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1.
Abstract

A linear analysis is used to study the stability of a rapidly rotating, electrically-conducting, self-gravitating fluid sphere of radius r 0, containing a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance from the rotation axis. The Lorentz force is of a magnitude comparable with that of the Coriolis force and so convective motions are fully three-dimensional, filling the entire sphere. We are primarily interested in the limit where the ratio q of the thermal diffusivity κ to the magnetic diffusivity η is much smaller than unity since this is possibly of the greatest geophysical relevance.

Thermal convection sets in when the temperature gradient exceeds some critical value as measured by the modified Rayleigh number Rc. The critical temperature gradient is smallest (Rc reaches a minimum) when the magnetic field strength parameter Λ ? 1. [Rc and Λ are defined in (2.3).] The instability takes the form of a very slow wave with frequency of order κ/r 2 0 and its direction of propagation changes from eastward to westward as Λ increases through Λ c ? 4.

When the fluid is sufficiently stably stratified and when Λ > Λm ? 22 a new mode of instability sets in. It is magnetically driven but requires some stratification before the energy stored in the magnetic field can be released. The instability takes the form of an eastward propagating wave with azimuthal wavenumber m = 1.  相似文献   

2.
Tsunami generated by submarine slumps and slides are investigated in the near-field, using simple source models, which consider the effects of source finiteness and directivity. Five simple two-dimensional kinematic models of submarine slumps and slides are described mathematically as combinations of spreading constant or slopping uplift functions. Tsunami waveforms for these models are computed using linearized shallow water theory for constant water depth and transform method of solution (Laplace in time and Fourier in space). Results for tsunami waveforms and tsunami peak amplitudes are presented for selected model parameters, for a time window of the order of the source duration.The results show that, at the time when the source process is completed, for slides that spread rapidly (cR/cT≥20, where cR is the velocity of predominant spreading), the displacement of the free water surface above the source resembles the displacement of the ocean floor. As the velocity of spreading approaches the long wavelength tsunami velocity the tsunami waveform has progressively larger amplitude, and higher frequency content, in the direction of slide spreading. These large amplitudes are caused by wave focusing. For velocities of spreading smaller than the tsunami long wavelength velocity, the tsunami amplitudes in the direction of source propagation become small, but the high frequency (short) waves continue to be present. The large amplification for cR/cT1 is a near-field phenomenon, and at distances greater than several times the source dimension, the large amplitude and short wavelength pulse becomes dispersed.A comparison of peak tsunami amplitudes for five models plotted versus L/h (where L is characteristic length of the slide and h is the water depth) shows that for similar slide dimensions the peak tsunami amplitude is essentially model independent.  相似文献   

3.
Abstract

Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height zc. The height zc , where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above zc. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to values inferred from radar measurements of the stratosphere.

The Fourier spectrum of the solution for z ≫ zc is shown to decay exponentially at large vertical wave numbers n. In comparison, a spectral decay law n ?-8/3 characterizes the marginal state of the wave at z = zc .  相似文献   

4.
Currently, numerical simulations of seismic channel waves for the advance detection of geological structures in coal mine roadways focus mainly on modeling twodimensional wave fields and therefore cannot accurately simulate three-dimensional (3-D) full-wave fields or seismic records in a full-space observation system. In this study, we use the first-order velocity–stress staggered-grid finite difference algorithm to simulate 3-D full-wave fields with P-wave sources in front of coal mine roadways. We determine the three components of velocity Vx, Vy, and Vz for the same node in 3-D staggered-grid finite difference models by calculating the average value of Vy, and Vz of the nodes around the same node. We ascertain the wave patterns and their propagation characteristics in both symmetrical and asymmetric coal mine roadway models. Our simulation results indicate that the Rayleigh channel wave is stronger than the Love channel wave in front of the roadway face. The reflected Rayleigh waves from the roadway face are concentrated in the coal seam, release less energy to the roof and floor, and propagate for a longer distance. There are surface waves and refraction head waves around the roadway. In the seismic records, the Rayleigh wave energy is stronger than that of the Love channel wave along coal walls of the roadway, and the interference of the head waves and surface waves with the Rayleigh channel wave is weaker than with the Love channel wave. It is thus difficult to identify the Love channel wave in the seismic records. Increasing the depth of the receivers in the coal walls can effectively weaken the interference of surface waves with the Rayleigh channel wave, but cannot weaken the interference of surface waves with the Love channel wave. Our research results also suggest that the Love channel wave, which is often used to detect geological structures in coal mine stopes, is not suitable for detecting geological structures in front of coal mine roadways. Instead, the Rayleigh channel wave can be used for the advance detection of geological structures in coal mine roadways.  相似文献   

