A Multipixel Time Series Analysis Method Accounting for Ground Motion, Atmospheric Noise, and Orbital Errors

Abstract

Interferometric synthetic aperture radar time series methods aim to reconstruct time‐dependent ground displacements over large areas from sets of interferograms in order to detect transient, periodic, or small‐amplitude deformation. Because of computational limitations, most existing methods consider each pixel independently, ignoring important spatial covariances between observations. We describe a framework to reconstruct time series of ground deformation while considering all pixels simultaneously, allowing us to account for spatial covariances, imprecise orbits, and residual atmospheric perturbations. We describe spatial covariances by an exponential decay function dependent of pixel‐to‐pixel distance. We approximate the impact of imprecise orbit information and residual long‐wavelength atmosphere as a low‐order polynomial function. Tests on synthetic data illustrate the importance of incorporating full covariances between pixels in order to avoid biased parameter reconstruction. An example of application to the northern Chilean subduction zone highlights the potential of this method.

Interseismic Loading of Subduction Megathrust Drives Long‐Term Uplift in Northern Chile

“…We use SAR data acquired by the Envisat satellite over the 2003–2010 period to derive a map of LOS ground velocity (Figure ). We use a multipixel method to infer displacement time series, displacement rates averaged over the observation period, and earthquake‐related offsets accounting for spatial covariances as well as other nuisance parameters (Jolivet & Simons, ). Our approach resolves long wavelength signals in SAR acquisitions, hence does not require input from GNSS data.…”

“…Arrows on the top map are GNSS‐derived velocities from Metois et al () for the interseismic period preceeding the 2014 earthquake. Color indicates ground velocity in the direction of the satellite line of sight for Envisat acquisitions along track 96 (Jolivet & Simons, ). Dark red contour lines are 2‐m slip contours for earthquakes of magnitude larger than 8, including the Antofagasta, Mw w 8.1, 1995 event (Pritchard et al, ) and the Iquique, M w 8.1, 2014 event (Duputel et al, ).…”

“…For comparison, typical vertical displacement rates over geological times for the coastal domain are generally one order of magnitude lower than typical interseismic uplift or subsidence rates (a fraction of millimeter per year vs several millimeters per year, e.g., Figure 1 Béjar- Pizarro et al, 2013;Hashima & Sato, 2017;Jolivet & Simons, 2018;Melnick, 2016;Regard et al, 2010). Comparatively, large megathrust earthquakes will generate meter-scale vertical displacements every time they occur (e.g., Simons et al, 2011;Vigny et al, 2011).…”

A Kalman Filter Time Series Analysis Method for InSAR

“…The pixel‐by‐pixel approach of our KFTS implies that we do not account for spatial covariance (Jolivet & Simons, 2018). This covariance may take the form of a function of the pixel‐to‐pixel distance, which empirically models the isotropic part of the InSAR signal not due to ground deformation.…”

“…Without connectivity, it is impossible to reconstruct a common phase history between temporally disconnected sets of interferograms. Various methods propose to derive a temporally parametrized model of the phase evolution, either assuming constant velocities between subnetworks (Berardino et al., 2002) or more complex ad hoc models (e.g., Hetland et al., 2012; Jolivet & Simons, 2018; Jolivet et al., 2012; López‐Quiroz et al., 2009).…”