Three-dimensional numerical simulations of the Downie Slide to test the influence of shear surface geometry and heterogeneous shear zone stiffness

Massive slow-moving landslides often exhibit deformation patterns which vary spatially across the landslide mass and temporally with changing boundary conditions. Understanding the parameters controlling this behaviour, such as heterogeneous material properties, complex landslide geometry and the distribution of groundwater, is fundamental when making informed design and hazard management decisions. This paper demonstrates that significant improvements to the geomechanical analysis of massive landslides can be achieved through rigorous, three-dimensional numerical modelling. Simulations of the Downie Slide incorporate complex shear zone geometries, multiple water tables and spatial variation of shear zone stiffness parameters to adequately reproduce real slope behaviour observed through an ongoing site monitoring program. These three-dimensional models are not hindered by shortfalls typically associated with two-dimensional analysis, for example the ability to accommodate lateral migration of material, and they out-perform more simplified three-dimensional models where bowl-shaped shear geometries are incapable of reasonably reproducing observed deformation patterns.     

Geomechanical interpretation of the Downie Slide considering field data and three-dimensional numerical modelling

Downie Slide has been interpreted as a massive, composite rockslide, and a number of landslide zones have been defined based on the interpretation of morphological features and a detailed assessment of spatially discriminated slope behaviour. Key factors controlling the mechanics of massive slow-moving landslides can be interpreted through the observation and detailed study of the slope behaviour and physical characteristics. Once identified, key components influencing slope deformation can be tested using three-dimensional numerical models. Two series of numerical simulations have been developed to test how explicitly defined internal shear zones, and the interaction between landslide morphological regions, influence global landslide behaviour. Results from these numerical simulations, when compared to field monitoring data, indicate that internal shear zones have little influence on Downie Slide deformation, while the interaction between morphological zones plays a larger role in slope kinematics.     

Moving Surface Spline Interpolation Based on Green’s Function

Some commonly used interpolation algorithms are analyzed briefly in this paper. Among all of the methods, biharmonic spline interpolation, which is based on Green’s function and proposed by Sandwell, has become the mainstream method for its high precision, simplicity and flexibility. However, the minimum curvature method has two flaws. First, it suffers from undesirable oscillations between data points, which is solved by interpolation with splines in tension. Second, the computation time is approximately proportional to the cube of the number of data constraints, making the method slow for situations with dense data coverage. Focusing on the second problem, this paper introduces the moving surface spline interpolation method based on Green’s function, and the interpolation error equations are deduced. Because the proposed method only chooses the nearest data points by using the merge sort algorithm for interpolating, the computation time is greatly decreased. The optimal number of the nearest points can be determined by using the interpolation error estimation equation. No matter how many data points there are, this method can be implemented without difficulty. Examples show that the proposed method can obtain high interpolation precision and high computation speed at the same time.     

Non-parametric machine learning methods for interpolation of spatially varying non-stationary and non-Gaussian geotechnical properties

Spatial interpolation has been frequently encountered in earth sciences and engineering.A reasonable appraisal of subsurface heterogeneity plays a significant role in planning,risk assessment and decision making for geotechnical practice.Geostatistics is commonly used to interpolate spatially varying properties at un-sampled locations from scatter measurements.However,successful application of classic geostatistical models requires prior characterization of spatial auto-correlation structures,which poses a great challenge for unexperienced engineers,particularly when only limited measurements are available.Data-driven machine learning methods,such as radial basis function network(RBFN),require minimal human intervention and provide effective alternatives for spatial interpolation of non-stationary and non-Gaussian data,particularly when measurements are sparse.Conventional RBFN,however,is direction independent(i.e.isotropic)and cannot quantify prediction uncertainty in spatial interpolation.In this study,an ensemble RBFN method is proposed that not only allows geotechnical anisotropy to be properly incorporated,but also quantifies uncertainty in spatial interpolation.The proposed method is illustrated using numerical examples of cone penetration test(CPT)data,which involve interpolation of a 2D CPT cross-section from limited continuous 1D CPT soundings in the vertical direction.In addition,a comparative study is performed to benchmark the proposed ensemble RBFN with two other non-parametric data-driven approaches,namely,Multiple Point Statistics(MPS)and Bayesian Compressive Sensing(BCS).The results reveal that the proposed ensemble RBFN provides a better estimation of spatial patterns and associated prediction uncertainty at un-sampled locations when a reasonable amount of data is available as input.Moreover,the prediction accuracy of all the three methods improves as the number of measurements increases,and vice versa.It is also found that BCS prediction is less sensitive to the number of measurement data and outperforms RBFN and MPS when only limited point observations are available.     

