Tube wave modeling by the finite-difference method with varying grid spacing

A finite-difference approach of aP-SV modeling scheme is applied to compute seismic wave propagation in heterogeneous isotropic media, including fluid-filled boreholes. The discrete formulation of the equation of motion requires the definition of the material parameters at the grid points of the numerical mesh. The grid spacing is chosen as coarse as possible with respect to the accurate representation of the shortest wavelength. If we assume frequencies lower than 250 Hz then the grid spacing is usually chosen in the range of a few meters. One encounters difficulties because of the large-scale difference between the grid spacing and the size of the borehole, usually several centimeters.These difficulties can be overcome by a grid refinement technique. This technique provides the construction of grids with varying grid spacing. The grid spacing in the vicinity of the borehole is chosen such that the borehole is properly represented. An example demonstrates the accuracy of this technique by comparisons with other methods. Unlike many analytical methods, the FD method can handle complex subsurface geometries. Further numerical examples of walk-awayVSP configurations show tube wave propagation within fluid-filled boreholes of realistic diameters.     

不同网格间距的小剪跨比网格剪力墙抗震性能研究

为研究网格间距对网格剪力墙抗震性能的影响,对两个竖肢中心距不同的小剪跨比网格剪力墙进行了拟静力试验及有限元分析。结果表明：横肢中心距相同、竖肢中心距分别为200 mm及300 mm的网格剪力墙破坏模式不同,竖肢中心距为200 mm的网格剪力墙下部和墙底角部混凝土破坏,破坏模式为剪压破坏;竖肢中心距为300 mm的网格剪力墙沿对角线主斜裂缝错动并产生滑移,破坏模式为剪拉破坏。两个试件的极限位移角均在1/100左右,竖肢中心距为300 mm的网格剪力墙刚度和承载力略大。有限元模拟结果与试验吻合良好,验证了模拟方法的有效性。提出了适用于不同间距网格墙的等效厚度计算方法,网格剪力墙可等效为实体剪力墙计算刚度和承载力。     

Dip and anisotropy effects on flow using a vertically skewed model grid

Darcy flow equations relating vertical and bedding-parallel flow to vertical and bedding-parallel gradient components are derived for a skewed Cartesian grid in a vertical plane, correcting for structural dip given the principal hydraulic conductivities in bedding-parallel and bedding-orthogonal directions. Incorrect-minus-correct flow error results are presented for ranges of structural dip (0 < or = theta < or = 90) and gradient directions (0 < or = phi < or = 360). The equations can be coded into ground water models (e.g., MODFLOW) that can use a skewed Cartesian coordinate system to simulate flow in structural terrain with deformed bedding planes. Models modified with these equations will require input arrays of strike and dip, and a solver that can handle off-diagonal hydraulic conductivity terms.     

Analytical solution to the 3D tide-induced Lagrangian residual current in a narrow bay with vertically varying eddy viscosity coefficient

Ocean Dynamics - The 3D Lagrangian residual velocity (LRV) is solved analytically in a narrow bay employing a vertically varying eddy viscosity coefficient. The nondimensional vertical profile of...     

三维起伏地表条件下地震波走时计算的不等距迎风差分法

三维起伏地表条件下的地震波走时计算技术是研究三维起伏地表地区很多地震数据处理技术的基础性工具.为了获得适应于任意三维起伏地表且计算精度高的走时算法,提出三维不等距迎风差分法.该方法采用不等距网格剖分三维起伏地表模型,通过在迎风差分格式中引入不等距差分格式、Huygens原理及Fermat原理来建立地表附近的局部走时计算公式,并通过在窄带技术中设定新的网格节点类型来获得三维起伏地表条件下算法的整体实现步骤.精度及算例分析表明:三维不等距迎风差分法具有很高的计算精度且能够适应于任意三维起伏地表模型.     

