  Full-waveform inversion (FWI) is a high-resolution and computationally
intensive imaging technique to reconstruct unknown parameters in the
computational model in which the waves propagate; however, an accurate model of
only part of this medium is required for some applications. To decrease the
computational burden of such problems, target-oriented FWI was proposed where
the redatumed data on the part of the medium or localized solvers for the wave
equation are used. On the other hand, the classical formulation of FWI suffers
from non-linearity and ill-posedness, which makes FWI sensitive to the initial
model, the low-frequency content of the data, and limited illumination. In this
study, we propose a localized version of the alternating direction method of
multipliers (ADMM)-based FWI method, which was proposed to solve these problems
in classical FWI. In our localized FWI or LWI, the medium is decomposed into a
few subdomains, where some of them are updated, and the others are kept fixed
based on an adaptation of multi-block ADMM, which is a powerful algorithm for
solving inverse problems with decomposition and block separability. Numerical
tests on the Marmousi model for a time-lapse application confirm the
computational efficiency and robustness against background velocity model
errors.
