Using the Wiener–Levinson algorithm to suppress ground-roll

In land seismic surveys, the seismic data are mostly contaminated by ground-roll noise, high amplitude and low frequency. Since the ground-roll is coherent with reflections and depends on the source, the spectral band of seismic signal and ground-roll always overlap, which can be clearly seen in the spectral domain. So, separating them in time or frequency domain commonly causes waveform distortions and information missing due to cut-off effects. Therefore, the combination of these factors leads to search for alternative filtering methods or processes. We applied the conventional Wiener–Levinson algorithm to extract ground-roll from the seismic data. Then, subtracting it from the seismic data arithmetically performs the ground-roll suppression. To set up the algorithm, linear or nonlinear sweep signals are used as reference noise trace. The frequencies needed in creating a reference noise trace using analytical sweep signal can be approximately estimated in spectral domain. The application of the proposed method based on redesigning of Wiener–Levinson algorithm differs from the usual frequency filtering techniques since the ground-roll is suppressed without cutting signal spectrum. The method is firstly tested on synthetics and then is applied to a shot data from the field. The result obtained from both synthetics and field data show that the ground-roll suppression in this way causes no waveform distortion and no reduction of frequency bandwidth of the data.     

Bayesian analysis of stage–fall–discharge models for gauging stations affected by variable backwater

Parsimonious stage–fall–discharge rating curve models for gauging stations subject to backwater complications are developed from simple hydraulic theory. The rating curve models are compounded in order to allow for possible shifts in the hydraulics when variable backwater becomes effective. The models provide a prior scientific understanding through the relationship between the rating curve parameters and the hydraulic properties of the channel section under study. This characteristic enables prior distributions for the rating curve parameters to be easily elicited according to site‐specific information and the magnitude of well‐known hydraulic quantities. Posterior results from three Norwegian and one American twin‐gauge stations affected by variable backwater are obtained using Markov chain Monte Carlo simulation techniques. The case studies demonstrate that the proposed Bayesian rating curve assessment is appropriate for developing rating procedures for gauging stations that are subject to variable backwater. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of methods for applying the Priestley–Taylor equation at a regional scale

The scenario assumed for this study was that of a region with a complete or first‐order weather station surrounded by a network of second‐order stations, where only monthly air temperature data were available. The objective was to evaluate procedures to estimate the monthly α parameter of the Priestley–Taylor equation in the second‐order stations by adjusting and extrapolating α values determined at the first‐order station. These procedures were applied in two climatic zones of north‐east Spain with semi‐arid continental and semi‐arid Mediterranean climates, respectively. Procedure A assumed α to be constant over each zone for each month (direct extrapolation). Procedure B accounted for differences in vapour pressure deficit and available energy for evapotranspiration between the first‐ and second‐order stations. Procedure C was based on equating the Penman–Monteith (P–M) and Priestley–Taylor (P–T) equations on a monthly basis to solve for α. Methods to estimate monthly mean vapour pressure deficit, net radiation and wind speed were developed and evaluated. A total of 11 automated first‐order weather stations with a minimum period of record of 6 years (ranging from 6 to 10 years) were used for this study. Six of these stations were located in the continental zone and five in the Mediterranean zone. One station in each zone was assumed to be first‐order whereas the remainder were taken as second‐order stations. Monthly α parameters were calibrated using P–M reference crop evapotranspiration (ET₀) values, calculated hourly and integrated for monthly periods, which were taken as ‘true’ values of ET₀. For the extrapolation of monthly α parameters, procedure A was found to perform slightly better than procedure B in the Mediterranean zone. The opposite was true in the continental zone. Procedure C had the worst performance owing to the non‐linearity of the P–M equation and errors in the estimation of monthly available energy, vapour pressure deficit and wind speed. Procedures A and B are simpler and performed better. Overall, monthly P–T ET₀ estimates using extrapolated α parameters and R_n?G values were in a reasonable agreement with P–M ET₀ calculated on an hourly basis and integrated for monthly periods. The methods presented for the spatial extrapolation of monthly available energy, vapour pressure deficit and wind speed from first‐ to second‐order stations could be useful for other applications. Copyright © 2001 John Wiley & Sons, Ltd.     

