How Does Neural Network Reparametrization Improve Geophysical Inversion?

Full waveform inversion (FWI) is a high-resolution seismic inversion technique and great efforts have been made to mitigate the multi-solution problem, such as the traditional total variation (TV) regularization. Different from traditional regularization, a new regularization design approach named neural network (NN) reparametrization (Deep Image Prior) was presented recently. The existing NN parametrization-based FWI was implemented using an over-parametrization framework. On the contrary, we adopt an under-parameterized framework Deep Decoder (DD) and propose a new under-parameterized NN regularization framework, so-called Attention Deep Decoder (ADD). Further applying DD and ADD to seismic inversion, we propose Deep Decoder-based full waveform inversion and Attention Deep Decoder-based full waveform inversion, a new formulation of NN-FWI that uses an under-parameterized network to represent the velocity model in FWI and minimizes an objective function over the network parameters. Inspired from this formulation, NN reparametrization can be a model-domain multiscale strategy and the interpolation operator is the key component to regularize the inversion. Besides, we discover the potential relationship between interpolation-based reparametrization, traditional TV regularization and wavelet transform from the mathematical aspect. Experiments show the effectiveness of our proposal overcoming the requirement of initial model in the case of data obtained from a streamer acquisition system and lacking the low-frequency component below 10 Hz. Moreover, the comparison experiments of FWI using TV regularization, over- and under-parameterized NN regularization indicate that the proposed method might move further towards practical application and proves a way to develop inverse problems through an under-parameterized NN regularization framework.