Probabilistic modeling of seismically triggered landslides using Monte Carlo simulations

The 2004 Chuetsu earthquakes of Niigata (Japan) triggered numerous landslides, and the most widespread types of landslides were highly disrupted, relatively shallow slides and soil (debris) flows. This paper presented a method to evaluate slope instability using Newmark displacement on a pixel-by-pixel basis in a given area. The proposed method was able to integrate Newmark displacement modeling and Monte Carlo simulations within geographical information systems. In the modeling, an empirical attenuation relationship was utilized to calculate Arias intensity over this study area, and the variability of geotechnical parameters was taken into account to calculate coseismic landslide displacement. Before deriving the displacement from related inputs, the Monte Carlo simulations ran 1,500 times and generated 1,500 displacement values for each grid cell, and then means and standard deviations of displacement were calculated and probabilistic distributions can be obtained. Finally, given 10 cm as a threshold value of displacement, estimated probabilities of displacement exceeding 10 cm were shown as a map of seismic landslide hazards. The resulting hazard map was classified into four categories from very low to high level.     

顾及DEM误差自相关的坡度计算模型精度分析

基于DEM的坡度计算,其误差来源于DEM误差、DEM结构和坡度计算模型。在顾及DEM误差自相关的前提下,对四种DEM坡度计算模型进行了分析和评价。研究表明,三阶不带权差分能给出较高的坡度计算精度;在局部窗口中,格网点数量越多,坡度计算越准确;等权比不等权的坡度计算模型更准确;DEM误差自相关结构形式对坡度计算无影响。进一步的理论分析和试验分析还表明：DEM误差自相关性的存在,不仅能够改善地形分析的精度,也能改善DEM自身精度。     

Efficient generation of conditional simulations by chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix

Consider the problem of generating a realization y₁ of a Gaussian random field on a dense grid of points ₁ conditioned on field observations y₂ collected on a sparse grid of points ₂. An approach to this is to generate first an unconditional realization y over the grid =_{1 2}, and then to produce y₁ by conditioning y on the data y₂. As standard methods for generating y, such as the turning bands, spectral or Cholesky approaches can have various limitations, it has been proposed by M. W. Davis to generate realizations from a matrix polynomial approximations to the square root of the covariance matrix. In this paper we describe how to generate a direct approximation to the conditional realization y₁, on ₁ using a variant of Davis' approach based on approximation by Chebyshev polynomials. The resulting algorithm is simple to implement, numerically stable, and bounds on the approximation error are readily available. Furthermore we show that the conditional realization y₁ can be generated directly with a lower order polynomial than the unconditional realization y, and that further reductions can be achieved by exploiting a nugget effect if one is present. A pseudocode version of the algorithm is provided that can be implemented using the fast Fourier transform if the field is stationary and the grid ₁ is rectangular. Finally, numerical illustrations are given of the algorithm's performance in generating various 2-D realizations of conditional processes on large sampling grids.     

Comparison of structural and least-squares lines for estimating geologic relations

Two different goals in fitting straight lines to data are to estimate a true linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating true straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal—predicting the dependent variable—OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples.     

Temporal behavior of the background seismicity rate in central Japan, 1998 to mid-2003

We studied the temporal behavior of the background shallow seismicity rate in 700 circular areas across inland Japan. To search for and test the significance of the possible rate changes in background seismicity, we developed an efficient computational method that applies the space–time ETAS model proposed by Ogata in 1998 to the areas. Also, we conducted Monte Carlo tests using a simulated catalog to validate the model we applied. Our first finding was that the activation anomalies were found so frequently that the constant background seismicity hypothesis may not be appropriate and/or the triggered event model with constraints on the parameters may not adequately describe the observed seismicity. However, quiescence occasionally occurs merely by chance. Another outcome of our study was that we could automatically find several anomalous background seismicity rate changes associated with the occurrence of large earthquakes. Very significant seismic activation was found before the M6.1 Mt. Iwate earthquake of 1998. Also, possible seismic quiescence was found in an area 150 km southwest of the focal region of the M7.3 Western Tottori earthquake of 2000. The seismicity rate in the area recovered after the mainshock.     

The Tornquist Zone, a north east inclining lithospheric transition at the south western margin of the Baltic Shield: Revealed through a nonlinear teleseismic tomographic inversion

From July 1996 to August 1997 the TOR project operated 130 seismographs in North Germany, Denmark and South Sweden, with the aim of collecting signals from local, regional and teleseismic earthquakes. This data set is particularly interesting since the seismic antenna crosses the most significant geological boundary in Europe, the Tornquist Zone, which in the northern part is the border between the Baltic Shield and the younger European lithosphere. Previous studies have shown significant physical changes in the crust and upper mantle across this transition zone, including two independent teleseismic tomographic studies of the TOR data set. But these two studies disagree on the orientation of the slope of the transition. Both studies used an iterative linearized inversion method. We will in this work Preprint submitted to Elsevier Science 27 July 2005 present an inversion based on Bayesian statistics, where the solution space is examined in order to study a very large number of tomographic solutions and to examine the solution uniqueness and uncertainty. The method is applied to measurements of 3345 relative teleseismic P-phase travel times from 48 teleseismic earthquakes with good azimuthal coverage with respect to the great circle arc of the TOR array. We find the lithospheric transition to be a north east inclination of around 30° to 45° off vertical.     

