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A Probability of Detection Method for Reducing Short-Period m_b–M_s False Alarm Rates

¹ Los Alamos National Laboratory
Geophysics Group, EES-11
Los Alamos, New Mexico 87545

^* Present address: Rocky Mountain Geophysics, 167 Piedra Loop, Los Alamos, New Mexico 87544, Rocky_Mountain_Geophysics@comcast.net.

The 20-sec m_b–M_s discriminant is one of the most reliable and best understood methods for identifying underground nuclear explosions. To extend the discriminant to lower magnitude thresholds at regional distances it is necessary to perform the M_s measurement at shorter periods. Although short-period Rayleigh- wave measurements have lower detection thresholds than those at 20 sec, they are more influenced by the effects of earthquake depth that cause overlap of earthquake and explosion populations. We present a technique using a probability of detection model (PXD) to estimate the probability that a surface-wave detection came from an underground explosion. The key to the method is the development of a simple analytic model to predict the maximum expected amplitude probability distribution (upper tail) from an underground explosion of a given body-wave magnitude recorded at a specified distance. The model assumes full coupling and accounts for material effects, attenuation, and amplification from tectonic release. The detection classifier is applicable when there is a signal detection above a specified signal-to-noise cutoff and the detection is of greater amplitude than the maximum expected explosion amplitude. We assume that in general, earthquakes generate larger 6- to 12-sec Rayleigh-wave amplitudes than explosions for a given body-wave magnitude. For a given sensor we define the probability of detection given that the source was an explosion. Using Bayes’ Rule we determine the probability that the signal detection originated from an explosion. The surface-wave probability of detection curve for a given period and the prior probability that an explosion occurred can also be included in the formulation.

We compute the conditional probability (represented as a p value) that the detected signal originated from an explosion. No assumptions regarding the non-explosion source are necessary other than the fact that the maximum amplitudes are expected to be greater than those from the explosion under full coupling conditions. Under the specified conditions, the p value will always be a small value indicating a low probability that the detected signal originated from an explosion. The p value can also be thought of as a random variable that can be combined with other discriminants in a multivariate setting. We show results of the signal detection formulation using short- period Rayleigh waves from earthquakes and explosions in Eurasia and compare to the traditional m_b–M_s at different periods. For a set of earthquakes and explosions recorded at WMQ measured at a 6- to 12-sec period, false alarm rates are reduced from 28.3% for m_b–M_s to 18.6% using the probability of detection model. Using PXD by itself as an earthquake identifier, 78% of all events are assigned a p value resulting in a false alarm rate of 22% that is better than m_b–M_s alone for this dataset.