Magmatic sheet intrusions (dykes) constitute the main form of magma transport in the Earth's crust. The size distribution of dykes is a crucial parameter that controls volcanic surface deformation and eruption rates and is required to realistically model volcano deformation for eruption forecasting. Here we present statistical analyses of 3,676 dyke thickness measurements from different tectonic settings and show that dyke thickness consistently follows the Weibull distribution. Known from materials science, power law-distributed flaws in brittle materials lead to Weibull-distributed failure stress. We therefore propose a dynamic model in which dyke thickness is determined by variable magma pressure that exploits differently sized host-rock weaknesses. The observed dyke thickness distributions are thus site-specific because rock strength, rather than magma viscosity and composition, exerts the dominant control on dyke emplacement. Fundamentally, the strength of geomaterials is scale-dependent and should be approximated by a probability distribution.

In addition to seismically mapped fault structures, a large number of faults below the limit of seismic resolution contribute to subsurface deformation. However, a correlation between large- and small-scale faults is difficult because of their strong variation in orientation. A workflow to analyze deformation over different scales is described here. Based on the combination of seismic interpretation, coherency analysis, geostatistical analysis, kinematic modeling, and well data analysis, we constrained the density and orientation of subseismic faults and made predictions about reactivation and opening of fractures. We interpreted faults in seismic and coherency volumes at scales between several kilometers and a few tens of meters. Three-dimensional (3-D) retrodeformation was performed on a detailed interpreted 3-D structural model to simulate strain in the hanging wall at the time of faulting, at a scale below seismic resolution. The modeling results show that (1) considerable strain is observed more than 1 km (0.62 mi) away from the fault trace and (2) deformation around the fault causes strain variations, depending on the fault morphology. This strain variation is responsible for the heterogeneous subseismic fracture distribution observed in wells. We linked the fracture density from the well data with the modeled strain magnitude and used the strain magnitude as a proxy for fracture density. With this method, we can predict the relative density of small-scale fractures in areas without well data. Furthermore, knowing the orientation of the local strain axis, we predict a fault strike and opening or reactivation of fractures during a particular deformation event.