Symes, William W.2018-12-032018-12-032008Sun, Dong. "The nonlinear differential semblance algorithm for plane waves in layered media." (2008) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/103605">https://hdl.handle.net/1911/103605</a>.https://hdl.handle.net/1911/103605This thesis proposes an alternative approach to the output least-squares (OLS) seismic inversion for layered-media. The latter cannot guarantee a reliable solution for either synthetic or field data, because of the existence of many spurious local minima of the objective function for typical data, which lack low-frequency energy. To recover the low-frequency lacuna of typical data, I formulate waveform inversion into a differential semblance optimization (DSO) problem with artificial low-frequency data as control variables. To my knowledge, this approach is the first version of differential semblance with non-linear modeling that may properly account for nonlinear effects of wave propagation, such as multiple reflections. Numerical experiments with synthetic data indicate the smoothness and convexity of the proposed objective function. These results suggest that gradient-related algorithms may successfully approximate a global minimizer from a crude initial guess for typical band-limited data.79 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.GeophysicsMathematicsPure sciencesEarth sciencesThesis304510345THESIS MATH. SCI. 2009 SUN [Dong]