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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.
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This content will become publicly available on December 20, 2025
A direct reconstruction method for radiating sources in Maxwell’s equations with single-frequency data
Abstract This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell’s equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad applications, such as antenna synthesis and design, medical imaging, and pollution source tracing. We introduce new imaging functions and a computational algorithm to determine the number of point sources, their locations, and associated moment vectors, even when these vectors have notably different magnitudes. The number of sources and locations are estimated using significant peaks of the imaging functions, and the moment vectors are computed via explicitly simple formulas. The theoretical analysis and stability of the imaging functions are investigated, where the main challenge lies in analyzing the behavior of the dot products between the columns of the imaginary part of the Green’s tensor and the unknown moment vectors. Additionally, we extend our method to reconstruct small-volume sources using an asymptotic expansion of their radiated electric field. We provide numerical examples in three dimensions to demonstrate the performance of our method.
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- Award ID(s):
- 2208293
- PAR ID:
- 10633196
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Inverse Problems
- Volume:
- 41
- Issue:
- 1
- ISSN:
- 0266-5611
- Page Range / eLocation ID:
- 015003
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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