Subsurface mass transport affects the radioxenon signatures that are used to identify clandestine nuclear tests

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 1 5, doi: /2012gl053885, 2013 Subsurace mass transport aects the radioxenon signatures that are used to identiy clandestine nuclear tests J. D. Lowrey, 1 S. R. Biegalski, 1 A. G. Osborne, 1 and M. R. Deinert 1 Received 14 September 2012; revised 19 November 2012; accepted 20 November [1] The ratios o noble gas radioisotopes can provide critical inormation with which to veriy that a belowground nuclear test has taken place. The relative abundance o anthropogenic isotopes is typically assumed to rely solely on their ission yield and decay rate. The xenon signature o a nuclear test is then bounded by the signal rom directly produced ission xenon, and by the signal that would come rom the addition o xenon rom iodine precursors. Here we show that this signal range is too narrowly deined. Transport simulations were done to span the range o geological conditions within the Nevada Test Site. The simulations assume a 1 kt test and the barometric history ollowing the nuclear test at Pahute Mesa in March Predicted xenon ratios all outside o the typically assumed range 20% o the time and situations can arise where the ground level signal comes entirely rom the decay o iodine precursors. Citation: Lowrey,J.D.,S.R. Biegalski, A. G. Osborne, and M. R. Deinert (2013), Subsurace mass transport aects the radioxenon signatures that are used to identiy clandestine nuclear tests, Geophys. Res. Lett., 40, doi: / 2012GL Introduction [2] On 3 October 2006, the Democratic People s Republic o Korea gave warning o its intention to conduct a nuclear test, and 6 days later claimed that one had been successully carried out. Radioxenon isotopes were the only ission products to be measured o-site aterward and served as critical evidence that a nuclear explosion had taken place [Ringbom et al., 2009]. Anthropogenic isotopes are in act the only deinitive evidence or nuclear test and are an important component o a broader veriication system [Hannon, 1985;Zuckerman, 1996]. Because o their short hal-lives, relatively high production yields, and ability to move through geological structures, radioxenon isotopes are ideal or veriying 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 o a weapon be 1 Department o Mechanical Engineering, The University o Texas at Austin, Austin, Texas, USA. Corresponding author: M. R. Deinert, Department o Mechanical Engineering, The University o Texas at Austin, 1 University Station, C2200, Austin, TX USA. (mdeinert@mail.utexas.edu) American Geophysical Union. All Rights Reserved /13/2012GL distinguished rom those o other sources and the ratios o 131m Xe, 133m Xe, 133 Xe, and 135 Xecanbeusedtohelpdothis. [3] When a ission weapon detonates, it produces radioxenon directly as well as precursors that decay to xenon. What comes out o the ground is a mixture o xenon isotopes rom both o these sources. Figure 1 shows the activity ratios or 133m Xe/ 131m Xe versus 135 Xe/ 133 Xe that would result rom a 235 U ueled weapons test in which radioxenon precursors are absent or present [Kalinowski et al., 2010]. Here ully ractioned corresponds to the xenon signal that would be expected i all the isotopes that decay to xenon are lost and do not contribute to the signal. The nonractioned curve reers to the xenon signal that would be expected i all the isotopes that decay to xenon are contained and contribute to the signal. Figure 1 also shows the radioxenon signature that would result rom the operation o 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 o anthropogenic xenon isotopes is solely a unction o how and when they were produced [Le Petit et al., 2008]. As a result, it has been suggested that a radioxenon signal that alls between the nonractioned (red) and ully ractioned (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 diuse to cracks in the geology along which they then preerentially move to the surace. The rate o movement within cracks is itsel strongly aected by variations in barometric conditions, being largest during periods o decreasing pressure [Carrigan et al., 1996, 1997]. The eect o luctuations in atmospheric pressure on the transport o nonradioactive gasses through dry media has been modeled using a double porosity model or the medium through which the gas travels. Here a convection-diusion ormulation is applied along with the assumption that the geology is comprised o homogenous slabs o material through which vertical cracks run a reasonable assumption or 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 eect o radioactive decay in the transport equations. Previous work with this ormulation suggests that some orms o geology combine to aect xenon isotope ratios that result rom well-contained underground tests [Lowrey et al., 2012]. Here we show that the region between the ully ractioned and nonractioned curves is in act too narrowly deined to encompass the xenon signals that could result rom a nuclear test. The xenon signature o a 1

