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1.
Wave decay over a muddy seabed has been widely reported. In previous studies, the fluid-mud layer is usually treated as a homogeneous layer with a certain thickness lying on the rigid bottom. However, the muddy seabed beneath a fluid-mud layer is usually movable in practice. This study aims to find out the influence of the movable seabed beneath a fluid-mud layer. For this purpose, a numerical model for wave propagation over a multilayered muddy seabed is developed, in which water is treated as a Newtonian fluid, and the rheology of mud is described by a visco-elastic–plastic model. The laboratory experiments of Sakakiyama and Bijker (J Waterw Port Coast Ocean Eng 115(5):614–633, 1989) are chosen to validate the numerical model. The model is then employed to investigate the movement of a fluid-mud layer with different conditions of the underlying mud layer and its influence on wave decay. It is found that the underlying mud layer plays a very important role in the wave–mud interaction and greatly affects the wave decay rate.  相似文献   

2.
Summary Thirty wave records taken by the O. W. S. Weather Explorer in the Atlantic Ocean, studied in a previous paper (J. Darbyshire [1959a]), are taken and the statistical distribution of wave heights and wave periods found. The mean height for each observed period is also found.The three methods described by D. E. Cartwright and M. S. Longuet-Higgins [1956], are used to evaluate which indicates the departure of the height distribution from a Rayleigh distribution. Agreement between the three results is good enough to verify the accuracy of the theoretical distribution. The relation giving the variation of withT f , the period of maximum energy on the frequency spectrum, derived in the previous paper (J. Darbyshire [1959b]) is verified.The distribution of wave heights on thirty wave records taken by the Morecambe Bay Lightship is also worked out. In this case there is a marked lack of symmetry between the distribution of the heights of crests and troughs, measured from mean sea level. Estimates of by the three methods do not agree so well in this case although the values derived from the frequency spectra vary withT f as would be expected from the relationship derived by J. Darbyshire [1959b].
Die relative Frequenz von Wellenhöhen und -perioden im Atlantischen Ozean und in der Irischen See
Zusammenfassung Dreißig vom O. W. S. 'Weather Explorer im Atlantischen Ozean aufgenommene und in einer früheren Abhandlung (J. Darbyshire [1959a]) untersuchte Seegangs-registrierungen werden zur Ermittlung der statistischen Verteilung von Wellenhöhen und Wellenperioden benutzt. Die mittlere Höhe jeder beobachteten Periode wird ebenfalls bestimmt.Die drei von D. E. Cartwright und M. S. Longuet-Higgins [1956] entwickelten Methoden werden dazu verwendet, den Wert von, das die Abweichung der Höhenverteilung von der Rayleighschen Verteilung ausdrückt, zu berechnen. Die Übereinstimmung zwischen den drei Ergebnissen ist groß genug, um die Genauigkeit der auf theoretischem Wege gewonnenen Verteilung zu bestätigen. Es wird die Richtigkeit der Beziehung bestätigt, die aus der Veränderlichkeit von in Abhängigkeit vonT f resultiert, der Periode der größten Energie im Frequenzspektrum, die bereits in einer früheren Arbeit von J. Darbyshire [1959b] abgeleitet wurde.Die Verteilung der Wellenhöhen für die dreißig Seegangsregistrierungen wird ebenfalls ausgewertet. Hierbei machte sich ein beträchtlicher Mangel an Symmetrie zwischen der Verteilung der Höhen und Tiefen von Wellenkämmen und Wellentälern bemerkbar, die unter Zugrundelegung des mittleren Wasserstandes gemessen wurden. Berechnungen von mit Hilfe dieser drei Methoden zeigen in diesem Falle keine allzu gute Übereinstimmung, obgleich die vom Frequenzspektrum abgeleiteten Werte in Abhängigkeit vonT f variieren, wie dies nach der von J. Darbyshire [1959b] abgeleiteten Beziehung zu erwarten war.
Les fréquences relatives des hauteurs et des périodes des vagues en océan Atlantique et en mer d'Irlande
Résumé Trente enregistrements des vagues obtenus par le navire météorologique «Weather Explorer» en océan Atlantique et analysés antérieurement par J. Darbyshire [1959a] sont utilisés pour. déterminer la distribution des hauteurs et des périodes des vagues. La hauteur moyenne de chaque période observée est également déterminée.Les trois méthodes décrites par D. E. Cartwright et M. S. Longuet-Higgins [1956] servent à estimer la grandeur qui indique la différence entre la distribution des hauteurs et la distribution d'après Rayleigh. L'accord entre les trois résultats est assez satisfaisant pour vérifier l'exactitude de la distribution estimée d'une manière théorique. La relation donnant la variation en fonction deT f , qui sur le