Repressurization following eruption from a magma chamber with a viscoelastic aureole

Abstract

I analyze an approximate solution for spherical magma chambers (radius R1) surrounded by Maxwell viscoelastic shells (radius R2) in elastic half-spaces following a sudden decrease in pressure. Mass flux into the chamber is proportional to the pressure difference between a deep source and chamber, p∞ − p(t). Solutions depend on R2∕R1, β≡βc∕(βm + βc), where βm,βc are magma and chamber compressibilities, tR is the relaxation time, and τ is the recharge time for the elastic system. Without recharge the system exhibits either posteruptive deflation or, for incompressible magmas, partial reinflation. More generally, immediate posteruptive inflation is favored by large β, tR∕τ and small R2∕R1 . With short tR and large β the time for magma chamber pressure to recover increases significantly. Posteruptive creep increases the chamber pressure, decreasing the pressure gradient driving recharge, delaying pressure recovery. Following eruption the hoop stresses, which are initially compressive, relax toward the radial stress causing them to go through a local (relative tension) maximum. The magma pressure in excess of the dike normal compression at the chamber wall can recover to preeruptive values well before the chamber pressure or erupted mass recovers. This suggests that dikes could nucleate at the chamber margin well before sufficient pressure has recovered to drive them far from the chamber. For some parameters coeruptive deflation has not fully recovered when the magma overpressure relative to hoop stress in the elastic region is restored to preeruptive values, a condition assumed to be sufficient for eruption.