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Pollard & Muller 1976
Pollard, D.D. and Muller, O.H. (1976). The effect of gradients in regional stress and magma pressure on the form of sheet intrusions in cross section. Journal of Geophysical Research 81: doi: 10.1029/JB081i005p00975. issn: 0148-0227.

Elasticity theory predicts that a slit in homogeneous and isotropic material subjected to uniform internal pressure and uniform regional stresses will have a symmetric, elliptical form. The form in cross section of a dike from the Spanish Peaks, Colorado, and a sill from the Henry Mountains, Utah, is asymmetrical and similar to an elongate teardrop. The asymmetry of the dike and sill could be a function of gradients in the regional stress and magma pressure at the time of intrusion. An elasticity theory analysis for a slit subjected to linear gradients in regional stress and magma pressure predicts an asymmetrical teardrop form. The amount of asymmetry is controlled by the slit length, the difference between pressure and stress gradients (effective stress gradient), and the difference between the average pressure and regional stress (average driving pressure). A least squares regression curve for the theoretical form of the slit shows a good correlation with the measured form of the sheet intrusions. For the dike, a stress gradient sufficient to produce the asymmetrical form could have been generated by a ground surface slope of less than 5¿ or by bending the host rock into the La Veta syncline, which is cut by the dike. A pressure gradient of sufficient magnitude could have been generated in static magma with a strength of at least 104 dyn/cm2. Because the sill dilated in part by bending the relatively thin overburden, our model is inappropriate.

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Journal of Geophysical Research
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