Some remarks about the degree-one deformation of the Earth

The degree-one deformation of the Earth (and the induced discrepancy between the figure centre and the mass centre of the Earth) is computed using a theoretical approach (Love numbers formalism) at short timescales (where the Earth has an elastic behaviour) as well as at long timescales (where the Earth has a viscoelastic or quasi-fluid behaviour). For a Maxwell model of rheology, the degree-one relaxation modes associated with the viscoelastic Love numbers have been investigated: the M_o mode does not exist and there is only one transition mode (instead of two) generated by a viscosity discontinuity.
The translations at each interface of the incompressible layers of the earth model [surface, 670 km depth discontinuity, core-mantle boundary (CMB) and inner-core boundary (ICB)] are computed. They are elastic with an order of magnitude of about 1 mm when the excitation source is the atmospheric continental loading or a magnetic pressure acting at the CMB. They are viscoelastic when the earth is submitted to Pleistocene deglaciation, with an order of magnitude of about 1 m. In a quasi-fluid approximation (Newtonian fluid) because of the mantle density heterogeneity their order of magnitude is about 100 m (except for the ICB, which is in quasi-hydrostatic equilibrium at this timescale).     

A probabilistic relaxation approach for matching road networks

Geospatial data matching is an important prerequisite for data integration, change detection and data updating. At present, crowdsourcing geospatial data are attracting considerable attention with its significant potential for timely and cost-effective updating of geospatial data and Geographical Information Science (GIS) applications. To integrate the available and up-to-date information of multi-source geospatial data, this article proposes a heuristic probabilistic relaxation road network matching method. The proposed method starts with an initial probabilistic matrix according to the dissimilarities in the shapes and then integrates the relative compatibility coefficient of neighbouring candidate pairs to iteratively update the initial probabilistic matrix until the probabilistic matrix is globally consistent. Finally, the initial 1:1 matching pairs are selected on the basis of probabilities that are calculated and refined on the basis of the structural similarity of the selected matching pairs. A process of matching is then implemented to find M:N matching pairs. Matching between OpenStreetMap network data and professional road network data shows that our method is independent of matching direction, successfully matches 1:0 (Null), 1:1 and M:N pairs, and achieves a robust matching precision of above 95%.     

Analytical approach for the toroidal relaxation of viscoelastic earth

This paper is concerned with post-seismic toroidal deformation in a spherically symmetric, non-rotating, linear-viscoelastic, isotropic Maxwell earth model. Analytical expressions for characteristic relaxation times and relaxation strengths are found for viscoelastic toroidal deformation, associated with surface tangential stress, when there are two to five layers between the core–mantle boundary and Earth's surface. The multilayered models can include lithosphere, asthenosphere, upper and lower mantles and even low-viscosity ductile layer in the lithosphere. The analytical approach is self-consistent in that the Heaviside isostatic solution agrees with fluid limit. The analytical solution can be used for high-precision simulation of the toroidal relaxation in five-layer earths and the results can also be considered as a benchmark for numerical methods. Analytical solution gives only stable decaying modes—unstable mode, conjugate complex mode and modes of relevant poles with orders larger than 1, are all excluded, and the total number of modes is found to be just the number of viscoelastic layers between the core–mantle boundary and Earth's surface—however, any elastic layer between two viscoelastic layers is also counted. This confirms previous finding where numerical method (i.e. propagator matrix method) is used. We have studied the relaxation times of a lot of models and found the propagator matrix method to agree very well with those from analytical results. In addition, the asthenosphere and lithospheric ductile layer are found to have large effects on the amplitude of post-seismic deformation. This also confirms the findings of previous works.     

新近系红层软岩流变特性试验研究

流变是控制岩体稳定的主要因素之一。流变试验结果显示,新近系红层软岩蠕变和松弛曲线具有明显的三阶段变化特征。对比研究新近系粉砂质泥岩和泥质粉砂岩的流变结果,得出粉砂质泥岩较泥质粉砂岩强度低,蠕变量大,达到稳定需要的时间长。经过模型辨识,认为红层软岩流变符合伯格斯模型（Burgers model）。利用改进后的麦夸托（Marquardt）算法求取了红层软岩的流变参数。结果显示,反映岩石流变特性的两个主要指标弹性模量和黏滞系数远低于硬岩的同类指标,充分说明新近系红层软岩具有显著的流变性。获取的流变参数可用于伯格斯模型计算。     

Integration of linear programming and GIS for land-use modelling

Abstract

Geographical Information Systems (GIS) are becoming basic tools for a wide variety of earth science and land-use applications. This article presents linear programming (LP) as a promising tool for spatial modelling within a GIS. Although LP is not properly a spatial technique, it may be used to optimize spatial distributions or to guide the integration of variables. An example of the use of LP in land-use planning is described, with minimizing rural unemployment as the main goal. Technical, financial and ecological constraints are established to show the influence of several limitations on achieving the optimal solution. LP makes it possible to achieve optimal land-use, where the objective is maximized and the constraints respected. LP can also be used to simulate different planning scenarios, by modifying both the objective function coefficients and the constraints. The integration of LP and GIS is presented in two phases: (i) acquisition of attribute data for the LP model, and (ii) modelling and mapping the results.     

Fractal structure of the time distribution of microfracturing in rocks

Using acoustic emission data obtained from laboratory double torsion tests, we have analysed the fractal nature of a series of 29 granite microfracturing processes in time. The data represent a wide variety of timescales, stress environments (increasing load with a constant displacement rate, relaxation, creep), soaking conditions [air, water, dodecyl trimethyl ammonium bromide (DTAB), polyethelene oxide (PEO) ], and material anisotropy. We find that the time distribution of rock microfracturing displays fractal and multifractal properties. In some cases, it has a single fractal or a multifractal structure. In other cases, it changes from a single fractal structure into a multifractal structure as the system evolves dynamically. We suggest that the heterogeneity of the rock, the distribution of joints or weak planes, the stress level, and the nature of the microfracturing mechanism lead to these multifractal properties. Whatever the fractal structure of the system, a lower fractal dimension is generally produced at near-failure of the rock due to an increased clustering. This result concerning the fractal-dimension decrease is consistent with the conclusion drawn from the spatial distribution of rock microfracturing. Therefore, from the vantage point of observation of the time distribution of rock microfracturing, the decrease of the fractal dimension has a potential use as a rock failure predictor.