三维起伏地表条件下地震波走时计算的不等距迎风差分法

三维起伏地表条件下的地震波走时计算技术是研究三维起伏地表地区很多地震数据处理技术的基础性工具.为了获得适应于任意三维起伏地表且计算精度高的走时算法,提出三维不等距迎风差分法.该方法采用不等距网格剖分三维起伏地表模型,通过在迎风差分格式中引入不等距差分格式、Huygens原理及Fermat原理来建立地表附近的局部走时计算公式,并通过在窄带技术中设定新的网格节点类型来获得三维起伏地表条件下算法的整体实现步骤.精度及算例分析表明:三维不等距迎风差分法具有很高的计算精度且能够适应于任意三维起伏地表模型.     

Solution of the linear diffusion equation for modelling erosion processes with a time varying diffusion coefficient

In the present paper the differential equation of the temporal development of a landform (mountain) with a time dependent diffusion coefficient is solved. It is shown that the shape and dimensions of the landform at time t are independent of the specific variation of the diffusion coefficient with time; they only depend on the mean value of the diffusion coefficient in the time interval where the erosion process takes place. Studying the behaviour of the solution of the differential equation in the wave number domain, it is concluded that Fourier analysis may help in estimating, in quantitative terms, the initial dimensions, the age or, alternatively, the value of the diffusion coefficient of the landform. The theoretical predictions are tested on a hill of the southern part of the Ural mountainous region, in order to show how the results of the mathematical analysis can be used in describing, in quantitative terms, the morphological development of landforms due to erosion processes. Copyright © 2007 John Wiley & Sons, Ltd.     

Phase-shift migration with a variable-length spatial transform–an algorithm for moderately varying lateral velocities1

A migration algorithm appropriate for moderately varying lateral velocity changes is developed as an extension of phase-shift migration by using a variable-length spatial transform. This process significantly reduces the number of lateral wave-numbers necessary to downward continue the data, and it replaces the spatial FFT with a simple recursion relationship. For a given frequency and position x, ten lateral wavenumbers are typically sufficient, and the migration algorithm produces accurate images when the velocity structure V (X, z) changes over a few depth intervals of thickness Δz, with lateral velocity gradients up to 1.4 to 1.0.     

Ground motion modelling with a stochastically perturbed excitation

We present a new hybrid method combining deterministic and stochastic features. The aim is to describe the crustal propagation better than deterministic or stochastic methods can do separately. We start from the deterministic hybrid method based on Discrete- Wavenumber and Finite-Difference techniques (DW–FD). First we modify the DW–FD procedure by introducing topographical variations and a spatially varying Q factor. Then, to take into account effects due to small-scale heterogeneities of the crust, we add a stochastic noise (perturbation) to the deterministic signal propagated through the crust. The stochastic noise is constructed using a kind of Markov-like process generator with two physical constraints: to have the Brune spectrum, and to reproduce the spatial decay of coherence reported in literature for real sites. We have chosen a Markov-like technique because it allows us to get stochastic noise, with the given coherence spatial decay, directly in time domain. This new hybrid method is applied in a numerical test, the parameters of which approximate the case of the 12 June, 1995 Rome earthquake. It is found that the coherence decay with distance at the alluvial valley surface is slower than the prescribed coherence decay inside the bedrock.     

A note on magnetic modelling with remanence

The general problem of magnetic modelling involves accounting for the effect of both remanent magnetization and the application of an external magnetic field. However, as far as the disturbing field of a magnetic body in a magnetic environment is concerned, there is an equivalence between the effects of these two causations that allows the remanence to be represented in terms of an equivalent primary magnetic H field. Moreover, due to the linearity of the magnetic field in terms of its causations, the general modelling problem involving an applied magnetic field in the presence of remanence can be simply and more efficiently dealt with in terms of an equivalent primary field acting in the absence of any remanent magnetization.     

Optimal implicit staggered‐grid finite‐difference schemes based on the sampling approximation method for seismic modelling

