MAGNETIC SUSCEPTIBILITY ANISOTROPY OF VARIOUS ROCK TYPES AND ITS SIGNIFICANCE FOR GEOPHYSICS AND GEOLOGY*

In the interpretation of magnetic anomalies and in paleomagnetism, the anisotropy of magnetic susceptibility is commonly neglected. Nevertheless, this property has basic significance, because, owing to susceptibility anisotropy, the directions of the vectors of induced and remanent magnetization are deflected from the direction of the Earth's magnetic field. Almost all rock types investigated possess higher or lower degree of the susceptibility anisotropy. Effusive and sedimentary rocks have the lowest degree of anisotropy. For the latter, the “masking effect” of the paramagnetic mineral components has some influence on the anisotropy degree due to the low mean susceptibility of sedimentary rocks. Metamorphic and plutonic rocks usually exhibit a considerable degree of anisotropy. The highest degree of anisotropy has been found in the rocks containing ferromagnetic minerals with mimetic fabric. The dependence of the degree of the susceptibility anisotropy on the degree of metamorphism proved to be very complicated; of the rock sequence from slates to gneisses, the transient rocks (roofing slates and mica-schist-gneisses) showed the highest degree of anisotropy. This result can be used in geology for reliable determination of these rock types.     

Influence of magnetic interactions on the anisotropy of magnetic susceptibility: the case of single domain particles packed in globule aggregates

The influence of magnetic interactions on the anisotropy of magnetic susceptibility (AMS) have been largely studied by several theoretical models or experiments. Numerical models have shown that when magnetostatic interactions occur, the distributions of particles over the volume rather than their individual orientations control the AMS. We have shown recently from a comprehensive rock magnetic study and from a theoretical 2-dimensional (2-D) model that single domain particles closely packed in globule aggregates could produce strong local random interaction magnetic fields which could influence the magnetic susceptibility and decrease the degree of anisotropy. In this paper, we first present in detail this 2-D theoretical model and then we extend it to the 3-D case. The possible distribution function of the magnetostatic interaction fields comprises two extreme states: it is either isotropic or ordered. The former case corresponds to the thermal-demagnetized state while the second case corresponds to the alternating field (AF) demagnetized state. We show that when easy axes of magnetization are not uniformly distributed, the degree of anisotropy decreases as the interaction field increases in both AF- and thermal-demagnetized states in 2-D and 3-D geometry. Thus we conclude that random magnetic fields generated by a random arrangement of magnetic particles over the sample volume decrease the degree of anisotropy of AMS and may alter the magnetic fabric.     

Anisotropy of magnetic susceptibility of rocks in the Rayleigh Law region: Modelling errors arising from linear fit to non-linear data

The anisotropy of magnetic susceptibility (AMS) within the Rayleigh Law range was investigated theoretically, using mathematical modelling. It was revealed that the orientations of the principal susceptibilities and the shape parameter vary with field so weakly that these variations can be regarded as negligible from the practical point of view. The degree of AMS increases with field according to the degree of anisotropy of the initial susceptibility used and according to the intensity of susceptibility change with field of the mineral considered. The degree of AMS calculated using linear theory is very near to the degree of AMS following from the analysis of AMS within the Rayleigh Law range. If it is desirable to correct the field-dependent degree of AMS, a simple technique is suggested based on measurement of the AMS in two fields. fhrouda@agico.cz     

一种三维正交方位各向异性介质岩石 物理建模及弹性波正演模拟方法

通过线性滑动理论和岩石物理等效理论, 将两组正交直立裂隙介质等效为一种正交方位各向异性介质进行三维岩石物理建模, 通过高阶交错网格有限差分求解弹性波动方程模拟地震波在该种介质中的传播过程. 在建模过程中改变物性参数, 分析不同裂隙密度条件下的炮集和波场特征, 以及正交各向异性的方位特征. 研究结果表明, 各向异性强度随裂隙密度等物性增大而增强, 而且这些特征在共炮点道集和波场中均有所体现.      

