The value of large amount of location-based mobile data has received wide attention in many research fields including human behavior analysis, urban transportation planning, and various location-based services. Nowadays, both scientific and industrial communities are encouraged to collect as much location-based mobile data as possible, which brings two challenges: (1) how to efficiently process the queries of big location-based mobile data and (2) how to reduce the cost of storage services, because it is too expensive to store several exact data replicas for fault-tolerance. So far, several dedicated storage systems have been proposed to address these issues. However, they do not work well when the ranges of queries vary widely. In this work, we design a storage system based on diverse replica scheme which not only can improve the query processing efficiency but also can reduce the cost of storage space. To the best of our knowledge, this is the first work to investigate the data storage and processing in the context of big location-based mobile data. Specifically, we conduct in-depth theoretical and empirical analysis of the trade-offs between different spatial-temporal partitioning and data encoding schemes. Moreover, we propose an effective approach to select an appropriate set of diverse replicas, which is optimized for the expected query loads while conforming to the given storage space budget. The experiment results show that using diverse replicas can significantly improve the overall query performance and the proposed algorithms for the replica selection problem are both effective and efficient.