A Feasible Approach for Improving Accuracy of Ground Deformation Measured by D-InSAR

J China Univ Mining & Technol 2007, 17(2): 0262–0266

A Feasible Approach for Improving Accurac y

of Ground Deformation Measured by

D-InSAR

CHANG Zhan-qiang1,2, GONG Hui-li1,2, ZHANG Jing-fa3, GONG Li-xia3

1College of Resource, Environment & Tourism, Capital Normal University, Beijing 100037, China 2Key Lab of 3D Information Acquisition and Application, Ministry of Education, Beijing 100037, China

3Institute of Crustal Dynamics, National Seismological Bureau, Beijing 100085, China Abstract: D-InSAR is currently one of the most popular research tools in the field of Microwave Remote Sensing. It is unrivaled in its aspect of measuring ground deformation due to its advantages such as high resolution, continuous spa-tial-coverage and dynamics. However, there are still a few major problems to be solved urgently as a result of the intrin-sic complexity of this technique. One of the problems deals with improving the accuracy of measured ground deforma-tion. In this paper, various factors affecting the accuracy of ground deformation measured by D-InSAR are systemati-cally analyzed and investigated by means of the law of measurement error propagation. At the same time, we prove that the ground deformation error not only depends on the errors of perpendicular baselines as well as the errors of the inter-ferometric phase for topographic pair and differential pair, but also on the combination of the relationship of perpen-dicular baselines for topographic pairs and differential pairs. Furthermore, a feasible approach for improving the accu-racy of measured ground deformation is proposed, which is of positive significance in the practical application of D-InSAR.

K ey words: D-InSAR; ground deformation; perpendicular baseline; interferometric phase

CLC number: P 236

1 Introduction

As well known, SAR (Synthetic Aperture Radar) interferometry is a new development of earth-obser-vation technique and currently one of the more popu-lar research tools in the field of Microwave Remote Sensing. It has been applied in many fields, such as topographic mapping, geodynamics, glacier excursion, forest investigation and oceanic surveys [1–7]. Differ-ential interferometry SAR (D-InSAR) is unrivalled in its aspect of measuring ground deformation as a result of its advantages such as high resolution, continuous spatial-coverage and dynamics. However, there are still several major problems to be solved urgently. One of these problems deals with improving the ac-curacy of measured ground deformation, after which a feasible approach for effectively improving the ac-curacy of ground deformation by D-InSAR will be analyzed and investigated (Fig. 1).

Fig. 1 Sketch map for 3-pass SAR interferometr y

2 Theoretical Model of D-InSAR

In differential interferometry SAR, three SAR im-ages covering the same ground area are required; two SAR images are acquired before the ground deforma-tion occurs and the other after ground deformation

Received 20 February 2006; accepted 15 July 2007

Projects 400471090 supported by the National Natural Science Foundation of China and 1421 by the European Space Agency Corresponding author. Tel: +86-10-66362819; E-mail address: changkkll@https://www.360docs.net/doc/a013353099.html,

occurs. The basic idea behind D-InSAR is to form two interferograms using two pairs of SAR images with the same master SAR image, where one is the differential pair interferogram indicating the defor-mation phase and the other is the topographic pair interferogram indicating the topographic phase. Ground deformation is obtained by subtracting the deformation phase from the corresponding topog-raphic phase. The theoretical model is expressed as follows [8–9]

1124π

2f f B r B ??λ

??=? (1)

where r ? is the ground deformation along LOS; 1f ?,2f ?are the interferometric phases of the differen-tial pair and the topographic pair, respectively, from which the flat-earth trend phase has been re-moved;and respectively denote the perpen-dicular baselines for the differential and topographic pairs and 1B 2B λ is the wavelength of the SAR system.

