REFRACTION LE LONG DES BANCS MINCES RAPIDES ET EFFET D'ECRAN POUR LES MARQUEURS PROFONDS *

Refraction along thin high velocity layers and along basement is investigated in two cases. a) high velocity layer just on the basement. b) high velocity layer higher above. Period and attenuation of refracted waves are givers as a function of the layer thickness H. Refracted arrivals along thin high velocity layers are visible at significant distances if the layer thickness is not smaller than A/6, where A is the longitudinal wavelength in high velocity medium. The pseudoperiod is proportional to the layer thickness H. The attenuation at large distance follows an x^-ne^-k1x law, where n is close to I and k₁ is inversely proportional to H. Refracted arrivals along the basement are observable even in the case of thin high velocity layers situated in the overburden; their intensity is smaller and their pseudo-period larger than when no layer exists in the overburden. The intensity of the basement arrival decreases and the pseudoperiod increases with increasing layer thickness. The pseudoperiod and the attenuation of refracted arrivals along high velocity layers and along the basement are also highly dependent on acoustic contrasts. Both arrivals from a high velocity layer and from the basement can be recorded simultaneously, provided the frequency spectrum of the seismic chain is sufficiently broad. In all cases layer arrivals show a character very different from basement arrivals.     

INDUCTIVE SOUNDING OF A STRATIFIED EARTH WITH TRANSITION LAYER RESTING ON DIPPING ANISOTROPIC BEDS *

The generalised three layer boundary value problem with a transition layer sand-witched between an isotropic overburden and dipping anisotropic substratum is discussed assuming that plane electro-magnetic waves are incident normally over the air-earth inter-face. The tangential electric (E_y) and magnetic (H_x) fields and the expression for surface-impedance (E_y/H_x) have been evaluated at the earth's surface. Through numerical analysis it is shown that changes in the values of the parameters m (coefficient of anisotropy), h (thickness of the transition layer), α (angle of inclination of the dipping beds), and b (conductivity ratio between substratum and upper layer) modify the amplitude and phase-variation curves (with skindepth) significantly.     

Two field applications of the rotating current EM method1

The rotating current EM method has been applied to the delineation of two conductive orebodies, Elura near Cobar, NSW, and Thalanga near Charter's Towers, Queensland. The field data were collected in the form of observations of the vertical magnetic field strength ratio and phase difference using a Turam-style receiver with twin vertical coils. By reconstituting this data back to the ring source field and phase, i.e. the observed H_z, phasor, it is possible to present contoured maps of the EM field. Anomaly phasors are obtained by subtracting theoretical phasors from the observed phasors in the complex plane of the H_z phasor. The theoretical phasors for the finite source are based on horizontally layered, half-space earth models, computed at each point of the survey grids, then normalized to selected points of the observed fields. Use is made of the intrinsic circular symmetry of the method in X–Y plots of field versus source-receiver distance to ascertain geoelectric parameters for the earth models. A steel picket fence at Thalanga is modelled by a line source grounded at each end and its H_z, phasor is removed by the same process. A considerable improvement in anomaly delineation is gained over previous Turam-style anomalies and the two survey examples illustrate the limitations of the method in the presence of a conductive overburden (Elura) and its abilities in the absence of a conductive overburden (Thalanga).     

Estimation of sedimentary layer shear wave velocity using micro-tremor H/V ratio measurements for Bangalore city

For assessing earthquake hazard of metro cities, knowledge of soil amplification, thickness and properties of sedimentary layer are essential. In order to map the soil thickness using microtremor survey method, in Bangalore city, it is required to calibrate the relation between fundamental resonance frequency of the soil layer and its thickness for the region. For this purpose microtremor survey was carried out at 34 locations in the city where borehole log was available. The resonance frequency of the soil is evaluated from the microtremor recordings using the H/V ratio technique. A nonlinear regression relation between the thickness of sedimentary layer h (m), from the borehole logs, and the resonance frequency f_r (Hz), was derived as h=(58.3±8.8)f_r^{−(0.95)±0.1}. Using the model of shear wave velocity increasing with depth at these locations, the derived average shear wave velocity and the corresponding soil thickness were used, to get an empirical relation between V_S (m/s) and depth z(m), as V_s=(174±28)(1+z)^0.16±0.07. This relation also compares reasonably with the fit obtained between simulated V_S and depth from borehole logs for Bangalore city. The calibrated relations can be used at locations in Bangalore city where borehole logs are not available, for finding the thicknesses and shear wave velocities of the local soil layers at the survey locations.     

