The effect of water on stress relaxation of faulted and unfaulted sandstone

A series of stress relaxation experiments have been carried out on faulted and intact Tennessee sandstone to explore the influence of pore water on strength at different strain rates. Temperatures employed were 20, 300 and 400°C, effective confining pressure was 1.5 kb and strain rates as low as 10^–10 sec^–1 were achieved. Most samples were prefaulted at 2.5 kb confining pressure and room temperature. This is thought to have secured a reproducible initial microstructure.The strength of the dry rock was almost totally insensitive to strain rate in the range 10^–4 to 10^–10 sec^–1. In contrast, the strength of the wet rock decreased rapidly with strain rate at rates less than 10^–6 sec^–1. Brittle fracture of the quartz grains which constitute this rock is the most characteristic mode of failure under the test conditions used.The experimental data are discussed in terms of the possible deformation rate controlling processes, and it is suggested that in the wet experiments at intermediate to high strain rates (10^–7 to 10^–4 sec^–1) the observed deformation rate is controlled by the kinetics of water assisted stress corrosion, whilst deformation at low strain rates (ca. 10^–9 sec^–1) is controlled by a pressure solution process.The results have implications for the rheology of fault rocks at depths of perhaps 10 to 15 km in sialic crust.     

A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, _N=αcotβ (in which β is the beach slope, α is the amplitude parameter and is the shallow water parameter) and are limited to tan⁻¹(α)βπ/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as and α increase, and reaches 7% of the linear solution.     

Zero-frequency tidal distrotion due to the orbital elements of tide-forming bodies

Summary It has been proved that orbital elements of perturbing bodies should be taken into account when 10^–10 accuracy is required for zero-frequency tidal distortion in the second zonal Stokes parameter of the geopotential. A solution at the 10^–15 level of magnitude has been presented. The zero-frequency tidal distortion in the fourth zonal Stokes parameter has been derived as 1·3×10^–10 if the secular Love number is unity. It should be reflected in the geopotential models respecting the 10^–10 level of magnitude.     

Explicit solution of a free boundary problem for a nonlinear absorption model of mixed saturated-unsaturated flow

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem.A closed-form analytic solution is presented for a nonlinear diffusion model under conditions of ponding at the surface. The soil water diffusivity is restricted to the special functional form D(θ) = a/(b − θ)², where θ is the water content field to be determined and a, b are positive constants. The explicit solution depends on a parameter C (determined by the data of the problem), according to two cases: 1 < C < C₁ or C ≥ C₁, where C₁ is a constant which is obtained as the unique solution of an equation. This result complements the study given in P. Broadbridge, Water Resources Research, 1990, 26, 2435–2443, in order to established when the explicit solution is available. The behavior of the bifurcation parameter C₁ as a function of the driving potential is studied with the corresponding limits for small and large values. Moreover, the sorptivity is proven to be continuously differentiable function of the variable C.     

Differences between Mean Sea Levels for the Pacific,Atlantic and Indian Oceans From Topex/Poseidon Altimetry

Geopotential values W of the mean equipotential surfaces representing the mean ocean topography were computed on the basis of four years (1993 - 1996) TOPEX/POSEIDON altimeter data: W = 62 636 854.10m ² s ^–2 for the Pacific (P), W = 62 636 858.20m ² s ^–2 for the Atlantic (A), W = 62 636 856.28m ²s^–2 for the Indian (I) Oceans. The corresponding mean separations between the ocean levels were obtained as follows: A – P = – 42 cm, I– P = – 22 cm, I – A = 20 cm, the rms errors came out at about 0.3 cm. No sea surface topography model was used in the solution.     

