Spatial prediction using bivariate exponential distribution

In this paper, a certain bivariate exponential distribution is used for the spatial prediction. The unobserved random variable is predicted by the projection onto the space of all linear combinations of the powers, up to degree m, of the observed random variables plus the constant 1. We obtain a solution by assuming that all the bivariate distributions follow Gumbel’s type III or logistic form of bivariate exponential. The method is implemented on two data sets and the results are presented. The predictions are compared with the original values through Mean Structural Similarity (MSSIM) index of Wang et al. (IEEE Trans Image Process 13(4):600–612, 2004). Using the MSSIM index the proposed method is also compared with Ordinary Kriging and with Simple Kriging after normal score transform.     

Use of spectral acceleration data for determination of three-dimensional attenuation structure in the Pithoragarh region of Kumaon Himalaya

Three-dimensional attenuation structures are related to the subsurface heterogeneities present in the earth crust. An algorithm for estimation of three-dimensional attenuation structure in the part of Garhwal Himalaya, India has been presented by Joshi (Curr Sci 90:581–585, 2006b; Nat Hazards 43:129–146, 2007). In continuation of our earlier approach, we have presented a method in which strong motion data have been used to estimate frequency-dependent three-dimensional attenuation structure of the region. The border district of Pithoragarh in the Higher Himalaya, India, lies in the central seismic gap region of Himalaya. This region falls in the seismic zones IV and V of the seismic zoning map of India. A dense network consisting of eight accelerographs has been installed in this region. This network has recorded several local events. An algorithm based on inversion of strong motion digital data is developed in this paper to estimate attenuation structure at different frequencies using the data recorded by this network. Twenty strong motion records observed at five stations have been used to estimate the site amplification factors using inversion algorithm defined in this paper. Site effects obtained from inversion has been compared with that obtained using Nakamura (1988) and Lermo et al. (Bull Seis Soc Am 83:1574–1594, 1993) approach. The obtained site amplification term has been used for correcting spectral acceleration data at different stations. The corrected spectral acceleration data have been used as an input to the developed algorithm to avoid effect of near-site soil amplification term. The attenuation structure is estimated by dividing the entire area in several three-dimensional block of different frequency-dependent shear wave quality factor Q _β (f). The input to this algorithm is the spectral acceleration of S phase of the corrected accelerogram. The outcome of the algorithm is given in terms of attenuation coefficient and source acceleration spectra. In the present study, this region has been divided into 25 rectangular blocks with thickness of 10 km and surface dimension of 12.5 × 12.1 km, respectively. Present study gives three-dimensional attenuation model of the region which can be used for both hazard estimation and simulation of strong ground motion.     

ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

An inexact stochastic mixed integer linear semi-infinite programming (ISMISIP) model is developed for municipal solid waste (MSW) management under uncertainty. By incorporating stochastic programming (SP), integer programming and interval semi-infinite programming (ISIP) within a general waste management problem, the model can simultaneously handle programming problems with coefficients expressed as probability distribution functions, intervals and functional intervals. Compared with those inexact programming models without introducing functional interval coefficients, the ISMISIP model has the following advantages that: (1) since parameters are represented as functional intervals, the parameter’s dynamic feature (i.e., the constraint should be satisfied under all possible levels within its range) can be reflected, and (2) it is applicable to practical problems as the solution method does not generate more complicated intermediate models (He and Huang, Technical Report, 2004; He et al. J Air Waste Manage Assoc, 2007). Moreover, the ISMISIP model is proposed upon the previous inexact mixed integer linear semi-infinite programming (IMISIP) model by assuming capacities of the landfill, WTE and composting facilities to be stochastic. Thus it has the improved capabilities in (1) identifying schemes regarding to the waste allocation and facility expansions with a minimized system cost and (2) addressing tradeoffs among environmental, economic and system reliability level.     

