary between normal and anomalous.     

Synergistic effect of vegetation and air temperature changes on soil water content in alpine frost meadow soil in the permafrost region of Qinghai‐Tibet

Seasonal changes over 2 years (2004–2006) in soil moisture content (θ_v) of frozen alpine frost meadow soils of the Qinghai‐Tibet plateau permafrost region under three different levels of vegetation cover were investigated. Vegetation cover and air temperature changes had significant effects (synergistic effect) on θ_v and its distribution in the soil profile. During periods of soil freezing or thawing, the less the vegetation cover, the quicker the temperature drop or rise of soil water, and the shorter the duration of the soil water freeze–thaw response in the active soil layer. Under 30% and 65% vegetation cover the amplitude of variation in θ_v during the freezing period was 20–26% greater than that under 93% cover, while during the thawing period, it was 1·5‐ to 40·5‐fold greater. The freezing temperature of the surface soil layer, ^fT_s, was 1·6 °C lower under 30% vegetation cover than under 93% vegetation cover. Changes in vegetation cover of the alpine frost meadow affected θ_v and its distribution, as well as the relationship between θ_v and soil temperature (T_s). As vegetation cover decreased, soil water circulation in the active layer increased, and the response to temperature of the water distribution across the soil profile was heightened. The quantity of transitional soil phase water at different depths significantly increased as vegetation cover decreased. The influence of vegetation cover and soil temperature distribution led to a relatively dry soil layer in the middle of the profile (0·70–0·80 m) under high vegetation cover. Alpine meadow θ_v and its pattern of distribution in the permafrost region were the result of the synergistic effect of air temperature and vegetation cover. Copyright © 2007 John Wiley & Sons, Ltd.     

A bimodal four‐parameter lognormal linear model of soil water repellency persistence

Soil water repellency may be characterized in terms of the delayed infiltration time of a water droplet resting on the soil surface, which is, water drop penetration time (WDPT), or repellency persistence. Such repellency persistence varies nonlinearly with soil water content (θ_g), although no models have been proposed to reproduce the variation of WDPT with θ_g in soils. Dynamic factor analysis (DFA) is used to identify two common patterns of unexplained variability in a scattered dataset of WDPT versus θ_g measurements. A four‐parameter lognormal distribution was fitted to both common patterns obtained by DFA, and these were combined additively in a weighted multiple linear bimodal model. We show how such an empirical model is capable of reproducing a large variety of WDPT versus θ_g curve shapes (N = 80) both within a wide range of measured WDPTs (0–17 000 s) and for samples with organic matter content ranging from 21·7 to 80·6 g (100 g)^?1. Copyright © 2009 John Wiley & Sons, Ltd.     

Peak surface strains during strong earthquake motion

Peak amplitudes of surface strains during strong earthquake ground motion can be approximated by ε = Aν_max/β₁, where ν_max is the corresponding peak particle velocity, β₁ is the velocity of shear waves in the surface layer, and A is a site specific scaling function. In a 50 m thick layer with shear wave velocity β₁ 300 m/s, A 0·4 for the radial strain ε_rr, A 0·2 for the tangential strain ε_rθ, and A 1·0 for the vertical strain, ε_z. These results are site specific and representative of strike slip faulting and of soil in Westmoreland, in Imperial Valley, California. Similar equations can be derived for other sites with known shear wave velocity profile versus depth.     

Equations for the Estimation of Strong Ground Motions from Shallow Crustal Earthquakes Using Data from Europe and the Middle East: Horizontal Peak Ground Acceleration and Spectral Acceleration

This article presents equations for the estimation of horizontal strong ground motions caused by shallow crustal earthquakes with magnitudes M_w 5 and distance to the surface projection of the fault less than 100km. These equations were derived by weighted regression analysis, used to remove observed magnitude-dependent variance, on a set of 595 strong-motion records recorded in Europe and the Middle East. Coefficients are included to model the effect of local site effects and faulting mechanism on the observed ground motions. The equations include coefficients to model the observed magnitude-dependent decay rate. The main findings of this study are that: short-period ground motions from small and moderate magnitude earthquakes decay faster than the commonly assumed 1/r, the average effect of differing faulting mechanisms is not large and corresponds to factors between 0.8 (normal and odd) and 1.3 (thrust) with respect to strike-slip motions and that the average long-period amplification caused by soft soil deposits is about 2.6 over those on rock sites. Disappointingly the standard deviations associated with the derived equations are not significantly lower than those found in previous studies.     