2 LOWREY ET AL.: SUBSURFACE MASS TRANSPORT AFFECTS RADIOXENON SIGNATURES Figure 1. Xenon isotope ratios or dierent sources. The plot shows expected radioxenon signals generated rom three types o sources. Here ully ractioned corresponds to the xenon signal that would be expected rom an open air nuclear detonation, where all o the isotopes that decay to xenon are lost and do not contribute to the signal. The nonractioned curve reers to the xenon signal expected rom a belowground nuclear test, where all the isotopes that decay to xenon are ully contained and thus contribute to the signal. The signature generated by a commercial power reactor is also shown. The region between the nonractioned (red) and ully ractioned (blue) curves is currently assumed to indicate that a nuclear weapon has been detonated. The data were generated by perorming a depletion calculation using ORIGEN 2.6. belowground test is more appropriately bounded by the ully ractioned curve and the signal that would come solely rom the decay o iodine precursors. 2. Methods [6] The position-dependent concentration o the i th isotope is given by [Chen, 1989; Lowrey et al., 2012; Nilson and Lie, ð ð Z d=2 0 Þ i Þ ð y þ Cx; ð yþ i vx; ð yþ m D i þ Cx; ð yþ i ux; ð yþ ¼ Þ i ð D (1) m l i Cx; ð yþ i Þ i (2) l i Cx; ð yþ i [7] Here m and are the matrix and racture porosities {dimensionless}, C(x,y) i is the concentration o the i th isotope {Ci/m 3 }, v(x,y) is the bulk low velocity {m/s} through the matrix, D i {m 2 /s} is the diusion coeicient o the i th xenon isotope, l i is its decay constant {1/s}, u(x,y) isthe bulk low velocity {m/s} in a racture centered at x, and d is the spacing between ractures {m}. Time is expressed in seconds. Equation (1) describes the horizontal transport o gas in the bulk matrix medium at a given height y {m}, and equation (2) describes transport along a racture where x is taken to be 0. These equations take into account diusion and advection as well as the radioactive decay o the isotopes. The cross-sectional area per unit length along the racture is assumed or simplicity to be constant, but it could also be included as a unction o depth. [8] A similar set o coupled dierential equations is used to determine the response o the pressure at each point in the model, p(x,y;t) {Pa} due to a change in the surace pressure at time t. Here a semicolon indicates that the symbol to its right is held ð yþ a yþ ¼ Z d 2 yþ yþ a [9] The notation p(0,y) indicates that equation (4) represents the rate o change o pressure in the racture, where the coordinate x is equal to zero. The pneumatic diusivities o the matrix and racture, a m and a,{m 2 /s}, are assumed to be constant at a given depth. [10] The low velocities, u(x,y) and v(x,y), in equations (1) and (2) are unctions o the dierential pressures within the cracks that arise rom variations in atmospheric pressure. The diusivity o each species is taken to be mass-dependent [Carrigan et al., 1996] and a unction o the matrix tortuosity [Chen, 1989; Gringarten, 1984; Neretnieks and Rasmuson, 1984]. Details on how D i, u(x,y), v(x,y), a m, and a, are computed are given in the auxiliary material. 1 [11] Equations (1) (4) are discretized by using irst-order backward dierencing or irst-order derivatives and secondorder centered dierencing or the second-order diusive operators. The discretized equations are ormulated as a set o tridiagonal matrix equations. Solution o these equations or each time step is made by Gaussian elimination with periodic boundary conditions at the interior o 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 thereore be solved separately or each layer, and or the racture. [12] Equation (1) is solved at every layer to ind the isotopic concentrations within the matrix. The concentrations are 1 Auxiliary materials are available in the HTML. doi: / 2012GL

