A semi-analytical model of expected areal-average infiltration under spatial heterogeneity of rainfall and soil saturated hydraulic conductivity

A semi-analytical model for the estimate of expected areal-average infiltration rate at hillslope scale is presented. It accounts for spatial heterogeneity of the saturated hydraulic conductivity, K_s, and rainfall rate, r. The K_s field is characterized by a lognormal probability density function while the rainfall rate r is represented by a uniform distribution between two extreme values. The model formulation relies upon the use of cumulative infiltration as the independent variable which is then expressed as a function of an expected time for use in practical applications. The solution is applicable for those ranges of r and K_s that allow for neglecting the infiltration of surface water running downslope into pervious soils (run-on process). The model was tested by comparisons with Monte Carlo simulations carried out for a variety of coefficients of variation of r and K_s over a clay loam soil and a sandy loam soil. The model was found to be very reliable both with coupled spatial variability of r and K_s and when only one variable is characterized by spatial heterogeneity while the other is uniform.     

Radiation damping in the context of one-dimensional wave propagation: A teaching perspective

This paper has two objectives: to connect directly radiation damping and 1D elastic wave propagation, and to create a simple teaching tool to introduce the subject to students and engineers trained in Structural Dynamics. The first objective is achieved by obtaining the equivalent radiation modal damping using time domain solutions for the fundamental mode in shear of an elastic layer (soil) on flexible rock, for the case in which the rock–soil Impedance Ratio in shear, I=(ρ_rV_r)/(ρ_sV_s)>1, where ρ=mass density and V=shear wave velocity. These time domain solutions are developed for the case of steady-state input sinusoidal shear waves propagating vertically in the rock as well as for horizontal free vibration of the layer. Both derivations result in the same approximate expression for the modal radiation damping in the first mode, ζ_r1≈2/(πI), which is in turn identical to the approximate equation obtained by Roesset and Whitman [11] using a frequency domain approach. This expression for ζ_r1 is linked to the fact that, during free vibration, the ratio between two successive positive displacement peaks u_so and u_s1 at the ground surface is u_s0/u_s1=[(1+I)/(1−I)]², associated with two wave reflections at the soil–rock interface. From this ratio, and after applying the standard expression to obtain modal damping from damped free vibration, the same expression for ζ_r1 is reached again, ζ_r1≈[1/(2π)] ln(u_s0/u_s1)≈[1/(2π)] ln[(1+I)/(1−I)]²≈2/(πI). This finding allows development of the simple teaching tool proposed at the end of the paper. While only a crude approximation lacking in rigor, this teaching tool is physically intuitive, links directly wave propagation and modal damping in a simple way and gives the correct result.     

Resistive instabilities in rapidly rotating fluids: Linear theory of the convective modes

Abstract

This paper analyzes the linear stability of a rapidly-rotating, stratified sheet pinch in a gravitational field, g, perpendicular to the sheet. The sheet pinch is a layer (O ? z ? d) of inviscid, Boussinesq fluid of electrical conductivity σ, magnetic permeability μ, and almost uniform density ρ _o; z is height. The prevailing magnetic field. B _o(z), is horizontal at each z level, but varies in direction with z. The angular velocity, Ω, is vertical and large (Ω ? V_A/d, where V_A = B₀√(μρ₀) is the Alfvén velocity). The Elsasser number, Λ = σB² ₀/2Ωρ₀, measures σ. A (modified) Rayleigh number, R = gβd²/ρ₀V² _A, measures the buoyancy force, where β is the imposed density gradient, antiparallel to g. A Prandtl number, P_K = μσK, measures the diffusivity, k, of density differences.     