Spatial prediction of soil properties in a watershed scale through maximum likelihood approach

Surface map of soil properties plays an important role in various applications in a watershed. Ordinary kriging (OK) and regression kriging (RK) are conventionally used to prepare these surface maps but generally need large number of regularly girded soil samples. In this context, REML-EBLUP (REsidual Maximum Likelihood estimation of semivariogram parameters followed by Empirical Best Linear Unbiased Prediction) shown capable but not fully tested in a watershed scale. In this study, REML-EBLUP approach was applied to prepare surface maps of several soil properties in a hilly watershed of Eastern India and the performance was compared with conventionally used spatial interpolation methods: OK and RK. Evaluation of these three spatial interpolation methods through root-mean-squared residuals (RMSR) and mean squared deviation ratio (MSDR) showed better performance of REML-EBLUP over the other methods. Reduction in sample size through random selection of sampling points from full dataset also resulted in better performance of REML-EBLUP over OK and RK approach. The detailed investigation on effect of sample number on performance of spatial interpolation methods concluded that a minimum sampling density of 4/km² may successfully be adopted for spatial prediction of soil properties in a watershed scale using the REML-EBLUP approach.     

Application of kriging technique to areal precipitation mapping in Arizona

The classical methods for interpolating and spatial averaging of precipitation fields fail to quantify the accuracy of the estimate. On the other hand, kriging is an interpolation method for predicting values of regionalized variables at points (punctual kriging) or average values over an area (block kriging).This paper demonstrates the use of the kriging method for mapping and evaluating precipitation data for the State of Arizona. Using 158 rain gauge stations with 30 years or more of record, the precipitation over the state has been modeled as a realization of a two dimensional random field taking into consideration the spatial variability conditions.Three data sets have been used: (1) the mean annual precipitation over the state; (2) the mean summer rainy season; and (3) the mean winter rainy season. Validation of the empirical semi-variogram for a constant drift case indicated that the exponential model was appropriate for all the data sets. In addition to a global kriging analysis, the data have been examined under an anisotropic assumption which reflects the topographic structure of the state.     

Comparison of regression-based and combined versions of Inverse Distance Weighted methods for spatial interpolation of daily mean temperature data

This paper focuses on the performance of two regression-based and one Inverse Distance Weighted (IDW) and two combined versions of IDW methods for interpolation of daily mean temperature at the Black Sea Region of Turkey. Simple linear regression (SLR) and multiple linear regression (MLR) are used as regression-based methods. Combinations of IDW with TLR (temperature lapse rate) and gradient plus inverse distance squared (GIDS) are used as combined versions of IDW. This study targets to compare five spatial interpolation methods based on RMSE (root-mean-square error) statistics of interpolation errors for daily mean temperatures from 1981 to 2012. In order to compare the interpolation errors of the five methods, the leave-one-out cross-validation method was applied over long periods of 32 years on 52 different sites. The algorithms of the five interpolation methods’ codes were written in MATLAB by the authors of the paper.     

Evaluation of Interpolation Accuracy of Neural Kriging with Application to Temperature-Distribution Analysis

