Regional deep sounding at high latitudes of the Northern Hemisphere

Methods were developed for carrying out spherical harmonical analysis of disturbed diurnal variations over a limited territory at high latitudes of the Northern Hemisphere. The ratios ?_n^{|staggered||m} of the external and internal parts of the magnetic potential were evaluated for spherical harmonics 4 ? n ? 12. Different from generally accepted ?_n^{|staggered||m} values for S_q variations (2 ÷ 3), they proved to be considerably higher and attained 10 for n ? 8. This result testifies to a small contribution of induced fields into disturbed diurnal variations observed at high latitudes.A deep sounding was carried out from spherical analysis data. It is shown that the mean distribution of the electrical conductivity at high latitudes σ(r) is the same as the global mean distribution for the whole Earth and that, consequently, it may serve as a reference for local soundings.     

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.     

Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes

Diverse linear and nonlinear statistical parameters of rainfall under aggregation in time and the kind of temporal memory are investigated. Data sets from the Andes of Colombia at different resolutions (15 min and 1-h), and record lengths (21 months and 8-40 years) are used. A mixture of two timescales is found in the autocorrelation and autoinformation functions, with short-term memory holding for time lags less than 15-30 min, and long-term memory onwards. Consistently, rainfall variance exhibits different temporal scaling regimes separated at 15-30 min and 24 h. Tests for the Hurst effect evidence the frailty of the R/S approach in discerning the kind of memory in high resolution rainfall, whereas rigorous statistical tests for short-memory processes do reject the existence of the Hurst effect.Rainfall information entropy grows as a power law of aggregation time, S(T) ∼ T^β with 〈β〉 = 0.51, up to a timescale, T_MaxEnt (70-202 h), at which entropy saturates, with β = 0 onwards. Maximum entropy is reached through a dynamic Generalized Pareto distribution, consistently with the maximum information-entropy principle for heavy-tailed random variables, and with its asymptotically infinitely divisible property. The dynamics towards the limit distribution is quantified. Tsallis q-entropies also exhibit power laws with T, such that S_q(T) ∼ T^β(q), with β(q) ? 0 for q ? 0, and β(q) ? 0.5 for q ? 1. No clear patterns are found in the geographic distribution within and among the statistical parameters studied, confirming the strong variability of tropical Andean rainfall.     

Crustal structure beneath the central and western North China from receiver function analysis

The North China Craton (NCC) is one of the oldest cratons on earth. Several important tectonic transformations of Mesozoic-Cenozoic tectonic regime led to the destruction of the North China craton. The knowledge of crustal structure can provide important constraints for the formation and evolution of cratons. New maps of sediment thickness, crustal thickness (H) and v_P/v_S (κ) in the central and western NCC were obtained using sequential H-κ stacking. P-wave receiver functions are calculated using teleseismic waveform data recorded by 405 stations from ChinArray project. Benefiting from the densely distribution of temporary seismic stations, our results reveal details of the crustal structure in the study area. The thickness of sedimentary layer in North China ranges from 0–6.4 km, and the thickest sedimentary layer is in Ordos block and its surroundings (about 2.8–6 km); The thickness of sedimentary layer in the Mongolia fold belt and Yinshan orogenic belt is relatively thin (less than 1 km). The crustal thickness of the study area varies between 27–48 km, of which the crust of the North China Plain is about 30–33 km, the central NCC is about 33–40 km, and the Ordos block is 40–48 km thick. The average v_P/v_S ratios in the study area is mostly between 1.66 and 1.90, and that in the Yanshan-Taihang mountain fold belt is between 1.70 and 1.85, and that in the Ordos block is between 1.65 and 1.90, with an average value of 1.77, indicating the absence of a thick basaltic lower crust. The obvious negative correlation between crustal thickness and average v_P/v_S ratio within Ordos and Central Asia orogenic belt may be related to magmatic underplating during the crustal formation. There is no significant correlation between the crustal thickness and the v_P/v_S ratio in the Lüliang-Taihang mountain fold belt, which may be related to the multiple geological processes such as underplating and crustal extension and thinning in this area. The lack of correlation between crust thickness and topography in the central orogenic belt and the North China Basin indicates the topography of these areas are controlled not only by crustal isostatic adjustment but also by the lithospheric mantle processes.     

