The existing conventional inversion algorithm does not provide satisfactory results due to the complexity of propagated wavefield though the gas cloud. Acoustic full waveform inversion has been developed and applied to a realistic synthetic offshore shallow gas cloudfeature with Student-t approach, with and without simultaneous sources encoding. As a modeling operator, we implemented the grid based finite-difference method in frequency domain using second order elastic wave equation. Jacobin operator and its adjoint provide a necessary platform for solvingfull waveform inversion problem in a reduced Hessian matrix. We invert gas cloud model in 5 frequency band selected from 1 to 12 Hz, each band contains 3 frequencies. The inversion results are highly sensitive to the misfit. The model allows better convergence and recovery of amplitude losses. This approach gives better resolution then the existing least-squares approach. In this paper, we implement the full waveform inversion for low frequency model with minimum number of iteration providing a better resolution of inversion results. © 2015 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved.