Amplitude-preserving depth-domain prestack inversion using the point-spread function (PSF) has emerged as a powerful approach for quantitative reservoir characterization. This technique employs the PSF to approximate the Hessian operator, illumination-induced blurring is compensated during imaging, thereby improving amplitude fidelity and spatial resolution. However, most existing depth-domain inversion studies have focused on poststack applications. Systematic investigations of prestack inversion—particularly for quantitative fluid characterization—remain limited. To address this limitation, we develop a depth-domain prestack inversion framework that leverages an angle-domain Gaussian-beam PSF. Under high-frequency asymptotic assumptions, we derive an analytical expression for the angle-domain Gaussian-beam PSF and compute PP-wave PSFs to approximate the local Hessian, which we incorporate directly into the inversion operator as a local-Hessian preconditioner. The framework combines a nonstationary convolution model with the Aki–Richards approximation to simultaneously invert for elastic parameters in the depth domain. Applied to a 2D marine streamer line from the Northern Viking Graben in the North Sea, the method reveals multiple low-Vp/Vs anomalies within Paleocene and Jurassic sandstones that correspond to hydrocarbon-bearing intervals identified from well data. A depth-domain ϕw (water-filled porosity) section is then constructed through a well-log-calibrated Vp/Vs–ϕw relationship established for this study area, which effectively discriminates potential hydrocarbon reservoirs. These results demonstrate that the angle-domain PSF–based depthdomain prestack inversion exhibits robust applicability and geological consistency in structurally complex rift basins, providing a novel pathway for quantitative depth-domain reservoir characterization.