Correlations Between Shear Wave Velocity and In-Situ Penetration Test Results for Korean Soil Deposits

Shear wave velocity (V _S) can be obtained using seismic tests, and is viewed as a fundamental geotechnical characteristic for seismic design and seismic performance evaluation in the field of earthquake engineering. To apply conventional geotechnical site investigation techniques to geotechnical earthquake engineering, standard penetration tests (SPT) and piezocone penetration tests (CPTu) were undertaken together with a variety of borehole seismic tests for a range of sites in Korea. Statistical modeling of the in-situ testing data identified correlations between V _S and geotechnical in-situ penetration data, such as blow counts (N value) from SPT and CPTu data including tip resistance (q _t), sleeve friction (f _s), and pore pressure ratio (B _q). Despite the difference in strain levels between conventional geotechnical penetration tests and borehole seismic tests, it is shown that the suggested correlations in this study is applicable to the preliminary determination of V _S for soil deposits.     

On the statistical distribution of seismic velocities in Earth's deep mantle

The existence of uncoupled shear (S) and compression (P) wave velocity variations in Earth's mantle is a characteristic that might only be explained by the presence of significant chemical and/or phase heterogeneity, with important implications for the dynamics and evolution of Earth's interior. While making a one-to-one comparison between tomographic models for P and S velocity (V_P and V_S) variations for a particular geographic region is ill-posed, their global statistical distributions reveal several robust characteristics indicative of the nature of uncoupled V_P and V_S in the deep mantle. We find that all of the V_P and V_S model distributions at a given depth are Gaussian-like throughout the lowermost mantle. However, a distinct low velocity feature is present in V_S distributions below ≈ 2200 km depth that is not present or is relatively weak in V_P models. The presence of anomalously low V_S material cannot be explained as an artifact, nor can the absence of a similarly strong feature in P models be ascribed to under-resolution. We propose that this feature can be partly explained by laterally variable occurrences of post-perovskite (pPv) lenses in the D″ layer, however, the persistence of significantly slow V_S regions at heights up to ≈ 700 km or more above the core–mantle boundary is likely to be incompatible with a pPv origin and might only be explained by the presence of a laterally discontinuous layer of chemically distinct material and/or some other kind of phase heterogeneity. There also exist significant discrepancies between tomographic models with respect to the width of the distributions as well as differences between the modeled peak values. We propose a scheme for comparison between different seismic models in which the widths of the dominant features in their statistical distributions is exploited.     

Probability of earthquake occurrence and magnitude estimation in the post shut-in phase of geothermal projects

Induced seismicity in geothermal projects is observed to continue after shut-in of the fluid injection. Recent experiments show that the largest events tend to occur after the termination of injection. We use a probabilistic approach based on Omori??s law and the Gutenberg?CRichter magnitude?Cfrequency distribution to demonstrate that the probability of exceeding a certain maximum magnitude still increases after shut-in. This increase is governed by the exponent of Omori??s law q and the Gutenberg?CRichter b value. For a reduced b value in the post-injection phase, the probability of occurrence directly after shut-in can be even higher than the corresponding probability for an ongoing injection. For the reference case of q?=?2 and a 10% probability at shut-in time t _S to exceed a given maximum magnitude, we obtain an increase to 14.6% for t?=?2t _S at a constant Gutenberg?CRichter b value after shut-in. A reduction of the b value by one quarter leads to a probability of 20.5%. If we consider a constant probability level of occurrence for an event larger than a given magnitude at shut-in time, this maximum magnitude increases by 0.12?units for t?=?2t _S (0.26?units for a reduced b value). For the Soultz-sous-Forêts (France) injection experiment in 2000, recent studies reveal q?=?9.5 and a b value reduction by 14%. A magnitude 2.3 event 9?h after shut-in falls in the phase with a probability higher than for the continued injection. The probability of exceeding the magnitude of this post-injection event is determined to 97.1%.     