An interpolation method based on a multilayer neural network (MNN), has been examined and tested for the data of irregular sample locations. The main advantage of MNN is in that it can deal with geoscience data with nonlinear behavior and extract characteristics from complex and noisy images. The training of MNN is used to modify connection weights between nodes located in different layers by a simulated annealing algorithm (one of the optimization algorithms of the network). In this process, three types of errors are considered: differences in values, semivariograms, and gradients between sample data and outputs from the trained network. The training is continued until the summation of these errors converges to an acceptably small value. Because the MNN trained by this learning criterion can estimate a value at an arbitrary location, this method is a form of kriging and termed Neural Kriging (NK). In order to evaluate the effectiveness of NK, a problem on restoration ability of a defined reference surface from randomly chosen discrete data was prepared. Two types of surfaces, whose semivariograms are expressed by isotropic spherical and geometric anisotropic gaussian models, were examined in this problem. Though the interpolation accuracy depended on the arrangement pattern of the sample locations for the same number of data, the interpolation errors of NK were shown to be smaller than both those of ordinary MNN and ordinal kriging. NK can also produce a contour map in consideration of gradient constraints. Furthermore, NK was applied to distribution analysis of subsurface temperatures using geothermal investigation loggings of the Hohi area in southwest Japan. In spite of the restricted quantity of sample data, the interpolation results revealed high temperature zones and convection patterns of hydrothermal fluids. NK is regarded as an interpolation method with high accuracy that can be used for regionalized variables with any structure of spatial correlation.     

无单元法布点优化的一种新方法

研究了无单元法中单个影响域内的布点形式对误差的影响,提出了半径权值的概念。在经过充分的数值计算后,给出在半径权值对无单元法插值结果的精度的影响值的大小。研究对优化无单元法的节点布置、减小模拟误差有很大的作用,并且使得影响域的大小不再依靠点数的多少来确定,避免了影响域过大的情况和为了单个影响域内有足够多的插值点而使得整体插值点数目过多的弊端。运用单个区域内的插值点健康度的理论,研究了整个区域布点对无单元法模拟函数--滑动最小二乘法模拟精度的影响,并运用遗传算法对整个布点区域上的插值点进行了优化,给出了区域上的优化值。通过一个实例,得到一个具有普遍意义的插值点优化值与插值点密度的关系,并给出无单元法布点的一般性原则。     

Geostatistical Mapping with Continuous Moving Neighborhood

An issue that often arises in such GIS applications as digital elevation modeling (DEM) is how to create a continuous surface using a limited number of point observations. In hydrological applications, such as estimating drainage areas, direction of water flow is easier to detect from a smooth DEM than from a grid created using standard interpolation programs. Another reason for continuous mapping is esthetic; like a picture, a map should be visually appealing, and for some GIS users this is more important than map accuracy. There are many methods for local smoothing. Spline algorithms are usually used to create a continuous map, because they minimize curvature of the surface. Geostatistical models are commonly used approaches to spatial prediction and mapping in many scientific disciplines, but classical kriging models produce noncontinuous surfaces when local neighborhood is used. This motivated us to develop a continuous version of kriging. We propose a modification of kriging that produces continuous prediction and prediction standard error surfaces. The idea is to modify kriging systems so that data outside a specified distance from the prediction location have zero weights. We discuss simple kriging and conditional geostatistical simulation, models that essentially use information about mean value or trend surface. We also discuss how to modify ordinary and universal kriging models to produce continuous predictions, and limitations using the proposed models.     

Sensitivity of MM5 and WRF mesoscale model predictions of surface winds in a typhoon to planetary boundary layer parameterizations

Sea surface winds and coastal winds, which have a significant influence on the ocean environment, are very difficult to predict. Although most planetary boundary layer (PBL) parameterizations have demonstrated the capability to represent many meteorological phenomena, little attention has been paid to the precise prediction of winds at the lowest PBL level. In this study, the ability to simulate sea winds of two widely used mesoscale models, fifth-generation mesoscale model (MM5) and weather research and forecasting model (WRF), were compared. In addition, PBL sensitivity experiments were performed using Medium-Range Forecasts (MRF), Eta, Blackadar, Yonsei University (YSU), and Mellor–Yamada–Janjic (MYJ) during Typhoon Ewiniar in 2006 to investigate the optimal PBL parameterizations for predicting sea winds accurately. The horizontal distributions of winds were analyzed to discover the spatial features. The time-series analysis of wind speed from five sensitivity experimental cases was compared by correlation analysis with surface observations. For the verification of sea surface winds, QuikSCAT satellite 10-m daily mean wind data were used in root-mean-square error (RMSE) and bias error (BE) analysis. The MRF PBL using MM5 produced relatively smaller wind speeds, whereas YSU and MYJ using WRF produced relatively greater wind speeds. The hourly surface observations revealed increasingly strong winds after 0300 UTC, July 10, with most of the experiments reproducing observations reliably. YSU and MYJ using WRF showed the best agreements with observations. However, MRF using MM5 demonstrated underestimated winds. The conclusions from the correlation analysis and the RMSE and BE analysis were compatible with the above-mentioned results. However, some shortcomings were identified in the improvements of wind prediction. The data assimilation of topographical data and asynoptic observations along coast lines and satellite data in sparsely observed ocean areas should make it possible to improve the accuracy of sea surface wind predictions.     

