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1.
The following Poisson’s equation with the Stokes’ boundary condition is dealt with $$\left\{ \begin{gathered} \nabla ^2 T = - 4\pi Gp outside S, \hfill \\ \left. {\frac{{\partial T}}{{\partial h}} = \frac{1}{\gamma }\frac{{\partial y}}{{\partial h}}T} \right|_s = - \Delta g, \hfill \\ T = O\left( {r^{ - 3} } \right) at infinity, \hfill \\ \end{gathered} \right.$$ whereS is reference ellipsord. Under spherical approximation transformation, the ellipsoidal correction terms about the boundary condition, the equation and the density in the above BVP are respectively given. Therefore, the disturbing potentialT can he obtained if the magnitudes aboveO(ε4) are neglected.  相似文献   

2.
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3.
The flow rate of SO2, HCl and HF was calculated from a transfer coefficient obtained by measuring the concentration of a tracer gas (SF6) emitted at the plume and analysed down wind with a field gas chromatograph. The results obtained are: $$\begin{gathered} SO_2 = 2.3 \pm 0.4 t/day \hfill \\ HCl = 6.4 \pm 0.4 t/day \hfill \\ HF = 0.11 \pm 0.3 t/day \hfill \\ \end{gathered} $$   相似文献   

4.
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5.
Applications of the entrainment process to layers at the boundary, which meet the self similarity requirements of the logarithmic profile, have been studied. By accepting that turbulence has dominating scales related in scale length to the height above the surface, a layer structure is postulated wherein exchange is rapid enough to keep the layers internally uniform. The diffusion rate is then controlled by entrainment between layers. It has been shown that theoretical relationships derived on the basis of using a single layer of this type give quantitatively correct factors relating the turbulence, wind and shear stress for very rough surface conditions. For less rough surfaces, the surface boundary layer can be divided into several layers interacting by entrainment across each interface. This analysis leads to the following quantitatively correct formula compared to published measurements. 1 $$\begin{gathered} \frac{{\sigma _w }}{{u^* }} = \left( {\frac{2}{{9Aa}}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \left( {1 - 3^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \frac{a}{k}\frac{{d_n }}{z}\frac{{\sigma _w }}{{u^* }}\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ = 1.28(1 - 0.945({{\sigma _w } \mathord{\left/ {\vphantom {{\sigma _w } {u^* }}} \right. \kern-\nulldelimiterspace} {u^* }})({z \mathord{\left/ {\vphantom {z L}} \right. \kern-\nulldelimiterspace} L})^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ \end{gathered} $$ where \(u^* = \left( {{\tau \mathord{\left/ {\vphantom {\tau \rho }} \right. \kern-0em} \rho }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) , σ w is the standard deviation of the vertical velocity,z is the height andL is the Obukhov scale lenght. The constantsa, A, k andd n are the entrainment constant, the turbulence decay constant, Von Karman's constant, and the layer depth derived from the theory. Of these,a andA, are universal constants and not empirically determined for the boundary layer. Thus the turbulence needed for the plume model of convection, which resides above these layers and reaches to the inversion, is determined by the shear stress and the heat flux in the surface layers. This model applies to convection in cool air over a warm sea. The whole field is now determined except for the temperature of the air relative to the water, and the wind, which need a further parameter describing sea surface roughness. As a first stop to describing a surface where roughness elements of widely varying sizes are combined this paper shows how the surface roughness parameter,z 0, can be calculated for an ideal case of a random distribution of vertical cylinders of the same height. To treat a water surface, with various sized waves, such an approach modified to treat the surface by the superposition of various sized roughness elements, is likely to be helpful. Such a theory is particularly desirable when such a surface is changing, as the ocean does when the wind varies. The formula, 2 $$\frac{{0.118}}{{a_s C_D }}< z_0< \frac{{0.463}}{{a_s C_D (u^* )}}$$ is the result derived here. It applies to cylinders of radius,r, and number,m, per unit boundary area, wherea s =2rm, is the area of the roughness elements, per unit area perpendicular to the wind, per unit distance downwind. The drag coefficient of the cylinders isC D . The smaller value ofz o is for large Reynolds numbers where the larger scale turbulence at the surface dominates, and the drag coefficient is about constant. Here the flow between the cylinders is intermittent. When the Reynolds number is small enough then the intermittent nature of the turbulence is reduced and this results in the average velocity at each level determining the drag. In this second case the larger limit forz 0 is more appropriate.  相似文献   

