Allan Variance Computed in Space Domain: Definition and Application to InSAR Data to Characterize Noise and Geophysical Signal,
Résumé
The Allan variance was introduced 50 years ago for analyzing the stability of frequency standards. In addition to its metrological interest, it may be also considered as an estimator of the large trends of the power spectral density (PSD) of frequency deviation. For instance, the Allan variance is able to discriminate different types of noise characterized by different power laws in the PSD. The Allan variance was also used in other fields than time and frequency metrology: for more than 20 years, it has been used in accelerometry, geophysics, geodesy, astrophysics, and even finances. However, it seems that up to now, it has been exclusively applied for time series analysis. We propose here to use the Allan variance on spatial data. Interferometric synthetic aperture radar (InSAR) is used in geophysics to image ground displacements in space [over the synthetic aperture radar (SAR) image spatial coverage] and in time thanks to the regular SAR image acquisitions by dedicated satellites. The main limitation of the technique is the atmospheric disturbances that affect the radar signal while traveling from the sensor to the ground and back. In this paper, we propose to use the Allan variance for analyzing spatial data from InSAR measurements. The Allan variance was computed in $XY$ mode as well as in radial mode for detecting different types of behavior for different space-scales, in the same way as the different types of noise versus the integration time in the classical time and frequency application. We found that radial Allan variance is the more appropriate way to have an estimator insensitive to the spatial axis and we applied it on SAR data acquired over eastern Turkey for the period 2003-2011. Spatial Allan variance allowed us to well characterize noise features, classically found in InSAR such as phase decorrelation producing white noise or atmospheric delays, behaving like a random walk signal. We finally applied the spatial Allan variance to an InSAR time ser- es to detect when the geophysical signal, here the ground motion, emerges from the noise
Mots clés
Analysis of variance
frequency-domain analysis
geophysical image processing
noise measurement
radar interferometry
radar signal processing
synthetic aperture radar
Allan variance
space domain
InSAR data
geophysical signal
characterize noise
frequency standards
metrological interest
power spectral density
PSD
frequency deviation
accelerometry
geophysics
geodesy
astrophysics
time series analysis
Interferometric synthetic aperture radar
InSAR
image ground displacements
image spatial coverage
SAR image acquisitions
dedicated satellites
radar signal
spatial axis
Spatial Allan variance
phase decorrelation
Yttrium
Noise
Atmospheric measurements
Acoustics
Frequency control
Geophysical measurements
Kernel