A simple statistical estimation procedure for Monte Carlo Inversion in geophysics

Summary This paper examines the use of Monte Carlo Inversion (MCI) as an effective means for inverting ((geo)physical) data. Press, following Keilis-Borok and Yanovskaya, has used it successfully as an independent method for density modelling. However, to-date, no statistical basis for the interpretation of the results determined by it in geophysical applications has been developed. Since its future success and credibility will rest heavily on the development of such a basis, we give a simple statistical estimation procedure which defines in a natural way the procedure which must be used when applying, and interpreting the results obtained from, MCI. In addition, it is shown that MCI complements, rather than competes with, the work of Backus and Gilbert.     

Site effect assessment using KiK-net data: Part 1. A simple correction procedure for surface/downhole spectral ratios

When data is available, the estimation of site effects is usually performed using the “standard spectral ratio” (SSR) technique with respect to an outcropping, reference rock site. This study uses the Japanese KiK-net network, which has more than 600 pairs of surface-downhole stations allowing the computation of empirical borehole transfer functions, consisting of mean spectral ratios of surface over downhole recordings. The borehole transfer function deviates from the SSR in two respects: the reference is located at depth, and the downhole velocity varies from one site to another. These differences bias the estimation of the transfer function with reference to a standard outcrop rock site. The goal of this paper is to develop a simple and robust methodology to correct for such bias. The proposed correction procedure consists of two steps: a depth correction designed to account, in a simplified and physically acceptable way, for the existence at depth of destructive interferences and the absence of free-surface effects in the high-frequency range; and an impedance correction designed to normalize the shear wave velocity at depth. The depth correction involves a simple, frequency-dependent curve to be adapted for each site as a function of the first destructive interference frequency at depth. The impedance normalization combines the use of “generic” rock velocity profiles and a quarter-wavelength approach, resulting in a smooth frequency-dependent amplitude correction. The proposed methodology is applied on a large subset of KiK-net data in view of analysing the correlation between site amplification factors and site parameters in a companion paper.     

A residual flow procedure and application for free surface flow in porous media

A finite element procedure based on the extension of the saturated flow domain into the partially saturated zone above the free surface is proposed. The finite element equations are derived by using a pseudo variational principle which results into a residual or correction load vector. The steady or transient free surface is corrected by using the residual load in an iterative scheme. The proposed procedure uses only one (initial) mesh and does not require modification of the mesh during iterations. It is compared (qualitatively) with other procedures such as variable mesh and variational inequalities. The procedure provides satisfactory comparisons with a number of closed-form solutions and laboratory test results; two applications involving the latter are described in the paper.     

A simple procedure to approximate slip displacement of freestanding rigid body subjected to earthquake motions

A simple calculation procedure for estimating absolute maximum slip displacement of a freestanding rigid body placed on the ground or floor of linear/nonlinear multi‐storey building during an earthquake is developed. The proposed procedure uses the displacement induced by the horizontal sinusoidal acceleration to approximate the absolute maximum slip displacement, i.e. the basic slip displacement. The amplitude of this horizontal sinusoidal acceleration is identical to either the peak horizontal ground acceleration or peak horizontal floor response acceleration. Its period meets the predominant period of the horizontal acceleration employed. The effects of vertical acceleration are considered to reduce the friction force monotonously. The root mean square value of the vertical acceleration at the peak horizontal acceleration is used. A mathematical solution of the basic slip displacement is presented. Employing over one hundred accelerograms, the absolute maximum slip displacements are computed and compared with the corresponding basic slip displacements. Their discrepancies are modelled by the logarithmic normal distribution regardless of the analytical conditions. The modification factor to the basic slip displacement is quantified based on the probability of the non‐exceedence of a certain threshold. Therefore, the product of the modification factor and the basic slip displacement gives the design slip displacement of the body as the maximum expected value. Since the place of the body and linear/nonlinear state of building make the modification factor slightly vary, ensuring it to suit the problem is essential to secure prediction accuracy. Copyright © 2006 John Wiley & Sons, Ltd.     

