Nonlinear prediction via Volterra series and applications to geophysical data

Linear filter theory has proven useful in many seismic data analysis applications. However, the general development of linear filter theory is limited by the implicit approximations typically found in seismic processing; one reason for this is to avoid effects of nonlinearity. This thesis concentrates on the implementation of nonlinear time series modeling based on an autoregressive method. The developed algorithm utilizes third-order Volterra kernels to improve predictability of events that cannot be predicted using linear prediction theory.;Volterra series are analyzed. The application and implementation of a nonlinear autoregressive algorithm to the problem of modeling complex waveforms in the f -- x domain is studied. Problems of random noise attenuation and adaptive subtraction of multiples are reexamined by the new Volterra autoregressive algorithm. Synthetic and field data examples are used to illustrate the theory and methods presented in this thesis.