Performance Analysis of Tandem-L Mission for Modeling ...seom.esa.int/fringe2015/files/presentation213.pdfModelling Precision-Okada II DLR.de • Chart 15 > Tandem-L Performance Analysis

Performance Analysis of Tandem-L Mission for Modeling Volcanic and

Seismic Deformation Sources

Homa Ansari 1,2

Kanika Goel 1, Alessandro Parizzi 1, Henriette Sudhaus 3, Nico Adam 1 , Michael Eineder 1,2

> Tandem-L Performance Analysis > Homa Ansari • EGU 2015 > 15.04.2015 DLR.de • Chart 1

(1) German Aerospace Center (DLR) (2) Technical University of Munich (TUM) (3) University of Potsdam

Technical

University

of Munich

The Proposed Tandem-L Mission

• Systematic monitoring of dynamic processes of the Earth


Data Characteristics

Wide Swath ~ 350 [km]

High Resolution Rg.: 85 , 20 + 5 [MHz]

Az. : 3 , 10 [m]

Coherent Revisit 16 [Days]

Wavelength ~ 24 [cm]

Tandem-L Coverage for Seismology and Volcanos


• Biomass/forest areas

• High strain areas (Twice in 16 days)

• Volcanos (Twice in 16 days)

Why performance analysis

• Assessing the geometric acquisition modes in deformation monitoring

In particular: Do we need the expensive left-looking acquisition mode for better precision?

• Assessing the performance of InSAR in deformation source modeling

• Having a flavor of the significance of different InSAR noise components on the modeling

• The achievable precision of the L-band data


Satellite ground track

Antenna right looking swath

Antenna left looking swath

Why performance analysis

• Assessing the geometric acquisition modes in deformation monitoring

In particular: Do we need the expensive left-looking acquisition mode for better precision?

• Assessing the performance of InSAR in deformation source modeling

• Having a flavor of the significance of different InSAR noise components on the modeling

• The achievable precision of the L-band data


Deformation Source Modeling with InSAR


𝑑 → 𝑑𝐿𝑂𝑆

Differential InSAR Geophysical model

© ESA, Bam EQ

𝑥7

𝑥3

𝑥4

𝑥1

𝑑 = 𝐺(𝑥 )

Parameter Estimation : 𝒙 = 𝐺−1 𝑑𝐿𝑂𝑆

𝒙 =

𝑥1𝑥2⋮𝑥𝑛

→ Precision assessment: 𝒑𝒅𝒇(𝒙 )

Volcanic Modelling

• Point source model: (Mogi)

• Location of the centroid:

East

North

Depth

• Volume change inside the spherical chamber

Δ𝑉


centroid

Depth

Δ𝑉

Seismic Modelling

Rectangular dislocation model: (Okada)

Fault plane parameters

Location: east, north, depth

Extension: width, length

Orientation: strike, dip

Fault displacement parameters

Magnitude of the relative displacement: slip

Direction of the displacement: rake


Depth

dip

strike width

hypocenter

Precision Assessment

• First order reliability method: 𝑗𝑖,𝑘 = 𝜕𝑑𝑖/𝜕𝑥𝑘


1. Geometric assessment: (Acquisition and Ground Motion ) 𝑄𝑥 = 𝐽 . 𝐽𝑇

2. Stochastic assessment: (InSAR noise) 𝑄𝑥 = 𝐽. 𝑄𝐼𝑛𝑆𝐴𝑅 . 𝐽𝑇

𝑄𝑥 =

𝜎21,1 𝜎1,2 … 𝜎1,𝑛

𝜎2,1 𝜎22,2 … 𝜎2,𝑛

⋮𝜎𝑛,1

⋮𝜎𝑛,2

⋱…

⋮𝜎2𝑛,𝑛

→ 𝑄𝑖,𝑗 = 𝜎2𝑖,𝑖 𝜎𝑖,𝑗

𝜎𝑖,𝑗 𝜎2𝑗,𝑗

→ Eigen Value Analysis →

Error ellipses: cross section of the bivariate Gaussian distribution

• Approximations: Gaussian pdf, linearization

Geometric Performance (Acquisition and Ground Motion)