5.
Rossby wave propagation in the presence of a nonseparable Brunt-Väisälä frequency,N(y,z), and the associated geostrophic zonal flow,U(y,z), is examined in this paper. The usual quasi-geostrophic potential vorticity equation only includes vertical variations in Brunt-Väisälä frequency (i.e.N(z)). We derive a linearised quasi-geostrophic potential vorticity equation which explicitly includesN(y, z), where variations inN may occur on the internal Rossby radius length scale. A mixed layer distribution that monotonically deepens in the poleward direction leads to a nonseparableN(y,z). The resulting meridional pressure gradient is balanced by an eastward zonal geostrophic flow.By assuming mixed layer depth changes occur slowly, relative to a typical horizontal wavelength of a Rossby wave, a local analysis is presented. The Rossby wave is found to have a strongly modulated meridional wavenumber,l, with amplitude proportional to |l|–1/2. To elucidate whether the modulations of the Rossby wave are caused by the horizontal variations inN orU we also consider the cases where eitherN orU vary horizontally. Mixed layer depth changes lead to largestl where the mixed layer is deepest, whereasl is reduced in magnitude whereU is nonzero. When bothU(y,z) andN(y,z) are present, the two effects compete with one another, the outcome determined by the size of |c|/U max, wherec is the Rossby wave phase speed. Finally, the slowly varying assumption required for the analytical approach is removed by employing a numerical model. The numerical model is suitable for studying Rossby wave propagation in a rectangular zonal channel with generalN(y, z) andU(y, z).  相似文献   

6.
This paper examines a model for estimating canopy resistance rc and reference evapotranspiration ETo on an hourly basis. The experimental data refer to grass at two sites in Spain with semiarid and windy conditions in a typical Mediterranean climate. Measured hourly ETo values were obtained over grass during a 4 year period between 1997 and 2000 using a weighing lysimeter (Zaragoza, northeastern Spain) and an eddy covariance system (Córdoba, southern Spain). The present model is based on the Penman–Monteith (PM) approach, but incorporates a variable canopy resistance rc as an empirical function of the square root of a climatic resistance r* that depends on climatic variables. Values for the variable rc were also computed according to two other approaches: with the rc variable as a straight‐line function of r* (Katerji and Perrier, 1983, Agronomie 3 (6): 513–521) and as a mechanistic function of weather variables as proposed by Todorovic (1999, Journal of Irrigation and Drainage Engineering, ASCE 125 (5): 235–245). In the proposed model, the results show that rc/ra (where ra is the aerodynamic resistance) presents a dependence on the square root of r*/ra, as the best approach with empirically derived global parameters. When estimating hourly ETo values, we compared the performance of the PM equation using those estimated variable rc values with the PM equation as proposed by the Food and Agriculture Organization, with a constant rc = 70 s m?1. The results confirmed the relative robustness of the PM method with constant rc, but also revealed a tendency to underestimate the measured values when ETo is high. Under the semiarid conditions of the two experimental sites, slightly better estimates of ETo were obtained when an estimated variable rc was used. Although the improvement was limited, the best estimates were provided by the Todorovic and the proposed methods. The proposed approach for rc as a function of the square root of r* may be considered as an alternative for modelling rc, since the results suggest that the global coefficients of this locally calibrated relationship might be generalized to other climatic regions. It may also be useful to incorporate the effects of variable canopy resistances into other climatic and hydrological models. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