The thermodynamic properties of the earth's lower mantle

The thermodynamic properties of the lower mantle are determined from the seismic profile, where the primary thermodynamic variables are the bulk modulus K and density ρ. It is shown that the Bullen law (K ∝ P) holds in the lower mantle with a high correlation coefficient for the seismic parametric Earth model (PEM). Using this law produces no ambiguity or trade-off between ρ₀ and K₀, since both K₀ and K′₀ are exactly determined by applying a linear K?ρ relationship to the data. On the other hand, extrapolating the velocity data to zero pressure using a Birch-Murnaghan equation of state (EOS) results in an ambiguous answer because there are three unknown adjustable parameters (ρ₀, K₀, K′₀) in the EOS.From the PEM data, K = 232.4 + 3.19 P (GPa). The PEM yields a hot uncompressed density of 3.999 ± 0.0026 g cm^?3 for material decompressed from all parts of the lower mantle. Even if the hot uncompressed density were uniform for all depths in the lower mantle, the cold uncompressed mantle would be inhomogeneous because the decompression given by the Bullen law crosses isotherms; for example, the temperature is different at different depths. To calculate the density distribution correctly, an isothermal EOS must be used along an isotherm, and temperature corrections must be placed in the thermal pressure P_TH.The thermodynamic parameters of the lower mantle are found by iteration. Values of the three uncompressed anharmonic parameters are first arbitrarily selected: α₀ (hot), the coefficient of thermal expansion; γ₀, the Grüneisen parameter; and δ, the second Grüneisen parameter. Using γ₀ and the measured ρ₀ (hot) and K₀ (hot), the values of θ₀ (Debye temperature) and q = dlnγ/dlnρ are found from the measured seismic velocities. Then from (αK_T)₀ and q the thermal pressure P_TH at all high temperatures is found. Correlating P_TH against T to the geotherm for the lower mantle, P_TH is found at all depths Z. The isothermal pressure, along the 0 K isotherm, at every Z is found by subtracting P_TH from the measured P given by the seismic model. Using the isothermal pressure at depth Z, the solution for the cold uncompressed density ρ_0C and the cold uncompressed bulk modulus, K_T0 is found as a trace in the K_T0?_ρ0C plane. A narrow band of solutions is then found for ρ_0C and K_T0 at all depths.The thermal expansion at all T is found from [ρ_0C ? ρ₀ (hot)/ρ_0C. From Suzuki's formula, the best fit to the thermal expansion determines γ₀ and α₀ (hot). When the values of these two parameters do not agree with the original assumptions, the calculation is repeated until they do agree. In this way all the important thermodynamic parameters are found as a self-consistent set subject only to the assumptions behind the equations used.     

Correlation of Geoelectric Data with Aquifer Parameters to Delineate the Groundwater Potential of Hard rock Terrain in Central Uganda

Knowledge of aquifer parameters is essential for management of groundwater resources. Conventionally, these parameters are estimated through pumping tests carried out on water wells. This paper presents a study that was conducted in three villages (Tumba, Kabazi, and Ndaiga) of Nakasongola District, central Uganda to investigate the hydrogeological characteristics of the basement aquifers. Our objective was to correlate surface resistivity data with aquifer properties in order to reveal the groundwater potential in the district. Existing electrical resistivity and borehole data from 20 villages in Nakasongola District were used to correlate the aquifer apparent resistivity (ρ _e) with its hydraulic conductivity (K _e), and aquifer transverse resistance (TR) with its transmissivity (T _e). K _e was found to be related to ρ _e by; $ {\text{Log }}(K_{\text{e}} ) = - 0.002\rho_{\text{e}} + 2.692 $ . Similarly, TR was found to be related to T by; $ {\text{TR}} = - 0.07T_{\text{e}} + 2260 $ . Using these expressions, aquifer parameters (T _c and K _c) were extrapolated from measurements obtained from surface resistivity surveys. Our results show very low resistivities for the presumed water-bearing aquifer zones, possibly because of deteriorating quality of the groundwater and their packing and grain size. Drilling at the preferred VES spots was conducted before the pumping tests to reveal the aquifer characteristics. Aquifer parameters (T _o and K _o) as obtained from pumping tests gave values (29,424.7 m²/day, 374.3 m/day), (9,801.1 m²/day, 437.0 m/day), (31,852.4 m²/day, 392.9 m/day). The estimated aquifer parameter (T _c and K _c) when extrapolated from surface geoelectrical data gave (7,142.9 m²/day, 381.9 m/day), (28,200.0 m²/day, 463.4 m/day), (19,428.6 m²/day, 459.2 m/day) for Tumba, Kabazi, and Ndaiga villages, respectively. Interestingly, the similarity between the K _c and K _o pairs was not significantly different. We observed no significant relationships between the T _c and T _o pairs_. The root mean square errors were estimated to be 18,159 m²/day and 41.4 m/day.     

