THEORETICAL ANALYSIS OF APPARENT RESISTIVITY OVER A DYKE OF ARBITRARY SHAPE*

This paper deals with the apparent resistivity as observed on the surface due to a dyke of arbitrary shape. In order to give a closed analytical solution it has been necessary to assume that the dyke is either perfectly conductive or resistive relative to the enclosing medium. Furthermore we have considered an infinite line source instead of a conventional point current source; however a simple integral transform is given to transform the point-source-data into the line-source-data. So the present study is equally useful where line sources are inconvenient to handle. Besides considering the conventional method of electrical surveying (bipole method) where the source and sink are separated by a finite distance, we have considered a new variation (unipole method) where the source and sink are separated by an infinite distance, and the source is split into two separate sources each of half strength. A series of apparent resistivity curves for both methods are presented for different parameters of the dyke. The usefulness of these curves lies mainly in the fact that they may provide the necessary guide-lines for semi-quantitative interpretation of the observed data.     

Interpretation of self-potential anomalies of some simple geometric bodies

Summary An entirely new procedure for interpreting selfpotential anomalies of spheres, rods and dipping sheets is presented. The anomaly of a sphere is divided into two parts — the anomaly of odd symmetry and the anomaly of even symmetry — from which the depth can be obtained by fitting them with the master curves. The self-potential anomalies of a finite rod are transformed to the anomalies of a veritcal sheet, for which standard curves are presented. The case of a sheet was divided into three parts; (a) finite line of poles; (b) infinite double line of poles and (c) finite double line of poles. For the first case logarithmic curves were prepared and presented; by their comparison with the field profile, different parameters can be obtained. In the second case, a geometrical construction is provided to obtain the various values. In the third case, the anomalies of finite sheet (finite double line of poles) are transformed into those due to an infinite double line of poles for interpretation.     

What is the cause of the accelerated drift of the north magnetic pole: Jerk or reversal?

For the last 20–30 years, the drift velocity of the north magnetic pole (NMP) has increased by a factor of almost 5. It is unclear whether this is the cyclic process, according to which NMP twice changed the direction of its drift (in 1580 and 1860) and should turn once again in approximately 2140, or this acceleration is related to the effect of jerk-69, or the NMP acceleration shows the beginning of geomagnetic field reversal. Both magnetic poles have been drifting poleward (toward each other) beginning from 1860: NMP, in the Western Hemisphere; south magnetic pole (SMP), in the Eastern Hemisphere. Both poles move along the paths typical of the motion of virtual magnetic poles during reversal. The velocity of SMP drift during the period of instrumental measurements slightly decreased: from 8 km/yr at the initial stage to 4 km/yr at the present. A possible cause of NMP drift acceleration and SMP drift deceleration is discussed. It has been indicated that the NMP position can be estimated based on a change in the geomagnetic field horizontal components registered at the nearest observatories. Measurements of the NMP position, which can be performed during the next three-five years, can make it possible to answer the question whether NMP continue accelerating or starts decelerating. It is discussed whether NMP acceleration and an increase in the jerk occurrence frequency are interrelated and whether these facts points to the beginning of reversal.     

Pacific Plate motion and undulations in geoid and bathymetry

Previous studies have shown that the Pacific geoid and gravity fields exhibit lineated anomalies, trending approximately in the direction of absolute plate motion over the underlying mantle. Because the undulations obliquely cross fracture zones they have often been attributed a convective origin. Recently, lithospheric boudinage caused by diffuse extension has been proposed as a possible mechanism. We have examined the undulations in the free-air anomalies, geoid and bathymetry over a portion of the Pacific Plate to determine quantitatively how the undulations are related to plate motion. We compare the observed data to an axisymmetric, sinusoidal undulation defined in an arbitrary frame of reference; in particular, we seek the north pole of this reference frame that maximizes the correlation between data and model. Poles that are close to the Pacific hotspot pole represent copolar undulations possibly related to plate motion. The distance between the best-fitting poles and the hotspot pole is determined as a function of undulation wavelength and reveals several minima (with distance < 10°) for discrete geoid wavebands centered on wavelengths of 160 km, 225 km, 287 km, 400 km, 660 km, 850 km, 1000 km and 1400 km. Bathymetry data have copolar bathymetric expressions as well, giving an implied admittance of 2–3 m/km. The most co-polar geoid/bathymetry undulations (with poles within 2–3° of the average Pacific Euler pole) have wavelengths of 280 km and 1050 km, respectively. The latter could have a convective origin or be related to the spacing of hotspot swells. The former may reflect lithospheric boudinage formed in response to diffuse extension, but could also have a dynamic origin since flexural dampening may only have attenuated the bathymetric amplitude by 50% or less. Radiometric dating of volcanic ridges found in the troughs of prominent gravity lineations gives ages that correlate well with documented changes in Pacific and Indo/Australian Plate motion, suggesting the ridges formed in response to intermittent plate boundary stresses and not as a direct consequence of small-scale convection or diffuse extension.     