3 Analysis on Ground Deformation Error

According to the law of measurement error propa-gation and equation (1), the deviation of the ground deformation along LOS is expressed as follows

1222222

2222

(

)[(

)(4π

()()]

f r f f f B B r r r r B B ?2λ

σσ???σσ?????=+??????+??σ+

(2)

And the root mean square deviation of the ground

deformation is r σ?=

Obviously, the error of ground deformation meas-ured by D-InSAR originates from the interferometric phase errors of both the differential and the topog-raphic pairs as well as from the perpendicular base-line errors of both differential and topographic pairs. We analyzed the propagation effect of perpendicular baselines and interferometric phase on the error of ground deformation.

3.1 Effect of perpendicular baselines on ground

deformation errors According to equation (3), the effect of perpen-dicular baselines on ground deformation errors is felt in two ways. First, the root mean square error of measured deformation r ?σ is a monotone and in-creasing function of the root mean square error of the differential pair baseline 1B σand the root mean square error of the topographic pair baseline 2B σ. Secondly,

the lengths of perpendicular baselines for topographic

and differential pairs evidently affect the root mean square error of ground deformation r ?σ. However, their roles are completely different. When the per-pendicular baseline length of topographic pair 2in-creases, the propagation effect of several kinds of errors on the ground deformation error r ?B σwill de-crease, including the perpendicular baseline errors of both topographic and differential pairs as well as the interferometric phase error of the topographic pair. That is to say, the perpendicular baseline length of the topographic pair 2plays a role of “diminishing” the propagation effect of the perpendicular baseline er-rors of the topographic and differential pairs as well as the interferometric phase error of the topographic pair on the ground deformation error, especially for the propagation effect of the perpendicular baseline error of the topographic pair. Conversely, the propa-gation effect of the perpendicular baseline error and the interferometric phase error of the topographic pair on the ground deformation error will increase when the perpendicular baseline length of the differential pair 1increases. That is to say, the perpendicular baseline length of the differential pair 1plays a role of “amplifying” the propagation effect of the perpen-dicular baseline error and the interferometric phase error of the topographic pair on the ground deforma-tion error. On the whole, the roles of the perpendicu-lar baselines for topographic and differential pairs are the complete reverse of each other, the former playing the role of diminishing propagation effect of several kinds of error sources on the ground deformation er-ror, while the latter plays a role of amplifying the propagation effect of some error sources on the ground deformation error. Apparently, the function of the former is more powerful than that of the latter. B B B 3.2 Origin of interferometric phase and its effect

on ground deformation errors Similar to the perpendicular baseline, the ground deformation error is a monotone and increasing func-tion of the interferometric phase errors of the topog-raphic and differential pairs. Since the interferometric phase is produced by other parameters, both the in-terferometric phase error of the differential pair and the interferometric phase error of the topographic pair are not the original errors, which are induced by other error sources. Therefore, it is necessary to analyze their sources.

There are many factors that may induce the inter-ferometric phase error in some procedures, such as signal acquisition, signal processing and differential SAR interferometry. These are listed in Table 1[10]. In the procedure of D-InSAR, the main factors inducing interferometric phase errors include SAR thermal noise, co-registration errors and perpendicular base-line errors.

Table1 Factors inducing interferometric phase errors

Type Influencing factors Satellite orbit Positioning error, baseline error

SAR image Co-registration error

SAR signal Frequency, thermal noise, focusing error

Terrain

V olume scattering, slope Climate condition

Wind, snow, atmosphere refraction

The interferometric phase error caused by SAR thermal noise is random and has no systematic effect on the interferometric phase. Generally, it can be re-strained by mean of filtering, such as multi-look av-eraging. The effect of co-registration error can be weakened or eliminated by accurate co-registration, such as maximal coherence algorithm or maximal frequency spectrum algorithm so that the effect of co-registration error on the interferometric phase er-ror can almost be ignored, while the effect of perpen-dicular baseline errors on the interferometric phase is systematic and most prominent in the entire inter-ferometric area [11]. It embodies the fact that the per-pendicular baseline error can induce the calculating error of the flat terrain phase difference, which leads to the interferometric phase errors of the topographic and differential pairs. In equation (1), 1f ?and 2f ? are the interferometric phases removed from the flat-Earth phase trend. The phase difference caused by flat terrain is illustrated in Fig. 2, and expressed as

4πcos tan y B y R θ

?λθ

⊥??=?