We propose new implicit staggered‐grid finite‐difference schemes with optimal coefficients based on the sampling approximation method to improve the numerical solution accuracy for seismic modelling. We first derive the optimized implicit staggered‐grid finite‐difference coefficients of arbitrary even‐order accuracy for the first‐order spatial derivatives using the plane‐wave theory and the direct sampling approximation method. Then, the implicit staggered‐grid finite‐difference coefficients based on sampling approximation, which can widen the range of wavenumber with great accuracy, are used to solve the first‐order spatial derivatives. By comparing the numerical dispersion of the implicit staggered‐grid finite‐difference schemes based on sampling approximation, Taylor series expansion, and least squares, we find that the optimal implicit staggered‐grid finite‐difference scheme based on sampling approximation achieves greater precision than that based on Taylor series expansion over a wider range of wavenumbers, although it has similar accuracy to that based on least squares. Finally, we apply the implicit staggered‐grid finite difference based on sampling approximation to numerical modelling. The modelling results demonstrate that the new optimal method can efficiently suppress numerical dispersion and lead to greater accuracy compared with the implicit staggered‐grid finite difference based on Taylor series expansion. In addition, the results also indicate the computational cost of the implicit staggered‐grid finite difference based on sampling approximation is almost the same as the implicit staggered‐grid finite difference based on Taylor series expansion.     

Ground penetrating radar sounding of a temperate glacier; modelling of a multilayered medium1

A numerical simulation of electromagnetic propagation through a multilayered medium is performed in order to explain and interpret the signal received from the radar sounding of a temperate glacier. During the winter of 1990, several radar profiles were obtained on the Mont-de-Lans glacier in the French Alps with a ground penetrating radar which uses a phase modulation of the transmitted pulse by coded sequences. The pulse compression is obtained by applying the matched filter to the received signal, which provides a range-resolution of about 8 m in the ice. The profiles recorded on the temperate glacier do not show a single clear reflection from the ice-bedrock interface, but they exhibit widely distributed energy decreasing with depth. This may be due to the inhomogeneous inner structure of the temperate glacier and we use a simple model of a layered medium to compute a simulation of the propagation. Thus, partial reflection at each layer and scattering from a rough basal interface may explain the observed signal. A computer-based technique is used to locate on the data the bottom of the glacier in order to estimate the ice thickness. The results from the different radar profiles are consistent and are a good fit to the thickness which has been determined by other geophysical methods.     

变厚度钢板内芯防屈曲支撑试验研究

提出了一种变厚度钢板内芯防屈曲支撑（VTBRB）。设计了2个足尺变厚度钢板内芯防屈曲支撑试件,其中:1个试件在变厚度内芯端部设置加劲肋;另1个试件采用无肋式变厚度内芯。通过拟静力试验分析了2种内芯构造形式对变厚度钢板内芯防屈曲支撑的滞回性能、失效模式、受压承载力调整系数和累计塑性变形等的影响。研究表明:2个变厚度钢板内芯防屈曲支撑均表现较好的抗震耗能特性,其受压承载力调整系数均满足相关规范的限值要求。设置加劲肋可以减少变厚度内芯端部无粘结材料的磨损,并可以有效提高变厚度内芯防屈曲支撑的低周疲劳性能。     

Incremental distributed modelling investigation in a small agricultural catchment: 1. Overland flow with comparison with the unit hydrograph model

A distributed overland flow model is presented and the test results compared with those of the unit hydrograph (UH) model. Infiltration excess in the overland model was calculated using both a modified Green and Ampt (G–A) method and a more complicated method that keeps track of the soil moisture content. The two‐dimensional partial differential flow equations with kinematic flow approximation were solved using both backward‐central explicit and implicit finite‐difference schemes. Moreover, a baseflow component was added to the flow model. Each part of the model was built by replacing a process by a parallel process or by adding a completely new component. When the model was developed and validated in small agricultural fields in southern Finland, comparisons were made between corresponding processes and the significance of added components were estimated in order to find out whether increased model complexity improves the model performance. Apart from the basic model, all the other distributed models outperformed the UH approach. The implicit scheme was clearly more accurate than the explicit scheme, and the baseflow component improved the results significantly. There was no major difference between the performances of the infiltration models, but the G–A method was more stable and much faster. The approaches that were best in the calibration were also the best in the verification. The full distributed model provides a potential method for running water‐quality models and testing their different processes. Copyright © 2006 John Wiley & Sons, Ltd.     

