Modeling of Atmospheric Effects on InSAR Measurements with Method of Stochastic Simulation

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Modeling of Atmospheric Effects on InSAR
Measurements with Method of Stochastic
Simulation (Cat 1 Project 1227)
X.L. Ding and Z.W. Li Department of Land
Surveying and Geo-Informatics Hong Kong
Polytechnic University
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Outline

• Introduction
• Atmospheric effects on InSAR measurements
• Drawbacks of Kriging interpolator
• Experiments with stochastic simulation method
• Conclusions

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Introduction

• Atmospheric effect is one of the main error
  sources in InSAR measurements
• Calibratory method has been studied and proposed
• External data points are always much sparse than
  resolution of SAR data
• Data interpolation is important in calibratory
  method
• This study tests the method of stochastic
  simulation

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Atmospheric Effects on InSAR

• Responsible atmospheric layers
• Troposphere
• Ionosphere
• Effect of atmosphere

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Atmospheric Effects on InSAR (cont)

• Affect both DEM and surface deformation mapping
• Only affect repeat-pass InSAR configuration
• For repeat-pass configuration, atmospheric
  effects will be cancelled if
• Atmospheric profiles remain the same for two
  acquisitions
• Uniform effect over an entire area

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Determination of Atmospheric Effect

• Estimated from GPS (Rosen, 1996)
• gt12cm peak-to-peak variability
• Estimated from tropospheric model (Zebker.,1997)
• 1014cm error for deformation products
• 80290m error for DEM (baseline from 400 to
  100m)
• Estimated from InSAR interferograms
• Generally 0.32.3 cycles extreme case 4.5 cycles
  (Hanssen, 1998)
• peak-to-peak error 2.8cm, RMS about 0.3cm
  (Goldstein,1995)
• Estimated with ps technique
• 0.25-1.35 radians (Ferretti et al., 2000, 2001)

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Mitigation of Atmospheric Effect

• Stacking method
• Zebker et al., 1997 Williams et al., 1998
• Degrade temporal resolution, not desirable for
  continuously deforming area
• PS technique
• Ferretti et al., 2000, 2001
• Large amount of images
• Calibratory method
• Calibration
• Bock, 1997 Williams, 1998 Webley, 2002 Ge,
  2002 (with GPS observations)
• Delacourt, 1998 (with meteorological observation)
• Bonforte, 2001 Li, 2002 (with both GPS and
  meteorological data)
• Wadge (with tropospheric models)
• Depending on the accuracy, density of
  observations and effectiveness of interpolator

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Example for Hong Kong

• 6 CGPS stations
• 22 ground meteorological stations

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Distribution of the GPS stations in Hong Kong
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Distribution of meteorological stations in Hong
Kong
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Interpolators Suggested for Calibratory Methods

• Inverse distance weighted averaging
• Williams, et al., 1998 Ge, et al., 2002
• Bilinear interpolation
• Williams, et al., 1998
• Spline interpolation
• Ge, et al., 2002
• Polynomial
• Webley, et al., 2002
• Kriging
• Williams, et al., 1998 Webley, et al., 2002 Ge,
  et al., 2002 Li, et al., 2002

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Kriging Interpolator and Its Limitations

• Basic Kriging formulation
• where
  , and weight set
  determined by

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Kriging Interpolator and Its Limitations (cont)

• Limitation 1 smoothing effect
• The variance of estimated value does not
  reproduce the variance of the model
• Smaller values tend to be overestimated, whereas
  large values tend to be underestimated
• The smoothing effect increases further away from
  the data points

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Example of Smoothing Effects
Reference data (left) and their Kriging
estimation (right) (after Journel et al.)
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Kriging Interpolator and Its Limitations (cont)

• Limitation 2 not reproducing spatial structure
• Aims at local accuracy, i.e., being
  best estimate
• Cannot represent well the spatial structure,
  e.g., not considering

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Methods of Stochastic Simulation

• Key consideration simulate data points based on
  joint probability density function
• Conditional
• Reproduce the covariance model evenly over entire
  area
• Provide multiple equiprobable realizations

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Methods of Stochastic Simulation (cont)

• Methods of stochastic simulation
• Sequential simulation
• p-field simulations
• Simulation annealing

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Experiment with Stochastic Simulation

• A field of differential atmospheric effect is
  derived from an ERS tandem pair
• 50 points are sampled from the atmospheric field
  and considered as known data points
• Reconstruct the atmospheric field with both
  stochastic simulation and Kriging methods, based
  on the 50 sampled points
• Assess the results

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Derivation of Field of Differential Atmospheric
Effect

• Interferogram from a tandem SAR pair of Hong Kong
  (acquired on 18/3/1996 and 19/3/1996, track 404,
  frame 3159)
• A known DEM to remove the topographic phase

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Atmospheric Field from Sequential Gaussian
Simulation

• Transform the original data to standard normal
  score data
• Define a random path that visit each node of the
  grid
• Use Simple Kriging method to determine the
  Gaussian distribution (mean and variance) at each
  node based on a number of conditional data
  including known and previously simulated data
  points
• Draw a simulated value from the Gaussian
  distribution

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• Proceed to the next node, and loop all nodes
  defined
• Back-transform the simulated normal values

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Atmospheric Field from Kriging Interpolator

• Ordinary Kriging
• Omni directional semivariogram model
• where are fitted to
  sampled data

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Results of Stochastic Simulation (1)
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Results of Stochastic Simulation (2)
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Results of Stochastic Simulation (3)
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Results of Stochastic Simulation (4)
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Results of Stochastic Simulation (5)
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Mean of Five Simulations
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Results of Kriging Interpolation
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Comparison of Semivariogram (1)

• Solid line reference model
• Red dots Kriging
• Green dots Stochastic simulation

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Comparison of semivariogram (2)

• Solid line reference model
• Red dots Kriging
• Green dots Stochastic simulation

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Comparison of semivariogram (3)

• Solid line reference model
• Red dots Kriging
• Green dots Stochastic simulation

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Comparison of semivariogram (4)

• Solid line reference model
• Red dots Kriging
• Green dots Stochastic simulation

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Comparison of semivariogram (5)

• Solid line reference model
• Red dots Kriging
• Green dots Stochastic simulation

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Quantitative Results(from a more extensive study)
Note in each group, 200 realizations are
simulated, and a most probabilistic one is drawn

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Conclusions

• Data interpolation is important in modeling
  atmospheric effects on InSAR measurements
• Commonly used interpolators, e.g., Kriging
  interpolator, have drawbacks
• Stochastic simulation can overcome some of the
  drawbacks

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Acknowledgments

• ESA
• Research Grants Council of HK