Multi-scale inversion using wave-equation tomography and full waveform inversion

In this dissertation, I have developed a multi-scale wave-equation-based inversion strategy by combining wave-equation tomography and full waveform inversion. Wave-equation tomography aims to obtain the long-wavelength velocity model by minimizing the cross-correlation traveltime difference between real and modeled data. This method is able to explore the band-limited feature of the seismic wave-field, hence providing a better resolution than ray-based approaches. Wave-equation tomography also shares the same modeling and inversion schemes of full waveform inversion, which makes it a convenient supplement to full waveform inversion. It is straightforward to combine refraction wave-equation tomography with full waveform inversion through a hybrid misfit function. One practical issue with wave-equation tomography is window picking of the complex refraction phases, which is solved by a semi-automatic picking strategy that locates the coherent phases by maximizing the semblance. I apply the inversion strategy to a 2D deep-water seismic dataset offshore Sumatra. In order to improve the resolution of the shallow structures and to reduce the computation burden for deep-water wave-field simulation, a downward continuation process is applied to the data to map the acquisition geometry to a 4.2-km-deep horizon just above the seafloor. The new geometry after downward continuation boosts up the shallow refraction arrivals, while avoiding cumbersome modeling through the thick water column, thus reducing computation cost by 85%. The inversion result from the new dataset shows high-resolution shallow structures and the migration images illustrate the superiority of the inversion result over the conventional tomography result. The limitations of wave-equation tomography using only the refracted waves are: (1) limited lateral resolution due to the mostly horizontal traveling patterns of the refracted waves, and (2) difficulty of illuminating the deep part of the model by the refracted waves due to acquisition limitations. Therefore, reflected waves are further included in wave-equation tomography. To simulate reflected waves, long- and short-wavelength structures are separated and independently mapped into the velocity and density models, respectively. The velocity model update is constrained to long-wavelength. To match the amplitude of the reflected waves, full waveform inversion is applied to the near-offset data, where all the short-wavelength impedance contrasts are mapped into the density model. The density model is then converted to the zero-offset travel time domain in which it is invariant with respect to the change of the long-wavelength velocity model. As the velocity is updated using wave-equation tomography, density is converted back into depth domain for wave-field modeling. To alleviate the problem of nonlinearity, an offset continuation strategy is used for wave-equation tomography. Refracted waves are used first to provide vertical and shallow constraints on the velocity model, then reflected waves are included to provide lateral constraints. After wave-equation tomography has derived the satisfactory long-wavelength velocity model, FWI is used to invert all the data to retrieve the short-wavelength velocity structures. This multi-scale strategy is applied to a wide-angle towed streamer dataset. Our results show that one can recover robustly a high-resolution velocity model starting from a poorly-constrained model with the wave-equation-based inversion strategy.