Optimum expression for computation of the magnetic field of a homogeneous polyhedral body12

An expression which is optimum with respect to the simplicity of the numerical computations is obtained for the magnetic field of a polyhedron with constant magnetization. The high accuracy of the results is illustrated using a realistic numerical model. The existence of the magnetic field at points inside the source and on its boundary is discussed and related to real magnetic data modelling.     

Integration of the life of field seismic data with the reservoir model at the Valhall Field‡

The frequent time‐lapse observations from the life of field seismic system across the Valhall field provide a wealth of information. The responses from the production and injection wells can be observed through time‐shift and amplitude changes. These observations can be compared to modelled synthetic seismic responses from a reservoir simulation model of the Valhall Field. The observed differences between the observations and the modelling are used to update and improve the history match of the reservoir model. The uncertainty of the resulting model is reduced and a more confident prediction of future reservoir performance is provided. A workflow is presented to convert the reservoir model to a synthetic seismic response and compare the results to the observed time‐lapse responses for any time range and area of interest. Correlation based match quality factors are calculated to quantify the visual differences. This match quality factor allows us to quantitatively compare alternative reservoir models to help identify the parameters that best match the seismic observations. Three different case studies are shown where this workflow has helped to reduce the uncertainty range associated with specific reservoir parameters. By updating various reservoir model parameters we have been able to improve the match to the observations and thereby improve the overall reservoir model predictability. The examples show positive results in a range of different reservoir modelling issues, which indicates the flexibility of this workflow and the ability to have an impact in most reservoir modelling challenges.     

Modern trends in the solution of forward and inverse 3D electromagnetic induction problems

The main results obtained during the last 5–8 yr in the solution of forward and inverse problems of 3D induction studies are summarized. The up-to-date status of 3D modelling is presented and prospective improvements in the formulation and numerical solution of forward problems are discussed. Approximate techniques and practical aspects of 3D modelling are specially considered. The general scheme of 3D interpretation of electromagnetic geophysical observations is outlined and realistic formalized approaches to solving 3D inverse problems, namely direct inversion and formalized model fitting, are studied.     

Improving the predictions of a MIKE SHE catchment‐scale application by using a multi‐criteria approach

This paper suggests a multi‐criteria protocol for appropriately evaluating the predictions of hydrologic models during calibration and evaluation stages. The protocol includes different statistical, analytical and visual criteria such as analysis of peak and low flows, cumulative volumes, extreme value statistics, performance statistics, etc. Furthermore, the protocol assesses the physical consistency of model predictions by filtering the total observed hydrograph into different flow‐components (baseflow, interflow and overland flow) and using these filtered data in the calibration and evaluation processes. Based on the distributed modelling of a medium size catchment, it is shown that application of the suggested protocol, and in particular the use of the filtered flow‐components in model calibration, enhances the physical consistency of model predictions, adding considerable value to the calibration process. Copyright © 2007 John Wiley & Sons, Ltd.     

2.5维地震波场褶积微分算子法数值模拟

早期的褶积微分算子都是基于正反傅立叶变换而实现的,其精度比四阶有限差分的精度稍高,本文将计算数学中的Forsyte广义正交多项式微分算子与褶积算子相结合,构建了一个新的快速、高精度褶积微分算子,其计算结果非常接近实验函数微分的精确值,精度与16阶有限差分的精度相当,远优于错格伪谱法的精确度.另外,2.5维数值模拟比二维模拟可以更真实地模拟三维介质的臬个剖面的波场,并且2.5维地震波模拟的计算量比三维模拟的计算量及计算耗时要大大减少.本文利用基于Forsyte广义正交多项式褶积微分算子法计算2.5维非均匀介质地震波场,模拟结果表明,该算法的计算速度快,计算精度高,能够直观、高效地反映复杂介质中波场的传播规律,并且2.5维波场数值模拟具有更高的计算效率,是一种非常值得深入研究并广泛应用的方法.     

