基于EEMD分解的气压改正方法研究

利用超导重力仪观测数据精确测定低于1 mHz的地球自由振荡简正模式的分裂频率，是在不与任何弹性系数发生联系的情况下改善一维密度模型的有效方法.但在该频段台站局部气压变化对重力观测数据的影响成为主要干扰来源，且具有频率依赖特性，因此精细地开展气压改正成为利用超导重力数据检测低频自由振荡信号的必要手段.本文基于EEMD方法，提出了一种具有频率依赖特性的气压改正方法.该方法将重力观测和气压变化分解成处于不同频段的本征模态函数，并在相应频段上分别进行重力-气压变化的回归分析，计算得到具有频率依赖特性的气压导纳值，精细地消除气压变化对重力观测的影响，并以此对微弱低频地球自由振荡信号开展高分辨率分析.基于本文提出的气压改正方法，利用大地震后的超导重力数据检测了频率小于1.5 mHz的低频地球自由振荡及其频谱分裂现象.研究结果表明：利用该方法进行气压改正后检测得到的各简正模具有更高的信噪比，估计的本征频率误差水平明显降低，获得的基频球型振荡₀S₂和₀S₃以及一阶球型振荡₁S₂的分裂谱峰的估计精度更高，同时还检测到了部分环型振荡在重力观测中的耦合现象.对低频地球振荡的高分辨率检测结果验证了基于EEMD分解提出的气压改正方法的有效性，同时再次证明了超导重力仪观测数据在低频地球自由振荡检测中的优势.

Method to correct atmospheric pressure effects based on ensemble empirical mode decomposition

The precise determination of the frequency splitting of seismic normal modes below 1 mHz using Superconducting Gravimeter (SG) data is an effective way to improve 1D density models without any trade-off with elastic parameters, as they are directly linked to the 1D-density profile. In the frequency band below 1 mHz, local atmospheric pressure around the SG sites becomes a major error source with the frequency-dependent characteristics. Therefore, an elaborate atmospheric-pressure correction on the SG data is necessary to detect low-frequency free oscillations of the Earth. Based on the Ensemble Empirical Mode Decomposition (EEMD), we propose an atmospheric-pressure correction method with frequency-dependent characteristics. With this method, gravity and atmospheric pressure are decomposed into a set of Intrinsic Mode Functions (IMFs) which are located in the different frequency bands respectively, then the gravity-pressure admittances are calculated in different frequency bands by applying a regressive analysis between gravity and atmospheric pressure. Finally, the influence of atmospheric pressure on the SG observation is elaborately removed. Using this method, we carried out a high-resolution analysis of low-frequency seismic normal modes and discovered their frequency splitting below 1.5 mHz by SG data after a great earthquake. The results demonstrate that seismic normal modes obtained from the atmospheric-pressure correction method proposed in this paper have higher signal-to-noise ratio, the standard deviations of estimated eigen-frequencies are distinctly reduced and the singlets of the fundamental spheroidal modes ₀S₂ and ₀S₃ and the degree one spheroidal mode ₁S₂ have high estimated precisons. Some spheroidal-toroidal mode couplings are also clearly detected in the SG data. The high-resolution analysis of low-frequency seismic normal modes not only has verified the atmospheric-pressure correction method based on EEMD but also has demonstrated the superiority of applying the SG data to detecting low-frequency seismic normal modes.