Study of calibration function for surface wave magnitude of DK1 seismographs

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Ion microprobe studies of water in silicate melts. Concentration-dependent water diffusion in obsidian

The ion microprobe at Johnson Space Center has been calibrated for in situ water determinations on a 10-μm scale over the range 0.2 wt.% H₂O to 1.8, 6.8, and 3.7 wt.%, for basaltic, albitic, and rhyolitic glasses, respectively. The basalt glass calibration curve differs substantially from those of albite and rhyolite glasses, indicating a need to carefully match composition and/or melt structure between H₂O standards and unknowns.A value for the diffusivity of water as a function of concentration and time has been calculated from water diffusion profiles measured in rhyolite glasses prepared at 850°C and 700 barsP_t(H₂O) [1]. Transient diffusion into a semi-infinite medium is described by the equation:?(φ/2)?¸/?φ=?(D_w?¸/?φ)/?φ #x003B8;=1, φ=0, θ→ 0, θ→∞, wherex =distance from the cylinder edge,t =time,C₀ =initial concentration,C_s =concentration at the edge,C =concentration at x,θ = C ? C₀/C_s ? C₀,φ = x/t^1/2, andD_w =diffusivity of water. An iterative technique has been used to calculate solutions to the diffusion equation as a function ofD_w [2]. Comparison of these solutions with the ion probe data indicate that, for0.2wt.% ≤ C ≤ 3.7wt.%H₂O,D_w can be described by an exponential function of θ, of the formD_w = D₀exp(bθ), withD₀ (i.e.,D_w at 0.2%) = (0.8?2.2) × 10^?8 cm²/s and2 ≤ b ≤ 4.     

Hydraulics of runoff and loess loam deposition

On many more or less loamy soils, rill erosion is reported to start on slopes that are equal to or steeper than 2–3°; critical Froude numbers for the start of rill wash on these slopes vary between 2·0 and 3·0. This explains why colluvial deposition often occurs on slopes below 2–3°, when water spreads out at the downslope extremities of the rills. The critical hydraulic conditions for loess loam deposition were tested in the laboratory for slopes of 0·5° and 2°, applying unit-discharges (q) up to 10 cm²/s. It appeared from these experiments that for afterflow, without raindrop impact, deposition starts for critical load concentrations (c_cr) varying between several g/1 and about 60 g/l. Under rain c_cr amounts to a minimum value of 100–125 g/l and it increases when the runoff film becomes thinner. Nevertheless, deposition in pluvial runoff is also possible, as was the case during the Weichselian, according to data from quarries in Belgium and in The Netherlands. A modified Kalinske equation is proposed for c_cr prediction, with the introduction of a typical empirical coefficient C_r and considering such factors as shear stress and mean particle size. Massive sedimentation may occur when it stops raining and afterflow starts, since c_cr values are then much lower. It is shown from the Shields' diagram that loamy suspensions are more sensitive to sedimentation than sands in clear water.     

Ground motion attenuation of MS8.0 Wenchuan earthquake

The great M_S8.0 Wenchuan earthquake has been the most destructive earthquake since 1949 in China. The earthquake occurred no more than half a year after the establishment of the National Strong Motion Observation Network System (NSMONS) of China; what is more, the epicenter was located in the area with dense strong motion observation stations so that a large number of strong motion records of the main shock were obtained. In this paper, 501 strong motion records from 167 observation stations are utilized to establish the ground motion attenuation relations in three directions in the range of fault distance less than 600 km. The result shows the difference of seismic motion attenuation in two horizontal directions is insignificant. It is the first time that strong-motion records are used to establish the ground motion attenuation relations of the M_S8.0 earthquake in China.

