Modeling the growth of laccoliths and large mafic sills: Role of magma body forces

The use of elastic plate theory to model the emplacement of laccoliths and large mafic sills has been debated for nearly 40 years. These intrusions typically attain a horizontal width that is large relative to the emplacement depth. Provided that large-scale plasticity and/or heterogeneity is not observed in the overlying host rock, it should then be valid to approximate its deformation based on analysis of a thin elastic plate with effective properties that are the consequence of interaction among heterogeneities that are small relative to the size of the intrusion. But the predictions that are usually cited from elastic plate theory are characterized by bell-shaped geometry, in contrast to the flat-topped, steep-sided geometry typical of many laccoliths or the nearly uniform thickness typical of large mafic sills. This fact has motivated several alternate explanations of laccolith and large mafic sill emplacement. Nonetheless, elastic plate theory should be revisited in light of the fact that previous elastic plate-based predictions have, in general, not taken into account an appropriate fracture propagation condition, fluid flow in the growing intrusion, and, importantly, the influence of the weight of the magma on intrusion growth. We present a model for the growth of circular intrusions that accounts for all of these factors. The model predicts the appropriate geometry for both laccoliths and large mafic sills. The predicted thickness to length relationships are also consistent with field data. Hence, while it may sometimes be appropriate, there is, in general, no fundamental need to appeal to large-scale rock plasticity in order to explain observed intrusion geometries, and it may, in fact, be appropriate to understand the growth of laccoliths and large sills in light of a single underlying mechanical model.