Wave equation inversion of skeletalized seismic data

This dissertation describes a new inversion method that employs the wave equation to invert for velocities from seismic traveltime data. It also provides a methodology for inverting skeletal data (e.g., traveltimes) that are not related to the model parameters (e.g., velocities) by the fundamental equations (e.g., the wave equation). The key idea is to use a connective function to bridge the skeletal data with the fundamental data that appear explicitly in the fundamental equations. This then allows for the approximation-free computation of the skeletal Frechet derivative. Prior to this development, the skeletal Frechet derivative could be computed only by invoking restrictive asyptotic approximations.; The major advantages of this new methodology are: (1) Robust and fast convergence. Skeletal data can be selected to ensure robust convergence and to avoid the confusion of trying to invert every detail in the seismograms. (2) Elimination of approximations. Fundamental equations (e.g., the wave equation) are used to derive inversion methods using different types of data. There is no need for an asymptotic equation to link the skeletal data to the model parameters. (3) Optimized hybridization of inversion methods. We can now invert for the model parameters by simultaneously using several types of skeletal data in conjunction with the same fundamental equations. Although this dissertation demonstrates the application of this new methodology to seismic inversion, the methodology can also be applied to inverse problems in other related fields, such as in the electromagnetic field.; This dissertation consists of the contents of three papers: (1) Wave Equation Traveltime Inversion, (2) Wave Equation Traveltime and Waveform Inversion, and (3) The Calculation of Wavepaths for Bandlimited Seismic Waves. The wave equation traveltime inversion (WT) methodology is derived in the first paper. It shows that ray tracing traveltime inversion method is a special case of the WT method under the high-frequency assumption, and that the WT method can be successful for velocity models that cause ray tracing methods to fail. The second paper attempts to improve the model resolution of the WT method by using both traveltime and waveform information simultaneously. We call this method wave equation traveltime and waveform inversion (WTW) and its advantage is that it retains the merits of both traveltime inversions and full wave inversions. That is, robust convergence and high resolution. The third paper proposes a method to compute paths (wavepaths) along which bandlimited seismic waves propagate. The bandlimited wavepaths describe the physical processes of wave propagation more realistically than high frequency raypaths. The concept of the wavepaths is a useful and intuitive tool for understanding the paths used for the back-propagation of data residuals in the WT and WTW methods.