Least squares AVF inversion
Christopher W. Bird, Kristopher A. H. Innanen, Mostafa Naghizadeh
A frequency by frequency method (AVF) of inverting for Q exists which requires as input an estimate of the local spectrum of the absorptive reflection coefficient. We have a calibrated fast S-transform (FST) which we have demonstrated provides a high fidelity estimate of the local spectra of seismic reflection events and is suitable as input for AVF inversion. We formulate the AVF inverse problem in a least-squares formalism. The opportunity for optimization offered by a least squares approach my bring stability to the estimates of Q yielded by AVF inversion. We also formalize this least-squares approach to use the estimate of a source wavelet, as opposed to removing the wavelet via deconvolution, which appears to offer stability to the estimates of Q and wavespeed. We also extend our least-squares approach to the broader problem of AVO by including angle of incidence. Finally, we use input from the FST as input into our least-squares AVF approach. Using numerically modeled data we find that the inversion results are accurate up to angles of incidence up to roughly 35 degrees. Also we find that bringing an estimate of the wavelet into the inversion scheme stabilizes the inversion results of Q and wavespeed.