A finite element solution for the fractional advection–dispersion equation

The fractional advection–dispersion equation (FADE) known as its non-local dispersion, has been proven to be a promising tool to simulate anomalous solute transport in groundwater. We present an unconditionally stable finite element (FEM) approach to solve the one-dimensional FADE based on the Caputo definition of the fractional derivative with considering its singularity at the boundaries. The stability and accuracy of the FEM solution is verified against the analytical solution, and the sensitivity of the FEM solution to the fractional order α and the skewness parameter β is analyzed. We find that the proposed numerical approach converge to the numerical solution of the advection–dispersion equation (ADE) as the fractional order α equals 2. The problem caused by using the first- or third-kind boundary with an integral-order derivative at the inlet is remedied by using the third-kind boundary with a fractional-order derivative there. The problems for concentration estimation at boundaries caused by the singularity of the fractional derivative can be solved by using the concept of transition probability conservation. The FEM solution of this study has smaller numerical dispersion than that of the FD solution by Meerschaert and Tadjeran (J Comput Appl Math 2004). For a given α, the spatial distribution of concentration exhibits a symmetric non-Fickian behavior when β = 0. The spatial distribution of concentration shows a Fickian behavior on the left-hand side of the spatial domain and a notable non-Fickian behavior on the right-hand side of the spatial domain when β = 1, whereas when β = −1 the spatial distribution of concentration is the opposite of that of β = 1. Finally, the numerical approach is applied to simulate the atrazine transport in a saturated soil column and the results indicat that the FEM solution of the FADE could better simulate the atrazine transport process than that of the ADE, especially at the tail of the breakthrough curves.     

On a monotonicity preserving Eulerian–Lagrangian localized adjoint method for advection–diffusion equations

Eulerian–Lagrangian localized adjoint methods (ELLAMs) provide a general approach to the solution of advection-dominated advection–diffusion equations allowing large time steps while maintaining good accuracy. Moreover, the methods can treat systematically any type of boundary condition and are mass conservative. However, all ELLAMs developed so far suffer from non-physical oscillations and are usually implemented on structured grids. In this paper, we propose a finite volume ELLAM which incorporates a novel correction step rendering the method monotone while maintaining conservation of mass. The method has been implemented on fully unstructured meshes in two space dimensions. Numerical results demonstrate the applicability of the method for problems with highly non-uniform flow fields arising from heterogeneous porous media.     

A systematic approach to the input determination for neural network rainfall–runoff models

Input determination has a great influence on the performance of artificial neural network (ANN) rainfall–runoff models. To improve the performance of ANN models, a systematic approach to the input determination for ANN models is proposed. In the proposed approach, the irrelevant inputs are removed. Then an adequate ANN model, which only includes highly relevant inputs, is constructed. Unlike the trial‐and‐error procedure, the proposed approach is more systematic and avoids unnecessary trials. To demonstrate the effectiveness of the proposed approach, an application to actual typhoon events is presented. The results show that the proposed ANN model, which is constructed by the proposed approach, has advantages over those obtained by the trial‐and‐error procedure. The proposed ANN model has a simpler architecture, needs less training time, and performs better. The proposed ANN model is recommended as an alternative to existing rainfall–runoff ANN models. Copyright © 2007 John Wiley & Sons, Ltd.     