spectre de fréquences représente la période de l'énergie maximum, dérivée antérieurement par J. Darbyshire [1959b], se vérifie.Les trente enregistrements, provenant du bateau feu stationné dans la baie de Morecambe, sont analysés pour en obtenir la distribution des hauteurs de vagues. Ces analyses montrent que dans ce cas il existe un défaut remarquable de la Symmetrie entre la distribution des hauteurs des crêtes et celle des profondeurs des creux, mesurées à partir du niveau moyen de la mer. Les estimations de effectuées au moyen de trois méthodes citées ci-dessus, ne s'accordent pas trop bien dans ce cas, bien que les valeurs, dérivées des spectres de fréquences, varient avecT f à mesure que l'on pourrait s'y attendre d'après la relation dérivée par J. Darbyshire [1959b].
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3.
Recent work at three contrasting sites in England and Wales has shown characteristics atypical of those frequently reported elsewhere. These differences are:
  • (a) Taking each entire beach system there is no uniform trend of erosion or accretion, nor a progressive variation in beach elevation or volume alongshore, from one survey to the next. However, for Swansea Bay the ‘long-term’ (i. e. 18 months) range in profile height along that stretch of coast where the alignment of the beach is normal to the direction of wave approach, correlates well with computed wave energy derived from relevant offshore wave directions.
  • (b) While beach variability is greatest during the ‘winter’ (i. e. storm) period there is no overall tendency for a drawdown of sediment from the intertidal zone at that time. Response times are relatively short. Thus high beach levels need not necessarily be associated with ‘summer’ conditions.
  • (c) Although in Swansea Bay there is a tendency for the beach height to fluctuate least at mid-tide level this is not true of the other two sites. In no area does sediment eroded from the upper exposed part of the beach regularly appear to be deposited on the lower exposed part, or vice versa.
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4.
In a companion article Akkar et al. (Bull Earthq Eng, doi:10.1007/s10518-013-9461-4, 2013a; Bull Earthq Eng, doi:10.1007/s10518-013-9508-6, 2013b) present a new ground-motion prediction equation (GMPE) for estimating 5 %-damped horizontal pseudo-acceleration spectral (PSA) ordinates for shallow active crustal regions in Europe and the Middle East. This study provides a supplementary viscous damping model to modify 5 %-damped horizontal spectral ordinates of Akkar et al. (Bull Earthq Eng, doi:10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi:10.1007/s10518-013-9508-6, 2013b) for damping ratios ranging from 1 to 50 %. The paper also presents another damping model for scaling 5 %-damped vertical spectral ordinates that can be estimated from the vertical-to-horizontal (V/H) spectral ratio GMPE that is also developed within the context of this study. For consistency in engineering applications, the horizontal and vertical damping models cover the same damping ratios as noted above. The article concludes by introducing period-dependent correlation coefficients to compute horizontal and vertical conditional mean spectra (Baker in J Struct Eng 137:322–331, 2011). The applicability range of the presented models is the same as of the horizontal GMPE proposed by Akkar et al. (Bull Earthq Eng, doi:10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi:10.1007/s10518-013-9508-6, 2013b): as for spectral periods $0.01 \hbox { s}\le \,\hbox {T}\le \,4\hbox { s}$ as well as PGA and PGV for V/H model; and in terms of seismological estimator parameters $4\le \hbox {M}_\mathrm{w} \le 8, \hbox { R} \le 200 \hbox { km}, 150\hbox { m/s}\le \hbox { V}_\mathrm{S30}\le $ 1,200 m/s, for reverse, normal and strike-slip faults. The source-to-site distance measures that can be used in the computations are epicentral $(\hbox {R}_\mathrm{epi})$ , hypocentral $(\hbox {R}_\mathrm{hyp})$ and Joyner–Boore $(\hbox {R}_\mathrm{JB})$ distances. The implementation of the proposed GMPEs will facilitate site-specific adjustments of the spectral amplitudes predicted from probabilistic seismic hazard assessment in Europe and the Middle East region. They can also help expressing the site-specific design ground motion in several formats. The consistency of the proposed models together with the Akkar et al. (Bull Earthq Eng, doi:10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi:10.1007/s10518-013-9508-6, 2013b) GMPE may be advantageous for future modifications in the ground-motion definition in Eurocode 8 (CEN in Eurocode 8, Design of structures for earthquake resistance—part 1: general rules, seismic actions and rules for buildings. European Standard NF EN 1998-1, Brussels, 2004).  相似文献   

