Central Kalimantan - Tetuko - A Physical Method to Analyse Scattered Waves From Burnt Coal Seam -...

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. . , 2003, . 24, . 15, 31193136

A physical method to analyse scattered waves from burnt coal seam

and its application to estimate thickness of fire scars in central Borneo

using L-Band SAR data

J. TETUKO S.S., R. TATEISHI and N. TAKEUCHI

Centre for Environmental Remote Sensing, Chiba University, 1-33, Yayoi,Inage, Chiba 263-8522, Japan, [email protected] or [email protected]

(Received 19 March 2001; in final form 20 May 2002 )

Abstract. A physical method was conducted to analyse scattered waves fromburnt coal seam in order to estimate the thickness of fire scars. The model wascomposed of three media namely; air, burnt coal seam and peat. For computationpurposes, the equivalent circuit of this model was conducted using a classicaltransmission line circuit method. The relationship between backscattering coeffi-cient and thickness of burnt coal seam was defined in terms of the logarithm ofthe reflection coefficient (in power). The analysis result was confirmed by simula-tion using a Finite Difference Time Domain (FDTD) method. The simulationwas performed using a two-dimensional (2-D) finite-difference model for scatteredwaves from a burnt coal seam. The model used the equations of scattered electro-magnetic fields that were derived from Maxwells equations. A Mur method wasused to surround the simulation space and absorb the outward travelling waves.Analysis and simulation results were similar. Subsequently, the model was appliedto estimate the thickness of burnt coal seam in central Borneo fire events, thatoccurred in 1997, using a Japanese Earth Resources Satellite (JERS-1) SAR data.Results showed that fire scars in the study area reached 0.52m in depth (thickness).This agrees with ground measurements.

1. Introduction

In 1995, the Indonesian Government released a peat area in central Borneo forconversion into cultivated land. It was known as the One Million Hectares Peatland

Project (Sarbini 2000). The project, consisting of four areas, was called the Peatland

Project (PLG)A to D, where PLG-A was chosen for this study.

The ground data of the study area were collected in the period 1995 to 1997

(figure 1). Figure 2 shows the master plan of this project, where solid lines show

irrigation canals (Csar 1997). Dotted lines show areas covered by JERS-1 SAR data

and Satellite Pour lObservation de la Terre (SPOT) High Resolution Visible (HRV)

data. Construction of the canals was begun in April 1996 by the Indonesian

Department of Public Works. Colours in this figure show the distribution of thickness

of the coal seam. In this project, vegetation was burnt to open up the area. These

fire events caused coal seam fires that were difficult to extinguish, because the fire

penetrated the peat and was difficult to detect visually (Hadi 1999, Kasdi 1999). It

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online 2003 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/0143116021000021215


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J. T etukoet al.3120

Figure 1. Photographs of field survey expeditions 1995 to 1997. (a) and (b) show mainvegetation; tengkawang (Dipterocarpus spp), pule tree and purun grass, respectively.(c) Burnt forest and coal seam. (d) Staffmeasuring thickness of coal seam.

is important to investigate the thickness j or depth of the burnt coal seam to assistin the prevention of the spreading of fire and to efficiently detect fire spots at an

early stage of forest fire monitoring. This technique can also be applied to monitor

the post-crisis management of fire events by estimating the damage suffered by the

soil and the carbon released into the atmosphere.

Figure 3 shows SPOT HRV data acquired on 6 June 1997 (prior to the fire),

29 July 1997 and 7 August 1997 (during the fire), and 8 September 1997 (after the

fire). Figure 3(a) shows the drainage canals in PLG-A (6 June 1997) that wereconstructed in order to reduce the excess water that is commonly associated with

natural peat (Radjagukguk 1997). Figure 3(b) and (c) show the peat during the

burning of the man-made fires on 29 July and 7 August 1997. Figure 3(d) shows the

area after the fire occurred. This area will be used as cultivated area by the Indonesian

Department of Forestry and Estate Crops. In this study, the JERS-1 SAR data

acquired on 29 July 1997 (during the fires) was used to estimate the thickness j ofthe burnt coal seam at the study area, and SPOT HRV data were used to determine

the origins of fire hot spots.

