建筑土木系探地雷达外文中英对照翻译

外文文献

3 PHYSICAL PROPERTIES I

3.1 WHY ARE PHYSICAL PROPERTIES IMPORTANT?

GPR investigates the subsurface by makinguse of electromagnetic fields which propagate into the subsurface. EM fields which are time varying consist of coupled electric (E) and magnetic (H) fields. As discussed in section 2 the fields interact with the surrounding media. This interaction is macroscopically described by the constitutive equations 2.5 to 2.7. The manner in which the electromagnetic fields interact with natural materials controls how electro-magnetic fields spread into the medium and are attenuated in the medium. In addition, the variation in physical properties gives rise to the observed subsurface reflections obtained with a GPR system.

In most geological and NDT (non-destructive testing) applications of GPR, electrical properties tend to be the domi-nant factor controlling GPR responses. Magnetic variations are usually weak. Occasionally magnetic properties can affect radar responses and GPR users should be cognizant of magnetic effects.

An electric field in a material gives riseto the movement of electric charge, (i.e., electric current). The current flow depends on the nature of the material. There are two types of charge in a material, namely bound and free, which give rise to two types of current flow, namely displacement and conduction. In the following, we will provide a simple overview of the two types of current flow. An in-depth discussion of electrical properties can be found in the text by

Von Hippel,(1954).

Magnetic properties are controlled by the electric charge circulation character at the atomic and molecular level. Macroscopic magnetic properties are addressed briefly in these notes. Von Hippel (1954) addresses some of the basic concepts.

3.2 CONDUCTION CURRENTS

Most people are very familiar with electrical conduction currents. Conduction currents are created when unbound(free) charges move in a material. The electrons which flowin a metal wire are an example of conduction current. In a metal, electrons move through the metallic matrix to transfer charge from one point to another. Another common conduction mechanism is the movement of ions in a water solution. The later is much more important in most GPR applications.

Conduction currents arise whenfree charge accelerates to a terminal velocity (basically instantaneously) when an electric field (E) is applied. As long as the electric field is applied, the charge moves; when the electric field is removed, the charge

decelerates and stops moving Figure 3-1 illustrates these concepts.

Figure: 3-1 Conceptual illustration of charge movement for conduction currents.

a) Charge velocity versus time after E field applied.

b) Energy is extractedfrom the applied electric field versus time.

Figure: 3-2 When an electric field is applied, unbound electrical charges accelerate to a terminal velocity. After initial acceleration, velocity becomes constant and a continual transfer of energy to

the surrounding material in the form of heat occurs

All the time that charge is moving, the moving charge is working against

its

surroundings dissipating energy in the form of heat. The moving charge bumps into 'non-moving'objects and transfers mechanical energy which appears in the form of heat in the medium. Conduction currents represent an energy dissipating mechanism for an electromag-netic field. Energy is extracted from the electromagnetic field and transferred irreversibly into the medium as heat.

Mathematically one describes the relationship between conduction current and the applied electric field as indicated

in Equation 3-1.

（3-1） =

In simple materials, the relationship is linear and the proportionality constant is referred to as the electrical conductiv-ity. Electrical conductivity has units ofSiemens per meter (S/m). For many applications, however, it is more useful to work with units of milliSiemens per meter (mS/m). Conductivity is dependent on the charge density and the inter-nal statistical mechanical interaction ofthe charge with its surroundings. These details are beyond the scope of this discussion.

It should be noted that electrical conductivity and resistivity are directly related. Refer toFigure 3-3 for the relation-ship and the expression of Ohm's law. Electrical resistivity is the inverse of electrical conductivity.

Figure: 3-3 Relationship between current and applied field as well as the relationship will Ohm's

law and resis-tively.

It is important to note that there are simplifications in the above discussion from the general form shown in Chapter 2.

The conductivity is shown as being a constant. In fact it can be a function of the rate of change of the electric field,the amplitude of electric field itself, as well

as

temperature, pressure and many other factors. As a result, one should not be surprised to see both non-linearity and frequency dependent conductivity in real materials. Generally these are second order effects but they must be considered when advanced use of GPR is contemplated. For this basic GPR overview, they will be treated as secondary issues.

