For a fast and accurate extraction of important information in seismic signals, a sparse representation based on physical parameters of the given data is crucial. In this paper we use the Asymmetric Gaussian Chirplet Model (AGCM) and establish a dictionary free variant of the Orthogonal Matching Pursuit (OMP), 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 the seismic signal consists of non-stationary compressed plane waves, i.e., symmetric or asymmetric chirplets. Thus AGCM is a general model for seismic wave simulation, and its model parameters include envelope part and phase part. In this paper, we mainly concentrate on the parameters of envelope part such as envelope amplitude and arrival time. We will show numerical examples using the algorithm for seismic signal approximation and arrive-time detection. The results show a promising performance but may be improved considering also spatial correlations of seismic data.