Figure 3.

Validation of the analytical solution derived for case 3, as described by equation (22). (a) Evolution of the reservoir pressure following a ramping inlet pressure history, for a spheroidal reservoir with semimajor axes a = b = 6200 m, semiminor axis c = 100 m, and located at depth d = 4.5 km (solid black line) and for a sphere of equivalent volume (dotted blue line). The compressibility of the magma chamber walls β _w was chosen to fit the numerical solution as calculated using COMSOL for this geometric configuration (red dots). Agreement is within 0.01 MPa, that is about 0.15% of the total imposed pressure of 5 MPa/yr during 2 years. The analytical solution derived by Amoruso and Crescentini [2009] for a deep oblate spheroid is shown for comparison (dashed black line). (b) Resulting surface vertical displacement at a site located 1 km east of the maximum uplift, as calculated using the horizontal circular crack approximation of Fialko et al. [2001]. (inset) Histogram of the residuals, indicating that the analytical solution agrees with the numerical solution within 8 mm or 0.25% of the maximum uplift signal.