3.3 DISPLACEMENT (POLARIZATION) CURRENTS

Displacement currents are associated with bound charges which are constrained to limited distance of movement. Examples of this are the electron cloud around an atomic nucleus, the electricalcharge in a small metal object imbed-ded in an insulating environment, and the redistribution ofthe molecular dipole moment intrinsic to some molecules. Figure 3-4 depicts the concept. When an electric field is applied, bound charge moves to another static configuration.This transition occurs virtually instantaneously after which the charges no longer move. During the transition, energy is extracted from the electric field and the energy is stored in the material. When the field is removed, the charge moves back to the original equilibrium distribution and energy is released. This type of behavior is typical of what happens in a capacitor in an electric circuit. Energy is stored by the buildup of charge in the capacitor and then energy is extracted by the release ofthat charge from the device.

Figure: 3-4 Conceptual illustration of charge movement associated with displacement currents. Figure 3-5 depicts the characterization of charge separation in a material. When an electrical field is applied, dis-placement of charge in a bulk material gives rise to a dipole moment distribution in the material. The charge separa-tion is described in terms of a dipole moment density, D.In a more formal derivation, D is called the electric displacement field (see chapter 2). In simple materials, the induced dipole moment densityis directly proportional to the applied electric field and the proportionality constant is referred to as the dielectric permittivity of the material and

has units of Farads/m (F/m).

Figure: 3-5 Dipole moment density induced by applied electric field and relation to displacement

current.

The creation of a dipole moment distribution in the material is associated with charge movement. The electric current associated with this charge movement is referred to as displacement current. The displacement current is mathemati-cally defined as the time rate of change of the dipole moment density.

The electric permittivity is never zero. Even in a vacuum, the permittivity, takes on a finite value of 8.85 x 10-12F/m (Farads per meter). The explanation for this lies in the field of quantum electrodynamics and is far beyond the scope of this discussion.

It is often more convenient to deal with a dimensionless term called relative permittivity or dielectric constant, K. As depicted in Figure 3-6 , the relative permittivity is the ratio of material permittivity to the permittivity of a vacuum.

Figure: 3-6 Dielectric constant or relative permittivity is the ratio of permittivity of material to that

of free space.

3.4 TOTAL CURRENT FLOW

In any natural material, the current which flows in response to the application of

an electric field is a mixture of con-duction and displacement currents. Depending on

the rate of change of the electric field, one or other of the two types of current may dominate the response. Mathematically, the total current consists of two terms; one which depends on the electric field itself and one which depends onthe rate of change of the electric field.

= + (3-2)

= +∈ (3-3)

Quite often it is useful to deal with sinusoidally time varying excitation fields. In this situation, one finds that the dis-placement currents are proportional to the angular frequency.

=( + ∈) (3-4)

where is the angular frequency.

The displacement currents are out of phase with the conductioncurrents by 90° which is what ascribing an imaginary =√( 1) aspect to the displacement component implies. Those familiar with electrical engineering circuitry termi-nology will realize that there is a phase shift between the conduction currents and the displacement currents which indicates that one term is an energy dissipation mechanism and the other one is an energy storage mechanism .A simplified plot of displacement current and conduction currents as well as total current versus frequency is pre-sented in Figure 3-7. Usually there is some frequency above which the displacement currents exceed the conduction currents. In a simple material where the conductivity and the dielectric permittivity are constant, there is a transition frequency, , where the displacement currents and conduction currents are equal. Above this frequency, displace-ment currents dominate; below this frequency, conduction currents dominate. This factor is important when we deal with EM wave propagation. This frequency defines the on set of the low-loss regime important to GPR.

Figure: 3-7 Conduction, displacement and total current versus frequency.

Mathematically the transitionfrequency is defined.

=∈ （3-5）

In addition, another term called the loss tangent is defined. The loss tangent is the ratio of conduction to displace-ment currents in a material. =

=∈ （3-6） The term loss target tends to be most common in electrical engineering contexts.

Conductivity and permittivity are not independent of the excitation frequency. There is always some variation. This topic is beyond the scope of this chapter of the notes but there is considerable literature (i.e., Olhoeft, 1975) on fre-quency dependent electric

3.5 MAGNETICPERMEABILITY

Magnetic permeability is seldom of major importance for GPR applications. For completeness and to address those exceptional situations where permeabilitymay become important, we review some of the basic aspects of magnetic permeability.

Magnetic permeability is actually related to the intrinsic electrical characteristics of the basic building blocks of phys-ical materials. In simple terms, charged particles, which form atoms , which in turn make molecules, have a quantum mechanical property referred toas spin. When combined with the charge on the particle, spin results in the particle having a magnetic dipole moment. When an electron moves around an atomic nucleus, the charge motion can also create a magnetic moment.

The simple analogy is to have electrical charge uniformly distributed on a spherical ball and then spin ball. The resulting rotating charge appears to be a circular loop of current, which in turn gives on rise to a magnetic dipole.

