Ambient noise full waveform inversion for noise source distribution

We use full waveform inversion of ambient noise to estimate noise source distributions and model parameters. We derive the sensitivity kernel with respect to a noise source distribution from ambient noise data. To evaluate the capability of the algorithm, we perform several numerical examples. Our approach is to a simulate propagation of a diffusive wavefield and to calculate interstation correlograms. Waveform differences are used to measure differences between predicted correlograms, and correlation functions computed from observed seismic recordings. This measurement is used as a adjoint source to propagate the adjoint wavefield, and to calculate the associated gradients. Due to the low resolution and accuracy, we apply L1 model regularization in the Fourier domain to constrain the inversion result and remove artifacts. As with conventional full waveform inversion, the inversion with ambient noise information suffers from multi-parameter problems. We test the capability of ambient noise full waveform inversion with a complicated velocity model. The inversion results illustrate that full waveform inversion of ambient noise algorithm can give an accurate estimation of noise source distribution with sparse data acquisition.