Two‐dimensional controlled‐source electromagnetic interferometry by multidimensional deconvolution: spatial sampling aspects

We use numerically modelled data sets to investigate the sensitivity of electromagnetic interferometry by multidimensional deconvolution to spatial receiver sampling. Interferometry by multidimensional deconvolution retrieves the reflection response below the receivers after decomposition of the fields into upward and downward decaying fields and deconvolving the upward decaying field by the downward decaying field. Thereby the medium above the receiver level is replaced with a homogeneous half‐space, the sources are redatumed to the receiver level and the direct field is removed. Consequently, in a marine setting the retrieved reflection response is independent of any effect of the water layer and the air above. A drawback of interferometry by multidimensional deconvolution is a possibly unstable matrix inversion, which is necessary to retrieve the reflection response. Additionally, in order to correctly separate the upward and the downward decaying fields, the electromagnetic fields need to be sampled properly. We show that the largest possible receiver spacing depends on two parameters: the vertical distance between the source and the receivers and the length of the source. The receiver spacing should not exceed the larger of these two parameters. Besides these two parameters, the presence of inhomogeneities close to the receivers may also require a dense receiver sampling. We show that by using the synthetic aperture concept, an elongated source can be created from conventionally acquired data in order to overcome these strict sampling criteria. Finally, we show that interferometry may work under real‐world conditions with random noise and receiver orientation and positioning errors.     

Past and present magnetism of the Moon

The characteristics of the remanent magnetism of lunar samples suggests that it was acquired in a magnetic field on the Moon. The most likely origin of the field is a dynamo process in a molten, electricallyconducting core, but generation of a transient magnetic field during large meteorite impacts cannot be entirely ruled out. The magnetizing process may be thermoremanence, acquired when the rocks cooled through, the Curie point of the constituent iron grains which carry the remanent magnetization, or it may involve shock at the time of a meteorite impact, with or without a partial thermoremanence arising from heating.Evidence from absolute and relative determinations of the ancient field strength from the sample magnetizations strongly favours a global lunar field. This is implied by a trend which shows the field rising to a maximum value of 100 T between about 3.9–3.7 by ago and then decaying to 5–10 T until3.1 by. Such a systematic variation of field with time is not expected to be derived from magnetizations acquired in transient, impact-generated fields varying randomly in intensity.Contributory evidence for a dynamo field is provided by measurements of present lunar surface fields, the present very small dipole moment of the Moon and accumulating evidence of variation of the axis of the lunar field with time. Although there is no direct evidence for the existence of a lunar core the relevant observations are consistent with the presence of a core of up to 400 km, in radius. There are some difficulties associated with the lunar dynamo mechanism and its energy source but the evidence for a lunar dynamo is accumulating, with important implications for the structure and thermal history of the Moon.     

LINEAR TRANSFORMATIONS OF GRAVITY AND MAGNETIC FIELDS*

The spectral representation of gravity and magnetic fields shows that the mathematical expressions describing these fields are the result of convolution of factors which depend on the geometry of the causative body, the physical properties of the body and the type of field being observed. If a field is known, it is possible to remove or alter these factors to map other fields or physical parameters which are linearly related to the observed field. The transformations possible are: continuation, reduction to the pole, converting between gravity and magnetic fields, converting between components of measurement, calculation of derivatives, and mapping magnetization and density distribution, relief on interfaces, and vertical thicknesses of layers.     

Excitation of hide waves in the core due to transient-spatially periodic stress in the lower mantle

Summary Forced hydromagnetic oscillations in the outer core due to stress at its top are studied by means of a simple linear theoretical model originally proposed byHide [1] for the free oscillation studies. Both the magnetic and the inertial modes are excited. The expressions for the velocity, magnetic and vorticity fields are presented for a variety of stresses. They depend upon the wave number and frequency. In a numerical example wherein the stress varies periodically both in the space and the time, the amplitude of the induced magnetic field is found to be significant for reasonable values of various parameters.     

