Abstract
 Top of page
 Abstract
 1 Introduction
 2 Methods
 3 Results and Discussion
 Acknowledgments
 References
 Supporting Information
[1] The ratios of noble gas radioisotopes can provide critical information with which to verify that a belowground nuclear test has taken place. The relative abundance of anthropogenic isotopes is typically assumed to rely solely on their fission yield and decay rate. The xenon signature of a nuclear test is then bounded by the signal from directly produced fission xenon, and by the signal that would come from the addition of xenon from iodine precursors. Here we show that this signal range is too narrowly defined. Transport simulations were done to span the range of geological conditions within the Nevada Test Site. The simulations assume a 1 kt test and the barometric history following the nuclear test at Pahute Mesa in March 1992. Predicted xenon ratios fall outside of the typically assumed range 20% of the time and situations can arise where the ground level signal comes entirely from the decay of iodine precursors.
1 Introduction
 Top of page
 Abstract
 1 Introduction
 2 Methods
 3 Results and Discussion
 Acknowledgments
 References
 Supporting Information
[2] On 3 October 2006, the Democratic People's Republic of Korea gave warning of its intention to conduct a nuclear test, and 6 days later claimed that one had been successfully carried out. Radioxenon isotopes were the only fission products to be measured offsite afterward and served as critical evidence that a nuclear explosion had taken place [Ringbom et al., 2009]. Anthropogenic isotopes are in fact the only definitive evidence for nuclear test and are an important component of a broader verification system [Hannon, 1985; Zuckerman, 1996]. Because of their short halflives, relatively high production yields, and ability to move through geological structures, radioxenon isotopes are ideal for verifying that a nuclear explosion has taken place [Bowyer et al., 2002, 2011; Carman et al., 2002; Saey, 2009; Van der Stricht and Janssens, 2001]. However, several xenon isotopes are also produced by other anthropogenic sources such as commercial nuclear reactors and medical isotope production [Biegalski et al., 2010; Bowyer et al., 2011; Kalinowski et al., 2010]. As a result, it is essential that the radioxenon signatures of a weapon be distinguished from those of other sources and the ratios of ^{131m}Xe, ^{133m}Xe, ^{133}Xe, and ^{135}Xe can be used to help do this.
[3] When a fission weapon detonates, it produces radioxenon directly as well as precursors that decay to xenon. What comes out of the ground is a mixture of xenon isotopes from both of these sources. Figure 1 shows the activity ratios for ^{133m}Xe/^{131m}Xe versus ^{135}Xe/^{133}Xe that would result from a ^{235}U fueled weapons test in which radioxenon precursors are absent or present [Kalinowski et al., 2010]. Here “fully fractioned” corresponds to the xenon signal that would be expected if all the isotopes that decay to xenon are lost and do not contribute to the signal. The “nonfractioned” curve refers to the xenon signal that would be expected if all the isotopes that decay to xenon are contained and contribute to the signal. Figure 1 also shows the radioxenon signature that would result from the operation of a commercial power reactor [Carman et al., 2002; Kalinowski et al., 2010; Le Petit et al., 2008]. It is currently assumed that the relative abundance of anthropogenic xenon isotopes is solely a function of how and when they were produced [Le Petit et al., 2008]. As a result, it has been suggested that a radioxenon signal that falls between the nonfractioned (red) and fully fractioned (blue) curves can be assumed to determine whether or not a nuclear weapon has been detonated [e.g., Kalinowski et al., 2010; Saey, 2009].
[4] Work done with nonradioactive tracers at the Nevada Test Site has shown that heavy gases released below ground will diffuse to cracks in the geology along which they then preferentially move to the surface. The rate of movement within cracks is itself strongly affected by variations in barometric conditions, being largest during periods of decreasing pressure [Carrigan et al., 1996, 1997]. The effect of fluctuations in atmospheric pressure on the transport of nonradioactive gasses through dry media has been modeled using a double porosity model for the medium through which the gas travels. Here a convectiondiffusion formulation is applied along with the assumption that the geology is comprised of homogenous slabs of material through which vertical cracks run—a reasonable assumption for many locations [Carrigan et al., 1996, 1997; Chen, 1989; Gringarten, 1984; Neretnieks and Rasmuson, 1984; Nilson and Lie, 1990; Nilson et al., 1991].
[5] We have extended the double porosity approach to include the effect of radioactive decay in the transport equations. Previous work with this formulation suggests that some forms of geology combine to affect xenon isotope ratios that result from wellcontained underground tests [Lowrey et al., 2012]. Here we show that the region between the fully fractioned and nonfractioned curves is in fact too narrowly defined to encompass the xenon signals that could result from a nuclear test. The xenon signature of a belowground test is more appropriately bounded by the fully fractioned curve and the signal that would come solely from the decay of iodine precursors.
