Radio Propagation and Remote Sensing of the Environment - Chapter 1 docx

Radio propagation and remote sensing of the environment / N.A.. 278 10.2 Electromagnetic Waves Used for Remote Sensing of Environment.... In addition, radiowave devices for remote sensin

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of the Environment

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Armand, N A.

Radio propagation and remote sensing of the environment / N.A Armand, V.M Polyakov.

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ISBN 0-415-31735-5 (alk paper)

1 Radio wave propagation 2 Earth sciences—Remote sensing I Poliakov, Valerii Mikhailovich II Title.

TK6553.A675 2004 621.36'78—dc22

2004047816

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Chapter 1 Electromagnetic Field Equations 1

1.1 Maxwell’s Equations 1

1.2 Energetic Relationships 3

1.3 Solving Maxwell’s Equations for Free Space 4

1.4 Dipole Radiation 7

1.5 Lorentz’s Lemma 11

1.6 Integral Formulas 12

1.7 Approximation of Kirchhoff 17

1.8 Wave Equations for Inhomogeneous Media 18

1.9 The Field Excited by Surface Currents 19

1.10 Elements of Microwave Antennae Theory 22

1.11 Spatial Coherence 25

Chapter 2 Plane Wave Propagation 31

2.1 Plane Wave Definition 31

2.2 Plane Waves in Isotropic Homogeneous Media 32

2.3 Plane Waves in Anisotropic Media 35

2.4 Rotation of Polarization Plane (Faraday Effect) 39

2.5 General Characteristics of Polarization and Stokes Parameters 40

2.6 Signal Propagation in Dispersion Media 44

2.7 Doppler Effect 50

Chapter 3 Wave Propagation in Plane-Layered Media 53

3.1 Reflection and Refraction of Plane Waves at the Border of Two Media 53

3.2 Radiowave Propagation in Plane-Layered Media 59

3.3 Wave Reflection from a Homogeneous Layer 60

3.4 Wentzel–Kramers–Brillouin Method 67

3.5 Equation for the Reflective Coefficient 70

3.6 Epstein’s Layer 74

3.7 Weak Reflections 75

3.8 Strong Reflections 79

3.9 Integral Equation for Determining the Permittivity Depth Dependence 81

Chapter 4 Geometrical Optics Approximation 85

4.1 Equations of Geometrical Optics Approximation 85

4.2 Radiowave Propagation in the Atmosphere of Earth 92

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4.3 Numerical Estimations of Atmospheric Effects 97

4.4 Fluctuation Processes on Radiowave Propagation in a Turbulent Atmosphere 102

Chapter 5 Radiowave Scattering 111

5.1 Cross Section of Scattering 111

5.2 Scattering by Free Electrons 114

5.3 Optical Theorem 116

5.4 Scattering From a Thin Sheet 118

5.5 Wave Scattering by Small Bodies 120

5.6 Scattering by Bodies with Small Values of ε – 1 126

5.7 Mie Problem 127

5.8 Wave Scattering by Large Bodies 133

5.9 Scattering by the Assembly of Particles 141

5.10 Effective Dielectric Permittivity of Medium 145

5.11 The Acting Field 148

5.12 Incoherent Scattering by Electrons 150

5.13 Radiowave Scattering by Turbulent Inhomogeneities 152

5.14 Effect of Scatterer Motion 154

Chapter 6 Wave Scattering by Rough Surfaces 157

6.1 Statistical Characteristics of a Surface 157

6.2 Radiowave Scattering by Small Inhomogeneities and Consequent Approximation Series 161

6.3 The Second Approximation of the Perturbation Method 167

6.4 Wave Scattering by Large Inhomogeneities 171

6.5 Two-Scale Model 178

6.6 Impulse Distortion for Wave Scattering by Rough Surfaces 182

6.7 What Is Σ? 187

6.8 The Effect of the Spherical Waveform on Scattering 192

6.9 Spatial Correlation of the Scattered Field 198

6.10 Radiowave Scattering by a Layer with Rough Boundaries 199

Chapter 7 Radiowave Propagation in a Turbulent Medium 211

7.1 Parabolic Equation for the Field in a Stochastic Medium 211

7.2 The Function of Mutual Coherence 215

7.3 Properties of the Function H 217

7.4 The Coherence Function of a Plane Wave 219

7.5 The Coherence Function of a Spherical Wave 220

Chapter 8 Radio Thermal Radiation 221

8.1 Extended Kirchhoff’s Law 221

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8.2 Radio Radiation of Semispace 224

