An analytical near-source shock wave model explaining anomalous periods of volcanic lamb waves: evidence from the 2022 hunga tonga eruption

Abstract

Using the dimensional analysis a novel model for shock wave generation during explosive volcanic eruptions is proposed. An analytical derivation of the dependence of the shock wave’s peak pressure on the initial energy and the distance from the epicenter in the case of a volcanic explosion has been obtained, whose predictions agree with the results of numerical modeling within the margin of error. A relationship between the parameters of the shock wave in the vicinity of the source and those of the atmospheric Lamb wave is established, offering an explanation for the phenomenon of longer-than-expected periods in volcanic Lamb waves, first observed following the 1980 eruption of Mount St. Helen’s. Differences between atmospheric Lamb waves generated by volcanic explosive eruptions and thermonuclear tests are studied. Additionally, based on the introduced model, a method for estimating the composition of volcanic gases based solely on observational data from points distant from the epicenter is proposed. The model’s consistency with observational data is demonstrated through a comparison with barographic measurements from the January 15, 2022, Hunga-Tonga eruption, provided by Albuquerque Seismological Laboratory, where the Lamb wave was recorded at 50 stations worldwide. The evolution of Lamb wave parameters with distance and its attenuation characteristics were investigated using observational data.