Generalized Coarse Graining Procedures for Flow in Porous Media

This paper focuses on heterogeneous soil conductivities and on the impact their resolution has on a solution of the piezometric head equation: owing to spatial variations of the conductivity, the flow properties at larger scales differ from those found for experiments performed at smaller scales. The method of coarse graining is proposed in order to upscale the piezometric head equation on arbitrary intermediate scales. At intermediate scales large scale fluctuations of the conductivities are resolved, whereas small scale fluctuations are smoothed by a partialy spatial filtering procedure. The filtering procedure is performed in Fourier space with the aid of a low-frequency cut-off function. We derive the partially upscaled head equations. In these equations, the impact of the small scale variability is modeled by scale dependent effective conductivities which are determined by additional differential equations. Explicit results for the scale dependent conductivity values are presented in lowest order perturbation theory. The perturbation theory contributions are summed up with using a renormalisation group analysis yielding explicit results for the effective conductivity in isotropic media. Therefore, the results are also valid for highly heterogeneous media. The results are compared with numerical simulations performed by Dykaar and Kitanidis (1992). The method of coarse graining combined by a renormalisation group analysis offers a tool to derive exact and explicit expressions for resolution dependent conductivity values. It is, e.g., relevant for the interpretation of measurement data on different scales and for reduction of grid-block resolution in numerical modeling. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling of the OASIS Energy Flux Measurements Using Two Canopy Concepts

Two land surface schemes, SCAM and CSIRO9, were used to model the measured energy fluxes during the OASIS (Observations At Several Interacting Scales) field program. The measurements were taken at six sites along a 100 km rainfall gradient. Two types of simulations were conducted: (1) offline simulations forced with measured atmospheric input data at each of the six sites, and (2) regional simulations with the two land surface schemes coupled to the regional climate model DARLAM.The two land surface schemes employ two different canopy modelling concepts: in SCAM the vegetation is conceptually above the ground surface, while CSIRO9 employs the more commonly used `horizontally tiled' approach in which the vegetation cover is modelled by conceptually placing it beside bare ground. Both schemes utilize the same below-ground components (soil hydrological and thermal models) to reduce the comparison to canopy processes only. However, the ground heat flux, soil evaporation and evapotranspiration are parameterised by the two canopy treatments somewhat differently.Both canopy concepts reproduce the measured energy fluxes. SCAM has a slightly higher root-mean standard error in the model-measurement comparison for the ground heat flux. The mean surface radiative temperature simulated by SCAM is approximately 1K lower than in the CSIRO9 simulations. However, the soil and vegetation temperatures (which contribute to the radiative temperature) varied more in the CSIRO9 simulations. These larger variations are due to the absence of a representation of the aerodynamic interactions between vegetation and ground.     

Modelling the Venice Lagoon

In this paper, an overview is given on the modelling activities at the National Research Council in Venice (ISDGM-CNR) concerning the Venice Lagoon. A short history of former modelling efforts is given. A finite element hydrodynamic model is presented that has been created especially for the Venice Lagoon. This model has been applied to various situations. Residual currents have been computed for one year. A specific storm surge event has been simulated with spatially varying real winds. A transport diffusion model has been applied to model the impact of a treatment plant on the central lagoon. And a sub-basin has been modeled with a high resolution grid.     

Neural dynamic modelling on earthquake magnitude series

Earthquake magnitude prediction is of vital importance for human safety. The earthquake is a very complicated and non-linear dynamic process. It cannot be described adequately by any deterministic models. In this paper a neural dynamic modelling for earthquake magnitude prediction is reported. Historical records of earthquake magnitude series are used to construct the optimal non-linear dynamic model, and the consequent outcome of the earthquake behaviour is then predicted by this model. In turn, the latest recorded data set can be fed back to improve the accuracy of the neural dynamic model. The modelling of experiments of three earthquake magnitude series in China and Japan and their extrapolated predictions are included in this paper. The values predicted by extrapolation are in good agreement with the historical data.     

P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation

P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.     

Estimation of in situ viscoelastic parameters of weak floor strata by plate-loading tests

Summary This paper explores an approach to estimation of the viscoelastic parameters of weak floor strata using plate-loading tests. Mathematical equations are derived to describe deformation-time history for the standard Burgers model under three-dimensional stress-strain conditions, which are verified with a finite element model. A number of time-dependent in-mine plate-loading tests were conducted and the values of the viscoelastic parameters were estimated based on the derived equation. It is shown that large discrepancies between the parameter values estimated from the plate-loading tests and those acquired from the in-mine convergence data are the results of neglecting adjacent pillar interaction. Finite element modelling was conducted to investigate the effects of adjacent pillar interactions upon the pillar settlement. Based on the finite element analyses, a correction curve was developed to adjust the viscoelastic parameter values to take into account the interaction between adjacent pillars. With the correction, the parameter values estimated from the plate-loading tests compared favourably with those acquired from the in-mine convergence results.     

Modelling of soil temperature profiles using data from the pilot experiment at Anand

We present some preliminary results from a multi-layer soil temperature finite-difference model using the data set obtained during the pilot experiment on land surface processes at Anand. We hope that the present results will prove useful during the final field experiments scheduled for the coming monsoon season.