THE QUANTITATIVE ANALYSIS OF FREQUENCY-DOMAIN INDUCED POLARIZATION SOUNDINGS OVER HORIZONTAL BEDS*

Following up our recent study of an indirect procedure for the practical determination of the maximum frequency-effect, defined as fe = 1 ? pρ_∞/ρdc with ρ_∞ the resistivity at infinite frequency, we show at first how, through the Laplace transform theory, ρ_∞ can be related to stationary field vectors in the simple form of Ohm's law. Then applying the equation of continuity for stationary currents with a suitable set of boundary conditions, we derive the integral expression of the apparent resistivity at infinite frequency ρ_∞,a in the case of a horizontally layered earth. Finally, from the definition of the maximum apparent frequency-effect, analytical expressions of fe_α are obtained for both Schlumberger and dipole arrays placed on the surface of the multi-layered earth section in the most general situation of vertical changes in induced polarization together with dc resistivity variations not at the same interfaces. Direct interpretation procedures are suggested for obtaining the layering parameters directly from the analysis of the sounding curves.     

A dripper-TDR method for in situ determination of hydraulic conductivity and chemical transport properties of surface soils

Field determined hydraulic and chemical transport properties can be useful for the protection of groundwater resources from land-applied chemicals. Most field methods to determine flow and transport parameters are either time or energy consuming and/or they provide a single measurement for a given time period. In this study, we present a dripper-TDR field method that allows measurement of hydraulic conductivity and chemical transport parameters at multiple field locations within a short time period. Specifically, the dripper-TDR determines saturated hydraulic conductivity (K_s), macroscopic capillary length (λ_c), immobile water fraction (θ_im/θ), mass exchange coefficient (α) and dispersion coefficient (D_m). Multiple dripper lines were positioned over five crop rows in a field. Background and step solutions were applied through drippers to determine surface hydraulic conductivity parameters at 44 locations and surface transport properties at 38 locations. The hydraulic conductivity parameters (K_s, λ_c) were determined by application of three discharge rates from the drippers and measurements of the resultant steady-state flux densities at the soil surface beneath each dripper. Time domain reflectometry (TDR) was used to measure the bulk electrical conductivity of the soil during steady infiltration of a salt solution. Breakthrough curves (BTCs) for all sites were determined from the TDR measurements. The K_s and λ_c values were found to be lognormally distributed with average values of 31.4 cm h⁻¹ and 6.0 cm, respectively. BTC analysis produced chemical properties, θ_im/θ, α, and D_m with average values of 0.23, 0.0036 h⁻¹, and 1220 cm² h⁻¹, respectively. The estimated values of the flow and transport parameters were found to be within the ranges of values reported by previous studies conducted at nearby field locations. The dripper TDR method is a rapid and useful technique for in situ measurements of hydraulic conductivity and solute transport properties. The measurements reported in this study give clear evidence to the occurrence of non-equilibrium water and chemical movement in surface soil. The method allows for quantification of non-equilibrium model parameters and preferential flow. Quantifying the parameters is a necessary step toward determining the influences of surface properties on infiltration, runoff, and vadose zone transport.     

