## 1 Introduction  
Channel sand bodies are of great importance in many petroliferous reservoirs and are targets in oil and gas explorations [1]. The appropriate distribution of sand bodies, particularly sand thicknesses, aids in the investigation of sedimentary facies [2]. Therefore, the precise interpretation of seismic geological channels is highly demanding. Ascribing to the continuous channel migration and frequent vertical superposition of sand bodies, sedimentary patterns of the channels in seismic records are always complicated. Doubly inhibited by varied physical properties and oil-bearing properties on seismic data, traditional attribute-based analytical methods have difficulties in recognition, especially for identifying the precise edges and geological patterns of paleo-channels [3, 4]. With spectral decomposition techniques, initial broadband seismic data can be decomposed into a sequence of frequency-decomposed seismic volumes of various frequencies. Separating the frequency bands of seismic data is theoretically valid for extracting the information on varied geological scales [5]. The spectral characteristics of relatively narrow band components are usually used to delineate the anomalous geologic features that would otherwise be hidden within the full-bandwidth seismic response; thus, appropriate bands would effectively increase resolution and reliability in seismic interpretation [6, 7]. Accordingly, spectral decomposition-based methods were developed and widely applied in seismic data analysis, including sequence stratigraphy analysis [8], reservoir characterization [9], thin-layer thickness estimation [10], and hydrocarbon detection [11]. Conventionalspectral decomposition methods include short-time Fourier transform (STFT) [12], continuous wavelet transform (CWT) [13], and S transform (ST) [14]. The STFT, CWT, and ST are all bound by the Heisenberg uncertainty principle with a tradeoff between time and frequency localization [15]. In order to identify the intrinsic hidden properties contained in the nonlinear and non-stationary signals, the empirical mode decomposition (EMD) method is introduced by [PERSON] et al. as a data-driven signal decomposition technique without using predefined wavelet libraries or base functions [16]. The EMD-based time-frequency analysis of seismic data shows the relative high resolutions in both the temporal and frequent realms, as it is effective on the instantaneous attributes of nonlinear and nonstationary signals. However, with a deficiency on the bandlimited assumption of the instinct mode function, the usage of the EMD method is limited. Further, the variational mode decomposition (VMD) method was developed, which can decompose the seismic signals into a sequence of quasi-orthogonal intrinsic mode functions, with the most compact bandwidth [17]. The VMD method was applied in seismic data analysis, including denoising [18; 19], sequence stratigraphy analysis [7; 20], seismic time-frequency analysis [21], and seismic facies analysis [22; 23]. The VMD-based method, which calculates trace-by-trace, is unable to maintain the lateral continuity of 2D or 3D seismic data, causing difficulties in subtle geological feature discriminations [7], and consequently, including the seismic channels. [PERSON] and [PERSON] recently proposed the multivariate variational mode decomposition (MVMD) that is valid for multivariate or multichannel datasets [24]. In the MVMD method, the lateral continuity of the decomposed intrinsic mode functions (IMFs) is improved by applying lateral constraints, which are valid for extracting the spatial aspects of seismic reflection on different geological scales [25]. The tangled geo-features ascribed to the subtle discontinuities have brought difficulties in recognition by the original variational mode decomposition-based method. Taking into account the horizontal consistency of 3D seismic data, we propose a multi-trace variational mode decomposition-based seismic spectral decomposition method for geological feature discrimination in this study.