The knowledge of the Earth subsurface poses economic, environmental, human and sci- entiic issues. Seismic imaging is a procedure to image the Earth subsurface from the data observed at the surface. In the context of hydrocarbon exploration, seismic imaging techniques are widely used to characterise the irst few kilometres of the Earth¡¯s interior. Full Waveform Inversion (FWI) is one of the eicient seismic imaging method. Recent ad- vances in high performance computer make FWI feasible for large applications. In theory, FWI could reconstruct a high-resolution subsurface image provided that low frequency and wide angle/aperture/azimuth data are available. FWI is a data-itting procedure and is resolved as an optimization problem. Depending on the frequency content of the data, the objective function of FWI may be highly nonlinear and has many local minima. If a data set mainly contains relections, this problem particularly prevents the gradient-based methods from recovering the long wavelengths of the velocity model.
The model of the subsurface could be separated into two parts by scale separation. One part is the short-wavelength part which contains the singularities of the model and the other part is the long-wavelength part which is a smooth version of the model. In this thesis, I propose a variant of FWI based on the scale separation of these two parts to mitigate the nonlinearity of the problem.
In the irst section, methodologies of the conventional FWI and the new proposed method are presented. The new method is a Relection-based Waveform Inversion (RWI) method . It consists of decomposing the gradient of FWI into a short-wavelength part and a long-wavelength part and the inversion is performed in an alternating fashion between these two parts. The gradient decomposition is achieved by decomposing the waveields into their one-way components. Diferent waveield decomposition methods are also pre- sented.
In the second section, we implement the FWI and the new method to several case studies. For numerical modeling, we use a inite-diference approach to resolve the acoustic wave equation with constant density in the time domain. The model update is based on the L-bfgs algorithm and the waveield is decomposed using the 2D FFT-based method in the ?-? domain. These case studies show the diiculties associated with FWI to recover the long-wavelength part of the velocity model when low frequency and large-ofset data are absent, and the initial model is far from the true one. The new method shows its robustness in this case especially for constructing the long-wavelength model.