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Realistic Error Modelling for InSAR

Tim J Wright(1) and Chuck Wicks(2)

(1) COMET, Oxford University, Oxford, OX1 3PR, United Kingdom
(2) USGS, 345 Middlefield Road, Menlo Park, CA-94025, United States

Abstract

Over the past decade, InSAR has developed into a widely-used geodetic tool, with a wide variety of geophysical applications. In principle, InSAR is capable of mapping deformation with a precision of a few millimetres and a spatial resolution of a few tens of metres. A major limitation of the technique arises from changes in tropospheric water vapour concentrations. These can be distributed over distances of tens of kilometres and, if interpreted as surface deformation, can cause errors in measurement as large as 10 cm. In addition, poor knowledge of satellite orbits can lead to long-wavelength errors in interferograms. Spatial correlation of InSAR noise are typically ignored when estimating the uncertainties of model parameters derived from InSAR data, which can lead to dramatic underestimates of parameter uncertainties. Here we present a simple method for analysing spatially-correlated noise in an interferogram, and assessing its impact using Monte Carlo simulation.

To produce realistic uncertainties, the data's full variance-covariance matrix (VCM), including the off-diagonal terms, must first be determined. A practical approach for this is to first determine the 1D covariance function (the radially averaged 2D autocovariance function), either spatially or from the interferogram's power spectrum using the Wiener-Khinchine theorem (e.g. Hanssen, 2001). Initially, the noise component of the interferogram must be isolated. For volcanic sources or earthquakes with magnitudes less than ~6.5, the deformation may only occupy a small part of the SAR scene, and an area away from the deformation can be analysed. Where this is not possible, a proxy for the noise (such as the difference between two coseismic interferograms), or a residual interferogram after a preliminary model has been removed, may be used. Alternatively, it is possible to analyse a small area of the interferogram and use the power-law relationships determined by Hanssen (2001) to estimate longer-wavelength correlations. Using the covariance function, an approximate VCM can be generated for the sampled points of the interferogram, assuming the noise is radially symmetric and uniform across the interferogram. An ensemble of perturbed data sets that have the statistical properties of the VCM can then by synthesised using simple matrix algebra. Derived parameter uncertainties are determined from the distribution of best-fit solutions to these data sets.

We apply the method to determine realistic errors for a number of earthquake and volcanic sources. An additional benefit of this method is that it allows parameter tradeoffs (model covariance) to be determined. A common example for earthquake sources is the trade off between the orientation and magnitude of the slip vector; source strength and depth typically trade off for Mogi models of volcanic inflation/deflation. We examine how these tradeoffs can be mitigated, and errors reduced, by using additional InSAR data, or by carrying out joint inversions with complementary data (e.g. seismology and GPS). We investigate the implications for future SAR missions.

 

Workshop presentation

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry