In this chapter we will take a brief look at several promising new developments. None of the new methods described here are as yet widely employed, and questions of viability remain for some of them. Some exciting new instruments are still in a stage of testing or exist only on the drawing board. The emphasis will be on showing the connection with the material presented in this book, rather than on a full development.

Beyond Born

Though the Born approximation improves on the ray-theoretical approximation, it also binds our hands considerably, since the amplitude of the perturbed wave δu must be much smaller than that of the zero-order wavefield in order to justify the neglect of higher-order scattering (the repeated scattering of scattered waves). Especially at higher frequency the limitations of Born theory discussed in Section 7.5 may become prohibitive. Iterative methods that start with low frequencies and slowly increase the frequency content as the model becomes more complicated may offer some relief, if ray theory can be used to model the first-order perturbation, as is done in methods like PWI. Meier et al. formulated a waveform inversion algorithm that combines 3D Born inversion with this strategy. It becomes potentially very powerful when combined with a 3D adjoint algorithm (see next section).

Encouraging progress has also been made to model the scattering of surface waves in a more complete manner.