An Efficient Subspace Detector for Rayleigh Waves, Demonstrated Against Explosions

ABSTRACT We present a new set of Rayleigh-wave detection algorithms (a module) that we derive from two competing, approximate models for elliptically polarized seismic data. This module processes three-component seismograms with sliding windows to output estimates of test statistics and source back azimuths that it can combine from multiple frequency bands. The module automatically adjusts declaration thresholds to maintain a fixed false alarm rate against noise and adapts its sliding window lengths to include a fixed number of waveform cycles per frequency band. We demonstrate these capabilities against real Rayleigh waves that are sourced from airborne explosions in Ukraine. The module shows reliable detection rates against explosions and reasonable estimates of source back azimuths at computational costs akin to those of power detectors. Performance curves show that the detection module exceeds a 0.80 true positive detection rate against a real, ∼75 kg Trinitrotoluene yield equivalent source at ranges of 25 km. Back-azimuthal estimates achieve mean errors of ∼3° with median absolute deviations of ∼10°. Our module thereby demonstrates a capability to automatically detect and directionally locate airborne explosions from three-component seismic data, simultaneously. Plain Language Summary: Rayleigh waves are a type of seismic surface wave that moves each point on the ground in the shape of an ellipse. This article develops and tests a new set of algorithms, or a module, to detect such Rayleigh waves with sensors that record ground motion in the east, north, and vertical directions. Our module operates like the scan feature of traditional car radios, but against seismic data. During its “scan” operation, our module consistently tests a fixed number of waveform cycles for Rayleigh-wave motion and adjusts its sensitivity to falsely trigger fewer than a set number of times per year. Our module also estimates the direction from which the source of this motion came. We test our module against data that we predict from airborne explosion simulations and from real explosions recorded in Ukraine. We thereby detect real events with the energy of about 75 kg of Trinitrotoluene explosive from 25 km away, about 80 out of 100 times. We also correctly estimate the direction back to the source within about 10°. Our article and its supplemental material provide the mathematics, physics, and some data required to understand and use this module.