Estimating field‐saturated soil hydraulic conductivity by a simplified Beerkan infiltration experiment

Field‐saturated soil hydraulic conductivity, K_fs, is highly variable. Therefore, interpreting and simulating hydrological processes, such as rainfall excess generation, need a large number of K_fs data even at the plot scale. Simple and reasonably rapid experiments should be carried out in the field. In this investigation, a simple infiltration experiment with a ring inserted shortly into the soil and the estimation of the so‐called α* parameter allowed to obtain an approximate measurement of K_fs. The theoretical approach was tested with reference to 149 sampling points established on Burundian soils. The estimated K_fs with the value of first approximation of α* for most agricultural field soils (α* = 0.012 mm^?1) differed by a practically negligible maximum factor of two from the saturated conductivity obtained by the complete Beerkan Estimation of Soil Transfer parameters (BEST) procedure for soil hydraulic characterization. The measured infiltration curve contained the necessary information to obtain a site‐specific prediction of α*. The empirically derived α* relationship gave similar results for K_fs (mean = 0.085 mm s^?1; coefficient of variation (CV) = 71%) to those obtained with BEST (mean = 0.086 mm s^?1; CV = 67%), and it was also successfully tested with reference to a few Sicilian sampling points, since it yielded a mean and a CV of K_fs (0.0094 mm s^?1 and 102%, respectively) close to the values obtained with BEST (mean = 0.0092 mm s^?1; CV = 113%). The developed method appears attractive due to the extreme simplicity of the experiment. Copyright © 2012 John Wiley & Sons, Ltd.     

On the content and vertical distribution of K,Th and U in the continental crust

The content of K, Th and U in the continental crust is estimated based on the assumption that the concentration of these elements decreases with depth asA_x = A₀e^?x/D [11], withA_x andA₀ the heat production rates at depthx and at the surface, respectively. Taking the weighted mean heat production rate of the intrusive rocks of the upper crust asA₀ = 2.33 μWm^?3, that of the granulites representing the lower crust asA_x = 0.72 μWm^?3, and the mean scale heightD= 9.5km [1] the average vertical distancex = b between these intrusives and granulites is 11.2 km. Withb known and the average concentrations of K, Th and U in granulites and intrusive rocks of the upper crust the scale heights of the vertical distribution of these elements areD_K = 71km,D_Th = 9.5km,D_U = 5.8km. The knowledge of these parameters permits to calculate the average concentrations of these elements in a 33.3 km thick crust:K= 2.19%,Th= 4.43ppm,U= 0.66ppm; Th/U = 6.7 and K/U = 3.3 × 10⁴. The resulting heat flow is 23.0 mW m^?2 which is practically identical with the value deduced from heat flow measurements. Assuming that the Th/U ratio of the entire crust—including the sediments—is 3.9, the high ratio of 6.7 in the crystalline crust indicates that about 7.2 × 10¹² t U were extracted from it. All rocks with Th/U ratios <3.9 are possible sinks of this U. About half that amount is deposited in sedimentary rocks, mainly in black shales. The second important sink are the volcanic rocks of the continental margins.     

Short-period rayleigh waves recorded in the western carpathians during dss

Summary The periods, the maximum absolute displacement amplitudes and the maximum particle velocities of the surface waves, propagating in the weathered layer are investigated. Dependences of the parameters under discussion on the distance r (km) between sites and shot points are expressed for distances from 3.6 to 38.6 km by the functions: T(s)=0.40r ^0.30 , A _max (m)==502.73r ^–1.93 and v _max (mm s –1)=7.95 r –2.22.     

Evaluation and modeling of runoff and sediment yield for different land covers under simulated rain in a semiarid region of Brazil

This paper quantifies the runoff and sediment yield for four different land covers in a semiarid region of Brazil. The WESP model, a distributed, event-oriented runoff-erosion model, was applied and its physical parameters, N_s and K_R, were adjusted based on observed runoff and sediment yield data using simulated rainfall with an average intensity of 53 mm h^-1. The sediment yield obtained was 53.02 kg ha^-1 (caatinga vegetation), 231.96 kg ha^-1 (bare soil), 309.75 kg ha^-1 (beans), and 847.38 kg ha^-1(corn). The results showed that caatinga cover yields the lowest erosion and runoff when compared to the other treatments. The results also show that the sediment yield and runoff values simulated with N_s, K_I, and K_R parameters were well calibrated, within acceptable deviations. The caatinga vegetation was more effective in protecting the soil, when compared to the other types of coverage. The beans and corn covers had the highest values of runoff and sediment yield, even higher than those observed for bare soil.     