(4)

where y ?? is the phase difference caused by flat terrain, the distance from the SAR sensor to the target, R λ represents the radar wavelength and θ is the incidence angle. Hence, the root mean square er-ror of the phase difference induced by flat terrain is

4πcos tan y

B y R ?θ

σσλθ⊥

??=?

(5)

Fig. 2 Phase difference induced by flat terrain

Apparently, the error of the phase difference in-duced by flat terrain is a linear function of the per-pendicular baseline error. When the latter increases the former will simultaneously increase linearly. In other words, the perpendicular baseline error not only directly affects the ground deformation error, but also can lead to the flat terrain phase difference error. So

there is no doubt that the perpendicular baseline is the

most important factor affecting the ground deforma-tion error. 4 Analysis on Improving Accuracy of

Ground Deformation

The error of ground deformation measured by D-InSAR lies formally with the interferometric phase errors of the topographic and differential pairs as well as the perpendicular baseline errors of the topog-raphic and differential pairs, but actually it largely depends on the perpendicular baseline errors of the topographic and differential pairs, which have a direct and systematic effect on the accuracy of measured deformation. Apart from that, the lengths of perpen-dicular baselines for topographic and differential pairs play a role of “diminishing or amplifying” the propagation effect of the perpendicular baseline error and the interferometric phase error on the ground de-formation error. In other words, the ground deforma-tion error not only depends on the accuracy of per-pendicular baselines but also on the combination of the relationship between the perpendicular baselines for topographic and differential pairs. The perpen-dicular baselines and their errors play a decisive role in the accuracy of ground deformation. Therefore, in order to improve the accuracy of ground deformation, it not only needs to obtain higher accurate perpen-dicular baseline lengths for topographic and differen-tial pairs but also take the combination of their rela-tionship into account.

Generally, there are three kind of methods to ac-quire perpendicular baselines: 1) inversion from the parameters of a satellite orbit; 2) inversion by a Fou-rier transform based on the distribution of interfer-ometric phase fringes and 3) inversion by a Least Squares Method on the basis of ground control points.

Because of the limitation of satellite-orbit measur-ing and positioning accuracy as well as the effect of the terrain, it is almost impossible to acquire high accurate perpendicular baseline lengths by methods 1) and 2). Hence, it does make sense to apply the Least Squares Method to obtain highly accurate perpen-dicular baseline lengths to improve the accuracy of the interferomeric phase. Unfortunately, it is very difficult or unrealistic to obtain the data from ground control points in most cases. Therefore, it is more feasible and practical to optimize the combination of perpendicular baselines of topographic and differen-tial pairs. Under the precondition of fine coherence, it is reasonable to select the SAR images with longer perpendicular baseline as a topographic pair and the ones with shorter perpendicular baseline as a differ-ential pair, so that the effect of various errors on the ground deformation error will be further diminished and higher accurate deformation will be likely

Table 3 Combination 2 of topographic and differential

achieved. This is especially true when the ratio of the perpendicular baseline length of the differential pair to the perpendicular baseline length of the topog-raphic pair is small enough or even close to 0, i.e. 02

→B B , then equation (3) can be approximated by:

perpendicular baselines

Topographic pairs Differential pairs

Groups Date

Baselines

(m)

Date Baselines (m) A 2193/04/12–94/02/14159.3 93/04/12–93/02/27–1148.1A 2296/04/16–95/02/01–754.1 96/04/16–96/05/30996.2 A 23

98/03/21–98/09/13

–123.4 98/03/21–98/02/05

293.2

r σ?=

(6)

