ARMA order model detection using minimum of Kurtosis: application on seismic data
- 25 Downloads
The objective of this study is to find the order and coefficients of non-low-phase causal filters for ARMA (auto regressive moving average) filter model, using the Kurtosis minimization criterion. This method is based on the Kurtosis calculation of the treated sample at the input level and its identification at the output of the ARMA model. For this purpose, the order and coefficients of the AR (auto regressive) part are identified using the Yule-Walker algorithm at order two and then extended to order four. To obtain the MA (moving average) part, the AR components are calculated at first from the ARMA filter by deconvolution. Then, spectrally equivalent and minimum phase (SEMP) MA filter is identified using the Durbin algorithm at second and fourth order. Finally, the correct filter is found when the Kurtosis value of the output ARMA filter reconstituted is the closest to the Kurtosis of introduced signal. The proposed method is then tested on simulated processes and applied to real seismic data to perform blind deconvolution and obtain the reflectivity coefficients of subsoil studied.
KeywordsFourth-order cumulants ARMA filters Kurtosis Blind identification Seismic traces Reflectivity coefficients
The first author would like to express his sincere gratitude to Professor Jean Michel Rouvaen, his co-supervisor in doctoral studies, for his supervision and advice in the IEMN laboratory. He also thanks his former teacher, Dr. Chahed Idir.
- Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Proceed 2nd Internat’l Symp on Inform Theory, Budapest (Hung), pp 267–281Google Scholar
- Bellahsene H, Chahed I, Djeddi M (1999) Identification de filtres ARMA à phase non minimale par maximum de kurtosis. In: Proceedings of the 2nd Internat. Conf on Electron, Signals, Systems and Automatics, Algeria, pp 107–111Google Scholar
- Bellahsene H, Fatani IFE (2011) Utilisation des HOS pour le calcul du filtre optimal et de la rduction du temps de convergence en DMT, ICGST, ACSE journal on computer and engineering, pp 69–74, Istanbul, TurkeyGoogle Scholar
- Boumahdi M, Lacoume JL (1994) Blind identification of FIR systems using the kurtosis. In: Proceedings of the 7th workshop on statistical signal and array processing, Québec (Can), pp 191–194Google Scholar
- Boumahdi M, Lacoume JL (1994) Blind identification of non-minimum phase filters by maximising the kurtosis, EUSIPCO 1994 - Special HOS session, Edinburgh, UKGoogle Scholar
- Moddermeijer R (1999) Testing composite hypotheses applied to AR order estimation; the Akaike criterion revisited, Signal Proc., Symp Proceed, Leuven (Belgium), pp 135–138Google Scholar
- Shuichi O, Hideaki S, Hironori Y (1999) Adaptive blind equalization of multichannel FIR systems. Proc IEEE, Internat’l Symp Circuits Systems 3:66–73Google Scholar