The viscous damping of internal waves on the rotating earth

Summary A formula is derived for the spatial attenuation of the two possible modes of oscilation of a two-layer, rotating system. If the long-wave approximation is made, it is found with reference to the internal mode that this formula disagrees with an earlier result obtained byRattray [8]²).     

Relative performances of central and dipole frequency soundings over a layered earth

Variable frequency soundings in the audio-range replaces shallow conventional direct current methods for determination of layer parameters when surface layer resistivity is high. Central frequency soundings (CFS) is one such method that involves measurement of the existing vertical magnetic field component induced at the centre of a horizontal circular or square loop. Dipole method of frequency sounding using small horizontal coplanar loops (abbreviated DFS) measuring the same field component is also considered. Theoretical studies on CFS and DFS over two- and three-layer horizontally stratified earth are carried out and the response characteristics computed and analysed.Theoretical response curves for CFS and DFS over two- and three-layer earth models are presented in convenient forms. Response curves under similar geological-physical conditions are compared. The study indicates that the relative superiority of a method is controlled largely by the nature of the conductivity contrast and the ratio of the first layer thickness to loop radius or dipole separation. While CFS shows a better resolution of conductivity contrast, DFS works better at high frequencies. For resistive substratum, however, both lack proper resolution.     

Magnetovariational information to improve distortion diagnostics in deep magnetotelluric soundings

An interpretative experience from nine magnetotelluric soundings was accomplished in the central region of Argentina (32°S?C34°S; 63°W?C69°W), from the Andean region in the west to the platform zone in the east. To do this, magnetovariational information was used to improve the distortion diagnostics in magnetotelluric curves. Using Pilar Geomagnetic Observatory as a reference site, horizontal magnetic transfer functions were estimated, which were compared with the integrate conductivity at each location in field. As a result, a rather simple methodology is proposed to better approach the accurate positions of normal curves. Results suggest that, in this way, better formal interpretations of soundings may be reached. In addition, a more clear and comprehensible knowledge about the nature of lateral in-homogeneities is obtained; e.g., discovering 3-D effects no suspected from tectonic maps. This methodology seems to be particularly useful when-as in the present case-magnetotelluric soundings are far away each others; i.e., when effective volumes of soundings are not interpenetrated. Horizontal magnetovariational information suggests two elongate conductivity anomalies (about N25°?C30°E), possibly associated with deep seated faults belonging to the South American regmatic network. These anomalies would be produced by partial melting in lower crust and possibly in the asthenospheric zone next to Andean Range. Another elongate anomaly (possibly of graphitic nature) is shown in the study region. It seems to be a marginal fault following the border between The Sierras Pampeanas dynamic zone and the South American craton. Magnetotelluric results indicate the study region can be considered as divided in a dynamic belt next to Andean Range and a cratonic zone eastward. The dynamic zone presents a well developed lower crust, with conductances ranging 300?C4300 Siemens and depths of about 20?C30 km. An asthenosphere close to the Andes with 1000 Siemens of conductance at 74 km depth is also observable. Heat flows of 63?C70 mW/m² are estimated next to Andes and 48 mW/m², eastward, close to South American platform. The cratonic zone presents a first conductive layer with a conductance of 270 Siemens underneath BUL sounding site, but it does not seem to present lateral development. An intermediate conductive layer is also present in this region, but it does not have so much development. Therefore, this layer would not have asthenospheric character; so, the lithosphere would be tied to upper mantle. Heat flows ranging 40?C35 mW/m² were estimated for this cratonic region.     

Results of deep seismic soundings along international profile VII in Czechoslovakia and poland

