Quasi-static deformation of a viscoelastic half-space by a displacement dislocation

The correspondence principle is used to get the Laplace transformed solution of the problem of the quasi-static deformation of a viscoelastic half-space by a shear displacement dislocation from the corresponding static elastic results. The transformed solution is inverted for the Voigt and the Maxwell viscoelastic models. It is shown that, for a vertical dip-slip fault, the surface displacements for the viscoelastic case are identical with the elastic displacements. In the case of a vertical strike-slip fault, detailed numerical results are obtained for both a point source and a finite rectangular source. It is found that the results for the viscoelastic models differ significantly from the corresponding elastic results.     

A note on 2-D lithospheric deformation due to a blind strike-slip fault

Analytical solution for the problem of a surface-breaking long strike-slip fault in an elastic layer overlying an elastic half-space is well known. The purpose of this note is to obtain the corresponding solution for a blind fault. Since the solution is valid for arbitrary values of the fault-depth and the dip angle, the effects of these two important fault parameters can be studied numerically. The variation of the parallel displacement and shear stress with the distance from the fault is studied numerically for different values of the fault-depth and dip angle.     

Static deformation of two welded half-spaces due to dip-slip faulting

Closed-form expressions for the displacements and stresses at any point of either of two elastic half-spaces in welded contact caused by a dip-slip line source obtained earlier are integrated analytically to derive the elastic residual field due to a long dip-slip fault of finite width. The results are valid for an arbitrary dip of the fault. The variation of the displacement field with the distance from the fault as well as with the distance from the interface is studied numerically. It is found that the displacement field is heavily dependent on the dip angle. Contour maps showing the residual elastic field in the two half-spaces caused by a vertical dip-slip fault located in one of the half-spaces are also obtained.     

Saturation states of carbonate minerals in a freshwater-seawater mixing zone of small tropical island’s aquifer

Groundwater is a crucial resource on the Manukan Island as it is the only source of freshwater available on the island. The aquifer has deteriorated to a high degree, during the last decade. Nine domestic wells were sam-pled from March 2006 to January 2007 to probe the hydrochemical components that influence the water quality. Geochemical data on dissolved major constituents in groundwater samples from the Manukan Island revealed the main processes responsible for their geochemical evolution. The results using statistical analyses, graphical method and numerical model output (PHREEQC) showed that the groundwater was chemically highly enriched in Na and Cl, indicative of seawater intrusion into the aquifer as also supported from the Na-Cl signature on the Piper diagram. From the PHREEQC simulation model, calcite, dolomite and aragonite solubility showed positive values of the saturation indices (SI), indicating supersaturation which led to mineral precipitation condition of water by these min-erals.     

Deformation of two welded elastic half-spaces due to a long inclined tensile fault

The calculation of the deformation caused by shear and tensile faults is necessary for the investigation of seismic and volcanic sources. The solution of the two-dimensional problem of a long inclined shear fault in two welded half-spaces is well known. The purpose of this note is to present the corresponding solution for a tensile fault. Closed-form analytical expressions for the Airy stress function for a tensile line source in two welded half-spaces are first obtained. These expressions are then integrated analytically to derive the Airy stress function for a long tensile fault of arbitrary dip and finite width. Closed-form analytical expressions for the displacements and stresses follow immediately from the Airy stress function. These expressions are suitable for computing the displacement and stress fields around a long inclined tensile fault near an internal boundary.     

Rayleigh wave group velocity in a spherically symmetric gravitating earth model

Expressions for kinetic energy, elastic potential energy and gravitational potential energy for the spheroidal oscillations of a spherically symmetric, self-gravitating, elastic earth model have been obtained. Some inconsistencies in the expressions given by earlier authors have been pointed out. The principle of equipartition of energy and the Rayleigh principle have been used to derive a formula for Rayleigh wave group velocity in terms of energy integrals. This formula can be used to compute the group velocity without the numerical differentiation implied in its definition     

Displacements and stresses due to a single force in a half-space in welded contact with another half-space

Closed-form analytical expressions for the displacements and stresses induced by a single force of arbitrary orientation located in an elastic half-space in welded contact with another elastic half-space are obtained. These expressions are valid for arbitrary values of the Poisson's ratio and for arbitrary source and observer locations. The final results are given in a form that makes numerical computation straightforward and accurate.     

Stability Behavior and Thermodynamic States of Iron and Manganese in Sandy Soil Aquifer,Manukan Island,Malaysia

A total of 20 soil samples were collected from 10 boreholes constructed in the low lying area, which included ancillary samples taken from the high elevation area. Redox processes were investigated in the soil as well as groundwater in the shallow groundwater aquifer of Manukan Island, Sabah, Malaysia. Groundwater samples (n = 10) from each boreholes were also collected in the low lying area to understand the concentrations and behaviors of Fe and Mn in the dissolved state. This study strives to obtain a general understanding of the stability behaviors on Fe and Mn at the upper unsaturated and the lower-saturated soil horizons in the low lying area of Manukan Island as these elements usually play a major role in the redox chemistry of the shallow groundwater. Thermodynamic calculations using PHREEQC showed that the groundwater samples in the study area are oversaturated with respect to goethite, hematite, Fe(OH)₃ and undersaturated with respect to manganite and pyrochroite. Low concentrations of Fe and Mn in the groundwater might be probably due to the lack of minerals of iron and manganese oxides, which exist in the sandy aquifer. In fact, high organic matters that present in the unsaturated horizon are believed to be responsible for the high Mn content in the soil. It was observed that the soil samples collected from high elevation area (BK) comprises considerable amount of Fe in both unsaturated (6675.87 mg/kg) and saturated horizons (31440.49 mg/kg) compared to the low Fe content in the low lying area. Based on the stability diagram, the groundwater composition lies within the stability field for Mn²⁺ and Fe²⁺ under suboxic condition and very close to the FeS/Fe²⁺ stability boundary. This study also shows that both pH and Eh values comprise a strong negative value thus suggesting that the redox potential is inversely dependent on the changes of pH.     

Static deformation of an orthotropic multilayered elastic half-space by two-dimensional surface loads

The transfer matrix approach is used to solve the problem of static deformation of an orthotropic multilayered elastic half-space by two-dimensional surface loads. The general problem is decoupled into two independent problems. The antiplane strain problem and the plane strain problem are considered in detail. Integral expressions for displacements and stresses at any point of the medium due to a normal line load and a shear line load, acting parallel to a symmetry axis, are obtained. In the case of a uniform half-space, closed form analytic expressions for displacements and stresses are derived. The procedure developed is quite easy and convenient for numerical computations.