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1.
Analytic solutions are presented for steady interface flow in aquifers consisting of a confined and a semi-confined section. The total discharge is constant in the confined section and is directed towards the semi-confined section, which is bounded on top by a leaky layer that separates the aquifer from the sea. All solutions are based on the Dupuit approximation. The interface position is fully determined by two dimensionless parameters. The first parameter is the product of the uniform gradient towards the sea and the dimensionless leakage factor divided by the dimensionless density difference. The second dimensionless parameter is the length of the semi-confined section divided by the leakage factor. Four types of flow are distinguished. For cases I and II the interface does not reach the end of the semi-confined section, while it does for cases III and IV. For cases I and III the interface extends into the confined section, while for cases II and IV it remains entirely in the semi-confined section. Analytic solutions are presented for the position of the interface for all four cases. Diagrams are presented to determine the type of flow and the position of the interface toe based on the two dimensionless parameters. The pre-development position of the interface along the Georgia coast is computed as an illustration of the practical application of the presented formulas. Another practical application is the estimation of how far a numerical model of seawater intrusion should be extended into the sea for accurate simulations. 相似文献
2.
The kinematic‐wave and diffusive‐wave approximations were investigated for unsteady overland flow resulting from spatially varying rainfall excess. Three types of boundary conditions were adopted: zero flow at the upstream end, and critical flow and zero depth‐gradient at the downstream end. Errors were derived by comparing the dimensionless profiles of the flow depth over the plane with those computed from the dynamic‐wave solution. It was found that the mean errors for both the approximations were independent of the type of rainfall excess distribution for KF02 > 5, where K is the kinematic‐wave number and F0 is the Froude number. Therefore, the regions (KF02, F0) where the kinematic‐wave and diffusive‐wave solutions would be fairly accurate and for any distribution of spatially varying rainfall, were characterized. The kinematic‐wave approximation was reasonably accurate, with a mean error of less than 5% and for the critical depth at the downstream end, for KF02 ≥ 20 with F0 ≤ 1; if the rainfall excess was concentrated in a portion of the plane, the field where the kinematic‐wave solution was found accurate, it was more limited and characterized for KF02 > 35 with F0 ≤ 1. The diffusive‐wave solution was in good agreement with the dynamic‐wave solution with a mean error of less than 5%, in the flow depth, for KF02 ≥ 15 with F0 ≤ 1; for rainfall excess concentrated in a portion of the plane, the accuracy of the diffusion wave solution was in a region more restricted and defined for KF02 ≥ 30 with F0 ≤ 1. For zero‐depth gradient at the downstream end, the accuracy field of the kinematic‐wave was found to be greater and characterized for KF02 > 10 with F0 ≤ 1; for rainfall excess concentrated in a portion of the plane, the region was smaller and defined for KF02 > 15 with F0 ≤ 1. The diffusive‐wave solution was found accurate in the region defined for KF02 > 7·5, whereas for rainfall excess concentrated in a portion of the plane, the field of accuracy was for KF02 > 12·5 with F0 ≤ 1. The lower limits of the regions, defined on KF02, can be considered generally valid for both approximations, but for F0 < 1 smaller lower limits were also characterized. Finally, the accuracy of these approximations was influenced significantly by the downstream boundary condition. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
3.
Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with infiltration were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1·4% for KF20≥7·5, and up to 14% for KF20≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F0 is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF20 (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary, both in terms of the magnitude of the error and the segment of the channel reach for which these approximations would be applicable. © 1998 John Wiley & Sons, Ltd. 相似文献
4.
In the analytic element method, strings of line-sinks may be used to model streams and strings of line-doublets may be used to model impermeable walls or boundaries of inhomogeneities. The resulting solutions are analytic, but the boundary conditions are met approximately. Equations for line elements may be derived in two ways: through integration of point elements (the integral solution) and through application of separation of variables in elliptical coordinates (the elliptical solution). Using both approaches, two sets of line elements are presented for four flow problems: line-sinks and line-doublets in (un)confined flow, and line-sinks and line-doublets in semi-confined flow. Elliptical line elements have the advantage that they do not need a far-field expansion for accurate evaluation far away from the element. The derivation of elliptical line elements is new and applicable to both (un)confined flow and semi-confined flow; only the resulting expressions for elliptical line elements for semi-confined flow have not been found in the current groundwater literature. Existing solutions for elliptical line elements for (un)confined flow were intended for the modeling of isolated features. Four examples are presented, one for each flow problem, to demonstrate that strings of elliptical line elements may be used to obtain accurate solutions; elliptical line-doublets for semi-confined flow can only be strung together in combination with two integral line-doublets. For a zigzag canal in (un)confined flow, a string of elliptical line-sinks performed better than a string of integral line-sinks of the same order when the smallest angle between two adjacent segments is less than 130°. Elliptical line-doublets performed better than integral line-doublets for a square inhomogeneity in a uniform, confined flow field; the difference was smaller for an octagonal inhomogeneity. For semi-confined flow, the difference between the integral and elliptical line-sinks was small when modeling a zigzag canal. 相似文献
5.
Orson L. Anderson 《Earth and Planetary Science Letters》1973,20(1):73-76
It is shown that Birch's formula for the isothermal pressure derivative of the isothermal bulk modulus, K′, can be used to generate reasonable values of K′0 for a sequence of silicates with various ambient densities and constant mean atomic mass, m¯. The theory predicts values in fairly good agreement with experimental results, although there is a regrettable spread of experimental values of K′0 for each solid. This first-order approximation theory for scaling between K′0 and ?0 is analogous to the law of corresponding states which scales K0 and ?0. 相似文献
6.
《Advances in water resources》2005,28(10):1003-1009
The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W−1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W−1 function and vice versa. An infinite family of asymptotic expansions to W−1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green–Ampt infiltration with immediate ponding), a method is presented for approximating W−1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green–Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10−5%. This error is orders of magnitude lower than any existing analytical approximations. 相似文献
7.
The thermodynamic properties of the lower mantle are determined from the seismic profile, where the primary thermodynamic variables are the bulk modulus K and density ρ. It is shown that the Bullen law (K ∝ P) holds in the lower mantle with a high correlation coefficient for the seismic parametric Earth model (PEM). Using this law produces no ambiguity or trade-off between ρ0 and K0, since both K0 and K′0 are exactly determined by applying a linear K?ρ relationship to the data. On the other hand, extrapolating the velocity data to zero pressure using a Birch-Murnaghan equation of state (EOS) results in an ambiguous answer because there are three unknown adjustable parameters (ρ0, K0, K′0) in the EOS.From the PEM data, K = 232.4 + 3.19 P (GPa). The PEM yields a hot uncompressed density of 3.999 ± 0.0026 g cm?3 for material decompressed from all parts of the lower mantle. Even if the hot uncompressed density were uniform for all depths in the lower mantle, the cold uncompressed mantle would be inhomogeneous because the decompression given by the Bullen law crosses isotherms; for example, the temperature is different at different depths. To calculate the density distribution correctly, an isothermal EOS must be used along an isotherm, and temperature corrections must be placed in the thermal pressure PTH.The thermodynamic parameters of the lower mantle are found by iteration. Values of the three uncompressed anharmonic parameters are first arbitrarily selected: α0 (hot), the coefficient of thermal expansion; γ0, the Grüneisen parameter; and δ, the second Grüneisen parameter. Using γ0 and the measured ρ0 (hot) and K0 (hot), the values of θ0 (Debye temperature) and q = dlnγ/dlnρ are found from the measured seismic velocities. Then from (αKT)0 and q the thermal pressure PTH at all high temperatures is found. Correlating PTH against T to the geotherm for the lower mantle, PTH is found at all depths Z. The isothermal pressure, along the 0 K isotherm, at every Z is found by subtracting PTH from the measured P given by the seismic model. Using the isothermal pressure at depth Z, the solution for the cold uncompressed density ρ0C and the cold uncompressed bulk modulus, KT0 is found as a trace in the KT0?ρ0C plane. A narrow band of solutions is then found for ρ0C and KT0 at all depths.The thermal expansion at all T is found from [ρ0C ? ρ0 (hot)/ρ0C. From Suzuki's formula, the best fit to the thermal expansion determines γ0 and α0 (hot). When the values of these two parameters do not agree with the original assumptions, the calculation is repeated until they do agree. In this way all the important thermodynamic parameters are found as a self-consistent set subject only to the assumptions behind the equations used. 相似文献
8.