MAGNETOTELLURIC RESPONSE ON VERTICALLY INHOMOGENEOUS EARTH HAVING CONDUCTIVITY VARYING LINEARLY WITH DEPTH*

Magnetotelluric response is studied for an inhomogeneous medium having conductivity varying linearly with depth as σ(z) =σ₁+αz. For a medium having conductivity increasing linearly with depth, the phase of the impedance approaches 60° at long periods and the apparent resistivity becomes log (ρ_a) = 2 log (1.36/α^1/3) — 1/3 log (T'). The asymptote of log (ρ_a, T'→∞) when plotted against log (T') has a constant gradient —1/3 and has an intercept on the log (T') axis, which equals 6 log (1.36/α^1/3). When a homogeneous layer with a moderate thickness overlies an inhomogeneous half-space, this layer does not affect the asymptote, but it affects the cut-off period and pushes this toward the long period direction. For a medium having conductivity decreasing linearly with depth, the impedance is equivalent to that of a Cagniard two-layer model; the intercept period related to the thickness is T'₀=σ₁(h₂/2)². Homogeneous multilayer approximations to an inhomogeneous layer are also investigated, and it is shown that the fit to the model variation depends on the number of layers and the layer parameters chosen.     

ELECTROMAGNETIC FIELDS DUE TO A THIN RESISTIVE LAYER*

Using approximate boundary conditions, expressions for electromagnetic fields have been derived for a thin, highly resistive layer lying between two homogeneous layers excited by an electric dipole grounded on the surface of the earth. The variations of the fields with the parameter T/T₁ (ratio of the transverse resistance of the thin layer to the transverse resistance of the first layer) were studied in relation to frequency, time, the normalized separation source—receiver, and the angle between the source and the radius to the observation point. For a value of h₂/h₁ (ratio of thickness of second layer to the thickness of the first layer) approximately equal to 0.2, the general three-layer medium case gives the same results as this approach. It was found that the electric fields have a very strong dependence on the parameter T (transverse resistance) which characterizes the thin, highly resistive layer. However, the magnetic fields depend only very weakly on this parameter.     

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.     

APPROXIMATE INVERSION OF AIRBORNE EM DATA FROM A MULTILAYERED GROUND1

A complex transfer function c (or generalized skin depth) can be derived from data for the secondary magnetic field measured by a dipole system with small coil spacing at height h above the ground. This function has a useful property: For a uniform or layered ground, the real part of c yields the‘ centroid depth’z* of the in-phase current system as a function of frequency. This parameter can be combined with the apparent resistivity ρ_a derived by conventional methods. The function ρ_a(z*), if known over a broad frequency range, yields a smoothed approximation of the true distribution ρ(z) without an initial model. The relations between ρ_a(z*) and ρ(z) are studied for a number of multilayer models. An example of the application of the ρ_a*) algorithm to data from a groundwater survey is given.     

Finite-amplitude mountain waves in a compressible atmosphere including the effects of dissipation

Abstract

Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height z_c. The height z_c , where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above z_c. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to values inferred from radar measurements of the stratosphere.

The Fourier spectrum of the solution for z ≫ z_c is shown to decay exponentially at large vertical wave numbers n. In comparison, a spectral decay law n ^?-8/3 characterizes the marginal state of the wave at z = z_c .     