InSAR Sensitivity to 3D Deformation

• Single-aspect InSAR : Projection of 3D deformation on LOS

𝑑𝐿𝑜𝑆 = 𝑒 𝐿𝑂𝑆 . 𝑑

𝑒 𝐿𝑜𝑆 = −sin 𝜃 cos 𝛼 sin 𝜃 sin 𝛼

cos 𝜃 , 𝑑 =

𝑑𝑒𝑑𝑛𝑑𝑢


Near-polar sun-synchronous orbit Min sensitivity to the north component

• Multi-aspect fusion : improving the sensitivity to 3D motion

Scenario Heading ang.: α Incidence ang.: θ Mode

Single aspect -12° 43° Asc. R.

Multi-aspect Right looking -12° 43° Asc. R.

-168° 43°, 23° Desc. R.

Multi-aspect Left/Right looking

-12° 43° Asc. R.

-168° 43° Desc. R.

-12 -23° Asc. L.

-168 -23° Desc. L.

Normalization by the number of

measurements

↓ Isolating the effect of geometry

Modelling Precision-Mogi


-500 0 500-1000

-500

0

500

1000

East Coor.

No

rth

Co

or.

-500 0 500-1000

-500

0

500

1000

East Coor.

Dep

th

-500 0 500-2

-1

0

1

2x 10

6

East Coor.

Vo

lum

e C

han

ge

-1000 -500 0 500 1000-1000

-500

0

500

1000

North Coor.

Dep

th

-1000 -500 0 500 1000-2

-1

0

1

2x 10

6

North Coor.

Vo

lum

e C

han

ge

-1000 0 1000-2

0

2x 10

6

Depth

Vo

lum

e C

han

ge

Single Aspect

Multi Aspect Right

Multi Aspect Left/Right

Single Aspect Multi Aspect Right Multi Aspect Left/Right175

180

185

ST

D [

m]

East Coor


200

210

ST

D [

m]

North Coor


240

250

ST

D [

m]

Depth

Single Aspect Multi Aspect Right Multi Aspect Left/Right5.5

6

6.5x 10

5

ST

D [

m3]

Volume Change

Simulated source parameters: [east, north, depth, Volume change] = [0, 0, 3 km, 6 × 106 m³]

Modelling Precision-Okada I

• Asymmetric horizontal deformation pattern governed by fault and slip orientation: strike, dip, rake


Defo

rmati

on

[m

]

0

0.2

0.4

0.6

0.8

1

Defo

rmati

on

[m

]

0

0.2

0.4

0.6

0.8

1

First case: strike, dip, rake = 90°, 26°, 90° Second case: strike, dip, rake = 0°, 50°, 90°

Min North Deformation Max North Deformation

Simulated Source

Parameters

Mw 7

Depth 5.5 [km]

Length 20 [km]

Width 11 [km]

Slip 5 [m]

Modelling Precision-Okada II


First case: max. north deformation

strike, dip, rake = 90°, 26°, 90°

Second case: min. north deformation

strike, dip, rake = 0°, 50°, 90°

Simulated Source

Parameters

Mw 7

Depth 5.5 [km]

Length 20 [km]

Width 11 [km]

Slip 5 [m]


0.5

1

1.5

2

ST

D [

deg

]

Strike

Dip

Rake

Single Aspect Multi Aspect Right Multi Aspect Left/Right

0.06

0.08

0.1

0.12

ST

D [

m]

Slip


60

80

100

120

140

ST

D [

m]

East Coor

North Coor

Depth


150

200

250

ST

D [

m]

Width

Length


80

100

120

140

STD

[m

]

East Coor

North Coor

Depth


150

200

250

STD

[m

]

Width

Length


0.5

1

1.5

2

ST

D [

deg]

Strike

Dip

Rake


0.06

0.08

0.1

0.12

ST

D [

m]