Salem A. Al-Jabri Jaehoon Lee Anju Gaur Robert Horton Dan B. Jaynes 《Advances in water resources》2006
Field determined hydraulic and chemical transport properties can be useful for the protection of groundwater resources from land-applied chemicals. Most field methods to determine flow and transport parameters are either time or energy consuming and/or they provide a single measurement for a given time period. In this study, we present a dripper-TDR field method that allows measurement of hydraulic conductivity and chemical transport parameters at multiple field locations within a short time period. Specifically, the dripper-TDR determines saturated hydraulic conductivity (Ks), macroscopic capillary length (λc), immobile water fraction (θim/θ), mass exchange coefficient (α) and dispersion coefficient (Dm). Multiple dripper lines were positioned over five crop rows in a field. Background and step solutions were applied through drippers to determine surface hydraulic conductivity parameters at 44 locations and surface transport properties at 38 locations. The hydraulic conductivity parameters (Ks, λc) were determined by application of three discharge rates from the drippers and measurements of the resultant steady-state flux densities at the soil surface beneath each dripper. Time domain reflectometry (TDR) was used to measure the bulk electrical conductivity of the soil during steady infiltration of a salt solution. Breakthrough curves (BTCs) for all sites were determined from the TDR measurements. The Ks and λc values were found to be lognormally distributed with average values of 31.4 cm h−1 and 6.0 cm, respectively. BTC analysis produced chemical properties, θim/θ, α, and Dm with average values of 0.23, 0.0036 h−1, and 1220 cm2 h−1, respectively. The estimated values of the flow and transport parameters were found to be within the ranges of values reported by previous studies conducted at nearby field locations. The dripper TDR method is a rapid and useful technique for in situ measurements of hydraulic conductivity and solute transport properties. The measurements reported in this study give clear evidence to the occurrence of non-equilibrium water and chemical movement in surface soil. The method allows for quantification of non-equilibrium model parameters and preferential flow. Quantifying the parameters is a necessary step toward determining the influences of surface properties on infiltration, runoff, and vadose zone transport. 相似文献
9.
Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with momentum exchange included were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1% for KF20≥7·5 and up to 12% for KF20≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F0 is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF20 (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary condition both in terms of the error magnitude and the segment of the channel reach for which these approximations would be applicable. © 1997 by John Wiley & Sons, Ltd. 相似文献
10.
11.
《Advances in water resources》2001,24(5):565-573
Analytical studies are carried out to investigate groundwater-head changes in a coastal aquifer system in response to tidal fluctuations. The system consists of an unconfined aquifer, a semi-confined aquifer and a semi-permeable confining unit between them. An exact analytical solution is derived to investigate the influences of both leakage and storage of the semi-permeable layer on the tide-induced groundwater-head fluctuation in the semi-confined aquifer. This solution is a generalization of the solution obtained by Jiao and Tang (Water Resource Research 35 (1999) 747–751) which ignored the storage of the semi-confining unit. The analytical solution indicates that both storage and leakage of the semi-permeable layer play an important role in the groundwater-head fluctuation in the confined aquifer. While leakage is generally more important than storage, the impact of storage on groundwater-head fluctuations changes with leakage. With the increase of leakage the fluctuation of groundwater-head in the confined aquifer will be controlled mainly by leakage. The study also demonstrates that the influence of storativity of the semi-permeable layer on groundwater-head fluctuation is negligible only when the storativity of the semi-permeable layer is comparable to or smaller than that of the confined aquifer. However, for aquifer systems with semi-permeable layer composed of thick, soft sedimentary materials, the storativity of the semi-permeable layer is usually much greater than that of the aquifer and its influence should be considered. 相似文献
12.
