A comment on Honkasalo's correction

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Paper presented at the IUGG XVII Plenary Meeting, Canberra, Dec. 1979.     

A dispersion scale effect in model calibrations and field tracer experiments

Field tracer experiments and model calibrations indicate that the magnitude of dispersivity increases as a function of the scale at which observations are made. Calculations presented in this study suggest that some part of this scaling may be explained as an artifact of the models used. Specifically, a scaling-up of dispersivity will occur whenever an (n − 1)-dimensional model is calibrated or otherwise employed to describe an n-dimensional system. The calibrated coefficients for such models will depend not only on size of the contaminant plume or tracer experiment at the time of calibration, but will exhibit a size dependency beyond the calibration period. The magnitude of scaling appears to be sufficient to encompass the range of differences between laboratory measurements of dispersivity and model calibrations.     

Cavity effect on Rayleigh wave dispersion and P-wave refraction

Sinkholes and cavities can represent serious hazards to human safety and urban infrastructures,cause roadbed subsidence,and so on.It is therefore essential to evaluate various sinkholes in different depths and sizes to assess the risk of collapse.This paper evaluates the effect of different cavities on Rayleigh-wave propagation and body(P)wave refraction.Rayleigh(R)wave propagation is analyzed according to the classical multi-channel analysis of surface waves(MASW)method also considering the R-wave backscattering.Synthetic seismic traces are computed by means of finite element modeling(FEM)for cavity and intrusion at different depths and sizes.Furthermore,field acquisition data is used to verify the detection effect of a cavity on R-and P-waves.The results show that the presence of backscattered R-waves and the changes in the R-wave velocity spectrum can help in cavity identification.Additional possible evidence is represented by significant changes in the refraction travel times over the cavity location.It can be concluded that the field data are in good agreement with the synthetic,and it could be effective to consider the results of both R-and P-wave analysis in order to efficiently identify the cavities.     

A semi-implicit semi-Lagrangian global nonhydrostatic model and the polar discretization scheme

The Global/Regional Assimilation and PrEdiction System(GRAPES) is a newly developed global non-hydrostatic numerical prediction model,which will become the next generation medium-range opera-tional model at China Meteorological Administration(CMA).The dynamic framework of GRAPES is featuring with fully compressible equations,nonhydrostatic or hydrostatic optionally,two-level time semi-Lagrangian and semi-implicit time integration,Charney-Phillips vertical staggering,and complex three-dimensional pre-conditioned Helmholtz solver,etc.Concerning the singularity of horizontal momentum equations at the poles,the polar discretization schemes are described,which include adoption of Arakawa C horizontal grid with ν at poles,incorporation of polar filtering to maintain the computational stability,the correction to Helmholtz equation near the poles,as well as the treatment of semi-Lagrangian interpolation to improve the departure point accuracy,etc.The balanced flow tests validate the rationality of the treatment of semi-Lagrangian departure point calculation and the polar discretization during long time integration.Held and Suarez tests show that the conservation proper-ties of GRAPES model are quite good.     

Lithologic control of bedrock meander dimensions in the appalachian valley and ridge province: A comment on a comment

Abrahams' comment relates meander length to channel cross-section shape and recurrence interval so that meander length can be both directly and inversely proportional to rock resistance. This reply notes that either meander length is directly proportional to rock resistance or it is not; one cannot have it both ways. Many Appalachian Valley and Ridge bedrock meanders are shown to be the same size as alluvial meanders, and appear to be somewhat underfit. A hypothesis is proposed where modest discharge increases may have accelerated bedrock meander cutting although present streams remain capable of slowly cutting the meanders.     

Magnetotelluric dispersion relations in a two-dimensional model of the coastal effect

Numerical modeling is performed for seafloor magnetotelluric sounding in a 2-D offshore zone in a period range of 0.25–16 h. An anomaly of the seafloor longitudinal impedance observed at distances of 20–260 km from the shore is analyzed. Dispersion relations are violated for the longitudinal impedance within the anomalous zone.     

