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

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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 high-precision 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.