     

TDR pressure cell for monitoring water content retention and bulk electrical conductivity curves in undisturbed soil samples

The water retention curve (θ(ψ)), which defines the relationship between soil volumetric water content (θ) and matric potential (ψ), is of paramount importance in characterizing the hydraulic behaviour of soils. However, few methods are so far available for estimating θ(ψ) in undisturbed soil samples. We present a new design of TDR‐pressure cell (TDR‐Cell) for estimating θ(ψ) in undisturbed soil samples. The TDR‐Cell consists of a 50‐mm‐long and 50‐mm internal diameter stainless steel cylinder (which constitutes the outer frame of a coaxial line) attached to a porous ceramic disc and closed at the ends with two aluminium lids. A 49‐mm‐long and 3‐mm‐diameter stainless steel rod, which runs longitudinally through the centre of the cylinder, constitutes the inner rod of a coaxial TDR probe. The TDR‐Cell was used to determine the θ(ψ) curves of a packed sand and seven undisturbed soil samples from three profiles of agricultural soils. These θ(ψ) curves were subsequently compared to those obtained from the corresponding 2‐mm sieved soils using the pressure plate method. Measurements of bulk electrical conductivity, σ_a, as a function of the water content, σ_a(θ), of the undisturbed soil samples were also performed. An excellent correlation (R² = 0·988) was found between the θ values measured by TDR on the different undisturbed soils and the corresponding θ obtained from the soil gravimetric water content. A typical bimodal θ(ψ) function was found for most of the undisturbed soil samples. Comparison between the θ(ψ) curves measured with the TDR‐Cell and those obtained from the 2‐mm sieved soils showed that the pressure plate method overestimates θ at low ψ values. The σ_a(θ) relationship was well described by a simple power expression (R² > 0·95), in which the power factor, defined as tortuosity, ranged between 1·18 and 3·75. Copyright © 2011 John Wiley & Sons, Ltd.     

Source parameters of bohai earthquake, July 18, 1969 and yongshan earthquake, May 11, 1974 determined by synthetic seismograms of teleseismic P waves

The source parameters of the Bohai Sea earthquake, July 18, 1969 and Yongshan, Yunnan earthquake, May 11, 1974 were determined by full — wave theory synthetic seismograms of teleseismic P waves. P+pP+sP wereform were calculated with WKBJ approximation and real integral paths. One — dimensional unilateral, finite propagation source was also considered. By trail — and — error in comparing the theoretical seismograms with the observational ones of WWSSN stations, the source parameters were obtained as follow: for Bohai earthquake, φ=195°, δ=85°, λ=65°,M _o=0.9×10¹⁹Nm,L=59.9km.V _R=3.5km/s, ∧ _R =160°; for Yongshan earthquake, φ=240°, δ=80°, ∧=150°,M _o=1.3×10¹⁸Nm,L=48.8km,V _R=3km/s, ∧ _R =−10°, where φ is strike, δ dip angle, λ slip angle,M _o seismic moment,L rupture length,V _R rupture propagation speed. As III type fractures the faulting propagated along the fault planes, and ∧ _R is the angle from the strike to the propagation direction. Yongshan earthquake showed complexity in its focal process, having four sub—ruptures during the first 60 seconds. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 1–8, 1991.     

Estimate of seasonal changes in the intensity of the infrared atmospheric system of molecular oxygen

On the basis of measurements of the intensity of 1.58-μm emissions of the Infrared Atmospheric System of molecular oxygen (IRAO₂) conducted at the Zvenigorod scientific station of the Institute of Atmospheric Physics of the Russian Academy of Sciences (φ = 55.7°N, λ = 36.8°E), seasonal variations are estimated for various solar zenith angles. Their amplitude has the maximum value at the solar zenith angles χ _S ∼ 105–110°. It decreases at χ _S ∼ 125–130° and tends to zero at χ _S ∼ 80–85°. The comparison of currently measured values of the 1.58-μm emission intensity of the Infrared Atmospheric System of molecular oxygen with published data on the intensity of this emission obtained in 1961–1966 reveals their decrease over approximately 50 years. This fact is in good agreement with similar behavior of the emission intensity of atomic oxygen (557.7 nm) over the period considered.     