The effect of dispersion on the stability of density-driven flows in saturated homogeneous porous media

This work is a continuation of Musuuza et al. [37] in which a stability criterion for density-driven flow in a saturated homogeneous medium was derived. The criterion predicted the stability of a system as a function of the density and viscosity contrasts, the magnitude of the flow velocity and the concentration gradients for flow aligned orthogonal to gravity. It could not accurately predict stability transition with increasing velocity, a failure we attributed to dispersion effects that were not included. Small-scale dispersion and molecular diffusion, the main stabilising mechanisms in homogeneous media can stabilise flow if the instability wavelengths are below a certain cutoff. The width of the mixing zone is also central in controlling the range of wavelengths that persist into fingers. We propose a method of quantifying the cutoff wavelength and the width of the mixing zone, which are incorporated into the earlier criterion as constituents of the dispersive part. The earlier criterion is reformulated in terms of the Rayleigh number and with the dispersive part added, we attempt to predict the number of fingers formed which is directly related to the physical stability of the system. The inclusion of the Rayleigh number and dispersion into a single stability criterion provides new insight in the way dispersion affects vertical flow systems. Stability numbers computed with the new criterion are in reasonable agreement with numerical simulations for a range of physical variables. The numerical computations are performed with the software package d³f, which uses the cell-centred finite volume and the implicit Euler methods for the spatial and temporal discretisations, respectively. The admission of the density and dispersivities as inputs into the criterion makes it usable in practical problems.     

Heat dispersion effect on thermal convection in a porous medium layer

Thermal convection resulting from vertical temperature gradients in porous media is analyzed. The effect of heat dispersion is taken into account. It is found that heat dispersion increases the thermal stability of the flow field and may inhibit the appearance of convection currents, which would appear if dispersion effects are omitted.The longitudinal as well as the lateral dispersivities affect the thermal stability and the dimensions of the convection cells. As a result of the convection currents the horizontal streamlines in the steady state are distorted. The thermal convection exhibits internal waves in the field.     

A comment on determining the induced magnetic field in bodies of arbitrary shape

Summary The authors prove that the solution of Laplace's equation under Neumann's boundary conditions can be transformed to an advantage into determining the field which is generated by charges, induced by the external field at surfaces of discontinuity.     

流体黏度对砂岩弹性模量频散与衰减影响规律的实验及理论验证

波诱导的孔隙流体流动是造成地震波速度频散与衰减的重要机制, 其中孔隙流体性质(尤其是黏度)是影响速度频散变化特征的关键因素之一.为了研究孔隙流体黏度对速度频散的影响, 本文在饱和不同黏度流体条件下对2块低孔隙度砂岩和3块中孔隙度砂岩样品进行了低频应力-应变岩石物理测试, 获得了岩石样品1~3 kHz的杨氏模量、泊松比和衰减曲线.实验结果发现: 两种砂岩样品都表现出随着有效压力增加, 杨氏模量增加, 频散程度减弱的特征; 同时随着流体黏度增大, 频散梯度增大, 特征频率向较低频率移动.为了更好地解释不同流体黏度条件下的实验数据, 本文采用现有经典岩石物理频散模型对实测速度频散进行了描述.研究结果表明, 经典的Gurevich喷射流模型、Biot模型、White模型、Gassmann方程和BISQ模型在数值上和趋势上均难以定量刻画实测低频数据, 其预测结果存在明显的特征频率且中间过渡频段较小, 而实测速度则随频率的增大呈缓慢递增趋势, 且具有较宽的中间过渡频段.对于中孔隙度砂岩样品, 考虑Biot宏观流作用、软孔与软孔以及软孔与硬孔喷射流效应的扩展Gurevich喷射流模型能够给出与实验数据较为吻合的预测结果; 对于低孔隙度砂岩, 扩展Gurevich喷射流模型的预测结果也能在趋势上与实验数据保持一致.实验数据和理论模型共同指出归一化参数E(f)/E(1 Hz)具有提高储层流体预测与流体识别精度的潜力和重要意义.

     

A study on determining the theoretical dispersion curve for Rayleigh wave propagation

A method has been presented to establish the theoretical dispersion curve for performing the inverse analysis for the Rayleigh wave propagation. The proposed formulation is similar to the one available in literature, and is based on the finite difference formulation of the governing partial differential equations of motion. The method is framed in such a way that it ultimately leads to an Eigen value problem for which the solution can be obtained quite easily with respect to unknown frequency. The maximum absolute value of the vertical displacement at the ground surface is formed as the basis for deciding the governing mode of propagation. With the proposed technique, the numerical solutions were generated for a variety of problems, comprising of a number of different layers, associated with both ground and pavements. The results are found to be generally satisfactory.     