A simple model of hillslope response for overland flow generation

This paper deals with the derivation of the hydrological response of a hillslope on the assumption of quick runoff by surface runoff generation. By using the simple non‐linear storage based model, first proposed by Horton, an analytical solution of the overland flow equations over a plane hillslope was derived. This solution establishes a generalization for different flow regimes of Horton's original solution, which is valid for the transitional flow regime only. The solution proposed was compared successfully with that of Horton and, for the turbulent flow regime, to the one derived from kinematic wave theory. This solution can be applied easily to both stationary and non‐stationary rainfall excess events. An analytical solution for the instantaneous response function (IRF) was also derived. Finally, simple expressions to compute peak and time to peak of IRF are proposed. Copyright © 2001 John Wiley & Sons, Ltd.     

A new fish-based multi-metric assessment index for cyprinid streams in the Iranian Caspian Sea Basin

A major issue for water resource management is the assessment of environmental degradation of lotic ecosystems. The overall aim of this study is to develop a multi-metric fish index for the cyprinid streams of the Caspian Sea Basin (MMICS) in Iran. As species diversity and composition as well as population structure in the studied streams are different to other regions, there is a substantial need to develop a new fish index. We sampled fish and environmental data of 102 sites in medium sized streams. We analysed human pressures at different spatial scales and determined applicable fish metrics showing a response to human pressures. In total, five structural and functional types of metrics (i.e. biodiversity, habitat, reproduction, trophic level and water quality sensitivity) were considered. In addition, we used 29 criteria describing major anthropogenic human pressures at sampling sites and generated a regional pressure index (RPI) that accounted for potential effects of multiple human pressures.For the MMICS development, we first defined reference sites (least disturbed) and secondly quantified differences of fish metrics between reference and impaired sites. We used a Generalised Linear Model (GLM) to describe metric responses to natural environmental differences in least disturbed conditions. By including impaired sites, the residual distributions of these models described the response range of each metric to human pressures, independently of natural environmental influence.Finally, seven fish metrics showed the best ability to discriminate between impaired and reference sites. The multi-metric fish index performed well in discriminating human pressure classes, giving a significant negative linear response to a gradient of the RPI. These methods can be used for further development of a standardised monitoring tool to assess the ecological status and trends in biological condition for streams of the whole country, considering its complex and diverse geology and climate.     

A simple error estimator and adaptive time stepping procedure for dynamic analysis

A simple local error estimator is presented for time integration schemes in dynamic analysis. This error estimator involves only a small computational cost. The time step size is adaptively adjusted so that the local error at each time step is within a prescribed accuracy. It is found that the estimator performs well under various circumstances and provides an economical adaptive process. Attempts to estimate the global time integration error are also reported.     

On the leakage assumption applied to equations of groundwater flow

The behaviour and the delayed response of flow to a well in an unconfined aquifer is considered on the basis of recognition of the variable vertical movement of flow inherent in unconfined flow. The effect of elastic storage is taken into account.The typical S-shaped form of the characteristic time-drawdown curve of an unconfined aquifer is analysed. A procedure for determining the unconfined parameters is described.It is shown that the vertical components of flow are a significant factor in the delayed response of an unconfined aquifer while the contribution of the unsaturated zone is essentially subordinate. An equation including allowance for the drainage from the unsaturated zone is derived.     

Morphological assessment of reconstructed lowland streams in the Netherlands

Channelisation measures taken halfway the 20th century have had destructive consequences for the diversity of the ecology in the majority of the lowland streams in countries such as the Netherlands. Re-meandering is the common practice in restoring these lowland streams. Three reconstructed streams were monitored during the initial two years after construction of a new channel. The monitoring program included morphological surveys, sediment sampling, habitat pattern surveys, and discharge and water level measurements. Adjustments of the longitudinal bed profile formed the main morphological response. These adjustments were most likely caused by a lack of longitudinal connectivity of the streams as a whole, interrupting transport of sediment at locations of weirs and culverts. Bank erosion was observed only in a limited number of channel bends, and was often related to floodplain heterogeneity. Longitudinal channel bed adjustments and bank erosion were mainly caused by exogenous influences. In channel bends, the cross-sectional shape transformed from trapezoidal to the typical asymmetrical shape as found in meandering rivers. This behaviour can be attributed to an autogenous response to the prevailing flow conditions. Due to the prevailing fine sediment characteristics, bed material is readily set in motion and is being transported during the entire year. The existing design principles fail to address the initial morphological development after reconstruction. An evaluation of pre-set targets to realise water depth and flow velocity ranges shows the current procedures to be deficient. Based on this unfavourable evaluation, and the two-dimensional nature of habitat patterns needed to improve the conditions for stream organisms, we recommend to predict morphological developments as part of the design procedures for lowland stream restoration in the Netherlands.     

