Distribution of volcanoes in active margins

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Abstract
We report a comprehensive study of the distribution of volcanoes in 16 active plate margins, corresponding to a total of 479 volcanic systems. The active volcanic arcs are found to have a ribbon geometry with an average length / width ratio of around 10. The shape of the volcanic arc is compared to the shape of the associated trench by projecting one onto the other. The projection direction agrees with the direction of plate convergence, which shows that plate motion is the main factor constraining magma generation on the lithospheric scale. There is no characteristic spacing between volcanoes. In each arc, the distribution of volcano spacing is best represented by a Gamma distribution which corresponds to randomly generated points in the same geometrical conditions. In order to explain how such distributions may be generated, we have investigated in the laboratory the gravitational instability of a layer of buoyant liquid which is fed at a constant rate at the bottom of denser fluid. Different dynamic regimes are reached for different values of the viscosity ratio between the two fluids. For low viscosity contrasts, there is only one initial instability event, with buoyant plumes organized in a periodic pattern. These plumes are fed continuously by the source, even at large times. For high viscosity contrasts, which is relevant to the geological problem, plumes are produced intermittently by individual instability events. They take the form of “cavity” plumes fed by narrow tails. Once the plumes have reached the surface, they continue to be fed from below by material rising through their shrinking tail. In successive instability events, plume generation is not repeated at the same locations which leads to a complex plan‐form. With time, and hence with increasing number of instability events, the cumulative distribution of plume spacing changes from periodic to random. Material from a single plume is able to sustain volcanic eruptions for a period longer than the time between two instability events, and hence the distribution of active volcanic centers reflects the cumulative distribution of several instability events. This is consistent with the observed distributions.