Piezomagnetic monitoring in the South Pacific region

Data from an array of piezomagnetic stations in the South Pacific Islands indicate that noise limitations on piezomagnetic stress monitoring reported for California (Mueller andJohnston, 1981;Johnston et al., 1984) are probably pessimistic since they seem to include significant diurnal residual. Raw station differences could be significant at the 1.0 nT level out to distances of several hundred kilometres. Two large earthquakes have occurred within the network, and no coseismic anomalies were observed. However, changes in observed magnetic field for several stations within 200 km of the earthquakes indicate that stress propagation effects are observable prior to the events, and that these effects dominate the simple elastic effects previously investigated which accompany the stress drops for moderate to large earthquakes.     

Piezomagnetic fields produced by dislocation sources

Tectonomagnetic modeling based on the linear piezomagnetic effect is reviewed with special attention to dislocation models. Stacey's scheme was the prototype for such modeling, as proposed in his first seismomagnetic calculations in 1964. The linear piezomagnetic law is presented, in which the stress-induced magnetization is expressed as a linear combination of stress components. The Gauss law for magnetic field and the Cauchy-Navier equation for static elastic equilibrium are combined through linear piezomagnetism and the Hooke law to yield the basic equation for piezomagnetic potential. A representation theorem for its solution is given by surface integrals of the displacement and its normal derivative over the strained body.A Green's function method is developed to compute the piezomagnetic field produced by a dislocation surface in an elastic half-space. Volterra's formula for piezomagnetic potential is derived by modifying Stacey's scheme for tectonomagnetic modeling. The Green's functions for the problem are called elementary piezomagnetic potentials, which are defined as potentials produced by elementary dislocations. Special consideration is required to construct the elementary piezomagnetic potentials, because the stress field around a point dislocation has a singularity of orderr ^–3. The integral representing elementary piezomagnetic potentials is not uniformly convergent. Owing to inappropriate convergency, the Green's functions obtained in an earlier study led to a puzzling outcome. Revised Green's functions give consistent results with those obtained so far by numerical integrations. Generally the piezomagnetic field produced by dislocation sources is weak in the case of a homogeneous earth model. Two enhancement effects for piezomagnetic signals are suggested: one due to inhomogeneous magnetization and the other via bore-hole observations.     

The thermal diffusivity of red sandy soil at Waltair

Summary The study of heat exchanges or temperature changes in the surface layers of the soil are important in agricultural science at tropical latitudes. The quantity, thermal diffusivity largely determines the temperature change produced in any layer of the soil when heat is conducted there from an adjacent layer. Therefore, the authors have determined the thermal diffusivity of the soil from range and lag methods suggested byJohnson andDavies [15]²) andCoutis [7] respectively. The values of diffusivity cbtained from these methods agree well with each other. The effect of soil moisture on diffusivity has been studied. The diffusivity increases with the increase of moisture in the surface layers of the scil. The ratio of ranges of soil temperature at different depths is found to be approximately constant which is in agreement with the theory of heat flow into the soils. The results of diffusivity obtained from these methods agree well with those results of past workers. The mean value of the thermal diffusivity of red sandy soil at the experimental site of Waltair is found to be 6.336×10^–3 cm²/sec.     

Electromagnetic effect stimulated by strain wave in rocks

ＥｌｅｃｔｒｏｍａｇｎｅｔｉｃｅｆｅｃｔｓｔｉｍｕｌａｔｅｄｂｙｓｔｒａｉｎｗａｖｅｉｎｒｏｃｋｓＸＩＡＯＨＥＸＵ（徐小荷）ＧＵＯＪＵＮＸＩＮＧ（邢国军）ＢＩＡＯＷＡＮＧ（王标）ＭｉｎｉｎｇＤｅｐａｒｔｍｅｎｔｏｆＮｏｒｔｈｅａｓｔｅｒｎＵｎｉ...     