The electric field produced in the mantle by the dynamo in the core

A rigorous singular perturbation theory is developed to estimate the electric field E produced in the mantle M by the core dynamo when the electrical conductivity σ in M depends only on radius r, and when |r?_rln σ| ? 1 in most of M. It is assumed that σ has only one local minimum in M, either (a) at the Earth's surface ?V, or (b) at a radius b inside the mantle, or (c) at the core-mantle boundary ?K. In all three cases, the region where σ is no more than e times its minimum value constitutes a thin critical layer; in case (a), the radial electric field E_r ≈ 0 there, while in cases (b) and (c), E_r is very large there. Outside the critical layer, E_r ≈ 0 in all three cases. In no case is the tangential electric field E_S small, nearly toroidal, or nearly calculable from the magnetic vector potential A as ??_tA_S. The defects in Muth's (1979) argument which led him to contrary conclusions are identified. Benton (1979) cited Muth's work to argue that the core-fluid velocity u just below ?K can be estimated from measurements on ?V of the magnetic field B and its time derivative $\text{?}{}_{\mathrm{t}}\text{B}$. A simple model for westward drift is discussed which shows that Benton's conclusion is also wrong.In case (a), it is shown that knowledge of σ in M is unnecessary for estimating E_S on ?K with a relative error |r?_r 1nσ|^?1from measurements of E_S on ?V and knowledge of ?_tB in M (calculable from ?_tB on ?V if σ is small). Then, in case (a), u just below ?K can be estimated as $\text{?}\text{r}\text{×}\text{E}{}_{\mathrm{S}}\text{/B}{}_{\mathrm{r}}$. The method is impractical unless the contribution to E_S on ?V from ocean currents can be removed.The perturbation theory appropriate when σ in M is small is considered briefly; smallness of σ and of |r?_r ln σ|^?1 a independent questions. It is found that as σ → 0, B approaches the vacuum field in M but E does not; the explanation lies in the hydromagnetic approximation, which is certainly valid in M but fails as σ → 0. It is also found that the singular perturbation theory for |r?_r ln σ|^?1 is a useful tool in the perturbation calculations for σ when both σ and |r?_r ln σ|^?1 are small.     

The relationship between vertical eddy diffusion and buoyancy gradient in the deep sea

Vertical eddy diffusivities (K_v's) have been estimated at fourteen widely separated locations from fourteen²²²Rn profiles and two²²⁸Ra profiles measured near the ocean floor as part of the Atlantic and Pacific GEOSECS programs. They show an inverse proportionality to the local buoyancy gradient [(g/?)(??_pot/?z)] calculated from hydrographic measurements. The negative of the constant of proportionality is the buoyancy flux [?K_v(g/?)(??_pot/?z)] which has a mean of ?4 × 10^?6 cm²/sec³. Our results suggest that the buoyancy flux varies very little near the ocean floor. K_v's for the interior of the deep Pacific calculated from the relationship K_v = (4 × 10^?6cm²/sec³)/[(g/?)(??_pot/?z)] agree well with published estimates. K_v's calculated for the pycnocline are one to two orders of magnitude smaller than upper limits estimated from tritium and⁷Be distributions.Heat fluxes calculated with the model K_v's obtained from the²²²Rn profiles average 31 μcal cm^?2 sec^?1 in the Atlantic Ocean and 8 μcal cm^?2 sec^?1 in the Pacific Ocean.     

Research on the time changes of transfer functions at Heze observatory before and after Heze earthquake of magnitude 5.9

In this paper, the coefficients of Parkinson vectora, b and the in-phase partA _r, B_r and quadrature-phase partA _i, B_i of transter functions are calculated by using two kinds of data processing methods, respectively. The results of both methods are close to each other. All these six parameters above are low in value, showing that the electric structure in Heze area is rather uniform. It seems that the anomalous changes appeared in both results, and the values of parameters decrease before and after Heze earthquake.     