6.
The Aegean and surrounding area (34°N–43°N, 18°E–30°E) is separated into 76 shallow and intermediate depth seismogenic sources. For 74 of these sources intervent times for strong mainshocks have been determined by the use of instrumental and historical data. These times have been used to determine the following empirical relations: $$\begin{gathered} \log T_t = 0.24M_{\min } + 0.25M_p - 0.36\log \dot M_0 + 7.36 \hfill \\ M_f = 1.04M_{\min } - 0.31M_p + 0.28\log \dot M_0 - 4.85 \hfill \\ \end{gathered} $$ whereT 1 is the interevent time, measured in years,M min the surface wave magnitude of the smallest mainshock considered,M p the magnitude of the preceding mainshock,M f the magnitude of the following mainshock, \(\dot M_0 \) the moment rate in each source per year. A multiple correlation coefficient equal to 0.74 and a standard deviation equal to 0.18 for the first of these relations were calculated. The corresponding quantities for the second of these relations are 0.91 and 0.22. On the basis of the first of these relations and taking into consideration the time of occurence and the magnitude of the last mainshock, the probabilities for the occurrence of mainshocks in each seismogenic source of this region during the decade 1993–2002 are determined. The second of these relations has been used to estimate the magnitude of the expected mainshock.  相似文献   

7.
Strong motion data from various regions of India have been used to study attenuation characteristics of horizontal peak acceleration and velocity. The strong ground motion data base considered in the present work consists of various earthquakes recorded in the northern part of India since 1986 with magnitudes 5.7 to 7.2. Using these data, relations for horizontal peak acceleration and velocity, which are $$\begin{gathered} log_{10} a = 1.14 + 0.31M + 0.65log_{10} R \hfill \\ log_{10} v = 0.571 + 0.41M + 0.768log_{10} R \hfill \\ \end{gathered} $$ have been proposed wherea is the peak horizontal acceleration in cm/sec2,v is the peak horizontal velocity in mm/sec,M is body wave magnitude, andR is the hypocentral distance in km. The proposed relations are in reasonable agreement with the small amount of strong ground motion data available for the northern part of India. The present results will be useful in estimating strong ground motion parameters and in the earthquake resistant design in the Himalayan region.  相似文献   

8.
A simple law of wear rate is examined for the process of gouge generation during the frictional sliding of simulated faults in rocks, by use of the Pi theorem method (dimensional analysis) and existing experimental data. The relationship between wear rate (t/d) and the applied stress can be expressed by the power-law relations $$\frac{t}{d} = C_\sigma \sigma ^{m\sigma } ,\frac{t}{d} = C_\tau \tau ^{m\tau }$$ wheret is the thickness of the gouge generated on the frictional surfaces,d is the fault displacement, σ and τ are normal stress and shear stress, respectively, andC σ,C τ,m σ andm τ are constants. These results indicate that the exponent coefficientsm σ andm τ and the coefficientsC σ andC τ depend on the material hardness of the frictional surfaces. By using the wear rates of natural faults, these power-law relationships may prove to be an acceptable palaeopiezometer of natural faults and the lithosphere.  相似文献   

