Deconvolution of seismograms by the autoregressive method

The purpose of deconvolution in seismology is to estimate the basic seismic wavelet and the transfer function of the transmission medium. In reflection seismology, this transfer function refers to the reflectivity function, while in seismograms of earthquakes and explosions it represents the combined effects of the source crust and the receiver crust responses along with the attenuation function. Some of the techniques used for deconvolution of discrete time series data are Wiener inverse filtering (Robinson and Treitel, 1967), homomorphic deconvolution (Ulrych, 1971), and Kalman filtering (Crump, 1974). In the present paper, a method of deconvolution of single-channel seismic data based on an autoregressive (AR) model of the time series is discussed. With it one can estimate the primary pulse and the deconvolution function simultaneously in an objective manner. Examples are provided to substantiate the applicability of the method using synthetic data simulating single and multiple explosions. The method is also applied to actual data for a presumed underground explosion from Eastern Kazakh.