Intrusion

Cooling

where ${\displaystyle T_{0}}$ is the initial temperature of the hot material, k is the thermal diffusivity (typically close to 10 m s for most geologic materials), x is the distance from the contact, and t is the time since intrusion. This formula suggests that the magma close to the contact will be rapidly chilled while the country rock close to the contact is rapidly heated, while material further from the contact will be much slower to cool or heat. Thus a chilled margin is often found on the intrusion side of the contact, while a contact aureole is found on the country rock side. The chilled margin is much finer grained than most of the intrusion, and may be different in composition, reflecting the initial composition of the intrusion before fractional crystallization, assimilation of country rock, or further magmatic injections modified the composition of the rest of the intrusion. Isotherms (surfaces of constant temperature) propagate away from the margin according to a square root law, so that if the outermost meter of the magma takes ten years to cool to a given temperature, the next inward meter will take 40 years, the next will take 90 years, and so on.