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We presented and tested a method to invert for all wavelengths of the velocity model simultaneously from seismic reflection data. The method does not suffer from the global convergence limitations of conventional full waveform inversion. The method is based on the extension of the velocity model to subsurface offsets and on the addition of a reflection focusing objective function to the conventional FWI data-fitting objective function. The Marmousi model numerical tests indicate that the method can robustly converge to very accurate models when FWI fails. The numerical solution of the wave equation with the extended velocity is computationally expensive. The excellent results, and the computational expense, justify the search of an approximate solution that still enables the simultaneous solution for all wavelengths in the model. We present such approximation in a companion report (Almomin and Biondi, 2012).