Applications of variational mode decomposition in seismic time-frequency analysis

Abstract

We have introduced a novel time-frequency decomposition approach for analyzing seismic data. This method is inspired by the newly developed variational mode decomposition (VMD). The principle of VMD is to look for an ensemble of modes with their respective center frequencies, such that the modes collectively reproduce the input signal and each mode is smooth after demodulation into baseband. The advantage of VMD is that there is no residual noise in the modes and it can further decrease redundant modes compared with the complete ensemble empirical mode decomposition (CEEMD) and improved CEEMD (ICEEMD). Moreover, VMD is an adaptive signal decomposition technique, which can nonrecursively decompose a multicomponent signal into several quasi-orthogonal intrinsic mode functions. This new tool, in contrast to empirical mode decomposition (EMD) and its variations, such as EEMD, CEEMD, and ICEEMD, is based on a solid mathematical foundation and can obtain a time-frequency representation that is less sensitive to noise. Two tests on synthetic data showed the effectiveness of our VMD-based time-frequency analysis method. Application on field data showed the potential of the proposed approach in highlighting geologic characteristics and stratigraphic information effectively. All the performances of the VMD-based approach were compared with those from the CEEMD- and ICEEMD-based approaches.

Intrinsic Frequencies of the Resting-State fMRI Signal: The Frequency Dependence of Functional Connectivity and the Effect of Mode Mixing

“…Our study incorporates the usage of the recently proposed variational mode decomposition (VMD) method (Dragomiretskiy and Zosso, 2014) to decompose the BOLD rs-fMRI time series into its IMFs. Recently, the VMD method has recently found application in the analysis of geological signals (Liu et al, 2016; Xiao et al, 2016) and electrocardiographic data (Lahmiri, 2014; Mert, 2016; Tripathy et al, 2016). The theory of VMD has been described in detail elsewhere (Dragomiretskiy and Zosso, 2014), and will not be repeated here.…”

Depositional sequence characterization based on seismic variational mode decomposition

“…The number K of EMD outputs cannot be controlled. Liu et al (2016) also find that very small unexpected oscillatory interference patterns can change the number of final output modes. In contrast to EMD, VMD obtains IMFs that exhibit specific sparsity properties in the frequency domain.…”

“…To address this drawback, Dragomiretskiy and Zosso (2014) develop the variational mode decomposition (VMD) to decompose a nonstationary signal into an ensemble of band-limited IMFs. Liu et al (2016) compare VMD with the alternative of EMD-based methods, and they find that VMD can express the same seismic data with fewer intrinsic modes. The STFT, CWT, and MP spectral decompositions provide laterally consistent images for each spectral component.…”

IMF-Slices for GPR Data Processing Using Variational Mode Decomposition Method

“…Specifically, though the decomposition results can still be seen as IMFs, the computation is implemented by solving an optimization problem. Some references have demonstrated that the VMD is able to avoid mode-mixing phenomena [13][14][15], and therefore the decomposition results match the input signal's intrinsic vibration mode better. In this study, we test VMD decomposition on GPR data, and based on the VMD decomposition results, we propose a new method for GPR imaging which we refer as "the IMF-slice".…”