Relative location of seismic events using broadband frequency-wavenumber analysis: Application to the North Korean Nuclear Test Site

Abstract Accurate relative location estimates for nuclear explosions can reduce greatly the uncertainty in absolute location and provide crucial additional constraints. Broadband frequency-wavenumber or f-k analysis is routinely used to estimate the direction of seismic arrivals on arrays and we show that standard implementations of f-k analysis can be applied to locating one seismic event relative to another in Cartesian geometry using the cross-correlation traces. Such relative location estimates obviate the need to estimate times of the correlation maxima explicitly. The advantages of f-k analysis over explicit time-delay measurements in array processing apply also to the relative event location problem; the contributions from poorer correlation functions are typically reduced without explicitly downweighting measurements. Using the f-k analysis implementation in ObsPy, we demonstrate the technique for the six declared DPRK nuclear tests. The locations of the six explosions, given a fixed reference event, are inverted for from the complete set of mutual relative location estimates, providing a picture consistent with the map displayed by the DPRK in May 2018. We note the sensitivity of the location estimates to the assumed propagation of the outgoing wavefield, and also that the complete set of observations with a simple 1-dimensional velocity model for the outgoing wavefield is internally inconsistent. The Cartesian vector representation of the outgoing wavefield opens for easily implemented off-azimuth empirical corrections. We also describe how to invert for relative locations directly from sets of relative time measurements. All source code, examples, solutions, and instructions are available for download from github and Zenodo.