Abstract
<p>Based upon SG (superconducting gravimeter) records, the autoregressive method proposed by Chao and Gilbert [1980] is used to determine the frequencies of the singlets of seven spheroidal modes (<sub>0</sub>S<sub>2</sub>, <sub>2</sub>S<sub>1</sub>, <sub>0</sub>S<sub>3</sub>, <sub>0</sub>S<sub>4</sub>, <sub>1</sub>S<sub>2</sub>, <sub>0</sub>S<sub>0</sub>, and <sub>3</sub>S<sub>1</sub>) and the degenerate frequencies of three toroidal modes (<sub>0</sub>T<sub>2</sub>, <sub>0</sub>T<sub>3</sub>, and <sub>0</sub>T<sub>4</sub>) below 1 mHz after two recent huge earthquakes, the 2010 Mw8.8 Maule earthquake and the 2011 Mw9.1 Tohoku earthquake. The corresponding quality factor <em>Q</em>s are also determined for those modes, of which the <em>Q</em>s of the five singlets of <sub>1</sub>S<sub>2</sub> and the five singlets (<em>m</em>=0, <em>m</em>=±2, and <em>m</em>=±3) of <sub>0</sub>S<sub>4</sub> are estimated for the first time using the SG observations. The singlet <em>m</em>=0 of <sub>3</sub>S<sub>1</sub> is clearly observed from the power spectra of the SG time series without using other special spectral analysis methods or special time series from pole station records. In addition, the splitting width ratio <em>R</em> of <sub>3</sub>S<sub>1</sub> is 0.99, and consequently we conclude that <sub>3</sub>S<sub>1</sub> is normally split. The frequencies and <em>Q</em>s of the modes below 1mHz may contribute to refining the 3D density and attenuation models of the Earth.</p>
Highlights
The normal modes below 1mHz are very sensitive to density heterogeneities of the Earth, and precise determination of the splitting frequencies of these modes can provide further information to constrain the 3D models, especially the core and mantle density distribution and structures
All of the singlets of 0S2 and 0S3 were completely observed by Buland et al [1979] using seismic datasets from the International Deployment of Accerometers (IDA) network, and the triplet of 2S1 was first observed by Rosat et al [2003] based on five SG records
It should be noted that a Hanning taper should be multiplied by each new time sequence prior to Fourier transform (FT) to weaken the spectral leakage
Summary
The normal modes below 1mHz are very sensitive to density heterogeneities of the Earth, and precise determination of the splitting frequencies of these modes can provide further information to constrain the 3D models, especially the core and mantle density distribution and structures. In order to obtain a sufficient frequency resolution, for each mode, the selection of the data length needs not following that criterion [e.g., Rosat et al 2005, Roult et al 2010]. According to Equation (2), one needs only to know the complex frequency of a mode, and the corresponding Q can be estimated. Rosat et al [2008] proposed a non-linear damped harmonic analysis (NLDHA) method, which can be used to estimate the complex frequencies of a normal mode. Due to the fact that the validity of the AR method has been verified by previous studies [Chao 1983, Masters and Gilbert 1983], we use this method to estimate the complex frequencies of those modes.
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