# INV

## Seminar

### Alternative formulations for full waveform inversion

Seminar Room 1, Newton Institute

#### Abstract

Classical full waveform inversion is a powerful tool to retrieve the Earth properties (P- and S-velocities) from seismic measurements at the surface. It simply consists of minimizing the misfit between observed and computed data. However, the associated objective function suffers from many local minima, mainly due the oscillatory aspect of seismic data. A local gradient approach does not usually converge to the global minimum.

We first review the classical full waveform inversion and its limitations. We then present two alternatives to avoid local minima in the determination of the background (large scale) velocity model. The first method is referred as the Normalized Integration Method (Liu et al., 2011). The objective function measures the misfit between the integral of the envelope of the signal. Because we only compare functions increasing with time, the objective function has a more convex shape.

The second method is a differential version of the full waveform inversion. This method is closely related the differential semblance optimization method (Symes, 2008) used in seismic imaging to automatically determine the Earth properties from reflected data.

We illustrate the two methods on basic 2-D examples to discuss the advantages and limitations.

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