Data-driven redatuming and compressive sensing in complex media for subsurface monitoring

Seismic imaging of subsurface structures situated deep beneath complex overburden structures, such as sub-salt, remains challenging for researchers. However, the Marchenko method has offered a new and promising perspective on data-driven redatuming. While it has proven successful for media characterized by smoothly varying interfaces, it has shown only moderate success for complex media. To address this limitation, we present an alternative form of the Marchenko representation that retrieves only the unknown perturbations to both focusing functions and redatumed fields using a scattering framework. A second redatuming step is then used to reconstruct a local virtual response at a preset datum level, leveraging multidimensional deconvolution. We reformulate the problem in the time domain, which was previously believed to be computationally intractable, and introduce several physical constraints that naturally drive the inversion towards a reduced set of reliable and stable solutions. By solving the problem in the time domain, we were able to successfully reconstruct the overburden-free reflection response beneath a complex salt body from noise-contaminated data. This study is supplemented with low-rank interpolation techniques that aim at enabling large-scale 3D field surveys to be considered in current production flows. We propose a novel transform domain revealing the low-rank character of seismic data that prevents the inherent matrix enlargement introduced when the data are sorted in the midpoint-offset domain and develop a robust extension of the current matrix completion framework to account for lateral physical constraints that ensure a degree of proximity similarity among neighbouring points.