Uncertainty analysis for infrasound waveform inversion: Application to explosion yield estimation

Abstract

While the acoustic waveform inversion method is increasingly used in geophysical acoustics to constrain source parameters, the inversion results are often provided without any uncertainty analysis. This study presents a probabilistic representation for acoustic waveform inversion and method to evaluate the inversion uncertainty using ground-truth data. A posteriori probability distribution of source estimate is described by a priori waveform misfit covariance and the variance of acoustic source model. The probabilistic framework is applied to local explosion infrasound to estimate the yields of explosions and uncertainty. Estimated yields showed overall good agreement with the true yields (less than 25% errors). The uncertainty of the estimated yield is represented by the sum of the waveform inversion uncertainty and source model uncertainty. It is shown that the yield uncertainty attributed to local infrasound inversion (within 10 km) is as small as the uncertainty caused by 10% prediction errors in the acoustic source model. These results indicate that the acoustic source model uncertainty should also be considered for accurate yield estimation and that local infrasound can be a valuable tool to understand the magnitude of the source uncertainty.

Synthetic Evaluation of Infrasonic Multipole Waveform Inversion

“…Yasur is a 361 m tall volcano in the Vanuatu archipelago that has two sub-craters separated by a crater wall, making the influence of topography on infrasound propagation notable. While infrasound source inversion methods discussed here have been applied to both anthropogenic (e.g., Kim et al, 2018Kim et al, , 2020Kim & Rodgers, 2016) and volcanic explosions (e.g., Diaz-Moreno et al, 2019;Fee et al, 2017;Iezzi et al, 2019;Kim et al, 2015), we chose to use an idealized volcanic explosion represented by a Blackman-Harris window function as the example source in this study, as volcanic topography and potential source time functions are likely more complex. We note that for this type of study, the input source characteristics and choice of topographic variability (as represented by a digital elevation model, DEM) are significantly less important than our ability to recover the input source time functions for a given network geometry.…”

“…We note that even when studies attempt to account for the effects of topography, inaccuracies in the topography model used may still be present that limit the accuracy of the 3-D Green's functions. 3-D Green's functions that account for the effects of topography (and atmospheric conditions) allow for source inversions to yield a better characterization of the acoustic source (Diaz-Moreno et al, 2019;Fee et al, 2017;Iezzi et al, 2019;Kim et al, 2015Kim et al, , 2018Kim & Rodgers, 2016).…”

Seismoacoustic Analysis of Chemical Explosions at the Nevada National Security Site

“…Acoustic signals at local distance, here defined as within 15‐km propagation distance (Kim & Rodgers, ), are inverted for acoustic source time functions which represent expanding volume of air at detonation and can be used as a proxy for explosion energy (Kim & Rodgers, ). Details of the acoustic waveform inversion and associated probability representation were described in Kim et al (), Kim, Rodgers, & Wright, (), and Kim and Rodgers (). Here we briefly review the key equations for yield estimation.…”

“…This model relates air‐blast impulses to scaled distances and scaled height‐of‐burst in a hard rock setting. While the KG85 model can constrain only explosion yields by assuming detonations on the surface (Kim & Rodgers, ; Kim, Rodgers, & Wright, ), the acoustic impulse model in this study allows for the determination of both explosion yield and height‐of‐burst simultaneously. Unlike the scaled displacement of seismic waves, the relation for the scaled impulse includes scaling factors for ambient pressure ( P ) and temperature ( T ; Sachs, ).…”

“…Here we assumed a 20% error in the observed impulse ( I obs ) to estimate the variance for FSE. Full 3‐D waveform simulation with local atmospheric data can provide fairly accurate signal prediction at local distance (<10 km) reducing the uncertainty of waveform inversion (Kim, Rodgers, & Seastrand, ; Kim, Rodgers, & Wright, ). Errors in the empirical source model (equation ) has not been fully explored yet.…”