The invention relates to a seismic signal spectrum decomposition method based on a sparse time-frequency analysis method, a terminal device and a storage device. The method comprises the following steps of S1, inputting a seismic signal to be analyzed, obtaining N sub-signals si of an length M by an overlapped sliding rectangular window function, and weighting the sub-signals si by a Gaussian window function to obtain weighted sub-signals yi=gosi; S2, subjecting a spectrum solving model, which is described in the specification, to iteration for k times by using a forward-backward splitting method to obtain a reconstructed spectrum x; S3, subjecting the reconstructed spectrum x obtained in the step S2 to a centralization operation, which is described in the specification, in order to place the zero spectrum line in center of the spectrum. Based on short-time measurement, the seismic signal spectrum decomposition method has no Cohen-like cross-term problem. The high-precision time-frequency resolution is ensured by the L1 constraint, thereby avoiding the low resolution of the traditional the short-time Fourier transform and making it possible to obtain a seismic signal spectrum with high-precision time-frequency resolution.