A response-propagation decoupling framework for efficient spherical-wave reflection modeling and inversion

The characterization of seabed properties is critical for shallow-water acoustic applications. Although plane-wave reflection coefficients (PRCs) are computationally efficient for inversions, accurate forward modeling requires accounting for spherical-wave effects. However, accurate modeling of spherical-wave reflection coefficients (SRCs) requires the numerical evaluation of Sommerfeld integrals, which is computationally expensive in iterative inversion problems. Based on the distinction between medium-dependent and propagation-dependent quantities in the Sommerfeld integral, this study develops a local Taylor response-propagation decoupling framework for efficient SRC modeling. The medium-dependent PRC is locally expanded in a Taylor series, transforming the Sommerfeld integral into a finite-dimensional representation involving response-derivative vectors and reusable propagation-moment matrices. The propagation moments are independent of the seabed model parameters and can be evaluated offline for each frequency and reflection geometry using high-accuracy quadrature, while the response-expansion resolution is selected independently of the propagation-integral quadrature resolution. During inversion, only the response-derivative vectors are updated, removing oscillatory numerical integration from the online loop. Theoretical analysis and numerical simulations characterize truncation error and validate modeling accuracy. Bayesian Markov chain Monte Carlo inversions show that decoupling-induced differences in posterior estimates remain small relative to posterior uncertainties, while computation is substantially accelerated relative to conventional integration.