A comment on the continuity equation model of slope profile development and its boundary conditions

The constant base boundary condition used by Kirkby to derive characteristic form solutions to the continuity equation are unlikely in practice. Constant form solutions relying on constant basal erosion are however more probable.     

Spatial discretization of large watersheds and its influence on the estimation of hillslope sediment yield

The combined use of water erosion models and geographic information systems has facilitated soil loss estimation at the watershed scale. Tools such as the Geo‐spatial interface for the Water Erosion Prediction Project (GeoWEPP) model provide a convenient spatially distributed soil loss estimate but require discretization to identify hillslopes and channels. In GeoWEPP, the TOpographic PArameteriZation (TOPAZ) model is used as an automated procedure to extract a watershed boundary, hillslopes and channels from a digital elevation model (DEM). Previous studies in small watersheds have shown that the size of the hillslopes and the channel distribution affect the model estimates, but in large watersheds, the effects on the soil loss estimates have yet to be tested. Therefore, the objective of this study was to evaluate the effect of discretization on the hillslope sediment yield estimates using GeoWEPP in two large watersheds (>10 km²). The watersheds were selected and discretized varying the TOPAZ parameters [critical source area (CSA) and minimum source channel length (MSCL)] in a 30‐m resolution digital elevation model. The drainage networks built with TOPAZ were compared with each other using the drainage density index. The results showed that the discretization affected hillslope sediment yield estimates and their spatial distribution more than the total runoff. The drainage density index and the hillslope sediment yield were proportional but inversely related; thus, soil loss estimates were highly affected by the spatial discretization. As a result of this analysis, a method to choose the CSA and MSCL values that generates the greatest fraction of hillslopes having profile lengths less than 200 m was developed. This slope length condition is particularly crucial when using the WEPP and GeoWEPP models, in order for them to produce realistic estimates of sheet and rill erosion. Finally, and as a result of this analysis, a more reliable method was developed for selecting the TOPAZ channel network parameters (CSA and MSCL). Copyright © 2015 John Wiley & Sons, Ltd.     

A method for solving relative dispersion of the cloud droplet spectra

The relative dispersion of the cloud droplet spectra or the shape parameter is usually assumed to be a constant in the two-parameter cloud microphysical scheme, or is derived through statistical analysis. However, observations have revealed that the use of such methods is not applicable for all actual cases. In this study, formulas were derived based on cloud microphysics and the properties of gamma function to solve the average cloud droplet radius and the cloud droplet spectral shape parameter. The gamma distribution shape parameter, relative dispersion, and cloud droplet spectral distribution can be derived through solving the droplet spectral shape parameter equation using the average droplet radius, volume radius, and their ratio, thereby deriving an analytic solution. We further examined the equation for the droplet spectral shape parameter using the observational droplet spectral data, and results revealed the feasibility of the method. In addition, when the method was applied to the two-parameter cloud microphysical scheme of the Weather Research and Forecast(WRF) model to further examine its feasibility, the modeling results showed that it improved precipitation simulation performance, thereby indicating that it can be utilized in two-parameter cloud microphysical schemes.     

A comment on the use of spectral characteristics of teleseismic body waves to evaluate fine crustal structure

An investigation of the crustal response in the time and frequency domains is presented to show that for models with similar crustal transit times of P and S waves, any important changes in the internal configuration of the crust such as layering, layer thickness and velocity contrast only influence the amplitudes of the transfer function ratio. Frequency positions of peaks and troughs remain unperturbed unless the total transit time of P and/or S waves through the crust are varied. This would imply that fine crustal structure derived from a matching of peak positions of observed spectral ratios with theoretical transfer function ratios, as is commonly practiced, is not very meaningful. This limitation in the application of the spectral ratio method for detailed crustal structure is demonstrated using two recent applications of this technique.     

A new method for laboratory estimation of the transverse dispersion coefficient

We introduce a method for identifying the transverse dispersion coefficient in laboratory experiments based on the analytical solution of a pulse injection of a nonreactive solute in a soil column (cylindrical geometry) packed with a homogeneous porous medium. This method takes into account the effect of boundary conditions such as no flux on the column perimeter, and it does not need a priori knowledge of the longitudinal dispersion coefficient. Numerical applications of the method show that it is stable and robust and that the results are reasonably in accordance with those found using the classical maximum likelihood method.