Application of Autoregressive Extrapolation to Seismic Tomography

Seismic tomography used in the laboratory, as well as in the field, is strongly affected by limited and nonuniform ray coverage. A two-stage autoregressive extrapolation technique is proposed that can be used to extend the observed data and provide better tomographic images. The algorithm is based on the principle that the extrapolated data add minimal information to the existing data. The first stage of the extrapolation is to find the optimal prediction-error (PE) filter. The second stage is to use the PE filter to find the values of the missing data. The missing data are estimated to have the same spectrum as the observed data and are similar to maximizing an entropy criterion. To test the method, synthetic tomography experiments for laboratory rock samples are used in which full ray coverage can be obtained. Autoregressive methods are then used to extrapolate the partial ray coverage and the tomographic results are compared with the full ray coverage case. The synthetic tests show that the autoregressive method can extrapolate known data to find missing data and can provide improved tomographic images. The autoregressive extrapolation is also tolerant to noise. Although the method was applied to a laboratory geometry where the ray coverage can be controlled, autoregressive methods may have important applications to tomography experiments in the field where complete ray coverage often cannot be easily realized.