2 Methods
 Top of page
 Abstract
 1 Introduction
 2 Methods
 3 Results and Discussion
 Acknowledgments
 References
 Supporting Information
[6] The positiondependent concentration of the i'th isotope is given by [Chen, 1989; Lowrey et al., 2012; Nilson and Lie, 1990]
 (1)
 (2)
[7] Here ϕ_{m} and ϕ_{f} are the matrix and fracture porosities {dimensionless}, C(x,y)_{i} is the concentration of the i'th isotope {Ci/m^{3}}, v(x,y) is the bulk flow velocity {m/s} through the matrix, D_{i} {m^{2}/s} is the diffusion coefficient of the i'th xenon isotope, λ_{i} is its decay constant {1/s}, u(x,y) is the bulk flow velocity {m/s} in a fracture centered at x, and δ is the spacing between fractures {m}. Time is expressed in seconds. Equation ((1)) describes the horizontal transport of gas in the bulk matrix medium at a given height y {m}, and equation ((2)) describes transport along a fracture where x is taken to be 0. These equations take into account diffusion and advection as well as the radioactive decay of the isotopes. The crosssectional area per unit length along the fracture is assumed for simplicity to be constant, but it could also be included as a function of depth.
[8] A similar set of coupled differential equations is used to determine the response of the pressure at each point in the model, p(x,y;t) {Pa} due to a change in the surface pressure at time t. Here a semicolon indicates that the symbol to its right is held constant
 (3)
 (4)
[9] The notation p(0,y) indicates that equation ((4)) represents the rate of change of pressure in the fracture, where the coordinate x is equal to zero. The pneumatic diffusivities of the matrix and fracture, α_{m} and α_{f}, {m^{2}/s}, are assumed to be constant at a given depth.
[10] The flow velocities, u(x,y) and v(x,y), in equations (1) and (2) are functions of the differential pressures within the cracks that arise from variations in atmospheric pressure. The diffusivity of each species is taken to be massdependent [Carrigan et al., 1996] and a function of the matrix tortuosity [Chen, 1989; Gringarten, 1984; Neretnieks and Rasmuson, 1984]. Details on how D_{i}, u(x,y), v(x,y), α_{m}, and α_{f}, are computed are given in the auxiliary material.^{1}
[11] Equations (1)–(4) are discretized by using firstorder backward differencing for firstorder derivatives and secondorder centered differencing for the secondorder diffusive operators. The discretized equations are formulated as a set of tridiagonal matrix equations. Solution of these equations for each time step is made by Gaussian elimination with periodic boundary conditions at the interior of the matrix and a closed bottom boundary. It is assumed that there is no interaction between vertical layers in the matrix, and equations (1)–(4) can therefore be solved separately for each layer, and for the fracture.
[12] Equation ((1)) is solved at every layer to find the isotopic concentrations within the matrix. The concentrations are used to compute the integral term in equation ((2)), which is solved to yield the isotopic concentrations in the fracture. The bulk flow velocities in the system are computed using the matrix pressures, which are solved for in both the matrix and the fractures using equations ((3)) and ((4)). Additional details on the computational implementation of equations (1)–(4), mesh reduction study, and benchmarking can be found in the auxiliary material.
[13] Implementation of equations ((1))–((4)) requires information on the depth of detonation, initial isotope concentration, fracture width, and spacing as well as the porosity and conductivity of the matrix material. A boundary pressure at the surface is also required (a noflux boundary condition is assumed at the bottom of the simulated geology). Detailed knowledge of the geology at the location of a suspected test site may be difficult to obtain. However, considerable information on the range of porosity, conductivity, fracture width, and fracture spacing are available for the Nevada Test Site (Table 1) [McCord, 2007]. Hourly atmospheric pressure data for the Test Site can be compiled from the weather history at the Desert Rock airfield in Mercury, Nevada. Interpolation is used to provide resolution at 1 min intervals.
Table 1. Range of Radioxenon Transport Parameters for the Nevada Test Site and Simulation Seta  Nevada Test Site Parameter Range  Parameter Set for Simulations 


Detonation Depth (m)  450–600  {450, 525, 600} 
Medium Porosity  0.01–0.05 and 0.35–0.45  {0.01, 0.05, 0.1, 0.3, 0.37, 0.45} 
Medium Permeability (m^{–2})  1e17 to 1e15  {1e17, 1e16, 1e15} 
Fracture Spacing (m)  1.0–15.0  {1.0, 2.5, 5.0, 10, 15} 
Fracture Width (mm)  0.005–1.5  {0.01, 0.1, 0.5, 1.0, 2.0} 
[14] The radioisotopes at time t = 0 (immediately after detonation) were assumed to be contained in a region of contaminated matrix. The initial concentration of each tracked isotope was determined by dividing its total quantity in Ci by the approximate volume of material vaporized in a 1 kt nuclear explosion [Carman et al., 2002]. The contaminated matrix in the model is the region between the bottom of the system (450 m depth) up to the depth of the fresh air buffer (a variable) and the initial isotope concentrations within this region were assumed to be uniform.