5.
Erosion of hard‐rock coastal cliffs is understood to be caused by a combination of both marine and sub‐aerial processes. Beach morphology, tidal elevation and significant wave heights, especially under extreme storm conditions, can lead to variability in wave energy flux to the cliff‐toe. Wave and water level measurements in the nearshore under energetic conditions are difficult to obtain and in situ observations are rare. Here we use monthly cliff‐face volume changes detected using terrestrial laser scanning alongside beach morphological changes and modelled nearshore hydrodynamics to examine how exposed cliffs respond to changes in extreme wave conditions and beach morphology. The measurements cover the North Atlantic storms of 2013 to 2014 and consider two exposed stretches of coastline (Porthleven and Godrevy, UK) with contrasting beach morphology fronting the cliffs; a flat dissipative sandy beach at Godrevy and a steep reflective gravel beach at Porthleven. Beach slope and the elevation of the beach–cliff junction were found to influence the frequency of cliff inundation and the power of wave–cliff impacts. Numerical modelling (XBeach‐G) showed that under highly energetic wave conditions, i.e. those that occurred in the North Atlantic during winter 2013–2014, with Hs = 5.5 m (dissipative site) and 8 m (reflective site), the combination of greater wave height and steeper beach at the reflective site led to amplified wave run‐up, subjecting these cliffs to waves over four times as powerful as those impacting the cliffs at the dissipative site (39 kWm‐1 compared with 9 kWm‐1). This study highlighted the sensitivity of cliff erosion to extreme wave conditions, where the majority (over 90% of the annual value) of cliff‐face erosion ensued during the winter. The significance of these short‐term erosion rates in the context of long‐term retreat illustrates the importance of incorporating short‐term beach and wave dynamics into geomorphological studies of coastal cliff change. © 2017 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.  相似文献   

6.
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7.
Generous statistical tests   总被引：1，自引：1，他引：0  
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   

8.
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   

9.
On December 12, 1992 a large earthquake (M s 7.5) occurred just north of Flores Island, Indonesia which, along with the tsunami it generated, killed more than 2,000 people. In this study, teleseismicP andSH waves, as well asPP waves from distances up to 123°, are inverted for the orientations and time histories of multiple point sources. By repeating the inversion for reasonable values of depth, time separation and spatial separation, a 2-fault model is developed. Next, the vertical deformation of the seafloor is estimated from this fault model. Using a detailed bathymetric model, linear and nonlinear tsunami propagation models are tested. The data consist of a single tide gauge record at Palopo (650 km to the north), as well as tsunami runup height measurements from Flores Island and nearby islands. Assuming a tsunami runup amplification factor of two, the two-fault model explains the tide gauge record and the tsunami runup heights on most of Flores Island. It cannot, however, explain the large tsunami runup heights observed near Leworahang (on Hading Bay) and Riangkroko (on the northeast peninsula). Massive coastal slumping was observed at both of these locations. A final model, which in addition to the two faults, includes point sources of large vertical displacement at these two locations explains the observations quite well.  相似文献   