Analysis and simulation of waves scattered from the burnt coal seam will be

introduced in order to estimate the relationship between j and its backscatteringcoefficient. In 2, modelling of the scattered wave from the burnt coal seam and the

mathematical formulation of this description are reviewed using the classical trans-

mission line circuit method. In 3, simulation of Transverse Magnetic (TM) wavepropagation in the burnt coal seam is conducted using the Finite Di fference Time

Domain (FDTD) method. In 4, analytical results are verified by comparing them

with results of simulations. Application of these results is presented in 5, where the

possible relationship between backscattering coefficient and its use to estimate the


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Estimating the thickness of fire scars 3121

Figure 2. The study area: master plan of One Million Hectares Peatland Project (PLG) incentral Borneo, Indonesia.

thickness j of fire scars from JERS-1 SAR data is evaluated. Finally, conclusionsare given in 6.

2. Analysis

Several field surveys were carried out over the period 1995 to 1997 to collect

ground data. Ground data shows that fire scars in central Borneo were covered by

burnt coal seam produced by burnt tropical tree trunk and burnt peat (figure 1(c)

and 1(d)). In this study, burnt coal seam that is mainly composed of soil carbon

(Hadiet al. 2000a), is assumed to be a microwave absorber ( Hashimoto 1997). Based

on the ground data, a model of scattered waves from burnt coal seam is considered.

Figure 4(a) shows a two-dimensional analysis model composed of three media; infinite

length of air, thickness j of burnt coal seam, and infinite depth of peat. In thisresearch, to simplify the analysis, the impact of surface roughness on the scattered

waves was not considered. The incident wave was assumed to be a plane wave in

the TM mode at an incident angle hi. In the model used in this analysis, E

rm, E

tmand E

bm are the electric fields of the waves reflected from the first interface (at the


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Figure 3. SPOT HRV data of fire events in the study area. (a) 6 June 1997 (prior to fire).(b) 29 July 1997 (during fire). (c) 7 August 1997 (during fire). (d) 8 September 1997 (after fire).

surface), the transmitted waves passing through this surface and waves reflected from

the peat or at the second interface, respectively, where m=1, 2, 3, ... indicates themth reflected waves, see figure 4(a). E

0 is the initial electric field of the incidence

wave that is shown in Figure 4(a). This model also shows that waves were trapped

by the burnt coal seam when propagating through. The total reflected wave is

approximated by E scati =E

r1+E

r2+E

r3+. . . .

The equivalent circuit of the model used in this analysis is shown in figure 4(b),

where the effective impedance of the burnt coal seam, including the impedance of

burnt tree, stand or fire scars, the impedance of peat, and the input impedance are

ZC

, ZL

, and ZTM

, respectively. In this analysis, the peat layer is assumed to be an

infinitely deep perfect conductor because the water content is high (Hadi et al.

2000b). Consequently, ZL

is zero. Based on a transmission line theory method

(Tanaka 1972, Gotohet al. 2000), the input impedanceZTM

is derived from figure 4(b)

and determined by

ZTM=Z

C

ZL+Z

Ctanhc

Cj

ZC+ZLtanhcCj (1)

where cC

and j are the propagation constant and thickness of burnt coal seam,respectively.

Figure 5 shows the propagation of the TM wave transmitted from the air to the

burnt coal seam. Referring to this figure, the propagation constantcC

is derived from


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Figure 4. Geometry of analysis. (a) Analysis model. (b) Equivalent circuit.

Maxwells equations as;

cC=j

2p

le

rmrcos h

t (2)

whereer,m

r,h

t, andl are complex dielectric constant, complex specific permeability,

transmission angle, and wavelength, respectively. j is equal to 1. The waveimpedanceZ

Cof the transmitted wave in the burnt coal seam is obtained from the

component of the electromagnetic field perpendicular to the propagation axis (x-axis).

ZC=E

yt/H

zt=Z

0m

r/ercosh

t (3)

whereZ0

(=m0/e

0) is the wave impedance in air or free space (=120pohms). Based

on Snells law, the relationship between incidence angle hi and transmission angle htgives

sinhi/sinh

t=e

rmr

(4)

Substituting equations (2)(4) into equation (1), the wave impedance ZTM

of the


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Figure 5. Geometry of wave propagation in two media.

incident TM wave in the burnt coal seam becomes:

ZTM=

Z0

er

ermrsin2h

itanh Aj

2pj

l e

rmrsin2h

iB (5 )Furthermore, the reflection coefficient becomes:

C=ZTMZ

0cos h

iZTM+Z

0cos h

i

(6)

Then the backscattering coefficients0anl is defined as:

s0anl=20 log (|C |) (7)

Finally, the relationship between backscattering coefficient s0anl

and thickness j ofburnt coal seam can be obtained from equations ( 5)( 7). To find the dielectric

constanter of burnt coal seam, several samples were measured experimentally using

dielectric probe kit HP85070B, and an average dielectric constant of 2.5j0.1 was

obtained.