Evaluation of spatially clustered ordnance when using compliance sampling surveys after clean-up at military training sites

After site clean-up teams have removed all of what they believe to be UXO within a specific impact area, statistical compliance sampling is a possible method for verifying with a specified probability that this area has been cleaned to specifications. Schilling [J Qual Technol 10(2):47–51, 1978, Acceptance sampling in quality control. Marcel Dekker, Inc., New York, 1982] developed a compliance sampling methodology based on the hypergeometric distribution. Bowen and Bennett (1987) also use compliance sampling where they provide an approximation for estimating the number of samples (n) required to state with desired probability that the entire population of sample units (N, where n < N) are in compliance with cleanup goals. This article describes two methods (anomaly and transect) for applying the Schilling [J Qual Technol 10(2):47–51, 1978, Acceptance sampling in quality control. Marcel Dekker, Inc., New York, 1982] compliance sampling method to military training sites. After describing these methods, a simulation study is presented which demonstrates the performance of transect compliance sampling calculations based on varied degrees of clustered UXO within a specific impact area and different types of sampling routines.     

Estimating the confidence of earthquake damage scenarios: examples from a logic tree approach

Earthquake loss estimation is now becoming an important tool in mitigation planning, where the loss modeling usually is based on a parameterized mathematical representation of the damage problem. In parallel with the development and improvement of such models, the question of sensitivity to parameters that carry uncertainties becomes increasingly important. We have to this end applied the capacity spectrum method (CSM) as described in FEMA HAZUS-MH. Multi-hazard Loss Estimation Methodology, Earthquake Model, Advanced Engineering Building Module. Federal Emergency Management Agency, United States (2003), and investigated the effects of selected parameters. The results demonstrate that loss scenarios may easily vary by as much as a factor of two because of simple parameter variations. Of particular importance for the uncertainty is the construction quality of the structure. These results represent a warning against simple acceptance of unbounded damage scenarios and strongly support the development of computational methods in which parameter uncertainties are propagated through the computations to facilitate confidence bounds for the damage scenarios.     

Numerical studies of dispersion due to tidal flow through Moskstraumen, northern Norway

The effect of horizontal grid resolution on the horizontal relative dispersion of particle pairs has been investigated on a short time scale, i.e. one tidal M ₂ cycle. Of particular interest is the tidal effect on dispersion and transports in coastal waters where small-scale flow features are important. A three-dimensional ocean model has been applied to simulate the tidal flow through the Moskstraumen Maelstrom outside Lofoten in northern Norway, well known for its strong current and whirlpools (Gjevik et al., Nature 388(6645):837–838, 1997; Moe et al., Cont Shelf Res 22(3):485–504, 2002). Simulations with spatial resolution down to 50 m have been carried out. Lagrangian tracers were passively advected with the flow, and Lyapunov exponents and power law exponents have been calculated to analyse the separation statistics. It is found that the relative dispersion of particles on a short time scale (12–24 h) is very sensitive to the grid size and that the spatial variability is also very large, ranging from 0 to 100 km² over a distance of 100 m. This means that models for prediction of transport and dispersion of oil spills, fish eggs, sea lice etc. using a single diffusion coefficient will be of limited value, unless the models actually resolves the small-scale eddies of the tidal current.     

Probabilistic aftershock hazard assessment I: numerical testing of methodological features

Probabilistic aftershock hazard assessment (PAHA, Wiemer, Geoph Res Lett 27:3405–3408, 2000), provided for California within the frame of the STEP project, is based on a methodology, two features of which are addressed in detail: (1) the parameters of Omori’s law and (2) application of attenuation relations in evaluating peak ground velocity exceedence probability. Concerning the first point, we perform a simple parametric study. We assume the generalized Omori’s law by Shcherbakov et al. (Geoph Res Lett 31:L11613, 2004), in which characteristic time c scales with aftershock magnitude. The study shows that, among all the parameters, the hazard is most sensitive to the choice of m* (controlling the overall aftershock productivity) and least sensitive to the scaling of c. We also conclude that the hazard is mainly due to very early (less than 1 day) aftershocks. As regards the second point, we employ various attenuation relations from different tectonic areas to study their effect on the hazard analysis. We conclude that the resulting variations are relatively large, comparable to those obtained for varying m*.     