Magnetic anisotropy of granitic rocks of the Bergell massif (Switzerland)

Magnetite as well as ilmenohematite are contained by the Bergell granitic rocks, but the fabric of low field susceptibility is due to the magnetite only and is equivalent to the macroscopic biotite fabric. Microscopic observations and high field anisotropy measurements show that the ilmenohematite trigonal axes are aligned parallel to the directions of minimum low field susceptibility anisotropy. The deflection of the stable direction of natural remanent magnetization caused by the alignment of ilmenohematite is corrected using the susceptibility anisotropy data. The resulting virtual palaeopole position deviates from other Oligocene to Miocene pole positions of stable Europe suggesting that since the time of intrusion some 25 my ago the Bergell massif has been rotated anti-clockwise by an angle of ～30° about a vertical axis.     

基于页岩岩石物理等效模型的地应力预测方法研究

地应力的精确预测是对页岩地层进行水平井钻井轨迹设计和压裂的基础.本文在分析页岩构造特征的基础上,提出了适用于页岩地层的岩石物理等效模型的建立流程,并以此为基础实现了最小水平地应力的有效预测.首先,通过分析页岩地层的矿物、孔隙、流体及各向异性特征,将其等效为具有垂直对称轴的横向各向同性介质,进行了页岩岩石物理等效模型的构建;然后建立了页岩地层纵横波速度经验公式,并将该经验公式与岩石物理等效模型均应用于实际页岩工区的横波速度预测中,二者对比表明,本文中建立的页岩气岩石物理等效模型具有更高的横波预测精度,验证了该模型的适用性;最后,利用该模型计算各弹性刚度张量,进而实现了页岩地层最小水平地应力的预测,与各向同性模型估测结果对比表明,该模型预测的最小水平地应力与地层瞬间闭合压力一致性更高,且储层位置更为明显,具有较高的实用性.     

Alteration induced changes of magnetic fabric as exemplified by dykes of the Koolau volcanic range

We studied 93 samples from 8 basaltic dykes of the Koolau volcanic range on the island of Oahu,Hawaii,USA,to determine the influence of hydrothermal alteration on the magnetic fabric as determined by anisotropy of magnetic susceptibility (AMS) measurements. Rock magnetic as well as microscopic investigations show that only ≈25% of the samples have retained their original magnetomineralogical composition of unaltered Ti-poor titanomagnetite. The remaining samples have undergone hydrothermal alteration which transformed the primary magnetic phase into a granular intergrowth of titanomagnetite, titanomaghemite and hematite. In both sample groups,this magnetic phase occurs in coarse (tens of microns),irregularly shaped particles as well as interstitial clusters of smaller (< 5 μm) grains. Our investigations show that hydrothermal alteration does change the bulk susceptibility and the degree of anisotropy but not the directions of principal axes of the AMS ellipsoid which are predominantly corresponding to normal magnetic fabric. The stability of AMS directions, regardless of the degree of alteration, points towards the model of distribution anisotropy as the controlling factor for the observed magnetic fabric.     

The impact of different clay minerals on the anisotropy of clay matrix in shale

Although clay is composed of disconnected anisotropic clay platelets, many rock physics models treat the clay platelets in shale as interconnected. However, the clay matrix in shales can be modelled as anisotropic clay platelets embedded within a soft isotropic interplatelet region, allowing the influence of disconnected clay platelets on the elastic properties of the clay matrix to be analysed. In this model, properties of the interplatelet region are governed by its effective bulk and shear moduli, whereas the effective properties of the clay platelets are governed by their volume fraction, aspect ratio and elastic stiffness tensor. Together, these parameters implicitly account for variations in clay and fluid properties, as well as fluid saturation. Elastic stiffnesses of clay platelets are obtained from the literature, including both experimental measurements and first-principles calculations of the full anisotropic (monoclinic or triclinic) elastic stiffness tensors of layered silicates. These published elastic stiffness tensors are used to compile a database of equivalent transverse isotropic elastic stiffness tensors, and other physical properties, for eight common varieties of layered silicates. Clay matrix anisotropy is then investigated by examining the influence of these different elastic stiffnesses, and of varying model parameters, upon the effective transverse isotropic elastic stiffness tensor of the clay matrix. The relationship between the different clay minerals and their associated anisotropy parameters is studied, and their impact on the resulting anisotropy of the clay matrix is analysed.     

