We performed high-resolution (8 Hz) three-dimensional simulations of ground motions from shallow explosions in the presence of rough surface topography near the North Korean nuclear test site to study elastic propagation effects with emphasis on theoretical aspects of shear wave generation. Interaction with rough topography causes significant P-to-Rg scattering along the surface with amplification of high-frequency (2–8 Hz) shear waves relative to the flat Earth case. Shear waves of different polarizations are coupled by topographic scattering. Rg precursors composed of P-to-Rg conversions traveling as surface waves have the spectral amplitudes comparable to the P wave, while the Rg phase has the low-frequency (0.5–3 Hz) spectral shape of the Rg from the flat case plus the high-frequency (3–8 Hz) P wave spectra. Motions at near-vertical takeoff angles corresponding to teleseismic propagation are increased or decreased indicating that waves are focused or defocused by topographic features above the source. Topographic roughness has a dramatic effect as short-wavelength features (<2–5 km) are included. Higher frequencies are amplified by topography, including frequencies corresponding to wavelengths shorter than the shortest topographic scale length. Overall topography enhances energy propagating along the surface near the source, amplifies surface waves, and tends to balance SV- and SH-polarized motions, all of which impact shear wave observations used for nuclear explosion monitoring. Further simulation studies could elucidate how the wavefield emerging from a topographically rough area ultimately propagates to regional and/or teleseismic distances.
 Shear waves are ubiquitously observed from underground nuclear explosions in the form of short-period regional Sn and Lg and long-period surface waves. An idealized explosion in an isotropic Earth model excites only compressional waves until the waves encounter changes in material properties such as the free surface or internal discontinuities. In this case of a plane-layered vertically varying (one-dimensional, 1-D) structure, vertically polarized shear waves (SV) are generated by the mode conversion of P-to-S at the free surface (i.e., pS and S* [Vogfjord, 1997]) and by material discontinuities within the Earth. Surface waves from pure explosions in 1-D Earth models are Rayleigh waves with SV polarizations and no Love (SH) waves are generated. In realistically heterogeneous Earth models, three-dimensional structure including volumetric material property variations and dipping interfaces causes P waves to be converted into both vertically (SV) as well as horizontally polarized shear waves (SH). The high-energy density of nuclear explosions in realistic Earth materials leads to numerous physical processes that can excite shear waves [e.g., Masse, 1981; Rodean, 1981]. Nonlinear effects in the immediate vicinity of the explosion causes rock damage that can easily generate shear waves provided that asymmetries exist in the damage pattern [Johnson and Sammis, 2001]. Tectonic release [Press and Archambeau, 1962] generates asymmetric surface wave radiation when explosions in prestressed media release stored elastic strain as a relaxation of tectonic stress on a fault or sympathetic nearby earthquake. Studies have shown that shear waves can be excited by tectonic release in the form of long-period body or Rayleigh and Love surface waves and have radiation patterns similar to earthquakes [e.g., Toksoz et al., 1971; Wallace et al., 1985]. Spall occurs when the material above the shot point is accelerated upward and falls back down and is common for most contained nuclear explosions [Springer, 1974; Day and McLaughlin, 1991], however it contributes to short-period response and is negligible at long periods [Day et al., 1983]. Spall has been represented by Compensated Linear Vector Dipole (CLVD) source [e.g., Patton and Taylor, 1995; Stevens et al., 2003]. A vertically oriented CLVD source generates P and SV energy, but no SH. Recently, Ben-Zion and Ampuero  showed that material damage, specifically changes in material properties during a seismic event, can lead to seismic radiation, however the nature of this radiation from plausible explosion sources (isotropic, deviatoric, CLVD) remains to be investigated.
