## 1 Introduction  
The last three decades have witnessed the increasing and widespread use of satellite synthetic aperture radar (SAR) imagery to retrieve key information on surface deformation processes affecting the Earth's surface using two- and three-pass differential interferometric SAR (InSAR) (e.g., [1, 2, 3]), and multi-pass/multi-temporal InSAR methods, such as persistent scatterers interferometry (PSI) (e.g., [4, 5]) and Small BASeline Subset (SBAS) (e.g., [6, 7]). Many SAR constellations have been developed since the 1990s and, as part of their background observation scenarios, have been tasked to acquire images regularly over major cities, targets with economic and/or strategic relevance (e.g., key infrastructure, polar regions, cultural heritage sites), regions affected by specific Earth hazards (e.g., tectonic zones and volcanoes), and entire nations or continents (e.g., [8, 9]). This means that the volume of SAR data collected to date, archived, and available for InSAR applications by far falls within the \"big data\" remit for such type of imagery (typically, 15-20 SAR scenes are needed as minimum input of an advanced InSAR analysis, e.g., [5], and usually a few to several tens of scenes are used in most InSAR applications), thus creating novel opportunities and opening new challenges for Earth sciences and observation (e.g., [10, 11]). For instance, since the beginning of its operations in late 2014, the Copernicus Sentinel-1 SAR constellation acquired over each area of Europe around 300 passes for each geometry, i.e., ascending and descending, with an initial repeat pass of 12 days with Sentinel-1A only (\(\sim\)180 scenes in 6 years), which was improved to 6 days in late 2016 thanks to the addition of Sentinel-1B to the constellation (another ~120 scenes in 4 years). This can be verified by consulting the ESA Copernicus Open Access Hub [12]. Thus, researchers willing to undertake multi-temporal InSAR studies of long-term (e.g., more than 3-5 years) dynamics of deformation processes face two main challenges. First, they need to find efficient combinations of computing infrastructure, algorithms, and software capable to run and optimize the big SAR data processing workflow. Second, they need to use tools to handle and analyze the outputs of such processing, which (proportionally to the processed area extent and its land cover) may consist of hundreds of thousands or millions of persistent or coherent targets, each equipped with information of geolocation, quality, annual displacement velocity, and a full deformation record, the length of which depends on the number of input SAR scenes processed. Parallelized InSAR processing chains running on cloud and grid computing infrastructure help to address the first challenge. They relieve researchers of demanding tasks for big data download and processing in local PCs, and drastically reduce processing times (e.g., [13; 14]). On the other side, InSAR dataset screening approaches and statistical methods to detect outliers, trend changes, accelerations/decelerations, and other deviations from the expected deformation behavior contribute to addressing the second challenge [15; 16; 17; 18]. In this respect, the present study has three main goals:  
1. First, to demonstrate that through parallelized InSAR processing chains running on data exploitation platforms, it is possible to process big SAR time series made of an unprecedented number of Sentinel-1 images, i.e., in the order of hundreds per single observation geometry. 2. Second, to showcase that big InSAR datasets can be generated across geographic areas of either urban or rural land cover (or a mixture of them), and later be post-processed to derive value-added products. These InSAR datasets are as \"big\" in the time-domain as the amount of input SAR images, and therefore as the number of observations composing the deformation time series of each persistent or coherent target obtained at the end of the multi-interferogram processing.