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1.
Generous statistical tests 总被引：1，自引：1，他引：0
T. V. Hromadka II R. J. Whitley S. B. Horton M. J. Smith J. M. Lindquist 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(1):9-12
A common statistical problem is deciding which of two possible sources, A and B, of a contaminant is most likely the actual
source. The situation considered here, based on an actual problem of polychlorinated biphenyl contamination discussed below,
is one in which the data strongly supports the hypothesis that source A is responsible. The problem approach here is twofold:
One, accurately estimating this extreme probability. Two, since the statistics involved will be used in a legal setting, estimating
the extreme probability in such a way as to be as generous as is possible toward the defendant’s claim that the other site
B could be responsible; thereby leaving little room for argument when this assertion is shown to be highly unlikely. The statistical
testing for this problem is modeled by random variables {X
i
} and the corresponding sample mean the problem considered is providing a bound ɛ for which for a given number a
0. Under the hypothesis that the random variables {X
i
} satisfy E(X
i
) ≤ μ, for some 0 < μ < 1, statistical tests are given, described as “generous”, because ɛ is maximized. The intent is to
be able to reject the hypothesis that a
0 is a value of the sample mean while eliminating any possible objections to the model distributions chosen for the {X
i
} by choosing those distributions which maximize the value of ɛ for the test used. 相似文献
2.
3.
4.
James W. Telford 《Pure and Applied Geophysics》1980,119(2):278-293
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
5.
The intrinsic dissipation and scattering attenuation in southwestern (SW) Anatolia, which is a tectonically active region,
is studied using the coda waves. First the coda quality factor (Qc) assuming single scattering is estimated from the slope of the coda-wave amplitude decay. Then the Multiple Lapse Time Window
(MLTW) analysis is performed with a uniform earth model. Three non-overlapping temporal data windows are used to calculate
the scattered seismic energy densities against the source-receiver distances, which, in turn, are used to calculate separate
estimates of the intrinsic and scattering factors. In order to explore the frequency dependency, the observed seismograms
are band pass-filtered at the center frequencies of 0.75, 1.5, 3.0, 6.0 and 12.0. The scattering attenuation (Qs−1) is found lower than the intrinsic attenuation (Qi−1) at all frequencies except at 0.75 Hz where the opposite is observed. Overall the intrinsic attenuation dominates over the
scattering attenuation in the SW Anatolia region. The integrated energy curves obtained for the first energy window (i.e.,
0–15 s) are somewhat irregular with distance while the second (i.e., 15–30 s) and third (i.e., 30–45 s) data windows exhibit
more regular change with distance at most frequencies. The seismic albedo B0 is determined as 0.61 at 0.75 Hz and 0.34 at 12.0 Hz while the total attenuation factor denoted by Le−1 changes in the range 0.034–0.017. For the source-station range 20–180 km considered the scattering attenuation is found strongly
frequency dependent given by the power law Qs−1 = 0.010*f−1.508. The same relations for Qi−1, Qt−1 (total), Qc−1 and
(expected) hold as Qi−1 = 0.0090*f−1.17, Qt−1 = 0.019*f−1.31, Qc−1 = 0.008*f−0.84 and
respectively. Compared to the other attenuation factors Qc−1 and
are less dependent on the frequency. 相似文献
6.
Estimation of coda wave attenuation in East Central Iran 总被引：1，自引：0，他引：1
The attenuation of coda waves, Q
c
, has been estimated in Zarand, Jiroft, and Bam regions of east central Iran using a single back-scattering model of S-coda
envelopes. For this purpose, the recordings of 97 earthquakes by three seismic networks and a local strong ground motion network
have been used. In this research, the frequency-dependent Q
c
values are estimated at central frequencies of 1.5, 3, 6, 8, 12, 16, and 24 Hz using different lapse time windows from 20
to 60 s. The frequency-dependent relationships obtained are for Zarand, for Jiroft, and for Bam region. From the strong ground motion data, we obtain the relation . The Q
c
frequency-dependent relationship for the entire region of east central Iran from all data (both seismograms and accelerograms)
is . The average Q
c
values estimated and their frequency dependent relationships correlate well with a highly heterogeneous and highly tectonically
active region. Results also show that the attenuation is higher in Bam region compared to Zarand and Jiroft regions. 相似文献
7.