—We investigate a new nonlinear inversion method for low frequencies to determine the bulk and shear modulus as well as the material density and the location of subsurface inhomogeneities. The solution is a direct exact nonlinear inversion of single scattered waves containing near- and far-field terms for incident P and scattered P and S waves, allowing for inversion of parameters in the vicinity and at distance from the sources and receivers. Because the approach is based on single scattering theory, the range of application includes single strong scattering anomalies of various sizes like magma chambers, gas- or fluid-filled cavities, or buried near-surface obstacles. The replacement of the material properties by a new set of parameters, referred to as scattering factors, allows the inverse problem to be solved analytically. The nonlinear nature of the scattering problem is investigated and implications for the inversion process are discussed. The deviations in the elastic parameters as a function of the scattering factors show a strong asymmetry about zero, and therefore linearized approximations will perform differently, depending on the sign of the perturbation. Based on the low frequency (Rayleigh) approximation, we introduce and evaluate a pair of approximations (Mie) derived by numerical and analytical integration of the Rayleigh approximation. Both approximations are based on the underlying principle of subdividing the inhomogeneities into a number of small noninteracting parts and subsequent integration over the total volume, thus increasing the Rayleigh limit and producing better resolution of the parameter estimates during the inversion. The two Mie approximations, when evaluated as a function of scattering angle and distance, produce similar results in the mid- and far-field of the inhomogeneity and reveal better resolution than the Rayleigh approximation. For three anomalies of ± 50% in bulk modulus, shear modulus, and density, the relative error between the exact solution and the two Mie approximations remains below 10%, 20%, and 30%, respectively, for values of k p R < 3.0, where R is the radius of the heterogeneity. However, smaller errors for individual cases are found for values up to k p R≈ 4.5. The performance of the inversion based on the analytically and the numerically integrated Mie approximation is tested for single parameter perturbations, revealing reliable and stable inversion results for the bulk and the shear modulus, reasonable results for the density, and crosstalk between the shear modulus and the density. The results show well-defined locations of the anomalies and slight deviations in the estimates of their magnitudes, which can be explained by amplitude and phase deviations between the analytical solution used for forward modeling and the approximations used for the inversion. The analytical Mie approximation provides a fast means to estimate elastic parameters compared to the more time consuming numerically integrated approximation, while the latter can be applied to more arbitrarily shaped inhomogeneities. 相似文献
13.
《Physics of the Earth and Planetary Interiors》2002,129(1-2):145-151
The evolution with pressure of the unit-cell parameters brownmillerite (Ca2Fe2O5), a stoichiometric defect perovskite structure, has been determined to a maximum pressure of 9.46 GPa, by single-crystal X-ray diffraction measurements at room temperature. Brownmillerite does not exhibit any phase transitions in this pressure range. A fit of a third-order Birch–Murnaghan equation-of-state to the P–V data yields values of KT0=127.0(5) GPa and K0′=5.99(13). Analysis of the unit-cell parameter data shows that the structure compresses anisotropically. Compressional moduli for the axes are Ka0=141(1) GPa, Kb0=118(3) GPa and Kc0=122.2(2) GPa, with Ka0′=8.9(3), Kb0′=6.2(6) and Kc0′=4. The stiffest direction (i.e. along a) coincides with the direction of the FeO4 tetrahedral chains. Comparison of these data with the elasticity systematics of Ca-perovskites shows that the presence of oxygen vacancies in the brownmillerite structure softens the structure by ∼25% and that the ordering of vacancies in the perovskite structure increases the anisotropy of compression. 相似文献
14.
15.
