Velocity Estimation with the Normalized Integration Method

In the context of velocity estimation, classical full waveform inversion suffers from many local minima. We propose an alternative method referred as the Normalized Integration Method, where the objective function measures the misfit between the integral of the square of the signal. By integrating a positive function, we only compare functions increasing with time. It appears that the objective function has a more convex shape. We first indicate how to efficiently compute the gradient of the misfit function. We then compare the new approach to the classical full waveform inversion through an application on a simple 2D synthetic data set. This example shows that the new approach can be useful for the determination of the long wavelengths of the velocity model.