TY  - JOUR
A1  - Esfahani, Reza Dokht Dolatabadi
A1  - Gholami, Ali
A1  - Ohrnberger, Matthias
T1  - An inexact augmented Lagrangian method for nonlinear dispersion-curve inversion using Dix-type global linear approximation
JF  - Geophysics
N2  - Dispersion-curve inversion of Rayleigh waves to infer subsurface shear-wave velocity is a long-standing problem in seismology. Due to nonlinearity and ill-posedness, sophisticated regularization techniques are required to solve the problem for a stable velocity model. We have formulated the problem as a minimization problem with nonlinear operator constraint and then solve it by using an inexact augmented Lagrangian method, taking advantage of the Haney-Tsai Dix-type relation (a global linear approximation of the nonlinear forward operator). This replaces the original regularized nonlinear problem with iterative minimization of a more tractable regularized linear problem followed by a nonlinear update of the phase velocity (data) in which the update can be performed accurately with any forward modeling engine, for example, the finite-element method. The algorithm allows discretizing the medium with thin layers (for the finite-element method) and thus omitting the layer thicknesses from the unknowns and also allows incorporating arbitrary regularizations to shape the desired velocity model. In this research, we use total variation regularization to retrieve the shear-wave velocity model. We use two synthetic and two real data examples to illustrate the performance of the inversion algorithm with total variation regularization. We find that the method is fast and stable, and it converges to the solution of the original nonlinear problem.
Y1  - 2020
U6  - https://doi.org/10.1190/GEO2019-0717.1
SN  - 0016-8033
SN  - 1942-2156
VL  - 85
IS  - 5
SP  - EN77
EP  - EN85
PB  - Society of Exploration Geophysicists
CY  - Tulsa
ER  -