Multi-parameter acoustic least-squares migration through the multi-parameter Hessian operator

Least-squares migration (LSM) offers significant advantages in producing high-resolution seismic images with accurate amplitude fidelity compared to conventional migration techniques. However, data-domain LSM faces substantial computational challenges due to the iterative application of forward and migration operators. To overcome this, we propose an efficient multi-parameter LSM imaging method that balances imaging quality and computational efficiency by directly deconvolving the migrated image. The technique explicitly computes the multi-parameter Hessian matrix within an inversion framework and solves it using a regularization-based technique. By assuming a band-dominant structure for each component of the Hessian, the computational cost is significantly reduced, making the method highly efficient for iterative solvers. Furthermore, the division-based migration and Hessian operators are used to accelerate convergence and enhance inverted images. The proposed method is validated through synthetic and field data examples. We show that the proposed algorithm is an efficient and practical alternative to the computationally expensive data-domain multi-parameter LSM. Furthermore, we show that it can effectively recover high-resolution, true-amplitude velocity and density images by mitigating amplitude distortions and limited-bandwidth blurring effects, demonstrating significant improvements over conventional migration techniques. This study highlights the potential of the proposed method to deliver computationally efficient and high-fidelity seismic imaging solutions.