This thesis investigates a particular prestack multiple attenuation method, bas ed on generalised linear inversion (GLI) and scattering matrix theory. The meth od uses GLI to obtain the reflectivity function that would produce a seismic tr ace as close as possible to that observed. The forward model for the inversion employs the scattering matrix method to compute the entire P-wave response of a seismic section possessing a given reflectivity function. The optimum reflecti vity function is then used to generate a multiples-only seismic trace, which is subtracted from the original seismic signal.
It is envisaged that this method will be of greatest use in situations where mu ltiple energy is dominant, since the reflectivity is being modelled to the mult iple reflections as well as the primary reflections. The use of the standard sc attering matrix approach currently limits the method to cases where horizontal layering and vertical incidence may be assumed. However, it is noted that tradi tional multiple attenuation methods have been least successful in such near-off set situations.
One of the chief problems with the approach presented here is that the signal r esponse tends to be insensitive to the high frequency information of the reflec tivity. It is necessary to include in the forward model a means of combating th is insensitivity. Four different forward models are tested on synthetic data. T wo reflectivity functions have been used to generate the synthetic traces. One of these is a simple sparse spike function, while the other has been generated from real well log data.
In the first method discussed, the reflectivity is parameterised by its complex frequency spectrum between two specified cutoff frequencies. This method is fo und to be unstable, and fails to converge for any but the simplest signals. It is suggested that this instability is due to an interface blurring that occurs when high-frequency information is not passed into the scattering matrix.
In the second method, the reflectivity is parameterised by the amplitudes and t wo-way time delays of a set of sparse reflections. This method is also unstable unless the starting reflectivity function is very close to the correct functio n.
The third method uses the reflectivity as a function of two-way time. However, the forward model includes convolution with a "high-pass" version of the intrin sic wavelet, thus eliminating the problem of insensitivity to high frequencies. This method is found to be quite successful for zero-delay wavelets, but fails to converge for minimum-delay wavelets. This may be due to the fact that the h igh-pass wavelet will tend to have an earlier peak than the corresponding band- pass wavelet.
The fourth method also uses reflectivity as a function of two-way time, but ove rcomes the high frequency instability by increasing by a certain percentage the diagonal of the product of the Jacobian matrix with its transpose. This method is successful for all cases except when applied to the well-log synthetic with a minimum-delay wavelet, using the signal as the initial reflectivity function .
Overall, the fourth method is the most successful. Since the best results are o btained when the intrinsic wavelet is zero-delay, it is suggested that signals involving minimum-delay wavelets be filtered appropriately. For full practical application, the forward model will need to be generalised to allow for realist ic finite offset situations. However, the computational conclusions of this the sis are expected to hold for more realistic models.