In order to evaluate the accuracy of the ground de-formation, we assumed the perpendicular baseline error 1B σ=2B σ= ±10 cm and the interferometric phase error 1f ?σ=2f ?σ= ±20°. Besides, it is well known that λ=23.5 cm for JERS. According to equation (3) and the relative parameters in Tables 2 and 3, we can compute the ground deformation errors for different baseline combinations. These are listed in Table 4. Obviously, the ground deformation errors in combination 1 are much less than the correspond-ing ground deformation errors in combination 2. The reason is that the lengths of the perpendicular base-lines of the topographic pair are all greater than the corresponding ones of the differential pair in combi-nation 1. That is to say, combination1 tallies with the above principle, while the combination of the rela-tionship of the perpendicular baselines in combina-tion 2 is the reverse. Actually, we chose the perpen-dicular baseline in combination1 to implement dif-ferential interferometry; consequently higher accurate deformation was retrieved. Fig. 3 shows the inter-ferograms of A 13.

That is to say, there is almost no propagation effect

of the perpendicular baseline error and interferometric phase error of the topographic pair on the ground de-formation error when the ratio of the perpendicular baseline length of the differential pair to the perpen-dicular baseline length of the topographic pair is close to 0 or small enough. The ground deformation error basically depends on the interferometric phase error and the perpendicular baseline error of the differential pair. When this condition is met, the accuracy of the measured deformation will be greatly improved.

5 Comparison Between Ground Deforma-tion Errors of Different Perpendicular

Baseline Combinations

We applied D-InSAR to measure the ground de-formation in the Wuan mining area, Hebei Province. Six image pairs were selected and thought to be suit-able for SAR interferometry from 17 scenes of JERS SAR data; the lengths of their perpendicular baselines are between 123 m and 1148 m [12]. Tables 2 and 3 illustrate the possible combinations of perpendicular baselines of the topographic and differential pairs for differential interferometry.

Table 4 Ground deformation errors of different baseline

combinations

Table 2 Combination 1 of topographic and differential

perpendicular baselines

Combination 1 Combination 2

Groups

Deformation errors

(cm)

Groups Deformation errors (cm) A 110.66 A 21 4.75 A 120.82 A 22 1.08 A 13

0.71 A 23

1.68

Topographic pairs Differential pairs

Groups Date

(m)

Date (m) A 1193/04/12–93/02/27 –1148.193/04/12–94/02/14159.3 A 1296/04/16–96/05/30 996.2 96/04/16–95/02/01–754.1A 13

98/03/21–98/02/05 293.2 98/03/21–98/09/13

–123.4

(a) Topographic pair (b) Differential pair (c) Differential interferogram

Fig. 3 Interferogram of A 13

6 Conclusion

Our investigation has demonstrated that the ground deformation error not only depends on the errors of perpendicular baselines and the errors of interfer-ometric phase for topographic and differential pairs, but also on the combination of the relationship of perpendicular baselines for topographic and differen-tial pairs. The roles of perpendicular baselines for topographic and differential pairs are completely the reverse from each other. The perpendicular baseline of the topographic pair plays a role of “diminishing” the propagation effect of the perpendicular baseline errors of the topographic and differential pairs as well as the propagation effect of the interferometric phase error of the topographic pair on the ground deforma-tion error. Conversely, the perpendicular baseline of the differential pair plays a role of “amplifying” the propagation effect of the perpendicular baseline error and interferometric phase error of the topographic pair on the ground deformation error. Especially, when the ratio of the perpendicular baseline length of the differential pair to the perpendicular baseline length of the topographic pair is small enough there is almost no propagation effect of the perpendicular baseline error and the interferometric phase error of the topographic pair on the ground deformation error. The ground deformation error basically depends on the interferometric phase error and the perpendicular baseline error of the differential pair.

Therefore, in order to achieve high accurate ground deformation, it makes sense to obtain high accurate perpendicular baseline lengths by the Least Squares Method on the basis of ground control points. On the other hand, it is more reasonable to select SAR image pairs with a longer perpendicular baseline as a topog-raphic pair and image pairs with a shorter perpen-dicular baseline as a differential pair, which is not only helpful to “balance” the coherence between the topographic and the differential pairs but also helpful to diminish the effect of various errors on the accu-racy of the ground deformation. In our point of view, optimizing the combination of perpendicular baseline according to the above principle is a feasible and practical approach for improving the accuracy of ground deformation measured by D-InSAR.