Capturing the essential spatial variability in distributed hydrological modelling: Hydraulic roughness

The spatial variability of each parameter affecting storm runoff must be accounted for in distributed modelling. The objective of the work reported here is to assess the effects of using distributed versus lumped hydraulic roughness coefficients in the modelling of direct surface runoff. A spatially variable data set composed of Manning roughness coefficients is used to model direct surface runoff. To assess the information content (as measured by entropy) of spatially variable data and its significance in distributed modelling, various degrees of smoothing are applied. The error resulting from smoothing the hydraulic roughness coefficients is determined by modelling overland flow using a finite element solution. The Manning roughness coefficients were taken from field measurements of the Manning roughness coefficient at 0.6 m on a 14 m hillslope. These values were then used in a numerical simulation of outflow hydrographs to investigate the dependence of error on spatial variability. Our study focuses on the characteristics of spatial data used in distributed hydrological modelling. The field sites have fractal dimensions of ≈? 1.4, which is close to a Brownian variation. The sampling interval that captures the essential spatial variability of the Manning roughness coefficient does not seem to matter due to its Brownian variation in the field sites. Hence due to the nearly uniform random distribution, measurements at 0.6 m intervals are not necessary and larger intervals would yield results that are just as acceptable provided the mean value together with a uniformly random distribution is maintained for any size of finite element or sampling resolution. Because detailed measurements of hydraulic roughness are not practically available for deterministic catchment modelling, it is important to know that larger sampling resolutions may be used than 0.6 m.     

Modelling the effects of Zostera noltei meadows on sediment dynamics: application to the Arcachon lagoon

A three-dimensional model has been modified to describe the complex interactions between hydrodynamics, sediment dynamics and biological parameters in the presence of Zostera noltei. The model treats seagrass leafs as flexible blades that bend under hydrodynamic forcing and alter the local momentum and turbulence fluxes and, therefore, the benthic shear conditions; these changes cause related changes to the mass balance at the boundary of the bed, in turn affecting the suspended matter in the column and ultimately primary productivity and the growth of the dwarf-grass. Modelling parameters related to the impact of Z. noltei to the local flow and to erosion and deposition rates were calibrated using flume experimental measurements; results from the calibration of the model are presented and discussed. The coupled model is applied in the Arcachon Bay, an area with high environmental significance and large abundance of dwarf-grass meadows. In the present paper, results from preliminary applications of the model are presented and discussed; the effectiveness of the coupled model is assessed comparing modelling results with available field measurements of suspended sediment concentrations and seagrass growth parameters. The model generally reproduces sediment dynamics and dwarf-grass seasonal growth in the domain efficiently. Investigations regarding the effects of the vegetation to the near-bed hydrodynamics and to the sediment suspension in the domain show that dwarf-grass meadows play an important part to velocity attenuation and to sediment stabilisation, with flow and suspended sediment concentrations damping, compared to an unvegetated state, to reach 35–50 and 65 %, respectively, at peak seagrass growth.     

Comparison of eigensensitivity and ANN based methods in model updating of an eight-story building

Analytical models prepared from field drawings do not generally provide results that match with experimental results.The error may be due to uncertainties in the property of materials,size of members and errors in the modelling process.It is important to improve analytical models using experimentally obtained data.For the past several years,data obtained from ambient vibration testing have been successfully used in many cases to update and match dynamic behaviors of analytical models with real structures.This paper presents a comparison between artificial neural network(ANN) and eigensensitivity based model updating of an existing multi-story building.A simple spring-mass analytical model,developed from the structural drawings of the building,is considered and the corresponding spring stiffness and lumped mass of all floors are chosen as updating parameters.The advantages and disadvantages of these updating methods are discussed.The advantage is that both methods ensure a physically meaningful model which canbe further employed in determining structural response and health monitoring.     

Correlation of dynamic characteristics of a super‐tall building from full‐scale measurements and numerical analysis with various finite element models

The Di Wang Tower located in Shenzhen has 79 storeys and is about 325 m high. Field measurements have been conducted to investigate the dynamic characteristics of the super‐tall building. In parallel with the field measurements, seven finite element models have been established to model the multi‐outrigger‐braced tall building and to analyse the effects of various arrangements of outrigger belts and vertical bracings on the dynamic characteristics and responses of the Di Wang Tower under the design wind load and earthquake action. The distributions of shear forces in vertical structural components along the building height are also presented and discussed. The results from detailed modelling of group shear walls with several types of finite elements are addressed and compared to investigate various modelling assumptions. Finally, the performance of the finite element models is evaluated by correlating the natural frequencies and mode shapes from the numerical analysis with the finite element models and the field measurements. The results generated from this study are expected to be of interest to professionals and researchers involved with the design of tall buildings. Copyright © 2004 John Wiley & Sons, Ltd.     

Implications of model uncertainty for the mapping of hillslope‐scale soil erosion predictions

An integrated modelling approach (MIRSED) which utilizes the process‐based soil erosion model WEPP (Water Erosion Prediction Project) is presented for the assessment of hillslope‐scale soil erosion at five sites throughout England and Wales. The methodology draws upon previous uncertainty analysis of the WEPP hillslope soil erosion model by the authors to qualify model results within an uncertainty framework. A method for incorporating model uncertainty from a range of sources is discussed as a first step towards using and learning from results produced through the GLUE (Generalized Likelihood Uncertainty Estimation) technique. Results are presented and compared to available observed data, which illustrate that levels of uncertainty are significant and must be taken into account if a meaningful understanding of output from models such as WEPP is to be achieved. Furthermore, the collection of quality, observed data is underlined for two reasons: as an essential tool in the development of soil erosion modelling and also to allow further constraint of model uncertainty. Copyright © 2001 John Wiley & Sons, Ltd.     

APPLICATION OF ELASTIC MODELLING IN PROCESSING AND INTERPRETATION OF VSP DATA: A CASE HISTORY1

Data from offshore Norway is used to study applications of elastic VSP modelling in detecting shear waves and observing the effects of successive mode conversion in field-recorded VSP data. The shear-wave velocities and densities from log data are used in conjunction with compressional wave velocities determined from surface seismic and log data in the VSP modelling. The time domain non-normal incidence elastic VSP modelling technique of Aminzadeh and Mendel is used as the modelling algorithm. Two surface seismograms are computed first. One is the vertical component and the other is the horizontal component for plane waves that have specified incident angles. A downward continuation method is then applied to generate seismograms at different depth points. The collection of these seismograms constitutes non-normal incidence VSPs. Both vertical and horizontal components of VSP data can be obtained by this procedure. In this paper non-normal incidence VSPs are generated for a 12.5° incident plane wave. The modelling results of layered earth systems of thin layers and thick layers are both compared with field data, and the effect of mode conversions in thin layers is observed. Several events in the field data can be explained by this elastic VSP modelling. Comparison of the model data and field data enabled a probable tube wave or out-of-plane event to be identified, the removal of which significantly improved the final VSP section. This study also shows how the VSP data helped the interpretation of the surface 3D data.     

Capabilities and limitations of detailed hillslope hydrological modelling

Hillslope hydrological modelling is considered to be of great importance for the understanding and quantification of hydrological processes in hilly or mountainous landscapes. In recent years a few comprehensive hydrological models have been developed at the hillslope scale which have resulted in an advanced representation of hillslope hydrological processes (including their interactions), and in some operational applications, such as in runoff and erosion studies at the field scale or lateral flow simulation in environmental and geotechnical engineering. An overview of the objectives of hillslope hydrological modelling is given, followed by a brief introduction of an exemplary comprehensive hillslope model, which stimulates a series of hydrological processes such as interception, evapotranspiration, infiltration into the soil matrix and into macropores, lateral and vertical subsurface soil water flow both in the matrix and preferential flow paths, surface runoff and channel discharge. Several examples of this model are presented and discussed in order to determine the model's capabilities and limitations. Finally, conclusions about the limitations of detailed hillslope modelling are drawn and an outlook on the future prospects of hydrological models on the hillslope scale is given.The model presented performed reasonable calculations of Hortonian surface runoff and subsequent erosion processes, given detailed information of initial soil water content and soil hydraulic conditions. The vertical and lateral soil moisture dynamics were also represented quite well. However, the given examples of model applications show that quite detailed climatic and soil data are required to obtain satisfactory results. The limitations of detailed hillslope hydrological modelling arise from different points: difficulties in the representations of certain processes (e.g. surface crusting, unsaturated–saturated soil moisture flow, macropore flow), problems of small‐scale variability, a general scarcity of detailed soil data, incomplete process parametrization and problems with the interdependent linkage of several hillslopes and channel–hillslope interactions. Copyright © 1999 John Wiley & Sons, Ltd.     

