Illumination compensation for image-domain wavefield tomography

Wavefield tomography represents a family of velocity model building techniques based on full waveforms as the input and seismic wavefields as the information carrier. When these techniques are implemented in the image domain and use seismic images as the input, they are referred to as image-domain wavefield tomography. The objective function for image-domain approach is designed to optimize the coherency of reflections in extended common-image gathers. The function applies a penalty operator to the gathers, thus highlighting image inaccuracies due to the velocity model error. Minimizing the objective function optimizes the model and improves the image quality, by making use of the gradient of the objective function computed using the adjoint-state method. Uneven illumination is a common problem for complex geological regions, such as sub-salt, or the consequence of incomplete data. Imbalanced illumination not only creates shadow zone for migrated images, but also results in defocusing in common-image gathers even when the migration velocity model is correct. This additional defocusing violates the wavefield tomography assumption stating that the migrated images are perfectly focused in the case of the correct model. Therefore, defocusing rising from illumination mixes with defocusing rising from the model errors and degrades the model reconstruction. We address this problem by incorporating the illumination effects into the penalty operator such that only the defocusing by model errors is used for model construction. This method improves the robustness and effectiveness of wavefield tomography applied in the areas characterized by poor illumination. Our synthetic examples demonstrate that velocity models are more accurately reconstructed by our method using the illumination compensation, leading to more coherent and better focused subsurface images than those in the conventional approach without illumination compensation.