Full Waveform Inversion (FWI) is a powerful seismic imaging technique capable of constructing high resolution subsurface models from observed data. FWI is a nonlinear problem formulated as an optimization problem that seeks to minimize the objective function in an attempt to find values that can reduce the difference between modeled and observed data. With these models it is possible to perform seismic processing operations with greater precision. In this work, we studied strategies for frequency domain full waveform inversion (frequency inversion and small frequency bands inversion) with the Marmousi2 model in the presence and absence of noise. Additionally, a hybrid regularization based on Cauchy and Tikhonov constraints was proposed in order to balance smoothness and sparsity also in noise presence and absence situations. The tests showed a superiority in the use of small frequency bands inversion. In addition, for Marousi2, the proposed hybrid regularization was able to satisfactorily invert the initial model and is a good option for data inversions in the absence of noisy components while the Tikhonov regularization is more appropriate in the presence of noise.