Response characteristics of gas and water layers in tight sandstone reservoirs based on variational mode decomposition of array acoustic logging signals

After the array acoustic full wave train is decomposed by the mode decomposition method based on time domain, there is serious mode aliasing between each Intrinsic Mode Function(IMF), which leads to the reservoir fluid response of time–frequency characteristics of each Intrinsic Mode Function that is not obvious. To solve this problem, this paper explores and compares the effects of Empirical Mode Decomposition, Ensemble Empirical Mode Decomposition, Complementary Ensemble Empirical Mode Decomposition, and Variational Mode Decomposition (VMD) in array acoustic full wave train decomposition, proves that using VMD method to decompose array acoustic full wave train has better effect, extracts the time–frequency distribution characteristics (including time edge, frequency edge and cumulative energy) of the first four full wave train Intrinsic Mode Functions, and analyzes response of time–frequency characteristics of Intrinsic Mode Functions on gas and water layers. The results show that the VMD decomposition can suppress the phenomenon of mode aliasing better, and each component represents different mode waves information in the full wave train. On features of time–frequency distribution, the peak arrival time and dominant frequency energy of IMF2, IMF3, and IMF4 show obvious response on the gas and water layer, and the cumulative energy of IMF2 and IMF3 components shows obvious response on the gas and water layer. Compared with the other three mode decomposition methods, the time–frequency characteristics of the Intrinsic Mode Function decomposed by VMD have an obvious response on the tight sandstone gas and water layer.