The estimation of the parameters of a mathematical model by data-fitting procedures goes back more than 200 years. Mathematics historians seem to agree to credit C. F. Gauss for the introduction of this idea (Gauss, 2011). In the field of exploration geophysics, Lailly (1983) and Tarantola (1984) were the first to propose the use of data-fitting techniques to estimate model parameters that control the propagation of waves in the subsurface. The concept of full-waveform inversion (FWI) was born.

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