Recent data-driven efforts have utilized spectral decomposition techniques to uncover the geometrically self-similar features of dominant energy-containing motions in high-Reynolds number flows, thereby lending support to physics-based models that are derived from the attached-eddy hypothesis. In this study, we evaluate the predictive capability of the stochastically forced linearized Navier-Stokes equations in capturing such geometric signatures of turbulent flows. We overcome the shortcomings of linearized models by considering their statistical response to judiciously designed white- and colored-in-time stochastic forcing. This allows us to perfectly capture two-dimensional energy spectra at specific wall-normal locations and to provide good predictions of two-point correlations of the turbulent velocity field that comprise the cross-spectrum. We use the latter to construct spectral filters that can decontaminate the energy of logarithmic-layer turbulence from the contributions of wall-detached and very large-scale motions and study the geometric scaling of dominant flow structures that result from this spectral coherence analysis.