9.
In three representative nodules contained in an alkali-olivine basalt, a succession of cumulate cycles has been noted: $$\begin{gathered} 1) olivine - orthopyroxene + \varepsilon (Cpx + Sp.); \hfill \\ 2) ortho - clinopyroxene + \varepsilon (Ol. + Sp. + Plag); \hfill \\ 3) ortho - clinopyroxene + Plag + \varepsilon (Ol. + Sp.). \hfill \\ \end{gathered} $$ The element distribution in the minerals enables us to say that these mafic and ultramafic nodules formed near the stability line of plagioclase at about 10 kb. These cumulates, which belong to a comagmatic series, from picrites to basalts, were formed in the upper mantle. They are associated with norites — Plag. + Opr. + Cpx. +≡ (Il. + Bi) — belonging to the same series, but crystallized in the deep part of the crust. On the other hand, these norites could be xenoliths taken away from an infragranitic basement of granulite facies.  相似文献   

10.
Investigation of the time-dependent seismicity in 274 seismogenic regions of the entire continental fracture system indicates that strong shallow earthquakes in each region exhibit short as well as intermediate term time clustering (duration extending to several years) which follow a power-law time distribution. Mainshocks, however (interevent times of the order of decades), show a quasiperiodic behaviour and follow the ‘regional time and magnitude predictable seismicity model’. This model is expressed by the following formulas $$\begin{gathered} \log T_t = 0.19 M_{\min } + 0.33 M_p - 0.39 \log m_0 + q \hfill \\ M_f = 0.73 M_{\min } - 0.28 M_p + 0.40 \log m_0 + m \hfill \\ \end{gathered} $$ which relate the interevent time,T t (in years), and the surface wave magnitude,M f , of the following mainshock: with the magnitude,M min, of the smallest mainshock considered, the magnitude,M p , of the preceded mainshock and the moment rate,m 0 (in dyn.cm.yr?1), in a seismogenic region. The values of the parametersq andm vary from area to area. The basic properties of this model are described and problems related to its physical significance are discussed. The first of these relations, in combination with the hypothesis that the ratioT/T t , whereT is the observed interevent time, follows a lognormal distribution, has been used to calculate the probability for the occurrence of the next very large mainshock (M s ≥7.0) during the decade 1993–2002 in each of the 141 seismogenic regions in which the circum-Pacific convergent belt has been separated. The second of these relations has been used to estimate the magnitude of the expected mainshock in each of the regions.  相似文献   

11.
Seismic coda wave attenuation ( $ Q_{\text{c}}^{ - 1} $ ) characteristics in the Garhwal region, northwestern Himalaya is studied using 113 short-period, vertical component seismic observations from local events with hypocentral distance less than 250?km and magnitude range between 1.0 to 4.0. They are located mainly in the vicinity of the Main Boundary Thrust (MBT) and the Main Central Thrust (MCT), which are well-defined tectonic discontinuities in the Himalayas. Coda wave attenuation ( $ Q_{\text{c}}^{ - 1} $ ) is estimated using the single isotropic scattering method at central frequencies 1.5, 3, 5, 7, 9, 12, 16, 20, 24 and 28?Hz using several starting lapse times and coda window lengths for the analysis. Results show that the ( $ Q_{\text{c}}^{ - 1} $ ) values are frequency dependent in the considered frequency range, and they fit the frequency power law ( $ Q_{\text{c}}^{ - 1} \left( f \right) = Q_{0}^{ - 1} f^{ - n} $ ). The Q 0 (Q c at 1?Hz) estimates vary from about 50 for a 10?s lapse time and 10?s window length, to about 350 for a 60?s lapse time and 60?s window length combination. The exponent of the frequency dependence law, n ranges from 1.2 to 0.7; however, it is greater than 0.8, in general, which correlates well with the values obtained in other seismically and tectonically active and highly heterogeneous regions. The attenuation in the Garhwal region is found to be lower than the Q c ?1 values obtained for other seismically active regions of the world; however, it is comparable to other regions of India. The spatial variation of coda attenuation indicates that the level of heterogeneity decreases with increasing depth. The variation of coda attenuation has been estimated for different lapse time and window length combinations to observe the effect with depth and it indicates that the upper lithosphere is more active seismically as compared to the lower lithosphere and the heterogeneity decreases with increasing depth.  相似文献   