Surge dynamics of disaster displaced populations in temporary urban shelters: future challenges and management issues

A tropical cyclone (TC) precipitation prediction scheme has been developed based on the physical quantities of the NCEP/NCAR reanalysis data as potential predictors and using fuzzy neural network (FNN) model. TC precipitation samples from 172 tropical cyclones (TCs) affecting Guangxi, China, spanning 1980–2015 are used for model development. The FNN model input is constructed from potential predictors by employing both a stepwise regression method (SRM) and a locally linear embedding (LLE) algorithm. The LLE algorithm is capable of finding meaningful low-dimensional architectures hidden in their nonlinear high-dimensional data space and separating the underlying factors. In this scheme, the newly developed model, which is termed the FNN–LLE model, is used for daily TC precipitation prediction from 20:00 (Beijing Time, or BT) of the previous day to 20:00 BT of the current day at 89 stations covering Guangxi, China. Using identical modeling samples and independent samples, predictions of the FNN–LLE model are compared with the widely used SRM and interpolation method using the fine-mesh data of the European Centre for Medium-Range Weather Forecasts (ECMWF) in terms of the performance of TC rainfall prediction at 89 stations in Guangxi. The root-mean-square error (RMSE), bias, and equitable threat score (ETS) results were employed to assess the predicted outcomes. Results show that the FNN–LLE model is superior to the interpolation method by ECMWF and SRM for TC precipitation prediction with RMSE values of 21.94, 24.07, and 25.22 in FNN–LLE model, interpolation method by ECMWF and SRM, respectively. Moreover, FNN–LLE model having average bias and ETS values close to 1.0 gave better predictions than did the interpolation method by ECMWF and SRM.     

Generation of Aquifer Heterogeneity Maps Using Two-Dimensional Spectral Texture Segmentation Techniques

Numerical models that solve the governing equations for subsurface fluid flow and transport require detailed quantitative maps of spatially variable hydraulic properties. Recently, there has been great interest in methods that can map the spatial variability of hydraulic properties such as porosity and hydraulic conductivity (permeability). Presently, only limited data on natural permeability spatial structure are available. These data are often based on extensive discrete sampling in outcrops or boreholes. Then methods are used to interpolate between data values to map aquifer heterogeneity. Interpolation methods often mask critical local or intermediate scale heterogeneities. As sediment texture is directly correlated with many hydraulic properties we developed two new texture segmentation algorithms based on a space-local two-dimensional wavenumber spectral method known as the S-Transform. Existing texture segmentation algorithms could not delineate the subtle and continuous texture variations that exist in natural sediments. The S-Transform algorithms successfully delineated geologic structures and grain size patterns in photographs of outcrops in a glacial fluvial deposit; thus, no interpolation methods were required to produce continuous two-dimensional maps of texture facies. The S-Transform method is robust and is insensitive to changes in light intensity, and moisture variations. This makes the algorithm particularly applicable to natural sedimentary outcrops. The effectiveness of our methods are tested by correlating measured relative grain sizes in the images with actual grain size measurements taken from the sedimentary outcrops.     

Changes in the spatial distribution of subtidal macrobenthos due to predation by white shrimp (<Emphasis Type="Italic">Litopenaeus setiferus</Emphasis>)