MEASURED UNDERWATER NEAR-FIELD E-PATTERNS OF A PULSED,HORIZONTAL DIPOLE ANTENNA IN AIR: COMPARISON WITH THE THEORY OF THE CONTINUOUS WAVE,INFINITESIMAL ELECTRIC DIPOLE1

At Delft Geotechnics the technique of ground-penetrating radar is in use for the detection of buried objects such as pipes. To enable us to give our ‘measurements in the field’ a more quantitative interpretation than can be deduced from these alone, a series of experiments has been started under well-defined conditions. A cylindrical vessel containing water simulates wet soil. Mounted horizontally above the water surface is a pulsed triangular half-wave dipole which is used as a transmitting antenna (TA). It has a carrier-frequency of about 160 MHz and a pulse repetition-frequency of about 50 kHz. A movable receiving dipole (‘probe’) in the water measures the transverse, mutually orthogonal E_φ,- and E_θ-components of the pulses as a function of probe-position (r, θ, φ) and of the height h of the TA above the water surface. When these pulses are Fourier-transformed, the transverse electric fields E_φ and E_θ at 200 MHz are obtained. The resulting field patterns are compared with computational results on the basis of the theory of the continuous wave, infinitesimal electric dipole (‘point dipole’). It can be concluded that:

• 1 Far-field conditions have not fully developed at a depth of about 2.50 m, the largest value of the radius r at which field patterns were measured, although it represents a distance of about 15 wavelengths.
• 2 The attenuation constant of the tapwater used, as deduced from E-field measurements for θ= 0, 2.50 m < r < 2.75 m, is slightly less than the value measured using a network analyser and air line combination, in agreement with (1).
• 3 E _φ field patterns calculated using the value of the conductivity σ corresponding to the former value of the attenuation constant agree reasonably well with the measured patterns for r≤ 2.50 m and for θ < 20° at all antenna heights considered. Calculated Eφ patterns do not agree so well with the measured patterns when h is close to zero. With increasing height the agreement inproves.
• 4 In accordance with the theory of the point-dipole, the angular distribution of the radiation patterns of the TA becomes wider as the frequency decreases.
• 5 The normalized underwater pulse-spectra shift to lower frequencies with increasing r. This can be explained since the attenuation constant of the water rises with rising frequency.

     

QUASI-ANALYTIC CONVOLUTION SOLUTION OF THE ELECTROMAGNETIC FIELD*

The objective of this study is to generate the separation-distance-domain (r-domain) transformation of the theoretically calculated wave number domain (m-domain) electromagnetic induction field component B_z(m, ω) of a stratified medium and to search for interpretive information which has been absent in the previously achieved numerical solutions of the problem. The r-domain kernel R?(r, ω) function defining the induction field appears to adequately reflect the layering and electrical properties of the medium if it is expressed as a function of the frequency if the source-receiver separation r is small with respect to the thickness of the first layer. However, exact values of the conductivity cannot be distinguished from those of the neighboring values unless a resistive basement layer is present. This feature is the result of the truncation in series representation of the kernel function R?(m, ω). However, this truncation is regarded as significant in the case of a conductive first layer. In m-domain static-zone studies, a conductive first layer slightly influences its r-domain correspondent. Although the computational cost of obtaining the kernel B(r, ω) by evaluation of the convolution in a cylindrical coordinate system is high, this semi-analytic solution is still superior to those based on the asymptotic assumptions.     

Seismic prospection by Wiechert-Herglotz method of calculus

Summary TheWiechert-Herglotz method to investigate seismically the Earth structure, is adapted for refraction prospecting. The case of a single layer bounded by a sloping interface is considered. The velocity is assumed to be an increasing function of depth within the layer and constant beneath. A general procedure of computation is outlined. Special formulae are given in addition for the case in which the dromochroneD ₁ corresponding to disturbances propagated only through the layer are of parabolic shape. Table I was calculated using them and assuming an horizontal interface. It may be seen there that valuesh ₁ of the layer thickness furnished by these formulae may become considerably greater than those based on D₁ rectilinear. Computation ofh ₁ may easily be performed by means of the same table.     