A small-scale field check on the Fisher–Lehmann and Bakker–Le Heux cliff degradation models

The paper considers the development of initially straight, steep rock cliffs, bounded above and below by horizontal surfaces, in which basal debris removal is zero and degradation occurs by the weathering away of fine debris from the cliff face to form a scree at its foot. Of the slope degradation models available, the two earliest and simplest, namely the Fisher–Lehmann and the Bakker–Le Heux models, are regarded as most relevant and are briefly summarized. The main purpose of the paper is to check the predictions of these models, particularly with regard to the shape of the rock surface buried beneath the scree, against field data. Such data are sparse. It is concluded that the best field case currently available, despite its small scale, is that provided by the 1·75 m deep ditch which forms part of the experimental earthwork in the chalk on Overton Down, Wiltshire. The predictions of the two models are checked against field measurements made of the stage of degradation reached on each face of the ditch by July 1968, eight years after its excavation. These stages were influenced to different degrees by the presence of a surface turf layer. For the NE face, where this influence was least, the agreement of the predictions of the Fisher–Lehmann model with the actual rock profile is excellent and that of the Bakker–Le Heux model only marginally less so. For the SW face, as expected, the agreements are somewhat less close. These results may be to some extent fortuitous because of the influence of the turves and because the scree slopes tend to be concave rather than rectilinear, as assumed. Also, the free faces decline with time in a manner intermediate between those assumed in the two models. Larger scale field checks are clearly desirable before firm general conclusions can be drawn. Rates of crest recession for the Overton Down ditch are logarithmic with time after a very rapid initial phase. Extrapolation from the early phase of this logarithmic behaviour leads to a close estimate of the time needed for the slope to develop fully. The associated ultimate crest recession is also closely predicted by equations derived from both models. © 1998 John Wiley & Sons, Ltd.     

ELF propagation parameters for uniform models of the Earth–ionosphere waveguide

Uniform models for the Earth–ionosphere cavity are considered with particular attention to the physical properties of the ionosphere for the extremely low frequency (ELF) range. Two consistent features have long been recognized for the range: the presence of two distinct altitude layers of maximum energy dissipation within the lower ionosphere, and a “knee”-like change in the vertical conductivity profile representing a transition in dominance from ion-dominated to electron-dominated conductivity. A simplified two-exponential version of the Greifinger and Greifinger (1978) technique widely used in ELF work identifies two slopes in the conductivity profile and, providing accurate results in the ELF communication band (45–75 Hz), simulates too flat a frequency dependence of the quality factor within the Schumann resonance frequency range (5–40 Hz). The problem is traced to the upward migration, with frequency increasing, of the lower dissipation layer through the “knee” region resulting in a pronounced decrease of the effective scale height for conductivity. To overcome this shortcoming of the two-exponential approximation and still retain valuable model analyticity, a more general approach (but still based on the Greifinger and Greifinger formalism) is presented in the form of a “knee” model whose predictions for the modal frequencies, the wave phase velocities and the quality factors reasonably represent observations in the Schumann resonance frequency range.     

A coupling model of FE–BE–IE–IBE for non-linear layered soil–structure interactions

A coupling model of Finite Elements (FEs), Boundary Elements (BEs), Infinite Elements (IEs) and Infinite Boundary Elements (IBEs) is presented for analysis of soil–structure interaction (SSI). The radiation effects of the infinite layered soil are taken into account by FE–IE coupling, while the underlying bed rock half-space is discretized into BE–IBE coupling whereby the non-horizontal bed rock surface can be accounted for. Displacement compatabilities are satisfied for all types of aforementioned elements. The equivalent linear approach is employed for approximation of nonlinearity of the near field soil. This model has some advantages over the current SSI program in considering the bed rock half-space and non-vertical wave incidence from the far field. Examples of verification demonstrate the applicability and accuracy of the method when compared with the FLUSH program. Finally, the effects of the relative modulus ratio E_r/E_s of rock and soil and the incident angles of non-vertical waves on the responses of the structure and the soil are examined. Copyright © 1999 John Wiley & Sons, Ltd.     