Flow direction and magnetic mineralogy of lava flows from the central parts of the Peninsula of Baja California,Mexico

Magnetic properties of two apparently unrelated lava suites (one tholeiitic and the other alkalic) coexisting in the central parts of the Peninsula of Baja California, Mexico, were measured in this study. Macroscopic indicators and measurements of anisotropy of magnetic susceptibility (AMS) were combined to infer the flow direction on those lavas. These measurements were used to investigate the likelihood of the existence of an abnormally long tholeiitic lava flow in this part of the Peninsula. The obtained results indicate that the tholeiitic flows in the region constitute regular length flows, and are likely to have been issued through vents located within the area of study. Additionally, comparison of the magnetic signature of tholeiitic and alkalic lavas reveals a systematic difference in some of the magnetic parameters (bulk susceptibility and Curie temperatures). In particular, it is proposed that the narrow range of Curie temperatures characteristic of each lava type can be used as a reliable proxy for the identification of each lava type in the region. All of these findings show that the alkalic and tholeiitic lavas of the region are more closely related to each other than previously suspected.Editorial responsibility: R. Cioni     

西秦岭温泉岩体的磁组构特征及其侵位机制意义

结合岩石磁学、磁化率各向异性度与区域构造分析了西秦岭温泉岩体的侵位机制及意义.温泉岩体的样品的平均磁化率k_m值总体很大,岩石磁学表明对于磁化率较低的样品,顺磁性矿物（如黑云母等）对磁化率的贡献较大,而少量铁磁性矿物（如磁铁矿等）可能作为剩磁载体.对于磁化率较高的样品,其主要载磁矿物为磁铁矿;花岗岩样品的校正磁化率各向异性度P_J总体小于1.2,显示了岩体为流动磁组构的特征,磁化率椭球体形态参数T总体大于0,扁率E总体大于1,以压扁椭球体为主;岩体的磁面理同磁线理相比更为发育,样品的磁面理普遍表现出围绕岩体边界分布的特点,且倾角较陡;而在岩体内部磁线理与磁面理分布相对散乱,定向性差,这一特征说明温泉岩体的磁组构主要由侵位时的侧向挤压作用形成的;虽然岩体的磁组构特征总体显示了N-NEE和SW向的挤压作用,但岩体侵位时由商丹缝合带闭合所产生的垂直于缝合带方向的挤压作用已相对较弱.本文认为,温泉岩体侵位时是一种弱挤压环境,或者是一种相对稳定的环境甚至可能是一种相对引张的背景,这与温泉岩体形成于后碰撞环境,秦岭造山带已演化至后碰撞拆沉作用发生的伸展阶段所反映的区域构造背景是一致的.     

COMPARISON OF TIME,FREQUENCY, AND PHASE MEASUREMENTS IN INDUCED POLARIZATION*

In comparing the similarity between time, frequency, and phase measurements as used in the induced polarization method of geophysical prospecting, parameters must first be defined and the basis for comparison established. The conditions for mathematical equivalence then follow in a natural sequence. Laboratory measurements are made on a variety of rock samples to indicate the type of comparison and correlation expected from field measurements. Results indicate that frequency domain and phase measurements are equivalent, but two frequency domain measurements are needed to produce the same amount of polarization information as a single phase measurement. Frequency and time domain measurements will be similar but never equivalent due to the basic differences in their respective parameter definitions.     