Using a transient infiltrometric technique for intensively sampling field‐saturated hydraulic conductivity of a clay soil in two runoff plots

The point measurement of soil properties allows to explain and simulate plot scale hydrological processes. An intensive sampling was carried out at the surface of an unsaturated clay soil to measure, on two adjacent plots of 4 × 11 m² and two different dates (May 2007 and February–March 2008), dry soil bulk density, ρ_b, and antecedent soil water content, θ_i, at 88 points. Field‐saturated soil hydraulic conductivity, K_fs, was also measured at 176 points by the transient Simplified Falling Head technique to determine the soil water permeability characteristics at the beginning of a possible rainfall event yielding measurable runoff. The ρ_b values did not differ significantly between the two dates, but wetter soil conditions (by 31%) and lower conductivities (1.95 times) were detected on the second date as compared with the first one. Significantly higher (by a factor of 1.8) K_fs values were obtained with the 0.30‐m‐diameter ring compared with the 0.15‐m‐diameter ring. A high K_fs (> 100 mm h^?1) was generally obtained for low θ_i values (< 0.3 m³m^?3), whereas a high θ_i yielded an increased percentage of low K_fs data (1–100 mm h^?1). The median of K_fs for each plot/sampling date combination was not lower than 600 mm h^?1, and rainfall intensities rarely exceeded 100 mm h^?1 at the site. The occurrence of runoff at the base of the plot needs a substantial reduction of the surface soil permeability characteristics during the event, probably promoted by a higher water content than the one of this investigation (saturation degree = 0.44–0.62) and some soil compaction due to rainfall impact. An intensive soil sampling reduces the risk of an erroneous interpretation of hydrological processes. In an unstable clay soil, changes in K_fs during the event seem to have a noticeable effect on runoff generation, and they should be considered for modeling hydrological processes. Copyright © 2012 John Wiley & Sons, Ltd.     

Heat transfer and thermal boundary layers in high amplitude annulus waves

Abstract

The heat transfer by a rotating, differentially-heated annulus of fluid is measured throughout the high amplitude wave regime. Only Δr_w T was varied (although v(T₁₅ ).K(T₁₅ ) varied by 46%), and it is found that Nu = C₁(λ)Ra^? away from the symmetry and low amplitude to wave transition curves and this is independent of ω. (λ is the wavelength.) On the wave side of these transition curves a region exists in which Nu (symmetry) λ Nu λ C₁(λ)Ra^?. The local heat transfer rate also varies strongly with wave phase.

Using a selection of measured internal thermal fields in the steady, high amplitude wave regime, the side-wall thermal boundary layer structure is examined. It is found that Nu, = C₂·Gr₂ ^A2; both C ₂ and A ₂ are independent of ω and λ to first order. For the time mean profiles, A ₂ ≈ 0.25; in the high heat transfer portion of the wave A ₂ < ¼ and in the low heat transfer portion of the wave A ₂ > ?. These relations hold over most of the vertical extent of the side walls. The deviations of the boundary layers from the above behavior which occur on the remainder of the walls is illustrated. The average thicknesses of the wall boundary layers ∞ Ra^?¼ except in that phase of the wave in which the wall to mid-gap temperature difference is the largest.     

Inverse modelling techniques for determining hydraulic properties of coarse-textured porous media by transient outflow methods

A series of multi-step outflow experiments was carried out to identify the unsaturated hydraulic properties of two homogeneous coarse-textured porous media (glass beads and sand). Because of the measured sharp fronts of water content decrease during these experiments the hydraulic functions are assumed to be represented by the complete van Genuchten–Mualem closed-form expressions with variable coefficients α, n, m and θ_r. The values of θ_s and K_s were measured directly. A sensitivity analysis with respect to α, n, and m shows that conditions of local identifiability are satisfied if measurements of water content at some inner points inside the column are considered. The inverse modelling technique consists of two steps: first, computation of objective function values based on water content data responses to obtain initial parameter estimations, and second, a more detailed parameter determination using a Levenberg–Marquardt scheme. In both steps a numerical model incorporating the hydraulic functions is utilized to simulate theoretical pressure head and water content distributions along the column. For both porous media unique solutions of the inverse problem could be obtained, and afterwards, the corresponding hydraulic functions were verified from additional drainage experiments.©1998 Elsevier Science Limited. All rights reserved     

