## 1. Introduction

[2] Differential interferometric synthetic aperture radar (InSAR) provides high resolution observations of ground surface motion [*Bürgmann et al.*, 2000; *Hanssen*, 2001]. The procedure of InSAR involves interfering two overlapping SAR images acquired from similar viewing geometry and subtracting geometrical phase contributions using satellite ephemeris data and a reference Digital Elevation Model (DEM) [*Ferretti et al.*, 2007]. The observed interferometric phase in each interferogram mostly contains contributions from ground displacement, DEM inaccuracy, atmospheric delay, and satellite state vector errors [*Ferretti et al.*, 2007].

[3] In particular, atmospheric delay often imposes significant artifacts in radar data and comprises three major components; wet, hydrostatic and ionospheric, which are induced by variation in refractivity index of the atmosphere due to dipole components of troposphere water vapor, pressure to temperature ratio changes of the troposphere and spatiotemporal variations in ionospheric electron density, respectively [*Lin et al.*, 2010]. The effect of atmospheric delay consists of two parts [*Hanssen*, 2001]; 1) the effect of 3D heterogeneities of the atmosphere, which similarly affects plains and mountains, and 2) vertical stratification of the atmosphere that causes height-dependent refractivity variations. The first component is mostly topography independent and varies gradually over an area, can be characterized as a second-order stationary process and is well parameterized using fractal statistics [*Hanssen*, 2001]. The second component correlates with topography and may vary as a linear function of the altitude, therefore, a model assuming a linear relation between deformation and topography can be used to correct it [e.g., *Cavalie et al.*, 2007].

[4] Correcting the topography correlated atmospheric delay (TCAD) is not a trivial task as it may correlate in time and has a variable spatial pattern related to the surface topography. Moreover, this effect depends on the scale of local relief; it may be non-linear function of elevation and may vary across an area. Several methods have already been suggested to correct TCAD, which require external data or redundant observation and/or deal only with the linearly correlated atmospheric delay [e.g.,*Cavalie et al.*, 2007; *Doin et al.*, 2009; *Jolivet et al.*, 2011; *Lin et al.*, 2010]. Here, we propose and test a new approach to correct TCAD that employs wavelet transforms. In this method we use wavelet multiresolution analysis [*Mallat*, 1989] to decompose the InSAR range-change map and DEM into their building blocks based on different spatial scales. Then by cross correlating their associated wavelet coefficients, we identify the common coefficients of the DEM and InSAR data. The correction is obtained by down-weighting the wavelet coefficients with high correlation values during inverse wavelet analysis. In the following sections we describe the details of our method and validate it on real and synthetic data sets.