Unified global and regional wave model on a multi-resolution grid

Models for ocean surface wave forecasting in weather centres comprise global and regional systems in order to efficiently meet service demands. Regional models cannot run alone and have to use large area or global models to provide boundary wave spectra. The modern two-way nesting technique is to run the two models together with the regional model domain covered by both resolutions. An alternative method is to use a single multi-resolution grid that fits irregular coastlines and provides refined resolutions in selected regions. This paper presents a multi-resolution model based on a spherical multiple-cell (SMC) grid, which is designed to relax the CFL restriction of Eulerian advection time step at high latitudes by merging the conventional latitude-longitude grid cells. The implementation of the SMC grid in WAVEWATCH III is described, and a multi-resolution (6, 12 and 25 km) global SMC configuration is compared with a suite of nested grid ocean surface wave models, including 35-km global, 8-km European and 4-km UK regional models. Verification against buoy and platform wave observations indicates that the unified model is better than the 35-km global and very close in performance to the two regional models.     

Impacts of spatially and temporally varying snowmelt on subsurface flow in a mountainous watershed: 1. Snowmelt simulation

Abstract

The dominant source of streamflow in many mountainous watersheds is snowmelt recharge through shallow groundwater systems. The hydrological response of these watersheds is controlled by basin structure and spatially distributed snowmelt. The purpose of this series of two papers is to simulate spatially varying snowmelt and groundwater response in a small mountainous watershed. This paper examines the spatially and temporally variable snowmelt to be used as input to the groundwater flow modelling described in the second paper. Snowmelt simulation by the Simultaneous Heat and Water (SHAW) model (a detailed process model of the interrelated heat, water and solute movement through vegetative cover, snow, residue and soil) was validated by applying the model to two years of data at three sites ranging from shallow transient snow cover on a west-facing slope to a deep snow drift on a north-facing slope. The simulated energy balances for several melt periods are presented. Snow depth, density, and the magnitude and timing of snow cover outflow were simulated well for all sites.     

Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction

A finite-element method for computing the electric field in a 3-D conductivity model of the Earth for plane wave sources, thus enabling magnetotelluric responses to be calculated, is presented. The method incorporates in the iterative solution of the electric-field system of equations the divergence correction technique introduced for finite-difference solutions by Smith (1996). The correction technique accelerates the development of the discontinuity of the normal component of the approximate electric field across conductivity discontinuities. The convergence rate of the iterative solution is improved significantly, especially for low frequencies. The correction technique involves computing the divergence of the current density for the approximate electric field, computing the static potential whose source is this divergence of the current density, and ‘correcting’ the approximate electric field by subtracting from it the gradient of the potential. This is repeated at regular intervals during the iterative solution of the electric-field system of equations. For the method presented here, the Earth model is discretised using a rectilinear mesh comprising uniform cells. Edge-element basis functions are used to approximate the electric field and nodal basis functions are used to approximate the correction potential. The Galerkin method is used to derive the systems of equations for the approximate electric field and correction potential from the respective differential equations. A bi-conjugate gradient solver was found to be adequate for the system of equations for the correction potential; a generalised minimum residual solver was found to be better for the electric-field system of equations. The method is illustrated using the COMMEMI 3D-1A and 3D-2A models.     

Stochastic modelling at Stromboli: a volcano with remarkable memory

The assessment of potential volcanic eruptions is a critical aspect when evaluating the safety of populated areas. A stochastic approach has been developed for the analysis and simulation of data sampled at active volcanoes. This approach allows for the detection and quantification of time correlation, volcanic event forecasts using Cox model based simulations and volcanic tremor decomposition in order to identify potential precursors of major eruptions. The stochastic approach has been applied to data monitored at Stromboli volcano. Significant time correlation has been detected which makes Stromboli a volcano with a remarkable memory of its recent activity in comparison to other volcanoes. Forecasting of the number of strombolian events for the next few days has been performed by Monte Carlo simulations. Finally, kriging analysis of the tremor intensity has enabled time component estimation which could furnish additional monitoring variables for the forecast of paroxysmal phases at Stromboli.     

Electric and magnetic field of a direct-current source in a medium with a continuously varying conductivity

Fields due to an electric current source in the atmosphere where the conductivity increases exponentially with altitude have been calculated. Characteristics of the field are described. The current source is assumednot to vary with time.Department of Electronic Engineering, Gumma University.