单轴压力下岩石磁化率的变化

利用感应法测定了北京、唐山地区五类强磁性火成岩在单轴压力下的压磁曲线。实验发现,曲线可划分为两个形态不同的阶段。在加压的初始阶段,压磁曲线表现为上升;尔后,几乎以不变的速率直线下降。曲线形态与岩样的种类、循环次数有一定的关系。压磁系数变化范围为-(0.9—3.0)×10~(-4)cm~2kg。从加压开始到岩石破坏,磁化率一般下降20—30%。还发现,磁化率的变化与岩样的体膨胀关系不太明显。运用铁磁学中的磁畴理论对上述压磁曲线作了初步的解释。     

Über die Bindung der Aerosolteilchen auf der Oberfläche der Wolkenelemente

Summary The importance ofStefan's flow by collection of insoluble aerosol particles on the surface of the evaporating droplets by condensation has recently been emphasized mainly in connection with the possible wash-out mechanism in the atmosphere. A simple theory is deduced for the collection efficiency of insoluble particles on droplets under theStefan's force and a comparision is made with the binding of aerosol particles byBrown's motion and microturbulence of air flow. In general we must take in account the influence ofStefan's flow by calculating the wash-out efficiency.     

Ueber Anwendungen einer Formel zur Berechnung des Vertikal-gradienten der Schwere

Summary A formula is derived, which allows to calculate the vertical gradient of gravity from gravity anomalies with consideration of the whole gravitational field of the earth. It is shown that the formula given byEvjen for a plane surface in practical cases is nearly always sufficient. The accuracy of calculation is to be checked with regard to the geophysical applications. Two examples give an idea of the variations of the vertical gradient at the earth's surface. FurthermoreEvjen's method of direct structural calculation by means of the vertical gradient is discussed.

---

Résumé On déduit une formule qui permet de calculer, par rapport au champ total de gravité de la Terre, le gradient vertical de la pesanteur résultant des anomalies gravimétriques. Il s'en suit que la formule donnée parEvjen pour une surface plate est presque toujours suffisante dans les cas pratiques. On examine la précision du calcul à l'égard des applications géophysiques. Deux examples nous donnent une idée des variations du gradient vertical sur la surface de la Terre. Enfin on discute la méthode d'Evjen de calculer directement la structure a l'aide du gradient vertical.

     

单轴应力作用下两种不同方法研究岩石磁化率变化的结果

本文介绍了对北京——唐山地区八种强磁性岩石标本的压磁实验结果,观察了它们在高压应力下,直至破坏前后的磁化率变化特征。发现磁化率的变化只是其应力值的函数,与体积变化过程、微裂膨胀过程关系甚微。磁化率的压力系数取值范围为——(0.4——3.0)10-3MPa-1。同时,本文还得到了标本中出现破裂后岩石的压磁曲线。 运用铁磁学理论,对上述压磁实验结果作了初步的分析解释。      

Sulla divergenza del campo gravimetrico normale

Sommario In alcuni moderni procedimenti per lo studio delle anomalie della gravità figura come elemento essenziale la divergenza del gradiente superficiale del modulo della gravità (secondo parametro differenziale diBeltrami) su di una superficie di livello del campo. Tale divergenza è espressa semplicemente mediante gli elementi geometrici e dinamici del campo, in particolare mediante le derivate seconde del modulo della gravità secondo le linee di forza. Nella presente Nota si applicano le formule generali al campo diSomigliana, riferito alle sue coordinate intrinseche e si calcolano i valori numerici di tale divergenza e di altri elementi del campo normale, di 10° in 10° di latitudine.

---

Summary In some modern procedures for the study of gravity anomalies, the divergence of the surface gradient of gravity (second differential parameter ofBeltrami) on a level surface is considered. Such divergence is connected with the geometrical and dynamical elements of the field by simple relations, in particular to with second derivatives of gravity along the lines of force. In the present paper the general formulae are applied toSomigliana's field referred to its intrinsic coordinates, and the values of the surface divergence and other elements of the normal field are given from 10° in 10° in latitude.