3 Results and Discussion
 Top of page
 Abstract
 1 Introduction
 2 Methods
 3 Results and Discussion
 Acknowledgments
 References
 Supporting Information
[15] We performed 990 separate simulations, each for a different combination of transport parameters within the Nevada Test Site. The barometric data used in the simulations were chosen to coincide with the 55 days succeeding the 26 March 1992 US test of a fission device at Pahute Mesa. Isotopic ratios were compiled from successive simulated 24 h outflow averages of xenon gas that reached the surface. Figure 2 shows the results, colorcoded by the number of days postdetonation, along with the atmospheric pressures that were recorded on each day. The wide range in isotopic ratios can be explained by source mixing and the subsurface differential transport of xenon gas.
[16] The isotopic signal seen above ground is the result of xenon that was produced directly by the fission event and a timedependent source term that results from the decay of iodine precursors. Low pressure spikes can have a significant effect by drawing gas to the surface and depleting the fission xenon. The ratios of radioxenon isotopes emitted above ground after such lowpressure periods would then be heavily influenced by xenon coming from radioiodine decay. Figure 2 shows several instances of this (beginning around day 38) where the simulated xenon ratios are pushed toward the signal that would come solely from decay of radioiodine precursors (indicated by the dashed line). In situations such as these, monitoring of downwind air samples (which would detect the purged xenon) and onsite sampling (which would detect xenon from recently decayed iodine) could produce very different signals, even if the measurements were made on the same day. Importantly, after 10 days postdetonation, none of the simulated data coincide with the radioxenon signal from a commercial light water reactor, which makes it easy to rule this source out during an onsite inspection if all four radioxenon isotopes of interest are measured.
[17] Xenon ratios that fall to the left and right of the iodine and fully fractioned lines can be explained in terms of differential transport. Decreasing atmospheric pressure will increase the rate of xenon movement into fractures as well as its upward convection within them. The individual xenon isotopes can be thought of as comprising separate, overlapping plumes. The rate at which isotopes diffuse through the geology is inversely proportional to the square root of their mass [Bird et al., 1960]. As a result, lighter xenon isotopes will travel faster than do the heavier ones. While the difference in diffusion rates is small, it will cause the leading edge of the isotope plumes to reach the surface at slightly different times. Because isotope concentrations can vary by orders of magnitude across a plume's leading edge, this can significantly skew the isotope ratios, pushing the ^{133m}Xe/^{131m}Xe and ^{135}Xe/^{133}Xe signals to the left of the iodine line. Increases in pressure would correspondingly force gases back down the fractures. Rapid fluctuations in atmospheric pressure can then set up a situation where lighter isotopes are preferentially depleted from the geology, which would push the ^{133m}Xe/^{131m}Xe and ^{135}Xe/^{133}Xe signals to the right of the fully fractioned line. In both cases the effect would be most pronounced during the first few days after a detonation, when the location of a plume's leading edge is most important, which is what is seen in Figure 2.
[18] It is clear from the simulations that geological transport of xenon gas can significantly affect the isotopic ratios that are used to determine whether or not a clandestine nuclear test has taken place. Critically, our work shows that the radioxenon signal from a 26 March 1992 test would have met the previously reported criteria for a nuclear weapon only if the test had taken place at certain locations within the Nevada Test Site. Although much of the simulation data fall within the expected range, there are many instances in which radioxenon isotope ratios are well outside of the standard domain. Verification of a nuclear weapons test under the Comprehensive NuclearTestBan Treaty [1996] can only be done through the detection of anthropogenic isotopes. The effect that geological transport has on radioxenon isotope ratios needs to be considered when using these data to determine whether or not a test has taken place. Importantly, the results of the simulations presented here show that the region between fully fractioned and nonfractioned curves is too narrowly defined to encompass the xenon signals that could result from a nuclear test. The xenon signature of a belowground test is more appropriately bounded by the fully fractioned curve and the signal that would come solely from the decay of iodine precursors. Radioxenon ratios that sit between the radioiodine and nonfractioned signal curves should be considered when evaluating data on a suspected nuclear test.
Acknowledgments
 Top of page
 Abstract
 1 Introduction
 2 Methods
 3 Results and Discussion
 Acknowledgments
 References
 Supporting Information
[19] This material is based upon work supported by the Department of Energy, National Nuclear Security Administration, under Award Number DEAC5209NA28608. Special thanks to Geoff Recktenwald for discussions about simulation methods, to Charles Carrigan for discussions about subsurface transport of noble gases and to William H. Press and Sara L. Sawyer for editorial comments and suggestions. Disclaimer: “This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would infringe privately owned rights. Reference herein to any specific commercial product, process, or service by name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation or favoring by the United States Government or any agency thereof.”