Convolution Coding and Amplitude Attenuation-Based Full Waveform Inversion

Full waveform inversion (FWI) is a powerful method to reconstruct the properties of the subsurface media. However, the standard FWI is a non-unique and ill-posed inversion problem, which requires proper techniques to avoid cycle skipping phenomena. Sufficient low-frequencies in the observed data and a good initial model are helpful to mitigate cycle skipping problem, but they are hard to be provided in real cases. Therefore, to reduce the non-linearity and improve the convergence of FWI, we developed a novel approach inspired by using the convolutional neural network to mitigate the cycle skipping problem. We use the 1-dimentional (1-D) convolution kernels of different lengths to convolve each seismic trace of the synthetic and observed data to extract the different features of each time sample, and then we use the Sigmoid function to encode each time sample of the synthetic and observed data according to the polarity of the features. By comparing the coding similarity for the time sample of the synthetic and observed data at the corresponding time, we can identify which part of the synthetic data is well matched with the observed data and which part is mismatched. For the mismatched synthetic data, we attenuate them to reduce their interference on the gradient, thereby the cycle skipping problem can be mitigated. In this case, we use the global-correlation misfit function which behaves better in mitigating the interference of the incorrect amplitude information and highlighting the phase information with weaker non-linearity. In addition, the convolution coding and amplitude attenuation-based method has a strong anti-noise capability and can be combined with the encoded multisource scheme to save the computational costs. Marmousi model tests demonstrate that convolution coding and amplitude attenuation-based FWI behaves better than the standard FWI in generating convergent inverted result.