Recent advances have enabled large language model (LLM) agents to solve complex tasks by orchestrating external tools. However, these agents often struggle in specialized, tool-intensive domains that demand long-horizon execution, tight coordination across modalities, and strict adherence to implicit tool constraints. Earth Observation (EO) tasks exemplify this challenge due to the multi-modal and multi-temporal data inputs, as well as the requirements of geo-knowledge constraints (spectrum library, spatial reasoning, etc): many high-level plans can be derailed by subtle execution errors that propagate through a pipeline and invalidate final results. A core difficulty is that existing agents lack a mechanism to learn fine-grained, tool-level expertise from interaction. Without such expertise, they cannot reliably configure tool parameters or recover from mid-execution failures, limiting their effectiveness in complex EO workflows. To address this, we introduce \textbf{GeoEvolver}, a self-evolving multi-agent system~(MAS) that enables LLM agents to acquire EO expertise through structured interaction without any parameter updates. GeoEvolver decomposes each query into independent sub-goals via a retrieval-augmented multi-agent orchestrator, then explores diverse tool-parameter configurations at the sub-goal level. Successful patterns and root-cause attribution from failures are then distilled in an evolving memory bank that provides in-context demonstrations for future queries. Experiments on three tool-integrated EO benchmarks show that GeoEvolver consistently improves end-to-end task success, with an average gain of 12\% across multiple LLM backbones, demonstrating that EO expertise can emerge progressively from efficient, fine-grained interactions with the environment.