| In this dissertation, the source signature is modeled and estimated as an Autoregressive Moving Average (ARMA(p,q)) process. This is a z-transform representation involving a polynomial numerator of order p, and denominator of order q. The ARMA(p,q) model order is provided by the modified Akaike information criterion and the ARMA(p,q) wavelet is simulated by using the Yule-Walker equations. The method needs an initial reflectivity sequence estimate to simulate the seismic traces. If a reflectivity sequence estimate is not available, the seismic data are deconvolved with the inverse operator of the initial ARMA wavelet to simulate the reflectivity sequence. In this case, the reflectivity sequence is assumed to possess Gaussian random reflectivity. In the optimization part of the method, the Scaled-Weighted-Marquardt-Levenberg (SWML) algorithm is used to minimize the objective function, which is the difference between the observed and estimated data.; Synthetic data were used to test the method for different ARMA(p,q) model orders and different signal to noise ratios. From these synthetic tests, an important result was found: raising the ARMA model order improved the results up to a particular model order. Beyond that model order, there was no significant improvement. This model order is called the ARMA model order limit.; The method was applied to a marine seismic shot gather and produced good results. The initial ARMA model order provided by the modified Akaike information criterion was ARMA(6,6). Increasing the model order to ARMA(8,8) improved the match between the source wavelet and the estimated ARMA wavelet. No model order limit was observed in this case.; To compare the ARMA method with other methods, the minimum-phase equivalent of the source signature was computed and compared with the seismic wavelet and the estimated ARMA wavelet. The match between the source wavelet and the estimated ARMA wavelet was better than the match between the source wavelet and the minimum-phase equivalent of the source wavelet. In addition, spiking deconvolution and signature deconvolution results were produced. Signature deconvolution with the estimated ARMA(8,8) wavelet was closer to the deconvolution result obtained using the measured signature than was the spiking deconvolution result. |
