Geometric Scaling of Tabular Igneous Intrusions: Implications for Emplacement and Growth

  • A. R. CrudenEmail author
  • K. J. W. McCaffrey
  • A. P. Bunger
Part of the Advances in Volcanology book series (VOLCAN)


The horizontal (L) and vertical (T) dimensions of broadly tabular, sub-horizontal intrusions of mafic to felsic composition emplaced into shallow to mid-crustal levels of continental crust reveal two well-defined and continuous curves in log L vs. log T space. The data set spans six and five orders of magnitude in L (1 m to 1000 km) and T (10 cm to 10 km), respectively. Small tabular sheets and sills (mafic and felsic) define a straight line with a slope ~ 0.5 at all horizontal length scales, similar to the known geometric scaling of mafic dikes, indicating that the L/T ratio of these intrusions to increases with increasing L (horizontal lengthening dominates over vertical thickening). Laccoliths, plutons, layered mafic intrusions and batholiths define an open, continuous S-shaped curve that bifurcates from the tabular sheets and sills curve at L ~ 500 m towards higher T values. For L ~ 0.5 to 10 km the slope of this curve is ~ 1.5, corresponding to laccoliths that are characterized by a decrease in L/T ratio with increasing L (vertical thickening dominates over horizontal lengthening). Between L ~ 10 and 100 km the slope has a mean value ~ 0.8, indicating that plutons and layered mafic intrusions have a tendency for horizontal lengthening over vertical thickening as L increases. Batholiths and very large layered mafic intrusions with L > 100 km lie on a slope ~ 0 with a threshold thickness ~ 10 km. The continuous nature of the dimensional data over such a wide range of length scales reflects a spectrum of igneous emplacement processes repeated in space and time. We discuss how thresholds and transitions in this spectrum, defined by bifurcations between the curves (e.g., between sill and laccolith emplacement) and changes in slope, largely reflect depth- and time-dependent changes in emplacement mechanisms rather than factors such as magma viscosity, composition and temperature.



We are grateful to Sergio Rocchi and Christoph Breitkeuz for their forbearance and editorial input, and two anonymous reviewers for positive comments and suggestions. Michael Lishman is thanked for introducing ARC to the Whin Sill at High Cup Nick and for Fig. 3a.


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© Springer International Publishing AG 2017

Authors and Affiliations

  • A. R. Cruden
    • 1
    Email author
  • K. J. W. McCaffrey
    • 2
  • A. P. Bunger
    • 3
    • 4
  1. 1.School of Earth, Atmosphere and EnvironmentMonash UniversityMelbourneAustralia
  2. 2.Department of Earth SciencesUniversity of DurhamDurhamUK
  3. 3.Department of Civil and Environmental EngineeringUniversity of PittsburghPittsburghUSA
  4. 4.Department of Chemical and Petroleum EngineeringUniversity of PittsburghPittsburghUSA

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