Azimuthal resistivity soundings over a steeply dipping anisotropic formation: A case history in central Tunisia

Azimuthal Resistivity Soundings (ARS), using the so-called “Arrow-type array” as proposed by Bolshakov et al. were carried out in Central Tunisia, together with azimuthal resistivity tomography, because of the known anisotropic behaviour of the nearly vertical formations.First, the developments designed by Bolshakov et al. are reviewed: they deal with the separation between the effects of anisotropy and of heterogeneities, the design of the Arrow-type array and the introduction of the azimuthal spectral analysis.Second, the main methodological results obtained near Gouazine Lake are presented: (1) the clear effect of a quasi-vertical contact and (2) the characterisation of the anisotropic substratum below a thin superficial layer in one site close to the axis of the valley: the strike direction (α = 50°N), and a rather high anisotropy coefficient (λ ≈ 4) are determined.And lastly two directions for further developments are suggested.     

Scaling model experiments on propagation of electromagnetic waves using salt solution to simulate the Earth's crust: Loma Prieta and Kobe earthquakes

Propagation of electromagnetic (EM) waves from an earthquake focus in the conductive Earth has been investigated using 1/1,000,000 scaling models taking earth-ionosphere and ocean-Moho plane parallel-plate waveguides into account. Microwaves at a frequency, ω_m, a million times higher than that of seismic EM signal (SEMS), ω, were generated at the model focus. They are propagated in a salt solution modeling the earth's crust and reflected by ocean, fault planes, ionosphere and Moho plane all made by aluminum. Distribution of EM power was mapped by scanning a detector antenna over the model Earth's surface. The skin depth, δ, calculated by the exact skin depth equation, 1/δ=ω(μ/2)^1/2 [(1+(1/ωρ)²)^1/2 −1]^1/2 where dielectric constant, and permeability, μ are the same but resistivity, ρ, 10⁻⁶ times smaller than that of Earth, gave 10⁻⁶ times small skin depth validating the model scaling index. Images for evanescent and wave-ripple standing waves disturbed by normal, strike-slip and dip-slip conductive fault planes have been obtained using an aluminum plate. The co-circular contour map above the epicenter due to evanescence was pushed to the north east direction from the epicenter by the presence of ocean for the Loma Prieta earthquake, while to north direction for the Kobe earthquake. The intensity of EM ULF emissions for the Loma Prieta earthquake is discussed quantitatively.     

Downslope flow models of a Bingham liquid: Implications for lava flows

It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses (σ 10³dyne/cm²), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σ = 10⁴ dyne/cm², if the flow rate is greater than 10⁵ g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.     

Crustal strain observation for nine years with a laser strainmeter in Kobe, Japan

We carried out precise crustal strain observation using a laser strainmeter system at the Rokko-Takao station in Kobe, Japan from 1989 to 1997. The long-term strain record is characterized by remarkable annual changes of the order of 2–3×10⁻⁶ and linear strain accumulation of −4.4×10⁻⁷/year (in contraction). The annual strain changes are inversely proportional to temperature changes that precede the strain changes by about 1 month. The apparent annual strain changes were mainly caused by refractive-index changes in the light path due to the ambient temperature changes. After eliminating the annual temperature effect, linear strain accumulation is corrected to be −6.3−6.7×10⁻⁷/year. Residual strains show the oscillating behavior, in which the oscillating cycle seems to become shorter and shorter as time goes by. During the period, a destructive earthquake of M=7.2 occurred near the Kobe City on 17 January 1995. We investigated the oscillating behavior in secular variations of ground-strains by introducing the deterministic approach of earthquake prediction to search for the “critical point” of the occurrence of an earthquake in the extended power law equation. However, we could not obtain a unique solution to determine eight unknown parameters including the “critical point”. This may be mainly due to lack of data for 4 months from August to November in 1994 by the failure of the laser source before the occurrence of earthquake on 17 January 1995. After removing environmental effects and tidal components, we carefully re-examined strain changes in 7 days and 1 day before the occurrence of the earthquake, but we could not detect anomalous strain changes exceeding 1×10⁻⁸ before the earthquake.     