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Unit5 Reading An Exciting Job 说课稿 Liu Baowei Part 1 My understanding of this lesson The analysis of the teaching material:This lesson is a reading passage. It plays a very important part in the English teaching of this unit. It tells us the writer’s exciting job as a volcanologist. From studying the passage, students can know the basic knowledge of volcano, and enjoy the occupation as a volcanologist. So here are my teaching goals: volcanologist 1. Ability goal: Enable the students to learn about the powerful natural force-volcano and the work as a volcanologist. 2. Learning ability goal: Help the students learn how to analyze the way the writer describes his exciting job. 3. Emotional goal: Make the Students love the nature and love their jobs. Learn how to express fear and anxiety Teaching important points: sentence structures 1. I was about to go back to sleep when suddenly my bedroom became as bright as day. 2. Having studied volcanoes now for more than twenty years, I am still amazed at their beauty as well as their potential to cause great damage. Teaching difficult points: 1. Use your own words to retell the text. 2. Discuss the natural disasters and their love to future jobs. Something about the S tudents: 1. The Students have known something about volcano but they don’t know the detailed information. 2. They are lack of vocabulary. 3. They don’t often use English to express themselves and communicate with others.

an exciting job 翻译

我的工作是世界上最伟大的工作。我跑的地方是稀罕奇特的地方，我见到的是世界各地有趣味的人们，有时在室外工作，有时在办公室里，有时工作中要用科学仪器，有时要会见当地百姓和旅游人士。但是我从不感到厌烦。虽然我的工作偶尔也有危险，但是我并不在乎，因为危险能激励我，使我感到有活力。然而，最重要的是，通过我的工作能保护人们免遭世界最大的自然威力之一，也就是火山的威胁。我是一名火山学家，在夏威夷火山观测站（HVO）工作。我的主要任务是收集有关基拉韦厄火山的信息，这是夏威夷最活跃的火山之一。收集和评估了这些信息之后，我就帮助其他科学家一起预测下次火山熔岩将往何处流，流速是多少。我们的工作拯救了许多人的生命，因为熔岩要流经之地，老百姓都可以得到离开家园的通知。遗憾的是，我们不可能把他们的家搬离岩浆流过的地方，因此，许多房屋被熔岩淹没，或者焚烧殆尽。当滚烫沸腾的岩石从火山喷发出来并撞回地面时，它所造成的损失比想象的要小些，这是因为在岩石下落的基拉韦厄火山顶附近无人居住。而顺着山坡下流的火山熔岩造成的损失却大得多，这是因为火山岩浆所流经的地方，一切东西都被掩埋在熔岩下面了。然而火山喷发本身的确是很壮观的，我永远也忘不了我第一次看见火山喷发时的情景。那是在我到达夏威夷后的第二个星期。那天辛辛苦苦地干了一整天，我很早就上床睡觉。我在熟睡中突然感到床铺在摇晃，接着我听到一阵奇怪的声音，就好像一列火车从我的窗外行驶一样。因为我在夏威夷曾经经历过多次地震，所以对这种声音我并不在意。我刚要再睡，突然我的卧室亮如白昼。我赶紧跑出房间，来到后花园，在那儿我能远远地看见基拉韦厄火山。在山坡上，火山爆发了，红色发烫的岩浆像喷泉一样，朝天上喷射达几百米高。真是绝妙的奇景！就在这次火山喷发的第二天，我有幸做了一次近距离的观察。我和另外两位科学被送到山顶，在离火山爆发期间形成的火山口最靠近的地方才下车。早先从观测站出发时，就带了一些特制的安全服，于是我们穿上安全服再走近火山口。我们三个人看上去就像宇航员一样，我们都穿着白色的防护服遮住全身，戴上了头盔和特别的手套，还穿了一双大靴子。穿着这些衣服走起路来实在不容易，但我们还是缓缓往火山口的边缘走去，并且向下看到了红红的沸腾的中心。另外，两人攀下火山口，去收集供日后研究用的岩浆，我是第一次经历这样的事，所以留在山顶上观察他们