12.
The TKE dissipation rate in the northern South China Sea   总被引：1，自引：0，他引：1  
The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε p〉 of the deep basin and on the shelf. Linear correlation between 〈ε p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ reaches 17–19 mW/m2, dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{p}} $ was mostly ～10–30 % of $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ . A weak dependence of bin-averaged dissipation $ \overline{\varepsilon} $ on the Richardson number was noted, according to $ \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} $ , where ε 0 + ε m is the background value of $ \overline{\varepsilon} $ for weak stratification and Ri cr?=?0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.  相似文献   

13.
We estimate the corner frequencies of 20 crustal seismic events from mainshock–aftershock sequences in different tectonic environments (mainshocks 5.7 < M W < 7.6) using the well-established seismic coda ratio technique (Mayeda et al. in Geophys Res Lett 34:L11303, 2007; Mayeda and Malagnini in Geophys Res Lett, 2010), which provides optimal stability and does not require path or site corrections. For each sequence, we assumed the Brune source model and estimated all the events’ corner frequencies and associated apparent stresses following the MDAC spectral formulation of Walter and Taylor (A revised magnitude and distance amplitude correction (MDAC2) procedure for regional seismic discriminants, 2001), which allows for the possibility of non-self-similar source scaling. Within each sequence, we observe a systematic deviation from the self-similar \( M_{0} \propto \mathop f\nolimits_{\text{c}}^{ - 3} \) line, all data being rather compatible with \( M_{0} \propto \mathop f\nolimits_{\text{c}}^{ - (3 + \varepsilon )} \) , where ε > 0 (Kanamori and Rivera in Bull Seismol Soc Am 94:314–319, 2004). The deviation from a strict self-similar behavior within each earthquake sequence of our collection is indicated by a systematic increase in the estimated average static stress drop and apparent stress with increasing seismic moment (moment magnitude). Our favored physical interpretation for the increased apparent stress with earthquake size is a progressive frictional weakening for increasing seismic slip, in agreement with recent results obtained in laboratory experiments performed on state-of-the-art apparatuses at slip rates of the order of 1 m/s or larger. At smaller magnitudes (M W < 5.5), the overall data set is characterized by a variability in apparent stress of almost three orders of magnitude, mostly from the scatter observed in strike-slip sequences. Larger events (M W > 5.5) show much less variability: about one order of magnitude. It appears that the apparent stress (and static stress drop) does not grow indefinitely at larger magnitudes: for example, in the case of the Chi–Chi sequence (the best sampled sequence between M W 5 and 6.5), some roughly constant stress parameters characterize earthquakes larger than M W ~ 5.5. A representative fault slip for M W 5.5 is a few tens of centimeters (e.g., Ide and Takeo in J Geophys Res 102:27379–27391, 1997), which corresponds to the slip amount at which effective lubrication is observed, according to recent laboratory friction experiments performed at seismic slip velocities (V ~ 1 m/s) and normal stresses representative of crustal depths (Di Toro et al. in Nature in press, 2011, and references therein). If the observed deviation from self-similar scaling is explained in terms of an asymptotic increase in apparent stress (Malagnini et al. in Pure Appl Geophys, 2014, this volume), which is directly related to dynamic stress drop on the fault, one interpretation is that for a seismic slip of a few tens of centimeters (M W ~ 5.5) or larger, a fully lubricated frictional state may be asymptotically approached.  相似文献   