 Source discrimination studies generally show that regional high-frequency P/S amplitude ratios offer an excellent means of identifying small nuclear explosions. P/S ratios are especially important when the MS:mb discriminant becomes observationally challenged by low signal-to-noise (20 s) Rayleigh waves at low magnitudes, such as for the 9 October 2006 North Korean explosion [Bonner et al., 2008; Selby and Bowers, 2009]. Source models for the direct P waves from nuclear explosions are well developed and generally successful at predicting observed variations in amplitude with yield, depth-of-burial, and emplacement materials [Mueller and Murphy, 1971; Helmberger and Hadley, 1981; Denny and Johnson, 1991; Saikia et al., 2001]. Fisk [2006, 2007] proposed a model for S wave generation by underground nuclear explosions based on the same functional form as the Mueller and Murphy P wave model but which reduces the S wave corner frequency by the ratio of near-source shear to compressional velocities. This model is successful at explaining the regional P/S amplitude spectral ratio and increased separation with frequency of explosion and earthquake P/S ratios. These results suggest that a major contribution to S wave generation by explosions occurs very near the source, however its detailed nature remains elusive and it is quite possible that the aforementioned sources of shear wave generation act to some degree at all nuclear test sites, emplacement conditions and propagation environments. These various physical phenomena contribute to the difficulties of finding global yield scaling relationships and universally transportable discriminants.
 In this study we report results from three-dimensional purely elastic simulations of shallow explosions including the effects of free surface topography to better understand the mode conversion and scattering that occurs near the source and the partitioning of energy into various propagation modes. Numerical simulations provide an excellent means of investigating propagation effects because the wavefield can be more easily and densely sampled and analyzed than for equivalent field experiments. Many numerical modeling studies have advanced knowledge of explosion generated seismic waves at regional [e.g., Wu et al., 2000a, 2000b; Fu et al., 2002; Bonner et al., 2003; Stevens et al., 2003; Xie et al., 2005; Myers et al., 2005, 2007] and teleseismic distances [e.g., McLaughlin and Jih, 1988; Frankel and Leith, 1992]. We study the area of rugged terrain around the nuclear tests conducted by the Democratic People's Republic of Korea (DPRK, also referred to as North Korea) on 9 October 2006 and 25 May 2009. Unfortunately, no seismic data are openly available for near-field studies of topographic effects so this study focuses on theoretical aspects of topographic scattering. Where possible we try to connect the results of numerical simulations to observable features in the available regional and teleseismic data and must await the development or application of existing computational tools to directly compute seismograms from the source to the available seismic stations.
 Many studies have been conducted to investigate the effects of free-surface topography on ground motion (see review by Geli et al. ). Earlier theoretical studies of topographic effects on ground motion were based on incident plane waves [Aki and Larner, 1970; Bouchon, 1973; Bard, 1982; Sanchez-Sesma, 1983; Campillo and Bouchon, 1985] and relatively few on elastic finite difference (FD) modeling [e.g., Boore, 1970, 1972a, 1972b]. These studies generally showed that topography impacts seismic motions when the seismic wavelength is comparable to the horizontal size of topographic features and effects are more variable when topography is steeply sloped. However, these studies were mostly concerned with understanding topographic site effects for near-vertical incidence for earthquake ground motion and were typically limited to two-dimensional (2-D) geometries. Such studies generally did not reproduce the large amplifications reported by some field studies, suggesting that three-dimensional (3-D) effects and/or more accurate models of subsurface seismic velocity structure are needed to model topographic effects on observed ground motions [e.g., Geli et al., 1988]. More recent studies of topographic effects on ground motion have used various methods: near-vertical incidence using a boundary-integral method in 3-D [e.g., Bouchon et al., 1996]; shallow explosion motions using a boundary element method in 2-D [e.g., He et al., 2008] or finite difference methods [Myers et al., 2005, 2007]; regional long-period earthquake motions using a finite element method in 3-D [Ma et al., 2007]; or local earthquake motions using a spectral element in 3-D [e.g., Lee et al., 2008; Chaljub et al., 2007, 2010].