Motion of the Earth’s magnetic poles in the last decade

Based on vector magnetic data from the CHAMP German satellite, average daily spherical harmonic models of the main geomagnetic field to n = m = 10 have been constructed for the period from May 2001 to the end of 2009 at an interval of 4 days. The obtained 16 models, which were averaged over half a year, have been used to calculate the coordinates of the north and south magnetic poles (the points where magnetic field lines are vertical). The changes in these coordinates during these eight and a half years have been traced. Both poles continue moving northward and westward. The north magnetic pole has traveled 400 km during this period. The velocity of its motion has increased up to the year 2003, reaching 62.5 km yr⁻¹, and then started decreasing and reached 45 km yr⁻¹ by the end of 2009. In addition, the direction of motion changed from north-northwestward to northwestward; i.e., the pole started turning slightly towards Canada. The south magnetic pole moved slower by an order of magnitude and has traveled 42 km during this period. The coordinates of the geomagnetic (dipole) poles and the eccentric dipole parameters have also been calculated. The dynamics of these poles has been traced.     

The location of infinite electrodes in pole–pole electrical surveys: consequences for 2D imaging

In 2D-multielectrode electrical surveys using the pole–pole array, the distance to ‘infinite electrodes' is actually finite. As a matter of fact, the available cable length generally imposes a poor approximation of theoretical location of these electrodes at infinity. This study shows that in most of the cases, the resulting apparent resistivity pseudosection is strongly distorted. Numerical simulation validated by field test also shows that a particular finite array provides results that are as close as possible to the ones of the ideal pole–pole array. This is achieved when two conditions that are weaker than an infinite location are fulfilled: (i) the ‘infinite electrodes' are placed symmetrically on both sides of the in-line electrodes with a spread angle of 30° and (ii) the length of ‘infinite lines' is at least 20 times the greatest distance between in-line electrodes. The electrical 2D image obtained with this enhanced array is the least distorted one with respect to the pole–pole image. The apparent resistivities are generally underestimated, but this deviation is almost homogeneous. Though the shift cannot be determined a priori, the interpretation of such an image with direct or inverse software designed for pole–pole data provides an accurate interpretation of the ground geometry.     

Interpretation of gravity and magnetic anomalies when observation plane is inclined

Summary Not infrequently, in mining geophysics, measurements have to be made on the slopes of a hill that contain mineralisation. In this paper, procedures are evolved for interpreting gravity and vertical component magnetic data collected on such slopes and caused by geological bodies that can be approximated by infinite line pole, point pole, infinite line dipole and point dipole. From sets of theoretical magnetic anomaly curves (not reproduced), graphs have been constructed using characteristic points and are reproduced in Figures 5 to 10 and 12 to 17. These can be used for direct determination of depths, offsets, etc., by using information from suitably chosen field profiles. In the case of gravity, the mass can be computed as usual by a surface integration, provided a correction factor (1/cos²) is used, being the angle of the slope.     

Paleomagnetism and potassium-argon age of the Messejana dike (Portugal and Spain): angular limitation to the rotation of the Iberian Peninsula since the Middle Jurassic

A paleomagnetic and potassium-argon dating investigation has been carried out on a 530-km-long dike system which transects the western Iberian Peninsula in a northeasterly direction. The K-Ar age determinations were made on mineral separates exclusively. They range between 160 and 200 Ma and the authors suppose that this reflects the actual time interval of the intrusion, in accord with previous results. The paleomagnetic pole derived from 12 sites regularly distributed along the dike (71°N, 236°E) coincides well with other Mesozoic paleomagnetic poles from the western Africa. A contemporaneous pole from stable Europe is tentatively deduced from African and North American Late Triassic/Early Jurassic poles using different reconstruction models around the North Atlantic Ocean. The divergence between this pole and the Iberian pole corresponds to the result obtained for Permian poles.     

Poles of rotation

One of the concepts introduced into the theory of plate tectonics is that of poles of rotation. It is supposed that the relative motion between two rigid plates can be described by the rotation of one of the plates about a pole of rotation, which shows the direction of the rotation vector. It has been pointed out that in general poles of rotation will not remain fixed. The consequences of poles of rotation which move slowly with time are examined. In particular, it is shown that fracture zones may lie very close to small circles, but that the centers of these small circles may lie as much as 20° away from the average pole of rotation. The establishment of poles of rotation from individual fracture zones is thus an inaccurate method unless it can also be shown that the pole of rotation has remained fixed.     

