Simple analytical Green's functions for ray perturbations in layered media

The total Green's function for two-point boundary-value problems can be related to the propagator for initial-value problems. A very simple expression for the Green's function is obtained when the unperturbed medium may be described by material with a constant gradient in quadratic slowness. The derivation requires a correct understanding of assumptions made in the propagator solution. Expressions are also obtained for Green's function in multilayered media.     

Use of Fuzzy Membership Input Layers to Combine Subjective Geological Knowledge and Empirical Data in a Neural Network Method for Mineral-Potential Mapping

Use of GIS layers, in which the cell values represent fuzzy membership variables, is an effective method of combining subjective geological knowledge with empirical data in a neural network approach to mineral-prospectivity mapping. In this study, multilayer perceptron (MLP), neural networks are used to combine up to 17 regional exploration variables to predict the potential for orogenic gold deposits in the form of prospectivity maps in the Archean Kalgoorlie Terrane of Western Australia. Two types of fuzzy membership layers are used. In the first type of layer, the statistical relationships between known gold deposits and variables in the GIS thematic layer are used to determine fuzzy membership values. For example, GIS layers depicting solid geology and rock-type combinations of categorical data at the nearest lithological boundary for each cell are converted to fuzzy membership layers representing favorable lithologies and favorable lithological boundaries, respectively. This type of fuzzy-membership input is a useful alternative to the 1-of-N coding used for categorical inputs, particularly if there are a large number of classes. Rheological contrast at lithological boundaries is modeled using a second type of fuzzy membership layer, in which the assignment of fuzzy membership value, although based on geological field data, is subjective. The methods used here could be applied to a large range of subjective data (e.g., favorability of tectonic environment, host stratigraphy, or reactivation along major faults) currently used in regional exploration programs, but which normally would not be included as inputs in an empirical neural network approach.     

Exploring space–time paths in physical and social closeness spaces: a space–time GIS approach

Exploring the evolution of people’s social interactions along with their changing physical locations can help to achieve a better understanding of the processes that generate the relationships between physical distance and social interactions, which can benefit broad fields of study related to social networks. However, few studies have examined the evolving relationships between physical movements and social closeness evolution. This is partially related to the shortage of longitudinal data in both physical locations and social interactions and the lack of an exploratory analysis environment capable of effectively investigating such a process over space and time. With the increasing availability of sociospatiotemporal data in recent years, it is now feasible to examine the relationships between physical separation and social interactions at the individual level in a space–time context. This research was intended to offer a spatiotemporal exploratory analysis approach to address this challenge. The first step was to propose the concept of a social closeness space–time path, which is an extension of the space–time path concept in time geography, to represent evolving human relationships in a social closeness space. A space–time geographical information system (GIS) prototype was then designed to support the representation and analysis of space–time paths in both physical and social closeness spaces. Finally, the effectiveness of the proposed concept and design in gaining insight into the impact of physical migration on online social closeness was demonstrated through an empirical study. The contributions of this study include an extension of the time–geographic framework from physical space to social closeness space, the development of a multirepresentation approach in a GIS to integrate an individual’s space–time paths in both physical and social closeness spaces, and an exploratory analysis of the evolving relationships between physical separation and social closeness over time.     

Crack nucleation in saturated porous media

Crack nucleation has been the subject of important contributions in the last two last decades. However, it seems that few attention has been granted to the case of saturated porous media. This is the question addressed in the present paper which is devoted to nucleation in traction mode. From a physical point of view, nucleation is a sudden phenomenon, so that the material response is both adiabatic and undrained. In the spirit of the variational approach, the nucleated crack is viewed as the final state of a region of space in which the material undergoes a full damage process. In traction mode, the opening of a saturated crack in undrained condition induces a drop of fluid pressure. In case of low fluid compressibility, the presence of the fluid delays the brittle failure usually associated with nucleation, as long as the fluid pressure remains above the saturation vapor pressure. Nucleation is therefore possible only if a partial vaporization of the fluid takes place.     

Analytical modeling of a deep tunnel inside a poro-viscoplastic rock mass accounting for different stages of its life cycle

An analytical approach of the viscoplastic behavior of a porous saturated rock mass surrounding a deep tunnel in different stages of a simplified life cycle is presented. The viscoplasticity is modeled by means of a simple (linear) Norton-Hoff’s law. Some numerical examples are performed to examine the consistency and relevance of the solutions. Parametric studies illustrate the influence of key parameters such as rock mass viscosity, Poisson’s ratio, rock mass permeability, lining emplacement, etc. This analytical approach constitutes a useful reference to facilitate more complex numerical simulation and making it possible to obtain practical estimations of the poromechanical behavior of underground structures.