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.     

Interpolation using a generalized Green's function for a spherical surface spline in tension

A variety of methods exist for interpolating Cartesian or spherical surface data onto an equidistant lattice in a procedure known as gridding. Methods based on Green's functions are particularly simple to implement. In such methods, the Green's function for the gridding operator is determined and the resulting gridding solution is composed of the superposition of contributions from each data constraint, weighted by the Green's function evaluated for all output–input point separations. The Green's function method allows for considerable flexibility, such as complete freedom in specifying where the solution will be evaluated (it does not have to be on a lattice) and the ability to include both surface heights and surface gradients as data constraints. Green's function solutions for Cartesian data in 1-, 2- and 3-D spaces are well known, as is the dilogarithm solution for minimum curvature spline on a spherical surface. Here, the spherical surface case is extended to include tension and the new generalized Green's function is derived. It is shown that the new function reduces to the dilogarithm solution in the limit of zero tension. Properties of the new function are examined and the new gridding method is implemented in Matlab® and demonstrated on three geophysical data sets.     

Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling

The perfectly matched layer (PML) absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme, thus resulting in an irregular-grid PML method. We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations. The irregular-grid PML method is implemented under a discretization of triangular grid cells, which has the ability to absorb incident waves in arbitrary directions. This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries. As a result, the computational domain can be constructed with smaller nodes, for instance, to represent the 2-D half-space by a semi-circle rather than a rectangle. By using a smooth artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media. The numerical simulations of a VTI lamb's problem, wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method.     

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.     

2013年洱源M_S5.5地震序列M_L≥3.4地震的震源机制解研究

利用云南省地震台网的宽频带数据,采用CAP方法计算了2013年3月3日洱源MS5.5地震前后共10次ML≥3.4地震的震源机制解,分析了洱源MS5.5地震前后震源机制解的一致性变化特征,结合精定位结果、震后现场灾害评估报告及震区地质构造情况,判定维西—巍山断裂以西的苍山西麓炼铁盆地东缘主边界断裂带为洱源MS5.5地震的发震构造,震源机制解节面Ⅱ(走向160°、倾角48°、滑动解-99°)为其发震断层面。     

A new series solution method for two-dimensional elastic wave scattering along a canyon in half-space

This paper presents a semi-analytical method for studying the two-dimensional problem of elastic wave scattering by surface irregularities in a half-space. The new method makes use of the member of a c-completeness family of wave functions to construct the scattering fields, and then applies equal but opposite tractions to those of the foregoing constructed scattering fields on the horizontal surface of the half-space to produce additional scattering fields. These additional scattering fields are a series of Lamb's solutions. Thus the whole scattering field constructed in the series automatically satisfies the Navier equations, the condition of zero traction on the half-space surface, and the radiation boundary conditions at infinity. Using the traction-free conditions along the canyon surface, the coefficients of the series solutions are determined via a least-squares method. For incident P, SV, and Rayleigh waves, the numerical results are presented for the scattering displacements in the vicinity of a semi-circular canyon in the half-space.     

Computer thermodynamic modeling of the transport and deposition of Sb and Au during the formation of Au-Sb deposits

Using the Chiller computer program, we performed modeling of the mechanisms of the joint transport and deposition of Au and Sb from various ore-forming solutions during the formation of Au-Sb deposits. Three models are considered by the example of the Uderei Au-Sb deposit in the Yenisei Ridge: (1) simple cooling (cooling only), (2) iso-enthalpy boiling (P = f(T)), and (3) solution–rock interaction (rock titration model). The behavior of Sb(III) and Au(I) in the system Au–Sb–Fe–Cu–Pb–Zn–As–H₂O–Cl–H₂S–CO₂ under hydrothermal conditions was studied. It is shown that both weakly alkaline (near-neutral) and reduced acidic Fe_aq²⁺-enriched low-chloride high-CO₂ and high-chloride hydrothermal solutions play a crucial role in the formation of gold parageneses of Au-Sb ores.     

On the frontal condition for finite amplitude α2Ω-dynamo wave trains in stellar shells

Abstract

In a previous paper, Bassom et al. (Proc. R. Soc. Lond. A, 455, 1443–1481, 1999) (BKS) investigated finite amplitude αΩ-dynamo wave trains in a thin turbulent, differentially rotating convective stellar shell; nonlinearity arose from α-quenching. There asymptotic solutions were developed based upon the small aspect ratio ε of the shell. Specifically, as a consequence of a prescribed latitudinally dependent α-effect and zonal shear flow, the wave trains have smooth amplitude modulation but are terminated abruptly across a front at some high latitude θ_F. Generally, the linear WKB-solution ahead of the front is characterised by the vanishing of the complex group velocity at a nearby point θ_f; this is essentially the Dee–Langer criterion, which determines both the wave frequency and front location.

Recently, Griffiths et al. (Geophys. Astrophys. Fluid Dynam. 94, 85–133, 2001) (GBSK) obtained solutions to the α²Ω-extension of the model by application of the Dee—Langer criterion. Its justification depends on the linear solution in a narrow layer ahead of the front on the short O(θ_f—θ_F) length scale; here conventional WKB-theory, used to describe the solution elsewhere, is inadequate because of mode coalescence. This becomes a highly sensitive issue, when considering the transition from the linear solution, which occurs when the dynamo number D takes its critical value D _c corresponding to the onset of kinematic dynamo action, to the fully nonlinear solutions, for which the Dee—Langer criterion pertains.

In this paper we investigate the nature of the narrow layer for α²Ω-dynamos in the limit of relatively small but finite α-effect Reynolds numbers R _α, explicitly ε^½ ? R ² _α ? 1. Though there is a multiplicity of solutions, our results show that the space occupied by the corresponding wave train is generally maximised by a solution with θ_f—θ_F small; such solutions are preferred as evinced by numerical simulations. This feature justifies the application by GBSK of the Dee—Langer criterion for all D down to the minimum D _min that the condition admits. Significantly, the frontal solutions are subcritical in the sense that |D _min| ≤ |D _c|; equality occurs as the α-effect Reynolds number tends to zero. We demonstrate that the critical linear solution is not connected by any parameter track to the preferred nonlinear solution associated with D _min. By implication, a complicated bifurcation sequence is required to make the connection between the linear and nonlinear states. This feature is in stark contrast to the corresponding results for αΩ-dynamos obtained by BKS valid in the limit R _{2 α} ? ε^½, which, though exhibiting a weak subcriticality, showed that the connection follows a clearly identifiable nonbifurcating track.