Some thoughts on the use of InSAR data to constrain models of surface deformation: Noise structure and data downsampling

Abstract

[1] Repeat-pass Interferometric Synthetic Aperture Radar (InSAR) provides spatially dense maps of surface deformation with potentially tens of millions of data points. Here we estimate the actual covariance structure of noise in InSAR data. We compare the results for several independent interferograms with a large ensemble of GPS observations of tropospheric delay and discuss how the common approaches used during processing of InSAR data affects the inferred covariance structure. Motivated by computational concerns associated with numerical modeling of deformation sources, we then combine the datacovariance information with the inherent resolution of an assumed source model to develop an efficient algorithm for spatially variable data resampling (or averaging). We illustrate these technical developments with two earthquake scenarios at different ends of the earthquake magnitude spectrum. For the larger events, our goal is to invert for the coseismic fault slip distribution. For smaller events, we infer the hypocenter location and moment. We compare the results of inversions using several different resampling algorithms, and we assess the importance of using the full noise covariance matrix.

Constraining crustal velocity fields with InSAR for Eastern Turkey: Limits to the block‐like behavior of Eastern Anatolia

“…We calculated a mean profile and 1σ bounds for each data set by inverting all the rate map data within 10 km along-profile bins, weighting the inversion using a spatial variance-covariance matrix (VCM) to account for spatial correlation between rate map pixels. The spatial VCM was estimated by fitting a 1-D autocovariance function of the form to signals in a 100 km × 100 km nondeforming region of each rate map, where C ij and d ij are the covariance and distance between pixels i and j, A 2 is maximum variance, and b is 1-D e-folding distance [Wright et al, 2003;Lohman and Simons, 2005;Parsons et al, 2006]. However, while the estimates of b are reasonable at around 10 km, the estimates of A from this method are 0.5-1.4 mm/yr and are all lower than the 1.20-1.85 mm/yr 1σ values estimated from the differences between rate maps.…”

Line‐of‐sight displacement from ALOS‐2 interferometry: Mw 7.8 Gorkha Earthquake and Mw 7.3 aftershock

“…The LOS measurements are downsampled using the QuadTree technique [Lohman and Simons, 2005]; the distribution of downsampled data and residuals are shown in Figure S1 in the supporting information. The inverse problem is ill posed, so the inversion is regularized by applying minimum norm smoothing.…”

Deformation and seismicity near Sabancaya volcano, southern Peru, from 2002 to 2015

“…We process data from the satellite tracks displayed in Figure 1 and listed in Table S1 in the supporting information using the ROI_PAC software [Rosen et al, 2004]. Deformation is modeled by slip on a fault plane embedded in a homogeneous elastic half-space [Okada, 1992], and best fit parameters are inferred using a Neighborhood Algorithm [Sambridge, 1999] after interferogram downsampling [Lohman and Simons, 2005].…”