Quantifying the response of optical backscatter devices and transmissometers to variations in suspended particulate matter

Optical instruments have been used effectively in studies of sediment dynamics for several decades. Without accurate instrument calibrations, calculated concentrations of suspended particulate matter (SPM) may be unreliable, with implications for interpretations of sedimentary processes and sediment fluxes. This review aims to quantify the effect of variations in SPM characteristics on the response of optical instruments (optical backscatter sensors OBS and transmissometers) and to note the implications for users of these instruments. A number of factors have a significant impact on instrument response, for example; a change in grain size from medium sands to fine silts may lead to a×100 increase in instrument response; flocculation of fine particles may decrease instrument response by×2; and the presence of plankton in suspension may lead to poor instrument calibrations of SPM concentration. Calibrations carried out in environments either with multi-modal bottom sediments, where flocculation of fine-grained sediments is likely, or where the hydrodynamics or grain type are highly variable must also include a determination of the changing nature of the suspended load in space and time. A more complete understanding of instrument response to SPM and of calibration requirements may enable optical devices to be used to a greater potential as long-term measures of SPM concentration, and also enable improvements in calculations of net sediment fluxes.     

ATTEM系统中电流关断期间瞬变电磁场响应求解的研究

在瞬变电磁法中,由于发射电流关断时间不为零、接收线圈的谐振频率有限,早期瞬变电磁信号发生畸变,只能舍弃,因此存在着探测盲区. 针对这一问题,研究了瞬变电磁方法中发射电流关断期间总磁场的形成过程,论证了一次场、二次场和总瞬变场的关系,分析了接收线圈的频率特性和关断时间对瞬变电磁场的影响,提出从总磁场中剔除一次磁场影响的方法,从而获得电流关断期间和电流关断后的早期瞬变电磁场. 采用吉林大学自主研制的瞬变电磁测量系统(ATTEM)在长春市伊通河活断层进行勘探,进一步验证了算法的有效性,缩短了瞬变电磁法的勘探盲区,实现了近地表4 m以下的勘探,可以清晰地分辨近地表的低阻异常,提高了浅层探测精度和分辨率.     

Modeling of the solar activity double cycle using dynamical systems

The generation and evolution of the Sun’s magnetic field and other stars is usually related to the dynamo mechanism. This mechanism is based on the consideration of the joint influence of the α effect and differential rotation. Dynamo sources can be located at different depths of the convection zone and can have different intensities. Based on such a system, the dynamical system in the case of the stellar dynamo in a two-layer medium has been constructed with regard to meridional fluxes in order to model the double cycle that corresponds to the simultaneous presence of 22-year and quasi-biennial magnetic field oscillations. It has been indicated that the regime of mixed oscillations can originate because a dynamo wave moves oppositely to the meridional flows in the upper layer of the convection zone. This results in the deceleration of the toroidal field propagation and in the generation of slow oscillations. In deeper layers, the directions of a dynamo wave and meridional flows coincide with each other, as a result of which fast magnetic fields originate. Therefore, the total contribution of two oscillations with different frequencies corresponds to the appearance of quasi-biennial cycles against 22-year cycles. It has been indicated that the beating regime, which can be related to the secular oscillations of solar magnetic activity, originates in the system when the meridional flows are weak.     

东北地区重磁场与地壳结构特征

分析了东北地区的重、磁场特征,同时对研究区的布格重力异常和航磁异常据进行了小波分析计算.根据分析与计算可知,东北地区重力场以北东走向为主,表现出该地区重力场的主要趋势.根据磁场的分布特征,可将研究区分为六个区域:呼和浩特以北磁场相对平静区;赤峰一带正负磁场交互变化区;海拉尔以南磁场缓变区;齐齐哈尔—依春磁场剧烈变化区;长春—沈阳负磁场平缓区;牡丹江—丹东磁场区.利用重力资料,应用调和级数法对研究区的莫霍界面进行了反演计算,得到了该地区莫霍界面深度分布.根据磁力资料采用遗传算法反演计算了研究区居里界面的深度分布.同时对研究区的地壳结构特征进行了探讨.     