3. Simulation

The JERS-1 SAR operates in horizontal (H) polarization on both transmit and

receive. Hence, in this study horizontal polarization or TM mode is considered.

Electromagnetic field components (Ex

,Ey

, 0) and (0, 0, Hz

) are considered. In this

study, scattered waves from burnt coal seam are simulated using a Finite Di fferenceTime Domain method (Uno 1998) in order to find the relationship between s0

simand j. Figure 6 shows the position of field components in the finite-difference grid(unit of sample spacing). Referring to this figure, detailed scattered fields Escat and

Hscatthat are derived from Maxwells equations are discussed in the Appendix, where


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Figure 6. Portion of the finite-difference grid.

the electromagnetic fields are shown as equations (A.22) to (A.24). In these equations,

Dt is the time step, and Dx, Dy are sample spacings in the x-axis and y-axis,respectively. Here, the notation of Yee (Yee 1966) is used to replace H(n+1/2)Dt by

H(n+1/2). Similarly, Escat,t (x,y) and Hscat,t (x,y) are expressed as Escat,n (i,j ) and

Hscat,n (i,j ), where t=nDt, x=iDx and y=jDy. Sampling leads to the characteristicstaggered finite-difference grid. In this grid, the electromagnetic field components are

offset by Dt/2 in time and Dx/2 and Dy/2 in space. In the former, the field components

are updated sequentially in time.

The finite-difference model is implemented in two dimensions (2-D) as shown in

figure 7. The simulation space is composed of three kinds of media; peat, burnt coal

seam and air, where each medium has infinite length in the z-axis direction.

Simulation space in this figure is sampled to INXINY grids (in this simulation,INX=INY=300 grids). In the model, peat thickness is 50 grids, the thickness ofburnt coal seam varies from 0 to 80 grids or 0 to 1 m. To observe the power of the

electric fields, the point of observation (Q) is located at (250Dx, 150Dy) which

corresponds to 1.5 m from the surface of the peat. The power of the scattered

electromagnetic fields is determined at this point.

The incident wave is a plane wave with amplitude assumed to be a Gaussian

pulse that is propagating from right to left of the simulation space at the speed of

light, as shown in figure 7. The Gaussian pulse is defined by the function p(t)

p(t)=Gea(tt0)2 , (0t2t0)

0, otherwise(8)

where t is time, t0

is pulse width, and a=(4/t0

)2 . Figure 8(a) and (b) show the

Gaussian pulse for t0=9109 s and its power spectrum, respectively.

To obtain values for the time step Dtand sample spacing (Dxand Dy), frequency

fmax

must be decided from figure 8(b). Here, fmax

is frequency in FFT intensity120 dB, which means that the calculation accuracy of the electromagnetic fieldcomponents in simulation space is assured to be six digits. By referring to this figure,

fmax

=2.6 GHz is obtained. Using the empirical equation Dx=Dy=v/10fmax

(Tetuko

et al. 1998, 2001a, 2001b), Dx=Dy=1.25102 m is obtained, where v is wave speed.


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Figure 7. Simulation model.

In this study, it is assumed to be the same as wave speed in air (c=3108 ms1 ),and running time is t=600Dt s to observe the scattered field. Finally, according tothe Courant condition (Uno 1998)

cDt1/(1/Dx)2+(1/Dy)2 (9)

the time step Dt is obtained as Dt=2.51011 s.When implementing the finite-difference scheme, boundary conditions must be

treated in a special manner. Two different kinds of boundaries exist: internal bound-

aries (i.e. boundaries within the medium marked by a change in material properties)

and external boundaries (i.e. the grid edges). To ensure numerical stability at the

internal boundaries (i.e. at the interfaces between different media), the material

properties must be averaged for components on the boundary. For transitions

between similar materials, the averaging may be omitted. However, this averaging

is necessary at an interface between media with greatly different material properties

(for example, at an air and burnt coal seam interface) in order to maintain stability.

