In seismic deconvolution, blind approaches must be considered in situations where reflectivity sequence, source wavelet signal, and noise power level are unknown. In the presence of long source wavelets, strong interference among the reflectors contributions makes the wavelet estimation and deconvolution more complicated. In this paper, we solve this problem in a two-step approach. First, we estimate a moving average (MA) truncated version of the wavelet by means of a stochastic expectation-maximization (SEM) algorithm. Then, we use Prony's method to improve the wavelet estimation accuracy by fitting an autoregressive moving average (ARMA) model with the initial truncated wavelet. Moreover, a solution to the wavelet initialization problem in the SEM algorithm is also proposed. Simulation and real-data experiment results show the significant improvement brought by this approach.