Logarithmic growth of dikes from a depressurizing magma chamber

Dike propagation is an intrinsically multiphase problem, where deformation and fluid flow are intricately coupled in a fracture process. Here we perform the first fully coupled simulations of dike propagation in two dimensions, accounting for depressurization of a circular magma chamber, dynamic fluid flow, fracture formation, and elastic deformation. Despite the complexity of the governing equations, we observe that the lengthening is well explained by a simple model a(t) = c₁ log(1 + t/c₂), where is the dike length, is time, and c₁ and c₂ are constants. We compare the model to seismic data from eight dikes in Iceland and Ethiopia, and, in spite of the assumption of plane strain, we find good agreement between the data and the model. In addition, we derive an approximate model for the depressurization of the chamber with the dike length. These models may help forecast the growth of lateral dikes and magma chamber depressurization.