Deep Learning for Low-Frequency Extrapolation of Multicomponent Data in Elastic FWI

Full waveform inversion (FWI) strongly depends on an accurate starting model\nto succeed. This is particularly true in the elastic regime: The cycle-skipping\nphenomenon is more severe in elastic FWI compared to acoustic FWI, due to the\nshort S-wave wavelength. In this paper, we extend our work on extrapolated FWI\n(EFWI) by proposing to synthesize the low frequencies of multi-component\nelastic seismic records, and use those "artificial" low frequencies to seed the\nfrequency sweep of elastic FWI. Our solution involves deep learning: we\nseparately train the same convolutional neural network (CNN) on two training\ndatasets, one with vertical components and one with horizontal components of\nparticle velocities, to extrapolate the low frequencies of elastic data. The\narchitecture of this CNN is designed with a large receptive field, by either\nlarge convolutional kernels or dilated convolution. Numerical examples on the\nMarmousi2 model show that the 2-4Hz low frequency data extrapolated from\nband-limited data above 4Hz provide good starting models for elastic FWI of\nP-wave and S-wave velocities. Additionally, we study the generalization ability\nof the proposed neural network over different physical models. For elastic test\ndata, collecting the training dataset by elastic simulation shows better\nextrapolation accuracy than acoustic simulation, i.e., a smaller generalization\ngap.\n