1
Supplementary material
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To obtain the expected gravitational field due to an inflating Mogi deformation source [Mogi,
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1958] three equations [Eq. 1, 2, 3,] were used from Lisowski [2007].
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go = G (ρo – ρc) ∆V (z/R3)
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g1 = G ρc 2(1 – ν) ∆V (z/R3) (2)
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g2 = -G ρc (1 – 2ν) ∆V (z/R3) (3)
(1)
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The gravitational change (∆g) is obtained by summing g0, g1, and g2, where G is the gravitational
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constant, ρo is the magma density, ρc is the density of the crust, ν is the Poisson's ratio, z is the
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depth to the source and R is (x2 + y2 + z2)1/2 or the position of a point on the Earth’s surface. To
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predict the gravitational field change due to a continual injection of material at depth, a realistic
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density must first be chosen for both the crust and magma. The crust in the uplift area is most
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likely a mix of both mafic rock, with densities between 2400 and 3100 kg m-3 [Keller et al.,
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1979; Moore, 2001], and plutonic silicic rocks with densities ~2600 kg m-3 [Bott and Smithson,
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1967]. While surface rocks have potentially lower densities, the average density of the crust is
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likely higher than 2600 kg m-3. Therefore, this study uses an average density of the crust (ρc) and
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magma (ρo) of 2600 kg m-3 to describe the situation where a magma body stalls due to buoyancy
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forces.
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To provide estimates of the change in the gravitational field due to viscoelastic
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deformation, the same gravitational equations above were used. While there is no intruding
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material, the process is essentially creating space; therefore the density representing the intruding
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fluid was set to - 2600 kg m-3. Using the deformation defined volume of 3.5 x 107 m3 (Dzurisin
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et al., 2006), the result is a gravity decrease of 24 µGal at CENTER. Since a Mogi point source
1
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assumes an elastic half space and not a viscoelastic one, the values obtained can only be used as
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an estimate.
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Appendix references
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Bott, M.H.P., and S.B. Smithson (1967), Gravity investigations of subsurface shape and mass
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distributions of granite batholiths, Geol. Soc. Am. Bull., 78, 859-878, doi:10.1130/0016-
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7606(1967).
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Dzurisin, D., M. Lisowski, C.W. Wicks, M.P. Poland, and E.T. Endo (2006), Geodetic
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observations and modeling of magmatic inflation at the Three Sisters volcanic center,
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central Oregon Cascade Range, USA, J. Volcanol. Geotherm. Res., 150, 1-3, 35-54,
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doi:10.1016/j.jvolgeores.2005.07.011.
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Keller, G.V., G. L. Trowbridge, J.C. Murray, and C.K. Skokan (1979), Results of an
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experimental drill hole at the summit of Kilauea volcano, Hawaii, J. Volcanol. Geoth. Res.,
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5(3–4), 345-385, doi:10.1016/0377-0273(79)90024-6.
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Lisowski, M. and D. Dzurisin (2006), Analytical volcano deformation source models, in Volcano
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Deformation, edited by D. Dzurisin, Springer Praxis Books, Publisher: Springer Berlin
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Heidelberg, 279-304, doi:10.1007/978-3-540-49302-0_8.
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Mogi, K., 1958. Relations between the eruptions of various volcanoes and the deformation of the
ground surfaces around them, Bull. Earth. Res. Inst. Univ. Tokyo, 36, 99-134.
Moore, J.G. (2001), Density of basalt core from Hilo drill hole, Hawaii, J. Volcanol. Geoth. Res.,
112(1-4), 221-230, doi:10.1016/S0377-0273(01)00242-6.
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Figure Captions for Auxiliary files
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Figure S1. Monthly rainfall for Bend, Oregon. The highlighted months represent completed
surveys starting in late June and repeated until early October [unpublished data, 2010, available
from http://www.noaa.gov/].
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