3 LOWREY ET AL.: SUBSURFACE MASS TRANSPORT AFFECTS RADIOXENON SIGNATURES Table 1. Range o Radioxenon Transport Parameters or the Nevada Test Site and Simulation Set a Nevada Test Site Parameter Range Parameter Set or Simulations Detonation Depth (m) {450, 525, 600} Medium Porosity and {0.01, 0.05, 0.1, 0.3, 0.37, 0.45} Medium 1e-17 to 1e-15 {1e-17, 1e-16, 1e-15} Permeability (m 2 ) Fracture Spacing (m) {1.0, 2.5, 5.0, 10, 15} Fracture Width (mm) {0.01, 0.1, 0.5, 1.0, 2.0} a Two ranges are given or the porosity o the medium and correspond to regions o clay and granite within the Nevada Test Site. used to compute the integral term in equation (2), which is solved to yield the isotopic concentrations in the racture. The bulk low velocities in the system are computed using the matrix pressures, which are solved or in both the matrix and the ractures using equations (3) and (4). Additional details on the computational implementation o equations (1) (4), mesh reduction study, and benchmarking can be ound in the auxiliary material. [13] Implementation o equations (1) (4) requires inormation on the depth o detonation, initial isotope concentration, racture width, and spacing as well as the porosity and conductivity o the matrix material. A boundary pressure at the surace is also required (a no-lux boundary condition is assumed at the bottom o the simulated geology). Detailed knowledge o the geology at the location o a suspected test site may be diicult to obtain. However, considerable inormation on the range o porosity, conductivity, racture width, and racture spacing are available or the Nevada Test Site (Table 1) [McCord, 2007]. Hourly atmospheric pressure data or the Test Site can be compiled rom the weather history at the Desert Rock airield in Mercury, Nevada. Interpolation is used to provide resolution at 1 min intervals. [14] The radioisotopes at time t = 0 (immediately ater detonation) were assumed to be contained in a region o contaminated matrix. The initial concentration o each tracked isotope was determined by dividing its total quantity in Ci by the approximate volume o material vaporized in a 1 kt nuclear explosion [Carman et al., 2002]. The contaminated matrix in the model is the region between the bottom o the system (450 m depth) up to the depth o the resh air buer (a variable) and the initial isotope concentrations within this region were assumed to be uniorm. 3. Results and Discussion [15] We perormed 990 separate simulations, each or a dierent combination o 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 o a ission device at Pahute Mesa. Isotopic ratios were compiled rom successive simulated 24 h outlow averages o xenon gas that reached the surace. Figure 2 shows the results, color-coded by the number o 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 subsurace dierential transport o xenon gas. [16] The isotopic signal seen above ground is the result o xenon that was produced directly by the ission event and a time-dependent source term that results rom the decay o iodine precursors. Low pressure spikes can have a signiicant eect by drawing gas to the surace and depleting the ission xenon. The ratios o radioxenon isotopes emitted above ground ater such low-pressure periods would then be heavily inluenced by xenon coming rom radioiodine decay. Figure 2 shows several instances o this (beginning around day 38) where the simulated xenon ratios are pushed toward the signal that would come solely rom decay o radioiodine precursors (indicated by the dashed line). In situations such as these, monitoring o down-wind air samples (which would detect the purged xenon) and on-site sampling (which would detect xenon rom recently decayed iodine) could produce very dierent signals, even i the measurements were made on the same day. Importantly, ater 10 days postdetonation, none o the simulated data coincide with the radioxenon signal rom a commercial light water reactor, which makes it easy to rule this source out during an on-site inspection i all our radioxenon isotopes o interest are measured. [17] Xenon ratios that all to the let and right o the iodine and ully ractioned lines can be explained in terms o dierential transport. Decreasing atmospheric pressure will increase the rate o xenon movement into ractures as well as its upward convection within them. The individual xenon isotopes can be thought o as comprising separate, overlapping plumes. The rate at which isotopes diuse through the geology is inversely proportional to the square root o their mass [Bird et al., 1960]. As a result, lighter xenon isotopes will travel aster than do the heavier ones. While the dierence in diusion rates is small, it will cause the leading