Global remote sensing and large-scale environment modeling have generated vast amounts of raster geospatial data. Performing spatial queries over such data has applications in many domains, such as climate impact studies, water and wildlife management, and urban planning. Processing those queries is greatly facilitated by the existence of spatial indices. However, I/O transfer is still a major bottleneck in the overall system performance. One of the solutions to this issue is to compress data before sending it over the I/O channel. Therefore, a lossless compression technique that also supports spatial indexing to improve query response time is highly desirable. To fill this gap, in this paper we propose two parallel GPGPU algorithms, called Multi-Block per Tile (MBPT) and One-Block per Tile (OBPT), to compress and index large-scale geospatial raster data using BQ-Trees. Experiments comparing our best performing proposed algorithm, OBPT, against HFPaC, a state-of-the-art geospatial parallel GPGPU compression algorithm, using three real datasets of satellite images, show that our algorithm achieves a compression time speedup of up to 2X, and a 2.5X increment in compression ratio. OBPT also yields a comparable average spatial query response time to HFPaC.