The FDTD method simulates a finite simulation space (INXINYgrids), but realscattering problems are often in infinite formations. In this case, artificial boundaries

must be applied in the FDTD method to solve external boundary conditions. Toprevent these artificial boundaries from reflecting electromagnetic waves, an absorb-

ing boundary condition is used. Gerrit Mur (Mur 1981) introduced simple absorbing

boundary conditions to truncate FDTD meshes. The second kind of Mur method

is applied in this analysis, because it involved small calculation-memory size and its


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Figure 8. Pulse of incident wave. (a) Gaussian pulse. (b) Power spectrum of Gaussian pulse.

accuracy was assured (Mur 1981). In this study, for example, the electric field at

i=1 is determined by

Eny(1,j )=E

n2y (2,j )+

vDtDxvDt+Dx {E

ny(2,j )+E

n2y (1,j )}

+ 2Dx

vDt+Dx{En1

y (1,j )+En1

y (2, j )}+

Dx(vDt)2

2Dy2(vDt+Dx){En1

y (1,j+1)

2En1y

(1, j )+En1y

(1, j1)+En1y

(2,j+1)2En1y

(2,j )+En1y

(2,j1)} (10)


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In the same manner, the other components of the electric field at i=INX, j=1, andj=INYcan be derived, where v is wave speed.

In this simulation, the scattered wave is the object to be analysed, hence the

incident and scattered fields need to be separated here. The incident electric fields

Eincx

, Eincy

andHincz

in equations (A.22) to (A.24) need to be derived. The geometry of

the incident wave is shown in figure 9, where a plane wave propagates at an angle

w0 with respect to the

x-axis. The propagated direction of the incident wave isdetermined by

r0=xcosw

0+ysinw

0 (11)

wherexandyare vector units. Hence the incident electromagnetic fields were derived

as

Hincz

(r,t)=E0

Z0

p(t+r0

r/c+t0

) (12)

Eincw

(r,t)=E0

(x sinw0+ycos w

0)p(t+r

0 r/c+t

0) (13)

where c is speed of light, E0

and Z0

are initial amplitude of incident electric field

(E0=1 Vm1) and wave impedance in air, respectively, p (t) is pulse function excited

by Gaussian pulse (8 ). By substituting the components of the electromagneticfields in (12) and ( 13), and considering Yees notation, each component of the

electromagnetic field of the incident wave is acquired as follows:

Hinc,n+1/2z

(i+D,j+D)=E0

Z0

p((n+D)Dt+{(i+D)Dxcosw0+(j+D)Dysinw

0}/cd/c)

(14)

Einc,nx

(i+D,j )=E0

(sinw0

) p(nDt+{(i+D)Dxcos w0+jDysinw

0}/cd/c) ( 15)

Einc,ny

(i,j+D)=E0

cosw0

p(nDt+{iD cosw0+(j+D)Dysinw

0}/cd/c) (16)

where t0=d/c means that the pulse head is at a distance d from the origin of the

coordinate system (0, 0) at initial time (t=0 s). For each time step, equations (14)( 16)

are added to the value calculated from the finite-difference scheme or equations(A.22) to (A.24).

Finally, the backscattering coefficient s0sim

is defined by equation (17), where

Escaty

and Eincy

are the scattered electric field and observed electric field at frequency

Figure 9. Geometry of incident wave.


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f=1.275 GHz of the scattered waves scattered by peat (perfect conductor) only,respectively:

s0sim=20 log A

|Escaty |

|Eincy | B

f=1.275GHz

(17)

4. Results

The relationship between backscattering coefficient and thickness of burnt coal

seam is obtained based on variables in equation (5) that are shown in table 1. To

simplify comparison of the analysis results with simulation results, the incident angle

is 0. By substituting these variables in equation (5), the reflection coefficient withrespect to each j is obtained. Further, by substituting these reflection coefficients in

equation (7), the correlation betweenj and s0anl

is obtained. This result is illustrated

in figure 11 (analysis). This figure shows that the incremental increase in thickness

of the burnt coal seam is directly proportional to the reduction in backscattering

coefficient. This implies that the burnt coal seam absorbs energy from the wave.