Summary The paper deals with the results of DSS measurements along international profile VII, carried out by Czechoslovak and Polish geophysicists in 1970 – 71. The profile situation is shown in Fig. 1. By 1971 part of the profile in the region of the Bohemian Massif between points 1 and 3 and in Poland between points 5 and 7 had been surveyed (Fig. 2). The seismograms were used to construct the travel-time curves of the fundamental types of waves P^K, P^M, P_n (Fig. 4). The mean velocities were computed from the travel-time curves of the reflected waves (P^M and P^K) and the refracted waves (P_g). Isolines of the mean velocities could be constructed for the region of the Bohemian Massif (Fig. 6). The velocity data found were used for the depth interpretation of the travel-time curves of the principal types of waves and to construct a seismic section (Fig. 8). In the region of the Pre-Sudeten block the thickness of the crust was found to be 34–37 km, and in the Sudeten it increased to 40 km. Towards the south the thickness of the crust gradually reduces to 30 km in the system of the Luice faults. In the Bohemian Cretaceous the thickness of the crust is about 30 km. Further to the south, in the region of the Moldanubicum, the thickness of the Earth's crust increases rapidly, and at the southern border of the Central Bohemian pluton it reaches values of about 42 km.     

Effect of earth tide on deep well water level

On the basis of the partial differential equations of the water level in a deep well that is affected by the bulk strain tide, the boundary conditions of permeating each other between aquifer and well are considered. The solutions of the equations have been obtained by the superposition principle, inpulse theorem and separation of the variations. Some suitable values are given to the parameters of well aquifer in the solutions. By means of the numerical calculation the relations among the well tide coefficients and phase lag phenomenon of response of the well level to earth tides is well interpreted. The parametric studies and the obtained graphs show that the more the radius of casing in a well, the porosity of an aquifer and the bulk compressibility for solid matrix of an aquifer, the less the transmissibility of an aquifer, then the less the tidal coefficient of well level, while the more the phase lag for well level to respond to the tide is. The response of the well level to the tide of longer period is better than the shorter period events. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 66–75, 1991.     

Introduction to deep earth electrical conductivity

Pure and Applied Geophysics -     

深地震测深揭示的华南地区地壳结构及其动力学意义

20世纪70年代以来,我国实施与华南地区有关的深地震测深剖面达57条.本文收集该区的深地震测深研究成果,利用保真能力强的三维克里金插值技术构建了100°E~125°E,18°N~34°N区域内的三维地壳速度模型.基于三维地壳结构模型,分别探讨了华南地区不同构造单元地壳厚度空间变化特征、地壳属性、上地幔顶部地震波速变化以及太平洋向欧亚板块的俯冲方向等.研究结果表明:(1)扬子地块平均地壳厚度为40 km左右,地壳平均速度为6.30 km/s;华夏地块平均地壳厚度32 km左右,地壳平均速度6.24 km/s.(2)扬子地块的四川盆地与全球地台区具有相似的地壳速度-深度变化特征,华夏地块与全球伸展区结构相似,台湾造山带具有较典型全球大陆弧的特点.(3)华夏地块上地幔顶部Pn波平均速度为8.02 km/s;台湾造山带Pn波平均速度为7.98 km/s;扬子地块的Pn波速度为7.94 km/s,包含四川盆地(Pn速度达8.02 km/s)和川滇地区(Pn速度最低为7.75 km/s).川滇地区和松潘—甘孜褶皱带东部构造活动性较强,四川盆地和华夏地块相对较稳定.(4)推测太平洋板块向欧亚板块俯冲的方向为NW-SE方向.     

Audiomagnetotelluric soundings on White Island volcano

Audiomagnetotelluric soundings in the frequency range 100-1 Hz have been made at three locations within the crater region of White Island volcano, New Zealand. Exceptionally low apparent resistivities are prevalent. Despite the possibility of terrain effects and static shift, and the three-dimensional nature of the island, the measured values appear to be indicative of the true electrical structure. One-dimensional modelling of the E polarisation responses has been used to obtain approximations to the electrical structure beneath each site. The results suggest a variable depth to the acid hydrothermal system which is believed to underly the crater region, with low resistivities coming closest to the surface near the active fumaroles of Donald Mound.     

Stresses in different rotating spherical earth models with rigid core

Summary A direct method has been applied in this paper to find the stresses in some steadily rotating, self-gravitating spherical earth models.     

