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.

Extension and Partitioning in an Oblique Subduction Zone, New Zealand: Constraints from Three-Dimensional Numerical Modeling

Contraction, strike slip, and extension displacements along the Hikurangi margin northeast of the North Island of New Zealand coincide with large lateral gradients in material properties. We use a finite- difference code utilizing elastic and elastic-plastic rheologies to build large- scale, three-dimensional numerical models which investigate the influence of material properties on velocity partitioning within oblique subduction zones. Rheological variation in the oblique models is constrained by seismic velocity and attenuation information available for the Hikurangi margin. We compare the effect of weakly versus strongly coupled subduction interfaces on the development of extension and the partitioning of velocity components for orthogonal and oblique convergence and include the effect of ponded sediments beneath the Raukumara Peninsula. Extension and velocity partitioning occur if the subduction interface is weak, but neither develops if the subduction interface is strong. The simple mechanical model incorporating rheological variation based on seismic observations produces kinematics that closely match those published from the Hikurangi margin. These include extension within the Taupo Volcanic Zone, uplift over ponded sediments, and dextral contraction to the south.

Tidal Flexure of Jakobshavns Glacier, West Greenland

Jakobshavns Glacier, a floating outlet glacier on the West Greenland coast, was surveyed during July 1976. The vertical displacements of targets along two profiles perpendicular to the fjord wall bounding the north margin of the glacier were analyzed to determine the effect of flexure caused by tidal oscillations within the fjord. An analysis based on the assumption that vertical displacements of the glacier reflected pure elastic bending yielded the conclusion that the effective thickness of the ice (i.e., the thickness which remained unaffected by surface and basal cracking and which behaved as a continuum) was ∼160 m 2.6 km upglacier from the calving front and ∼110 m 0.6 km from the calving front. An analysis based on the more realistic assumption that observed bending reflected elastic and viscoplastic deformation yielded the conclusion that the average effective thickness of the ice was 316 ± 74 m (∼40% of the estimated 800-m total thickness) 2.6 km from the calving front and 160 ± 48 m (∼21% of the estimated 750-m total) 0.6 km from the calving front. A constitutive relationship appropriate for hard glide during flexure was used.