Magnetic properties are essentially the properties of an electrical change moving around a closed path.al properties which can be referred to.

a）

b）

Figure: 3-8 a) A simple picture suggesting the origin of electron spin movement; b) relating the

magnetic moment induced in an electron cloud by a change in magnetic field

Figure: 3-9 Relating the magnetic moment to a simple electron orbit.

The details are obviously more complex but this provides a simple pictorial model to use.Atoms are formed of elec-trons and protons plus neutrons. The electrically changed components have intrinsic and orbital spin when they form molecules of a given type of material. The particular orientation of the spin axes of the individual particles can be aligned in random or structured ways and may be altered by an ambient magnetic field. If the molecular structure does not accept random spin orientation but requires a structured crystalline architecture, the material

can have a per-manent magnetization. If component parts can move to align parallel

or anti-parallel to an applied field, an induced magnetization response will arise.

Magnetic permeability measures the degree to which individual dipole moments of the building blocks can be aligned or moved from their normal orientation by an externally applied magnetic field. The more of the individual moments that can be moved into alignment, the more magnetically polarizable the material. The magnetic properties of materi-als are quantified by magnetic dipole moment density. When an electrical current flows in a closed loop, the mag-netic moments is.

= （3-7）

where M is the dipole moment, I is the current and A is the area of the loop enclosed by the current filament. M has units of Am2 For bulk materials, the material is characterized by dipole moment density

= （3-8）

which has units of A/m. V is volume. When a magnetic field, H, induces a

magnetic moment, the amount of moment is expressed as

（3-9） =

where k is the magnetic susceptibility (and is a dimensionless quantity). There is considerable similarity between induced magnetic moment and induced electric dipole momentdiscussed previously in the displacement current sec-tion.

In the material, the magnetic flux is expressed as

= 0( + ) （3-10）

and magnetic permeability is expressed as

= 0(1+ ) （3-11）

where

0=4 ×10 7 / （3-12）

The term relative magnetic permeability is expressed as

= =(1+ ) （3-13） 0

in an analogous fashion to relative permittivity. When both magnetic and electric properties vary, relative permittiv-ity is usually expressed as Ke to avoid confusion.

The presence of a magnetic field induces the individual dipole moment to change orientation and line up with the applied field. In some materials the alignment is in the same direction as the applied field, whereas in other materials the alignment maybe anti-parallel to the applied field. These two types of behavior referred to as paramagnetism and diamagnetism. Generally these responses are very weak and give rise to small variations in magnetic permeability. Typical values of magnetic susceptibility are less than 10-5.

In some situations, however, the magnetic moments can be aligned in large sections (called domains) of the crystal structure of a material. The moment ofdomains can be changed by the molecules in the crystal structure behaving in a sympathetic fashion and moving from one domain to another. Such materials are known as ferromagnetic materi-als.

In ferromagnetic materials, the polarization can be quite large and high values of Kmin the range of tens or even hun-dreds may be observed in materials such as iron, cobalt, and nickel. With ferromagnetic materials, the behavior is more complex in that the dipole moments when moved, or aligned, remain aligned. This is known as permanent magnetization. In such materials the permeability is very high and the dynamic behavior of the material complex. Such materials seldom form a large volume fraction of soilsand rocks but their presence in small amounts can be the dominant factor determining bulk permeability.

Behavior can be very complex. The behavior of dipolemoment density is controlled by how domains move, grow and change orientation which can be field dependent, frequency dependent and temperature dependent. The subjects are well beyond the scope of these notes.

Figure: 3-10 Ferromagnetic domain structures: a) single crystal, b) polycrystalline specimen.

Arrows represent the direction of magnetization.

Figure: 3-11 Magnetization of a ferromatic material: a) unmagnetized, b) magnetization by

domain wall motion, c) magnetization by domain rotation.

In soils and rocks, magnetic behavior is dictated by the amount of magnetite (or similar minerals such as meghemite or ilmenite). The graph (from Grant & West (1965)) in Figure 3-14 shows how susceptibility varies with magnetite volume fraction. The simple approximate formula is

=3.8 （3-14）

where q is the volume fraction of magnetite in the material. To put this result in perspective, 1% by volume magnetite (which is very high in most cases) content

yields Km=1.038. Only in rare cases will Kmbe significantly different from unity.

Figure: 3-12 Data from which the emperial formula for susceptibility k=2.89 x 10-3V1.01 was

derived. [Mooney and Bleifuss (7).]