A worldwide comparison of predicted S-wave delays from a three-dimensional upper mantle model with P-wave station corrections

This paper is a comparison, on a worldwide scale, between P-station corrections deduced from ISC residuals (Dziewonski and Anderson) and synthetic S-station corrections computed using a three-dimensional upper mantle model obtained from mantle wave data (Woodhouse and Dziewonski). The upper mantle S-velocity model is described by a spherical harmonic expansion up to degree 8; the P-station corrections are smoothed using a similar expansion, in order that the two data sets can be compared.Correlations between P-station corrections, δt_P, and synthetic S-station corrections, δt_S relevant to various depths of integration indicate that a station correction contains information about structures down to at least 670 km. For this depth of integration, the correlation coefficient of the two data sets is 0.59; the slope ‘a’ of the relation δt_S = aδt_P + b, obtained for the worldwide distribution of stations, is in good agreement with results of previous regional studies using direct readings of P and S arrival times (a = 3.61 ± 0.13).An analysis of regional variations of the relation δt_S = aδt_P + b is carried out on the basis of two published global tectonic patterns (Okal; Jodan). Results for oceanic regions are not reliable, due to the lack of data. On continental areas, a significant difference appears between mountains (a = 2.7 ± 0.3) and shields (a = 4.5 ± 0.4 for Okal's pattern, a = 5.7 ± 1.5 for Jordan's pattern). The largest a-value for shields rules out an explanation by partial melting, as proposed in previous studies. Thermal heterogeneities lead to low a-values; undulations of the lithosphere-asthenosphere boundary appear to be the most feasible explanation of the high slope beneath shields; they are also able to explain the range of variation of the station corrections; the lowest values of the station corrections correspond to a total vanishing of the low velocity zone beneath the oldest shields. For mountains, the mean values of the station corrections as well as the low a-value can be accounted for by a slight increase of Poisson's ratio together with a significant density increase.     

Investigations on cosmic-ray-produced nuclides in iron meteorites, 3. Exposure ages,meteoroid sizes and sample depths determined by mass spectrometric analyses of potassium and rare gases

Three physical quantities define the essentials of the cosmic ray exposure history of a sample of an iron meteorite: (1) the cosmic ray exposure age T, (2) the pre-atmospheric “size” S of the irradiated body, and (3) the location, i.e. the “depth” D, of the samples within the body. To establish these quantities for a given sample three independent quantities must be determined experimentally. In the present work T is ascertained by the ⁴¹K/⁴⁰K method and the ⁴He and ²¹Ne concentrations (C₄ and C₂₁) are measured by the isotope dilution method. Signer and Nier's evaluation of the rare gas distribution in the meteorite Grant and the measured exposure age for this meteorite provide the relationships allowing to ascertain for any meteorite the quantities S and D from the ²¹Ne production rate (P₂₁ = C₂₁/T) and the ⁴He/²¹Ne ratio.Earlier measurements have provided data on the isotopic composition of potassium in 74 different iron meteorites. New rare gas measurements are reported for some 40 samples. Results on the age, size and depth are obtained for almost 60 samples. These data suggest that Signer and Nier's model is well suited for describing not only the rare gas distribution in a single selected meteorite (Grant) but also the exposure histories of the great majority of all irons. For a few samples, however, secondary breakups of the meteoroid and a two- or multiple-stage irradiation must be invoked. Further measurements are proposed for testing and, possibly, refining the still somewhat uncertain relationships between the abundances of cosmogenic nuclides and the quantities T, S, and D in very large meteorites.Histograms are presented showing the age distributions for irons of different chemical groups and of different size ranges.The feasibility and the relative merits of other methods for the determination of T, S, and D are discussed.     

THEORETICAL RESISTIVITY SOUNDING RESULTS OVER A TRANSITION LAYER MODEL *

An earth model with a transition layer (anisotropic inhomogeneous) is considered. The inhomogeneity in σ_v (vertical conductivity) of the transition layer is represented by a power law variation. Expressions for potential distribution in the upper layer, transition layer and bottom layer are obtained by solving appropriate differential equation for each layer. By utilizing the boundary conditions, expressions of apparent resistivity for Wenner and Schlumberger configurations are derived. Numerical analysis is performed for linear and quadratic variation of σ_v. The results are presented in the form of theoretical apparent resistivity curves for both configurations. Negative apparent resistivities are the interesting feature of this analysis.     

