A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair-copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair-copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair-copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair-copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.
In the context of modeling regional freight the four-stage model is a popular choice. The first stage of the model, freight generation and attraction, however, suffers from three shortcomings: first of all, it does not take spatial dependencies among regions into account, thus potentially yielding biased estimates. Second, there is no clear consensus in the literature as to the choice of explanatory variables. Second, sectoral employment and gross value added are used to explain freight generation, whereas some recent publications emphasize the importance of variables which measure the amount of logistical activity in a region. Third, there is a lack of consensus regarding the functional form of the explanatory variables. Multiple recent studies emphasize nonlinear influences of selected variables. This article addresses these shortcomings by using a spatial variant of the classic freight generation and attraction models combined with a penalized spline framework to model the explanatory variables in a semiparametric fashion. Moreover, a Bayesian estimation approach is used, coupled with a penalized Normal inverse-Gamma prior structure, to introduce uncertainty regarding the choice and functional form of explanatory variables. The performance of the model is assessed on a real-world example of freight generation and attraction of 258 European NUTS-2 level regions, covering 25 European countries.
Mathematical models have become a crucial way for the Earth scientist to understand and predict how our planet functions and evolves through time and space. The finite element method (FEM) is a remarkably flexible and powerful tool with enormous potential in the Earth Sciences. This pragmatic guide explores how a variety of different Earth science problems can be translated and solved with FEM, assuming only basic programming experience.
Oil and Gas Exploration: Methods and Application presents a summary of new results related to oil and gas prospecting that are useful for theoreticians and practical professionals. The study of oil and gas complexes and intrusions occurring in sedimentary basins is crucial for identifying the location of oil and gas fields and for making accurate predictions on oil findings.
Volume highlights include:
Spatial heterogeneity has been regarded as an important issue in space–time prediction. Although some statistical methods of space–time predictions have been proposed to address spatial heterogeneity, the linear assumption makes it difficult for these methods to predict geographical processes accurately because geographical processes always involve complicated nonlinear characteristics. An extreme learning machine (ELM) has the advantage of approximating nonlinear relationships with a rapid learning speed and excellent generalization performance. However, determining how to incorporate spatial heterogeneity into an ELM to predict space–time data is an urgent problem. For this purpose, a new method called geographically weighted ELM (GWELM) is proposed to address spatial heterogeneity based on an ELM in this article. GWELM is essentially a locally varying ELM in which the parameters are regarded as functions of spatial locations, and geographically weighted least squares is applied to estimate the parameters in a local model. The proposed method is used to analyze two groups of different data sets, and the results demonstrate that the GWELM method is superior to the comparative method, which is also developed to address spatial heterogeneity.