Regional staining reverse time migration algorithm based on energy-constrained factors

Stained migration algorithms have the potential to enhance imaging results in specific geological structures, such as subsalt layers and steeply inclined layers, by incorporating the complex domain. However, conventional stained migration algorithms often require correct staining of the target geological body, which is challenging to achieve in practical applications, leading to inaccurate imaging results. To address this issue, we propose a novel regional staining algorithm that takes into account energy-constrained factors. First, we derive the discrete form of the complex domain wave equation and the imaging formula for the imaginary migration result. We then investigate the impact of stained region boundaries on seismic wave propagation when different migration velocities are used as input. By analyzing the energy difference between the reflected waves generated at the stained region boundary and those generated by the target geological body, we introduce positive and negative energy-constrained factors to control the interference waves caused by stained boundaries. The positive energy-constrained factor effectively filters out weak interference waves, while the negative energy-constrained factor eliminates strong interference waves. Numerical examples using a simple three-layer horizontal model and a complex salt model demonstrate that our new regional staining algorithm, based on energy-constrained factors, enhances the illumination of the target geological body and improves the imaging resolution of the target region, even when the stained areas are incorrect.