14.
The seismic behaviour of caisson foundations supporting typical bridge piers is analysed with 3D finite elements, with due consideration to soil and interface nonlinearities. Single-degree-of freedom oscillators of varying mass and height, simulating heavily and lightly loaded bridge piers, founded on similar caissons are studied. Four different combinations of the static ( $\text{ FS }_\mathrm{V}$ FS V ) and seismic ( $\text{ FS }_\mathrm{E}$ FS E ) factors of safety are examined: (1) a lightly loaded ( $\text{ FS }_\mathrm{V}= 5$ FS V = 5 ) seismically under-designed ( $\text{ FS }_\mathrm{E} < 1$ FS E < 1 ) caisson, (2) a lightly loaded seismically over-designed ( $\text{ FS }_\mathrm{E} >1$ FS E > 1 ) caisson, (3) a heavily loaded ( $\text{ FS }_\mathrm{V} = 2.5$ FS V = 2.5 ) seismically under-designed ( $\text{ FS }_\mathrm{E} < 1$ FS E < 1 ) caisson and (4) a heavily loaded seismically over-designed caisson. The analysis is performed with use of seismic records appropriately modified so that the effective response periods (due to soil-structure-interaction effects) of the studied systems correspond to the same spectral acceleration, thus allowing their inelastic seismic performance to be compared on a fair basis. Key performance measures of the systems are then contrasted, such as: accelerations, displacements, rotations and settlements. It is shown that the performance of the lightly loaded seismically under-designed caisson is advantageous: not only does it reduce significantly the seismic load to the superstructure, but it also produces minimal residual displacements of the foundation. For heavily loaded foundations, however ( $\text{ FS }_{V} = 2.5$ FS V = 2.5 ), the performance of the two systems (over and under designed) is similar.  相似文献   

15.
Analysis of data, covering four rainy seasons, of rain current, point-discharge current and potential gradient reveal novel relations in the form (i) $$Q_{r + } /Q_{r - } = k_1 (T_{r + } /T_{r - } )^{1.1} $$ for rain charge and duration ratios; and (ii) $$Q_{p - } /Q_{p + } = k_2 (T_{p - } /T_{p + } )^{1.1} $$ for point charge and duration ratios, where thek's are constants; and (iii) $$i_r = - \alpha (i_p - c)$$ for rain and point-discharge current densities, where α has the same value for all types of rain andc is a constant controlled by the rainfall intensityR. For rain not associated with point discharge the relation takes the familiar form $$i_r = - AR(E - \bar E)$$ Theoretical values are obtained for \ga andA on the basis of the Wilson ion-capture theory as worked out in detail by Whipple and Chalmers.  相似文献   

16.
Total content is used mostly for balances. In order to calculate the areas of different depths, the contours are cut out of a topographical map and weighed. The formula is derived from the substance concentration (taken as a linear function of the depth), times the volume of a truncated cone. Content of one layer: $$\frac{{\Delta z}}{{l2}}\left[ {\left( {f_l + f_u } \right)^2 \cdot \left( {c_l + c_u } \right) + 2c_l f_l^2 + 2c_u f_u^2 } \right]$$ fu Square root of upper area f1 Square root of lower area cu Concentration at upper depth c1 Concentration at lower depth Δz Difference of depths (i.e. thickness of layer) Sum of contents of all layers gives total content of the lake.  相似文献   

17.
In the last two decades, south-central Europe and the Eastern Alps have been widely explored by many seismic refraction experiments (e.g., CELEBRATION 2000, ALP 2002, SUDETES 2003). Although quite detailed images are available along linear profiles, a comprehensive, three-dimensional crustal model of the region is still missing. This limitation makes this region a weak spot in continental-wide comprehensive representations of crustal structure. To improve on this situation, we select and collect 37 published active-source seismic lines in this region. After geo-referencing each line, we sample them along vertical profiles—every 50?km or less along the line—and derive P-wave velocities in a stack of homogeneous layers (separated by discontinuities: depth of crystalline basement, top of lower crust, and Moho). We finally merge the information using geostatistical methods, and infer S-wave velocity and density using empirical scaling relations. We present here the resulting crustal model for a region encompassing the Eastern Alps, Dinarides, Pannonian basin, Western Carpathians and Bohemian Massif, covering the region within $45^{\circ}\text{--}51^{\circ}\hbox{N}$ and $11^{\circ} \text{--} 22^{\circ}\hbox{E}$ with a resolution of $0.2^{\circ} \times 0.2^{\circ}.$ We are also able to extend and update the map of Moho depth in a wider region within $35^{\circ}\text{--}51^{\circ}\hbox{N}$ and $12^{\circ}\text{--}45^{\circ}\hbox{E},$ gathering Moho values from the collected seismic lines, other published dataset and using the European plate reference EPcrust as a background. All the digitized profiles and the resulting model are available online.  相似文献   