8.3 Thermal Radiation of Bodies Limited in Size 231

8.4 Thermal Radiation of Bodies with Rough Boundaries 233

Chapter 9 Transfer Equation of Radiation 241

9.1 Ray Intensity 241

9.2 Radiation Transfer Equation 244

9.3 Transfer Equation for a Plane-Layered Medium 247

9.4 Eigenfunctions of the Transfer Equation 250

9.5 Eigenfunctions for a Half-Segment 255

9.6 Propagation of Radiation Generated on the Board 258

9.7 Radiation Propagation in a Finite Layer 259

9.8 Thermal Radiation of Scatterers 263

9.9 Anisotropic Scattering 264

9.10 Diffusion Approximation 268

9.11 Small-Angle Approximation 270

Chapter 10 General Problems of Remote Sensing 275

10.1 Formulation of Main Problem 276

10.1.1 Radar 277

10.1.2 Scatterometer 277

10.1.3 Radio Altimeter 278

10.1.4 Microwave Radiometer 278

10.2 Electromagnetic Waves Used for Remote Sensing of Environment 279

10.3 Basic Principles of Experimental Data Processing 281

10.3.1 Inverse Problems of Remote Sensing 295

Chapter 11 Radio Devices for Remote Sensing 303

11.1 Some Characteristics of Antenna Systems 303

11.2 Application of Radar Devices for Environmental Research 305

11.3 Radio Altimeters 306

11.4 Radar Systems for Remote Sensing of the Environment 308

11.5 Scatterometers 321

11.6 Radar for Subsurface Sounding 323

11.7 Microwave Radiometers 326

Chapter 12 Atmospheric Research by Microwave Radio Methods 335

12.1 Main A Priori Atmospheric Information 335

12.2 Atmospheric Research Using Radar 341

12.3 Atmospheric Research Using Radio Rays 347

12.4 Definition of Atmospheric Parameters by Thermal Radiation 356

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Chapter 13 Remote Sensing of the Ionosphere 365

13.1 Incoherent Scattering 365

13.2 Researching Ionospheric Turbulence Using Radar 370

13.3 Radio Occultation Method 372

13.4 Polarization Plane Rotation Method 373

13.5 Phase and Group Delay Methods of Measurement 373

13.6 Frequency Method of Measurement 375

13.7 Ionosphere Tomography 376

Chapter 14 Water Surface Research by Radio Methods 377

14.1 General Problems of Water Surface Remote Sensing and Basic A Priori Information 377

14.2 Radar Research of the Water Surface State 387

14.3 Microwave Radiometry Technology and Oceanography 396

Chapter 15 Researching Land Cover by Radio Methods 405

15.1 General Status 405

15.2 Active Radio Methods 405

15.3 Passive Radio Methods 420

References 427

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Airborne instruments designed for remote sensing of the surface of the Earth andits atmosphere are important sources of information regarding the processes occur-ring on Earth This information is used widely in the fields of meteorology, geog-raphy, geology, and oceanology, among other branches of the sciences Also, thedata gained by satellite observation have been applied to an increasing number ofother areas, such as cartography, land surveying, agriculture, forestry, building con-struction, and protection of the environment, to name a few Most developed coun-tries have a space agency within their governmental organizations, a central task ofwhich is development of remote sensing systems Airborne and ground-based tech-nologies for remote sensing are developed along with the space systems