 This study focuses on topographic effects on ground motions for shallow explosion sources using a finite difference method. We build upon previous work by performing simulations of shallow explosions in three dimensions with realistic surface topography and with numerical resolution that captures the frequency content of interest to high-frequency regional discrimination and yield estimation (0.5–8 Hz). Our modeling results clearly demonstrate that rough surface topography has a dramatic effect on seismic waves emerging from the source. Importantly P-to-Rg topographic scattering significantly impacts the near-source high-frequency (2–8 Hz) wavefield at the surface and alters the shear waves that propagate downward to ultimately be observed as teleseismic and regional phases. In the following we briefly summarize seismic analysis of the 2006 and 2009 North Korean nuclear tests. We follow this with detailed description of the simulation method and experiments to evaluate how surface topography and source location relative to the surface impact the response. We investigate the effect of surface roughness on the response and show that the shear wave response is critically dependent on the short-wavelength surface features. This is followed by a discussion and concluding remarks.
2. The 2006 and 2009 DPRK Nuclear Tests
 The Democratic People's Republic of Korea (DPRK) conducted declared underground nuclear tests on 9 October 2006 and 25 May 2009. Estimates of the event locations and magnitudes reported by various institutions are compiled in Table 1, and locations are shown in Figure 1a. Topography in this study is taken from the Shuttle Radar Topography Mission [Farr et al., 2007] with resolution of 90 m. Also shown in Figure 1a is the suspected tunnel entrance for access to the 2006 shot point [Kalinowski and Ross, 2006]. Differences in estimated locations arise from the use of different sets of stations, analyst picks, assumed propagation models and location methodologies. Despite these differences, the locations are reasonably close, with estimated locations for each event differing by at most about 8 km, and close to the suspected underground access. Notice that the 2009 event has closer relative locations, possibly due to better azimuthal coverage and higher signal-to-noise ratios for this larger event. Relative locations, based on delay times from correlated waveforms gave much closer locations of the two events [Wen and Long, 2010; S. Myers, personal communication, 2009]. Topographic relief near the test locations varies significantly, as shown in Figures 1a and 1b. Low-lying areas have elevations around 300 m above sea level along the valley south of the test site, while peaks and ridgelines rise to greater than 2300 m near the test site. Note that surface relief varies dramatically in the immediate vicinity of the estimated event locations, with peaks and valleys of characteristic scale lengths of 1–5 km. The DPRK test locations shown in Figure 1a are in a region of granite lithology (see for example the geologic map of Zhao et al. [2008, Figure 9]); however, the valley floors are probably filled with lower-velocity sediments. Some variations in the geology are reported to the east (basalt), south (calcite, marble) and west (basalt). However, we do not have detailed maps of these structures and did not attempt to include it in our modeling.
Table 1. Source Parameters for the Two North Korean Nuclear Testsa
USGS-PDE, United States Geological Survey-Preliminary Determination of Epicenters; IDC-REB, International Data Center-Reviewed Event Bulletin; ISC, International Seismological Centre; LLNL, Lawrence Livermore National Laboratory.
 High-frequency regional P/S ratios from the 2006 event and nearby earthquakes demonstrate explosion-like behavior [Richards and Kim, 2007; Kim and Richards, 2007; Walter et al., 2007; Koper et al., 2008; Zhao et al., 2008]. Similar results were obtained for the 2009 event [Fisk et al., 2009; Walter et al., 2009]. Lg amplitudes at South Korean stations reveal path dependence related to continental margin structure and these observations were successfully modeled by Hong et al. . Modeling of long-period regional waveforms clearly shows the events are consistent with a shallow explosive source rather than a normal crustal depth earthquake [Walter et al., 2007, 2009; Hong and Rhee, 2009; Ford et al., 2009]. The events were not very large having body wave magnitudes, mb, in the range 4.1–4.3 and 4.5–4.7 for the 2006 and 2009 events, respectively. Application of Murphy's  magnitude-yield relation for good coupling in stable tectonic regions results in inferred explosive yields of 0.34–0.63 kiloton and 1.2–2.2 kiloton for the 2006 and 2009 events, respectively. More sophisticated analysis including independent magnitude estimates and/or corrections for the depth-of-burial and hard rock (granitic) emplacement conditions gives ranges of 0.4–0.8 kilotons [Kim and Richards, 2007] and 0.2–2.0 kiloton [Koper et al., 2008] for the 2006 explosion, though these yield estimates trade off with depth. Walter et al.  show a good fit to regional P and S wave spectra for a yield of 0.5 kiloton at a depth of 100 m.
