Relaxation time spectra of basaltic lavas between 500–1150 °C reveal patterns of Kramers–Kronig inconsistency of the complex viscoelastic shear modulus

Abstract

An important, yet until now neglected, aspect of the viscoelastic behaviour of lavas is the Kramers–Kronig consistency of their complex viscoelastic shear modulus. The most general linear viscoelastic model – the generalized Maxwell body with continuous relaxation time spectrum – produces a consistent storage and loss modulus, as can be verified by Kramers–Kronig formulae. We reprocessed the original datasets of the highprecision laboratory data by James et al. (2004) supplied as pairs of magnitude of the complex viscoelastic shear modulus and the loss angle. We introduce the magnitude-borne and loss-angle-borne logarithmic relaxation time spectra and their ratio as a suitable indicator of the linear viscoelastic inconsistency. The basaltic lavas from Etna, Hawai’i and Vesuvius have shown a general convergence to the ideal consistency with increasing temperature, although each sample with an individual inconsistency pattern. The biggest surprise is the inconsistency ratio rising to ∼20 in Etna 1992 top sample at 786 °C. Such a high inconsistency level still waits for an explanation and for the discoveries of its class-mates either in laboratory or field experiments.

Keywords

• viscoelasticity, generalized maxwell body, kramers–kronig relationships, relaxation time spectrum, viscoelastic modulus inconsistency