Intrusion and cooling of magma - Comparison between 2D and 3D analyses

Steady thermal field associated with magma mass intrusion is studied in two-dimensional (2D) and three-dimensional (3D) spaces. It is proved that the latter model leads to surface heat flow substantially smaller than that for the former. A numerical approach based on a relaxation technique for solving the Laplace equation is made use of. Transient heat conduction is solved when a lava dome makes an appearance on the earth's surface. Converting the differential equation that governs the problem into a difference equation, 2D and 3D solutions are obtained. It becomes apparent that the 2D analysis results in a cooling rate considerably smaller than that for the 3D analysis. A similar transient problem related to the filling of a reservoir with high-temperature magma is also studied. Even in this case, a 2D analysis leads to cooling appreciably slower than that for a 3D analysis. The mode of heat flow anomaly development at the earth's surface for the 2D analysis is noticeably different from that for the 3D analysis. In short, 3D analyses of the geothermal problems are important for obtaining realistic results although 2D analyses have so far been customary in many cases.