Browsing by Author "Sun, Dong"

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    A Nonlinear Differential Semblance Algorithm for Waveform Inversion
    (2013-07-24) Sun, Dong; Symes, William W.; Heinkenschloss, Matthias; Zhang, Yin; Zelt, Colin A.
    This thesis proposes a nonlinear differential semblance approach to full waveform inversion as an alternative to standard least squares inversion, which cannot guarantee a reliable solution, because of the existence of many spurious local minima of the objective function for typical data that lacks low-frequency energy. Nonlinear differential semblance optimization combines the ability of full waveform inversion to account for nonlinear physical effects, such as multiple reflections, with the tendency of differential semblance migration velocity analysis to avoid local minima. It borrows the gather-flattening concept from migration velocity analysis, and updates the velocity by flattening primaries-only gathers obtained via nonlinear inversion. I describe a general formulation of this algorithm, its main components and implementation. Numerical experiments show for simple layered models, standard least squares inversion fails, whereas nonlinear differential semblance succeeds in constructing a kinematically correct model and fitting the data rather precisely.
  • Thumbnail Image
    Item
    A Nonlinear Differential Semblance Strategy for Waveform Inversion: Experiments in Layered Media
    (2009-04) Sun, Dong; Symes, William W.
    This paper 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, we formulate waveform inversion as a differential semblance optimization (DSO) problem with artificial low-frequency data as control variables. This version of differential semblance with nonlinear modeling properly accounts 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.
  • Thumbnail Image
    Item
    IWAVE Implementation of Adjoint State Method
    (2010-03) Sun, Dong; Symes, William W.
    Adjoint state method is a well-known method to efficiently compute the gradient of a cost or objective function for a simulation-driven optimization problem. Essentially, it computes the adjoint action of Born operator (the linearized forward map) on any given vector. This report presents a derivation of adjoint state algorithm for an acoustic system discretized by staggered grid finite difference schemes, and discusses its implementation based on the modeling package IWAVE. Our goal is to construct a C++ wrapper of IWAVE, which fits into a general framework for inversion. This report is the second of several describing an implementation of such a wrapper.
  • Thumbnail Image
    Item
    IWAVE Implementation of Born Simulation
    (2010-03) Sun, Dong; Symes, William W.
    The single-scattering (or Born) approximation is the most fundamental assumption shared by all seismic imaging methods, and plays a crutial role in the non-linear waveform inversion, an iterative process of linearized inversions. The Born simulator (linearized forward map) shares a computational core with the corresponding simulator (forward map), which has been well implemented in the modeling package IWAVE. This report focuses on implementing the Born simulator based on IWAVE, and reviews the main adaptations we made in IWAVE to accommodate such an implementation in C++. Our goal is to construct a C++ wrapper of IWAVE, which fits into a general framework for inversion. This report is the first of several describing an implementation of such a wrapper.
  • Thumbnail Image
    Item
    The nonlinear differential semblance algorithm for plane waves in layered media
    (2008) Sun, Dong; Symes, William W.
    This 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.
  • Thumbnail Image
    Item
    The Nonlinear Differential Semblance Algorithm for Plane Waves in Layered Media
    (2009-04) Sun, Dong
    This paper 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 nonlinear modeling that may properly accounts 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.