Slip

Modelling Precision-Okada II


First case: max. north deformation

strike, dip, rake = 90°, 26°, 90°

Second case: min. north deformation

strike, dip, rake = 0°, 50°, 90°

Simulated Source

Parameters

Mw 7

Depth 5.5 [km]

Length 20 [km]

Width 11 [km]

Slip 5 [m]


0.5

1

1.5

2

ST

D [

deg

]

Strike

Dip

Rake


0.06

0.08

0.1

0.12

ST

D [

m]

Slip


60

80

100

120

140

ST

D [

m]

East Coor

North Coor

Depth


150

200

250

ST

D [

m]

Width

Length


80

100

120

140

STD

[m

]

East Coor

North Coor

Depth


150

200

250

STD

[m

]

Width

Length


0.5

1

1.5

2

ST

D [

deg]

Strike

Dip

Rake


0.06

0.08

0.1

0.12

ST

D [

m]

Slip

Necessity of the Left-looking Acquisition scenario in source modeling:

• Complexity of the model in use

• Asymmetry of the horizontal deformation in the model

• Share of the north component in the total deformation

Models constrain our view of the reality!

Left looking scenario is more beneficial for retrieval of the model-free

deformation field

Precision of Motion Decomposition-Single Point


Data characteristics Azimuth resolution 10 m

Range resolution Asc. [2.5 - 4.5] m

Desc. [11 - 18] m

Multi look window 50 × 50 m²

Average coherence 0.4

Ionospheric error [0.8 – 1.3] cm

Tropospheric error 1.5 cm

Estimation Precision 𝝈𝐸𝑎𝑠𝑡 [m]

𝝈𝑁𝑜𝑟𝑡ℎ [m]

𝝈𝑈𝑝 [m]

Asc/Desc Right 0.02 0.32 0.05

Asc/Desc Left/Right 0.02 0.09 0.01

-0.04 -0.02 0 0.02 0.04-0.5

0

0.5

East [m]

Nort

h [

m]

Cor =0.32

Cor =0.12

-0.04 -0.02 0 0.02 0.04-0.1

0

0.1

East [m]

Up [

m]

Cor =0.33

Cor =0.013

-0.4 -0.2 0 0.2 0.4-0.1

0

0.1

North [m]

Up [

m]

Cor =0.96

Cor =0.26

-0.04 -0.02 0 0.02 0.04-0.1

0

0.1

East [m]

Up

[m

]

Asc./Desc. Right

Asc./Desc. Right/Left

Precision of Motion Decomposition-Single Point




𝝈𝑈𝑝 [m]



-0.04 -0.02 0 0.02 0.04-0.5

0

0.5

East [m]

Nort

h [

m]

Cor =0.32

Cor =0.12

-0.04 -0.02 0 0.02 0.04-0.1

0

0.1

East [m]

Up [

m]

Cor =0.33

Cor =0.013

-0.4 -0.2 0 0.2 0.4-0.1

0

0.1

North [m]

Up [

m]

Cor =0.96

Cor =0.26

-0.04 -0.02 0 0.02 0.04-0.1

0

0.1

East [m]

Up

[m

]

Asc./Desc. Right

Asc./Desc. Right/Left• Improved precision

• Resolved correlation/ambiguity between

the motion components


Stochastic Performance

InSAR Measurement Stochastic Model:

• Stochastic model:

𝑄InSAR = 𝑄Dec. + 𝑄APS + 𝑄Iono


𝛾tot = 𝛾𝑖𝑖 → 𝜎𝜙 → 𝜎𝑑𝐿𝑂𝑆

Residual ionospheric error after correction by the Split

Bandwidth methods:

𝜎𝑆.𝐵𝑊 → 𝜎𝑖𝑜𝑛𝑜 → 𝜎𝜙 → 𝜎𝑑𝐿𝑂𝑆 [2]

Spatial covariance between the

single measurements :