The effect of interstitial gaseous pressure on the thermal conductivity of a simulated Apollo 12 lunar soil sample

The thermal conductivity of a simulated Apollo 12 lunar soil sample was measured with a needle probe under vacuum. The result showed that the sample, with bulk densities of 1.70–1.85 g cm^?3 held in a vertical cylinder (2.54 cm in diameter and 6.99 cm long) has a thermal conductivity ranging from 8.8 to 10.9 mW m^?1 K^?1. This is comparable to the lunar regolith's thermal conductivity as determined in situ. Besides the dense packing of the soil particles, an enhanced intergranular thermal contact, due to the self-compression of the sample, is necessary to raise the sample's thermal conductivity from the level of loose soil (< 5 mW m^?1 K^?1) to that of the lunar regolith deeper than 35 cm (～ 10 mW m^?1 K^?1). A model of the lunar regolith, a thin layer of loose soil resting on a compacted self-compressed substratum, is consistent with the lunar regolith's surface structure as deduced from an observation of the lunar surface's brightness temperature. Martian regolith surface structure is similar, except that its surface layer may be missing in places because of aeolian activity. Measurements of thermal conductivity under simulated martian surface conditions showed that the thermal properties of loose and compacted soils agreed with the two peak values of the martian surface's thermal inertia as observed from “Viking” orbiters, suggesting that drifted loose soil and exposed compacted soil are responsible for the bimodal distribution of the martian surface's thermal inertia near zero elevation. For compacted soil exposed to the martian surface to have the same thermal conductivity as that buried under the surface layer, a cohesion of the soil particles must be assumed.     

A compact representation of magnetotelluric responses for two-layer models

In this paper the locations where ρ_app = ρ₁ and ? = π/4 and where these parameters reach an extreme value in two-layer magnetotelluric (MT) sounding curves are summarized in an extremely compact form. The key parameters over two-layer models with conductivities σ₁, σ₂ and upper layer thickness h are the real S and α, where S is the conductivity contrast and α is the distance between the observation site and the conductivity interface, normalized to the half skindepth in the first layer. If the impedance components, various resistivity definitions ( ρ_{Re Z}, ρ_{Im Z} and ρ_|Z|, based on different parts of the complex impedance Z ) and the magnetotelluric phase ? are derived as a function of S and α, then the conditions for the apparent resistivity ρ_app and the phase ? are that they either satisfy ρ_app = ρ₁ and ? = π/4 or attain extreme values which can be given in terms of simple algebraic equations between S and α. All equations are valid for observation sites at any depth 0 ≤ z ≤ h in the first layer. The set of equations, presented in a tabular form, may make it possible to determine a layer boundary from the short period part of the sounding curves, in particular the ρ_{Re Z} and the ?_MT curves.     

Moment tensor inversion and source rupture process of the September 27, 2003 <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>=7.9 earthquake occurred in the border area of China,Russia and Mongolia

We conducted moment tensor inversion and studied source rupture process for M _S=7.9 earthquake occurred in the border area of China, Russia and Mongolia on September 27 2003, by using digital teleseismic P-wave seismograms recorded by long-period seismograph stations of the global seismic network. Considering the aftershock distribution and the tectonic settings around the epicentral area, we propose that the M _S=7.9 earthquake occurred on a fault plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of M _S=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tensor is M ₀=0.97×10²⁰ N·m. Rupture mainly occurred on the shallow area with 110 km long and 30 km wide, the location in which the rupture initiated is not where the main rupture took place, and the area with slip greater than 0.5 m basically lies within 35 km deep middle-crust under the earth surface. The maximum static slip is 3.6 m. There are two distinct areas with slip larger than 2.0 m. We noticed that when the rupture propagated towards northwest and closed to the area around the M _S=7.3 hypocenter, the slip decreased rapidly, which may indicate that the rupture process was stopped by barriers. The consistence of spatial distribution of slip on the fault plane with the distribution of aftershocks also supports that the rupture is a heterogeneous process owing to the presence of barriers.     