基于典型地质特征分析的大同盆地VS30预测研究

土体剪切波速是进行土层地震反应分析的动力学参数，对场地地震动参数确定具有重要意义。基于地质地貌分析，将大同盆地划分为5类典型地质单元。对盆地1429个钻孔剪切波速资料进行分析，探讨V_S30与V_S20的相关性，研究土体埋深、岩性、地质单元、标贯击数及密实度等地质特征对V_S的影响，并基于地质单元、剪切波速比、密实度系数及第四系上部覆盖层厚度相关性分析给出土体V_S30预测模型。研究结果表明，基于典型地质特征的V_S30预测模型拟合优度R2>0.90，预测精度很高，对于离散性较大、直接拟合估算较差及无剪切波速场地来说，以区分地质单元及土体类型的方式进行V_S30分解预测是良好的研究思路。首次在区分地质单元及土体类型的前提下提出剪切波速比及密实度系数，并将其与第四系上部覆盖层厚度综合应用于V_S30预测研究。研究结果可为大同盆地城市防震减灾规划、震害预测、区域性地震安全评价提供重要技术支撑。     

A statistical model of the geomagnetic field

Summary A statistical model of the geomagnetic field is derived, based on the assumption of an axial geocentric dipole field of strengthH _e at the equator perturbed by randomly directed components of constant magnitudeh. The model fits the dispersions found from an analysis of the 1945 field, and the ratioh/H _e obtained for this field and from the palaeomagnetic data both average to about 0.4. The model predicts that during reversal of the dipole field, the field intensity falls to between 0.2 and 0.4 of the steady field intensity, and this agrees with estimates made from the palaeomagnetic observations.     

Nearshore circulation over transverse bar and rip morphology with oblique wave forcing

There is a paucity of field data to describe the transition in nearshore circulation between alongshore, meandering and rip current systems. A combination of in‐situ current meters and surf zone drifters are used to characterize the nearshore circulation over a transverse bar and rip morphology at Pensacola Beach, Florida in the presence of relatively low energy oblique waves. Current speeds vary in response to the relative wave height ratio (H_s/h), which defines the degree and extent of breaking over the shoal. In the absence of wave breaking the nearshore circulation was dominated by an alongshore current driven by the oblique waves. As waves begin to break across the shoal (0.2<H_s/ h<0.5) the nearshore circulation is characterized by a meandering alongshore current. As conditions became more dissipative (H_s/h>0.5), the meandering current is replaced by an unsteady rip circulation that moves offshore between the shoals before turning alongshore in the direction of wave advance outside the surf zone. The increase in wave dissipation is associated with an increase in very low frequency (VLF) variations in the current speed across the shoal and in the rip channel that caused the circulation to oscillate between an offshore and an alongshore flow. The unsteady nature of the nearshore circulation is responsible for 55% of all surf zone exits under these more dissipative conditions. In contrast, only 29% of the drifters released from the shoal exited the surf zone and bypassed the adjacent shoal with the alongshore‐meandering current. While the currents had a low velocity (maximum of ~0.4 m s^‐1) and would not pose a significant hazard to the average swimmer, the results of this study suggest that the transverse bar and rip morphology is sufficient to create an alongshore variation in wave dissipation that forces alongshore meandering and low‐energy rip circulation systems under oblique wave forcing. Copyright © 2013 John Wiley & Sons, Ltd.     

