We here describe the process of waveform inversion for earthquake data, by reference to inversion for 3-D structure in seismic wavespeed and density in the eastern Mediterranean region using numerical simulation with the spectral element technique. Such waveform inversion needs to start from a good initial model, using low frequencies in the first stage. As the inversion proceeds higher frequencies and additional data can be to incorporated to achieve model refinement. We also examine the issues of practical resolution assessment, and validation of proposed models.