An Asymptotic Analysis of a Simple Model for the Structure and Dynamics of the Ramdas Layer

This paper presents a complete asymptotic analysis of a simple model for the evolution of the nocturnal temperature distribution on bare soil in calm clear conditions. The model is based on a simplified flux emissivity scheme that provides a nondiffusive local approximation for estimating longwave radiative cooling near ground. An examination of the various parameters involved shows that the ratio of the characteristic radiative to the diffusive timescale in the problem is of order 10⁻³, and can therefore be treated as a small parameter (μ). Certain other plausible approximations and linearization lead to a new equation whose asymptotic solution as μ → 0 can be written in closed form. Four regimes, consisting of a transient at nominal sunset, a radiative-diffusive boundary (‘Ramdas’) layer on ground, a boundary layer transient and a radiative outer solution, are identified. The asymptotic solution reproduces all the qualitative features of more exact numerical simulations, including the occurrence of a lifted temperature minimum and its evolution during night, ranging from continuing growth to relatively sudden collapse of the Ramdas layer.     

Cosmogenic chlorine-36 production rates in terrestrial rocks

Chlorine-36 is produced in rocks exposed to cosmic rays at the earth surface through thermal neutron activation of ³⁵Cl, spallation of ³⁹K and ⁴⁰Ca, and slow negative moun capture by ⁴⁰Ca. We have measured the ³⁶Cl content of ¹⁴C-dated glacial boulders from the White Mountains in eastern California and in a ¹⁴C-dated basalt flow from Utah. Effective, time-intergrated production parameters were calculated by simultaneous solution of the ³⁶Cl production equations. The production rates due to spallation are 4160 ± 310 and 3050 ± 210 atoms ³⁶Cl yr⁻¹ mol⁻¹³⁹K and ⁴⁰Ca, respectively. The thermal neutron capture rate was calculated to be (3.07 ± 0.24) × 10⁵ neutrons (kg of rock)⁻¹ yr⁻¹. The reported values are normalized to sea level and high geomagnetic latitudes. Production of ³⁶Cl at different altitudes and latitudes can be estimated by appropriate scaling of the sea level rates. Chlorine-36 dating was performed on carbonate ejecta from Meteor Crater, Arizona, and late Pleistocene morainal boulders from the Sierra Nevada, California. Calculated ³⁶Cl ages are in good agreement with previously reported ages obtained using independent methods.     

Nickel isotope heterogeneity in the early Solar System

We report small but significant variations in the ⁵⁸Ni/⁶¹Ni-normalised ⁶⁰Ni/⁶¹Ni and ⁶²Ni/⁶¹Ni ratios (expressed as ε⁶⁰Ni and ε⁶²Ni) of bulk iron and chondritic meteorites. Carbonaceous chondrites have variable, positive ε⁶²Ni (0.05 to 0.25), whereas ordinary chondrites have negative ε⁶²Ni (− 0.04 to − 0.09). The Ni isotope compositions of iron meteorites overlap with those of chondrites, and define an array with negative slope in the ε⁶⁰Ni versus ε⁶²Ni diagram. The Ni isotope compositions of the volatile-depleted Group IVB irons are similar to those of the refractory CO, CV carbonaceous chondrites, whereas the other common magmatic iron groups have Ni isotope compositions similar to ordinary chondrites. Only enstatite chondrites have identical Ni isotope compositions to Earth and so appear to represent the most appropriate terrestrial building material. Differences in ε⁶²Ni reflect distinct nucleosynthetic components in precursor solids that have been variably mixed, but some of the ε⁶⁰Ni variability could reflect a radiogenic component from the decay of ⁶⁰Fe. Comparison of the ε⁶⁰Ni of iron and chondritic meteorites with the same ε⁶²Ni allows us to place upper limits on the ⁶⁰Fe/⁵⁶Fe of planetesimals during core segregation. We estimate that carbonaceous chondrites had initial ⁶⁰Fe/⁵⁶Fe < 1 × 10^− 7. Our data place less good constraints on initial ⁶⁰Fe/⁵⁶Fe ratios of ordinary chondrites but our results are not incompatible with values as high as 3 × 10^− 7 as determined by in-situ measurements. We suggest that the Ni isotope variations and apparently heterogeneous initial ⁶⁰Fe/⁵⁶Fe results from physical sorting within the protosolar nebula of different phases (silicate, metal and sulphide) that carry different isotopic signatures.     

