Study of frequency domain full waveform inversion based on Huber norm and L-BFGS algorithm

Full waveform inversion ( FWI ) is a high resolution inversion method , which can reveal detailed in- formation of the structure and lithology under complex geological background. It is limited by many kinds of noi- ses when the method applied to the real seismic data. Based on Huber function criterion , the objective function combinates the anti-noise of L 1 norm and the stability of L 2 norm in theory , the authors derive the gradient for- mula of the Huber function by using L-BFGS algorithm for FWI. The new method is proved by synthetic seismic data with the Gaussian noise and the impulse noise. Numerical test results show that L-BFGS algorithm is ap- plied to the frequency domain FWI with the convergence speed and high calculation accuracy , and can effec- tively reduce computer memory usage ; and the Huber function is more robust and stable than L 2 norm even with the noises.