TWO EFFICIENT STEEPEST-DESCENT ALGORITHMS FOR SOURCE SIGNATURE-FREE WAVEFORM INVERSION: SYNTHETIC EXAMPLES

摘要

We propose two methods of calculating the steepest descent direction for full waveform inversion. One is the deconvolution method, in which we construct a source-independent normalized objective function using division of wavefield in frequency domain. The other is the convolution method, using multiplication of wavefield in the frequency domain. We implemented our algorithm using a conventional back-propagation technique. However, owing to the structure of the objective functions, two different derivative wavefield terms occur. Therefore, we need to make a somewhat different formulation of the backpropagation algorithm and to define new residual terms. Through the synthetic Marmousi example, we demonstrate that our inversion algorithm can be used as an effective waveform inversion tool even though the source signature is not known.