中文翻译

3 物理性质I

3.1 为什么物理性质重要

探地雷达是利用电磁场的传播来研究地下空间。电磁场是随时间变化的一对耦合的电场（E）和磁场（H）。在第2节中讨论了场与周围介质的相互作用。本文方程2.5到2.7的宏观描述了这种相互作用。而电磁场的天然材料，互动的方式，控制电磁场在基质中的扩散、衰减。此外，在地下反射与雷达系统获得观测物理性能的产生到变化。

在大多数探地雷达的地质和NDT（无损检测）应用中，电气性能往往是主要控制探地雷达响应的因素。磁场的变化通常是弱的。磁性能偶尔的影响雷达的反应，探地雷达用户应该认识到磁效应。

电场在材料中产生电荷的运动，（即，电流）。当前的流动取决于材料的性质。材料中有两种类型的电荷，即束缚和自由，其产生两种类型的束流，即位移和传导。下面，我们将提供一个简单的的电流流动的两种类型的概述。在希佩尔文本（1954）可以看到关于电气特性的深入探讨。

原子和分子水平上的电荷循环特性控制着磁性。希佩尔（1954）的笔记提出宏观磁特性简要讨论和基本概念。

3.2、传导电流

大多数人都非常熟悉电流的传导。材料中未束缚的（自由）电荷运动创造出传导电流。金属丝的电子流是传导电流的一个例子。在一种金属，电子通过金属基体的电荷从一点传输到另一个。另一个常见的传导机制是在水溶液中的离子的运动，是探地雷达中更重要应用。

自由电荷加速到终端速度（基本上瞬间）时应用电场（E）产生传导电流。图3-1展示了仅利用电场使电荷运动拆下，减速和停止移动的这些理念。

图3-1：传导电流电荷运动的概念图。

a）应用E场后电荷的速度与时间。

b）施加的电场随时间提取的电能。

图3-2：当施加电场时，自由的电荷在初始加速度后，加速到终端速度。速度常数和在对周

围材料的能量连续转移为以热的形式出现。

运动消耗所有的时间，运动的电荷能量耗散是在其周围以热的形式。运动电荷碰到的静止物质并以热的形式在介质中传送机械能。

传导电流电磁场的能量耗

散的机制。从电磁场的能量转移到基质中提取和不可逆热。

数学描述传导电流和电场之间的关系表示公式。

（3-1） =

对简单的材料，导电性比例常数为线性关系。电导率的单位为西门子/米（S / M）。但是，对于许多应用程序，单位毫西门子每米（MS /米），它是更有用的。导电性电荷密度和内部统计力学是依赖于电荷与周围的环境的相互作用。这些细节超出了本文讨论的范围。值得注意的是，电导率和电阻率有直接的关系。引用3-3欧姆定律的表达的关系。

图3-3：电流和外加磁场的关系以及将欧姆定律，电阻性能之间的关系。

根据上文第二章所讨论的关于简化的重要性需重视。电导率显示为一常数。事实上，它可以对电场的变化率，电场振幅本身，以及温度，压力和许多其他因素的函数。其结果，应不要对两个非线性和频率所依据的真实材料感到惊奇。。通常这些都是二阶效应，但他们必须考虑使用探地雷达先进设想。这个基本的探地雷达概述，他们视其为次要的问题。

3.3 位移（极化）的电流

位移电流与电荷的运动有限距离的约束有关。这样的例子如原子核周围的电子云，在一个小的金属物体在绝缘环境嵌入的一个电荷，且再分配的分子偶极矩的一些分子特性。图3-4所描绘了这样的概念：当施加电场时，束缚电荷移动到另一个静态状态。这种转变发生几乎瞬间之后，不再动弹受指控。在过渡期间， 能源从电场和能量提取并存储在材料中。场被消除时，电荷回到原来的平衡分布且释放能量。这种发生在电子电路中的电容器行为是典型的。能量是由电容器中存储的电荷的积累，然后能源是由从器件释放的该电荷中提取。

图3-4：位移电流与电荷运动的有关概念图。

图3-5描述材料中电荷的分离表征。当一个电场，在散装材料的电荷位移引起材料中的偶极矩分布。电荷分离效果是用一个偶极矩密度来描述，根据一个更正式的推导，D.被称为电位移场（见第二章）。在简单的材料，诱导偶极矩密度成正比外加电场和比例常数称为材料的介电常数，单位为法拉/ 米（F / M）。

