Abstract: Method for removing coherent noise from a series of seismic traces. Each seismic trace included in the series is Fast Fourier Transformed into the frequency domain. For each frequency of the resultant f-x representation, a series of N complex numbers, one corresponding to each trace, is selected. The selected series of complex numbers corresponding to each frequency are processed to produce autoregressive model coefficients from which a polynomial rooting provides complex roots related to wavenumbers and decay constants. Amplitudes and phases for complex non-stationary spatial sinusoids associated with the estimated wavenumbers are then determined. For all frequencies f, the collection of determined wavenumbers, decay constants, amplitudes and phases constitute an f-k representation of the seismic traces.

Abstract: A seismic record is enhanced through trace restoration and extrapolation. A set of traces surrounding a missing trace or adjacent an edge of the seismic record are transformed into the frequency domain using a fast Fourier transform. Each frequency of the resultant x-f representation a series of complex numbers, one corresponding to each trace, is selected. Autoregressive model coefficients are estimated for this complex series using a recursive least squares method. A complex number is estimated for trace restoration and extrapolation from the series of complex numbers and autoregressive coefficients. After all frequency components are thus processed restored or extrapolated traces are obtained by an inverse Fourier transform.

Abstract: Method for restoring seismic data to missing or severely noise contaminated traces included in a seismic section. The seismic section is transformed into a data localizing space and muted to retain only the localized data components of the seismic section. The muted transform space is inverse-transformed into the x-t domain to produce first estimates of the seismic data to be restored. The first estimates of the restored data are substituted for the corresponding traces in the original seismic section. Fully restored traces corresponding to the missing or severly noise contaminated traces are determined from the single estimate of the restored traces.

Abstract: Method of restoring null traces in seismic records. The seismic record is transformed from the x-t domain to the f-k domain by a series of fast Fourier transforms. The f-k transform of the seismic record is filtered to retain only coherent events and the filtered f-k transform is inverse-transformed back to the x-t domain. A first determination of the restored trace corresponding to the null trace is selected and substituted for the null trace. The first determination of the restored trace is used to determine a fully restored trace.