Portable generator for deep electromagnetic soundings and monitoring of seismically active zones with the use of industrial power transmission lines

The structure and a possible practical application of the portable generator with extremely and super low frequency (ELF-SLF) range (0.1–200 Hz) and power of 2 kW are described. The generator is designed for deep sounding of the Earth’s crust for the purposes of mineral exploration and electromagnetic monitoring of source zones of earthquakes in seismically active regions. Computational and theoretical works, as well as numerical simulation for optimizing the generator’s parameters and element base, are carried out. The main constructive elements of the generator, namely, the power factor corrector, the driver control circuit for power transistors, the inverter of the high-frequency decoupling converter, the multichannel pulse power converter, the output inverter, and etc., are consistently described. The generator’s weight does not exceed 10 kg, and, therefore, the generator may be easily delivered to a testing site using any kind of transport, including planes. The generator is powered by the single-phase network with a voltage of 220 V. The full-scale testing of the generator is performed at the territory of the Yamalo-Nenets autonomous okrug via the connection to the high-voltage transmission line Urengoi-Pangody with a length of 114 km. The maximum current in the line is 12 A. The maximum distance of reliable signal recording is 110 km.     

On some effects connected with electromagnetic induction in a rotating earth

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Temperature profiles in the earth of importance to deep electrical conductivity models

Deep in the Earth, the electrical conductivity of geological material is extremely dependent on temperature. The knowledge of temperature is thus essential for any interpretation of magnetotelluric data in projecting lithospheric structural models. The measured values of the terrestrial heat flow, radiogenic heat production and thermal conductivity of rocks allow the extrapolation of surface observations to a greater depth and the calculation of the temperature field within the lithosphere. Various methods of deep temperature calculations are presented and discussed. Characteristic geotherms are proposed for major tectonic provinces of Europe and it is shown that the existing temperatures on the crust-upper mantle boundary may vary in a broad interval of 350–1,000°C. The present work is completed with a survey of the temperature dependence of electrical conductivity for selected crustal and upper mantle rocks within the interval 200–1,000°C. It is shown how the knowledge of the temperature field can be used in the evaluation of the deep electrical conductivity pattern by converting the conductivity-versustemperature data into the conductivity-versus-depth data.     

Propagator matrix formulation for earth currents of deep internal origin

Summary The problem of the distribution of the poloidal electric field in the mantle, originating from the core-mantle boundary, is formulated in terms of propagator matrices suitable for calculations for a wide variety of piece-wise continuous models of the mantle. The elements of the propagator matrix for some interesting variations of the electric conductivity are presented.     

Mathematical modeling of the influence of the coastal effect on marine magnetotelluric soundings

The influence of the coastal effect on bottom magnetotelluric soundings in the shelf zone is considered. For this purpose, the magnetotelluric field in a two-dimensional medium was mathematically modeled, and the model allowing the most effective calculations of the fields near the coastal line was chosen.     

Nonlinear dynamics of boussinesq convection in a deep rotating spherical shell-i

Abstract

Convection in a rotating spherical shell has wide application for understanding the dynamics of the atmospheres and interiors of many celestial bodies. In this paper we review linear results for convection in a shell of finite depth at substantial but not asymptotically large Taylor numbers, present nonlinear multimode calculations for similar conditions, and discuss the model and results in the context of the problem of solar convection and differential rotation. Detailed nonlinear calculations are presented for Taylor number T = 10⁵, Prandtl number P = 1, and Rayleigh number R between 1 |MX 10⁴ and 4 |MX 10⁴ (which is between about 4 and 16 times critical) for a shell of depth 20% of the outer radius. Sixteen longitudinal wave numbers are usually included (all even wave numbers m between 0 and 30) the amplitudes of which are computed on a staggered grid in the meridian plane.

The kinetic energy spectrum shows a peak in the wave number range m = 12–18 at R = 10⁴, which straddles the critical wave number m = 14 predicted by linear theory. These are modes which peak near the equator. The spectrum shows a second strong peak at m = 0, which represents the differential rotation driven by the peak convective modes. As R is increased, the amplitude of low wave numbers increases relative to high wave numbers as convection fills in in high and middle latitudes, and as the longitudinal scale of equatorial convection grows. By R = 3 |MX 10⁴, m = 8 is the peak convective mode. There is a clear minimum in the total kinetic energy at middle latitudes relative to low and high, well into the nonlinear regime, representing the continued dominance of equatorial and polar modes found in the linear case. The kinetic energy spectrum for m > 0 is maintained primarily by buoyancy work in each mode, but with substantial nonlinear transfer of kinetic energy from the peak modes to both lower and higher wave numbers.