7.
Evaluation of liquefaction potential using neural-networks and CPT results   总被引：1，自引：0，他引：1  
In this research, a reliable Cone Penetration Test data set was gathered with a wide range of parameters. This data was incorporated in a Neural-Networks computer software called STATISTICA Neural-Networks. The back propagation algorithm with a multilayer perceptron network is utilized to analyze the liquefaction occurrence in different sites. In this study, different sets of effective parameters for the neural-network analyses are selected such that to reduce the noise and to obtain more accurate results.Considering the relative importance of effective parameters in liquefaction assessment, it is indicated that σ0, σ′0 together play a more important role than what previously was assumed and hence the relative importance of the qc and seismic parameters are decreased compared with the previous works. The results presented here have more accuracy than previous works while at the same time, the range of the parameters used in this study is much wider than what was previously used. This range of parameters makes the proposed method applicable for practical purposes.  相似文献   

8.
Abstract

We investigate the evolution of a parallel shear flow which has embedded within it a thin, symmetrically positioned layer of stable density stratification. The primary instability of this flow may deliver either Kelvin-Helmholtz waves or Holmboe waves, depending on the strength of the stratification. In this paper we describe a sequence of numerical simulations which reveal for the first time the behavior of the Holmboe wave at finite amplitude and clarify its structural relationship to the Kelvin-Helmholtz wave.

The flows investigated have initial profiles of horizontal velocity and Brunt-Vaisala frequency given in nondimensional form by U = tanhζ and N 2=J sech2 RCζ, respectively, in which ζ is a nondimensional vertical coordinate, J is the value of the gradient Richardson number N 2/(dU/dζ)2 at ζ=0, and R = 3. Linear stability theory predicts that the flow will develop Holmboe instability when J exceeds some critical value Jc' and Kelvin-Helmholtz instability when J is less than Jc; Jc being approximately equal to 0.25 when R=3. We simulate the evolution of flows with J=0.9, J=0.45, and J = 0.22, and find that the first two simulations yield Holmboe waves while the third yields a Kelvin-Helmholtz wave, as predicted.

The Holmboe wave is a superposition of two oppositely propagating disturbances, a right-going mode whose energy is concentrated in the region above the centre of the shear layer, and a left-going mode whose energy is concentrated below the centre of the shear layer. The horizontal speed of the modes varies periodically, and the variations are most pronounced at low values of J. If J ζ Jc' the minimum horizontal speed of the modes vanishes and the modes become phase-locked, whereupon they roll up to form a Kelvin-Helmholtz wave as predicted by Holmboe (1962). When J is moderately greater than Jc' the Holmboe wave ejects long, thin plumes of fluid into the regions above and below the shear layer, as has often been observed in laboratory experiments, and we examine in detail the mechanism by which this occurs.  相似文献   

9.
Numerical modelling techniques are now becoming common for understanding the complicated nature of seismic wave propagation in fractured rock. Here the Indirect Boundary Element Method (IBEM) is applied to study scattering of elastic waves by cracks. The problem addressed in this paper is the diffraction of P and S waves by open 3-D cracks of arbitrary shape embedded in a homogeneous isotropic medium. The IBEM yields the value of the jump of displacements between opposite surfaces of the crack, often called Crack Opening Displacement (COD). This is used to evaluate the solution away from the crack. We use a multi-regional approach which consists of splitting a surface S into two identical surfaces S+ and S− chosen such that the crack lies at the interface. The resulting integral equations are not hyper-singular and wave propagation within media that contain open cracks can be rigorously solved. In order to validate the method, we compare results of displacements of a penny-shaped crack for a vertical incident P-wave with the classic results by Mal (1970) obtaining excellent agreement. This comparison gives us confidence to study cases where no analytic solutions exist. Some examples of incidence of P or S waves upon cracks with various shapes are depicted and the salient aspects of the method are also discussed. Both frequency and time-domain results are included.  相似文献   

10.
Abstract

The Seddon speed formula expressed mathematically as c = dQ/dA (or alternatively, as c = (1 + m)uo; where Q is the discharge, A is the area of cross-section, c is the wave speed, uo is the normal flow velocity, and m is a dimensionless parameter) is revisited in the context of elasticity and thermodynamics. Its link with the linearized solution of St Venant's equations for wave celerity, which does not appear to have been reported in the hydrological literature, is established. The rating exponent m is shown to be equivalent to the dimensionless relative celerity and is found to be the ratio of two specific heats, viz. cp and cv which are the specific heats at constant pressure and volume, respectively. The use of the parameter m as a complex variable helps describe shallow wave characteristics, the damping capacity of a wave, and the mechanism of occurrence of the hysteretic phenomenon. The damping capacity is found to describe the magnitude of wave subsidence, whereas the hysteresis also describes the speed of subsidence.  相似文献   

