Elastic Least-Squares Reverse Time Migration Based on Integration of the Hessian

Elastic least-squares reverse time migration (ELSRTM) effectively enhances imaging resolution and interprets multicomponent seismic data. However, traditional ELSRTM approaches, based on first-order gradient optimization methods, do not exploit the Hessian matrix, which is critical for inversion problems. To address this limitation, we propose a truncated Newton ELSRTM (TN-ELSRTM) method utilizing multiparameter Hessian-vector products to achieve efficient and high-quality seismic imaging. By neglecting the second-order nonlinear terms with minor influence in the Hessian matrix, the Gauss-Newton term is used to represent the Hessian matrix. The Hessian-vector products are computed through a single demigration and migration process, enabling the determination of the Newton update direction via a matrix-free conjugate gradient (CG) method. Implemented in a nested iterative framework, the outer loop focuses on gradient computation and model updating, while the inner loop solves for the Newton update direction in a matrix-free manner. This ensures the simultaneous minimization of misfits in the data and model spaces. Compared to traditional CG-ELSRTM, the proposed TN-ELSRTM method significantly accelerates convergence and requires fewer iterations. It effectively mitigates finite aperture effects, band-limited wavelet, geometric spreading, and multiparameter coupling. Numerical results demonstrate superior imaging quality, alleviating P- and S-wave reflectivity tradeoffs, enhancing deep illumination, expanding horizontal imaging range, increasing vertical high-wavenumber components, and improving resolution. The proposed TN-ELSRTM method produces balanced and high-resolution images for P- and S-wave reflectivity models with greater efficiency.