Predictive relations are developed for peak ground acceleration (PGA) from the engineering seismoscope (SRR) records of the
2001 Mw 7.7 Bhuj earthquake and 239 strong-motion records of 32 significant aftershocks of 3.1 ≤ Mw ≤ 5.6 at epicentral distances of 1 ≤ R ≤ 288 km. We have taken advantage of the recent increase in strong-motion data at
close distances to derive new attenuation relation for peak horizontal acceleration in the Kachchh seismic zone, Gujarat.
This new analysis uses the Joyner-Boore’s method for a magnitude-independent shape, based on geometrical spreading and anelastic
attenuation, for the attenuation curve. The resulting attenuation equation is,
where, Y is peak horizontal acceleration in g, Mw is moment magnitude, rjb is the closest distance to the surface projection of the fault rupture in kilometers, and S is a variable taking the values
of 0 and 1 according to the local site geology. S is 0 for a rock site, and, S is 1 for a soil site. The relation differs
from previous work in the improved reliability of input parameters and large numbers of strong-motion PGA data recorded at
short distances (0–50 km) from the source. The relation is in demonstrable agreement with the recorded strong-ground motion
data from earthquakes of Mw 3.5, 4.1, 4.5, 5.6, and 7.7. There are insufficient data from the Kachchh region to adequately judge the relation for the
magnitude range 5.7 ≤ Mw ≤ 7.7. But, our ground-motion prediction model shows a reasonable correlation with the PGA data of the 29 March, 1999 Chamoli
main shock (Mw 6.5), validating our ground-motion attenuation model for an Mw6.5 event. However, our ground-motion prediction shows no correlation with the PGA data of the 10 December, 1967 Koyna main
shock (Mw 6.3). Our ground-motion predictions show more scatter in estimated residual for the distance range (0–30 km), which could
be due to the amplification/noise at near stations situated in the Kachchh sedimentary basin. We also noticed smaller residuals
for the distance range (30–300 km), which could be due to less amplification/noise at sites distant from the Kachchh basin.
However, the observed less residuals for the longer distance range (100–300 km) are less reliable due to the lack of available
PGA values in the same distance range. 相似文献
8.
Strombolian-type volcanic activity is characterized by a series of gas bubbles bursting at the top of a magma column and leading
to the ejection of lava clots and gas emission at the surface. The quantitative analysis of physical parameters (e.g., velocity,
size, and mass fluxes) controlling the emission dynamics of these volcanic products is very important for the understanding
of eruption source mechanisms but remains difficult to obtain in a systematic fashion. Ground-based Doppler radar is found
to be a very effective tool for measuring ejecta velocities at a high acquisition rate and close to the emission source. We
present here a series of measurements carried out at Mt. Etna’s Southeast crater, using an L-band volcanological Doppler radar,
during the 4 July 2001 Strombolian eruptions. Doppler radar data are supplemented by the analysis of video snapshots recorded
simultaneously. We provide here a set of physical parameters systematically retrieved from 247 Strombolian explosions spanning
15 min and occurring during the paroxysm of the eruption from 21:30 to 21:45 UT. The time-average values give a maximum particle
velocity of
Vmaxp = 94.7±24 \textm/s V_{{\max }}^p = {94}.{7}\pm {24} {\text{m/s}} , a bulk lava jet velocity of
V\textPW - rad = 37.6±1.9 \textm/s {V_{{{\text{PW - rad}}}}} = {37}.{6}\pm {1}.{9} {\text{m/s}} , and an initial gas velocity at the source vent of
V0g = 118.4±36 \textm/s V_0^g = {118}.{4}\pm {36} {\text{m/s}} . The time-averaged particle diameter is found to be about
D\textPW - rad = 4.2±2.1 \textcm {D_{{{\text{PW - rad}}}}} = {4}.{2}\pm {2}.{1} {\text{cm}} . The volume and mass gas fluxes are estimated from time-averaged source gas velocities over the sequence duration at
Qvg = 3 - 11 ×103\textm3\text/s Q_v^g = {3} - {11} \times {1}{0^{{3}}}{{\text{m}}^{{3}}}{\text{/s}} and
Qmg = 0.5 - 2 ×103\textkg/s Q_m^g = 0.{5} - {2} \times {1}{0^{{3}}}{\text{kg/s}} , respectively. 相似文献
9.