Manipulative caging experiments were conducted in North Inlet, South Carolina, to measure the predatory effect of juvenile penaeid white shrimp,Litopenaeus setiferus, on their subtidal macrobenthic prey. We used the natural neighbor interpolation procedure within a Geographic Information System (GIS) to map macrobenthos distributions at both the start and end of the cage deployments. Moran’s I, a commonly used index of spatial autocorrelation, provided a quantitative metric for evaluating the statistical significance of the observed changes. We tested the hypothesis that juvenile white shrimp are optimal foragers by assessing whether their predatory behavior was targeted at higher density macrobenthos patches inside the enclosures, resulting in a more homogeneous distribution of prey after seven days. Since large changes in patchiness could occur over seven days without incurring a significant change in index value, we treated each index as a continuous measure of patchiness, and examined whether the value increased or decreased consistently among treatment replicates. Using Moran’s I, the abundance and spatial distribution of macrobenthos inside control, partial, open, and shrimp inclusion treatments varied in their response. After seven days, decreased patchiness was consistently observed in the high density shrimp treatment replicates, and increased patchiness in the open plots. The GIS natural neighbor interpolation created a succinct visual representation of dramatic changes in prey spatial distribution and prey densities throughout each cage. The GIS interpolation conveyed the dynamic nature of the spatial variability that would not have been evident by calculation of Moran’s I alone. Although we could only weakly support our hypothesis, the combination of visual interpolation methods with index calculations has great potential for gaining further insights into the role of different factors as they affect changes in spatial distribution of benthic infauna.     

Stationarity Scores on Training Images for Multipoint Geostatistics

This research introduces a novel method to assess the validity of training images used as an input for Multipoint Geostatistics, alternatively called Multiple Point Simulation (MPS). MPS are a family of spatial statistical interpolation algorithms that are used to generate conditional simulations of property fields such as geological facies. They are able to honor absolute “hard” constraints (e.g., borehole data) as well as “soft” constraints (e.g., probability fields derived from seismic data, and rotation and scale). These algorithms require 2D or 3D training images or analogs whose textures represent a spatial arrangement of geological properties that is presumed to be similar to that of a target volume to be modeled. To use the current generation of MPS algorithms, statistically valid training image are required as input. In this context, “statistical validity” includes a requirement of stationarity, so that one can derive from the training image an average template pattern. This research focuses on a practical method to assess stationarity requirements for MPS algorithms, i.e., that statistical density or probability distribution of the quantity shown on the image does not change spatially, and that the image shows repetitive shapes whose orientation and scale are spatially constant. This method employs image-processing techniques based on measures of stationarity of the category distribution, the directional (or orientation) property field and the scale property field of those images. It was successfully tested on a set of two-dimensional images representing geological features and its predictions were compared to actual realizations of MPS algorithms. An extension of the algorithms to 3D images is also proposed. As MPS algorithms are being used increasingly in hydrocarbon reservoir modeling, the methods described should facilitate screening and selection of the input training images.     

Neighborhood discontinuities in bivariate interpolation of scattered observations

Because of the need for computational efficiency, bivariate interpolation methods applied to scattered observations often involve two stages. Initially the variable is estimated at regular grid nodes using a running subset of data (usually of fixed number). This, however, will produce discontinuities in the interpolated surface. Thus a second stage, curvilinear interpolation technique, is applied to estimated values to smooth out the effect of discontinuities. Such problems can be overcome efficiently in processing large data sets by interpolating over natural neighbor subsets. Interpolation procedures that generate discontinuities in the interpolated surface are inappropriate for geological applications, where dislocations due to structural complications may be present.     

High-resolution regional gravity field model of Pakistan based on best residual terrain model (RTM) of topography and interpolation techniques

This study focuses on the development of absolute gravity model for Pakistan based on best possible residual terrain model of gravity using residual terrain modeling technique. The datasets used for the development of model are observed gravity, global gravity models, and Shuttle Radar Topographic Mission (SRTM30) elevation data. The residual terrain modeling technique has been used in the remove-restore procedure for smoothing the observed gravity field. Different topographic elevation models were tested in the model selection and one best possible model with minimum mean and standard deviation was selected for residual terrain effects. Least square collocation technique has been used for quality control and error estimates. The best possible covariance model was established from residual gravity for onward prediction of gravity anomalies at the earth surface for error and prediction analysis. The residual terrain effect of gravity, value of free air anomaly from EGM96, and observed free air anomaly are added to normal gravity to compute the absolute gravity at earth surface. The prediction of these parameters is made by employing Lagrange interpolation with least square adjustment. The results are compared with ～5% randomly selected data points not utilized for the development of covariance function and/or model development. Spline interpolation technique has also been used for the prediction of gravity field-related parameters. Lagrange interpolation exhibits relatively superior results over spline-based interpolation. This is as per expectation due to the reason that additional gridding for spline interpolation filters the signal part as well. This fact is evident from the results of spline interpolation of Grid-I and Grid-II with relatively better prediction results in Grid-I. This version of the model is capable of prediction having limiting error of 30 mGal. The predicted results show that 96.16% of prediction data falls within above-mentioned limit with Lagrange interpolation technique with least square adjustment for whole Pakistan area. The adverse effect of gridding is absent in case of Grid-I due to relatively flat areas and predicted data matches totally with control values for both spline as well as Lagrange interpolations. However, in case of Grid-II which includes high mountains of Himalaya, gridding effect is present and the accuracy of the predicted results falls to ～92%. The computed results have been compared with absolute values predicted using EGM96 and EGM2008 models as well. The gravity field recovered with PAKGM model is much better, i.e., ～ 96.16%, than both with EGM96 and EGM2008 which is about 85% only.     

