Seismic Pre-stack Inversion Using Iterative, Nonlinear Quasi-Second-Order Optimization Techniques

Abstract Seismic inversion contributes significantly to the estimation of subsurface properties based on seismic reflection data, serving as an essential step in reservoir modeling. Unlike conventional post-stack acoustic impedance inversion, this study presents a model-based nonlinear pre-stack inversion approach to estimate acoustic impedance, shear impedance, and density models, which are crucial for mapping subsurface lithofluid properties. The inversion algorithm comprises a convolutional model using a linearized amplitude versus offset approximation, the sum of squares of data misfit between theoretical model predictions and actual observations, and a Hessian-free conjugate gradient method and a nonlinear limited-memory quasi-Newton algorithm, which approximates second-order Hessian behavior, are employed to iteratively minimize the data misfit by fitting trial models to observed data. As the key novelty of this work, analytical adjoint-state gradients for acoustic (P-wave) and shear (S-wave) impedances are explicitly derived, which can eliminate the computational burden of finite-difference gradient approximations typically used in seismic inversion, while significantly improving the efficiency and scalability of large-scale seismic inversions. Meanwhile, Tikhonov and total variation regularization constraints are also applied to generate smooth estimated models for the ill-conditioned inverse problem. The proposed inversion technique is evaluated using a synthetic example based on one-dimensional well logs, a two-dimensional Marmousi model, and Troll field data from the Norwegian North Sea. Our investigations indicate that the estimated impedances and density models are accurate and stable, and the method provides good convergence to an optimal solution to the nonlinear inverse problem. A comparison of the sensitivity of the inversion results to the initial models is performed using Monte Carlo simulation and continuous ranked probability scores.