Thermal effects of intrusions

Abstract

The mathematical theory used in calculating temperatures of intrusions is reviewed, primarily from the point of view of finding temperatures in the country rock outside them. It is shown that the detailed behavior inside the intrusion, for example the mechanism of solidification and the possible effects of convection, becomes progressively less important as the distance from the contact increases, so that at distances of one-quarter of the thickness or more the simple theory of Lovering is adequate. The theory for sheets, stocks, laccoliths, and some irregularly shaped bodies is given, together with the effect of dissimilar thermal conductivities. The effects of latent heat, convection, and the circumstances of intrusion are discussed. Applications to metamorphism, rock magnetism, and argon loss caused by heating by intrusions are reviewed. NOTATIONT, temperature (excess of temperature over some arbitrary level, which is usually taken to be the initial temperature of country rock). T1 to T2, range of solidification of magma, T• To, initial temperature of magma. L, latent heat of magma. K, thermal conductivity of country rock. p, density of country rock. c, specific heat of country rock. • = K/pc, diffusivity of country rock. K•, p•, c•, •, thermal properties of solidified magma if different from those of country rock. ' ' thermal properties of liquid magma if different from those of K2', p2• C2 • country rock. c2 -c2' -•-L/(T• -T2) , equivalent specific heat of magma. To • -To + L/c, equivalen• initial •empera•ure. To, initial con•ac• •empera•ure. 2d, thickness of an intrusive sheee• (or diameter of a cylinder or sphere). t, •ime a•er intrusion. • -Kt/d 2, dimensionless time or Fourier number. x, distance from midplane of an intrusive shee•. • -x/d. Units are cgs, calorie, and øC unless otherwise stated. 443 444 J. C. JAEGER 1. INTRODUCTIONMany attempts have been made to calculate the cooling-history of igneous intrusions. The problem is a fairly definite one: a mass of magma at a known temperature and of a known shape is iniected into country rock at a known temperature; the subsequent variation of temperature at any point is to be calculated. Fortunately, most rocks and magma have much the same thermal properties, so that a simple approximation may be obtained by assuming these to be constant and equal; hence (neglecting the effects of latent heat, convection, and other complicating factors to be discussed later), the problem reduces to the conduction of heat in an infinite medium with a prescribed initial distribution of temperature, and the solution can be written down immediately. Ingersoll and Zobel [1913] gave solutions for intrusive and extrusive sheets and for a spherical laccolith. Lovering [1935] gave complete information for the sheet and laccolith in graphical form, stressing the fact that such numerical information for these bodies could be given in terms of two dimensionless parameters, so that special cases need not be considered, as had been done by many authors. A full review of this phase of ...

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