The viscosity of hydrous dacitic liquids: implications for the rheology of evolving silicic magmas 总被引：2，自引：1，他引：1
Alan G. Whittington Bridget M. Hellwig Harald Behrens Bastian Joachim André Stechern Francesco Vetere 《Bulletin of Volcanology》2009,71(2):185-199
The viscosity of a series of six synthetic dacitic liquids, containing up to 5.04 wt% dissolved water, was measured above
the glass transition range by parallel-plate viscometry. The temperature of the 1011 Pa s isokom decreases from 1065 K for the anhydrous liquid, to 864 K and 680 K for water contents of 0.97 and 5.04 wt% H2O. Including additional measurements at high temperatures by concentric-cylinder and falling-sphere viscometry, the viscosity
(η) can be expressed as a function of temperature and water content w according to: where η is in Pa s, T is temperature in K, and w is in weight percent. Within the conditions of measurement, this parameterization reproduces the 76 viscosity data with a
root-mean square deviation (RMSD) of 0.16 log units in viscosity, or 7.8 K in temperature. The measurements show that water
decreases the viscosity of the dacitic liquids more than for andesitic liquids, but less than for rhyolites. At low temperatures
and high water contents, andesitic liquids are more viscous than the dacitic liquids, which are in turn more viscous than
rhyolitic liquids, reversing the trend seen for high temperatures and low water contents. This suggests that the relative
viscosity of different melts depends on temperature and water content as much as on bulk melt composition and structure. At
magmatic temperatures, rhyolites are orders of magnitude more viscous than dacites, which are slightly more viscous than andesites.
During degassing, all three liquids undergo a rapid viscosity increase at low water contents, and both dacitic and andesitic
liquids will degas more efficiently than rhyolitic liquids. During cooling and differentiation, changing melt chemistry, decreasing
temperature and increasing crystal content all lead to increases in the viscosity of magma (melt plus crystals). Under closed
system conditions, where melt water content can increase during crystallization, viscosity increases may be small. Conversely,
viscosity increases are very abrupt during ascent and degassing-induced crystallization. 相似文献
10.
Attenuation of P,S, and coda waves in Koyna region,India 总被引：1，自引：0，他引：1
The attenuation properties of the crust in the Koyna region of the Indian shield have been investigated using 164 seismograms
from 37 local earthquakes that occurred in the region. The extended coda normalization method has been used to estimate the
quality factors for P waves and S waves , and the single back-scattering model has been used to determine the quality factor for coda waves (Q
c). The earthquakes used in the present study have the focal depth in the range of 1–9 km, and the epicentral distance vary
from 11 to 55 km. The values of
and Q
c show a dependence on frequency in the Koyna region. The average frequency dependent relationships (Q = Q
0
f
n) estimated for the region are , and . The ratio is found to be greater than one for the frequency range considered here (1.5–18 Hz). This ratio, along with the frequency
dependence of quality factors, indicates that scattering is an important factor contributing to the attenuation of body waves
in the region. A comparison of Q
c and in the present study shows that for frequencies below 4 Hz and for the frequencies greater than 4 Hz. This may be due to the multiple scattering effect of the medium. The outcome of this
study is expected to be useful for the estimation of source parameters and near-source simulation of earthquake ground motion,
which in turn are required in the seismic hazard assessment of a region. 相似文献
11.
Niu Zhiren 《Pure and Applied Geophysics》1984,122(5):645-661
A new estimate of the fracture parameters of earthquakes is provided in this paper. By theMuskhelishvili method (1953) a number of basic relations among fracture-mechanics parameters are derived. A scheme is proposed to evaluate the slip weakening parameters in terms of fault dimension, average slip, and rise time, and the new results are applied to 49 events compiled in the earthquake catalogue ofPurcaru andBerckhemer (1982). The following empirical relations are found in the paper: $$\begin{gathered} \frac{{\tau _B - \tau _f }}{{\tau _\infty - \tau _f }} = 2.339 \hfill \\ {{\omega _c } \mathord{\left/ {\vphantom {{\omega _c } {W = 0.113}}} \right. \kern-\nulldelimiterspace} {W = 0.113}} \hfill \\ \log G_c \left( {{{dyne} \mathord{\left/ {\vphantom {{dyne} {cm}}} \right. \kern-\nulldelimiterspace} {cm}}} \right) = 2 \log L (km) + 6.167 \hfill \\ \log \delta _c (cm) = 2 \log L (km) - 1.652 \hfill \\ \end{gathered} $$ whereG c is the specific fracture energy,ω c the size of the slip weakening zone,δ c the slip weakening displacement,τ B ?τ f the drop in strength in the slip weakening zone,τ ∞?τ f the stress drop,L the fault length, andW the fault width. The investigation of 49 shocks shows that the range of strength dropτ B ?τ f is from several doze to several hundred bars at depthh<400 km, but it can be more than 103 bars ath>500 km; besides, the range of the sizeω c of the strength degradation zone is from a few tenths of a kilometer to several dozen kilometers, and the range of the slip weakening displacementδ c is from several to several hundred centimeters. The specific fracture energyG c is of the order of 108 to 1011 erg cm?2 when the momentM 0 is of the order of 1023 to 1029 dyne cm. 相似文献
12.