edge o the isotope plumes to reach the surace at slightly dierent times. Because isotope concentrations can vary by orders o magnitude across a plume s leading edge, this can signiicantly skew the isotope ratios, pushing the 133m Xe/ 131m Xe and 135 Xe/ 133 Xe signals to the let o the iodine line. Increases in pressure would correspondingly orce gases back down the ractures. Rapid luctuations in atmospheric pressure can then set up a situation where lighter isotopes are preerentially depleted rom the geology, which would push the 133m Xe/ 131m Xe and 135 Xe/ 133 Xe signals to the right o the ully ractioned line. In both cases the eect would be most pronounced during the irst ew days ater a detonation, when the location o a plume s leading edge is most important, which is what is seen in Figure 2. [18] It is clear rom the simulations that geological transport o xenon gas can signiicantly aect 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 rom a 26 March 1992 test would have met the previously reported criteria or a nuclear weapon only i the test had taken place at certain locations within the Nevada Test Site. Although much o the simulation data all within the expected range, there are many instances in which radioxenon isotope ratios are well outside o the standard domain. Veriication o a nuclear weapons test under the Comprehensive Nuclear-Test-Ban Treaty [1996] can only be done through the detection o anthropogenic isotopes. The eect 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 o the simulations presented here show that the region between ully ractioned and nonractioned curves 3

4 LOWREY ET AL.: SUBSURFACE MASS TRANSPORT AFFECTS RADIOXENON SIGNATURES Figure 2. Subsurace transport ater an underground nuclear weapons test can cause radioxenon signatures to all outside o current detection criteria. Predicted xenon ratios generated rom a belowground nuclear test, taking into account subsurace transport phenomena. Each data point corresponds to xenon signatures that would result rom detonations within dierent geological conditions present within the Nevada Test Site, given the atmospheric pressures that were recorded during the 55 days that ollowed the 26 March 1992 weapons test at Pahute Mesa within the Nevada Test site. Approximately 20% o the simulated conditions produced signatures that all outside o the current boundaries or detection o such a test. Large low pressure spikes, or extended periods o low pressure, push the simulated xenon ratios toward the signal rom decay o radioiodine precursors (shown by the dashed line). It is clear that the current assumption o what constitutes a radioxenon signal or a belowground nuclear weapons test is too narrowly deined. The ull region between the radioiodine and ully ractionated signals should be considered when evaluating data on suspected nuclear tests. is too narrowly deined to encompass the xenon signals that could result rom a nuclear test. The xenon signature o a belowground test is more appropriately bounded by the ully ractioned curve and the signal that would come solely rom the decay o iodine precursors. Radioxenon ratios that sit between the radioiodine and nonractioned signal curves should be considered when evaluating data on a suspected nuclear test. [19] Acknowledgments. This material is based upon work supported by the Department o Energy, National Nuclear Security Administration, under Award Number DE-AC52-09NA Special thanks to Geo Recktenwald or discussions about simulation methods, to Charles Carrigan or discussions about subsurace transport o noble gases and to William H. Press and Sara L. Sawyer or editorial comments and suggestions. Disclaimer: This report was prepared as an account o work sponsored by an agency o the United States Government. Neither the United States Government nor any agency thereo, nor any o their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility or the accuracy, completeness, or useulness o any inormation, apparatus, product, or process disclosed, or represents that its use would inringe privately owned rights. Reerence herein to any speciic commercial product, process, or service by name, trademark, manuacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation or avoring by the United States Government or any agency thereo. Reerences (1996), Comprehensive Nuclear-Test-Ban Treaty, in United Nations A/50/ 1027, edited. Biegalski, S. R., T. Sallter, J. Heland, and K. M. Foltz Biegalski (2010), Sensitivity Study on Modeling Radioxenon Signals rom Radiopharmaceutical