Density profile and modern crustal and uppermost mantle geotherm of the Voronezh crystalline massif

A density profile and a modern temperature distribution in the lithosphere of the Voronezh crystalline massif (VCM) are derived through the use of the V_P(z), V_S(z) seismic velocity models, petrological data, measurements of V_P, V_S, density (ρ) and mean atomic weight ($\text{m}$) for several groups of rocks and minerals of different composition and genesis, as well as from pressure and temperature derivatives for different thermodynamic regimes.     

Electrical conductivity of molten FeNiSC core mix

The electrical conductivity of liquid (Fe₉₀Ni₁₀)₃S₂ saturated with 2.6 weight percent carbon averages 2.7·10⁵ mho/m at 1000°C and zero pressure. This may imply a slightly lower electrical conductivity for the earth's core than that obtained by extrapolating the properties of pure liquid iron and solid iron alloys to core pressures and temperatures. Although a sulphur-rich core would have a smaller proportion of sulphur, the effect of lowering the sulphur content of the FeNiSC liquid to about 15 weight percent would be unlikely to increase the conductivity above 5·10⁵ mho/m.     

Malleable disc base for direct infiltration measurements using the tension infiltrometry technique

The correct use of the tension disc infiltrometer requires the membrane of the disc base to be completely in contact with the soil surface. To achieve this contact, a thick layer of sand is commonly placed between the soil surface and the disc base. This paper presents an alternative disc (M_DB), which, by incorporating a malleable membrane, allows direct infiltration measurements without using a contact sand layer. Infiltration curves obtained with this new design in a soil under three different tillage management treatments were compared with the corresponding curves obtained with a conventional disc (C_DB) that uses a contact sand layer. The cumulative infiltration curves measured with C_DB were analysed by the differentiated linearization (DL) method, and the corresponding curves obtained with M_DB were analysed using both the DL and the cumulative linearization (CL) models. The values of hydraulic conductivity (K₀) and sorptivity (S₀) estimated with C_DB were also compared with those obtained with M_DB. Finally, the cumulative infiltration curves measured with C_DB and M_DB were compared with the corresponding modelled function for the respective K₀ and S₀ values calculated with the CL and DL models. The results show that, compared with C_DB without a contact sand layer, M_DB allows complete soil surface wetting even when non‐smoothed soil surfaces are used. The C_DB, which yielded average K₀ values 18% lower than those estimated with M_DB, gave the highest values of standard error for the hydraulic parameters calculated. Furthermore, the subjective method employed in the C_DB‐DL technique, which requires the first points of the differential infiltration line corresponding to the sand layer to be manually removed, introduces additional uncertainties in estimating S₀ and K₀. Comparison between the modelled and measured infiltration curves demonstrates that the DL or CL methods applied to M_DB gave excellent estimates of S₀ and K₀. Copyright © 2012 John Wiley & Sons, Ltd.     

Inhomogeneous structure of the Voronezh shield lithosphere from explosion seismology data

This paper presents the results of a seismological investigation of the Voronezh shield. The use of industrial quarry blasts, as the most economic seismic energy source, and telemetric arrays of the Taiga type for deep seismic sounding observations has enabled the Geophysical Research Group of the Voronezh State University to obtain complete and valid information concerning the deep structure of the shield.Seismic records of refracted and reflected P and S phases from the intracrustal and subcrustal discontinuities allow the determination of independent and compatible velocity models V_P(Z) and V_S(Z).Analysis of the travel-time and amplitude curves derived from the deep seismic sounding data reveals a complex and inhomogeneous structure of the Voronezh shield lithosphere. The major discontinuities are found in the middle part of the consolidated crust. Several rather thick layers can be resolved, which are separated by first-order seismic boundaries.In the consolidated crust beneath the southeastern part of the shield at depths from 6–7 to 11–13 km, a low-velocity layer is clearly established from the compressional wave data. Within the low-velocity channel, V_P appears to decrease by 5–6%. The low-velocity channel in the uppermost consolidated crust is assumed to be due to metamorphogeneous granitization. This is revealed by the Precambrian basement structure.Poisson's ratio calculated from the compatible velocity models V_P(Z) and V_S(Z) shows a systematic increase down to the crustal basement and becomes discontinuous only in the low-velocity channel. At the top of the mantle, Poisson's ratio decreases on all the deep seismic sounding profiles. The systematic variation of Poisson's ratio is related to changes in the composition and mineralogy of the Voronezh shield lithosphere.     