The Analytic Element Method (AEM) provides a convenient tool for groundwater flow analysis in unbounded continuous domains. The AEM is based on the superposition of analytic functions, known as elements, useful at both regional and local scales. In this study, analytic elements for strip aquifers are presented. Such aquifers occur in riverine or coastal deposits and in outcrop zones of confined aquifers. Local flow field is modelled indirectly, using a reference plane related to the aquifer domain through the Schwarz‐Christoffel transform. The regional flow is obtained as a solution of the one‐dimensional flow equation. The proposed methodology was tested by modelling two hypothetical situations, which were compared to exact solutions. It is shown that regional boundaries can be reproduced exactly while local fields are adequately reproduced with analytic elements. The developed elements are applied to simulate a real flow field in northeastern Brazil showing good agreement with measured water levels. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
16.
Jay D. Bass Robert C. Liebermann Donald J. Weidner Stephen J. Finch 《Physics of the Earth and Planetary Interiors》1981,25(2):140-158
Hydrostatic compression data for a number of high-pressure phases of oxides and silicates, which have been studied independently by acoustic techniques, have been analyzed by least-squares fitting of the Birch-Murnaghan equation of state to determine the zero-pressure bulk modulus K0 and its pressure derivative K′0 for each material. The standard deviations of K0 and K′0 so determined are generally underestimated unless the experimental errors in the measurements of volume and pressure are explicitly included. When the values of K0 determined from the acoustic and compression techniques are consistent, test results for quartz and rutile demonstrate that constraining K0 to be equal to the acoustic value significantly improves both the accuracy and the precision of K′0 obtained from the compression data. Similar analyses for high-pressure phases (e.g., pyrope garnet and silicate spinels) indicate that by combining the acoustic and P-V data, the standard deviation of K′0 is typically reduced by a factor of three. Thus, we conclude that this approach does allow precise determinations of K′0 even when neither technique alone is able to resolve this parameter. For some materials, however, the P-V and acoustic experiments do not define mutually consistent values of K0, invalidating any combination of these data. The compression data for stishovite clearly exhibit run to run effects, and we infer that systematic errors are present in some of the P-V data which are responsible for many of the interlaboratory inconsistencies. Such systematic biases in the P-V data can at least be partially compensated for by performing several duplicate experimental runs. 相似文献
17.
This study concludes that the elongation axis (K 1) of the ellipsoid of anisotropic magnetic susceptibility (AMS) is a suitable proxy for flow axis in ashflow tuffs. 153 oriented samples (176 specimens) were studied from 18 sites in the 1.1 Ma Tshirege member of the Bandelier Tuff. These sites are distributed around the Valles caldera at distances of 5–25 km outside of the rim.K 1 axes correlate well with postulated radial flow axes at 13 sites.K 1 also agrees with measured geological flow indicators, mainly imbricated larger clasts, at 7 sites. At 2 of the 5 sites where significant disagreement is seen between theoretical radial flow directions and measuredK 1 axes, theK 1 axes correspond well with geological flow indicators, indicating that the divergence of flow from the predicted radial flow pattern is real. Two major topographic buttresses are suggested as the cause of flow divergence for the Tshirege ash flows: the San Pedro buttress northwest of the caldera, and the San Miguel buttress in the southeast. In situK 1 axes plunge about 7° toward the source at two-thirds of the sites; therefore the plunge ofK 1 is a plausible in situ indicator for thedirection of flow. Multiple flow zones in sections of several meters thickness indicate changes of flow direction that are both rapid and large during ash-flow emplacement. These observations raisre the question of how best to represent ‘mean’ flow directions in ash-flow sheets: by eigenvector methods, by vector-sum methods, or by modes. A method for measuring imbrication of larger clasts using apparent dips in vertical joints is outlined. Imbrication, determined in this way at one-third of the sites, dips toward the source, i.e., up-flow. The minimum (K 3) axis of the AMS ellipsoid correlates with the flow foliation rather than with the larger clast imbrication. The flow axes of ash flows correspond with theK 1 axes, not with the declination ofK 3 axes as suggested by some authors. Initial dip of the sampled ash flows is not large and does not affect the paleomagnetic remanence direction, which is reversed with a mean ofD=173.5°,I=-38.4°, α95=3.4°N=18. This mean is not different at the 95% confidence level from that of earlier workers. The mean pole, at 098.0°E, 74.8°N,A 95=3.3°,N=18, is about 15° far-sided relative to the expected time-averaged geomagnetic pole, suggesting a history of emplacement too short to adequately average secular variation. 相似文献
18.
