Effective data collection in collaborative information-gathering systems relies heavily on maintaining uninterrupted connectivity. Yet, real-world communication disruptions often pose challenges to information-gathering processes. To address this issue, we introduce a novel method —a limited communication decentralized information gathering system for multiple robots to explore environmental phenomena characterized as unknown spatial fields. Our method leverages quadtree structures to ensure comprehensive workspace coverage and efficient exploration. Unlike traditional systems that depend on global and synchronous communication, our method enables robots to share local experiences within a limited transmission range and coordinate their tasks through pairwise and asynchronous communication. Information estimation is facilitated by a Gaussian Process with an Attentive Kernel, allowing adaptive capturing of crucial behavior and data patterns. Our proposed system is validated through simulated scalar field studies in non-stationary environments where multiple robots explore spatial fields. Theoretical guarantees ensure the convergence of distributed area coverage and the regret bounds of distributed online scalar field mapping. We also validate our method empirically in a water quality monitoring scenario featuring three Autonomous Surface Vehicles, tasked with constructing a spatial field.