We have solved the estimation of primaries by sparse inversion problem for a seismic record with large near-offset gaps and other contiguous holes in the acquisition grid without relying on explicit reconstruction of the missing data. Eliminating the unknown data as an explicit inversion variable is desirable because it sidesteps possible issues arising from overfitting the primary model to the estimated data. Instead, we have simulated their multiple contributions by augmenting the forward prediction model for the total wavefield with a scattering series that mimics the action of the free surface reflector within the area of the unobserved trace locations. Each term in this scattering series involves convolution of the total predicted wavefield once more with the current estimated Green’s function for a medium without the free surface at these unobserved locations. It is important to note that our method cannot by itself mitigate regular undersampling issues that result in significant aliases when computing the multiple contributions, such as source-receiver sampling differences or crossline spacing issues in 3D acquisition. We have investigated algorithms that handle the nonlinearity in the modeling operator due to the scattering terms, and we also determined that just a few of the terms can be enough to satisfactorily mitigate the effects of near-offset data gaps during the inversion process. Numerical experiments on synthetic data found that the final derived method can significantly outperform explicit data reconstruction for large near-offset gaps, with a similar computational cost and better memory efficiency. We have also found on real data that our scheme outperforms the unmodified primary estimation method that uses an existing Radon-based interpolation of the near-offset gap.

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