18.
This paper extends the theory of the entity and entrainment model of turbulence to obtain a numerical value of von Karman's constant,k=0.37. The formula is, $$k = (2a^3 /A)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \ln \beta $$ where,a=1/12 is the entrainment constant,A=1 is the turbulent decay constant, and β is the ratio in height of the successive self-similar layers of the theory, where β is evaluated as β=e 2. These new values fork and β improve the surface roughness length estimates derived from this theory.  相似文献   

19.
Calculations on the basis of the self-consistent approximation are used to study the effects of randomly distributed elliptical cracks and of non-randomly distributed circular cracks, either dry or saturated by a highly conductive material phase, on the electric conductivities of a cracked body. Analytic and numeric results are given for two special non-random distributions. In the first, the cracks are assumed randomly distributed in planes parallel to a given plane. In the second, the crack normals are randomly distributed in parallel planes. The results of the theoretical calculations indicate that the magnitudes of the crack induced variations of the dry cracked rock depend upon a crack density parameter ? rather than upon the crack porosity. Here, ? is defined as $$\varepsilon = \frac{{2N}}{\pi }< \frac{{A^2 }}{P} > $$ whereN is the average number of cracks per unit volume, andA andP are the crack area and perimeter respectively. (For circular cracks of radiusa, ?=N〈a3〉.) Although a straightforward relationship does connect ? with the porosity, it may be more meaningful for laboratory experiments to concentrate upon measuring crack-induced variations as functions of crack density rather than of porosity. For saturated cracked rocks, the results of the calculations indicate that, in addition to ?, variations in conductivity depend also upon a saturation parameter Ω, which relates crack aspect ratio α to matrix and fluid conductivities σ and σF $$\Omega = \frac{{{\sigma \mathord{\left/ {\vphantom {\sigma {\sigma _F }}} \right. \kern-\nulldelimiterspace} {\sigma _F }}}}{\alpha }.$$   相似文献   

20.
Presently available data on the reaction of SO2 with OH radicals (OH + SO2 + \(M\xrightarrow[{k_1 }]{}\) HSO3 +M) are critically reviewed in light of recent stratospheric sulfur budget calculations. These calculations impose that the net oxidation ratek of SO2 within the stratosphere should fall within the range 10?7≤k≤10?9, if the SO2 oxidation model for the stratospheric sulfate layer is assumed to be correct. The effective reaction rate constantk 1 * =k 1[M] at the stratospheric temperature is estimated as $$k_1^* = \frac{{(8.2 \pm 2.2) \times 10^{ - 13} \times [M]}}{{(0.79 \mp 0.34) \times 10^{ - 13} + [M]}}cm^3 /molecules sec$$ where [M] refers to the total number density (molecules/cm3). Using the above limiting values ofk 1 * , and the estimated OH density concentrations, the net oxidation rate is calculated as 3.6×10?7≤k≤1.3×10?8 at 17 km altitude. This indicates that the upper limit of thesek values exceeds the tolerable range imposed by the model by a factor of about four. Obviously the uncertainty of thek 1 * values and of the OH concentrations in the stratosphere is still too large to make definite conclusions on the validity of the SO2 model.  相似文献   

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