Moment inequality and complete convergence of moving average processes under asymptotically linear negative quadrant dependence assumptions

Let {Y, Y _i , −∞ < i < ∞} be a doubly infinite sequence of identically distributed and asymptotically linear negative quadrant dependence random variables, {a _i , −∞ < i < ∞} an absolutely summable sequence of real numbers. We are inspired by Wang et al. (Econometric Theory 18:119–139, 2002) and Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003). And Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003) have obtained Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions. In this paper, we prove the complete convergence of under some suitable conditions. The results obtained improve and generalize the results of Li et al. (1992) and Zhang (1996). The results obtained extend those for negative associated sequences and ρ^*-mixing sequences. CIC Number O211, AMS (2000) Subject Classification 60F15, 60G50 Research supported by National Natural Science Foundation of China     

Estimation of the internal pressure gradient in σ-coordinate ocean models: comparison of second-, fourth-, and sixth-order schemes

Sigma-coordinate ocean models are attractive because of their abilities to resolve bottom and surface boundary layers. However, these models can have large internal pressure gradient (IPG) errors. In this paper, two classes of methods for the estimation of the IPGs are assessed. The first is based on the integral approach used in the Princeton Ocean Model (POM). The second is suggested by Shchepetkin and McWilliams (2003) based on Green’s theorem; thus, area integrals of the pressure forces are transformed into line integrals. Numerical tests on the seamount problem, as well as on a northwestern Atlantic grid using both classes of methods, are presented. For each class, second-, fourth-, and sixth-order approximations are tested. Results produced with a fourth-order compact method and with cubic spline methods are also given. The results show that the methods based on the POM approach in general give smaller errors than the corresponding methods given in Shchepetkin and McWilliams (2003). The POM approach also is more robust when noise is added to the topography. In particular, the IPG errors may be substantially reduced by using the computationally simple fourth-order method from McCalpin (1994).     

Nonseparable stationary anisotropic space–time covariance functions

Obtaining new and flexible classes of nonseparable spatio-temporal covariances and variograms has resulted a key point of research in the last years. The goal of this paper is to introduce and develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Recent literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Here we propose a generalization of Gneiting’s (J Am Stat Assoc 97:590–600, 2002a) approach and obtain new classes of stationary nonseparable spatio-temporal covariance functions which are spatially anisotropic. The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability.Work partially funded by grant MTM2004-06231 from the Spanish Ministry of Science and Education.     

A reappraisal of shear wave splitting parameters from Italian active volcanic areas through a semiautomatic algorithm

Shear wave splitting parameters represent a useful tool to detail the stress changes occurring in volcanic environments before impending eruptions. In the present paper, we display the parameter estimates obtained through implementation of a semiautomatic algorithm applied to all useful datasets of the following Italian active volcanic areas: Mt. Vesuvius, Campi Flegrei, and Mt. Etna. Most of these datasets have been the object of several studies (Bianco et al., Annali di Geofisica, XXXXIX 2:429–443, 1996, J Volcanol Geotherm Res 82:199–218, 1998a, Geophys Res Lett 25(10):1545–1548, 1998b, Phys Chem Earth 24:977–983, 1999, J Volcanol Geotherm Res 133:229–246, 2004, Geophys J Int 167(2):959–967, 2006; Del Pezzo et al., Bull Seismol Soc Am 94(2):439–452, 2004). Applying the semiautomatic algorithm, we confirmed the results obtained in previous studies, so we do not discuss in much detail each of our findings but give a general overview of the anisotropic features of the investigated Italian volcanoes. In order to make a comparison among the different volcanic areas, we present our results in terms of the main direction of the fast polarization (φ) and percentage of shear wave anisotropy (ξ).     

Pseudo relative velocity spectra of earthquake ground motion at high frequencies

The currently available empirical scaling laws for estimation of spectral amplitudes are limited to periods longer than 0–04 s. However, for design of equipment and stiff structures on multiple and distant supports, exposed to strong shaking near faults where peak accelerations can exceed 1g, specification of design ground motions at higher frequencies is required. This paper presents a method for extrapolation of pseudo-relative velocity spectral amplitudes of strong earthquake shaking to short periods (0–01 < T < 0–04 sec). The extrapolated spectra can be used as a physical basis for defining design spectral amplitudes in this higher-frequency range. The analysis in this paper implies that for typical strong motion accelerations, particularly on sedimentary sites in California, the peak ground accelerations are projected to be unaffected by frequencies higher than those recorded. Consequently, in California, the high-frequency pseudo-acceleration spectra can be approximated from the recorded absolute peak accelerations.     

