Finite cube elements method for calculating gravity anomaly and structural index of solid and fractal bodies with defined boundaries

In this paper, we present the finite cube elements method (FCEM); a novel numerical tool for calculating the gravity anomaly g and structural index SI of solid models with defined boundaries and variable density distributions, tilted or in normal position (e.g. blocks, faulted blocks, cylinders, spheres, hemispheres, triaxial ellipsoids). Extending the calculation to fractal objects, such as Menger sponges of different orders and bodies defined by polyhedrons, demonstrates the robustness of FCEM. In addition, approximating the cube element by a sphere of equal volume makes the calculation of gravitation and related derivatives much simpler. In gravity modelling of a sphere, cubes with edges of 100 m and 200 m achieve a good compromise between running time and overall error.
Displaying the distribution of SI of the studied models on contour maps and profiles will have a strong impact on the forward and inverse modelling of potential field data, especially for Euler deconvolution.
For Menger sponges, plots of gravity elements g and its derivatives show similar patterns independent of fractal order. Moreover, both the pattern and magnitude of SI are independent of fractal order, allowing the use of SI as a new invariant measure for fractal objects. However, SI pattern and magnitude strongly depend on the depth to the buried bodies as do other elements
In this study, we also present a new type of plot; the structural index against distance variation diagrams from which we extract the three critical SI ( CSI ) values, one per axis. The inversion of gravity anomaly data at CSI values gives the optimal mean location of the buried body.     

The dependency of sand transport rate by wind on the atmospheric stability: A numerical simulation

A theoretical model of the process for wind–sand flow is developed through consideration of the coupling between wind flow and the motion of sand particles under different atmospheric stability conditions. Using this model, we studied the effects of atmospheric stability on the sand transport rate, the number of sand particles per unit area and time, and the duration before a steady state is achieved in detail. The results show that atmospheric stability has a strong effect on the movement of the wind–sand flow, and produces results with different characteristics from those previously reported in the literature which apply only to conditions of neutral stability. Under unstable conditions, the wind–sand flow reached equilibrium more quickly, with a higher total sand flux and sand flux at all heights than under neutral or stable conditions.     

Seismic radiation from dynamic coalescence, and the reconstruction of dynamic source parameters on a planar fault

The dynamic coalescence of two mode II cracks on a planar fault is simulated here using the elastodynamic boundary integral equation method. We focus on the complexity of the resultant slip rate and seismic radiation in the crack coalescence model (CCM) and on the reconstruction of a single crack model (SCM) that can reproduce the CCM waveforms from heterogeneous source parameters rather than coalescence. Simulation results reveal that localized higher slip rates are generated by coalescence as a result of stress interaction between the approaching crack tips. The synthesized seismic radiation exhibits a distinct coalescence phase that has striking similarities to stopping phases in the radiation and propagation properties. The corresponding SCM yields a singular increase in the stress drop distribution, which is accompanied by a sudden decrease in it across the point of coalescence in the CCM. This implies that the generation of high-frequency radiation is more efficient from coalescence than from stopping, although both phenomena exhibit the same strong  ω⁻²  -type displacement spectra.     

Quasi-static analysis of strike fault growth in layered media

We study the effects of structural inhomogeneity on the quasi-static growth of strike-slip faults. A layered medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space with different elastic property. Mode III crack is employed as a mathematical model of strike-slip fault, which is nucleated in the lower half-space and then propagates towards the interface. We adopt FEM-β, newly proposed analysis method for failure, to simulate the quasi-statistic crack growth governed by the stress distribution in layered media. Our results show that along planar traces across interfaces a compliant upper layer has significant effects on promoting/suppressing crack growth before/after its extension into the layer and vice versa for a rigid one. This proposes a possibility that surface breaks due to strike-slip faulting could be arrested by deposit layers at the topmost part of the Earth's crust.     

Long-term slow slip events are not necessarily caused by high pore fluid pressure at the plate interface: an implication from two-dimensional model calculations

A recent tomographic study proposed that high-pore pressure in the deeper portion of the locked zone of a subduction thrust resulting from metamorphic dehydration reactions may cause long-term slow slip events. The study used the concept of 'critical fault stiffness', which derives from laboratory-derived rate- and state-dependent friction laws. To test the proposition, we execute 2-D model calculations using laboratory-derived rate- and state-dependent friction laws. Our numerical result is against the proposition, but it can also be explained by the concept of the critical fault stiffness. We agree that metamorphic dehydration reactions definitely produce a bulk property of high fluid saturation, but we caution that they do not necessarily lead to high-pore pressure in the fault zone.     

