Seminar in Numerical Analysis: Ludovic Métivier (Université de Grenoble)

The Hessian operator in Full Waveform Inversion: quantitative imaging of complex subsurface structures

Full Waveform Inversion is an efficient seismic imaging technique for quantitative estimation of subsurface parameters such as the P-wave and S-wave velocities, density, attenuation and anisotropy parameters. The method is based on the iterative minimization of the misfit between observed and calculated data. During the past ten years, the method has been successfully applied to real data in 2D acoustic and elastic configuration, as well as in 3D acoustic configuration. The inverse Hessian operator plays an important role in the reconstruction process. Particularly, this operator should correct for illumination deficits, frequency bandlimited effects, and help to restore the correct amplitude of less illuminated parameters. In this presentation, we will focus on the methods we have to approximate this operator, from preconditioned gradient-based methods, to quasi-Newton methods (l-BFGS) and truncated Newton methods. We will present results obtained on 2D synthetic and real data for the reconstruction of P-wave velocity which illustrate the importance of the approximation of this operator. We will also present a simple illustration of the inverse Hessian operator effect in a multi-parameter framework. In this context, the operator helps to mitigate the trade-off between different classes of parameters.

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