As oil and gas extraction becomes more advanced, deep-water exploration becomes increasingly focused on imaging near or under complex salt geology, which necessitates detailed velocity models with strong contrast interfaces. These interfaces can be elegantly tracked using the level sets of an implicit surface. One can invert for the velocity model that best fits the recorded data in a full-waveform inversion (FWI) style objective function by reparameterizing the model in terms of an implicit surface representation of the salt interface. With this parameterization of the FWI objective function, we find the Hessian and solve a conjugate gradient system for the Newton step at every nonlinear iteration. We sparsify the representation of the implicit surface using radial basis functions, which can hasten convergence of the inner inversion by reducing the number of model parameters. We have developed a guided inversion approach that embeds information about the certainty of different salt boundary regions by the initialization of the implicit surface slope at the salt interface. This can help guide the inversion away from perceived local minima. The results of testing this inversion workflow on a 3D Gulf of Mexico data set show that it can be a useful tool for refining salt models because the initial and final seismic images show clearer and more consistent features below the updated salt area.