11.
景亮  吴琪  方怡 《震灾防御技术》2020,15(4):696-707
为探讨测试方法、试验条件以及级配特征对砂-粉混合料剪切波速的影响，对具有不同细粒含量FC，相对密度Dr以及初始有效围压$\sigma_{3 \mathrm{c}}^{\prime}$的砂-粉混合料进行弯曲元和共振柱试验。结果表明:当Dr =35%或50%时，剪切波速Vs随FC的增大先减小后增大；当Dr =60%时，Vs随FC的增大而减小；弯曲元试验测得的Vs明显大于共振柱试验测得的Vs，随着FC的增大，弯曲元试验与共振试验得到的Vs差值逐渐减小，而当FC＞20%时，两种试验得到的Vs基本相同。在考虑Vs弥散性之后，不同FC的混合料弯曲元与共振柱试验得到的Vs结果具有较好的一致性。基于Hardin模型建立的砂-粉混合料Vs预测方法具有较好的预测效果。  相似文献   

12.
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13.
Empirical scaling equations for Fourier amplitude spectra of strong ground motion are used to describe A0 and τ in the assumed (high-frequency) shape of strong motion amplitudes: FS(φ) = A0e-πτφ. The res of computed A0 and τ with other related estimates of spectral amplitudes; (2) smooth decay of strong motion spectral amplitudes up to φ = 25 Hz, without an abrupt low-pass filtering of high frequecies; and (3) good agreement with other estimates of the regionally specific attenuation of high-frequncy seismic waves.As the recorded strong earthquake shaking in the western United States typically samples only the shallow (10 km) and local (100km) characteristics of wave attenuation, the processed strong motion accelerograms can be used as the most direct means of describing the nature of the high-frequency attenuation of the entire strong motion signal for use in earthquake engineering applications. Seismological body wave, Lg and coda wave estimates of Q sample different volumes of the crust surrounding the station, and involve different paths of the waves. These differences must be carefully documented and understood before the results can be used in earthquake engineering characterization of strong motion amplitudes.  相似文献   

14.
Small local earthquakes from two aftershock sequences in Porto dos Gaúchos, Amazon craton—Brazil, were used to estimate the coda wave attenuation in the frequency band of 1 to 24 Hz. The time-domain coda-decay method of a single backscattering model is employed to estimate frequency dependence of the quality factor (Q c) of coda waves modeled using Qc = Q0 fhQ_{\rm c} =Q_{\rm 0} f^\eta , where Q 0 is the coda quality factor at frequency of 1 Hz and η is the frequency parameter. We also used the independent frequency model approach (Morozov, Geophys J Int, 175:239–252, 2008), based in the temporal attenuation coefficient, χ(f) instead of Q(f), given by the equation c(f)=g+\fracpfQe \chi (f)\!=\!\gamma \!+\!\frac{\pi f}{Q_{\rm e} }, for the calculation of the geometrical attenuation (γ) and effective attenuation (Qe-1 )(Q_{\rm e}^{-1} ). Q c values have been computed at central frequencies (and band) of 1.5 (1–2), 3.0 (2–4), 6.0 (4–8), 9.0 (6–12), 12 (8–16), and 18 (12–24) Hz for five different datasets selected according to the geotectonic environment as well as the ability to sample shallow or deeper structures, particularly the sediments of the Parecis basin and the crystalline basement of the Amazon craton. For the Parecis basin Qc = (98±12)f(1.14±0.08)Q_{\rm c} =(98\pm 12)f^{(1.14\pm 0.08)}, for the surrounding shield Qc = (167±46)f(1.03±0.04)Q_{\rm c} =(167\pm 46)f^{(1.03\pm 0.04)}, and for the whole region of Porto dos Gaúchos Qc = (99±19)f(1.17±0.02)Q_{\rm c} =(99\pm 19)f^{(1.17\pm 0.02)}. Using the independent frequency model, we found: for the cratonic zone, γ = 0.014 s − 1, Qe-1 = 0.0001Q_{\rm e}^{-1} =0.0001, ν ≈ 1.12; for the basin zone with sediments of ~500 m, γ = 0.031 s − 1, Qe-1 = 0.0003Q_{\rm e}^{-1} =0.0003, ν ≈ 1.27; and for the Parecis basin with sediments of ~1,000 m, γ = 0.047 s − 1, Qe-1 = 0.0005Q_{\rm e}^{-1} =0.0005, ν ≈ 1.42. Analysis of the attenuation factor (Q c) for different values of the geometrical spreading parameter (ν) indicated that an increase of ν generally causes an increase in Q c, both in the basin as well as in the craton. But the differences in the attenuation between different geological environments are maintained for different models of geometrical spreading. It was shown that the energy of coda waves is attenuated more strongly in the sediments, Qc = (78±23)f(1.17±0.14)Q_{\rm c} =(78\pm 23)f^{(1.17\pm 0.14)} (in the deepest part of the basin), than in the basement, Qc = (167±46)f(1.03±0.04)Q_{\rm c} =(167\pm 46)f^{(1.03\pm 0.04)} (in the craton). Thus, the coda wave analysis can contribute to studies of geological structures in the upper crust, as the average coda quality factor is dependent on the thickness of sedimentary layer.  相似文献   

