Full wave inversion (FWI) has received in the last ten years a renewed interest, due to its potential ability to perform simultaneously imaging and migration velocity analysis, But it appeared quickly that its resolution by local optimization methods is hampered by the cycle skip problem unless a very good initial guess of the background velocity is available. One approach suggested to overcome this difficulty is Migration Based Travel Time (MBTT), which uses a data space change of reflectivity unknown to alleviate the cycle skip problem of FWI. The method was originally presented in the time domain and with rather obscure notations, which made it difficult to understand to a geophysical audience. The author's reading of the literature on FWI has confirmed him that the method was essentially not understood. So the objective of this talk is to present the MBTT approach and its key feature, the data space reflectivity, with unified, and hopefully more geophysical notations, and to give, as far as possible, a geophysical insight into the motivations which presided to its inception, and into the reasons which make MBTT able to determine both the long and short wavelength of the velocity starting from a poor initial velocity model.


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