Experimental and computational validation and verification of the Stokes–Darcy and continuum pipe flow models for karst aquifers with dual porosity structure

In our previous study, we developed the Stokes–Darcy (SD) model was developed for flow in a karst aquifer with a conduit bedded in matrix, and the Beavers–Joseph (BJ) condition was used to describe the matrix–conduit interface. We also studied the mathematical well‐posedness of a coupled continuum pipe flow (CCPF) model as well as convergence rates of its finite element approximation. In this study, to compare the SD model with the CCPF model, we used numerical analyses to validate finite element discretisation methods for the two models. Using computational experiments, simulation codes implementing the finite element discretisations are then verified. Further model validation studies are based on the results of laboratory experiments. Comparing the results of computer simulations and experiments, we concluded that the SD model with the Beavers–Joseph interface condition is a valid model for conduit–matrix systems. On the other hand, the CCPF model with the value of the exchange parameter chosen within the range suggested in the literature perhaps does not result in good agreement with experimental observations. We then examined the sensitivity of the CCPF model with respect to the exchange parameter, concluding that, as has previously been noted, the model is highly sensitive for small values of the exchange parameter. However, for larger values, the model becomes less sensitive and, more important, also produces results that are in better agreement with experimental observations. This suggests that the CCPF model may also produce accurate simulation results, if one chooses larger values of the exchange parameter than those suggested in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

A complementary relationship evaporation model referring to the Granger model and the advection–aridity model

A complementary relationship evaporation model has been proposed and verified based on evaluations of the advection–aridity model and the Granger's complementary relationship model (Granger model) in dimensionless forms. Normalized by Penman potential evaporation, the Granger model and the advection–aridity model have been transformed into similar dimensionless forms. Evaporation ratio (ratio of actual evaporation to Penman potential evaporation) has been expressed as a function of dimensionless variable based on radiation and atmospheric conditions. Similar dimensionless variables for the different functions have been used in the two models. By referring to the dimensionless variable from the advection–aridity model and the function from the Granger model, a new model to estimate actual evaporation was proposed. The performance of the new model has been validated by the observed data from four sites under different land covers. The new model is an enhanced Granger model with better evaporation prediction over the aforementioned different land covers. It also offers more stable optimized parameters in a grassland site than the Granger model. The new model somewhat approximates the advection–aridity model under neither too wet nor too dry conditions, but without its system bias. Copyright © 2011 John Wiley & Sons, Ltd.     

A simplified storm index method to extrapolate intensity–duration–frequency (IDF) curves for ungauged stations in central Chile

Most of meteorological stations in Chile register rainfall amounts once every 24 h. The creation of intensity–duration–frequency (IDF) curves requires continuous recorded data, and this insufficiency of proper instrumentation has resulted in a lack of IDF curves nationwide. The objective of this study is to further develop and evaluate the feasibility of a new method to estimate IDF curves in ungauged stations under Mediterranean climates of central Chile. A technique used to address this problem is the use of a storm index (S_I), also known as the ‘K’ method, which allows the construction of IDF curves from stations with discontinuous data, by extrapolating data from stations with continuous records, as long as daily rainfall intensities for both stations differ by less than 2 mm h^?1. To test the applicability of this method, S_I values were calculated for 40 meteorological stations located throughout Central Chile (latitudes 30°S to 40°S). The extrapolated IDF curves were then compared with observed data, and the goodness of fit was determined. The results indicate that the storm index method can adequately estimate hourly IDF curve values for stations lacking of continuous rainfall data. Copyright © 2014 John Wiley & Sons, Ltd.     