15.
Small offsets in hard coal seams can be detected with the aid of seam (channel) waves. Transmission and reflection of seam waves depend, among other parameters, upon the symmetry properties of the sequence rock/coal/rock. Two typical unsymmetrical sequences are found in European coal deposits: (i) coal seams with roof and floor of differing acoustic impedance and (ii) coal seams interlayered with rock and soil. Two-dimensional analog models with appropriate impedance contrasts are used to study the effect of the unsymmetrical layers upon the propagation of Rayleigh seam waves. Data analysis is based upon amplitude measurements both parallel and perpendicular to the layers and dispersion curves. The effect of unsymmetrical roof (rock 1) and floor (rock 2) was studied with models containing homogeneous coal seams. Leaky mode wave groups with phase velocities (cR) in the range between the SV-wave velocities (βr1, 2) of the two rock materials, i.e. βr1≥cR > βr2, form a characteristic part of the Rayleigh seam wave signal. Using Knott's energy coefficient calculations it is shown that in that range energy leakage into the surrounding rock by refracted SV-waves is restricted to only one of the two interfaces, namely coal/rock 2. At the other interface, coal/rock 1, all waves are totally reflected. Thus, the high amplitudes of these leaky mode wave groups are explained by “quasi-normal mode” features. The influence of a dirt bed on wave propagation was studied in models where the roof and the floor have the same elastic properties. The maximum thickness of the dirt bed did not exceed 20% of the total seam thickness. The effect of the bed's location within the seam was also investigated. For all recorded normal-mode wave groups either the total seam or the coal layers could be regarded as wave guides. This was shown by the fact that the phases could be associated with the phase velocity dispersion curves calculated for the symmetrical sequence rock/coal/rock. These curves are relevant under the condition that the thickness of the coal layer assumed under the calculation coincides with the thickness of the effective wave guide of the respective wave groups. Wave groups guided in the total seam are not influenced by either the thickness or the position of the dirt bed. On the other hand, for wave groups guided in the coal layers, the quotient of signal amplitudes in the coal layers is influenced by the position of the dirt bed.  相似文献   