     

唐山地震与震磁效应的最佳观测

根据作者与Hastie和Stacey提出的三维压磁效应模式计算方法,围绕1976年唐山大地震,计算了七种不同断层模式的压磁效应,比较了在不同磁纬处,走向滑动断层的不同走向、倾角和埋深在地面上所引起的压磁异常场。结果表明,震磁效应的可观测性同地震的破裂机制有着紧密的关系。断层倾角45——60对应着最佳观测条件,其压磁异常峰值可高达12nT;在最差观测条件时压磁异常量几乎无法测出,这时断层位于磁纬0处,或走向为E-W,或埋深为10公里左右。在大多数模式中,垂直分量的异常略大于总强度异常,但在磁赤道附近可高达三倍左右。对唐山大地震的计算表明,压磁异常量约3——4nT,其异常大于1nT区域的线性尺度与断层长度之比仅为1.04——1.10。由于压磁场是地震过程的一种弱效应场,目前使用仪器的观测精度不够和磁测点的震中距过大,可能是未测出该地震明显的磁异常的原因。      

On the heat budget of the moon and the surface temperature variation during a lunar eclipse

Summary The analysis of surface temperature variations of the moon is based on the equations of heat conduction and heat continuity in the interior of the moon andStefan's law. During a well-defined process, as exemplified by a lunar eclipse, the local heat budget equation establishes a boundary condition at the moon surface which must be satisfied by solutions of the thermal diffusion equation in the interior. Three simplified models of the general case are discussed. They are characterized by special assumptions regarding the depth and time dependency of the thermic qualities of the material underlying the moon's surface. In short, the thermal diffusivity is assumed to be constant in the first model, a linear depth function in the second and a time function in the third. A unique solution can be obtained for model No. I such that the absolute surface temperature is approximately inversely proportional to the 6th root of time during the phase of total eclipse.Epstein's conclusion that the average surface of the moon might consist of highly porous rocks or fine dust is confirmed by the order of magnitude of the heat conductivity which produces the best fit between the theoretical curves and a plot ofPettit's observational data during the lunar eclipse of 1939. Existing differences between the observed and theoretical curves during the totality phase of the eclipse can be reduced by the employment of the second model. A crude estimate shows that the average dust cover resting on more solid ground of lunar rocks might possibly have a thickness of approximately 0.5 meters.     

Mineralogy and physical nature of clay gouge

Fault gouges have been observed in the surface outcrops, in shallow excavations, and in deep (300 meters below the surface) tunnels and mines in fault zones. The 2-microns fractions in these fault gouges may compose a few percent to more than fifty percent of the total mass in the outcrops, and the mineralogy of the 2-microns fractions consists of a variety of clays (the common ones are montmorillonite, illite, kaolinite, chlorite, vermiculite and mixed-layer clays) and some quartz, feldspars, etc.Although we cannot yet conclude directly from the studies of gouges that similar gouges exist at depths where many large shallow earthquakes are generated, there is a strong possibility that they do, based on (1) available equilibrium data on various clays — for example, kaolinite has been found to exist at 4 kb and 375°C (±15°C) (Thompson, 1970) and montmorillonite + kaolite has been found to exist at 450°C and 4 kb (Velde, 1969); (2) the compatibility of laboratory velocity data in gouge (Wang et al., 1977) with those in a model for central California (Healy andPeake, 1975); (3) the capability of clays to undergo sudden earthquake-like displacements (Summers andByerlee, 1977); (4) the petrology of intrafault cataclastic rocks in old fault zones (Kasza, 1977); and (5) the compatibility of gouge mineralogy with the mineralogy of hydrothermal clay deposits.If clay gouges are indeed significant components of the fault zone at depth, then the mechanical properties of clays under confining pressures up to 4 kb are important in the behavior of faults. Very few experiments have been performed under such high pressures. But from the physical makeup of clays, we can infer that (1) the range of possible behavior includes stable sliding with vermiculite and montmorillonite (asByerlee andSummers, 1977, have proven) to stick-slip-like behavior with kaolinite, chlorite, etc.; (2) the absence or presence of water will greatly affect the strengths of gouges — it is possible that water may reduce the strength of gouge to a fairly small value.     

A note on specific variability of long surface gravity waves and drag coefficient in coastal upwelling zone

In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. UsingGent andTaylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.     

