For a fast and accurate extraction of important information in seismic signals, a sparse representation based on the physical parameters of the given data is crucial. We have used the asymmetric Gaussian chirplet model (AGCM) and established a dictionary-free variant of the orthogonal matching pursuit, a greedy algorithm for sparse approximation. The atoms of AGCM, so-called chirplets, display asymmetric oscillation attenuation properties, which make the AGCM very suitable for sparse representation of absorption decay seismic signals. Unlike the Fourier transform, which assumes that the seismic signals consist of plane waves, the AGCM assumes that the seismic signal consists of nonstationary compressed plane waves, i.e., symmetric or asymmetric chirplets. Thus, AGCM is a general model for seismic wave simulation, and its model parameters include an envelope part and a phase part. We have mainly concentrated on the parameters of the envelope part, such as the envelope amplitude and arrival time. We provide numerical examples using the algorithm for seismic signal approximation and arrival-time detection. The results indicated promising performance but also may be improved considering the spatial correlations of seismic data.