It is now possible to download SAR data from the PALSAR satellite.
“Phased array L-band synthetic aperture radar (PALSAR) data from Japan’s Advanced Land Observing Satellite (ALOS-1) mission are now unrestricted, and can be accessed by scientists and researchers around the world. These data are processed, archived, and distributed by NASA’s Alaska Satellite Facility Distributed Active Archive Center (ASF DAAC), which is part of the Alaska Satellite Facility (ASF) at the University of Alaska Fairbanks Geophysical Institute and one of 12 NASA Earth Observing System Data and Information System (EOSDIS) DAACs.”
You can find more information about this here: https://earthdata.nasa.gov/unrestricted-palsar-asf-daac
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