 Long-period surface waves from the 2006 explosion were larger than expected for an explosion of such low yield. Patton and Taylor  suggested that the high surface wave magnitude, MS, for the 2006 explosion could have resulted from stronger Rayleigh wave radiation due to the absence of spall (tensile failure) at depth as a consequence of the test being conducted in strong material such as granite. Bonner et al.  demonstrated that the 2006 event is not clearly screened from earthquakes with the MS:mb (surface wave to body wave magnitude) discriminant and also showed that accounting for the strong (high wave speed) emplacement conditions brings the yield estimated from MS closer to that inferred from mb. Comparison of the long-period regional waveforms from two tests indicates the second test was larger (in seismic moment) by about a factor of six [Ford et al., 2009]. Though small, the North Korean nuclear tests were recorded at teleseismic seismic stations as well. Observations were made at CTBTO seismic arrays [Kvaerna et al., 2007] and single stations in the western United States at distances greater than 90° [Ammon and Lay, 2007], however signal-to-noise ratios (SNR) were low especially for the smaller 2006 test. In summary, reported analysis of the recent DPRK nuclear tests shows that the events discriminate from nearby earthquakes using either high-frequency P/S ratios or long-period complete waveform modeling, provided good signal-to-noise observations at regional distance are available.
3. Numerical Method and Simulations
 We modeled elastic seismic wave propagation in the immediate vicinity of the DPRK tests using the WPP computer code developed at Lawrence Livermore National Laboratory [Petersson, 2010]. WPP is an anelastic finite difference (FD) code based on a second-order accurate scheme [Nilsson et al., 2007] including mesh refinement (N. A. Petersson and B. Sjogreen, Stable grid refinement and singular source discretization for seismic wave simulations, submitted to Communications in Computational Physics, 2010) and a boundary conforming grid for the topographic free surface boundary condition [Appelo and Petersson, 2008]. WPP uses a node-centered (so-called full grid) approach and is different from the commonly used fourth-order accurate staggered grid approach [Virieux, 1984, 1986; Levander, 1988; Graves, 1996]. In particular, WPP solves the elastic wave equation as a second-order system of partial differential equations (PDEs) for the displacements without first rewriting the governing equations as a larger first-order system for the velocities and stresses. The most obvious advantage of our approach over the velocity-stress formulation is that the governing equations are a system of 3 PDEs instead of 9, thus reducing memory requirements. Furthermore, the current approach is stable for arbitrary heterogeneous elastic materials, thus removing the need to average any material properties, which often is necessary to prevent numerical instabilities in the velocity-stress formulation. The difference formulae in our approach is more compact than the fourth-order staggered grid scheme and thus requires fewer memory accesses, which is becoming increasingly more important for good computational efficiency on modern high-performance machines. However, these advantages are partially offset by the disadvantage that a second-order accurate method requires more spatial grid points per wavelength compared to a fourth-order method. All simulations presented in this paper are based on at least 15 grid points per wavelength.
 The energy conserving discretization in WPP was first implemented on a uniform Cartesian mesh with a planar free surface, which allows for a highly efficient algorithm due to the perfect regularity of the mesh. To account for realistic topography, our approach was generalized to curvilinear coordinates where the governing equations first are mapped to a rectangular computational domain before they are discretized. The curvilinear formulation contains metric coefficients due to the curvilinear mapping (i.e., coordinate transformation) and therefore involves more terms in the discretized system, but reverts back to the original discretization when the mesh is Cartesian. A curvilinear mesh could in principle be used to discretize the entire computational domain, but to increase computational efficiency WPP combines both discretizations in a composite grid approach. Hence a boundary conforming mesh is used near the surface topography down to a user specified elevation (i.e., depth below the surface), with a Cartesian mesh below that elevation. The depth is chosen so that the curvilinear mesh smoothly transitions from the topographic surface to a regular Cartesian grid, and the grid spacing does not become so small that it would severely decrease the time step. Note that WPP also provides optional depth varying mesh refinement with hanging nodes to increase the grid size in the deeper parts of the computational domain, where the wave speeds often are faster. However, this feature is not used in the current study because our material properties are constant throughout the computational domain.