Hydrothermal vent waters at 13°N on the East Pacific Rise: isotopic composition and gas concentration

Gas concentrations and isotopic compositions of water have been measured in hydrothermal waters from 13°N on the East Pacific Rise. In the most Mg-depleted samples ( 5 × 10⁻³ moles/kg) the gas concentrations are: 3–4.5 × 10⁻⁵ cm³ STP/kg helium, 0.62–1.24 cm³ STP/kg CH₄, 10.80–16.71 × 10⁻³ moles/kg CO₂. The samples contain large quantities (95–126 cm³/kg) of H₂ and some carbon monoxide (0.26–0.36 cm³/kg) which result from reaction with the titanium sampling bottles. δ¹³C in methane and CO₂ (−16.6 to −19.5 and −4.1 to −5.5 respectively) indicate temperatures between 475 and 550°C, whereas δ¹³C_CO is compatible with formation by reduction of CO₂ on Ti at 350°C close to the sampling temperature.³He/⁴He are very homogeneous at (7.5 ± 0.1)R_A(³He/⁴He = 1.0 × 10⁻⁵) and very similar to already published data as well as CH₄/³He ratios between 1.4 and 2.1 × 10⁶.¹⁸O and D in water show enrichments from 0.39 to 0.69‰ and from 0.62 to 1.49‰ respectively. These values correspond to W/R ratios of 0.4–7. The distinct¹⁸O enrichments indicate that the isotopic composition of the oceans is not completely buffered by the hydrothermal circulations. The³He-enthalpy relationship is discussed in terms of both hydrothermal heat flux and³He mantle flux.     

Mixing at the interface between fresh and salt waters in 3D steady flow with application to a pumping well in a coastal aquifer

We consider 3D steady flow of fresh water over a salt water body in a confined aquifer of constant thickness D, with application to a pumping well in a coastal aquifer. With neglect of mixing, a sharp interface separates the two fluid bodies and an existing analytical solution, based on the Dupuit assumption, is adopted. The aim is to solve for the mixing between the fresh and salt waters for α_T/D  1 (α_T transverse dispersivity), as field studies indicate that α_T = O(10⁻³ − 10⁻² m). The mixing zone around the interface is narrow and solutions by existing codes experience numerical difficulties. The problem is solved by the boundary layer (BL) approximation, extending a method, applied previously to two-dimensional flows. The BL equations of variable-density flow are solved by using the Von Karman integral method, to determine the BL thickness and the rate of entrainment of salt water along the interface. Application to the pumping well problem yields the salinity of the pumped water, as function of the parameters of the problem (well discharge, seaward discharge, well distance from the coast and density difference).     

The 1975 sub-terminal lavas, mount etna: a case history of the formation of a compound lava field

The 1975 sub-terminal activity was characterised by low effusion rates (0.3–0.5 m³ s⁻¹) and the formation of a compound lava field composed of many thousands of flow units. Several boccas were active simultaneously and effusion rates from individual boccas varied from about 10⁻⁴ to 0.25 m³s⁻¹. The morphology of lava flows was determined by effusion rate (E): aa flows with well-developed channels and levees formed when E > 2 × 10⁻³ m³ s⁻¹, small pahoehoe flows formed when 2 × 10⁻³ m³ s⁻¹ >E > 5 > 10⁻⁴ m³ s⁻¹ and pahoehoe toes formed when E < 5 × 10⁻⁴ m³ s⁻¹. There was very little variation with time in the effusion temperature, composition or phenocryst content of the lava.New boccas were commonly formed at the fronts of mature lava flows which had either ceased to flow or were moving slowly. These secondary boccas developed when fluid lava in the interior of mature aa flows either found a weakness in the flow front or was exposed by avalanching of the moving flow front. The resulting release of fluid lava was accompanied by either partial drainage of the mature flow or by the formation of a lava tube in the parent flow. The temperature of the lava forming the new bocca decreased with increasing distance from the source bocca (0.035°C m⁻¹). It is demonstrated from the rate of temperature decrease and from theoretical considerations that many of the Etna lavas still contained a substantial proportion of uncooled material in their interior as they came to rest. The formation of secondary boccas is postulated to be one reason why direct measurements of effusion rates tend, in general, to overestimate the total effusion rates of sub-terminal Etna lava fields.     

Strontium stable isotopes fractionate in the soil environments?

This study shows that the stable isotopic composition of strontium (the ⁸⁸Sr/⁸⁶Sr ratio expressed as δ^88/86Sr value relative to the NBS987 standard) varies significantly in sedimentary terrestrial environments. The abundances of ⁸⁶Sr, ⁸⁸Sr isotopes were analyzed by MC-ICP-MS “Nu Plasma”. All studied rocks and waters show δ^88/86Sr values that are distinctly different from the measured NBS987 standard (yielding 0.01 ± 0.05‰, all errors are reported as 2σ). Modern corals from the northern Gulf of Aqaba, Red Sea yielded significantly different value than seawater (δ^88/86Sr = 0.22 ± 0.07‰, compared to 0.35 ± 0.06‰, respectively), in an excellent correlation with the δ^88/86Sr analyses reported by Fietzke and Eisenhauer [Fietzke, J., Eisenhauer, A., 2006. Determination of temperature-dependent stable strontium isotopes (⁸⁸Sr/⁸⁶Sr) fractionation via bracketing standard MC-ICP-MS. Geochm. Geophys. Geosyst. 7 (no. 8)] on other coral samples. All carbonate samples that originated in the marine environment: corals (porites and acropora from the northern Gulf of Aqaba); Cretaceous limestone and runoff from the Judea Mountains as well as lacustrine evaporitic aragonite (Dead Sea); and Red Sea and Atlantic seawater yield an average δ^88/86Sr value of 0.26 ± 0.1‰. On the other hand, secondary materials (products of chemical weathering) from the terrestrial environment of the Judea Mountain such as terra rossa soil and speleothem calcite (that derives its Sr from the above-lying soil) yielded significantly lower δ^88/86Sr value of − 0.17 ± 0.06‰. This indicates that strontium isotopes fractionate in the soil environment calling for a possible development of strontium isotopes as a tracer for processes of chemical weathering and pedogenesis.     

Transport ofBe andBe in the ocean

Beryllium isotopes (¹⁰Be and⁹Be) have been measured in suspended particles of < 1 mm size collected by mid-water sediment traps deployed in the eastern Pacific at MANOP sites H (6°32′N, 92°50′W, water depth 3600 m) and M (8°50′N, 104°00′W, 3100 m). For comparison, surface sediments from box cores taken from the two sites were also studied. The concentrations of¹⁰Be and⁹Be in sediment-trap particles are about an order of magnitude smaller than those in the bottom sediments which contain about 8 × 10⁹ and 6 × 10¹⁶ atoms g⁻¹ of¹⁰Be and⁹Be, respectively. The sediment trap samples collected from 50 m off the bottom showed significant (26–63%) contributions from resuspended bottom sediments. The¹⁰Be/⁹Be ratio in trap samples varies from 3 to 20 × 10⁻⁸. The variation may partly result from varied proportion of authigenic/detrital material. The fluxes of both isotopes exhibit a very strong seasonality. The fluxes of¹⁰Be into the traps at about 1500 m are estimated as 9 × 10⁵ and 4 × 10⁵ atoms cm⁻² a⁻¹ at sites H and M respectively. These values are to be compared with the fluxes into the sediments of 4–5 × 10⁵ atoms cm⁻² a⁻¹ at both locations. Good correlations exist between¹⁰Be,⁹Be and²⁷Al indicating that the primary carrier phase(s) for the beryllium isotopes in the water column may be aluminosilicates.     

Determination of the Geopotential Scale Factor from TOPEX/POSEIDON Satellite Altimetry

The geopotential scale factor R _o = GM/W _o (the GM geocentric gravitational constant adopted) and/or geoidal potential Wo have been determined on the basis of the first year's (Oct 92 – Dec 93) ERS-1/TOPEX/POSEIDON altimeter data and of the POCM 4B sea surface topography model: R _o °=(6 363 672.58°±0.05) m, W _o °=(62 636 855.8°±0.05)m ² s ^–2 . The 2°–°3 cm uncertainty in the altimeter calibration limits the actual accuracy of the solution. Monitoring dW _o /dt has been projected.     

Al–Mg and Pb–Pb systematics of Allende CAIs: Canonical solar initial Al/Al ratio reinstated

The precise knowledge of the initial ²⁶Al/²⁷Al ratio [(²⁶Al/²⁷Al)₀] is crucial if we are to use the very first solid objects formed in our Solar System, calcium–aluminum-rich inclusions (CAIs) as the “time zero” age-anchor and guide future work with other short-lived radio-chronometers in the early Solar System, as well as determining the inventory of heat budgets from radioactivities for early planetary differentiation. New high-precision multi-collector inductively-coupled plasma mass spectrometry (MC-ICP-MS) measurements of ²⁷Al/²⁴Mg ratios and Mg-isotopic compositions of nine whole-rock CAIs (six mineralogically characterized fragments and three micro-drilled inclusions) from the CV carbonaceous chondrite, Allende yield a well-defined ²⁶Al–²⁶Mg fossil isochron with an (²⁶Al/²⁷Al)₀ of (5.23 ± 0.13) × 10^− 5. Internal mineral isochrons obtained for three of these CAIs (A44A, AJEF, and A43) are consistent with the whole-rock CAI isochron. The mineral isochron of AJEF with (²⁶Al/²⁷Al)₀ = (4.96 ± 0.25) × 10^− 5, anchored to our precisely determined absolute ²⁰⁷Pb–²⁰⁶Pb age of 4567.60 ± 0.36 Ma for the same mineral separates, reinstate the “canonical” (²⁶Al/²⁷Al)₀ of 5 × 10^− 5 for the early Solar System. The uncertainty in (²⁶Al/²⁷Al)₀ corresponds to a maximum time span of ± 20 Ka (thousand years), suggesting that the Allende CAI formation events were culminated within this time span. Although all Allende CAIs studied experienced multistage formation history, including melting and evaporation in the solar nebula and post-crystallization alteration likely on the asteroidal parent body, the ²⁶Al–²⁶Mg and U–Pb-isotopic systematics of the mineral separates and bulk CAIs behaved largely as closed-system since their formation. Our data do not support the “supra-canonical” ²⁶Al/²⁷Al ratio of individual minerals or their mixtures in CV CAIs, suggesting that the supra-canonical ²⁶Al/²⁷Al ratio in the CV CAIs may have resulted from post-crystallization inter-mineral redistribution of Mg isotopes within an individual inclusion. This redistribution must be volumetrically minor in order to satisfy the mass balance of the precisely defined bulk CAI and bulk mineral data obtained by MC-ICP-MS.The radiogenic ²⁰⁸Pb/²⁰⁶Pb ratio obtained as a by-product from the Pb–Pb age dating is used to estimate time-integrated ²³²Th/²³⁸U ratio (κ value) of CAIs. Limited κ variations among the minerals within a single CAI, contrasted by much larger variations among the bulk CAIs, suggest Th/U fractionation occurred prior to crystallization of igneous CAIs. If interpreted as primordial heterogeneity, the κ value can be used to calculate the mean age of the interstellar dust from which the CAIs condensed.