Amplitude-variation-with frequency (AVF) analysis of seismic data over anelastic targets
Christopher W. Bird
In this thesis we develop methods of estimating amplitude-variations-with-frequency (AVF) signatures in seismic data for the inversion of anelastic reflectivity. AVF inversion requires estimates of the anelastic reflection coefficient as input and allows for the determination of the target Q value. We start by calibrating a fast S-transform to use as our processing tool to estimate the local spectrum of reflection coefficients. We then modify the AVF inverse theory to operate in the S-domain and find accurate inversion results. In a synthetic data environment we test AVF inversion to manage a prioritized set of issues including random noise, nearby/difficult to isolate events, and a source wavelet. We find AVF inversion, in the presence of these seismic data phenomena, to be a tractable problem. We also identify and examine a target reflection from a VSP data set and observe an AVF signature.
A least-squares approach is developed with the goal of making AVF inversion more robust in the presence of a source wavelet. We also extend the least-squares formalism to oblique incidence. We find the least-squares approach is successful at inverting for Q when an estimate of the wavelet is brought into linear AVF inverse theory. Finally, we study the basic nature of full waveform inversion (FWI) on an anelastic reflection coefficient. We find that the first calculation of the gradient yields an imaginary step at the proper location of the anelastic reflector.