 The WPP code generates the computational mesh by first reading the input surface topography and the wave propagation parameters (grid spacing, density and wave speeds) and continues by estimating the shortest wavelength that can be propagated in the mesh. The code then spatially filters the topography to reduce effects of short-wavelength topographic features, which could introduce short-wavelength waves that cannot be resolved on the mesh. Figure 2 shows the mesh for two orthogonal cross sections through a domain with surface topography. The upper mesh (shown in red) conforms to the actual topography (solid line) and smoothly transitions to the regular Cartesian mesh (shown in black) at 4000 m below sea level. Note that in Figure 2 we used a grid spacing of 50 m, plotted every fifth point (plotted at 250 m in the Cartesian mesh), and display a central subregion of the domain used in the calculations described below. In Figure 2 the input topography is drawn as the solid line at the free surface and is indistinguishable from the filtered topography used by WPP in the calculation. Further details about WPP are available in the Reference Guide [Petersson and Sjogreen, 2010] and on the project website [Petersson, 2010].
 WPP has been verified by several methods. We have compared the response from WPP calculations to analytic (e.g., Lamb's problem), semianalytic and computed solutions (e.g., layer over a half-space) to canonical problems, such as the Pacific Earthquake Engineering Research Center Lifelines Project tests of 3-D elastodynamic codes [Day et al., 2001] and in models of three-dimensional heterogeneity by the method manufactured solutions [Nilsson et al., 2007]. Validation of wave propagation with topography is demonstrated in [Appelo and Petersson, 2008]. We used WPP to evaluate the USGS three-dimensional seismic model of the San Francisco Bay Area [Rodgers et al., 2008] and to compute ground motions for the 1906 San Francisco earthquake [Aagaard et al., 2008]. WPP with realistic topography was further verified in a recent study of Hayward Fault scenario earthquakes (B. T. Aagaard et al., Ground motion modeling of Hayward fault scenario earthquakes: II: Simulation of long-period and broadband ground motions, submitted to Bulletin of the Seismological Society of America, 2010).
 The objective of this study is to model the effects of rough topography in the near-source region in the frequency band of interest for seismic monitoring with body waves (0.5–8 Hz) such as regional phases (Pn, Pg, Sn, and Lg) or teleseismic P and S waves. While it is presently not possible to model the entire regional or teleseismic propagation path at resolutions allowing fidelity to 8 Hz, it is possible to simulate the region around the source and sample the emerging wavefield at ranges of azimuths and takeoff angles to understand how the response varies at further distances. We modeled the region around the North Korean nuclear tests with a computational domain centered near the presumed locations of the events and spanning 40 km in each horizontal dimension and 30 km in the vertical dimension. Figure 1b shows the topographic relief around the North Korean tests along with the computational domain at the surface. For this study we sought to investigate the effects of topography alone on ground motion and avoided the complexities of variations in wave speed and density or in attenuation. We assumed the density and seismic wave speeds were constant throughout the medium, assigning values to 5190 m/s, 3000 m/s and 2500 kg/m3 for the P and S wave velocity and density, respectively. We assumed relatively fast wave speeds corresponding to the presumed granitic geology [Zhao et al., 2008; Bonner et al., 2008; Ford et al., 2009]. Furthermore, we assumed purely elastic propagation for two reasons: it is much more computationally efficient to perform the calculations assuming no attenuation; and we are interested in isolating the effects of topographic scattering. The analysis presented here generally considers differential behavior between the topographic and flat cases or different topographic cases with each other (e.g., time series, band-passed amplitudes, or spectral ratios). The effect of propagation in an attenuating Earth model would be more or less equal and the differential behavior would remain unchanged. Furthermore, attenuation in granite should be relative low.
