A recent study has mathematically clarified how the presence of crystals and gas bubbles in magma affects the propagation of seismic P-waves. The researchers derived a new equation that characterizes the travel of these waves through magma, revealing how the relative proportions of crystals and bubbles influence wave velocity and waveform properties.

The ratio of crystals to bubbles in subterranean magma reservoirs is crucial for forecasting volcanic eruptions. Due to the inaccessibility of direct observations, scientists analyze seismic P-waves recorded at the surface to infer these internal characteristics.

Previous studies have predominantly focused on the influence of gas bubbles, with limited consideration given to crystal content. Moreover, conventional models have primarily addressed variations in wave velocity and amplitude decay, without capturing detailed waveform transformations.

In the study, published in Physics of Fluids, the researchers developed a new equation by integrating two distinct mathematical models of magma flow. The results show that P-wave velocity decreases as the proportion of bubbles increases relative to crystals, with bubbles exerting a more significant influence than crystals.

Conversely, attenuation effects were found to be more strongly affected by crystals. The analysis further revealed that waveform characteristics depend on frequency and bubble content, with discernible differences emerging between the two underlying models.

The new equation enables the time-dependent calculation of P-waveforms based on the bubble and crystal content in magma. Looking ahead, the research team intends to integrate this model with machine learning techniques to estimate the internal composition of magma from observed P-waveforms, with the goal of enhancing the accuracy of volcanic eruption prediction systems.