The analysis result is confirmed by simulation results. Figure 10 shows the simula-

tion result, where the scattered waves due to the Gaussian pulse of the incident wave

are shown. Only the scattered wave is shown as the scattering problem is the focusof this study. Scattered waves from the burnt coal seam surface and the peat surface

are seen to propagate over the running time t=0 to 500Dt s, and j is 0.5m. In thisfigure, A, B, C denote the scattered waves from the burnt coal seam surface, and the

first and second reflected waves from the peat surface (trapped waves), respectively.

In this simulation, a horizontally polarized electric field Escaty

is observed at

point Q (with incident angle w0=0). The power spectrum of the observed scattered

field is obtained by its fast Fourier transform. Then, the power of the electric field

Escaty

at frequency f=1.275 GHz (JERS-1 SAR) is obtained. By substituting theseelectric fields into equation (17), the backscattering coefficient s0

sim with respect to

the thicknessj is obtained and, is shown together with simulation results in figure 11

with the same incident angle (hi=0). This figure shows that the results are in good

agreement. Then the influence of JERS-1 SAR incident angle hi=38.7 (Davidet al.1997) was considered and the result is shown in the same figure.

In the next section, the results are applied to estimate the thickness j of the burnt

coal seam in the study area.

Table 1. Simulation parameters.

Parameter Value

Wave impedance Z0

120 p ohmsSpecific permeability m

r 1

Dielectric constant er

of burnt coal seam 2.5 j0.1Wavelengthl (JERS-1 SAR) 23.5 cmIncident angle w

0 0

Thickness of burnt coal seam 0 to 1 mSample spacing Dx=Dy 1.25102 mTime step Dt 2.51011 s


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Figure 10. Scattered waves in solution space. (a) t=150Dt s. (b) t=200Dt s. (c) t=250Dt s.(d) t=300Dt s. (e) t=350Dt s. (f) t=400Dt s. (g) t=450Dt s. (h) t=500Dt s.

5. Application

5.1. Study area

The study area extends from 114 23 to 114 45E and 2 23 to 2 47S, southBarito and Kapuas district, central Borneo, Indonesia. The altitude of this arearanges from 9 to 14 m above sea level. This area is mainly covered by peat (soil with

about 60% coal deposit) and peat swamp (peat with high water content). Borneo is

wet throughout the year with average annual rainfall of around 3500mm to 4500 mm,

while the relative humidity varies between 70% and 90%.


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Figure 11. Relationship between burnt coal seam thickness and backscattering coefficient:analysis, simulation and JERS-1 SAR.

Figure 1 shows photographs of the study area taken during the field survey.

Figure 1(a) and (b) show the main types of vegetation namely tengkawang

(Dipterocarpus spp), pule tree, and purun grass found around the Purun river (black

water river) in the study area. Figure 1(c) shows burnt tengkawang and pule trees

near Bunter lake. Figure 1(d) shows a staffboring through the peat to measure the

thickness of the coal seam. The field survey was carried out during the period 1995to 1997 as part of the One Million Hectares Peatland Project. The measurement

results were mapped and are shown in figure 2 (Csar 1997).

5.2. Data processing

JERS-1 SAR data (path 95, row 305) acquired on 29 July 1997 (dry season and

during fire events) were used to estimate the thickness of forest fire scars (burnt coal

seam) in the study area. These data were processed at level 2.1 or standard geocoded

data and were transformed to the Universal Transverse Mercator (UTM) projection

by the Earth Observation Research Centre (EORC) of the Japanese National Space

Development Agency (NASDA). First, a 33 median filter was employed and thesecond process used a 55 average filter to reduce inherent speckle noise (Sunar

et al. 1998). At the same time, the data were also referenced to the UTM coordinatesystem, through a polynomial rectification using 30 ground control points collected

from aerial (Bakosurtanal 1990) and topographic maps (Bakosurtanal 1991) at a

scale of 1:50 000. Then the SAR data was resampled to a sample spacing of 12.5 m.

In this process, calibration corrections applied to overcome antenna pattern variation

were not considered.

A supervised classification was performed to classify the data. The study area

was classified into six classes based on aerial and topographic maps and using

ground data as reference in the definition of training sets. The classes are paddy

field, bush swamp, forest, bush land, burnt coal seam, and settlement. In this research,

the thickness of the burnt coal seam class j was estimated. Furthermore, SPOTHRV data (figure 3) were assessed to identify fire spots in the study area visually.