 Given these values of the wave propagation parameters we discretized the domain with a grid spacing of 25 m allowing us to resolve frequencies up to 8 Hz with 15 points per minimum wavelength. The simulations each required slightly more than two billion (2 × 109) grid points. For the source we used an explosion (isotropic moment tensor) with an error function (integral of a Gaussian) for the source time (moment-rate) function. For the simulations shown the source risetime has an approximate duration of ∼0.1 s. We ran the simulations for at least 10 s allowing us to compute the direct P, reflected pP, converted S*, surface and coda waves propagating to more than 12 km or a few wavelengths of the lowest-frequency waves (∼1 Hz) of interest. Simulations were run on 2048 CPUs of the Atlas Linux cluster at Lawrence Livermore National Laboratory (LLNL) and took about 3.5 h.
 One of the powerful advantages of numerical simulation of seismic motions in three dimensions is that we can interrogate the wavefield anywhere within the computational domain. The wavefield emerging from the source in these simulations was sampled in two ways. We considered the full-field motions by plotting the velocity or its spatial derivatives (divergence and curl, corresponding to P and S wave motions, respectively). Second we output the ground motion time series at a constellation of marker points at the surface and within the model arranged in equidistant hemispherical or annular patterns. The advantage of this arrangement is that we can compare motions at different points without having to correct for differential geometric spreading. Figure 3 shows the arrangement of marker points in a hemispheric pattern. Because the wave propagation properties in the half-space are constant, we can decompose the wavefield from Cartesian to ray coordinates (P-SV-SH) assuming straight rays using simple rotations. This is a convenient approximation that allows us to compare the amplitudes of wave propagating in specific directions however it does not account for local distortions of the wavefront from diffractions. Similar analysis was performed by Frankel and Leith  to look at Novaya Zemlya explosions in the presence of steep topography. Note that for shallow explosions and marker points on the surface, the P-, SV-, and SH-polarized components of motion correspond to the radial, vertical and transverse components, respectively. For other cases shown below we output the motions on the surface for evenly spaced annular rings.
4. Simulation Results
4.1. Comparison of the Flat and Topographic Cases
 Simulation of the response of shallow explosions in the assumed half-space model demonstrates that topography in the DPRK test site region causes significant complexity in the wavefield within the high-frequency band of interest for nuclear explosion monitoring. Figure 4a shows images of the vertical component ground velocity field of the surface at 1.0 and 2.0 s after the event for the flat and topographic cases. For these simulations we used the LLNL location of the 2009 event and an explosion source at 600 m depth (Figure 1a, Table 1). Notice that the motions for the flat case show a very simple response with an azimuthally symmetric outward propagating P wave followed by the fundamental mode Rayleigh surface wave, Rg. Note that Rg is the only shear wave propagating on the surface and it travels without dispersion for the assumed half-space model with a flat surface. The particle motions of the windowed P and Rg phases are shown in Figure 4b for both the flat and topographic cases. For the flat surface the P wave has linear particle motion in the radial-vertical plane, while the Rg phase has retrograde elliptical motion.
 The response for the topographic case is much more complex. When surface topography is included the response contains the direct P wave and Rg surface wave, however one can also see large variations in the amplitude and duration, especially at 2 s after the event. The resulting ground motions are strongly azimuthally dependent and also indicate a shift to higher frequency (as seen by the shorter wavelengths in the images) for the surface wave energy propagating at approximately the shear wave velocity. These variations can only be caused by scattering and mode conversion by free surface topography. At 1.0 s, at which time the waves have traveled only a few kilometers from the source, the wavefield shows asymmetries related to the topography. The wavefield is elongated to the north due to the location of this event below a north-south oriented north-sloping valley; the free surface is closer to the source toward the north along the valley floor (e.g., shorter slant distance). A similar pattern is seen at the head of the steep canyon to the southeast of the epicenter, where the P wave strikes the surface at low elevations sooner than at locations at similar horizontal distances. Note that this feature also generates a strong surface wave that can be seen as the secondary wave traveling at the shear velocity following the initial compression-dilatational (blue-red) pulse (indicated by the arrow in Figure 4). This surface wave can be seen as a high-amplitude feature propagating to the southeast in the image at 2.0 s. For azimuths to the southwest the response is relatively simpler than for eastern azimuths, however the response is nowhere as simple as the flat case. Note that the color scale for these plots is scaled to the peak motions within the frame so some of the complexity in the response not visible because of the large amplitudes, especially at 2 s. However, it is possible to see energy inside the ring formed by the Rg phase that is caused by backscattering. Particle motions of the windowed P and Rg phases are more complex for the topographic case as well (Figure 4b). The P motions are mostly linear, but some nonrectilinear motion occurs due to the P coda, and the Rg motions vary rapidly due to higher-frequency content. The particle motions include out-of-plane motions as well (not shown).
