In this talk I explore how the computing continuum, spanning resources at the edges, in the core and in-between, can be harnessed to support urgent science, Early Earthquake Warning (EEW) in particular, and present a system stack that can enable the fluid integration of distributed analytics across a dynamic infrastructure. Specifically, I will describe programming abstractions to express what data to process and where in the continuum to process it, and middleware that automates the discovery of resources and the orchestration of computations across these resources.