Curve‐Number/Green–Ampt mixed procedure for streamflow predictions in ungauged basins: Parameter sensitivity analysis

A procedure combining the Soil Conservation Service‐Curve Number (SCS‐CN) method and the Green–Ampt (GA) infiltration equation was recently developed to overcome some of the drawbacks of the classic SCS‐CN approach when estimating the volume of surface runoff at a sub‐daily time resolution. The rationale of this mixed procedure, named Curve Number for Green–Ampt (CN4GA), is to use the GA infiltration model to distribute the total volume of the net hyetograph (rainfall excess) provided by the SCS‐CN method over time. The initial abstraction and the total volume of rainfall given by the SCS‐CN method are used to identify the ponding time and to quantify the hydraulic conductivity parameter of the GA equation. In this paper, a sensitivity analysis of the mixed CN4GA parameters is presented with the aim to identify conditions where the mixed procedure can be effectively used within the Prediction in Ungauged Basin perspective. The effects exerted by changes in selected input parameters on the outputs are evaluated using rectangular and triangular synthetic hyetographs as well as 100 maximum annual storms selected from synthetic rainfall time series. When applied to extreme precipitation events, which are characterized by predominant peaks of rainfall, the CN4GA appears to be rather insensitive to the input hydraulic parameters of the soil, which is an interesting feature of the CN4GA approach and makes it an ideal candidate for the rainfall excess estimation at sub‐daily temporal resolution at ungauged sites. Copyright © 2013 John Wiley & Sons, Ltd.     

A hybrid time frequency domain formulation for non-linear soil–structure interaction

Methods that combine frequency and time domain techniques offer an attractive alternative for solving Soil–Structure-interaction problems where the structure exhibits non-linear behaviour. In the hybrid-frequency-time-domain procedure a reference linear system is solved in the frequency domain and the difference between the actual restoring forces and those in the linear model are treated as pseudo-forces. In the solution scheme explored in this paper, designated as the hybrid-time-frequency-domain (HTFD) procedure, the equations of motion are solved in the time domain with due consideration for non-linearities and with the unbounded medium represented by frequency-independent springs and dampers. The frequency dependency of the impedance coefficients is introduced by means of pseudo-forces evaluated in the frequency domain at the end of each iteration. A criterion of stability for the HTFD approach is derived analytically and its validity is sustained numerically. As is often the case, the criterion takes the form of a limit of unity on the spectral radius of an appropriately defined matrix. Inspection of the terms in this matrix shows that convergence can be guaranteed by suitable selection of the reference impedance. The CPU times required to obtain converged solutions with the HTFD are found, in a number of numerical simulations, to be up to one order of magnitude less than those required by the alternative hybrid-frequency-time-domain approach. © 1998 John Wiley & Sons, Ltd.     

An upwind fast sweeping scheme for calculating seismic wave first‐arrival travel times for models with an irregular free surface

The topography‐dependent eikonal equation formulated in a curvilinear coordinate system has recently been established and revealed as being effective in calculating first‐arrival travel times of seismic waves in an Earth model with an irregular free surface. The Lax–Friedrichs sweeping scheme, widely used in previous studies as for approximating the topography‐dependent eikonal equation viscosity solutions, is more dissipative and needs a much higher number of iterations to converge. Furthermore, the required number of iterations grows with the grid refinement and results in heavy computation in dense grids, which hampers the application of the Lax–Friedrichs sweeping scheme to seismic wave travel‐time calculation and high‐resolution imaging. In this paper, we introduce a new upwind fast sweeping solver by discretising the Legendre transform of the numerical Hamiltonian of the topography‐dependent eikonal equation using an explicit formula. The minimisation related to the Legendre transform in the sweeping scheme is solved analytically, which proved to be much more efficient than the Lax–Friedrichs algorithm in solving the topography‐dependent eikonal equation. Several numerical experiments demonstrate that the new upwind fast sweeping method converges and achieves much better accuracy after a finite number of iterations, independently of the mesh size, which makes it an efficient and robust tool for calculating travel times in the presence of a non‐flat free surface.     

