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Swarms of non-volcanic tremor 1,2 occur with slow slip events 3 along the subduction zone of the Philippine Sea plate in southwest Japan. These episodic events are considered to be linked in a stress relaxation process at subducting plate interface 3-5. Tremor swarms often exhibit occurrences with a periodicity of about 12 or 24 hours 6,7. Here we show that the observed periodic tremor occurrences can be reproduced by the seismicity rate 8 calculated from the periodic stress due to Earth tide combined with the transient stress due to slow slip event. The value of fault constitutive parameter in tremor source region is very small, indicating a sensitive response of tremor occurrences to stress change. Observation of nonvolcanic tremor is therefore effective for monitoring the stress relaxation process at subducting plate interface.

Earth's free oscillations were considered to be transient phenomena occurring after large earthquakes. An analysis of records of the IDA (International Deployment of Accelerometers) gravimeter network shows that Earth is freely oscillating at an observable level even in seismically inactive periods. The observed oscillations are the fundamental spheroidal modes at frequencies between 2 and 7 millihertz. Numerical modeling indicates that these incessant excitations cannot be explained by stacked effects of a large number of small earthquakes. The observed "background" free oscillations represent some unknown dynamic process of Earth.

We, for the first time, report the evidence of incessant excitation of the Earth's free oscillations, mainly the fundamental spheroidal modes in a frequency range from 0.3 to 5 mHz, based on the three year record of a superconducting gravimeter at Syowa Station, East Antarctica. The frequency-time spectrogram of this record is striped by more than 30 lines at nGal level parallel to the time axis, mostly corresponding to the fundamental spheroidal modes. This spectrogram is characterized by relatively efficient excitation of gravest fundamental modes, enhancement of signal intensities in the austral winter and amplification of signal in the frequency band from 3 to 4 mHz. Assuming that earthquakes are only the sources for the free oscillations, we calculate the synthetic spectrograms, which have not shown such a series of parallel lines as observed. The result of this synthetic test and characteristics of the observed spectrogram suggest that the mode signals we found are not of earthquake origin. We tentatively suggest atmospheric or oceanic origin for this newly discovered phenomenon of the solid Earth.

[1] It has recently been established that the Earth's free oscillations are continuously excited by phenomena other than earthquakes and that these oscillations constitute the background noise in the normal mode band at quiet sites. On the basis of evidence that the excitation source is at or just above the Earth's surface, a normal mode theory of the Earth's free oscillations excited by random atmospheric loading is developed. The displacement field is expressed in the frequency domain in general terms of the crossspectral density of air pressure disturbance. For spatially homogeneous and isotropic disturbance the cross-spectral density is approximated by the power spectral density and the coefficient of coherence with a coherence length much shorter than the wavelengths of normal modes. With this approximation the spectrum of ground acceleration is represented as the product of the pressure force term and the Earth response term. The final expression of the acceleration spectrum includes the effect of the gravity attraction of a disturbed air mass. A synthetic spectrum is calculated, using a power law decaying air pressure spectrum consistent with observations, assuming a frequency-dependent coherence length of air pressure fluctuation, taking into account the effect of the gravity attraction of a disturbed air mass. This synthetic spectrum exhibits distinct peaks of fundamental modes and complex troughs consisting of overtone modes, in quantitative agreement with the peaks and troughs of the observed spectrum.

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