Recently, increased attention has been paid to development of microwave nology for remote sensing, particularly synthetic aperture radars and microwaveradiometers This interest is due primarily to two circumstances The first is con-nected with the fact that spectral channels other than optical are considered, thusproviding a new way to obtain additional information on the natural processes ofthe Earth and its atmosphere The second circumstance is the transparency of cloudsfor radiowaves, which allows effective operation of radio systems regardless ofweather In addition, radiowave devices for remote sensing do not require illumina-tion of the territory being observed so data can be collected at any moment of the day.The information gained from data collected by microwave instruments depends

tech-on the medium being studied Interpretatitech-on of these data is impossible withoutanalyzing the various mechanisms of interaction that may be present Such mecha-nisms are the primary scientific basis for designing any device of remote sensing,particularly with regard to choosing the frequency band, polarization, dynamic range,and sensitivity Stating remote sensing problems requires addressing the principles

of radio propagation and such processes as absorption, reflection, scattering, and so

on The interpretation algorithms for remote sensing data are properly based on theseprocesses

This book has generally been written in two parts based on the two circumstancesjust discussed The first part describes the processes of radio propagation and thephenomena of absorption, refraction, reflection, and scattering This discussion isintended to demonstrate determination of coupling between the radiowave parame-ters of amplitude, phase, frequency, and polarization and characteristics of the media(e.g., permittivity, shape) Solutions of well-posed problems provide a basis forestimation of the strength of various effects and demonstrate the importance of mediaparameters on the appearance of these effects, the possibility of detection of that orother effects against a background of noise and other masking phenomena, and so on

It is necessary to point out that only rather simple models can be analyzed;therefore, the numerical relations between the observed effects and parameters of a

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medium itself and radiowaves are of primary importance Only rarely can naturalmedia be described by simple models, and we must rely on experimental data whendetermining quantitative relations It is necessary to keep this in mind with regard

to the problems and solutions provided here

The second part of the book is dedicated to analysis of problems that used to

be referred to as inverse problems This analysis attempts to answer the question ofhow knowledge of radiowave properties allows us to estimate the parameters of themedium studied Very often, inverse problems are ill posed; as a matter of fact, anymeasurement happens against a background of noise, and in all cases this concept

of noise must be addressed sufficiently with regard to its additive interference with

a signal Inaccuracy of a model itself is also a factor to be considered A typicalpeculiarity of ill-posed problems is their instability, manifested in the fact that asmall error in the initial data (the data of measurement, in our case) can lead to abig error in the problem solution, in which case additional data must be inserted toremove the instability These data are often referred to as a priori, and they boundpossible solutions of the posed problem

The approximation of models of many natural media requires developing ical methods to interpret remote sensing data Some of these methods are described

empir-in this book, together with brief descriptions of the operational prempir-inciples of wave devices used in remote sensing Here, the authors do not intend to delve deeplyinto either the details of device construction or the algorithms of their data process-ing, as it is very difficult to do so within the limited framework of this book; therefore,only the principal fundamentals are presented

micro-The authors wish to thank the publisher for help in preparation of this book

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of complex oscillation propagation are practically the same as the propagationconditions for the time-harmonic oscillation of the carrier frequency This acceptedsupposition is also advantageous for broad-bandwidth oscillations The time-har-monic oscillation should only be considered as one of the harmonic components ofoscillation (Fourier’s theorem) Later on, magnetic media will not be involved, sopermeability is equal to unity On this basis, Maxwell’s equations may be written as:

(1.1)

in the Gaussian system of units Here, k = ω/c = 2π/λ is the wave number, where

ω is the cyclic frequency and c = 3 ⋅ 108 cm/sec is the light velocity; D is the electricinduction vector; and j is the external current density The continuity equationresulted from Equation (1.1) is defined as:

Material equations connecting E and D vectors are now introduced In the case of

an isotropic medium, this relation is given as:

(1.3)

where ε(ω,r) is the permittivity of the medium, which, in general, is a function offrequency ω and coordinates defined by vector r This local dependence on thecoordinates of r means that spatial dispersion is not taken into account

The permittivity is a complex value; that is,

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2 Radio Propagation and Remote Sensing of the Environment

where the coordinate dependence is omitted Here, ε″(ω) describes Joule losses inthe medium In particular, if for static conductivity σ, the corresponding component

of the imaginary part is:

In an anisotropic medium (for example, in the ionosphere), due to the magnetic field

of the Earth, a connection such as Equation (1.3) is substituted for the tensor:

Here, E1, E2, H1, and H2 are field components on either side of the boundary Insome cases, we will come across problems when the tangential field componentsare broken due to the electric and magnetic surface currents of densities Ke and Km;that is,

To the boundary conditions, as shown in Equation (1.7), we must add the conditions

of radiation, and only divergent (going away) waves must equal infinity

Sometimes, it is more convenient to use gap-type boundary conditions:

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Electromagnetic Field Equations 3

In the case of surface currents, it is necessary to insert surface charges δe and δm

relative to the currents using the continuity equation:

to assume that the field divergence in both cases is equal to zero Then, it is easy

to show that both fields satisfy the equations:

All coordinate components of fields satisfy similar equations in the Cartesian system

of coordinates In this case, these equations are called wave equations

1.2 ENERGETIC RELATIONSHIPS

Let us now input energetic relationships characterizing propagation and absorption

of electromagnetic field In this case, we will be dealing with squared values, so it

is necessary to set up rules of calculation for the complex values and harmonicdependence on time Assume that:

, (1.14)

where the pointers indicate agreement between the representations of oscillations inthe real and complex forms From here on, as is customary in the theory of harmonicsignals, let us consider squared values as an average in time (we are reminded aboutthe notion of effective voltage in electrical engineering) Then it is easy to show thatthis means:

ϕa ϕb

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Thus, the vector of the power flow density (Poynting’s vector S) is determined as:

(1.16)The divergence of this density is described by the transport equation:

The value:

(1.18)describes the mean for the period losses of the electromagnetic power density, and

(1.19)

is the work done by external currents (per unit volume)

In isotropic media, when Equation (1.3) is valid:

Let us now deal with the case of electromagnetic wave generation in space with ε

= 1 and not limited by any bodies It this case, it is convenient to use Fourier’stransform technique We can represent the fields, currents, and charges as integrals:

12

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Inserting these into Equation (1.1), we obtain this system of algebraic equations:

Vector represents the spatial spectrum of the current density, and, according

to the Fourier transform theory,

i

j

~ ( )

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Here,

(1.30)

is the Green function As a result,

(1.31)

The subscript r indicates that the operation of differentiation is taken with respect

to the observed point coordinates

The corresponding expression for E has the form:

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If kr >> 1 (wave zone), then operation ∇ is equivalent to multiplication on

such that:

This expression shows that, in the wave zone, vectors E and H are orthogonal toeach other and to the radiation direction r/r, which means, in this case, that thesource field has transverse waves in the wave zone

Poynting’s vector in the wave zone is:

First, we will consider the first term of this formula, which is indicated here as p

It is easy to show that:2

The latter equation is the definition of the electrical dipole moment of the chargessystem in the investigated volume So, the first term of Equation (1.40) describesthe dipole radiation of the currents system

The simplest model of electrical dipole is known to be a short compared towavelength wire segment with length l and current J Then,

Let us use χ to represent the angle between the dipole direction and the direction

of radiation, which is defined by Poynting’s vector direction The angular powerflow distribution at that point will be described by the formula:

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Here, θ = π/2 – χ The value θ = 0 corresponds to the radiation maximum, and it

is easy to conclude that G(0) = 1.5 for the dipole

The second term in Equation (1.40) becomes the main one for the system studiedhere, for which the electrical dipole moment is zero or is sufficiently small First,

2cos

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The formulas of radiated power are the same as in Equations (1.43) to (1.45), where

a magnetic dipole should be substituted for an electrical one

Densities of electrical and magnetic currents for dipole sources can be given by:

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The expressions obtained are true not only in the wave area but also in the

quasi-static area where kr << 1 It is important to observe the inequality r >> l to see that

the dipole field is not completely transversal in the quasi-static area

For a magnetic dipole, the appropriate part of the vector potential is:

In this case, we took into account the fact that the magnetic vector potential satisfies

the wave equation:

The fields Em and Hm satisfy Maxwell’s equations, which in this case must be written

as:

We leave to others consideration of Equation (1.48), which describes quadruple

radiation and is outside our range of interest in this text

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