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Subsidences estimation from ground based SAR: techniques and experimental results

Subsidences estimation from ground based SAR: techniques and experimental results

Advanced Remote Sensing Systemsa POLIMI spin-off

Davide D’Aria

A. Monti Guarnieri, F. Rocca

Dipartimento di Elettronica e Informazione Politecnico di Milano

G. Bernardini*, P. Ricci

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Abstract

From spaceborne C-band to ground-based ku-band

Processing

Target correlation properties

Atmospheric Phase Screen statistics

Accuracy in the estimation of subsidences

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ERS-ENVISAT vs IBIS-L

24 hoursFixed local timeAcquisition

0< 2 kmBaseline

5’1-35 daysRepeat interval

3500.7T synth (s)

0.59ρsr (m)

< 8.85ρaz (m)

0.01 -2820-870r0 (km)

1.85.6λ (cm)

IBIS-LERS-ENVISAT

Parameter

Radar position

Ran

gedi

rect

ion

Cross - Range direction

Clutter decorrelates (within acquistion time)

☺ but no volume decorrelation, and

☺ finer range resolution (50 cm)

Ph. unwrapping is critical (1 cycle = 9 mm)

☺ but sampling step is short (5’-20’)

☺ and shorter 2-way path (lower APS)

Large range spread (1 m – 4 km)

Significant occurrence of shadowing

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Focusing

Range Focusing(range IFFT)

Range Focusing(range IFFT)

RM correctionRM correction

Range IFFT Range IFFT

Range windowingRange windowing

Range data selectionRange data selection

Azimuth CZTAzimuth CZT

Range FFTRange FFT

Parabolic phase correction

Parabolic phase correction

Azimuth windowingAzimuth windowing

RADAR acquires in frequency steps (SFCW modulation)

Polar Format is quite suitable to accommodate for the large range spread.

Range migration compensation in (kx,ω) domain

Simple & efficient (2D FFT)

Geocoding is applied to the output of the interferometricprocessing

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θ

ρ

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Test site(s)

Three test sites with landslide in mountain & hilly areas have been analyzed, one (Tessina) is reported here.

Tessina (Chies D’Alpago, Belluno IT) is affected by a fast moving landslide (> 10 cm/day).

218 acquisitions (5’) for < 1 day:

23-Jun-06 16.40 to 24-Jun-06 14.27

GOOGLE

Vegetated areas + exposed rocks

Mountain slopes oriented S-SE

Some rain during night

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24-JUN-2006 10:10

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24-JUN-2006 07:28

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Short time coherence

Amplitude Coherence Amplitude Coherence

Short time coherence is highly non-stationary. Vegetated targets that decorrelate in the synthetic aperture time (5’) are defocused.

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Correlation matrix: vegetation

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Vegetation (brush)

Strong correlation during nightime (not rainy).

Loose and short correlation daytime

Similar behaviour verified in Test site 2 for praieries.

18:07

09:01

13:19

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Correlation matrix: Stable targets

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Exposed rocks are always coherent, rain and night/day variation exists (clutter).

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Correlation matrix: decorrelating target

The decorrelation decay is exponential, the span of the inverse matrix is (span = ±2 images = 10’)

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INV=

It is due to a velocity gradient in the estimation patch (150 x 150 m).Processing of smaller patches is recommended for such cases

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Optimal subsidence estimateA two step approach was proposed in [1], whatever the target decorrelation. It is optimal in Bayesian sense (consistent with the hybrid Cramer Rao bound),It allows the exploitation of a standard PS processor.

Ist stepEstimate the N linked phases form N images, by jointly exploiting all the N×(N-1)/2 interferograms, given the scene covariance matrix

Tebaldini-MontiGuarnieri: A new framework for multi-pass SAR Interferometry with distributed targets. IGARSS-07

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Target Covariance matrix

yN

y1

ML estimate(linking of Nx(N-1)

interferograms)

( )( )

( )⎥⎥⎥⎥

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Nj

jj

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exp

expexp

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N images

N linked

phases

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0LOS Subsidence rate

[mm/day]

IInd step. Given the N optical paths (the unwrapped linked phases), separate LOS displacement by Atmospheric Phase Screen by filtering in the space-time domain.