Conductivity as a predictor of a total cations and salinity in Ethiopian lakes and rivers: revisiting earlier models

We used regression analyses of water samples from 18 lakes, nine rivers, and one spring in Ethiopia to (a) test the hypothesis that water bodies of relatively higher salinity (K₂₅>1000 μS cm⁻¹) have a different conductivity to salinity relationship than waters of lower salinity (K₂₅ < 1000 μS cm⁻¹), and (b) develop models to predict total cations and salinity from conductivity that can be used for Ethiopian waters and other African aquatic systems of similar chemical composition. We found no statistical difference in the bilogarithmic relationships (total cations vs. conductivity; salinity vs. conductivity) for waters of higher salinity (K₂₅ > 1000 μS cm⁻¹) and waters of lower salinity (K₂₅ < 1000 μS cm⁻¹). However, comparison among our models and models from the literature suggests that developing separate equations for low and high salinity water bodies has some merit. We believe that the equations developed in this study can be used for Ethiopian waters and other African waters within the range of conductivity in this study.     

Regional induction studies: A review of methods and results

The geomagnetic skin-effect is specified by setting three length scales in relation to each other: L₁ for the overhead source. L₂ for the lateral non-uniformity of the subsurface conductor, L₃ for the depth of penetration of a quasi-uniform transient field into this conductor. Relations for the skin-effect of a quasi-uniform source in layered conductors are generalized to include sources of any given geometry by introducing response kernels as functions of frequency and distance. They show that only those non-uniformities of the source which occur within a distance comparable to L₃ from the point of observation are significant. The skin-effect of a quasi-uniform source in a laterally non-uniform earth is expressed by linear transfer functions for the surface impedance and the surface ratio of vertical/horizontal magnetic variations. In the case of elongated structures and E-polarisation of the source, a modified apparent resistivity is defined which as a function of depth and distance gives a first orientation about the internal distribution of conductivity. The skin-effect of a non-uniform source in a non-uniform earth is considered for stationary and “running” sources. Recent observations on the sea floor and on islands indicate a deep-seated change of conductivity at the continent—ocean transition, bringing high conductivity close to the surface, a feature which may not prevail, however, over the full width of the ocean. There is increasingly reliable evidence for high conductivities (0.02 to 0.1 micro ^?1 m^?1) at subcrustal or even at crustal depth beneath certain parts of the continents, in some cases without obvious correlation to geological structure.     

Time-dependent electromagnetic core-mantle coupling

The magnetic field in the Earth's mantle is computed using a depth-dependent electrical conductivity, of form σ = σ_a(r/a)^?α, and an approximation scheme in which the electromagnetic time constant of the mantle is assumed small compared with the time scales of the secular variation, and in which the induced currents and fields are obtained iteratively. We first associate the toroidal fields in the mantle with motions at the core surface (r = a) which create the observed geomagnetic field by flux rearrangement, and compute the resulting couple, Γ, parallel to the geographical axis. Using only zonal core motions, and values σ_a = 3 × 10³ω^?1m^?1, α = 30 for the conductivity profile, we find that the toroidal induced fields create a couple, Γ_T, that over most of this century has been roughly ten times greater than the poloidal part, Γ_S, of Γ, and has the same sign. The total couple, Γ, has fluctuations of order 10¹⁸ Nm as required for the observed decade fluctuations in the length of the day. Its average is ～ ?1.5 × 10¹⁸ Nm, i.e., it is too large to remain unbalanced. We suppose that an equally important couple in the opposite sense is created by flux leakage from the core, and we estimate the necessary gradient of toroidal field in the core to be of order ?0.5 Gs km^?1 at the core surface. During the course of the data analysis needed for the present work, we found some evidence for a torsional wave in the Earth's core with a period of ～ 60 y.