Then the burnt coal seam was classified into four classes as shown in figure 12. The

statistic value (average) of each class was obtained and the s0 were calculated usingthe equation s0=20 logI68.2 dB ( NASDA calibrated equation) ( Shimada 1998),where I is the pixel intensity of JERS-1 SAR data. By comparing the results with

the graph (JERS-1 SAR) in figure 11, j for each class were acquired (table 2) and inthe study area were found to be between 0.33 m and 0.52 m. This result was confirmed


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Figure 12. SPOT-HRV data and supervised classification results of JERS-1 SAR data (path95, row 305, 29 July 1997).

Table 2. Thickness of the burnt coal seam in the study area.

Class names Backscattering coefficient s0 (dB) Burnt coal seam thicknessj (m)

Burnt coal seam 1 7.0 0.52Burnt coal seam 2 6.5 0.48Burnt coal seam 3 5.8 0.37Burnt coal seam 4 5.0 0.33

by field survey data (figure 2), where areas A and B in figure 12 had coal seam

thicknesses of 0 m to 0.50 m and 0.51 m to 1 m, respectively. It can be seen that the

analysis results matched well with the field survey data.

6. ConclusionsA physical analysis was conducted to analyse the relationship between the back-

scattering coefficients s0 and the thickness j of the burnt coal seam. This analysisresult was confirmed by simulation using a FDTD method. The results obtained

were similar. By considering the incident angle of JERS-1 SAR (hi=38.7), the


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relationship between j and s0 for JERS-1 SAR data was obtained. This result wasapplied successfully in estimating the burnt coal seam thickness in central Borneo,

Indonesia. This was confirmed by field survey data collected during the period 1995

to 1997. Results showed that fire at the study area could reach 0.52 m in depth

(thickness) of the coal seam. This was in good agreement with field survey data.

AcknowledgmentsThe authors thank Professor Koichi Ito, Ichiro Ida, and Kazuyuki Saito for their

assistance in the measurement of dielectric constants of burnt coal seam samples;

MITI/NASDA and CNES for providing JERS-1 SAR and SPOT HRV data, respect-

ively; Franciscus Dwikoco S. S. and Pandhito Panji FoundationRemote Sensing

Research Centre (Innes Indreswari and J. Pandhito Panji Herdento) for ground data,

aerial and topographic maps; Nuraini of CSAR, Indonesia for photographs; Satoh

International Scholarship Foundation and Atsumi International Scholarship

Foundation for supporting this research.

Appendix. Derivation of scattered waves equation

Maxwells equations in homogeneous and non-dispersive medium are defined as

Et=s

eE+1

e(H (A.1)

Ht=

1

m(E (A.2)

where Eand Hare total electric and magnetic fields in simulation space, respectively.

e,m, andsare dielectric constant, permeability, and conductivity of simulation media,respectively. In this analysis, the incident wave is propagating in free space before

reaching the burnt coal seam. By considering Maxwells equations in free space, the

incident electric and magnetic fields are obtained as

Einc

t=

1

e0

(Hinc (A.3)

Hinct =

1

m(Einc (A.4)

In this research, scattered fields will be analysed, therefore, incident and scattered

fields must be separated. Thus total fields are given by

E=Einc+Escat (A.5)

H=Hinc+Hscat (A.6)

By substituting equation (A.3) into equations (A.4) and (A.5), (A.6) into (A.1), (A.2),

the following equations are obtained:

Escatt =

s

eEscat+

1

e(Hscat

s

eEinc

ee0e

Einct

(A.7)

Hscatt =

1

m(Escat

mm0

m

Hinct

(A.8)


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To obtain the stability condition of incident and scattered electric field components

at time t=(nD)Dt, they are sampled as

Escat |t=(n1/2)Dt

=Escat,n1+Escat,n

2 (A.9)

Einc|t=(n1/2)Dt=

Einc,n1+Einc,n

2 (A.10)

Additionally, the time difference of the electromagnetic fields is expressed as

Escatt K

t=(n1/2)Dt

=Escat,nEscat,n1

Dt (A.11)

EinctK

t=(n1/2)Dt

=Einc,nEinc,n1

Dt (A.12)

Hscatt K

t=nDt

=Hscat,nHscat,n1

Dt (A.13)