Internal waves in a randomly stratified fluid

Abstract

We discuss the propagation of internal waves in a rotating stratified unbounded fluid with randomly varying stability frequency, N. The first order smoothing approximation is used to derive the dispersion relation for the mean wave field when N is of the form N ² = N _o ²(1 + ?μ), where μ is a centered stationary random function of either depth (z) or time (t), N _o = constant and O < ?² ≦ 1. Expressions are then derived for the change in phase speed and growth rate due to the random fluctuations μ; in particular, attention is focused on the behaviour of these expressions for short and long correlation lengths (case μ = μ(z)) and times (case μ = μ(t)). For the case μ = μ(z), which represents a model for the temperature and salinity fine-structure in the ocean, the appropriate statistics of the fluctuations observed at station P (50°N, 145°W) have been incorporated into the theory to estimate the actual importance of the effects due to these random fluctuations. It is found that the phase speed of the mean wave decreases significantly if (i) the wavelength is short compared to g/N_o ² or (ii) the wave number vector is essentially horizontal and the wave frequency is very close to N _o. Also, the random fluctuations cause a significant growth (decay) in the amplitude of a wave propagating upwards (downwards) through a depth of a few kilometers. However, in the direction of energy propagation, the kinetic energy is conserved. Finally, it is shown that the average effect of the depth dependent fluctuations at station P is to slightly decrease the stability frequency and the magnitude of the group velocity.     

Tidal mixing in sill regions: influence of sill depth and aspect ratio

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (h _s) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number F _r as the sill depth (h _s) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U _s due to increased depth. Calculations show that the sill Froude number F _s based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F _s (namely F _s ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high F _s, calculations with a narrow sill show that for a given F _s value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant U _s show that for small values of h _s, a near surface mixed layer can occur on the downstream side of the sill. For large values of h _s, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of h _s, “internal mixing” dominates the solution and controls across thermocline mixing.     

THE INDUCTIVE RESPONSE OF A HORIZONTAL CONDUCTING CYLINDER BURIED IN A UNIFORM EARTH FOR A UNIFORM INDUCING FIELD*

The inductive response of a conducting horizontal cylinder embedded in a uniform earth is studied using numerical results obtained for an analytical solution for the problem of a conducting cylinder buried in a homogeneous earth for the case of a uniform inducing field. A check of the validity of the numerical results is made by a comparison with analogue model measurements for a number of cases. Numerical results for a range of cylinder radii (a = 1–10 km), depths of burial (d= 0–4 km), conductivity contrasts (σ₂= 10^?2-10 Sm^?1), and source frequencies (f= 10^?1-10^?4 Hz) of interest in the interpretation of magnetotelluric field measurements are presented. The results indicate that for a uniform inducing field the conductivity and depth of burial of a horizontal cylindrical inhomogeneity are best determined through a measurement of the amplitudes H_y, H_z and E_x and the phases φ_y and Ψ_x.     

NUMERICAL VLF MODELING*

The VLF response of laterally inhomogeneous and anisotropic models is calculated numerically using the finite element method. Some results are presented for a slab model in terms both of the polarization parameters, i.e., the tilt angle and ellipticity of the magnetic polarization ellipse, and the amplitude ratio |H_z/H_x|. On the basis of both the ellipticity and the tilt angle, it is possible to discriminate between a poor conductor and a good one. The direction of the dip can be determined from the anomaly profiles of all diagnostic parameters. The effect of the conductive overburden is most noticeable on the ellipticity profile: one observes attenuation for a poor conductor and “negative attenuation” for a good conductor. The anomaly profiles for anisotropic cases are consistent with the ones of the isotropic cases.     

A role of the altitude gradient of the thermospheric wind velocity in ionospheric <Emphasis Type="Italic">F</Emphasis>-region dynamics

By processing the data of vertical ionospheric sounding in Almaty for 2000–2009, we obtained the distributions of the heights of the maximum (h _m F) and bottom (h _bot F) of the F2-layer, incremental changes in its semi-thickness (δh), the characteristic time of losses (τ), and the vertical displacement velocity of the node of the thermospheric wind (V) during the transitional time of the day during nighttime increases in the electron concentration at the layer maximum. The comparison of the measured V and modeled V _m velocities showed a certain discrepancy. The influence of the altitude gradient of the meridional thermospheric wind velocity on the behaviors of h _m F, h _bot F, δh, and τ during nighttime increases in the electron concentration is studied.