ONE of the great successes of plate tectonics has been to provide a link between deformations of the lithosphere observed over widely varying timescales. For example, the slip between two plates as measured from young magnetic anomalies (and hence averaged over the past 1–2 Myr) has been found1–3to be compatible with estimates obtained from slip during recent earthquakes, despite the small time interval covered by the earthquake observations. Here we start from the idea4,5 that geological deformations are the long-term cumulative trace of short-term processes such as earthquakes, so that the latter can be described as a high-frequency 'noise' for the former. We return to a theoretical framework6 introduced to model large-scale and long-term tectonics, based on a nonlinear diffusion equation, but here explicitly associate the 'noise' term with earthquakes. The observed power-law relationship between earthquake frequency and magnitude, together with an assumption that strain is on average scale-independent, leads to the prediction that the largest earthquakes will have a Gutenberg-Richter 'b-value' of 1.5, as has recently been reported for large (Mw>7) earthquakes worldwide7.