HinctK

t=nDt

=Hinc,n+Hinc,n1

Dt (A.14)

Using equations (A.9), (A.11) and (A.13), equations (A.7) and (A.8) can be obtained

in the form

Escat,n=1sDt/2e1+sDt/2e

Escat,n1+ Dt/e

1+sDt/2e(Hscat,n1/2

sDt/e

1+sDt/2eEincK

t=(n1/2)Dt

(ee

0)Dt/e

1+sDt/2eEinctK

t=(n1/2)Dt

(A.15)

Hscat,n+1/2=Hscat,n+1/2Dt

m(Escat,nA

mm0

m BDtHinctK

t=nDt

(A.16)

In this study, horizontal polarization or the transverse magnetic (TM) mode is

considered. Hence, the electromagnetic field components considered are

Hscat=(0, 0,Hscatz

) and Escat=(Escatx

,Escaty

, 0). Then, the following relationships are

obtained:

(Hscat=xHscat

z

y y

Hscatz

x +z0 (A.17)

(Escat=xEscat

yz +y

Escatxz +zA

Escatyx

EscatxyB (A.18)

where these fields are considered in Cartesian coordinates andx,y,zare unit vectors


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along thex,y,zaxes. Equations (A.17) and (A.18) are then substituted into equations

(A.15) and (A.16), to obtain each component of the electromagnetic fields are as

Escat,nx =

1sDt/2e1+sDt/2e

Escat,n1x

+ Dt/e

1+sDt/2eHscat,n1/2

zy

sDt/e

1+sDt/2eEinc

xKt=(n1/2)Dt

(ee

0)Dt/e

1+

sDt/2e

Eincx

t

Kt=(n1/2)Dt

(A.19)

Escat,ny =

1sDt/2e1+sDt/2e

Escat,n1y

Dt/e

1+sDt/2eHscat,n1/2

zx

sDt/e

1+sDt/2eEinc

yKt=(n1/2)Dt

(ee

0)Dt/e

1+sDt/2eEinc

xtK

t=(n1/2)Dt

(A.20)

Hscat,n+1/2z

=Hscat,n+1/2z

Dt

mAEscat,n

yx

Escat,n

xy BA

mm0

m BDtHinc

ztK

t=nDt

(A.21)

By referring to figure 6, each electromagnetic field is obtained by substituting (A.10),

(A.12), and (A.14) into (A.19) to (A.21) as

Escat,nx

(i+D,j )=1s(i+D,j )Dt/2e(i+D,j )

1+s(i+D,j )Dt/2e(i+D,j )

Escat,n1x

(i+D,j )

+ Dt/e(i+D,j )

1+s(i+D,j )Dt/2e(i+D,j )Hscat,n1/2

z (i+D,j+D)Hscat,n1/2

z (i+D,jD)

Dy

s(i+D,j )Dt/2e(i+D,j )(e(i+D,j )e

0)/e(i+D,j )

1+s(i+D,j )Dt/2e(i+D,j ) Einc,n1

x (i+D,j )

s(i+D,j )Dt/2e(i+D,j )+(e(i+D,j )+e

0)/e(i+D,j )

1+s(i+D,j )Dt/2e(i+D,j ) Einc,n

x (i+D,j ) (A.22)

Escat,ny

(i,j+D)=1s(i,j+D)Dt/2e(i,j+D)1+s(i,j+D)Dt/2e(i,j+D)

Escat,n1y

(i,j+D)

Dt/e(i,j+D)

1+s(i,j+D)Dt/2e(i,j+D)

Hscat,n1/2z

(i+D,j+D)Hscat,n1/2z

(iD,j+D)

Dx

s(i,j+D)Dt/2e(i,j+D)(e(i,j+D)e

0)/e(i,j+D)

1+s(i,j+D)Dt/2e(i,j+D) Einc,n1

y (i,j+D)

s(i,j+D)Dt/2e(i,j+D)+(e(i,j+D)e

0)/e(i,j+D)

1+s(i,j+D)Dt/2e(i,j+D) Einc,n

y (i,j+D) (A.23)

Hscat,n+1/2z

(i+D,j+D)=Hscat,n1/2z

(i+D,j+D) Dt

m(i+D,j+D)Dt(Escat,n

y (i+1,j+D)Escat,n

y (i,j+D))

+ Dt

m(i+D,j+D)Dy(Escat,n

x (i+D,j+1)Escat,n

x (i+D,j ))

m(i+D,j+D)m

0

m(i+D,j+D) (Hinc,n+1/2

z (i+D,j+D)Hinc,n1/2

z (i+D,j+D) (A.24)

References

B, 1990, Aerial map: Sungai Mantangai 1713-51. Scale 1:50 000, NationalCoordination Agency for Surveys and Mapping, 1st edn (Cibinong:BAKOSURTANAL).