13.
Jinhai Yu 《中国科学D辑(英文版)》1997,40(3):322-328
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
14.
Lyapunov exponent and dimension of the strange attractor of elastic frictional system 总被引：1，自引：0，他引：1
ＬｙａｐｕｎｏｖｅｘｐｏｎｅｎｔａｎｄｄｉｍｅｎｓｉｏｎｏｆｔｈｅｓｔｒａｎｅａｔｔｒａｃｔｏｒｏｆｅｌａｓｔｉｃｆｒｉｃｔｉｏｎａｌｓｙｓｔｅｍＺｈｉ－ＲｅｎＮＩＵ（牛志仁）ａｎｄＤａｎｇ－ＭｉｎＣＨＥＮ（陈党民）（ＳｅｉｓｍｏｌｏｇｉｃａｌＢｕｒ... 相似文献
15.
Lucas Vieira Barros Marcelo Assumpção Ronnie Quintero Vinicius Martins Ferreira 《Journal of Seismology》2011,15(2):391-409
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
16.
D. H. Boteler 《Pure and Applied Geophysics》1990,134(4):511-526
A new approach to the theory of electromagnetic induction is developed that is applicable to moving as well as stationary sources. The source field is considered to be a standing wave generated by two waves travelling in opposite directions along the surface of the earth. For a stationary source the incident waves have velocities of the same magnitude, however for a moving source the velocities of the two incident waves are respectively increased and decreased by the velocity of the source. Electromagnetic induction in the earth is then considered as refraction of these waves and gives, for both stationary and moving sources, the magnetotelluric relation: $$\frac{{ - E_y }}{{H_x }} = \left( {\frac{{i\omega \mu }}{\sigma }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - i\frac{{v^2 }}{{\omega \mu \sigma }}} \right)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $$ where ν is the wavenumber of the source, μ is the permeability (4π·10?7) and σ is the conductivity of the earth. ω is the angular frequency of the variation observed on the earth. For a stationary source the observed frequency is the same as the source frequency, however the effect of moving a time-varying source is to make the observed frequency different from the frequency of the source. Failure to recognise this in previous studies led to some erroneous conclusions. This study shows that a moving source isnot “electromagnetically broader” than a stationary source as had been suggested. 相似文献
17.
Gerardo Severino Alessandro Santini Angelo Sommella 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(4):567-582
Average steady source flow in heterogeneous porous formations is modelled by regarding the hydraulic conductivity K(x) as a stationary random space function (RSF). As a consequence, the flow variables become RSFs as well, and we are interested into calculating their moments. This
problem has been intensively studied in the case of a Neumann type boundary condition at the source. However, there are many
applications (such as well-type flows) for which the required boundary condition is that of Dirichlet. In order to fulfill
such a requirement the strength of the source must be proportional to K(x), and therefore the source itself results a RSF. To solve flows driven by sources whose strength is spatially variable, we
have used a perturbation procedure similar to that developed by Indelman and Abramovich (Water Resour Res 30:3385–3393, 1994) to analyze flows generated by sources of deterministic strength. Due to the linearity of the mathematical problem, we have
focused on the explicit derivation of the mean head distribution G
d
(x) generated by a unit pulse. Such a distribution represents the fundamental solution to the average flow equations, and it
is termed as mean Green function. The function G
d
(x) is derived here at the second order of approximation in the variance σ2 of the fluctuation (where K
A
is the mean value of K(x)), for arbitrary correlation function ρ(x), and any dimensionality d of the flow domain. We represent G
d
(x) as product between the homogeneous Green function G
d
(0)(x) valid in a domain with constant K
A
, and a distortion term Ψ
d
(x) = 1 + σ2ψ
d
(x) which modifies G
d
(0)(x) to account for the medium heterogeneity. In the case of isotropic formations ψ
d
(x) is expressed via one quadrature. This quadrature can be analytically calculated after adopting specific (e.g.. exponential
and Gaussian) shape for ρ(x). These general results are subsequently used to investigate flow toward a partially-penetrating well in a semi-infinite
domain. Indeed, we construct a σ2-order approximation to the mean as well as variance of the head by replacing the well with a singular segment. It is shown
how the well-length combined with the medium heterogeneity affects the head distribution. We have introduced the concept of
equivalent conductivity
K
eq(r,z). The main result is the relationship where the characteristic function ψ(w)(r,z) adjusts the homogeneous conductivity K
A
to account for the impact of the heterogeneity. In this way, a procedure can be developed to identify the aquifer hydraulic
properties by means of field-scale head measurements. Finally, in the case of a fully penetrating well we have expressed the
equivalent conductivity in analytical form, and we have shown that (being the effective conductivity for mean uniform flow), in agreement with the numerical simulations of Firmani et al. (Water Resour
Res 42:W03422, 2006). 相似文献
18.
