Simple frequency domain full-waveform inversion (FWI) regularized by Sobolev space norm

(c) Vladimir Kazei and Oleg Ovcharenko (KAUST, 2019)

Helmholtz solver is a submodule, so clone with: git clone --recursive https://github.com/vkazei/fastFWI.git

Full-waveform inversion

Standard L2 full-waveform inversion
||D(m)-D_obs||^2 + F_reg(m_0, m) is minimized
where D_obs is the observed data D(m) is the data modeled in the model m
m is current model
m_0 is the starting model F_reg is the regularizing functional

generic FWI implementation (misfit functional and gradient) is based on SimpleFWI by Tristan van Leeuwen LBFGS-B-C optimization implementation by Stephen Becker

Sobolev space norm regularization

We add regularizing functional equivalent to Sobolev space norm for F_reg = ||m||_{W¹_p}.
Kazei et al., 2017 It can also be applied as a regularizing

Example

We demonstrate an application of FWI to Marmousi II benchmark velocity model. We initiate inversion from a linear velocity model and search for updates of model parameters by L-BFGS.

vladimir.kazei@kaust.edu.sa