3D Full Waveform Inversion: a Complex Recipe for Success

Waveform inversion has been an established technique for more than two decades<br>(Lailly 1983; Tarantola, 1984). Numerous 2D applications on synthetic and real data<br>have been published (Mora, 1988; Pratt et al., 1996, Operto et al., 2004, Sirgue and<br>Pratt, 2004). In particular, studies related to the influence of subsurface angle<br>illumination (Jannane et al., 1989, Sun and McMechan, 1992; Pratt et al., 1996;<br>Sirgue and Pratt , 2004) have demonstrated the importance of wide-angle/large offset<br>surface seismic data.<br>On the other hand, the highly non-linear nature of waveform inversion begs for the<br>need of low frequencies in the seismic data. Multi-scale strategies in either time or<br>frequency domains (Bunks et al, 1995; Forgues et al., 1998) have shown that inverting<br>initially for the low-end of the frequency spectrum may be an efficient approach for<br>the mitigation of non-linearity.<br>This need for low frequencies however may not be dissociated from the accuracy of<br>the starting model. As a result, inaccuracy of the starting model will results in more<br>demanding requirements in terms of low frequencies (Sirgue and Pratt, 2002). The<br>combination of wide-angle illumination, low frequencies and starting model hence<br>constitute the primary ingredients of a successful inversion (Sirgue, 2006). Each of<br>these ingredients plays a key role and interacts with one another in a complex<br>relationship that will depend on the geophysical problem that one is trying to solve.<br>More recently, the first examples of 3D waveform inversion were shown (Sirgue et<br>al., 2007; Ben-Hadj-Ali et al., 2007). While the extension of waveform inversion to<br>3D problems will not fundamentally change the importance of wide-angle data,<br>starting model and low frequencies, additional aspects will need to be assessed such<br>as the impact of the azimuthal coverage.