Recent advances in seismic acquisition and processing allowed enhancing significantly the imaging resolution, mainly by broadening the signal bandwidth towards the lower frequencies. So far, however, frequencies lower than a few Hz cannot be obtained by standard surveys, and this gap is normally filled by estimating those components using velocity analysis. In this paper we propose a similar approach for imaging the anelastic absorption, i.e., by merging a low-frequency component given by reflection tomography with the high-frequency component derived from the instantaneous frequency. First, a macro-model in depth is built by traveltime and Q-factor tomography; then, this model is combined with the high-frequency component obtained from the depth migrated instantaneous frequency. We get so a broadband Earth model for the Q factor, using a consistent velocity field provided by the traveltime inversion of direct and reflected arrivals. This new hybrid method is applied to a 2D synthetic example.

We have developed an iterative method for simultaneous source separation (deblending) suitable for data acquired with a high blending factor. Our technique adopts the robust sparse Radon transform to define a coherence pass operator that is used in conjunction with the steepest-descent method to guarantee solutions that honor simultaneous source records. We find that an important improvement in convergence is attainable when the coherence pass projection is derived from a robust sparse Radon transform. This is a consequence of having an iterative deblending algorithm that applies intense denoising to erratic blending noise in its initial iterations. The coherence pass robust Radon operator acts as a data projection operator that preserves coherent signals and annihilates incoherent blending noise right from the start of the iterative process. We compare the algorithm with its nonrobust version and find that a coherence pass nonrobust Radon operator will only achieve high-quality results for acquisitions with a moderate blending factor.

Iterative rank-reduction implemented via Multichannel Singular Spectrum Analysis (MSSA) filtering has been proposed for data deblending. The original algorithm is based on the projected gradient descent method with a projection given by the MSSA filter. Unfortunately, MSSA filters operate on data deployed on a regular grid. We propose to adopt a recently proposed modification to MSSA, Interpolated-MSSA (I-MSSA), to deblend and reconstruct sources in situations where the acquired blended data correspond to sources with arbitrary irregular-grid coordinates. In essence, we propose an iterative rank-reduction deblending method that can honor true source coordinates. In addition, we show how the technique can also be used for source regularization and interpolation. We compare the proposed algorithm with traditional iterative rank reduction that adopts a regular source grid and ignores errors associated with allocating off-the-grid source coordinates to the desired output grid. Synthetic and field data examples show how the proposed method can deblend and reconstruct sources simultaneously.

Denoisers can help solve inverse problems via a recently proposed framework known as regularization by denoising (RED). The RED approach defines the regularization term of the inverse problem via explicit denoising engines. Simultaneous source separation techniques, being themselves a combination of inversion and denoising methods, provide a formidable field to explore RED. We investigate the applicability of RED to simultaneous-source data processing and introduce a deblending algorithm named REDeblending (RDB). The formulation permits developing deblending algorithms where the user can select any denoising engine that satisfies RED conditions. Two popular denoisers are tested, but the method is not limited to them: frequency-wavenumber thresholding and singular spectrum analysis. We offer numerical blended data examples to showcase the performance of RDB via numerical experiments.

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