Reduced-order modeling for complex 3D seismic wave propagation

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 3D models of the Earth's elastic structure, 3D 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. Here, we use a reduced-order model (ROM) approach that enables the rapid evaluation of approximate Green's functions. The ROM technique developed approximates three-component surface velocity wavefields obtained from numerical simulations of seismic wave propagation. We apply our ROM approach to a 50 km x 40 km area in the greater Los Angeles area accounting for topography, site effects, 3D subsurface velocity structure, and viscoelastic attenuation. The ROM constructed for this region enables rapid computation (0.001 CPU hours) of complete, high-resolution, 0.5 Hz surface velocity wavefields that are accurate for a shortest wavelength of 1.0 km. Using leave-one-out cross validation, we measure the accuracy of our Green's functions in both the time-domain and frequency-domain. Averaged across all sources and receivers, the error in the rapid seismograms is less than 0.01 cm/s. 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 Mw 5.9 Whittier Narrows earthquake as an example. We envision that our rapid, approximate Green's functions will be useful for constructing rapid ground motion synthetics with high spatial resolution.