Simulating seismic wave propagation through three-dimensional geological structure is computationally expensive. A single earthquake scenario in the greater Los Angeles area — 50 by 40 kilometers, incorporating topography, subsurface velocity variations, and viscoelastic attenuation — requires thousands of CPU hours to resolve. Rekoske, May, and Gabriel compress this calculation into 0.001 CPU hours by building a reduced-order model that approximates the surface velocity wavefield with errors averaging less than 0.01 centimeters per second.
The method works by precomputing a basis of representative wavefields from a set of training simulations and then projecting any new earthquake source onto this basis. The projection is fast because the basis is small — a few hundred vectors capture the essential structure of wave propagation through the known geology. The geology does not change between earthquakes. Only the source changes. The reduced-order model exploits this separation: the expensive part — encoding how waves move through heterogeneous rock — is done once and reused.
The accuracy holds for wavelengths of one kilometer and longer, which covers the frequency range most relevant to structural engineering and seismic hazard. The researchers validated the approach against the 1987 Whittier Narrows earthquake, showing that the compressed model reproduces ground motion synthetics for both moment tensor and kinematic source representations.
The through-claim extends to any field where a complex medium is interrogated repeatedly by different sources. Medical imaging, acoustic monitoring, electromagnetic sensing — all face the same computational asymmetry. The medium is fixed and expensive to characterize. The source varies and is cheap to describe. Compressing the medium into a reusable basis transforms a sequence of expensive simulations into a sequence of fast projections. The geology becomes a lookup table, and the earthquake becomes a query.