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Adaptive mixed-norm seismic inversion for non-Gaussian errors

The discrepancies between geophysical measurements and forward-modelled data are commonly modelled as Gaussian errors, thereby necessitating the use of least-squares optimisation methods. However, given the many inevitable difficulties and ambiguities in data acquisition, processing, and interpretation, subsurface-property estimation from remote geophysical measurements is subject to non-Gaussian errors. We propose to minimise the misfit with a robust error measure, which is based on a generalised Gaussian distribution. A suboptimal solution is proposed through a mixed-norm functional combination of the l1 norm and l2 norm. A mixed-norm parameter is introduced to determine the relative importance between the l1 norm and l2 norm functional, which is a function of the kurtosis of the errors. The novelty of the proposed mixed-norm algorithm is that no knowledge of the seismic errors is required. The relative contributions of the l1 norm and l2 norm are adjusted based on the partially inverted elastic properties. Both synthetic and field data demonstrate the effectiveness of the proposed algorithm. Subsurface-property estimation from remote geophysical measurements is subject to non-Gaussian errors. We propose to minimise the misfit with a robust error measure, which is based on a generalised Gaussian distribution. A suboptimal solution is proposed through a mixed-norm functional combination of the l1 and l2 norms.