A generalized turbulent diffusion model has been developed which evaluates the time rate of growth of a simulated cloud of particles released into a turbulent (i.e. diffusive) atmosphere. The general model, in the form of second-order differential equations, computes the three-dimensional size of the cloud as a function of time. Parameters which influence the cloud growth, and which are accounted for in the model equations, are: (1) length scales and velocity magnitudes of the diffusive field, (2) rate of viscous dissipation , (3) vertical stability as characterized by the relative adiabatic lapse rate (1/T)(g/C
p
+T/z), and (4) vertical shear in the mean horizontal winds
, and
, for a given height and of spatial extent equal to that of the diffusing cloud. Sample results for near ground level and for upper stratospheric heights are given. For the atmospheric boundary layer case, the diffusive field is microscale turbulence. In the upper stratospheric case it is considered to be a field of highly interactive and dispersive gravity waves. 相似文献
19.
V. S. Savenko 《Water Resources》2016,43(6):862-872
A semiempirical mathematical model of iron and manganese migration from bottom sediments into the water mass of water bodies has been proposed based on some basic regularities in the geochemistry of those elements. The entry of dissolved forms of iron and manganese under aeration conditions is assumed negligible. When dissolved-oxygen concentration is <0.5 mg/L, the elements start releasing from bottom sediments, their release rate reaching its maximum under anoxic conditions. The fluxes of dissolved iron and manganese (Me) from bottom sediments into the water mass (J Me) are governed by the gradients of their concentrations in diffusion water sublayer adjacent to sediment surface and having an average thickness of h = 0.025 cm: \({J_{Me}} = - {D_{Me}}\frac{{{C_{Me\left( {ss} \right)}} - {C_{Me\left( w \right)}}}}{h}\) (D Me ≈ 1 × 10–9 m2/s is molecular diffusion coefficient of component Me in solution; C Me(ss) and C Me(w) ≈ 0 are Me concentrations on sediment surface, i.e., on the bottom boundary of the diffusion water sublayer, and in the water mass, i.e., on the upper boundary of the diffusion water sublayer). The value of depends on water saturation with dissolved oxygen (\({\eta _{{O_2}}}\)) in accordance with the empiric relationship \({C_{Me\left( {ss} \right)}} = \frac{{C_{_{Me\left( {ss} \right)}}^{\max }}}{{1 + k{\eta _{{O_2}}}}}\) (k is a constant factor equal to 300 for iron and 100 for manganese; C Me(ss) max is the maximal concentration of Me on the bottom boundary of the diffusion water sublayer with C Fe(ss) max ≈ 200 μM (11 mg/L), and C Mn(ss) max ≈ 100 μM (5.5 mg/L). 相似文献
20.
A modified formula of the cumulative frequency-magnitude relation has been formulated and tested in a previous paper by the authors of this study. Based on the modified relationship, the following reoccurrence formulas have been obtained.
- For the ‘T-years period’ larger earthquake magnitude,M T $$M_T = \frac{1}{{A_3 }}ln\frac{{A_2 }}{{(1/T) + A_1 }}.$$
- For the value of the maximum earthquake magnitude, which is exceeded with probabilityP inT-years period,M PT $$M_{PT} = \frac{{ln(A_2 .T)}}{{A_3 }} - \frac{{ln[A_1 .T - ln(1 - P)]}}{{A_3 }}.$$
- For the probability of occurrence of an earthquake of magnitudeM in aT-years period,P MT $$P_{MT} = 1 - \exp [ - T[ - A_1 + A_2 \exp ( - A_3 M)]].$$