An efficient wavefield inversion for transversely isotropic media with a vertical axis of symmetry

Conventional full waveform inversion (FWI) aims at retrieving a high-resolution velocity model directly from the wavefields measured at the sensor locations resulting in a highly nonlinear optimization problem. Due to the high nonlinearity (manifested in one form in the cycle-skipping problem), it is easy to fall into local minima. Considering that the Earth is truly anisotropic, a multi-parameter inversion imposes additional challenges in exacerbating the Null space problem and the parameter trade-off issue. We formulate an optimization problem to reconstruct the wavefield in an efficient matter with background models by using an enhanced source function (which includes secondary sources) in combination with fitting the data. In this two-term optimization problem to fit the wavefield to the data and to the background wave equation, the inversion for the wavefield is linear. As we keep the modeling operator stationary within each frequency, we only need one matrix inversion per frequency. The inversion for the anisotropic parameters are handled in a separate optimization using the wavefield and the enhanced source function. As velocity is the dominant parameter controlling the wave propagation, it is updated first. Thus, this reduces undesired updates for anisotropic parameters due to the velocity update leakage. We show the effectiveness of this approach in reducing parameter tradeoff with a distinct Gaussian anomaly model. We find that in using the parameterization vh, η, and ε to describe the VTI model in the inversion, we end up with high resolution and minimal tradeoff compared to conventional parameterizations for the anisotropic Marmousi model. Application on 2D real data also shows the validity of the proposed method.