Constrained spatial structure reconstruction for low-frequency model building in seismic inversion

The lack of low-frequency information in seismic inversion typically necessitates supplementation with well log data. Most existing methods rely on spatial interpolation techniques to build low-frequency models. Their core assumption is spatial continuity of subsurface structures and similarity of attribute values at adjacent locations, assigning uniform weights to well logs for lateral prediction. However, these methods inadequately account for the complexity of lateral stratigraphic variations and the vertical heterogeneity of well logs. When the actual structure deviates from these assumptions or when well data reliability is insufficient, they can often lead to artifacts such as the "bull's-eye effect" and horizon mixing in the model, significantly deviating from the true geological scenario. To overcome these limitations, this paper proposes a novel low-frequency model construction method for inversion, based on spatial structure and joint sparse representation. This method abandons the traditional single-weight interpolation scheme. Instead, it innovatively employs a 2D weighted substitution of dictionary atoms for interpolation. Simultaneously, it incorporates the lateral continuity characteristics of seismic data, spatial structure information, and the vertical heterogeneity characteristics of well logs by leveraging joint sparse representation. Furthermore, it establishes an inversion-like iterative framework to achieve continuous optimization and updating of the low-frequency model.Application results on both synthetic data and actual data from a specific work area demonstrate that, compared to conventional interpolation methods, the proposed method constructs a low-frequency model with higher accuracy and greater reliability.