We present a method to obtain a misfit function for robust waveform inversion. In this method, designated as adaptive traveltime inversion (ATI),a matching filter that matches predicted data to measured data is computed. If the velocity model is relatively accurate, the resulting matching filter is close to a Dirac delta function.Its traveltime shift,which characterizes the defocusing of the matching filter, is computed by minimization of the cross-correlation between a penalty function like t2 and the matching filter. ATI is constructed by minimization of the least square errors of the calculated traveltime shift. Further analysis shows that the resulting traveltime shift corresponds to a first-order moment, the mean value of the resulting matching filter distribution. We extend ATI to a more general misfit function formula by computing different order moment of the resulting matching filter distribution. Choosing the penalty function in adaptive waveform inversion (AWI) as t2, the misfit function of AWI is the second order moment, the variance of the resulting matching filter distribution with zero mean. Since the proposed ATI method is based on a global comparison using deconvolution, like AWI, it can resolve the
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank the associate editor F. Liu and the reviewers C. Chen and P. Williamson for their constructive comments that helped to improve the paper. The authors also thank the SWAG group for useful discussion and the resources of the shaheen supercomputing laboratory at KAUST.