英语选修六课文翻译第五单元

新目标英语七年级下册课文Unit04

新目标英语七年级下册课文Unit04 Coverstion1 A: What does your father do? B: He＇s a reporter. A:Really?That sounds interesting. Coverstion2 A:What does your mother do,Ken? B:She＇s a doctor. A:Really?I want to be a doctor. Coverstion3 A:What does your cousin do? B:You mean my cousin,Mike? A:Yeah,Mike.What does he do? B:He is as shop assistant. 2a,2b Coverstion1 A: Anna,doesyour mother work? B:Yes,she does .She has a new job. A:what does she do? B: Well ,she is as bank clerk,but she wants to be a policewoman. Coverstion2 A:Is that your father here ,Tony?

B:No,he isn't .He's working. B:But it's Saturday night.What does he do? B:He's a waiter Saturday is busy for him. A:Does he like it? B:Yes ,but he really wants to be an actor. Coverstion3 A:Susan,Is that your brother? B:Yes.it is A:What does he do? B:He's a student.He wants to be a doctor. section B , 2a,2b Jenny:So,Betty.what does yor father do? Betty: He's a policeman. Jenny:Do you want to be a policewoman? Betty:Oh,yes.Sometimes it's a little dangerous ,but it's also an exciting job.Jenny, your father is a bank clerk ,right? Jenny:Yes ,he is . Sam:Do you want to be a bank clerk,too? Jenny:No,not really.I want to be a reporter. Sam: Oh,yeah?Why? Jenny:It's very busy,but it's also fun.You meet so many interesting people.What about your father ,Sam. Sam: He's a reporter at the TV station.It's an exciting job,but it's also very difficult.He always has a lot of new things to learn.Iwant to be a reporter ,too

高中英语_An exciting job教学设计学情分析教材分析课后反思

人教版选修Unit 5 The power of nature阅读课教学设计 Learning aims Knowledge aims: Master the useful words and expressions related to the text. Ability aims: Learn about some disasters that are caused by natural forces, how people feel in dangerous situations. Emotion aims: Learn the ways in which humans protect themselves from natural disasters. Step1 Leading-in 1.Where would you like to spend your holiday? 2.What about a volcano? 3.What about doing such dangerous work as part of your job ? https://www.360docs.net/doc/a013353099.html, every part of a volcano. Ash cloud/volcanic ash/ Crater/ Lava /Magma chamber 【设计意图】通过图片激发学生兴趣，引出本单元的话题，要求学生通过讨论, 了解火山基本信息，引出火山文化背景，为后面的阅读做铺垫。利用头脑风暴法收集学生对课文内容的预测并板书下来。文内容进行预测，培养学生预测阅读内容的能力。同时通过预测激起进一步探究 Step2. Skimming What’s the main topic of the article?

新目标英语七年级下课文原文unit1-6

Unit1 SectionA 1a Canada, France ,Japan ,the United States ,Australia, Singapore ,the United Kingdom,China 1b Boy1:Where is you pen pal from,Mike? Boy2:He's from Canada. Boy1:Really?My pen pal's from Australia.How about you,Lily?Where's your pen pal from? Girl1:She's from Japan.Where is Tony's pen pal from? Gril2:I think she's from Singapore. 2b 2c Conversation1 A: Where's you pen pal from, John? B: He's from Japan, A:Oh,really?Where does he live? B: Tokyo. Conversation2 A: Where's your pen pal from, Jodie? B: She's from France. A: Oh, she lives in Pairs. Conversation3 A: Andrew, where's your pen pal from? B: She's from France. A: Uh-huh. Where does she live? B: Oh, She lives in Paris.