Full-waveform inversion (FWI) is now often used to retrieve high-resolution velocity models in marine datasets. Directly matching the predicted data with the recorded ones at the sensor locations, results in a highly nonlinear optimization problem. Besides its inherent high nonlinearity (manifested in one form in the cycle-skipping problem), considering the anisotropic reality of the true Earth, a multi-parameter inversion imposes additional Null space and the tradeoff issues. To solve these problems, we formulate an optimization problem referred to as an efficient wavefield inversion (EWI) to retrieve multi-parameters. EWI uses background models to reconstruct the wavefield efficiently by introducing an enhanced source function (which includes secondary sources). In this setup, the inversion for the wavefield is linear and efficient. The anisotropic parameters are inverted in a separate direct optimization using the wavefield and the enhanced source function in an efficient matter (no modeling involved). We demonstrate the effectiveness of the proposed method on an Australian marine real data, and compare inverted results with check shot velocity information from a well.