The effects of annealing and concentration on the hysteresis properties of magnetite around the PSD-MD transition

Hysteresis parameters H_cr, H_c, J_rs, J_s, and their ratios H_cr/H_c, J_rs/J_s have been measured for a large number of accurately prepared grain size fractions of magnetite in the range between 5 and 150 μm. For several grain size fractions three different concentrations of magnetite are used: 100, 0.1, and 0.002 vol.%. Most of the measurements were repeated after annealing the specimens to 600°C. For some specimens in the pseudo-single (PSD) and multidomain (MD) range H_c and H_cr have been measured as functions of temperature. Plots of the results from H_c, H_cr/H_c and J_rs/J_s versus the grain size reveal curves with a convex and a concave part. Concentration and annealing affects the values of the hysteresis parameters, especially for grains coarser than 25 μm but the shape of the curves remains the same. The inflection point from convex to concave for all curves occurs at 25 μm and it appears to be independent of concentration and annealing. It is therefore proposed to define the transition from PSD to MD as the inflection point of these curves.     

Heat flow studies: Constraints on the distribution of uranium,thorium and potassium in the continental crust

To study the amount of heat generated by radioactive decay in the continental crust, the usual practice in the literature is to fit to the heat flow and radioactivity data a relationship of the form: Q = Q_r + D · A where Q and A are the observed heat flow and radiogenic heat production. Q_r is the “reduced” heat flow and D is a depth scale. This procedure implicitly assumes that uranium, thorium and potassium have identical distributions in the crust. We suggest that significant information may be lost as the three radioelements may in fact be affected by processes operating over different depths.Data published for four heat flow provinces throughout the world are used to estimate the distributions of uranium, thorium and potassium in the continental crust. These distributions are characterized by a depth scales defined as follows: D_i =∫0h C_i(z)C_i(0)dz where h is the thickness of the layer containing the bulk of radioactivity and C_i(z) the concentration of element i at depth z. Three depth scales are computed from a least-squares fit to the following relationship: Q = Q_r + D_U · A_U + D_T · A_T + D_K · A_T where Q is the observed heat flow and Q_r some constant (a reduced heat flow). A_i is the heat generation rate due to the radioactive decay of element i, and D_i is the corresponding depth scale.The analysis suggests that the three distributions are different and that they have the same basic features in the four provinces considered. The depth scale for potassium is large in granitic areas, that for thorium is small and that for uranium lies between the other two.We propose a simple model according to which each radioelement essentially provides a record for one process. Potassium gives a depth scale for the primary differentiation of the crust. Thorium gives the depth scale of magmatic or metamorphic fluid circulation. Finally, the uranium distribution reflects the late effects of alteration due to meteoric water. We show that the heat flow and radioactivity data are compatible with this model.Our analysis and numerical results are supported by data from deep boreholes and by geochemical evidence, such as detailed investigations of plutonic series and studies of U-Th-Pb systematics.     

Some Probabilistic and Statistical Properties of the Seismic Regime of Zemmouri (Algeria) Seismoactive Zone

Statistical tests have been used to adjust the Zemmouri seismic data using a distribution function. The Pareto law has been used and the probabilities of various expected earthquakes were computed. A mathematical expression giving the quantiles was established. The extreme values limiting law confirmed the accuracy of the adjustment method. Using the moment magnitude scale, a probabilistic model was made to predict the occurrences of strong earthquakes. The seismic structure has been characterized by the slope of the recurrence plot γ, fractal dimension D, concentration parameter K_sr, Hurst exponents H_r and H_t. The values of D, γ, K_sr, H_r, and H_t diminished many months before the principal seismic shock (M = 6.9) of the studied seismoactive zone has occurred. Three stages of the deformation of the geophysical medium are manifested in the variation of the coefficient G% of the clustering of minor seismic events.