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| Fig. 1: An aerial view of the Nevada testing site. (Source: Wikimedia Commons) |
Underground nuclear tests release large amounts of energy in a very short time, producing seismic waves that can be detected at regional and even global distances. Because these signals resemble those generated by natural earthquakes, seismology has become one of the most important tools for nuclear test monitoring and treaty verification. In particular, seismic observations can be used not only to detect a suspicious event, but also to infer whether it was likely caused by a nuclear explosion and to estimate its approximate yield. However, these tasks are not straightforward, since the recorded signal depends not only on the explosion itself but also on the surrounding geological conditions.
Before we dive into earthquakes and nuclear explosions, it is helpful to understand a few terminologies in earthquake studies first. Seismic waves are generally divided into two main categories: surface waves and body waves. Surface waves travel along the earth's surface. Within the surface wave category, the relevant wave type is called a Rayleigh wave, in which the surface wave travels and causes the ground to move in an elliptical, rolling motion.
For body waves, they travel through earth's interior. There are two types of body waves: P-wave and S-wave. P-wave stands for compression wave. A compression wave causes the particles to move parallel to the direction of wave propagation. Think of a compression spring that is oscillating and traveling in the same direction as its compression/extension. S-wave stands for shear wave. A shear wave causes the particles to move perpendicular to the wave propagation direction. Visually, S-wave is similar to the Battle Ropes you see in any gym.
The body-wave magnitude, mb, is determined from the amplitude and period of body waves (typically P-waves), with empirical corrections applied for epicentral distance (the horizontal surface distance from an earthquake's epicenter to a specific seismometer) and source depth. The surface-wave magnitude, Ms, is determined from the amplitude and period of surface waves (typically Rayleigh waves with periods around 20 sec), also with corrections for epicentral distance. The mathematical expression for mb is:
Where A is the amplitude of ground motion in microns, T is the corresponding period in seconds, and Q is a correction factor that is a function of D and h. D is the distance between epicenter and station in degrees of arc, and h is the focal depth of the earthquake in kilometers. The mathematical expression for Ms is:
Where A is the amplitude of ground motion in microns, T is the corresponding period in seconds, and D is the distance between epicenter and station in degrees of arc.
A common starting point for estimating the yield of an underground nuclear explosion from seismic data is an empirical relation of the form
where mb is the measured body-wave magnitude, Y is the explosive yield in kilotons of TNT, and A and B are constants obtained from calibration data. [1] In theory, according to this equation, yield should scale with seismic magnitude. In practice, however, the constants A and B are not universal. Analyses must be done to correct for the geology of the test site, the depth of burial, the attenuation of seismic waves along the path to the station, station-specific biases, and even damage to the rock surrounding the explosion. As a result, seismic data do not measure yield directly. Instead, they measure a signal that has already been altered by many physical processes when the signal travels from the explosion center to the seismic sensors. This is why yield estimation is typically done for each individual testing site because of their geological variations. Some published values for Nevada (Fig. 1), Shagan River, and North Korean testing sites are shown in Table 1.
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| Table 1: Estimated numerical values for constants A and B in three testing sites. [1, 2, 3]- This table requires attribution. - RBL |
Underground nuclear explosions generate seismic waves that can propagate over regional and global distances and be recorded by seismic networks worldwide. Consequently, seismic monitoring has become an essential tool for detecting potential nuclear tests and plays a key role in the verification framework of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). For this reason, the reliable discrimination of nuclear explosions from other seismic sources, such as natural earthquakes, human-induced seismicity, and quarry blasts, is very important.
One widely used seismic discrimination technique is based on the relationship between mb and Ms. [4] Because nuclear explosions and earthquakes have distinct source mechanisms - isotropic volume expansion for nuclear explosions versus double-couple shear faulting for earthquakes - their radiated wavefields differ substantially. [5] Explosions typically generate relatively weak shear motion compared with compressional waves, leading to smaller surface waves, thus a higher mb-to-Ms ratio compared to regular earthquakes. This mb-Ms relationship is currently one of the experimental event-screening criteria used by the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO).
Additional discrimination approaches include analyzing the event depth and source location, as underground nuclear tests generally occur at shallow depths and in specific testing areas. Furthermore, the first motion of observed seismic waves can provide further diagnostic information about the source mechanism. [6] More recently, machine learning techniques have been introduced to improve the classification of seismic events. These methods utilize various features such as mb, Ms, and spectral ratios to distinguish explosions from earthquakes, and they have demonstrated improved accuracy compared to traditional analysis. [7,8]
Seismic monitoring provides a powerful way to study underground nuclear explosions from far away. The empirical relation between body-wave magnitude and yield offers a useful method for estimating explosive power, but the constants in that relation depend strongly on local geological and observational conditions. As a result, yield estimation is not a simple direct measurement, but a calibrated inference determined by a number of factors. At the same time, seismic discrimination methods make it possible to distinguish nuclear explosions from natural earthquakes by taking advantage of their different source mechanisms and wave-generation patterns. Together, these ideas show both the strength and the limitation of seismic analysis. It is a useful tool for nuclear test monitoring and yield estimation, but accurate results can only be determined after considerable experiments, empirical data, and calculations.
© Jason Ye. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] E. P. Chael, "Local Magnitudes of Small Contained Explosions," Sandia National Laboratory, SAND2009-7941, January 2010.
[2] F. Ringdal, P. D. Marshall, and R. W. Alewine, "Seismic Yield Determination of Soviet Underground Nuclear Explosions at the Shagan River Test Site," Geophys. J. Int. 109, 65 (1992).
[3] D. P. Voytan et al., "Yield Estimates For the Six North Korean Nuclear Tests From Teleseismic P Wave Modeling and Intercorrelation of P and Pn Recordings," J. Geophys. Res.d Solid Earth 124, 4916 (2019).
[4] D. Bowers and W. R. Walter, "Discriminating Between Large Mine Collapses and Explosions Using Teleseismic P Waves," Pure Appl. Geophys. 159, 803 (2002).
[5] S. R. Ford, D. S. Dreger, and W. R. Walter, "Source Analysis of the Memorial Day Explosion, Kimchaek, North Korea," Geophys. Res. Lett. 36, L21304 (2009).
[6] P. G. Richards, "Seismic Monitoring of Nuclear Explosions," in Encyclopedia of Solid Earth Geophysics, ed. by H. K. Gupta (Springer, 2011)
[7] S. H. Elkhouly and G. Ali, "Seismic Discrimination Between Nuclear Explosions and Natural Earthquakes using Multi-Machine Learning Techniques," Pure Appl. Geophys. 182, 4879 (2025).
[8] A. Pignatelli, "Deciphering Earth's Tremors: A Machine Learning Approach to Distinguish Earthquakes From Explosions," J. Seismol. 29, 525 (2025).