Large scale characteristic distance between strong earthquake

ＬａｒｇｅｓｃａｌｅｃｈａｒａｃｔｅｒｉｓｔｉｃｄｉｓｔａｎｃｅｂｅｔｗｅｎｓｔｒｏｎｇｅａｒｔｈｑｕａｋｅＸＩＡＮＦＵＤＵ（杜先富）ＳＨＡＯＸＩＥＸＵ（许绍燮）ＩｎｓｔｉｔｕｔｅｏｆＧｅｏｐｈｙｓｉｃｓ，ＳｔａｔｅＳｅｉｓｍｏｌｏｇｉｃａｌＢ...     

A model for attenuation and scattering in the Earth's crust

The mechanisms contributing to the attenuation of earthquake ground motion in the distance range of 10 to 200 km are studied with the aid of laboratory data, coda wavesRg attenuation, strong motion attenuation measurements in the northeast United States and Canada, and theoretical models. The frequency range 1–10 Hz has been studied. The relative contributions to attenuation of anelasticity of crustal rocks (constantQ), fluid flow and scattering are evaluated. Scattering is found to be strong with an albedoB ₀=0.8–0.9 and a scattering extinction length of 17–32 km. The albedo is defined as the ratio of the total extinction length to the scattering extinction length. TheRg results indicate thatQ increases with depth in the upper kilometer or two of the crust, at least in New England. CodaQ appears to be equivalent to intrinsic (anelastic)Q and indicates that thisQ increases with frequency asQ=Q _o f ⁿ , wheren is in the range of 0.2–0.9. The intrinsic attenuation in the crust can be explained by a high constantQ (500Q _o2000) and a frequency dependent mechanism most likely due to fluid effects in rocks and cracks. A fluid-flow attenuation model gives a frequency dependence (QQ _o f ^0.5) similar to those determined from the analysis of coda waves of regional seismograms.Q is low near the surface and high in the body of the crust.     

A discussion on the amplitude ratios of PP and P waves for earthquakes with different focal mechanisms

Using the WKBJ approximation method we calculate the synthetic teleseismograms of P and PP waves to match the observed ones of six large Chinese earthquakes with known focal mechanisms: Tibet earthquake of July 14, 1973; Haicheng earthquake of February 4, 1975; Songpan earthquakes of August 16, 1976, August 21, 1976 and August 23, 1976 and Nignhe earthquake of November 15, 1976. The focal mechanism of the Tibet earthquake is discussed to examine the technique used in the calculation. We note that the amplitude ratios of PP and P waves (A _PP/A _P) have different characteristics for dip—slip events and strike—slip events within certain epicentral distances. We calculate the synthetic teleseismograms of P and PP waves for the strike—slip and dip—slip events with fault angles of 330°, 240° and 0°, focal depths of 8 km, 17 km and 24 km, at the assumed station with an azimuth of 310° and epicentral distances from 40°; to 80°. The diagrams of maximum amplitude ratios of PP and P waves (A _PP/A _P) versus distances are given. The possibility to use the (A _PP/A _P) values to give an approximate estimation for the focal mechanism type is discussed. This work may be useful for determining the focal mechanism type for those earthquakes which have only few records such as the Chinese earthquakes from the 1930s to 1960s. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 150–160, 1991.     

