Analytical predictions for a natural spacing within dyke swarms

- Analysis of energy associated with growth of laterally propagating dyke swarms.
- Predicts spacing between first generation dykes within the swarm.
- First generation refers to the first set that grows prior to infilling.
- The model shows that the first generation dykes will be the thickest in the swarm.
- First generation spacing is predicted scaling with the height of the dykes.

Dykes often grow next to other dykes, evidenced by the widespread occurrence of dyke swarms that comprise many closely spaced dykes. In giant dyke swarms, dykes are observed to maintain a finite spacing from their neighbors that is tens to hundreds of times smaller than their length. To date, mechanical models have not been able to clarify whether there exists an optimum or natural spacing between the dykes. And yet, the existence of a natural spacing is at the heart of why dykes grow in swarms in the first place. Here we present and examine a mechanical model for the horizontal propagation of multiple, closely spaced blade-like dykes in order to find energetically optimal dyke spacings associated with both constant pressure and constant influx magma sources. We show that the constant pressure source leads to an optimal spacing that is equal to the height of the blade-like dykes. We also show that the constant influx source leads to two candidates for an optimal spacing, one which is expected to be around 0.3 times the dyke height and the other which is expected to be around 2.5 times the dyke height. Comparison with measurements from dyke swarms in Iceland and Canada lends initial support to our predictions, and we conclude that dyke swarms are indeed expected to have a natural spacing between first generation dykes and that this spacing scales with, and is on the order of, the height of the blade-like dykes that comprise the swarm.