Towards medium-term (order of months) morphodynamic modelling of the Teign estuary, UK

The main objective of this paper is to address the principal mechanisms involved in the medium-term (order of months to years) morphodynamic evolution of estuaries through the application of a process-based numerical modelling. The Teign estuary (Teignmouth, UK) is the selected site. The system is forced by the macrotidal semi-diurnal tide in the English Channel and is perturbed to a minor extent by high river discharge events (freshets). Although waves have a definite influence on the adjacent coastal area, Wells (Teignmouth Quay Development Environmental Statement: Changes to Physical Processes. Report R.984c:140. ABP Marine Environmental Research Ltd., Southampton, 2002b) suggested that swell waves do not enter the estuary. Hence, wave effects are neglected in this study, as only tides and the river discharge are taken into account. The sediment grain size is highly variable, but mainly sandy. Within the frame of the COAST3D project (), four bathymetric surveys of the adjacent coastal area were carried out at a nearly weekly intervals. The outer estuary and the adjacent coastal area were also surveyed every 6 months as part of the COASTVIEW project (). Based on these data and on continuously measured parameters, such as water level, waves, wind and river discharge, numerical modelling of the morphodynamic processes can be tested. To replicate the morphological changes in the medium-term within a feasible simulation time, forcing conditions are reduced through the use of an input reduction method (called ensemble technique). In this study, simulations are based on the coupling between Telemac-2D and its non-cohesive sediment transport module, Sisyphe (version 5.3 for both modules). Three different sediment transport formulae were tested: (1) Engelund and Hansen (A monograph on sediment transport in alluvial streams, 3rd edn. Technological University of Denmark, Copenhagen, 1967) including the modifications proposed by Chollet and Cunge (J Hydraul Eng 17(1):1–13, 1979); (2) Bijker (Mechanics of sediment transport by the combination of waves and current. In: Design and reliability of coastal structures. 23rd international conference on Coastal Engineering, pp 147–173, 1968) and (3) Soulsby (Dynamics of Marine Sands. A manual for practical applications. HR Wallingford, Wallingford, p 142, 1997) modified version of van Rijn [J Hydraul Eng 110(10):1431–1456, 1984a, J Hydraul Eng 110(11):1613–1641, 1984b] formulation. Both a qualitative (i.e. visual comparison) and a quantitative tool [Brier Skill Score (BSS); described in Sutherland et al. in Coast Eng 51:917–939, 2004b] are applied to assess the similarity of simulations when compared to model predictions and observations. Tests confirmed the reliability and time efficiency of the ensemble technique, since it reproduced very well the results of a reference run, a computation based on the observed boundary conditions. For the spring-neap cycle modelled, the BSS was of 0.91 (a perfect modelling would have a BSS of 1), with a reduction in the simulation time on the order of 80%. For the 6-month-period simulation, results were also excellent: BSS=0.92 and a computer time reduction of 85%. In principle, this method has the advantage of being applied to any process-based numerical model.     

An automatic scheme for baseline correction of strong-motion records in coseismic deformation determination

Coseismic deformation can be determined from strong-motion records of large earthquakes. Iwan et al. (Bull Seismol Soc Am 75:1225–1246, 1985) showed that baseline corrections are often required to obtain reliable coseismic deformation because baseline offsets lead to unrealistic permanent displacements. Boore (Bull Seismol Soc Am 91:1199–1211, 2001) demonstrated that different choices of time points for baseline correction can yield realistically looking displacements, but with variable amplitudes. The baseline correction procedure of Wu and Wu (J Seismol 11:159–170, 2007) improved upon Iwan et al. (Bull Seismol Soc Am 75:1225–1246, 1985) and achieved stable results. However, their time points for baseline correction were chosen by a recursive process with an artificial criterion. In this study, we follow the procedure of Wu and Wu (J Seismol 11:159–170, 2007) but use the ratio of energy distribution in accelerograms as the criterion to determine the time points of baseline correction automatically, thus avoiding the manual choice of time points and speeding up the estimation of coseismic deformation. We use the 1999 Chi-Chi earthquake in central Taiwan and the 2003 Chengkung and 2006 Taitung earthquakes in eastern Taiwan to illustrate this new approach. Comparison between the results from this and previous studies shows that our new procedure is suitable for quick and reliable determination of coseismic deformation from strong-motion records.     