基于电场总场矢量有限元法的接地长导线源三维正演

电磁场数值模拟的背景场/异常场算法是三维正演的有效策略之一,优点为采用解析法计算电磁场背景场代替场源项、克服了场源奇异性,缺点为不适用于发射源布置于起伏地表或背景模型复杂的情形.总场算法是直接对电磁场总场开展数值模拟,其难点是有效加载场源、保证近区与过渡区数值解精度.本文以水平电偶源形式分段加载接地长导线源,并以电场总场Helmholtz方程为矢量有限元法控制方程,实现了基于非结构化四面体网格剖分的接地长导线源频率域电磁法三维正演.通过与均匀全空间中水平电偶源产生的电场解析解对比,验证了本文算法的正确性,并分析了四面体外接圆半径与其最短棱边的最大比值和四面体二面角最小值对数值解精度的影响规律.通过与块状高导体地电模型的积分方程法、有限体积法和基于磁矢量势Helmholtz方程的有限元法数值解对比,进一步验证了本文算法正确性,同时说明了非结构化四面体网格能够更加精细地剖分电性异常体,利于获得精确数值解.     

Deriving the relationship among discharge,biomass and Manning's coefficient through a calibration approach

The subject of environmental engineering is currently of great interest. Field experiments as well as numerical models have proven their worth in this research field. An introduction to hydrodynamic modelling, coupled to the modelling of vegetation biomass is described. The developed Strive (STream RIVer Ecosystem) model is set up in the Femme (‘Flexible Environment for Mathematically Modelling the Environment’) environment and has already proven its worth in a large number of calculations (De Doncker et al., 2006 , 2008b ). Discharges and water levels are modelled together with modelling of electrical conductivity (EC). Extensive measurement campaigns are carried out to collect a large number of observations and calibration of the model is based on this data set. Furthermore, calibration methods and the discussion of this process are displayed. As a result, it is seen that the developed Strive model can model both, hydrodynamic and ecological processes, in an accurate way. The work highlights the importance of detailed determination of Manning's coefficient, dependent on discharge and amount of biomass, as an important calibration parameter for accurate modelling. Copyright © 2011 John Wiley & Sons, Ltd.     

Circulation in a Southern Italy coastal basin: Modelling and field measurements

The purpose of the present work is to study the hydrodynamic aspects in the Mar Piccolo, a coastal basin located on the northern side of the Gulf of Taranto in the Ionian Sea (Italy), by means of mathematical modelling and field measurements. The latter were assessed during three surveys carried out in the spring–summer of 2002. Collected data have been utilized as input by the 3-D Princeton Ocean Model, which is a sigma coordinate, free surface ocean model which was developed in the late 1970s by Blumberg and Mellor. Simulations in baroclinic condition were forced by a homogeneous and stationary wind field, a simple tidal wave, a constant outflow and vertical stratification of temperature and salinity. A comparison was made between the mathematical modelling results and the field measurements collected during the surveys, in terms of velocity. It was observed that during small tides, when the wind effect prevails over the stratification effect, the best model results were obtained for the most superficial layer and that superficial patterns reproduced by the model are more sensitive to wind direction than to stratification. On the contrary, when the wind effect decreases or the thermohaline effect rises, best results occurred in deeper layers.     

About the Efficiency of Numerical 1-D and 2-D Modelling of Site Effects in Basin Structures

—In the present study we compare results obtained from experimental estimates of local site amplification effects with those from numerical modelling using four different techniques. We benefit from an extremely precise knowledge of the near-surface structure and experimental estimates of the local amplification factors which are determined from seismic weak-motion data recorded by a dense array across a sedimentary basin at a European test-site in Northern Greece. The possibilities and limitations of the different modelling techniques (a 1-D technique, and three 2-D techniques) to model the effects of local amplification effects are tested. Amplifications calculated by the numerical techniques are only qualitatively compared with observed data from experimental studies in the time domain and directly in the frequency domain.¶As a result we conclude that, in the case of a complex subsurface geometry, 1-D modelling underestimates the amplification patterns in terms of absolute amplification level, and cannot correctly account for resonant frequencies, at least for modes higher than the fundamental mode. If a more realistic incident wave field than just a plane wave is taken into account, 2-D modelling reveals the fundamental frequency and shows adequate amplifications not only at the fundamental frequency but also at higher frequencies. The general trend of the amplifications at the lowest frequencies is well determined by the 2-D numerical modelling, and can therefore supply information for seismic risk analysis.     

Slopes of an airborne electromagnetic resistivity model interpolated jointly with borehole data for 3D geological modelling

We investigate a novel way to introduce resistivity models deriving from airborne electromagnetic surveys into regional geological modelling. Standard geometrical geological modelling can be strengthened using geophysical data. Here, we propose to extract information contained in a resistivity model in the form of local slopes that constrain the modelling of geological interfaces. The proposed method is illustrated on an airborne electromagnetic survey conducted in the region of Courtenay in France. First, a resistivity contrast corresponding to the clay/chalk interface was interpreted confronting the electromagnetic soundings to boreholes. Slopes were then sampled on this geophysical model and jointly interpolated with the clay/chalk interface documented in boreholes using an implicit 3D potential‐field method. In order to evaluate this new joint geophysical–geological model, its accuracy was compared with that of both pure geological and pure geophysical models for various borehole configurations. The proposed joint modelling yields the most accurate clay/chalk interface whatever the number and location of boreholes taken into account for modelling and validation. Compared with standard geological modelling, the approach introduces in between boreholes geometrical information derived from geophysical results. Compared with conventional resistivity interpretation of the geophysical model, it reduces drift effects and honours the boreholes. The method therefore improves what is commonly obtained with geological or geophysical data separately, making it very attractive for robust 3D geological modelling of the subsurface.     

Comparison of acoustic and elastic full-waveform inversion of 2D towed-streamer data in the presence of salt

Over the last years, full-waveform inversion has become an important tool in the list of processing and imaging technologies available to the industry. For marine towed-streamer data, full-waveform inversion is typically applied using an acoustic approximation because S-waves do not propagate in water and elastic effects in recorded data are generally assumed to be small. We compare acoustic and elastic modelling and full-waveform inversion for a field data set acquired offshore Angola over sediments containing a salt body with significant topology. Forward modelling tests reveal that such geological structures lead to significant mode conversions at interfaces and, consequently, to significant relative amplitude differences when elastically and acoustically modelled traces are compared. Using an acoustic approach for modelling in full-waveform inversion therefore leads to problems matching the synthetic data with the field data, even for recorded pressure data and with trace normalization applied. Full-waveform inversion is unable to find consistent model updates. Applying elastic full-waveform inversion leads to more consistent and reliable model updates with less artefacts, at the expense of additional computation cost. Although two-dimensional marine towed-streamer data are least favourable for the application of full-waveform inversion compared to three-dimensional data or ocean-bottom data, it is recommended to check on the existence of elastic effects before deciding on the final processing and imaging approach.     

Impact of wind on the spatial distribution of rain over micro‐scale topography: numerical modelling and experimental verification

The wind‐driven‐rain effect refers to the redistribution of rainfall over micro‐scale topography due to the existence of local perturbed wind‐flow patterns. Rainfall measurements reported in the literature point to the fact that the wind‐driven‐rain distribution can show large variations over micro‐scale topography. These variations should be taken into account in hillslope hydrology, in runoff and erosion studies and in the design of rainfall monitoring networks. In practice, measurements are often not suitable for determining the wind‐driven‐rain distribution. Therefore, a few researchers have employed numerical modelling. In order to provide confidence in using numerical models, experimental verification for a range of different topographic features is imperative. The objective of this study is to investigate the adequacy of a two‐dimensional Computational Fluid Dynamics (CFD) model to predict the wind‐driven‐rain distribution over small‐scale topography. The numerical model is applied to a number of topographic features, including a succession of cliffs, a small isolated hill, a small valley and a field with ridges and furrows. The numerical results are compared with the corresponding measurement results reported in the literature. It is shown that two‐dimensional numerical modelling can provide a good indication of the wind‐driven‐rain distribution over each type of micro‐scale topography that is considered in this study. It is concluded that more detailed verification procedures are currently inhibited due to the lack of available and detailed spatial and temporal rainfall data from field measurements. Copyright © 2005 John Wiley & Sons, Ltd.