For R = 1 to 2 |MX 10⁴, the differential rotation takes the form of an equatorial acceleration, with angular velocity generally decreasing with latitude away from the equator (as on the sun) and decreasing inwards. By R = 4 |MX 10⁴, this equatorial profile has completely reversed, with angular velocity increasing with depth and latitude. Also, a polar vortex which has positive rotation relative to the reference frame (no evidence of which has been seen on the sun) builds up as soon as polar modes become important. Meridional circulation is quite weak relative to differential rotation at R = 10⁴, but grows relative to it as R is increased. This circulation takes the farm of a single cell of large latitudinal extent in equatorial regions, with upward flow near the equator, together with a series of narrower cells in high latitudes. It is maintained primarily by axisymmetric buoyancy forces. The differential rotation is maintained at all R primarily by Reynolds stresses, rather than meridional circulation. Angular momentum transport toward the equator for R = 1–2 |MX 10⁴ maintains the equatorial acceleration while radially inward transport maintains the opposite profile at R = 4 |MX 10⁴.

The total heat flux out the top of the convective shell always shows two peaks for the range of R studied, one at the equator and the other near the poles (no significant variation with latitude is seen on the sun), while heat flux in at the bottom shows only a polar peak at large R. The meridional circulation and convective cells transport heat toward the equator to maintain this difference.

The helicity of the convection plus the differential rotation produced by it suggest the system may be capable of driving a field reversing dynamo, but the toroidal field may migrate with lime in each cycle toward the poles and equator, rather than just toward the equator as apparently occurs on the sun.

We finally outline additions to the physics of the model to make it more realistic for solar application.     

On the automatic interpretation of direct current resistivity soundings

A method for the automatic inversion of resistivity soundings is presented. The procedure consists of two main stages. First, application of linear filters which transforms the apparent resistivity curve into the kernel function, and vice versa. In the second stage the first and second derivatives of the kernel function are calculated and used in a second-order modified Newton-Raphson iterative fitting procedure. The model obtained is optimal in the least squares sense. The method has been tried on some field examples and produced resistivity models which show a good agreement with the geological well logs.     

Three-dimensional interpretation of TEM soundings

We describe the approach to the interpretation of electromagnetic (EM) sounding data which iteratively adjusts the three-dimensional (3D) model of the environment by local one-dimensional (1D) transformations and inversions and reconstructs the geometrical skeleton of the model. The final 3D inversion is carried out with the minimal number of the sought parameters. At each step of the interpretation, the model of the medium is corrected according to the geological information. The practical examples of the suggested method are presented.     

大地电场观测深埋铅电极测量系统试验

为使用铅电极替代不极化电极,以解决滨海地区大地电场观测系统稳定性差的问题,先后开展了浅埋的铅电极与不极化电极的大地电场对比观测,以及深埋铅电极与浅埋铅电极的对比观测试验。结果表明:铅电极与固体不极化电极的观测数据在短期内有较好的一致性;深埋铅电极的大地电场观测资料在长期稳定性上优于固体不极化电极;而观测数据的内在观测质量也高于浅埋铅电极。     

面向深地探测的光纤重力梯度仪测量原理与研制进展

发展深地探测技术对于推进地球物理发展有重要意义.基于重力梯度的深地传感技术具备自身独有的优势,可以有效弥补现有主要方法的局限.本文提出了一种基于光纤Sagnac干涉仪的重力梯度测量原理,将重力梯度转化为角加速度并利用光纤角加速度计进行精密传感.本文设计了重力梯度原型样机,并利用ANSYS有限元仿真论证了其可行性与稳定性,在此基础上对光纤重力梯度原型样机进行了长达14天的连续静态测试,得到角加速度测量本底噪声低于3×10^-10rad·s^-2·Hz^-1/2,对应重力梯度测量噪声达0.68 E·Hz^-1/2.基于光纤Sagnac干涉仪的重力梯度测量没有对传感单元一致性的要求,无需复杂的环境控制与辅助设备,测试结果展现了其高灵敏度特性以及应用于深地探测的巨大潜力.