Seismic waveform inversion consists of minimizing misfit between observed and calculated wavefields. Since this misfit function could be highly non-linear, the only way to be sure of arriving at the global solution is to use a Monte-Carlo search. This is feasible if the number of unknown parameters is not too large. If it is large, as is the case with the seismic inverse problems, it is extremely expensive to use the Monte-Carlo search to optimize for a single misfit function over the whole model space. However, if one uses a number of misfit functions depending up on the sensitivity of the model parameters on the data, one can implement the Monte-Carlo method efficiently. Fortunately, this is possible as the different wavelengths of the model parameters influence the different parts of the data.


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