Micro-seismic event estimation results depend highly on the velocity accuracy. Full waveform inversion (FWI) has been employed to invert for the velocity and micro-seismic source image, simultaneously. However, conventional FWI suffers from the infamous cycle-skipping problem, which is even more serious when the source location is unknown. To mitigate this issue, we formulate an optimization problem to linearly reconstruct the wavefield in an efficient matter using the background model information and allow an enhanced source function to absorb the secondary (perturbation) source information. This reconstructed wavefield is then used to update this enhanced source function using the same background wave equation modeling operator without any inversion or update process. We then use the reconstructed wavefield to extract from the enhanced source function the parts corresponding to the micro-seismic source image and those corresponding to secondary sources (velocity perturbations), which can be used to update the model. In the outer loop iterations we repeat the processes of inverting for the source and updating the model until we achieve convergence. This process and its effectiveness is demonstrated on a complicated synthetic model and a field dataset.