图3-5：偶极矩密度和电场诱导的位移电流的关系。

材料中创造的偶极矩的分布与电荷的运动有关。电流与此相关的电荷运动被称为位移电流。位移电流是数学上定义的时间变化率的偶极矩密度。

介电常数不会是零。即使在真空，介电常数，ε0为8.85×10-12 F / M（法拉每米）的有限值。在量子电动力学方面对此的解释，远远超出了本文的讨论范围。

它往往是更方便的处理的一个无量纲的术语称为相对介电常数和介电常数，K。图3-6所示，相对介电常数是材料介电常数与真空介电常数的比率

图3-6：介电常数或相对介电常数材料的介电常数，自由空间的比率

3.4 总电流

任何的天然材料，电场的应用电流是一种混合的传导和位移电流。根据电场的变化率，目前可能会占主导地位的有一个或其他的两种类型。在数学上，总电流包括两个方面；一个取决于电场本身和一个取决于电场的变化对率。

= + (3-2)

= +∈

通常是处理正弦时对变化激发场有用。在这种情况下，人们发现，位移电流与角频率成正比。

(3-3)

=( + ∈) (3-4)

角频率w

虚构方面的 =√位移分量位移电流和传导电流的相位相差90°。熟悉电气工程电路专门名词会意识到有一个相移之间的传导电流和位移电流是表示一个一个能量耗散机制术语，另一个是能量存储机构。一个简化的位移电流和传导电流和总电流与频率图3-7。通常有一些频率以上的位移电流超过传导电流。一个简单的材料的电导率和介电常数是恒定的，有一个过渡频率，和传导电流的位移电流是相等的。高于这个频率，位移电流占主导地位；低于这个频率，传导电流控制。这个因素很重要，当我们处理采用电磁波的传播。对探地雷达来说频 率是重要的定义上的低损耗。

图3-7：传导，位移和总电流频率。

数学上过度频率的定义

=∈ （3-5）

此外，另一项定义称为损耗角正切。传导材料中位移电流的损耗角正切比例。

=

=∈ （3-6）

该种损失往往在电气工程中是最常见的。

电导率和介电常数不是独立的激发频率。总有一些变化。这主题超出了本章的论述范围，但有相当多的文献（即，奥尔霍夫特，1975）涉及到电气性能对频率的依赖性的主题。

3.5导磁率

导磁率在探地雷达的重要应用中用的很少。常在解决一些特殊情况下，渗透率可能变得非常重要，我们回顾一些渗透性的基本磁性。

物理材料的基本构建块的内在相关与电气特性实际上是导磁率。简单来说，带电粒子，形成原子，从而使分子，有一个量子机械性能被称为自旋。结合颗粒上的电荷，在粒子的自旋结果具有磁偶极矩。当一个电荷的电子绕着原子核运动，也可以创建一个磁矩。

简单电荷均匀分布类比在球后旋绕。由此产生的旋转电荷似乎是圆电流，从而给一个磁偶极子上升。电的磁性能变化基本上在一个封闭的路径。

a）

b）

图3-8：a）一个简单的图片显示的电子自旋运动的起源；b）有关在磁场中电子云的变化引起的磁矩。

图3-9：一个简单磁矩的电子轨道。

详细的显然更复杂，所以使用一个简单的图形模型。原子由电子、质子和中子构成。自旋形成的时候电子改变组件的固有的轨道一个给定类型的物质分子。对单个粒子的自旋轴特定方向可随机或结构化的方式排列，可能是通过周围磁场的改变。如果分子结构不接受随机自旋取向而需要一个结构化的结晶结构，该材料可以有一个永久磁化。如果部件可以对齐平行或反平行的磁场，感应将产生的磁化响应。

导磁率具有可以排列的特征，单个的偶极矩的积累或从其正常的方向施加外部的磁场。更多可移动到互动位置，材料的磁性极化。当电流在一个闭合回路，材料的磁特性的磁偶极矩密度量化。磁矩

= （3-7）

其中M是偶极矩，I是电流，是由电流丝封闭的环路面积。M的单位是Am2 对于散装材料，该材料在通过偶极矩密度的特征。

= （3-8）

这单位的A / m。V是体积。当一个磁场,H,诱使一个磁矩,瞬时量表示为

（3-9） =

其中K是磁化率（是一个无量纲的量）。有较大的相似性的导磁矩和诱导的电偶极矩的电流截面位移在之前讨论过。

在材料中，磁通量表示为

= 0( + ) （3-10）

导磁率表示为

= 0(1+ ) （3-11）

其中

0=4 ×10 7 / （3-12）

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