非滞后剩磁各向异性

由于非滞后剩磁各向异性和等温剩磁各向异性的参数直接与岩石中的携磁矿物颗粒有关,它比传统的磁化率各向异性更明确地指示岩石组构,在构造地质研究中有较大应用前景．本文介绍了非滞后剩磁及其各向异性的测定方法,并以一个实例阐述了它在构造地质中的应用．     

各向异性介质中的AVO

分析了横向各向同性和方位各向异性介质的本构关系,由此讨论弹性波在两种各向异性介质中的传播特点,提出可表征这两种介质各向异性程度的广义参数．以此为基础讨论了两种各向异性介质中存在水平界面时的反射系数近似式,将Dely等人推导的横向各向同性介质中的反射系数公式推广到方位各向异性介质的主轴方向上．根据算例讨论修正的Banik和Thomsen的近似式,着重分析两种各向异性介质中的AVO关系及其对实际勘探的影响和指导意义．     

Magnetic susceptibility anisotropy,strain, and progressive deformation in Permian sediments from the Maritime Alps (France)

The relationships among magnetic susceptibility anisotropy, finite strain, and progressive deformation have been studied in Permian red shales and slates of the Maritime Alps (southeastern France). These rocks contain deformed reduction spots which serve as finite strain indicators. The magnetic fabric of undeformed regions is modified during deformation to yield characteristic magnetic susceptibility anisotropy patterns and a magnetic equivalent of the deformation path derived from strain measurements. The magnetic fabric changes progressively from oblate to prolate, and back to oblate as deformation increases. The quantitative relationships between natural strain and magnetic anisotropy in these rocks have been determined. They differ between the less and more deformed areas, perhaps due to a change in deformation mechanism accompanying an increase in metamorphism. The relationships provide a rapid means of strain determination using magnetic measurements but their variation emphasizes the need for local structural control.     

The anisotropy of magnetic susceptibility of lava flows: an experimental approach

Measurements of the anisotropy of magnetic susceptibility (AMS) of natural lavas have shown that AMS varies with depth within a lava flow. We have investigated the reasons for such variation by studying the effects of temperature and strain rate on the AMS of recent lava in the laboratory. Samples of lava from Kilauea were melted and subjected to a range of strain rate and cooling histories. The results show that the degree of anisotropy is a function of both the thermal and shearing history of a sample. High degrees of anisotropy were found only in samples that were deformed at temperatures close to those encountered during eruption and then rapidly quenched. Lavas subjected to similar shear stresses at high temperatures had low degrees of anisotropy if allowed to cool down slowly without further deformation. Additionally, lava subjected to complex shearing yield a lower degree of anisotropy even when high strain rates were imposed on it. These results lead to the conclusion that only the last phase of deformation is detectable using AMS and that high strain rates will not result in high degrees of anisotropy if either deformation ends while lava is still fluid or if the orientation of the maximum shear stress varies with time. The relation between the orientation of the principal susceptibilities and that of shear is less sensitive to variation on shear with time. Consequently, flow directions can be inferred confidently with this type of measurements.     

THE EFFECTS OF ANISOTROPY ON SQUARE ARRAY RESISTIVITY MEASUREMENTS*

An account is given of the use of the square array technique in investigating the surface effects of rotational anisotropy when the axes of anisotropy are inclined to the surface. It is shown that, as with other arrays, two anisotropy parameters and n can be derived by varying the array orientation. On the basis of these considerations, the effects of such anisotropy on the values of the mean apparent resistivity and azimuthal inhomogeneity ratio normally obtained in square array measurements is reviewed. Particular attention is paid to the variation of resistivity with orientation and it is noted that, in areas of moderate anisotropy, this variation is lower for the square than for the Schlumberger array. In addition to this advantage, the azimuthal inhomogeneity ratio obtained from square array measurements may be used to indicate the severity of anisotropy in an area and two field examples of this use are given. Where anisotropy is severe, gross variations of apparent resistivity with orientation are obtained with either square or collinear arrays. In these circumstances, the use of crossed measurements is considered and the particular stability of the crossed square array demonstrated.     