𝐶𝑜𝑣 𝜌, 𝜎 𝐴𝑃𝑆 [1]

[2] Gomba, G., et al., “Towards an Operational Split-Spectrum Processor for Compensation of Differential Ionospheric Propagation Delay in SAR Interferograms,” (in preparation)

[1] Knospe, S., & Jonsson, S.. “Covariance estimation for dInSAR surface deformation measurements in the presence of anisotropic atmospheric noise,” IEEE TGRS

Error Assessment-Volcanic Modelling


Simulated Source Parameters

East 0

North 0

Depth 3 [km]

𝚫𝐕 𝟔 × 𝟏𝟎𝟔 [m]

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

60

80

100

120

140

160

Average Coherence

ST

D [

m]

East Coor

North Coor

Depth

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 12.5

3

3.5

4

4.5x 10

5

Average Coherence

ST

D [

m3 ]

V

Multi-aspect right-looking (3 aspects)

Fixed APS (𝜎 ∶ 15 𝑚𝑚 , 𝜌. 1.5 𝑘𝑚)




East 0

North 0

Depth 3 [km]

𝚫𝐕 𝟔 × 𝟏𝟎𝟔 [m]

0 5 10 15 20 25 30 35 400

100

200

300

400

APS Error [mm]

STD

[m

]

East Coor

North Coor

Depth

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12x 10

5

APS Error [mm]

STD

[m

3 ]

V


Fixed Coherence (𝛾 ∶ 0.4)




East 0

North 0

Depth 3 [km]

𝚫𝐕 𝟔 × 𝟏𝟎𝟔 [m]

1000 1500 2000 2500 3000 3500 4000 4500 500060

80

100

120

140

APS Correlation Length [m]

ST

D [

m]

East Coor North Coor Depth

1000 1500 2000 2500 3000 3500 4000 4500 50002

3

4

5

6x 10

5

APS Correlation Length [m]

ST

D [

m3 ]

V


Fixed Coherence (𝛾 ∶ 0.4)

Correlation between the APS and

geophysical signal with similar spatial scale

Correlation of the APS and the Geophysical Signal


APS Cor. Length [km]

So

urc

e D

ep

th [

km

]

2 3 4 5

2

4

6

8


So

urc

e D

ep

th [

km

]

2 3 4 5

2

4

6

8


So

urc

e D

ep

th [

km

]

2 3 4 5

2

4

6

8


So

urc

e D

ep

th [

km

]

2 3 4 5

2

4

6

8

200

400

600

800

200

400

600

800

1000

200

400

600

800

1000

1200

2

4

6

8

10

12

14

x 105

East North

Depth 𝚫𝐕

East North

Depth 𝚫𝐕

East

APS Corr. Length [km]

Mogi D

epth

[km

]

1.5 2 2.5 3 3.5 4 4.5 5

2

3

4

5

6

7

8

North


Mogi D

epth

[km

]

1.5 2 2.5 3 3.5 4 4.5 5

2

3

4

5

6

7

8

Depth


Mogi D

epth

[km

]1.5 2 2.5 3 3.5 4 4.5 5

2

3

4

5

6

7

8Normalized Error


Mogi D

epth

[km

]

2 3 4 5

2

3

4

5

6

7

8

No

rmali

zed

Err

or

0.5

0.6

0.7

0.8

0.9

1


So

urc

e D

ep

th [

km

]

1.5 2 2.5 3 3.5 4 4.5 5

2

4

6

8


So

urc

e D

ep

th [

km

]

1.5 2 2.5 3 3.5 4 4.5 5

2

4

6

8


So

urc

e D

ep

th [

km

]

1.5 2 2.5 3 3.5 4 4.5 5

2

4

6

8


So

urc

e D

ep

th [

km

]

1.5 2 2.5 3 3.5 4 4.5 5

2

4

6

8

East North

Depth 𝚫𝐕

Error Assessment-Seismic Modelling


Simulated Source

Parameters

Mw 6.16

Depth 4 [km]

Length 10 [km]

