Tomographic full waveform inversion and linear modeling of multiple scattering |

We can achieve accurate modeling of perturbed wavefield by solving equations 5-6 instead of equations 7-8. Equations 5-6 can be solved numerically with a simple explicit method; that is, one that adds the scattered wavefield up to time to the right-hand side of equation 6 to compute the scattered wavefield at . Even in presence of large velocity variations, the scattered wavefield has now the correct time shift. Numerical solutions produce accurate results, although the scattered wavefield is still propagated with the background velocity, because multiple scattering is taken into account of.

The challenge with using these equations in a gradient-based inversion algorithm is that the relation between the scattered wavefield and the velocity perturbations is now nonlinear. In the next section, I present a method for linearizing this relation that is alternative to the conventional one represented by equations 7-8, and is based on an extension of the velocity model in time.

FWI-Norm-new
FWI norm as a function of the true velocity, when the starting velocity
is equal to 1.2 km/s.
Figure 1. | |
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FWI-Grad-new
FWI search direction as a function of the true velocity,
when the starting velocity is equal to 1.2 km/s.
Figure 2. | |
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Tomographic full waveform inversion and linear modeling of multiple scattering |

2012-10-29