Magma-Driven Multiple Dike Propagation and Fracture Toughness of Crustal Rocks

Dike swarms consisting of tens to thousands of subparallel dikes are commonly observed at Earth's surface, raising the possibility of simultaneous propagation of two or more dikes at various stages of a swarm's development. The behavior of multiple propagating dikes differs from that of a single dike owing to the interacting stress fields associated with each dike. We analyze an array of parallel, periodically spaced dikes that grow simultaneously from an overpressured source into a semi-infinite, linear elastic host rock. To simplify the analysis, we assume steady state (constant velocity) magma flow and dike propagation. We use a perturbation method to analyze the coupled, nonlinear problem of multiple dike propagation and magma transport. The stress intensity factor at the dike tips and the opening displacements of the dike surfaces are calculated. The numerical results show that dike spacing has a profound effect on the behavior of dike propagation. The stress intensity factors at the tips of parallel dikes decrease with a decrease in dike spacing and are significantly smaller than that for a single dike with the same length. The reduced stress intensity factor indicates that, compared to a single dike, propagation of parallel dikes is more likely to be arrested under otherwise the same conditions. It also implies that fracture toughness of the host rock in a high confining pressure environment may not be as high as inferred from the propagation of a single dike. Our numerical results suggest fracture toughness values on the order of 100 MPa root m. The opening displacements for parallel dikes are smaller than that for a single dike, which results in higher magma pressure gradients in parallel dikes and lower flux of magma transport.

Inference in Ecology: The Sea Urchin Phenomenon in the Northwestern Atlantic

We have reviewed the considerable body of research into the sea urchin phenomenon responsible for the alternation between macroalgal beds and coralline barrens in the northwestern Atlantic. In doing so, we have identified problems with both the scientific approach and the interpretation of results. Over a period of approximately 20 years, explanations for the phenomenon invoked four separate scenarios, which changed mainly as a consequence of extraneous events rather than experimental testing. Our specific concerns are that results contrary to the keystone-predator paradigm for the American lobster were circumvented, system components of the various scenarios became accepted without testing, and modifications of some components appeared arbitrary. Our review illustrates dilemmas that, we suggest, have hindered ecological progress in general. We argue for a more rigorous experimental approach, based on sound natural-history observations and strong inference. Moreover, we believe that the scientific community needs to be cautious about allowing paradigms to become established without adequate scrutiny.