Short-time-scale features of the Earth’s polar motion

The fundamental astrometric problem of high-accuracy interpolation and forecasting of the Earth’s polar motion on short time scales from 1–2 to 10–30 days is studied. Hierarchies of interval length and parameter accuracy are established using appropriate models for the process. Filtering algorithms are adjusted using a weighted least squares fit of measurements of the International Earth Rotation Service (IERS). Best-fit estimates for the main features of the motion are obtained for various time intervals; interpolations and forecasts are compared with the IERS measurements.     

Hidden Markov Model for quantitative prediction of snowfall and analysis of hazardous snowfall events over Indian Himalaya

A Hidden Markov Model (HMM) has been developed for prediction of quantitative snowfall in Pir-Panjal and Great Himalayan mountain ranges of Indian Himalaya. The model predicts snowfall for two days in advance using daily recorded nine meteorological variables of past 20 winters from 1992–2012. There are six observations and six states of the model. The most probable observation and state sequence has been computed using Forward and Viterbi algorithms, respectively. Baum–Welch algorithm has been used for optimizing the model parameters. The model has been validated for two winters (2012–2013 and 2013–2014) by computing root mean square error (RMSE), accuracy measures such as percent correct (PC), critical success index (CSI) and Heidke skill score (HSS). The RMSE of the model has also been calculated using leave-one-out cross-validation method. Snowfall predicted by the model during hazardous snowfall events in different parts of the Himalaya matches well with the observed one. The HSS of the model for all the stations implies that the optimized model has better forecasting skill than random forecast for both the days. The RMSE of the optimized model has also been found smaller than the persistence forecast and standard deviation for both the days.     

Slump-initiated and controlled syndepositional sandstone remobilization: an example from the Namurian of County Clare, Ireland

Remobilization of sandstones can dramatically reconfigure original depositional geometries and results in very unusually shaped sandstones, which resemble little, if any, of the original geometry. A number of deformational sandstone bodies, dykes and volcanoes from the upper part of the Carboniferous Ross Formation are described, which offer the opportunity to examine a suite of field-scale reconfigured sandstones. These structures are located in close proximity to the Ross Slide, which outcrops along a 2-km section on the northern coast of the Loop Head Peninsula, County Clare, Ireland. Dome- and ridge-shaped deformational sandstone bodies, dykes and volcanoes are interpreted to be the product of remobilization of a turbiditic sandstone. Liquification and remobilization were triggered by translation, cessation and loading of the underlying turbiditic sandstone by the Ross Slide. Deformational sand body, dyke and volcano development occurred in an asynchronous fashion with deformational sand bodies formed during slump translation. Sand dykes and volcanoes developed after the cessation of slump movement. During slump translation, the minimum principal stress (σ₃) was orientated vertically and the slump behaved in a `ductile' manner. After slump arrest, the minimum principal stress was oriented horizontally, and the unit regained shear strength to behave in a `brittle' manner. The relative change in rheological states with changing applied shear stress is indicative of thixotropic-like behaviour within the slump mass. Ridge-shaped deformational sand bodies are aligned parallel to slump folds, and their morphology is inferred to be controlled by compressional slump deformation associated with heterogeneous cessation of slump movement that was initiated by frontal arrest of the translating mass.