Width 8 [km]

Slip 0.7 [m]

0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

Average Coherence

ST

D [

m]

East

North

Depth

0.2 0.4 0.6 0.8 10

0.5

1

1.5

Average Coherence

ST

D [

deg

]

Strike

Dip

Rake

0.2 0.4 0.6 0.8 10

1000

2000

3000

4000

5000

Average Coherence

ST

D [

m]

Width

Length

0.2 0.4 0.6 0.8 10.01

0.015

0.02

0.025

0.03

Average Coherence

ST

D [

m]

Slip

10 20 300

1000

2000

3000

4000

APS Error [mm]

ST

D [

m]

East

North

Depth

10 20 300

0.5

1

1.5

2

2.5

APS Error [mm]

ST

D [

deg

]

Strike

Dip

Rake

10 20 300

2000

4000

6000

8000

APS Error [mm]

ST

D [

m]

Width

Length

10 20 300.01

0.02

0.03

0.04

0.05

0.06

APS Error [mm]

ST

D [

m]

Slip

1000 2000 3000 4000 50000

500

1000

1500

2000

2500

APS Cor. Length [m]

ST

D [

m]

East North Depth

1000 2000 3000 4000 50000

0.5

1

1.5

APS Cor. Length [m]

ST

D [

deg

]

Strike Dip Rake

1000 2000 3000 4000 50000

1000

2000

3000

4000

5000

APS Cor. Length [m]

ST

D [

m]

Width

Length

1000 2000 3000 4000 50000.015

0.02

0.025

0.03

APS Cor. Length [m]

ST

D [

m]

Slip

Summary

• Geometrical assessment:

• Multi aspect InSAR from left/right looking acquisitions:

• Improvement of the precision and resolving the ambiguity in motion decomposition

• Improvement of the modeling precision depends on the:

• Complexity of the model

• Asymmetry of the horizontal deformation

• Share of the north motion component

• Stochastic assessment:

• Quantification of the impact and significance of the coherence and correlated APS signals

on the precision of the inverted deformation source parameters

Ref. : Fringe2015 proceedings (Ansari et al.)



Thank you for your attention!

[email protected]


Back-Up Slides

Precision of Motion Decomposition-Single Point (Az. Res. : 3 m)


Data characteristics

Azimuth resolution 3 m

Range resolution Asc. [2.5 – 4.5 ] m

Desc. [11 - 18] m



Ionospheric error [0.4 – 1] cm




𝝈𝑈𝑝 [m]



-0.02 -0.01 0 0.01 0.02-0.5

0

0.5

East [m]

Nort

h [

m]

Cor =0.3

Cor =0.05

-0.02 -0.01 0 0.01 0.02-0.05

0

0.05

East [m]

Up [

m]

Cor =0.34

Cor =0.01

-0.4 -0.2 0 0.2 0.4-0.05

0

0.05

North [m]

Up [

m]

Cor =0.95

Cor =0.20

-0.04 -0.02 0 0.02 0.04-0.1

0

0.1

East [m]U

p [

m]

Asc./Desc. Right

Asc./Desc. Right/Left

Azimuth Shifts In 3D Decomposition (Az. Resolution = 10 m)




𝝈𝑈𝑝 [m]


Asc/Desc R. + Shifts 0.02 0.29 0.05




Range resolution Asc. [2.5 - 4.5] m

Desc. [11 - 18] m



Ionospheric error [0.8 – 1.3] cm


Azimuth Shifts In 3D Decomposition (Az. Resolution = 3 m)




𝝈𝑈𝑝 [m]


Asc/Desc R. + Shifts 0.02 0.19 0.03




Range resolution Asc. [2.5 – 4.5 ] m

Desc. [11 - 18] m



Ionospheric error [0.4 – 1] cm


Performance Analysis of Tandem-L Mission for Modeling ...seom.esa.int/fringe2015/files/presentation213.pdfModelling Precision-Okada II DLR.de • Chart 15 > Tandem-L Performance Analysis

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