Earthquake focal mechanisms and stress inversion in the Irpinia Region (southern Italy)

The goal of this study was to estimate the stress field acting in the Irpinia Region, an area of southern Italy that has been struck in the past by destructive earthquakes and that is now characterized by low to moderate seismicity. The dataset are records of 2,352 aftershocks following the last strong event: the 23 November 1980 earthquake (M 6.9). The earthquakes were recorded at seven seismic stations, on average, and have been located using a three-dimensional (3D) P-wave velocity model and a probabilistic, non-linear, global search technique. The use of a 3D velocity model yielded a more stable estimation of take-off angles, a crucial parameter for focal mechanism computation. The earthquake focal mechanisms were computed from the P-wave first-motion polarity data using the FPFIT algorithm. Fault plane solutions show mostly normal component faulting (pure normal fault and normal fault with a strike-slip component). Only some fault plane solutions show strike-slip and reverse faulting. The stress field is estimated using the method proposed by Michael (J Geophys Res 92:357–368, 1987a) by inverting selected focal mechanisms, and the results show that the Irpinia Region is subjected to a NE–SW extension with horizontal σ ₃ (plunge 0°, trend 230°) and subvertical σ ₁ (plunge 80°, trend 320°), in agreement with the results derived from other stress indicators.     

Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. I. A re-visit to regional homogeneity

As part I of a sequence of two papers, previously developed L-moments by Hosking (J R Stat Soc Ser B Methodol 52(2):105–124, 1990), and the LH-moments by Wang (Water Resour Res 33(12):2841–2848, 1997) are re-visited. New relationships are developed for regional homogeneity analysis by the LH-moments, and further establishment of regional homogeneity is investigated. Previous works of Hosking (J R Stat Soc Ser B Methodol 52(2):105–124, 1990) and Wang (Water Resour Res 33(12):2841–2848, 1997) on L-moments and LH-moments for the generalized extreme value (GEV) distribution are extended to the generalized Pareto (GPA) and the generalized logistic (GLO) distributions. The Karkhe watershed, located in western Iran is used as a case study area. Regional homogeneity was investigated by first assuming the entire study area as one regional cluster. Then the entire study area was designated “homogeneous” by the L-moments (L); and was designated “heterogeneous” by all four levels of the LH-moments (L₁ to L₄). The k-means method was used to investigate the case of two regional clusters. All levels of the L- and LH-moments designated the upper watershed (region A), “homogeneous”, and the lower watershed (region B) “possibly-homogeneous”. The L₃ level of the GPA and the L₄ level of the GLO were selected for regions A and B, respectively. Wang (Water Resour Res 33(12):2841–2848, 1997) identified a reversing trend in improved performance of the GEV distribution at the LH-moments level of L₃ (during the goodness-of-fit test). Similar results were also obtained in this research for the GEV distribution. However, for the case of the GPA distribution the reversing trend started at L₄ for region A; and at L₂ for region B. As for the case of the GLO, an improved performance was observed for all levels (moving from L to L₄); for both regions.     

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.     

Pseudo relative velocity spectra of earthquake ground motion at long periods

This paper analyses the processes which govern structural response, and uses observations of strong earthquake ground motion to propose quantitative extrapolation of pseudo relative velocity spectral amplitudes to long (100 > T > 1 s) periods. This will eliminate the current difficulties with rough estimation of long period spectral amplitudes and will open new possibilities by enabling the strong motion hazard calculations to be extended to the same long period band. So far, the scaling equations of response spectrum amplitudes have been valid only up to periods less than several seconds. The design of long structures and of structures on multiple distant supports requires knowledge and specification of design ground motions well beyond 1–10 s periods. With the results presented in this paper it will be possible to compute site-specific uniform hazard spectra and associated synthetic accelograms for essentially all long period response problems.