10.
In this work, we simulate the 2011 M9 Tohoku-Oki tsunami using new coseismic tsunami sources based on inverting onshore and offshore geodetic data, using 3D Finite Element Models (FEM). Such FEMs simulate elastic dislocations along the plate boundary interface separating the stiff subducting Pacific Plate from the relatively weak forearc and volcanic arc of the overriding Eurasian plate. Due in part to the simulated weak forearc materials, such sources produce significant shallow slip (several tens of meters) along the updip portion of the rupture near the trench. To assess the accuracy of the new approach, we compare observations and numerical simulations of the tsunami's far- and near-field coastal impact for: (i) one of the standard seismic inversion sources (UCSB; Shao et al. 2011); and (ii) the new FEM sources. Specifically, results of numerical simulations for both sources, performed using the fully nonlinear and dispersive Boussinesq wave model FUNWAVE-TVD, are compared to DART buoy, GPS tide gauge, and inundation/runup measurements. We use a series of nested model grids with varying resolution (down to 250 m nearshore) and size, and assess effects on model results of the latter and of model physics (such as when including dispersion or not). We also assess the effects of triggering the tsunami sources in the propagation model: (i) either at once as a hot start, or with the spatiotemporal sequence derived from seismic inversion; and (ii) as a specified surface elevation or as a more realistic time and space-varying bottom boundary condition (in the latter case, we compute the initial tsunami generation up to 300 s using the non-hydrostatic model NHWAVE). Although additional refinements are expected in the near future, results based on the current FEM sources better explain long wave near-field observations at DART and GPS buoys near Japan, and measured tsunami inundation, while they simulate observations at distant DART buoys as well or better than the UCSB source. None of the sources, however, are able to explain the largest runup and inundation measured between 39.5° and 40.25°N, which could be due to insufficient model resolution in this region (Sanriku/Ria) of complex bathymetry/topography, and/or to additional tsunami generation mechanisms not represented in the coseismic sources (e.g., splay faults, submarine mass failure). This will be the object of future work.  相似文献   

11.
Accurate determination of seismic velocity of the crust is important for understanding regional tectonics and crustal evolution of the Earth. We propose a stepwise joint linearized inversion method using surface wave dispersion, Rayleigh wave ZH ratio (i.e., ellipticity), and receiver function data to better resolve 1D crustal shear wave velocity (v S) structure. Surface wave dispersion and Rayleigh wave ZH ratio data are more sensitive to absolute variations of shear wave speed at depths, but their sensitivity kernels to shear wave speeds are different and complimentary. However, receiver function data are more sensitive to sharp velocity contrast (e.g., due to the existence of crustal interfaces) and v P/v S ratios. The stepwise inversion method takes advantages of the complementary sensitivities of each dataset to better constrain the v S model in the crust. We firstly invert surface wave dispersion and ZH ratio data to obtain a 1D smooth absolute v S model and then incorporate receiver function data in the joint inversion to obtain a finer v S model with better constraints on interface structures. Through synthetic tests, Monte Carlo error analyses, and application to real data, we demonstrate that the proposed joint inversion method can resolve robust crustal v S structures and with little initial model dependency.  相似文献   

12.
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   

13.
A Bremmer Series decomposition of the solution y(t) to the lossless wave equation in layered media is where the yj(t) are physically meaningful constituents (i.e., y1(t) are primaries, y2(t) are secondaries, etc.). This paper reviews Mendel's state space models for generating the constituents; reviews Bremmer's integral equation models for generating the constituents; and demonstrates how Mendel's state space models can be obtained by a careful decomposition of Bremmer's integral equation models. It shows that Mendel's equations can be viewed as approximate numerical solutions of Bremmer's integral equations. In a lossless homogeneous medium, the approximations become exact.  相似文献   

14.
Lozovatsky  Iossif  Liu  Zhiyu  Fernando  Harindra Joseph S.  Hu  Jianyu  Wei  Hao 《Ocean Dynamics》2013,63(11):1189-1201

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.

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15.
Laboratory experiments of tsunami runup on a circular island   总被引：2，自引：0，他引：2  
Laboratory experiments of a 7.2-m-diameter conical island were conducted to study three-dimensional tsunami runup. The 62.5-cm tall island had 1 on 4 side slopes and was positioned in the center of a 30-m-wide by 25-m-long flat-bottom basin. Solitary waves with height-to-depth ratios ranging from 0.05 to 0.20 and source lengths ranging from 0.30 to 7.14 island diameters were tested in water depths of 32 and 42 cm. Twenty-seven capacitance wave gages were used to measure surface wave elevations at incident and four radial transects on the island slope. Maximum vertical runup measurements were made at 20 locations around the perimeter of the island using rod and transit. A new runup gage was located on the back or lee side of the island to record runup time series.  相似文献   

