Allan variance computed in space domain: Application to InSAR data to characterize noise and geophysical signal

TL;DR

This paper extends the Allan variance, traditionally used for time series, to analyze spatial InSAR data, enabling better characterization of noise and detection of geophysical signals in ground displacement measurements.

Contribution

It introduces the use of Allan variance in the spatial domain for InSAR data analysis, providing a new method to characterize noise and detect signals in geophysical applications.

Findings

Radial AVAR is insensitive to spatial axis variations.

Space AVAR effectively characterizes noise types like decorrelation and atmospheric delays.

Application to SAR data over Turkey demonstrated its ability to detect ground motion signals.

Abstract

The Allan variance was introduced fifty years ago for analyzing the stability of frequency standards. Beside its metrological interest, it is also 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. But, it was also used in other fields: 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 onto spatial data. Interferometric synthetic aperture radar (InSAR) is used in geophysics to image ground displacements in space (over the SAR image spatial coverage) and in time thank 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 AVAR 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. Space AVAR allowed 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 space AVAR to an InSAR time series to detect when the geophysical signal, here the ground motion, emerges from the noise.