地球磁尾中重联产生的磁流通管的运动

本文通过MHD理论研究了细磁流通管在二维静止平衡介质中的运动.用地球磁尾中的一维细丝来表示流通管,通过数值模拟可以得到细丝随时间变化的一些性质.重联产生的细丝磁场比周围磁场偶极性更强,运动时表现出了很强的地向流.结果还显示了阿尔芬波、慢激波等MHD波从磁层的赤道面传播到地球电离层上并部分地反射回来.细丝在电离层上的足点的赤道向运动滞后于赤道面上的地向运动.虽然在模拟中细丝的初始等离子体压强低于周围压强,但是当它开始迅速向地球方向运动时,它的等离子体压强很快上升到与周围压强相当,甚至有时候大于周围压强的值.     

THE EFFECT OF A SUPERPARAMAGNETIC LAYER ON THE TRANSIENT ELECTROMAGNETIC RESPONSE OF A GROUND*

A thin superparamagnetic layer on the earth's surface greatly affects the transient electromagnetic response of a conducting ground. The effect of the layer is most evident for singleloop transient electromagnetic data where transient voltages decay as 1/t. Even when a separate transmitter and receiver are used, the effect of the superparamagnetic layer is still pronounced. In this case the effect of the 1/t term in the equation is much less. More dominant now is a 1/t² term. The effect of the superparamagnetism can readily be seen in the analytical expressions for the apparent resistivities. If the presence of the superparamagnetic layer is not recognized, then the apparent resistivities decrease with time rather than approach the true value of the host rock.     

Magnetic methods in tracing soil erosion,Kharkov Region,Ukraine

Magnetic measurements of soils are an effective research tool in assessing soil erosion. This approach is based on detecting layers showing different magnetic properties in vertical soil profiles and lateral catenas. The objective of this research is to compile data on magnetic susceptibility (MS) of soils in Eastern Ukraine to assess the soil erosion rates. The chernozems of Tcherkascy Tishki (Kharkov Region, Ukraine) have undergone a field crop rotation without proper soil conservation technologies being applied. We conducted an intrinsic element grouping of the magnetic susceptibility values and demonstrated that they can be used as MS cartograms in soil erosion mapping. The study showed a strong correlation between the MS values and the erosion index. MS and the erosion index were found to correlate with the humus content. Magnetic mineralogical analyses suggest the presence of highly magnetic minerals (magnetite and maghemite) as well as weakly magnetic goethite, ferrihydrite, and hematite. Stable pseudosingle-domain (PSD), single-domain (SD), and superparamagnetic (SP) grains of pedogenic origin dominate in the studied chernozems. Being an effective, quick and low cost alternative, magnetic methods can be successfully used in the soil erosion investigations.     

Generalized Tikhonov's algorithm for accurate calculation of one-dimensional transient responses directly in time domain

In the last two decades, forward modelling for the time domain (transient) electromagnetic method has concentrated almost entirely on multi-dimensional models and algorithms. At the same time, the interpretation of real field data is still mainly one dimensional. This is caused by the lack of an efficient multi-dimensional acquisition procedure supported by sufficiently fast and reliable inversion software, on the one hand, and by the great efficiency of one-dimensional field set up and interpretation of the data on the other hand. The latter is particularly true for the short offset transient electromagnetic method, which is much less sensitive to multi-dimensional effects, compared to long offset methods. The most commonly used one-dimensional forward modelling algorithms are based on the spectral method, which requires calculating rapidly oscillating Fourier–Bessel (Hankel) integrals. Due to the very fast decay of short offset responses, the integrals become computationally unstable at late times of the transient process. Although this problem has been successfully solved for practically feasible measurement times of conventional short offset systems using transverse electric and mixed transverse electric and transverse magnetic fields, it turned out crucial for novel methods based on the use of unimodal transverse magnetic fields. These methods are much more sensitive to geoelectric parameters of the Earth in general and those of resistive targets, in particular, but they generate responses, which drop at late times significantly faster than those of conventional methods. Such behaviour of transverse magnetic fields represents severe computational problem for the spectral method, but is successfully solved by direct time domain algorithms. This article describes a generalization of the well-known Tikhonov's solution to a boundary value problem directly in time domain, which is applied to an arbitrary one-dimensional earth model excited by an arbitrary source. Contrary to existing spectral algorithms, the described method allows accurate calculations of both transverse electric and transverse magnetic transient responses at arbitrarily late times. On the other hand, it is more time efficient than finite-difference/finite element direct time domain algorithms and provides analytical late-stage asymptotic solutions.     

Seismoelectric numerical simulation in 2D vertical transverse isotropic poroelastic medium

Seismoelectric coupling in an electric isotropic and elastic anisotropic medium is developed using a primary–secondary formulation. The anisotropy is of vertical transverse isotropic type and concerns only the poroelastic parameters. Based on our finite difference time domain algorithm, we solve the seismoelectric response to an explosive source. The seismic wavefields are computed as the primary field. The electric field is then obtained as a secondary field by solving the Poisson equation for the electric potential. To test our numerical algorithm, we compared our seismoelectric numerical results with analytical results obtained from Pride's equation. The comparison shows that the numerical solution gives a good approximation to the analytical solution. We then simulate the seismoelectric wavefields in different models. Simulated results show that four types of seismic waves are generated in anisotropic poroelastic medium. These are the fast and slow longitudinal waves and two separable transverse waves. All of these seismic waves generate coseismic electric fields in a homogenous anisotropic poroelastic medium. The tortuosity has an effect on the propagation of the slow longitudinal wave. The snapshot of the slow longitudinal wave has an oval shape when the tortuosity is anisotropic, whereas it has a circular shape when the tortuosity is isotropic. In terms of the Thomsen parameters, the radiation anisotropy of the fast longitudinal wave is more sensitive to the value of ε, while the radiation anisotropy of the transverse wave is more sensitive to the value of δ.     

Quasi-free-decay magnetic modes in planetary cores

A new category of hydromagnetic waves in a rotating conducting fluid within a spherical shell geometry is investigated. These quasi-free-decay magnetic modes are based on particular solutions of the induction equation where the magnetic diffusion plays the central role. These solutions, normally only decaying with time, become propagative owing to the combined action of the background magnetic field and the rotation. The amplitude and sign of their azimuthal phase drift strongly depend on morphology and magnitude of the background magnetic field. The validity domain of these quasi-free-decay (QFD)-modes is related to the Elsasser number and is written as Λ???1. It follows that these modes dissipate quickly before propagating out. This restriction falls when the above criterion is no longer fulfilled (Λ?～?1), the corresponding modes evolving towards distorted QFD-modes. A systematic study of these QFD-modes is made in the limit of small Elsasser number (Λ???1), for the different symmetries allowed. Application to the Earth's and other planetary cores is then examined for an Elsasser number up to Λ?≈?O(1), in relation to the geomagnetic secular variation and the frozen-flux approximation.     

Analysis and interpretation of anomalous conductivity and magnetic permeability effects in time domain electromagnetic data: Part I: Numerical modeling

Time domain electromagnetic (TDEM) response is usually associated with eddy currents in conductive bodies, since this is the dominant effect. However, other effects, such as displacement currents from dielectric processes and magnetic fields associated with rock magnetization, can contribute to TDEM response. In this paper we analyze the effect of magnetization on TDEM data. We use a 3-D code based on finite-difference method, developed by Wang and Hohmann [Geophysics 58 (1993) 797], to study transient electromagnetic field propagation through a medium containing bodies with both anomalous conductivity and anomalous magnetic permeability. The remarkable result is that the combination of anomalous conductivity and permeability within the same body could increase significantly the anomalous TDEM response in comparison with purely conductive or purely magnetic anomalies. This effect has to be taken into account in interpretation of TDEM data over electrical inhomogeneous structures with potentially anomalous magnetic permeability.     

Solar-wind induction and lunar conductivity

A summary review of electromagnetic induction driven in the Moon by the interplanetary magnetic field is given. The point of view developed centers on inversion of Fourier transforms of the magnetic field in the free-stream solar wind (forcing function) and the response on the lunar surface measured by Lunar Surface Magnetometers. Conductivity profiles are shown to depend upon the central angle between the magnetometer given by local time and the incident wave-normal direction. The induction excites at least magnetic dipole and quadrupole “radiation”, but any scattered field is confined to the Moon's interior, save for propagation down the cavity where a TE-mode surface wave is generated. Confinement of the induced field on the sunward hemisphere and near the subsolar point is nearly complete, decreasing to the limbs, while in the diamagnetic cavity downstream of the Moon, partial confinement takes place. Both time and spatial multipoles of the induced field are present in the lunar interior complicating inversion into conductivity profiles. Profiles are reviewed and resolution limits are given and compared to those obtained from transient analysis. Finally a qualitative comparison to conductivity in the Earth is given.     

On disturbances in an elastic medium in contact with a liquid medium and subjected to a magnetic field

Summary The present note makes use of electromagnetic equations of Maxwell and those of mechanical motions to work out the problem of disturbances in two perfectly conductive media—an ideal liquid and a perfectly elastic solid-acted upon by a magnetic field perpendicular to their plane of contact. The displacement suffered by solid medium has been determined when a tangential force, exponentially decaying with time, acts in the plane of contact of the two media. The solution of the problem is achieved by using the method of Laplace transform.     

Magnetic field reversals and galactic dynamos

We argue that global magnetic field reversals similar to those observed in the Milky Way occur quite frequently in mean-field galactic dynamo models that have relatively strong, random, seed magnetic fields that are localized in discrete regions. The number of reversals decreases to zero with reduction of the seed strength, efficiency of the galactic dynamo and size of the spots of the seed field. A systematic observational search for magnetic field reversals in a representative sample of spiral galaxies promises to give valuable information concerning seed magnetic fields and, in this way, to clarify the initial stages of galactic magnetic field evolution.     

Cone-shaped source characteristics and inductance effect of transient electromagnetic method

Small multi-turn coil devices are used with the transient electromagnetic method (TEM) in areas with limited space, particularly in underground environments such as coal mines roadways and engineering tunnels, and for detecting shallow geological targets in environmental and engineering fields. However, the equipment involved has strong mutual inductance coupling, which causes a lengthy turn-offtime and a deep “blind zone”. This study proposes a new transmitter device with a conical-shape source and derives the radius formula of each coil and the mutual inductance coefficient of the cone. According to primary field characteristics, results of the two fields created, calculation of the conical-shaped source in a uniform medium using theoretical analysis, and a comparison of the inductance of the new device with that of the multi-turn coil, show that inductance of the multi-turn coil is nine times greater than that of the conical source with the same equivalent magnetic moment of 926.1 A·m². This indicates that the new source leads to a much shallower “blind zone.” Furthermore, increasing the bottom radius and turn of the cone creates a larger mutual inductance but increasing the cone height results in a lower mutual inductance. Using the superposition principle, the primary and secondary magnetic fields for a conical source in a homogeneous medium are calculated; results indicate that the magnetic behavior of the cone is the same as that of the multi-turn coils, but the transient responses of the secondary field and the total field are more stronger than those of the multi-turn coils. To study the transient response characteristics using a cone-shaped source in a layered earth, a numerical filtering algorithm is then developed using the fast Hankel transform and the improved cosine transform, again using the superposition principle. During development, an average apparent resistivity inverted from the induced electromotive force using each coil is defined to represent the comprehensive resistivity of the conical source. To verify the forward calculation method, the transient responses of H type models and KH type models are calculated, and data are inverted using a “smoke ring” inversion. The results of inversion have good agreement with original models and show that the forward calculation method is effective. The results of this study provide an option for solving the problem of a deep “blind zone” and also provide a theoretical indicator for further research.