Changes of the magnetic susceptibility and its anisotropy of basalts by oxidation of titanomagnetites

Summary The changes of the anisotropy of the magnetic susceptibility of alkaline Tertiary basalts under titanomagnetite oxidation are investigated. The oxidation of the titanomagnetites was achieved by the following thermal processing of rock samples: 60 mins at a temperature of 400°C, 300 mins at T=400°C and 60 mins at T=500°C. It is shown that considerable changes of the values of the magnetic susceptibility, as well as of the degree of the preferred orientation of the titanomagnetites and of the ellipsoid of anisotropy in the sample occur as a result of the oxidation of titanomagnetites, contained in the samples, due to the said thermal processing. Moreover, the micro-structure of the grains, created by the oxidation of the titanomagnetites, causes the mostly linearly parallel configuration to change to a planar-parallel configuration.     

Stress‐dependent elastic anisotropy of sandstones

Elastic wave velocities in sandstones vary with stress due to the presence of discontinuities such as grain boundaries and microcracks within the rock. In the presence of non-hydrostatic stress fields the elastic wave velocities in sandstones often show significant stress-induced anisotropy. The elastic anisotropy due to any discontinuities within the rock can be written in terms of a second-rank and a fourth-rank tensor which quantify the effect on the elastic wave velocities of the orientation distribution and normal and shear compliances of the discontinuities. This allows elastic wave velocity measurements to be inverted to obtain the components of these tensors. Application of the method to ultrasonic velocity measurements made in a triaxial loading frame shows that a simple theory using only the second-rank tensor allows the P-wave stress-induced anisotropy to be predicted to reasonable accuracy from the S-wave anisotropy and vice versa, thus confirming the correctness of the underlying model. Deviations between the measurements and the predictions of this simplified theory are used to determine the ratio of the normal to shear compliance of the discontinuities. The discontinuities are found to be more compliant in shear than in compression.     

Seismic anisotropy in a hydrocarbon field estimated from microseismic data

The study of seismic anisotropy in exploration seismology is gaining interest as it provides valuable information about reservoir properties and stress directions. In this study we estimate anisotropy in a petroleum field in Oman using observations of shear‐wave splitting from microseismic data. The data set was recorded by arrays of borehole geophones deployed in five wells. We analyse nearly 3400 microearthquakes, yielding around 8500 shear‐wave splitting measurements. Stringent quality control reduces the number of reliable measurements to 325. Shear‐wave splitting modelling in a range of rock models is then used to guide the interpretation. The difference between the fast and slow shear‐wave velocities along the raypath in the field ranges between 0–10% and it is controlled both by lithology and proximity to the NE‐SW trending graben fault system that cuts the field formations. The anisotropy is interpreted in terms of aligned fractures or cracks superimposed on an intrinsic vertical transversely isotropic (VTI) rock fabric. The highest magnitudes of anisotropy are within the highly fractured uppermost unit of the Natih carbonate reservoir. Anisotropy decreases with depth, with the lowest magnitudes found in the deep part of the Natih carbonate formation. Moderate amounts of anisotropy are found in the shale cap rock. Anisotropy also varies laterally with the highest anisotropy occurring either side of the south‐eastern graben fault. The predominant fracture strikes, inferred from the fast shear‐wave polarizations, are consistent with the trends of the main faults (NE‐SW and NW‐SE). The majority of observations indicate subvertical fracture dip (>70° ). Cumulatively, these observations show how studies of shear‐wave splitting using microseismic data can be used to characterize fractures, important information for the exploitation of many reservoirs.     

Changes of anisotropy of the magnetic susceptibility of rocks induced by a magnetic field

Summary The changes of the anisotropy of magnetic susceptibility of igneous rocks, induced by a magnetic field, are studied. It is proved that changes in the degree of anisotropy of susceptibility and of the orientation of the susceptibility ellispoid of specimens occur due to the configuration of the domain structure under the effect of the magnetic field. The influence of this effect on the total anisotropy of rocks depends on the degree of anisotropy due to the shape factor and on the stability of the domain structure. A model concept is presented, explaining the qualitatively different pattern of the changes of the anisotropy of susceptibility under the effect of the magnetic field in various directions of the specimens.