Una semplice dimostrazione del teorema di bjerknes sulle circolazioni atmosferiche

Riassunto Si fa uso di una formula di derivazione di un integrale di superficie per dimostrare un teorema meteorologico diV. Bjerknes.

---

Summary Use is made of a differentiation's formula for surface integrals in showing aV. Bjerknes' meteorological theorem.

     

Theory of the seismomagnetic effect: a reassessment

Transient magnetic anomalies accompanying seismic stresses are more elusive than had been anticipated. We have, therefore, undertaken a more rigorous calculation than hitherto of the piezomagnetic effect accompanying representative seismic strain fields. We present a numerical method of treating faults of arbitrary area and orientation with fault displacement graded to zero at the fault boundaries to avoid stress discontinuities. The effect of grading the displacement in a realistic way is to give a more restricted and generally smaller piezomagnetic anomaly field than is indicated by simpler models. Seismomagnetism remains important in the search for earthquake prediction methods, but is more difficult to observe than had been hoped.     

岩石剩余磁化强度的应力效应

为模拟构造应力对岩石剩余磁化强度的影响,本研究对六种不同类型的44块岩样进行了应力实验,发现岩石天然剩磁随应力的变化规律比迄今所估计的要复杂得多.作者指出,这些变化可归属于三种类型:在弱不可逆的Ⅰ型效应中,剩磁随应力呈现规则的减小,应力解除后剩磁部分恢复;而在强不可逆的Ⅱ型效应中,应力去除后剩磁大部不恢复;在Ⅲ型效应中,剩磁随应力呈极不规律的变化.进一步的岩石磁学分析表明,不同应力效应的重要原因,在于天然剩磁中的粘滞剩磁的比例不同,微观上取决于磁性矿物成分及其磁畴状态等因素.因此,不能用单一的岩石压磁模式来解释地震压磁效应,须考虑各震源区的不同岩石组成.      

Depth calculation of piezomagnetic effect for earthquake prediction

Tectonic stresses acting in the lithosphere cause transitory changes in the magnetic properties of rock and thus of its observed magnetic field. Calculations have been made to estimate this piezomagnetic effect as a function of depth, by considering the relative stress sensitivity of magnetite with increasing temperature and hydrostatic pressure. The response of magnetization to seismotectonic stress is determined by an appropriate balancing of magnetocrystalline and magnetoelastic anisotropy energies. Magnetite becomes progressively more responsive to applied stress as depth increases, with the rate of change depending on the local geothermal gradient. The upper 15 km of the lithosphere is likely to be the most important in yielding observable piezomagnetic field anomalies for earthquake prediction.     

Disturbance produced in an elastic half-space by impulsive normal pressure

Summary The displacement produced in the half-space by uniform impulsive pressure acting over a circular portion of the surface has been obtained in terms of definite integrals. FollowingCagniard andGarvin, the displacement at an interior point on the axis of symmetry has been calculated. The approximate displacement at points far off from the axis of symmetry has been obtained by using saddle point method and Tauberian limit theorem.     

Motion in a non-homogeneous elastic medium by a twisting impulsive force on the surface of a spherical cavity

Summary In this paper, the propagation of disturbance due to a twisting impulsive force on the surface of a spherical cavity, in a non-homogeneous isotropic medium, in which the rigidity and density vary inversely as the distance from the centre is investigated. Numerical solution is done by the method suggested byKromm.     

On the application of turbulence theory to the determination of marine evaporation

Summary Simultaneous measurements of wind, air temperature, and humidity profiles as well as of evaporation, presented byTakahashi (1958), were compared with relevant formulae suggested by turbulence theory. Satisfactory agreement could be achieved if, near the sea surface, the influence of molecular diffusion and, at higher levels, the effect of thermal stratification on the profiles were taken into account in addition to a suitable reduction of the value of evaporation obtained by means of a floating pan.The chief results of this report have been presented on 27th April 1962 to the Tenth Yearly Meeting of theSocietà Italiana di Geofisica e Meteorologia (Genova: 26–28 April 1962).