Production Facilities, J. Radioanal. Nucl. Chem., 284, Bird, R. B., W. E. Stewart, and E. N. Lightoot (1960), Transport Phenomena, John Wiley & Sons, New York, New York. Bowyer, T. W., S. R. Biegalski, M. Cooper, P. W. Eslinger, D. Hass, J. C. Hayes, H. S. Miley, D. J. Strom, and V. Woods (2011), Elevated radioxenon detected remotely ollowing the Fukushima nuclear accident, J. Environ. Radioact., 102(7), Bowyer, T. W., et al. (2002), Detection and analysis o xenon isotopes or the comprehensive nuclear-test-ban treaty international monitoring system, J. Environ. Radioact., 59(2), Carman, A. J., J. I. McIntyre, T. W. Bower, J. C. Hayes, T. R. Heimbinger, and M. E. Panisko (2002), Discrimination between anthropogenic sources o atmospheric radioxenon, Trans. Am. Nucl. Soc., 87, Carrigan, C., R. Heinle, G. Hudson, J. Nitao, and J. Zucca (1996), Tracer gas emissions on geological aults as indicators o underground nuclear testing, Nature, 382, Carrigan, C., R. Heinle, G. Hudson, J. Nitao, and J. Zucca (1997), Barometric gas transport along aults and its application to nuclear test-ban monitoring Rep. UCRL-JC , US Department o Energy. Chen, Z. X. (1989), Transient low o slightly compressible luids through double-porosity, double-permeability systems, Transp. Porous Media, 4, Gringarten, A. C. (1984), Interpretation o tests in issured and multilayered reservoirs with double-porosity behavior, J. Pet. Technol., 36, Hannon, W. J. (1985), Seismic Veriication o a Comprehensive Test Ban, Science, 227, Kalinowski, M., et al. (2010), Discrimination o Nuclear Explosions against Civilian Sources Based on Atmospheric Xenon Isotopic Activity Ratios, Pure Appl. Geophys., 167(4), Le Petit, G., P. Armand, G. Brachet, T. Taary, J. P. Fontaine, P. Achim, X. Blanchard, J. C. Piwowarczyk, and F. Pointurier (2008), Contribution to the development o atmospheric radioxenon monitoring, Journal o Radio and Nuclear Chemistry, 276(2), Lowrey, J. D., S. R. Biegalski, and M. R. Deinert (2012), UTEX modeling o radioxenon isotopic raction rom subsurace transport, J. Radioanal. Nucl. Chem., doi: /s McCord, J. (2007), Phase I Contaminant Transport Parameters or the Groundwater Flow and Contaminant Transport Model o Corrective Action Unit 97: Yucca Flat/Climax Mine, Nevada Test Site, Nye County, Nevada, Revision 0 Rep. S-N/ Neretnieks, I., and A. Rasmuson (1984), An approach to modeling radionuclide migration in a medium with strongly varying velocity and block sizes along the low pat, Water Resour. Res., 20(12), Nilson, R. H., and K. H. Lie (1990), Double-porosity modeling o oscillatory gas motion and contaminant transport in a ractured porous medium, Int. J. Numer. Anal. Methods Geomech., 14, Nilson, R. H., P. E. Peterson, K. H. Lie, N. R. Burkhard, and J. R. Hearst (1991), Atmospheric pumping: a mechanism causing vertical transport 4

5 LOWREY ET AL.: SUBSURFACE MASS TRANSPORT AFFECTS RADIOXENON SIGNATURES o contaminated gases through ractured permeable media, J. Geophys. Res., 96, Ringbom, A., K. Elmgren, K. Lindh, J. Peterson, T. W. Bowyer, J. C. Hayes, J. I. McIntyre, M. E. Panisko, and R. Williams (2009), Measurements o radioxenon in ground level air in South Korea ollowing the claimed nuclear test in North Korea on October 9, 2006, J. Radioanal. Nucl. Chem., 282, Saey, P. R. J. (2009), The inluence o radiopharmaceutical isotope production on the global radioxenon background, J. Environ. Radioact., 100, Van der Stricht, S., and A. Janssens (2001), Radioactive eluents rom nuclear power stations and nuclear uel reprocessing plants in the European Union, Radiation Protection 127, Oice O. Publ. Eur. Comm., Luxembourg. Zuckerman, L. (1996), Prospects or a comprehensive test ban, Nature, 361,

6 Supplemental inormation. Cx, ( y) φ i m + ( t x Cx, ( y) vx, ( y) ) = i x φ Cx, ( y) i md i φ x m λ i Cx,y Cx,y ( ) φ i + ( t y Cx,y ( ) ux,y ( ) i )= δ 2 0 ( ) i Cx,y φ m t ( ) i dx + y φ Cx,y D i y φ λ i Cx,y ( ) i ( ) i Here φ m and φ are the matrix and racture porosities {dimensionless}, C(x,y) I is the concentration o the i th isotope {Ci/m 3 }, v(x,y) is the bulk low velocity {m/s} through the matrix, D i {m 2 /s} is the diusion coeicient o the i th xenon isotope, λ i is its decay constant {1/s}, u(x,y) is the bulk low velocity {m/s} in a racture centered at x, and δ is the spacing between ractures {m}. Time is expressed in seconds. Equation (1) describes the horizontal transport o gas in the bulk matrix medium at a given height y {m}, and Eq. (2) describes transport along a racture where x is taken to be 0, Fig. S1.

