Graduate and Postdoctoral Studies
Computational and Applied Mathematics
Nonlinear Waveform Inversion with Surface-Oriented Extended Modeling
Monday, March 27, 2017
to 5:00 PM
1049 Duncan Hall
This thesis investigates surface-oriented model extension approach to nonlinear
full waveform inversion (FWI).
Conventional least-squares (LS) approach is capable of reconstructing highly
detailed models of subsurface. Resolution requirements of the realistic problems
dictate the use of local descent methods to solve the LS optimization problem.
However, in the setting of any characteristic seismic problem, LS objective functional
has numerous local extrema, rendering descent methods unsuitable when
initial estimate is not kinematically accurate.
The aim of my work is to improve convexity properties of the objective
functional. I use the extended modeling approach, and construct an extended
optimization functional incorporating differential semblance condition. An important
advantage of surface-oriented extensions is that they do not increase
the computational complexity of the forward modeling. This approach blends
FWI technique with migration velocity analysis (MVA) capability to recover
long scale velocity model, producing optimization problems that combine global
convergence properties of the MVA with data fitting approach of FWI. In particular,
it takes into account nonlinear physical effects, such as multiple reflections.
I employ variable projection approach to solve the extended optimization
problem. I validate the method on synthetic models for the constant density