This thesis examines the problem of recovering the acoustic impedance from a band-limited normal-incidence reflection seismogram. Three post-stack seismic inversion techniques are examined and tested on synthetic and real examples to evaluate their performance.
Classical recursive inversion utilizes the well-known reflection coefficient equation to generate an estimate of the earth’s impedance. This technique assumes that preprocessing has accurately recovered the true reflectivity sequence from the seismic trace prior to inversion. In practice however, the effect of the source wavelet on the reflectivity series is not fully removed, and so missing frequency components must be derived from some geological model and incorporated into the impedance solution after inversion. Low frequencies are shown to play an extremely important role in the ’impedance domain’ because of the low-pass nature of the inversion algorithm. Impedance models generated from band-limited seismic traces contain only ’depthpositional’ information. Incoiporation of low frequency components in the form of a constraint spline improves the final impedance estimate.
Autoregressive (AR) spectral extension is representative of sparse-spike inversion techniques and involves predicting frequency information missing from the reflectivity series prior to inversion of the trace. This method assumes the seismic trace can be expressed in terms of the noise-free convolutional model. Results indicate that when sparse-spike assumptions are not met the extension algorithm becomes ineffective in predicting missing frequency information. Furthermore, when the reflectivity series does not exhibit a white spectrum, AR extension cannot accurately predict missing low frequency components. This limitation can be overcome to a degree by flattening the spectrum of the trace before AR extension, and returning the linear trend to the spectrum before inversioa When applied to real, non-sparse seismic data, the AR extension algorithm is unable to accurately predict crucial low frequency information from the band-limited reflectivity series. Consequently the inverted seismic trace is not a reliable estimate of the earth’s impedance.
Of the three inversion methods investigated, model-based linear inversion generates the most reliable impedance profiles. The principle of model-based inversion is to derive a geological model which best fits the observed seismic data in a least-squares sense. The seismic data are assumed to be consistent with the noise-free convolutional model. Modifications to previous linear inversion algorithms have been incorporated to remove the need for geological interpretation prior to inversion. In addition, the present implementation has been designed to avoid problems associated with inaccurate low frequency content and unrealistic oscillation of the final impedance profile. To ensure RMS velocity constraints can provide accurate low frequency control during the inversion of real seismic data, it is necessary to include a densityvelocity relationship in the inversion algorithm. When the effect of density on real seismic data is taken into account, model-based inversion can recover a reliable impedance estimate.