SOLITARY WAVES AND DEEP MAGMA MIGRATION IN THE 1959 ERUPTIONS AT KILAUEA IKI, KILAUEA VOLCANO, HAWAI'I

Solitary waves have first-order attributes that include shape- and volume-conserving packets of fluid that migrate with characteristic wavelengths, amplitudes, wave numbers, and pulse durations. For ascent in dike-like magma-filled fractures, the solitary wave pulse duration is directly proportional to the conduit wall region viscosity and inversely proportional to the density contrast that drives the flow. Relatively large values of wall rock viscosity induce long-wavelength magma pulses of narrow width, whereas diminished values of matrix viscosity induce shorter wavelength parcels of greater width. Long-lived historical eruption episodes of Kilauea volcano, Hawai’i, include the 1959 Kilauea summit series at Kilauea Iki. The eruptions displayed a variable time-series in their erupted volumes, as well as fountain heights and vent flow rates. The rhythmic ‘beat’ of eruptive episodes within a long-lived series (and their roughly regular repose periods) therefore arise directly from the solitary wave migration mechanism. Applying the governing equations for parabolic flow yields relationships for magma volumes and flow rates, for example, as functions of density contrasts, melt and country rock viscosity variations, and the geometry and dimensions of magma conduits, among other parameters. These relations show, for example, that higher matrix viscosities promote longer wave length solitary waves; higher density contrasts between magma and wall rock promote shorter solitary waves at higher flow rates, and low matrix viscosities, in turn, tend to promote smaller solitary waves. Analytic calculations of wave speed, wave length, batch volume, and parcel shapes reveal the dependence on material properties appropriate for Kilauea intrusions and eruptions. Overall, for a range of matrix viscosities from partially molten peridotites to the uppermost basaltic volcanic shield, there is a broad correspondence between the predictions of solitary wave mechanics and the observations of eruptive phase volumes for Kilauea Iki.