7 These equations take into account diusion and advection as well as the radioactive decay o the isotopes. The cross-sectional area per unit length along the racture is assumed or simplicity to be constant, but it could also be included as a unction o depth. The diusion coeicients D i appearing in Eqs. (1) and (2) are tortuosity-weighted according to: D i = φ τ D i,0 (3) where the tortuosity τ {dimensionless} and porosity ϕ have separate values within the racture and matrix media (1-3). The low velocities, u(x,y) and v(x,y) or bulk motion along the vertical racture and within the matrix are unctions o the dierential pressures within the cracks that arise rom variations in atmospheric pressure. A similar set o coupled dierential Eqs. (4) and (5) is used to determine the response o the pressure at each point in the model, p(x,y;t) {Pa} due to a change in the surace pressure at time t. Here we use a semicolon to indicate that the symbol to its right is held constant: p( x;y) = t x α p( x;y) m (4) x p( 0, y) = φ m t φ δ 2 0 ( ) t ( ) y px, y dx + y α p 0, y (5) The notation p(0,y) indicates that Eq. (5) represents the rate o change o pressure in the racture, where the coordinate x is equal to zero. The pneumatic diusivities o the matrix medium and racture, α m and α, {m 2 /s} are assumed to be constant as a unction o depth and are deined by:

8 α = δ 2 p 0 and α 12 μφ m = k p m 0 (6) μφ m where p 0 is the mean pressure o the system {Pa}, μ is the dynamic viscosity o air {Pa s}, and k m is the permeability o the bulk matrix medium {m 2 }. Then the luid velocities that result are given by: vx, ( y) = k p m ( x, y) μ x and ( ) = δ 2 uy 12μ ( ) y p x, y (7) Equations (1-7) are discretized by using irst-order backwards dierencing or irst-order derivatives and second-order centered dierencing or the second-order diusive operators. The discretized equations are ormulated as a set o tridiagonal matrix equations. Solution o these equations or each time step is made by Gaussian elimination with periodic boundary conditions at the interior o the matrix and a closed bottom boundary. It is assumed that there is no interaction between vertical layers in the matrix, thus Eqs. (1,2,4,5) may be solved separately or each layer, and or the racture. Equation (1) is solved at every layer to ind the isotopic concentrations within the matrix. The concentrations are used to compute the integral term in equation (2). Equation (2) is solved to yield the isotopic concentrations in the racture. The bulk low velocities in the system are computed using the matrix pressures, which are solved or in the matrix and racture using Eqs. (4) and (5). The tridiagonal matrix method used to solve Eqs. (1,2,4,5) was veriied in three separate ways: i) a comparison with analytically obtained results, ii) testing or convergence in a mesh reduction study and iii) a comparison with alternate numerical methods. The radioisotopes immediately ater detonation were assumed to be contained in a region o contaminated matrix, Fig. S1. The initial concentration o each tracked isotope

9 was determined by dividing its total quantity in Ci by the approximate volume o material vaporized in a 1kt nuclear explosion [5]. The contaminated matrix in our model is the region between the bottom o the system (450m depth) up to the depth o the resh air buer (a variable) and the initial isotope concentrations within this region were assumed to be uniorm. A mesh reduction study was conducted and it was ound that a time step o 60 seconds along with horizontal and vertical grid spacings o 0.05m and 4.5m were suicient or convergence o isotope concentrations to the 5 th decimal place. The surace pressure variations used were sampled at one hour intervals at Mercury, Nevada and linear interpolation was used to produce data with 60 second resolution. Comparison With Alternate Numerical Methods. An independent solution or Eqs. (1-2, 4-5) was computed using Newton's method. Equations (4) and (5) are coupled via the interaction between the racture and the matrix. The pressures converged ater ewer than six iterations, and Eqs. (4) and (5) were satisied to machine precision. A simultaneous solution method was also implemented Eqs. (1-4) which ormulated the racture-matrix system as a large, sparse block-diagonal matrix. The M x N pressure matrix was written as a column vector p o length MxN, and the matrix equation Ap = was solved using Gaussian elimination. In all cases, the computed pressures agreed to within machine precision. Similarly, Eqs. (1,2) were discretized and ormulated as a block-diagonal matrix. The concentrations computed using this method and using the tridiagonal Gaussian elimination method agreed to a precision attributable to round o error and approaching machine precision as well. Supplemental Reerences 1. Z. X. Chen, Transport in Porous Media 4, 147 (1989). 2. A. C. Gringarten, Journal o Petroleum Technology 36, 549 (1984). 3. I. Neretnieks, A. Rasmuson, Water Resources Research 20, 1823 (1984). 4. R. H. Nilson, E. W. Peterson, K. H. Lie, Journal o Geophysical Research 96, (1991). 5. P.J. Closmann, Journal o Geophysical Research 74, 15 (1969).