Least-squares reverse time migration based on second-order Born approximation

Abstract Least-squares reverse time migration (LSRTM) improves seismic image resolution by iteratively minimizing the data misfit between observed and simulated wavefields. However, conventional LSRTM methods based on the first-order Born approximation fail to account for multiple scattering, limiting their ability to resolve steeply dipping structures and small-scale features. To address this, we adopt the second-order Born approximation to more accurately model nonlinear wave propagation effects. Meanwhile, first-order gradient-based optimization algorithms often struggle to converge under this increased nonlinearity. To overcome this issue, we incorporate a truncated Gauss–Newton (TGN) scheme that leverages curvature information of the objective function. The gradient is derived using the first-order adjoint-state method, while the Hessian-vector product is obtained via the second-order adjoint-state method. A matrix-free conjugate gradient algorithm is then used in an inner loop to compute the Gauss–Newton update direction. Numerical experiments show that the proposed LSRTM-SOB-TGN method produces more focused images with higher resolution and reduced artifacts compared to conventional LSRTM and second-order Born methods using first-order optimization. These results illuminate the benefits of jointly considering second-order Born approximation and Hessian effects to enhance LSRTM performance in complex geological settings.