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SUMMARY Elastodynamic Green’s functions are an essential ingredient in seismology as they form the connection between direct observations of seismic waves and the earthquake source. They are also fundamental to various seismological techniques including physics-based ground motion prediction and kinematic or dynamic source inversions. In regions with established 3-D models of the Earth’s elastic structure, such as southern California, 3-D Green’s functions can be computed using numerical simulations of seismic wave propagation. However, such simulations are computationally expensive, which poses challenges for real-time ground motion prediction and uncertainty quantification in source inversions. In this study, we address these challenges by using a reduced-order model (ROM) approach that enables the rapid evaluation of approximate Green’s functions. The ROM technique developed approximates three-component time-dependent surface velocity wavefields obtained from numerical simulations of seismic wave propagation. We apply our ROM approach to a 50 km $$\times$$ 40 km area in greater Los Angeles accounting for topography, site effects, 3-D subsurface velocity structure, and viscoelastic attenuation. The ROM constructed for this region enables rapid computation ($$\approx 0.0001$$ CPU hr) of complete, high-resolution (500 m spacing), 0.5 Hz surface velocity wavefields that are accurate for a shortest wavelength of 1.0 km for a single elementary moment tensor source. Using leave-one-out cross validation, we measure the accuracy of our Green’s functions for the CVM-S velocity model in both the time domain and frequency domain. Averaged across all sources, receivers, and time steps, the error in the rapid seismograms is less than 0.01 cm s−1. We demonstrate that the ROM can accurately and rapidly reproduce simulated seismograms for generalized moment tensor sources in our region, as well as kinematic sources by using a finite fault model of the 1987 $$M_\mathrm{ W}$$ 5.9 Whittier Narrows earthquake as an example. We envision that rapid, accurate Green’s functions from reduced-order modelling for complex 3-D seismic wave propagation simulations will be useful for constructing real-time ground motion synthetics and source inversions with high spatial resolution.