An assessment of inversion methods for AEM data applied to environmental studies

Airborne electromagnetic (AEM) surveys are currently being flown over populated areas and applied to detailed problems using high flight line densities. Interpretation information is supplied through a model of the subsurface resistivity distribution. Theoretical and survey data are used here to study the character and reliability of such models. Although the survey data were obtained using a fixed-wing system, the corresponding associations with helicopter, towed-bird systems are discussed. Both Fraser half-space and 1D inversion techniques are considered in relation to their ability to distinguish geological, cultural and environmental influences on the survey data. Fraser half-space modelling provides the dual interpretation parameters of apparent resistivity and apparent depth at each operational frequency. The apparent resistivity was found to be a remarkably stable parameter and appears robust to the presence of a variety of at-surface cultural features. Such features provide both incorrect altitude data and multidimensional influences. Their influences are observed most strongly in the joint estimate of apparent depth and this accounts for the stability of the apparent resistivity. Positive apparent depths, in the example data, result from underestimated altitude measurements. It is demonstrated that increasingly negative apparent depths are associated with increasing misfits between a 1D model and the data. Centroid depth calculations, which are a transform of the Fraser half-space parameters, provide an example of the detection of non-1D influences on data obtained above a populated area. 1D inversion of both theoretical and survey data is examined. The simplest use of the 1D inversion method is in providing an estimate of a half-space resistivity. This can be undertaken prior to multilayer inversion as an initial assessment. Underestimated altitude measurements also enter the problem and, in keeping with the Fraser pseudo-layer concept, an at-surface highly resistive layer of variable thickness can be usefully introduced as a constrained parameter. It is clearly difficult to ascribe levels of significance to a ‘measure’ of misfit contained in a negative apparent depth with the dimensions of metres. The reliability of 1D models is better assessed using a formal misfit parameter. With the misfit parameter in place, the example data suggest that the 1D inversion methods provide reliable apparent resistivity values with a higher resolution than the equivalent information from the Fraser half-space estimates.     

The concept of dominant discharge applied to two gravel-bed streams in relation to channel stability thresholds

Dominant discharge may be defined as that discharge which transports most bed sediment in a stream that is close to steady-state conditions. The concept is examined in relation to two single thread gravel-bedded streams. One stream is alluvial and free to adjust its geometry whilst in the other, channel capacity and form are partially constrained by cohesive till-banks and a heavily compacted bed. The total quantity of bedload and its calibre were measured for every flood over a six year period, so that the relationship between the grain-size of bedload and the most effective discharge could be examined in the context of thresholds for channel change. The dominant discharge concept was applicable to the alluvial stream in that the bankfull value is an effective discharge for maintaining channel capacity. The concept applied less well to the ‘non-alluvial’ stream. Although in both streams the bankfull value was exceeded for less than 0.34 per cent of the time, overbank flows are important in instigating channel change. It is only during overbank flows that the largest bed material is entrained in quantity. For within-channel flows a threshold separates flows which winnow fine matrix from those which entrain the finer bed gravels. This threshold occurred at 60 per cent bankfull. It was concluded that the dominant discharge concept can be applied to streams close to steady-state which are alluvial, competent, and free to adjust their boundaries. An important proviso is that two channel-stability domains can be recognized. These domains represent channel maintenance and channel adjustment and are defined by intrinsic thresholds in the bed material entrainment function.     

