Development of a full waveform inversion method for acoustic waves in the presence of wind: application to synthetic and realistic cases

Inferring a model of the wind, pressure, velocity in the atmosphere is an inverse problem, for which the state of the art methods use the travel times of acoustic waves.
We aim to solve such an inverse problem by adding more information and using a full waveform (in this case pressure variation) as infrasound observation.
In particular, we place our study in the context of an inversion of infrasound due to an explosion (or quake) in a domain, without gravity, without attenuation but with the wind as a non isotropic parameter. The addition of wind is important because wind can have an significant impact on the waveform (like the wave guide). 
To this end, we adapted the adjoint method developed in seismology to a fluid in movement : sensitivity kernels have been computed in the case of acoustics waves in the presence of wind (linearised Navier-Stokes equations).
The sensitivity kernels play the role of a gradient in an optimization framework that recovers the variation of atmospheric parameters (density, wind, pressure, speed).
Sensitivity kernels have been studied on simple and more realistic cases in 1d and 2d.
We validated the sensitivity kernels acquired by the adjoint method by comparing them with those obtained by auto-differentiation. Discontinuities near the source and receivers are observed in the sensitivity kernels. We studied the influence of source frequency on the kernels and on these discontinuities.
These encouraging results on sensitivity kernels led us to test initial synthetic inversion in 1d and 2d.
We proposed an analysis of the efficiency of the inversion depending on the choice of parametrization, conjugate gradient method and regularization term.