Numerical aspects of a spline-based multiresolution recovery of the harmonic mass density out of gravity functionals

We show the numerical applicability of a multiresolution method based on harmonic splines on the 3-D ball which allows the regularized recovery of the harmonic part of the Earth's mass density distribution out of different types of gravity data, for example, different radial derivatives of the potential, at various positions which need not be located on a common sphere. This approximated harmonic density can be combined with its orthogonal anharmonic complement, for example, determined out of the splitting function of free oscillations, to an approximation of the whole mass density function. The applicability of the presented tool is demonstrated by several test calculations based on simulated gravity values derived from EGM96. The method yields a multiresolution in the sense that the localization of the constructed spline basis functions can be increased which yields in combination with more data a higher resolution of the resulting spline. Moreover, we show that a locally improved data situation allows a highly resolved recovery in this particular area in combination with a coarse approximation elsewhere which is an essential advantage of this method, for example, compared to polynomial approximation.     

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method.
  Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately.
  Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.     

Two-dimensional finite-difference model of seafloor compliance

Seafloor compliance is the measure of seafloor deformation under a pressure signal. Our new 2-D finite-difference compliance modelling algorithm presents several advantages over the existing compliance models, including the ability to handle any gridded subsurface structure with no limitations on the gradients of the material properties, as well as significantly improved performance. Applying this method to some of the problems inaccessible to previously existing methods, demonstrates that lateral variations in subsurface structure must be accounted for to adequately interpret compliance data. In areas with significant lateral variations, the utilization of 1-D modelling and inversion is likely to result in high interpretation errors, even when additional subsurface structure information is available. We find that flattened pure melt bodies have a significantly higher compliance than cylindrical melt bodies with the same cross-sectional area. The compliance created by such bodies often has side peaks over their edges, which are as strong as or stronger than the central peak, requiring a series of measurements to best constrain their size and shear velocity. Finally, we find that the compliance data are far and away most sensitive to the broad, thick, lower-crustal partial melt zone. Our simple data fitting model for the compliance measurements on the East Pacific Rise at 9°48'N required shear velocities as low as 700 m s⁻¹ in the centre of this zone, far below the values previously estimated using 1-D model based inversions, suggesting higher melt percentages than those previously estimated, while small melt bodies in the upper part of the crust were found to have little or no effect on the measured compliance.     

大河三角洲河口海岸演化机理模型研究:(I)模式理论与进展

从水沙通量变化对大河三角洲河口海岸建造及地貌演化的影响机理角度,通过研究目前国际上普遍采用的统计模型、几何模型、沉积动力学模型,以及数值模拟模型四种方法在建立大河三角洲河口海岸演化机理模型研究中的各自特点和不足,提出了建立宏观尺度机理模型的初步设想,并对运用Lagrange余流建立海岸演化机理模型所涉及的余流场的尺度转换、总余流场的建立和表达、用长期余流场构建泥沙起动、输运和沉积条件模式以及一线模型与三维动力模式耦合等关键性问题,提出了初步解决方案     

Numerical inversion of deformation caused by pressure sources: application to Mount Etna (Italy)

The interpretation of geodetic data in volcanic areas is usually based on analytical deformation models. Although numerical finite element (FE) modelling allows realistic features such as topography and crustal heterogeneities to be included, the technique is not computationally convenient for solving inverse problems using classical methods. In this paper, we develop a general tool to perform inversions of geodetic data by means of 3-D FE models. The forward model is a library of numerical displacement solutions, where each entry of the library is the surface displacement due to a single stress component applied to an element of the grid. The final solution is a weighted combination of the six stress components applied to a single element-source. The pre-computed forward models are implemented in a global search algorithm, followed by an appraisal of the sampled solutions. After providing extended testing, we apply the method to model the 1993–1997 inflation phase at Mt Etna, documented by GPS and EDM measurements. We consider four different forward libraries, computed in models characterized by homogeneous/heterogeneous medium and flat/topographic free surface. Our results suggest that the elastic heterogeneities of the medium can significantly alter the position of the inferred source, while the topography has minor effect.