A simple overland flow calculation method for distributed groundwater recharge models

A method to improve the calculation of overland flow in distributed groundwater recharge models is presented and applied to two sub‐catchments in the Thames Basin, UK. Recharge calculation studies tend to simulate the runoff flow component of river flow in a simplistic way, often as a fraction of rainfall over a particular period. The method outlined in this study intends to improve the calculation of groundwater recharge estimates in distributed recharge models but does not present an alternative to complex overland flow simulators. This method uses seasonally varying coefficients to calculate runoff for specified hydrogeological classes or runoff zones, which are used to model baseflow index variations across the basin. It employs a transfer function model to represent catchment storage. Monte Carlo simulation was applied to refine the runoff values. Decoupling the runoff zones between the two sub‐catchments produces a better match between the simulated and observed values; however, the difference between observed runoff and the simulated output indicates other factors, such as landuse and topographical characteristics that affect the generation of runoff flow, need to be taken into account when classifying runoff zones. British Geological Survey © NERC 2011. Hydrological Processes © 2011 John Wiley & Sons, Ltd.     

A novel simple procedure to consider seismic soil structure interaction effects in 2D models

A method is proposed to estimate the seismic soil-structure-interaction (SSI) effects for use in engineering practice. It is applicable to 2D structures subjected to vertically incident shear waves supported by homogenous half-spaces. The method is attractive since it keeps the simplicity of the spectral approach, overcomes some of the difficulties and inaccuracies of existing classical techniques and yet it considers a physically consistent excitation. This level of simplicity is achieved through a response spectra modification factor that can be applied to the free-field 5%-damped response spectra to yield design spectral ordinates that take into account the scattered motions introduced by the interaction effects. The modification factor is representative of the Transfer Function (TF) between the structural relative displacements and the free-field motion, which is described in terms of its maximum amplitude and associated frequency. Expressions to compute the modification factor by practicing engineers are proposed based upon a parametric study using 576 cases representative of actual structures. The method is tested in 10 cases spanning a wide range of common fundamental vibration periods.     

Classifying the flow regimes of Mediterranean streams using multivariate analysis

Rivers in the Mediterranean region often exhibit an intermittent character. An understanding and classification of the flow regimes of these rivers is needed, as flow patterns control both physicochemical and biological processes. This paper reports an attempt to classify flow regimes in Mediterranean rivers based on hydrological variables extracted from discharge time series. Long‐term discharge records from 60 rivers within the Mediterranean region were analysed in order to classify the streams into different flow regime groups. Hydrological indices (HIs) were derived for each stream and principal component analysis (PCA) and then applied to these indices to identify subsets of HIs describing the major sources of variations, while simultaneously minimizing redundancy. PCA was performed for two groups of streams (perennial and temporary) and for all streams combined. The results show that whereas perennial streams are mainly described by high‐flow indices, temporary streams are described by duration, variability and predictability indices. Agglomerative cluster analysis based on HIs identified six groups of rivers classified according to differences in intermittency and variability. A methodology allowing such a classification for ungauged catchments was also tested. Broad‐scale catchment characteristics based on digital elevation, climate, soil and land use data were derived for each long‐term station where these data were available. By using stepwise multiple regression analysis, statistically significant relationships were fitted, linking the three selected hydrological variables (mean annual number of zero‐flow days, predictability and flashiness) to the catchment characteristics. The method provides a means of simplifying the complexity of river systems and is thus useful for river basin management. Copyright © 2015 John Wiley & Sons, Ltd.     

A procedure on ground motion selection and scaling for nonlinear response of simple structural systems

This study presents a ground-motion selection and scaling methodology that preserves the basic seismological features of the scaled records with reduced scatter in the nonlinear structural response. The methodology modifies each strong-motion recording with known fundamental seismological parameters using the estimations of ground-motion prediction equations for a given target hazard level. It provides robust estimations on target building response through scaled ground motions and calculates the dispersion about this target. This alternative procedure is not only useful for record scaling and selection but, upon its further refinement, can also be advantageous for the probabilistic methods that assess the engineering demand parameters for a given target hazard level. Case studies that compare the performance of the proposed procedure with some other record selection and scaling methods suggest its usefulness for building performance assessment and loss models. Copyright © 2012 John Wiley & Sons, Ltd.