16.
On the basis of Parry’s method (1986), an improved method was established to determine the molar volume (Vm) and compositions (X) of the NaCl-H2O-CO2 (NHC) system inclusion. To use this method, the determination of Vm-X only requires three microthermometric data of a NHC inclusion: partial homog-enization temperature (Th ,CO2), salinity (S) and total homogenization temperature (Th). Theoretically, four associated equations are needed containing four unknown parameters: X CO2, XNaCl, Vm and F (volume fraction of CO2 phase in total inclusion when occurring partial homogenization). When they are released, the Vm-X are determined. The former three equations, only correlated with Th ,CO2, S and F, have simplified expressions:XCO2=f1(Th,CO2,S,F),XNaCl=f2(Th,CO2,S,F),Vm=f3(Th,CO2,S,F). The last one is the thermodynamic relationship of X CO2, XNaCl, Vm and Th:f4(XCO2,XNaCl,Vm,Th)=0.Since the above four associated equations are complicated, it is necessary to adopt iterative technique to release them. The technique can be described by:(i) Freely input a F value (0≤F≤1),with Th ,CO2 and S, into the former three equations. As a result,X CO 2,XNaCl and the molar volume value recorded as Vm1 are derived. (ii) Input the X CO2 and XNaCl gotten in the step above into the last equation, and another molar volume value recorded as Vm2 is determined. (iii) If Vm1 is unequal to Vm2, the calculation will be restarted from “(i)”. The iteration is completed until Vm1 is equal to Vm2, which means that the four associated equations are released. Compared to Parry’s (1986) solution method, the improved method is more convenient to use, as well as more accurate to determine X CO 2. It is available for a NHC inlusion whose partial homogenization temperature is higher than clatherate melting temperature and there are no solid salt crystals in the inclusion at parital homogenization.  相似文献   

17.
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.
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   

19.
In this work, we describe a stochastic method for delineating well capture zones in randomly heterogeneous porous media. We use a moment equation (ME) approach to derive the time-dependent mean capture zones and their associated uncertainties. The mean capture zones are determined by reversely tracking the non-reactive particles released at a small circle around each pumping well. The uncertainty associated with the mean capture zones is calculated based on the particle displacement covariances for nonstationary flow fields. The flow statistics are obtained either by directly solving the flow moment equations derived with a first-order ME approach or from Monte Carlo simulations (MCS) of flow. The former constitutes a full ME approach, and the latter is a hybrid ME-MCS approach. This hybrid approach is invoked to examine the validity of the transport component of the stochastic method by ensuring that the ME and MC transport approaches have the same underlying flow statistics. We compared both the full ME and the hybrid ME-MCS results with those obtained with a full MCS approach. It has been found that the three approaches are in excellent agreement when the variability of hydrologic conductivity is small (Y2=0.16). At a moderate variability (Y2=0.5), the hybrid ME-MCS and the full MCS results are in excellent agreement whereas the results from the full ME approach deviate slightly from the full MCS results. This indicates that the (first-order) ME transport approach renders a good approximation at this level of variability and that the first-order ME flow approximation may not be sufficiently accurate at this variability in the case of divergent/convergent flow. The first-order ME flow approach may need to be corrected with higher-order terms even for moderate Y2 although the literature results reveal that the first-order ME flow approach is robust for uniform mean flow (i.e., giving accurate results even with Y2 as large as four).  相似文献   

20.
During the ruptures of an earthquake,the strain energy.△E,.will be transferred into,at least,three parts,i.e..the seismic radiation energy(E_s),fracture energy(E_g),and frictional energy(E_f),that is,△E = E_s + E_g + E_f.Friction,which is represented by a velocity- and state-dependent friction law by some researchers,controls the three parts.One of the main parameters of the law is the characteristic slip displacement.D_c.It is significant and necessary to evaluate the reliable value of D_c from observed and inverted seismic data.Since D_c controls the radiation efficiency.η_R = E_s/(E_s+ E_g),the value of η_r is a good constraint of estimating D_c.Integrating observed data and inverted results of source parameters from recorded seismograms.the values of E_s and E_g of an earthquake can be measured,thus leading to the value of η_R.The constraint used to estimate the reliable value of D_c will be described in this work.An example of estimates of D_c.based on the observed and inverted values of source parameters of the September 20,1999 M_S 7.6 Chi-Chi(Ji-Ji).Taiwan region,earthquake will be presented.  相似文献   

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