Full waveform inversion aims to find the high-resolution subsurface model parameters. It is usually treaded as a nonlinear least square problem, and the minimum of the related misfit function is found by updating the model parameters. Simple gradient methods could mix different parameter types in the case of inversion with multi-parameter classes, which could lead to a poor convergence and strong dependence on the scaling of the different parameter types. Searching the step length in a subspace domain instead of treating the gradients of different parameters as the same could help solving this problem. The subspace used can be defined in a span of different sets of data or different parameter classes, which is a small amount of vectors compared to the whole model space. Using the subspace method, the basis vectors are needed to be defined first, and a local minimum is found in the spanned space to invert the perturbations. We are investigating this method to get a better update of density.
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