16.
A modified Jarvis–Stewart model of canopy transpiration (Ec) was tested over five ecosystems differing in climate, soil type and species composition. The aims of this study were to investigate the model's applicability over multiple ecosystems; to determine whether the number of model parameters could be reduced by assuming that site‐specific responses of Ec to solar radiation, vapour pressure deficit and soil moisture content vary little between sites; and to examine convergence of behaviour of canopy water‐use across multiple sites. This was accomplished by the following: (i) calibrating the model for each site to determine a set of site‐specific (SS) parameters, and (ii) calibrating the model for all sites simultaneously to determine a set of combined sites (CS) parameters. The performance of both models was compared with measured Ec data and a statistical benchmark using an artificial neural network (ANN). Both the CS and SS models performed well, explaining hourly and daily variation in Ec. The SS model produced slightly better model statistics [R2 = 0.75–0.91; model efficiency (ME) = 0.53–0.81; root mean square error (RMSE) = 0.0015–0.0280 mm h‐1] than the CS model (R2 = 0.68–0.87; ME = 0.45–0.72; RMSE = 0.0023–0.0164 mm h‐1). Both were highly comparable with the ANN (R2 = 0.77–0.90; ME = 0.58–0.80; RMSE = 0.0007–0.0122 mm h‐1). These results indicate that the response of canopy water‐use to abiotic drivers displayed significant convergence across sites, but the absolute magnitude of Ec was site specific. Period totals estimated with the modified Jarvis–Stewart model provided close approximations of observed totals, demonstrating the effectiveness of this model as a tool aiding water resource management. Analysis of the measured diel patterns of water use revealed significant nocturnal transpiration (9–18% of total water use by the canopy), but no Jarvis–Stewart formulations are able to capture this because of the dependence of water‐use on solar radiation, which is zero at night. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

17.
A two‐dimensional numerical model of the saltation process was developed on a parallel computer in order to investigate the temporal behaviour of transport rate as well as its downwind distribution. Results show that the effects of unsteady flow on the transportation of particulates (sediment) have to be considered in two spatial dimensions (x, y). Transport rate Q(x, t) appears in the transport equation for mass M(x, t): where A = ΔxW denotes unit area composed of unit streamwise length Δx and width W. S(x, t) (units kg m−2 s−1) stands for the balance over the splash process. A transport equation for transport rate itself is suggested with U c (x, t) a mean particle velocity at location x as the characteristic velocity of the grain cloud. For a steadily blowing wind over a 50 m long sediment bed it was found that downwind changes in Q cease after roughly 10–40 m, depending on the strength of the wind. The onset of stationarity (∂/∂t=0) was found to be a function of the friction velocity and location. The local equilibrium between transport rate and wind was obtained at different times for different downstream locations. Two time scales were found. One fast response (in the order of 1) to incipient wind and a longer time for equilibrium to be reached throughout the simulation length. Transport rate also has different equilibrium values at different locations. A series of numerical experiments was conducted to determine a propagation speed of the grain cloud. It was found that this velocity relates linearly to friction velocity. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

18.
Summary The introduction of precision radio navigation systems employing pulse techniques and the ever increasing interest in spherics have stimulated considerable interest in the propagation of the ground wave transient over the surface of the earth. The theory of the propagation of a transient radio frequency ground wave over a finitely conducting plane earth is presented for the particular case of theNorton surface wave by a consideration of a wave, interrupted abruptly at one point in time (t=0), a wave interrupted abruptly at two points in time (t=0,T 2) and a wave interrupted at one point in time followed by an exponential decay. The first case is illustrated by several numerical examples of a cosine current wave applied to a vertical electric dipole source. It is apparent that the method of the inverse aplace transform for the particular cases considered yields some simple mathematical formulas.  相似文献   

19.
Dependence of the energy released during earthquake on ambient shear stress   总被引：1，自引：0，他引：1  
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.  相似文献   

20.
For transient, high frequency, and pulse like excitation of structures in the near field of strong earthquakes, the classical design approach based on relative response spectrum and mode superposition may not be conservative. For such excitations, it is more natural to use wave propagation methods. In this paper (Part I), we review several two-dimensional wave propagation models of buildings and show results for theoretical dispersion curves computed for these models. We also estimate the parameters of these models that would correspond to a seven-story reinforced concrete building in Van Nuys, California. Ambient vibration tests data for this building imply vertical shear wave velocity βz=112 m/s and anisotropy factor βx/βz=0.55 for NS vibrations, and βz=88 m/s and βx/βz=1 for EW vibrations. The velocity of shear waves propagating through the slabs is estimated to be about 2000 m/s. In the companion paper (Part II), we estimate phase velocities of vertically and horizontally propagating waves between seven pairs of recording points in the building using recorded response to four earthquakes.  相似文献   

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