Аңдатпа
Abstract The paper develops a reliable numerical method to solve inverse dynamical problem of seismic waves’ propagation on the base of nonlinear least squares formulation which is widely known as Full Waveform Inversion (FWI). The key issue on this way is correct reconstruction of macrovelocity component of the model with input seismic data without time frequencies less than 5 – 7 Hz and reasonable source – recievers offsets. To provide correct macrovelocity reconstruction we modify regular nonlinear least squares formulation used in standard versions of FWI by decomposing the model space into two subspaces slowly varying in space functions (propagators p) which do not change direction of propagation of seismic energy, but governs travel times; sharply changing in space functions (space reflectivity r) which do not change travel time, but turn propagation direction towards acquisition. In turn this reflector is represented as application of migration operator to new unknown called time reflectivity s connecting with space reflectivity by migration operator M(p): This decomposition modifies the cost function in the following way: which opens the possibility to implement minimization with respect to propagator and reflectivity as two different step-by-step processes. We present results of comparative analysis of numerical Singular Value Decompositions for both cost functions which reveal much more sensititve of the modified one with respect to the perturbation of a space of propagators. We use the modified cost function to do the FWI for well known Marmoussi2 dataset. The numerical results are presented and discussed.