1992 THE RELATIONSItlP BETWEEN THE I-IEIG • OF A VOLCANO AND THE DEPTH TO ITS MAGMA SOURCE ZONE

It is commonly assumed that hydrostatic pressure balance arguments can be used to establish a relationship between the maximum height to which a volcanic edifice is able to grow and the depth at which the partial melts providing its magma supply are formed. Such a relationship has been used to infer various aspects of the thermal and stress tate of the lithosphere beneath volcanic constructs on Earth, Mars, Io and Venus. We exa_ine the assumptions behind this relationship (which are that: (1) a continuous pressure connection exists between source and summit, (2) the pressure around the magma source is the local hydrostatic pressure dictated by the depth below the geoid, and (3) the melt erupting at the summit has a net positive buoyancy), and show that many of them require geologically unreasonable conditions. We then critically assess the evidence cited in the literature for the relationship and find that there are other factors that may explain the observations. We conclude that volcano heights on the terrestrial planets cannot be related in any simple way to lithospheric thickness or depth to the magma source zone and we review the range of other factors controlling volcano height. Introduction. It is commonly assumed that the maximum height, measured above the regional geoid level, to which a volcanic edifice is able to grow can be simply related, using hydrostatic pressure balance arguments, to the depth at which the partial melts providing its magma supply are formed [Eaton and Murata, 1960; Vogt, 1974; Epp, 1984; Hartmann, 1983]. This relationship has been used to infer various aspects of the thermal and stress state of the lithosphere beneath volcanic constructs on Earth [Vogt and Smoot, 1984; Decker, 1987; Smith and Cann, 1992], Mars [Carr, 1981], Io [Carr, 1986] and Venus [Nikishin, 1990; Schaber, 1991]. We examine farst the assumptions and then the evidence on which this simple relationship sbased. Existing models of the links between the heights of volcanoes, their large-scale internal structures, and the depths to their magma source zones [Eaton and Murata, 1960; Vogt, 1974; Epp, 1984] make the basic assumptions, either explicitly or implieifiy, that: (i) a continuous pressure connection via a NewtonJan fluid exists within the volcanic edifice between the melt source zone and the vent; (ii) the pressure in the country rocks surrounding the melt source is the local hydrostatic pressure dictated by the depth below the geoid (with no load contribution by the edifice itself); and ('fii) the integral over depth of the density difference between the melt and the surrounding rocks is such that the melt erupting at the volcano summit has a net positive buoyancy. These assumptions are commonly used as follows. Let the depth from the geoid to the top of the melt source zone be Hs (measured positive downwards) and the height of the summit of the volcano above the geoid be Hv (measured positive upwards); the densities of the volcanic edifice rocks, the melt, 1Environmental Science Division, I stitute of Environmental & Biological Sciences, Lancaster University 2Department of G ological S iences, Brown U iversity Copyright 1992 by the American Geophysical Union. P0•4r number 92GL01073 -8534/92/92 GL-01073503.00 and the lithosphere in the vicinity of the volcano, averaged over the vertical distances to which they apply, are pv, Pm and Pl, respectively; g is the acceleration due to gravity. Then on balancing the pressures due to the weights of the magrna nd the country rocks at the partial melting level: pl g ! -Is = Ping (Hs +Hv) (1),