Yu Nishihara Ichiro Aoki Eiichi Takahashi Ken-ichi Funakoshi 《Physics of the Earth and Planetary Interiors》2005,148(1):73-84
In situ synchrotron X-ray diffraction experiments were conducted using the SPEED-1500 multi-anvil press at SPring-8 on majoritic garnet synthesized from natural mid-ocean ridge basalt (MORB), whose chemical composition is close to the average of oceanic crust, at 19 GPa and 2200 K. Pressure-volume-temperature data were collected using a newly developed high-pressure cell assembly to 21 GPa and 1273 K. Data were fit to the high-temperature Birch-Murnaghan equation of state, with fixed values for the ambient cell volume (V0 = 1574.14(4) Å3) and the pressure derivative of the isothermal bulk modulus (K′T = 4). This yielded an isothermal bulk modulus of KT0 = 173(1) GPa, a temperature derivative of the bulk modulus (∂KT/∂T)P = −0.022(5) GPa K−1, and a volumetric coefficient of thermal expansivity α = a + bT with values of a = 2.0(3) × 10−5 K−1 and b = 1.0(5) × 10−8 K−2. The derived thermoelastic parameters are very similar to those of pyrope. The density of subducted oceanic crust compared to pyrolitic mantle at the conditions in Earth's transition zone (410-660 km depth) was calculated using these results and previously reported thermoelastic parameters for MORB and pyrolite mineral assembledges. These calculations show that oceanic crust is denser than pyrolitic mantle throughout the mantle transition zone along a normal geotherm, and the density difference is insensitive to temperature at the pressures in lower part of the transition zone. 相似文献
19.
A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases. 相似文献
20.
Jennifer Kung Baosheng LiDonald J Weidner Jianzhong ZhangRobert C Liebermann 《Earth and Planetary Science Letters》2002,203(1):557-566
The elasticity of ferropericlase with a potential mantle composition of (Mg0.83,Fe0.17)O is determined using ultrasonic interferometry in conjunction with in situ X-radiation techniques (X-ray diffraction and X-radiography) in a DIA-type cubic anvil high-pressure apparatus to pressures of 9 GPa (NaCl pressure scale) at room temperature. In this study, we demonstrate that it is possible to directly monitor the specimen length using an X-ray image technique and show that these lengths are consistent with those derived from X-ray diffraction data when no plastic deformation of the specimen occurs during the experiment. By combining the ultrasonic and X-ray diffraction data, the adiabatic elastic bulk (KS) and shear (G) moduli and specimen volume can be measured simultaneously. This enables pressure scale-free measurements of the equation of state of the specimen using a parameterization such as the Birch-Murnaghan equation of state. The elastic moduli determined for (Mg0.83,Fe0.17)O are KS0=165.5(12) GPa, G0=112.4(4) GPa, and their pressure derivatives are KS0′=4.17(20) and G0′=1.89(6). If these results are compared with those for MgO, they demonstrate that KS0 and KS0′ are insensitive to the addition of 17 mol% FeO, but G0 and G0′ are reduced by 14% and 24%, respectively. We calculate that the P and S wave velocities of a perovskite plus ferropericlase phase assemblage with a pyrolite composition at the top of the lower mantle (660 km depth) are lowered by 0.8 and 2.3%, respectively, when compared with those calculated using the elastic properties of end-member MgO. Consequently, the magnitudes of the calculated wave velocity jumps across the 660 km discontinuity are reduced by about 11% for P wave and 20% for S wave, if this discontinuity is considered as a phase transformation boundary only (ringwoodite→perovskite+ferropericlase). 相似文献