The importance of data preconditioning strategies for envelope full waveform inversion methods: demonstration on marine seismic data

Envelope full-waveform inversion (EI) of seismic data has been proposed to overcome the cycle-skipping issue and recover long-wavelength velocity components for over a decade. However, we are aware of few published successful applications of EI on real data examples (except for some correlation- or phase-based EI methods). We implement EI methods (EI with Formula: see text, EI with p = 1, and improved EI) on 2D marine seismic data and find that the amplitude mismatching between the modeled and observed data is a critical factor that prevents the successful application of EI methods to real data. To match the amplitude better, we include a data weighting preconditioner in the objective function of the EI methods. The preconditioner term acts as a weighting factor to compensate for the amplitude mismatch between the observed and modeled data. We develop a method for calculating the preconditioner term using the amplitude of the head waves as a reference. Furthermore, we derive the adjoint source and gradient of the EI using the data preconditioning method. We illustrate the successful application of EI methods with the data preconditioning method using the 2D marine seismic data example. In comparison to the EI methods without the data preconditioning method, those using data preconditioning yield much more geophysically reasonable velocity models and Kirchhoff image sections and common-image gathers.