Paleomagnetic data from tertiary igneous rocks,northeast Jalisco,Mexico

New paleomagnetic measurements have been made on Tertiary volcanic rocks from northeast Jalisco, Mexico (20.7°N, 102.3°W). The pole position obtained from this study (68°N, 181°E) is consistent with two other Oligocene poles from Mexico. Mexican poles form a coherent group which differs from poles of similar ages from North America. This suggests a possible tectonic rotation of the sampling sites of Mexico with respect to “stable” North America.     

翁田台地电场观测受干扰的因素分析

海南省文昌翁田台地电场数据质量自2019年3月开始下降,地电场数据质量下降主要表现为日相关系数偏低、北南向长极距与短极距数据曲线呈反向变化、绝缘度趋向于零等情况.2019年3月—2020年10月,我们分别对观测室装置系统、室外外线路、连接口等逐一进行详细的排查工作和电极、电缆的对比实验工作,最终确定影响因素为电极故障和...     

Paleomagnetic and rock magnetic results from the Twin Creek Formation (Middle Jurassic), Wyoming

A magnetization which passes the fold test has been observed in 73 limestone samples (10 sites) from the Middle Jurassic Twin Creek Formation. The pole calculated from the site mean poles is located at 68.4°N, 145.0°E (K = 31.8,A₉₅ = 8.7°). This pole lies in a segment of the North American apparent polar wander (APW) path for which there are only a few reliable poles in the literature. The results corroborate earlier studies which conclude that the Jurassic segment of the APW path does not include the present north pole. However, the position of the Twin Creek pole suggests that significantly more APW took place prior to the late Jurassic than previous studies indicated.     

Paleomagnetic study of some Cretaceous and tertiary rocks on Hispaniola

Summary A reconnaissance paleomagnetic study of Hispaniola shows that three igneous units in the Dominican Republic possess meaningful directions of magnetism. A Late Cretaceous tonalite, an Eocene pyroxene diorite and a Miocene andesite porphyry have been investigated. The rock material studied is fresh, and has not been affected by secondary oxidation except in the case of the andesite which is occasionally weathered and reveals some hydrothermal alteration. Alternating field and thermal demagnetization result in removal of viscous remanence in some samples, while others reveal a good stability of NRM and little change in direction. The results disclose directions of magnetization substantially different from that of the present earth's field in Hispaniola and from those obtained from contemporaneous rocks of North America. They yield paleomagnetic poles at 23.1° N, 144.9° W for the Cretaceous tonalite and at 17.4° N, 138.0° W for the Eocene diorite, the positions of which are not significantly different from each other, suggesting no change of geomagnetic field direction during the two epochs. These poles have generally similar positions to those obtained from Late Cretaceous rocks on Jamaica and Puerto Rico. The Miocene data fall into two groups, one having a direction corresponding to a pole closely coinciding with the Miocene North American pole and the other giving a paleomagnetic pole at 68.3° N, 151.9° W coinciding with the Miocene pole for Jamaica. Paleotectonic interpretation of the results suggests that like other Greater Antilles, Hispaniola has been subject to large anticlockwise rotation since Late Cretaceous.     

Permo-Triassic magnetostratigraphy in China: northern Tarim

The upper boundary of the Permo-Carboniferous Reversed Polarity Superchron has been identified in a palaeomagnetic study of the Permo-Triassic of the northern part of the Tarim Basin, China. This boundary serves as an important marker horizon for correlation with other Permo-Triassic sequences both in China and world-wide. A Permo-Triassic palaeomagnetic pole for the Tarim Block is estimated to be at 71.8°N, 187.6°E.Comparison with similar age poles from the adjacent blocks of China and Asia suggests that the Tarim was widely separated from the Sino-Korean Block in Permo-Triassic times but was not yet sutured to Kazakhstan.     

Interpretation of total intensity magnetic anomalies when anomalous field is arbitrarily large

Summary Not infrequently, in mining geophysics, the anomalous field of the magnetized body is appreciably large and it varies from the direction of the earth's normal field within the vicinity of the magnetized body. Total magnetic intensity data collected on the ground over shallow magnetized bodies cannot be interpreted quantitatively, since all the available methods of interpretation assume that the resultant field lies in the direction of earth's normal field as the anomalous field is small. For geological bodies that can be magnetically represented by infinite line pole, point pole, infinite line dipole, and point dipole, this paper gives quantitative interpretation procedures for total magnetic intensity anomalies without the above assumption using the characteristic points from the theoretical curves (not reproduced). These characteristic curves can be used for the direct determination of depths and offsets by using information from suitably chosen field profiles.Contribution No. N.G.R.I.-71-233.     

框架结构水平和竖向地震耦合作用时程分析

一般情况下,地震波分量中的水平分量和竖向分量是造成框架结构破坏的重要因素。本文中以框架结构为研究对象,将空间框架结构简化为平面框架结构,基于平面杆系模型并忽略平面框架体系的水平杆件——梁的轴向变形,建立体系水平和竖向耦合振动的运动微分方程,并对结构进行了水平和竖向地震波耦合激励下的弹性动力时程计算。与体系单维输入竖向地震波之弹性动力响应进行对比后,发现耦合激励下框架边柱竖向响应变大而中柱竖向响应变小,在结构抗震设计中宜适当考虑地震的耦合影响。     

ENERGY DENSITY SPECTRUM AND AUTOCORRELATION FUNCTION OF ANOMALIES DUE TO SIMPLE MAGNETIC MODELS*

Formulae of the energy spectrum and autocorrelation function have been derived for magnetic anomalies due to four classes of bodies which can be represented in turn by (a) poles, (b) line of poles, (c) dipoles and (d) line of dipoles. The effects of the depth and dimensions of the magnetized sources on the spectrum and the autocorrelation function have been studied. In the case of the dipole models, the orientation of the polarization vector casts a significant influence on the characteristics of the two functions. In all cases, however, the functions change in size and shape as the inclination and declination of the geomagnetic vector are varied.     

多层地电断面视电阻率的高精度计算

目前地电的方法在我国已应用到地震预报的研究中,为了了解与地下力学场变化相联系的地电变化,需要了解台址下勘探体积内的电阻率分层情况,从而正确地认识各种影响因素对地电阻率的作用。     

由地震波初动求断层面方法的一些推广和改进

震源机制是地震学上很有意义的一个问题.关于这个问题,目前日本、苏联、美国、加拿大和印度尼西亚等国的学者都在研究.在这些国家中他们是各有一套方法的.在美国和加拿大所用的方法是很早以前P.Byerly提出的.这方法的原理如下:当断层错动时,在断层面两边的岩体中形成了压缩区与膨涨区。     

Relative Motion Between the Rivera and North American Plates Determined from the Slip Directions of Earthquakes

So far, the direction and rate of relative motion between the Rivera and the North American plates (RIV-NAM) has been determined by the combination of two Euler poles: Rivera (RIV), with respect to Pacific (PAC), and PAC with respect to North America. Here, we estimate the relative motion of this plate pair (RIV-NAM) assuming that the horizontal projection of the direction of slip of the earthquakes occurring on the RIV-NAM boundaries reflect their relative plate motion. A catalog of earthquakes for which focal mechanisms are reported since 1976 is used in the analysis. Earthquakes were considered in the three segments of the RIV-NAM plate boundary: the subduction zone of the Rivera plate beneath the Jalisco block, the Tres Marias Escarpment and the events associated with the Tamayo Fracture Zone. The best fitting Euler pole is determined using a grid search of 64 potential poles. The slip direction predicted for each grid point is compared to the slip direction of the focal mechanisms of the earthquakes on the plate boundary. The best fitting Euler pole, determined in a root mean square sense (RMS), is located at 21.8°N, 107.6°W. A rate of rotation of 5.3°/year is estimated assuming the seismic earthquake cycle of the 1932 and 1995 great earthquakes represents a lower bound of the rate of plate motion in the subduction zone. The best fitting Euler pole shows that the subduction of the Rivera plate takes place in a direction perpendicular to the trench with a relative velocity of 4.3 cm/year, offshore Manzanillo. The rate of relative motion RIV-NAM decreases from SE to NW. North of approximately 21°N, the subduction of the Rivera plate becomes oblique to the trench and the relative velocity between the two plates decreases to an average of 1.9 cm/year. This slow rate of convergence may explain the rapid decrease of seismicity in the trench and the apparent absence of large earthquakes in this region. In the Tres Marias Escarpment, our best-fitting pole suggests that subduction stops, giving way to high-angle reverse faulting perpendicular to the Tres Marias Escarpment, in agreement with the reverse faulting earthquakes occurring here. To the north of 22.5°N, the slip predicted by the best-fitting pole suggests right-lateral faulting in a direction parallel to the Tamayo Fracture Zone, at a very low velocity (0.5–1.0 cm/year). The best fitting Euler pole determined here lies very close to the RIV-NAM plate boundary in the vicinity of the Tamayo Fracture Zone. This location of our best fitting Euler pole explains the low relative plate velocity, the relatively low level of seismic activity and the presence of a broad zone of deformation that accommodates the RIV-NAM motion.