Full-Waveform Inversion is a powerful seismic imaging technique capable of recovering high-resolution subsurface models from observed data. This inversion is a nonlinear problem formulated as an optimization problem that seeks to minimize the objective function in an attempt to find values that fit the modeled and observed data. With these models, it is possible to perform seismic processing operations with greater precision, such as seismic migration. In this work, we studied the frequency domain Full-Wave Inversion strategies (frequency and small frequency band inversion) with the Marmousi 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 frequency band inversion. Moreover, for Marmousi, the proposed hybrid regularization was able to satisfactorily invert the initial model and it is a good option for data inversions in the absence of noisy components while Tikhonov regularization is more appropriate in the presence of noise.