Testing a conceptual hillslope recession model based on the storage–discharge relationship with the Richards equation

The conceptual recession model based on the storage–discharge relationship was proposed to account for the unsaturated–saturated water storage interaction. The recession model was formulated by combining the constitutive storage–discharge relationship with the integral balance equation for unsaturated and saturated water storage. The functional form of the constitutive storage–discharge relationship was determined from the spatial integration of the Richards equation. The performance of the recession model was tested by comparing with the solution of the Richards equation for different simulation geometric shapes and soil types. The conceptual recession model incorporating the unsaturated–saturated water storage interaction was in good agreement with the recession response of the Richards equation. However, the recession model that neglected the unsaturated–saturated water storage interaction was comparable to the Richards equation only for soils with the weak interaction between unsaturated water storage and saturated water storage. This result suggests the important role of the unsaturated–saturated water storage interaction in the formulation of the recession process when the derivative of the functional relationship between the unsaturated water storage and saturated water storage becomes significant. Copyright © 2007 John Wiley & Sons, Ltd.     

A distributed shear and flexural flexibility model with shear–flexure interaction for R/C members subjected to seismic loading

A beam–column‐type finite element for seismic assessment of reinforced concrete (R/C) frame structures is presented. This finite element consists of two interacting, distributed flexibility sub‐elements representing inelastic flexural and shear response. Following this formulation, the proposed model is able to capture spread of flexural yielding, as well as spread of shear cracking, in R/C members. The model accounts for shear strength degradation with inelastic curvature demand, as well as coupling between inelastic flexural and shear deformations after flexural yielding, observed in many experimental studies. An empirical relationship is proposed for evaluating the average shear distortion of R/C columns at the onset of stirrup yielding. The proposed numerical model is validated against experimental results involving R/C columns subjected to cyclic loading. It is shown that the model can predict well the hysteretic response of R/C columns with different failure modes, i.e. flexure‐critical elements, elements failing in shear after flexural yielding, and shear‐critical R/C members. Copyright © 2008 John Wiley & Sons, Ltd.     

An accurate strength amplification factor for the design of SDOF systems with P–Δ effects

The response of structures subjected to seismic actions is always influenced by P–Δ effects. The importance of this effect is generally modest for structures experiencing an elastic response but often relevant for structures responding well within the inelastic range of behaviour. Seismic codes indicate that P–Δ effects may be counterbalanced through an increase in the structural strength required by a first order analysis. This increase is calculated by means of a strength amplification factor. The expressions suggested in codes for this factor are simplistic and often criticized by researchers. In this paper, the effectiveness of some of the provisions reported in the literature or suggested in seismic codes is evaluated on single degree of freedom systems with different periods of vibration. As suggested by past studies, attention is focused on the influence of the interstorey drift sensitivity coefficient, significant duration of the ground motion, class of the site soil, displacement ductility and equivalent viscous damping ratio of the system. Finally, an accurate expression of the strength amplification factor is proposed. Copyright © 2013 John Wiley & Sons, Ltd.     

A numerical study on response factors for steel wall–frame systems

A numerical investigation was undertaken to evaluate the response of dual structural systems that consisting of steel plate shear walls and moment‐resisting frames. The primary objective of the study was to investigate the influence of elastic base shear distribution between the wall and the frame on the global system response. A total of 10 walls and 30 wall–frame systems, ranging from 3 to 15 stories, were selected for numerical assessment. These systems represent cases in which the elastic base shear resisted by the frame has a share of 10, 25, or 50% of the total base shear resisted by the dual system. The numerical study consisted of 1600 time history analyses employing three‐dimensional finite elements. All 40 structures were separately analyzed for elastic and inelastic response by subjecting them to the selected suite of earthquake records. Interstory drifts, top story drift, base shears resisted by the wall, and the frame were collected during each analysis. Based on the analysis results, important response quantities, such as the strength reduction, the overstrength, and the displacement amplification factors, are evaluated herein. Results are presented in terms of displacement measures, such as the interstory drift ratio and the top story drift ratio. Analysis results revealed that the increase in the strength reduction factor with the amount of load share is insignificant. Furthermore, there is an inverse relationship between the ductility reduction and the overtsrength. Copyright © 2010 John Wiley & Sons, Ltd.