Rapid computation of gravity anomalies and gradients using sparse decomposition in the wavenumber domain

Abstract Conventional gravity anomaly forward methods in the spatial-domain are grounded in the theoretical foundation of full-spectrum response. However, widely used gravity field spherical harmonic models such as Earth Gravitational Model (EGM) and European Improved Gravity model of the Earth (EIGEN) are finite-degree spherical harmonic expansions, inherently possessing a band-limited nature. This theoretical mismatch between the full-spectrum forward assumption and the band-limited data leads to unavoidable truncation errors, thereby compromising the accuracy and reliability of subsequent inversion. To address the above issues, this study systematically elaborates a wavenumber-domain rapid forward method for 3D gravity anomalies and their gradient tensors. By decomposing the dense Green's function matrix into the product of three sparse matrices in the wavenumber-domain, the computation workflow is straightforward. The truncation error between the wavenumber-domain and spatial-domain forward can systematically decreases as the observation points increases. The elaborated forward approach replaces the layer-by-layer calculation process with efficient sparse matrix multiplication; compared with spatial-domain methods, computational efficiency is significantly improved. The advantage of this method lies in the consistency between its inherent finite-frequency characteristics and the degree limitation of spherical harmonic models in the wave-number domain. This forward framework is more theoretically compatible with the band-limited nature of finite-degree gravity data, thereby effectively avoiding the theoretical mismatch problem inherent in traditional spatial-domain methods between the full-spectrum model and band-limited data. Therefore, the wave-number domain forward method elaborated provides a computationally efficient, low-memory, and theoretically self-consistent technical solution for processing modelling satellite, aerial, and ground-based gravity and its gradient tensor data. Graphical Abstract