Two steps approach

Unwrapping& APS

estimation

( )( )

( )⎥⎥⎥⎥

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exp

expexp

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N-1 estimatedphases

DEM

Atmospheric Phase Screen

Deformation map

Deformation parameters

DeformationModel

Same approach of a standard PS processor

Additional APS compensation step

DEM is not needed for 0 baseline

Same approach of a standard PS processor

Additional APS compensation step

DEM is not needed for 0 baseline

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APS statisticsThe separation of motion and APS is strongly dependent of the 3D space-time

correlation of the APS itself. Here we assume to monitor “slow” subsidences.

The APS statistics can be derived by the finite differences, in the 5’ step, of the data phases. In Tessina dataset we assume APS monodimensional (Δψ = 20°).

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time (min)

Differential APS (1 column = 1 image), smoothed

mm

APS noise varies up to ±1.5 mm, due to temperature excursions

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mm

09:0106:00 12:0413:19

Mean D-APS (mm)versus time

D-APS statistics

Std up to 1 mm, daytime, 400-1500 m

Std up to 1 mm, daytime, 400-1500 m

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Range (m)400 600 800 1000 1200 1400

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D-APS smooth compensationDifferential phase field, after compensating for a very smooth APS (IInd polynomial).

mm

Residual contributions are due to:

- LOS displacements

- uncompensated APS

- clutter noise

Residual contributions are due to:

- LOS displacements

- uncompensated APS

- clutter noise

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[mm]

Range (m)

Imag

e

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20406080

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Residual noise statistics

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[mm]

Differential “delay” std (mm) after compensating for smooth term.

250 μm 1.5 mm

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Range (m)

Imag

e

Residual DAPS std (mm)

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Residual noise statistics

Test-site #2range 3 km, mountain area, 3 days with strong rain.

Histogram of uncompensated differential delay std bottoms at ~ 200-300 μm.

This residual delay may be reduced to ~ 100 μm by removing motion and performing a further local (PS-like) APS compensation.

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Accuracy in subsidence rate estimate

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2 mm/day2 mm/day

Average Best CaseSNR dB 16 25Thermal phase std rad 0.11 0.04SCR dB 0 ∞Clutter phase std 0.71 0.00Total Target Phase std rad 0.72 0.04Target coherence 0.77 0.9992APS comp std rad 0.2Atmo+target std 0.74 0.20Distance accuracy mm 1.04 0.29Number of images 216Acquistion time interval min 5Conversion factor smpls/ 288Total time span (days) 0.8Rate estimate error (std) mm/da 1.39 0.382

The predicted accuracy is consistent with the histogram of estimated velocities (γ>0.7)

The predicted accuracy is consistent with the histogram of estimated velocities (γ>0.7)

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Accuracy in subsidence rate estimate

LOS subsidence rates starting from 1-2 mm/day show spatial consistence.

Can be as well attributed to residual time-domain correlated APS.

Phase unwrapping allows for tracking without errors fast moving landslides.

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t [min]

ΔRLOS [mm]

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Conclusions

The IBIS-L GB SAR provides a valuable monitoring system with 4 km range and frequent revisit that complements spaceborne SARs.

A processing algorithm has been shown to extract motion parameters form coherent and decorrelating targets.

Investigations on the APS shows fluctuations up to ±1.5 mm, due to temperature variation daytime.

The residual phase noise, due to clutter and uncompensated APS is 0.2 mm (night) -1.5 (day) mm. A final accuracy of subsidence rate estimate is 0.4-1.3 mm/day based on 1 day observation.

However, it would be impossible to separate motion form the slow-varying APS.