18/18

Estimating the thickness of fire scars3136

B, 1991, Topographic maps: Rimbun Tulang 1713-24, Jenamas 1713-52, Dadahup1713-23. Scale 1:50 000, National Coordination Agency for Surveys and Mapping, 1stedn (Cibinong: BAKOSURTANAL).

CSAR, 1997, Coal seam thickness map: One Million Hectares Peat Project: PLG-A. Scale1:50 000, Centre for Soil and Agroclimate Research, 1st edn ( Bogor: CSAR).

D, P., S, E. B., and S, J. M., 1997, Terrain influences on SAR backscatteraround Mt. Taranaki, New Zealand. IEEE T ransactions on Geoscience and RemoteSensing, 35, 924932.

G, K., and Y, J., 2000, Electromagnetics Problems Solving, 122nd edn (Tokyo:Kyoritsu).

H, A., 1999, Lambung Mangkurat University, Banjarmasin, Indonesia, Privatecommunication.

H, A., I, K., R, F., P, E., Y, F. H., and T, H., 2000a,Dynamics of methane and nitrous oxide in the tropical peats. In T he Impacts of L and-use/Cover Change on Greenhouse Gas Emissions in T ropical Asia, 1st edn, edited byD. Murdiyarso and H. Tsuruta (Bogor: IC-SEA NIAES), pp. 3551.

H, A., I, K., P, E., R,F., Y, and T, H., 2000b, Effectof land-use changes on nitrous oxide (N

2O) emission from tropical peats. International

Journal of ChemosphereGlobal Change Science, 2 , 347358.H, O., 1997, Introduction to Wave Absorber Media, 1st edn (Tokyo: Morikita).K, S., 1999, Centre for Soil Agroclimate Research, Bogor, Indonesia, Private

communication.M, G., 1981, Absorbing boundary conditions for the finite-difference approximation of the

time-domain electromagnetic-field equation. IEEE T ransactions on ElectromagneticCompatibility, 23, 377382.

R, B., 1997, Peat soil of Indonesia: location, classification and problems forsustainability. In Biodiversity of T ropical Peats, 1st edn, edited by J. O. Rieley andS. E. Page (London: Samara Publishing), pp. 4554.

S, B., 2000, Report of a million hectares peat project. Indonesian Ministry of Forestryand Estate Crops Meeting, 9 March 2000 (Jakarta: Planological Agency Press).

S, M., 1998, Users Guide to NASDAs SAR Products, 2nd edn (Tokyo: EarthObservation Research Centre (EORC), National Space Development Agency(NASDA).

S, F., T, M., M, D., K, S., M, N., and Y, E., 1998, Theuse of multitemporal radar data in agriculture monitoring: a case study in Kyocegiz-Dalaman ecosystem, Turkey. International Archives of Photogrammetry and RemoteSensing, 32, 559565.

T, S., 1972, Electronic L aboratory Work, 1st edn (Tokyo: Corona).

T, J., S, F., and I, Y. M. E., 1998, Scattered pulse analysis using Finite Differ-ence Time Domain ( FDTD) method. Scientific Journal of Electronics Engineering,4, 1223.

T, J., and W, K., 2001a, Simulation of scattered electromagnetics wave ontrunk of rasamala ( Altingia exelsa). Scientific Journal of Electronics Engineering, 6,1220.

T, J., and T, R., 2001b, Simulation of scattered waves from tropical forest treetrunks and its application. Journal of Japan Society of Photogrammetry and RemoteSensing, 40, 414.

U, T., 1998, Finite DiVerence T ime Domain Method for Electromagnetic Field and AntennaAnalyses, 1st edn (Tokyo: Corona).

Y, K. S., 1966, Numerical solution of initial boundary value problems involving Maxwellsequations in isotropic media.IEEE T ransactions on Antennas Propagation,14, 302307.

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