Natural hazards result in devastating losses in human life, environmental assets and personal, and regional and national economies. The availability of different big data such as satellite imageries, Global Positioning System (GPS) traces, mobile Call Detail Records (CDRs), social media posts, etc., in conjunction with advances in data analytic techniques (e.g., data mining and big data processing, machine learning and deep learning) can facilitate the extraction of geospatial information that is critical for rapid and effective disaster response. However, disaster response systems development usually requires the integration of data from different sources (streaming data sources and data sources at rest) with different characteristics and types, which consequently have different processing needs. Deciding which processing framework to use for a specific big data to perform a given task is usually a challenge for researchers from the disaster management field. Therefore, this paper contributes in four aspects. Firstly, potential big data sources are described and characterized. Secondly, the big data processing frameworks are characterized and grouped based on the sources of data they handle. Then, a short description of each big data processing framework is provided and a comparison of processing frameworks in each group is carried out considering the main aspects such as computing cluster architecture, data flow, data processing model, fault-tolerance, scalability, latency, back-pressure mechanism, programming languages, and support for machine learning libraries, which are related to specific processing needs. Finally, a link between big data and processing frameworks is established, based on the processing provisioning for essential tasks in the response phase of disaster management.