Seismicity anomalies before the great earth—quake of Ms=8.1 in the Kunlun Pass and its significance to earthquake prediction

A great earthquake of M _S=8.1 took place in the west of Kunlun Pass on November 14, 2001. The epicenter is located at 36.2°N and 90.9°E. The analysis shows that some main precursory seismic patterns appear before the great earthquake, e.g., seismic gap, seismic band, increased activity, seismicity quiet and swarm activity. The evolution of the seismic patterns before the earthquake of M _S=8.1 exhibits a course very similar to that found for earthquake cases with M _S≥7. The difference is that anomalous seismicity before the earthquake of M _S=8.1 involves in the larger area coverage and higher seismic magnitude. This provides an evidence for recognizing precursor and forecasting of very large earthquake. Finally, we review the rough prediction of the great earthquake and discuss some problems related to the prediction of great earthquakes.     

Moment tensor inversion and source rupture process of the September 27, 2003 M S=7.9 earthquake occurred in the border area of China, Russia and Mongolia

We conducted moment tensor inversion and studied source rupture process for M _S=7.9 earthquake occurred in the border area of China, Russia and Mongolia on September 27 2003, by using digital teleseismic P-wave seismograms recorded by long-period seismograph stations of the global seismic network. Considering the aftershock distribution and the tectonic settings around the epicentral area, we propose that the M _S=7.9 earthquake occurred on a fault plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of M _S=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tensor is M ₀=0.97×10²⁰ N·m. Rupture mainly occurred on the shallow area with 110 km long and 30 km wide, the location in which the rupture initiated is not where the main rupture took place, and the area with slip greater than 0.5 m basically lies within 35 km deep middle-crust under the earth surface. The maximum static slip is 3.6 m. There are two distinct areas with slip larger than 2.0 m. We noticed that when the rupture propagated towards northwest and closed to the area around the M _S=7.3 hypocenter, the slip decreased rapidly, which may indicate that the rupture process was stopped by barriers. The consistence of spatial distribution of slip on the fault plane with the distribution of aftershocks also supports that the rupture is a heterogeneous process owing to the presence of barriers.     

Hazard mapping of normalized peak strain in soils during earthquakes: microzonation of a metropolitan area

Seismic hazard maps of the Los Angeles metropolitan area are illustrated for normalized peak strain and for 50 years of exposure. The strain estimates are based on scaling in terms of peak ground velocity. The proportionality factor is the phase velocity with which the wave energy is propagating. A simplified seismicity model is used in which all earthquakes occur on faults represented by buried lines and in one zone of diffused seismicity. Poissonian model of earthquake occurrence is assumed. The same model was used in the 1980's to illustrate a method for microzoning of the same area for response spectral amplitudes. Maps of logarithms of normalized peak strain, cε_max, are presented for probabilities of at least one exceedance p = 0·99, 0·9, 0·5, 0·1 and 0·01. These can be used to construct site specific probability distribution functions of the normalized peak strain, cε_max. Such maps are useful for design of new and for retrofit of existing structures, sensitive to strain and differential ground motions (bridges, tunnels, pipelines, etc.).     

Distribution of ionospheric O<Superscript>+</Superscript> ion in synchronous altitude region

Based on satellite observation data, using dynamics equation, the ionospheric O⁺ ion’s distribution in the synchronous altitude region for different geomagnetic activity indexK _p is studied by theoretical modeling and numerical analyzing, and semi-empirical models for the O⁺ ion’s density and flux versus longitude in the synchronous altitude region for differentK _p are given. The main results show that in the synchronous altitude region: (i) The O⁺ ion’s density and flux in day-side are larger than those in nightside. (ii) With longitude changing, the higher the geomagnetic activity indexK _p is, the higher the O⁺ ion’s density and flux, and their variation amplitude will be. The O⁺ ion’s density and flux whenK _{p ≥} 6 will be about ten times as great as that whenK _p = 0. (iii) WhenK _p = 0 orK _{p ≥} 6, the O⁺ ion’s density reaches maximum at longitudes 120° and 240° respectively, and minimum in the magnetotail. WhenK _p = 3−5, the O⁺ ion’s density gets to maximum at longitude 0°, and minimum in the magnetotail. However, the O⁺ ion’s flux reaches maximum at longitude 120° and 240° respectively, and minimum in the magnetotail for anyK _p value.