Constrained optimization schemes for geophysical inversion of seismic data

Many experimental techniques in geophysics advance the understanding of Earth processes by estimating and interpreting Earth structure (e.g., velocity and/or density structure). These techniques use different types of geophysical data which can be collected and analyzed separately, sometimes resulting in inconsistent models of the Earth depending on data quality, methods and assumptions made. This dissertation presents two approaches for geophysical inversion of seismic data based on constrained optimization. In one approach we expand a one dimensional (1-D) joint inversion least-squares (LSQ) algorithm by introducing a constrained optimization methodology. Then we use the 1-D inversion results to produce 3-D Earth velocity structure models. In the second approach, we provide a unified constrained optimization framework for solving a 1-D inverse wave propagation problem. In Chapter 2 we present a constrained optimization framework for joint inversion. This framework characterizes 1-D Earth\u27s structure by using seismic shear wave velocities as a model parameter. We create two geophysical synthetic data sets sensitive to shear velocities, namely receiver function and surface wave dispersion. We validate our approach by comparing our numerical results with a traditional unconstrained method, and also we test our approach robustness in the presence of noise. Chapter 3 extends this framework to include an interpolation technique for creating 3-D Earth velocity structure models of the Rio Grande Rift region. Chapter 5 introduces the joint inversion of multiple data sets by adding delay travel times information in a synthetic setup, and leave the posibility to include more data sets. Finally, in Chapter 4 we pose a 1-D inverse full-waveform propagation problem as a PDE-constrained optimization program, where we invert for the material properties in terms of shear wave velocities throughout the physical domain. We facilitate the implementation and comparison of different constrained optimization methods, through a unified affine invariant approach that incorporates inequality constraints for solving the inverse problem. We expect to contribute in broadening the use of constrained optimization algorithms to solve geophysical inverse problems