Computational study of tetrahedral Al–Si and octahedral Al–Mg ordering in phengite

 As part of a wider study of the nature and origins of cation order–disorder in micas, a variety of computational techniques have been used to investigate the nature of tetrahedral and octahedral ordering in phengite, K₂ ^[6](Al₃Mg)^[4](Si₇Al)O₂₀(OH)₄. Values of the atomic exchange interaction parameters J _n used to model the energies of order–disorder were calculated. Both tetrahedral Al–Si and octahedral Al–Mg ordering were studied and hence three types of interaction parameter were necessary: for T–T, O–O and T–O interactions (where T denotes tetrahedral sites and O denotes octahedral sites). Values for the T–T and O–O interactions were taken from results on other systems, whilst we calculated new values for the T–O interactions. We have demonstrated that modelling the octahedral and tetrahedral sheets alone and independently produces different results from modelling a whole T–O–T layer, hence justifying the inclusion of the T–O interactions. Simulations of a whole T–O–T layer of phengite indicated the presence of short-range order, but no long-range order was observed. Received: 8 August 2002 / Accepted: 14 February 2003 Acknowledgements The authors are grateful to EPSRC (EJP) and the Royal Society (CIS) for financial support. Monte Carlo simulations were performed on the Mineral Physics Group's Beowulf cluster and the University of Cambridge's High Performance Computing Facility.     

The identifiability of parameters in a water quality model of the Biebrza River, Poland

The identifiability of model parameters of a steady state water quality model of the Biebrza River and the resulting variation in model results was examined by applying the Monte Carlo method which combines calibration, identifiability analysis, uncertainty analysis, and sensitivity analysis. The water quality model simulates the steady state concentration profiles of chloride, phosphate, ammonium, and nitrate as a function of distance along a river. The water quality model with the best combination of parameter values simulates the observed concentrations very well. However, the range of possible modelled concentrations obtained for other more or less equally eligible combinations of parameter values is rather wide. This range in model outcomes reflects possible errors in the model parameters. Discrepancies between the range in model outcomes and the validation data set are only caused by errors in model structure, or (measurement) errors in boundary conditions or input variables. In this sense the validation procedure is a test of model capability, where the effects of calibration errors are filtered out. It is concluded that, despite some slight deviations between model outcome and observations, the model is successful in simulating the spatial pattern of nutrient concentrations in the Biebrza River.     

Multivariate nonparametric resampling scheme for generation of daily weather variables

A nonparametric resampling technique for generating daily weather variables at a site is presented. The method samples the original data with replacement while smoothing the empirical conditional distribution function. The technique can be thought of as a smoothed conditional Bootstrap and is equivalent to simulation from a kernel density estimate of the multivariate conditional probability density function. This improves on the classical Bootstrap technique by generating values that have not occurred exactly in the original sample and by alleviating the reproduction of fine spurious details in the data. Precipitation is generated from the nonparametric wet/dry spell model as described in Lall et al. [1995]. A vector of other variables (solar radiation, maximum temperature, minimum temperature, average dew point temperature, and average wind speed) is then simulated by conditioning on the vector of these variables on the preceding day and the precipitation amount on the day of interest. An application of the resampling scheme with 30 years of daily weather data at Salt Lake City, Utah, USA, is provided.     

Stochastic Modelling of the Impact of Flood Protection Measures Along the River Waal in the Netherlands

River flooding is a problem of international interest. In the past few years many countries suffered from severe floods. A large part of the Netherlands is below sea level and river levels. The Dutch flood defences along the river Rhine are designed for water levels with a probability of exceedance of 1/1250 per year. These water levels are computed with a hydrodynamic model using a deterministic bed level and a deterministic design discharge. Traditionally, the safety against flooding in the Netherlands is obtained by building and reinforcing dikes. Recently, a new policy was proposed to cope with increasing design discharges in the Rhine and Meuse rivers. This policy is known as the Room for the River (RfR) policy, in which a reduction of flood levels is achieved by measures creating space for the river, such as dike replacement, side channels and floodplain lowering. As compared with dike reinforcement, these measures may have a stronger impact on flow and sediment transport fields, probably leading to stronger morphological effects. As a result of the latter the flood conveyance capacity may decrease over time. An a priori judgement of safety against flooding on the basis of an increased conveyance capacity of the river can be quite misleading. Therefore, the determination of design water levels using a fixed-bed hydrodynamic model may not be justified and the use of a mobile-bed approach may be more appropriate. This problem is addressed in this paper, using a case study of the river Waal (one of the Rhine branches in the Netherlands). The morphological response of the river Waal to a flood protection measure (floodplain lowering in combination with summer levee removal) is analysed. The effect of this measure is subject to various sources of uncertainty. Monte Carlo simulations are applied to calculate the impact of uncertainties in the river discharge on the bed levels. The impact of the “uncertain” morphological response on design flood level predictions is analysed for three phenomena, viz. the impact of the spatial morphological variation over years, the impact of the seasonal morphological variation and the impact of the morphological variability around bifurcation points. The impact of seasonal morphological variations turns out to be negligible, but the other two phenomena appear to have each an appreciable impact (order of magnitude 0.05–0.1 m) on the computed design water levels. We have to note however, that other sources of uncertainty (e.g. uncertainty in hydraulic roughness predictor), which may be of influence, are not taken into consideration. In fact, the present investigation is limited to the sensitivity of the design water levels to uncertainties in the predicted bed level.