The odds test reveals that the leading values are clustered at a few particular frequency bands. (e) and (f) show the odds ratios with a moving window of 5 events for a coherence > 0.35 in (c) and (d). Red (green) open circles denote that changes in ground velocity lead (lag) variations in air pressure. The coherence between the vertical ground velocity and air pressure at the SBCB and around Xinwu stations is shown in (c) and (d), respectively. The variations in the horizontal and vertical ground velocities at the SBCB and the TATO stations, which is located close to the Xinwu station, are shown in (a) and (b). The seismic data and analytical results at the SBCB and around Xinwu stations are shown in the left and right panels, respectively. Variations in horizontal and vertical ground velocities and their comparison with air pressure data at the SBCB and around Xinwu stations. Meanwhile, the results shed light on investigating the existence of acoustic waves near the Earth’s surface using a partially confined space underground due to that the assumptions of the waves can propagate upward into the atmosphere driving changes in the ionosphere. This suggests that the pressure-shear vertical ground vibrations can drive air pressure changes. When the horizontal and vertical ground velocities of ground vibrations yield a difference in the phase angle close to 90°, coherence values between the air pressure changes and ground vibrations become large. To expose causal mechanisms of the unusual phenomenon, continuous seismic waveforms are further conducted for examination. In contrast, the larger pressure changes at frequencies > ~ 5 × 10–4 Hz inside the cave at the SBCB station lead smaller changes outside at the Xinwu station.

Analytical results of phase angle differences reveal that the air pressure outside the cave at the Xinwu station often leads air pressure changes inside at the SBCB station at relatively low frequency bands. Accordingly, the comparison between the recorded data at the SBCB and Xinwu station can drive investigations of potential sources of the unusual phenomenon. A barometer in the cave of the SBCB station records an unusual phenomenon of larger amplitudes in air pressure changes inside than those at the Xinwu station (outside). However, causal mechanisms of couplings between sources in the lithosphere and responses in the atmosphere and the ionosphere are not fully understood, yet. Acoustic-gravity waves are generally considered to be one of the major factors that drive changes of the total electron content in the ionosphere.

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