 Decomposition of the wavefield into the divergence and curl separates waves propagating as compressional and shear waves, respectively. Figure 5 shows the divergence and curl of the ground velocities at the surface at 1.0 and 2.0 s after the event, for the same source location as shown in Figure 4 (topographic case). At 1.0 s after the event the divergence and curl have large amplitudes where the direct P wave strikes the surface and reflects as a downward propagating P wave (divergence) and mode-converted S wave. Asymmetries in the amplitude and timing of both the divergence and curl arise from variations in the local elevation and slope. Areas of smoother relief show less variation than rugged areas (e.g., the steep topographic slope to the southeast). At 2 s the P wave amplitudes along the surface do not vary greatly with azimuth except for the southeastern azimuth where the large-amplitude surface wave is generated. The Rg wave has large amplitudes in both the compressional and shear wave contributions (divergence and curl) contributions, as expected for a Rayleigh wave. These surface waves show much stronger azimuthal variations where the amplitude and duration of shaking is highly path dependent. Scattered waves between the P and Rg wave and following the Rg are seen, especially at 2.0 s. These features are P-to-Rg conversions and propagate with the Rg velocity (slightly less than the shear velocity).
 The variation in the response in the presence of topography can also be seen in the ground motion time series on the surface. Figure 6 shows the three-component ground velocity time series at a distance of 10 km and plotted as a function of azimuth for the flat and topographic cases using the same source location as above. The data are filtered in two bands: 0.5–2 Hz (Figure 6a) and 2–8 Hz (Figure 6b). The responses in the lower-frequency band (0.5–2 Hz) are broadly similar with a few azimuths showing deviations from the flat response on the vertical and radial components and the transverse component S waves (arriving ∼3.5 s) generally having a small fraction of the amplitude of the other components. The responses at higher frequency (2–8 Hz) are much more complex than the flat Earth response. Notice that the vertical and radial component P waves (arriving at ∼2 s) for the topographic case are similar to the flat case at most azimuths. Scattered energy in the P wave coda window between the direct P and Rg phase are composed of P-to-Rg conversions that is not present in the flat case is clearly apparent in the 2–8 Hz band (Figure 6b). There are large amplitudes before and during the expected Rg phase (∼3.5 s) on the vertical and radial components that are completely absent in the flat case. The P wave coda is predominately composed of P-to-Rg scattered energy as these features travel with the Rg velocity as precursors to the direct Rg.
 Interestingly, there is little Rg coda, however this is not unexpected in the simple half-space model because no energy is reflected upward by discontinuities or turned back to the surface by vertical velocity gradients. The high-frequency (2–8 Hz) transverse component motions for the topographic case show variable response with some azimuths having amplitudes equaling that on the vertical and radial components around the Rg arrival time. Energy is also present on the transverse component as early as the P wave arrival. This is generated by reflection/conversion by topographic slopes oblique to the raypath and perturbs the apparent back azimuth off the great circle path. Notice also that transverse component energy appears to be correlated in time with the other components. That is, large-amplitude SH arrivals tend to appear simultaneously with arrivals on the P-SV components of motion. This suggests that three-dimensional effects can homogenize the wavefield and distribute explosion-generated energy from the P-SV system to SH. Presumably a similar mechanism can transfer strong SH radiation from earthquakes to the P-SV system.
 Note that the ground velocities plotted in full-field view in Figures 4 and 5 and as time histories in Figure 6 show higher-frequency response for the topographic cases than the flat case, especially the Rg phase. Rg in the flat case is a fairly broad low-frequency pulse with duration of about 0.5 s. In contrast the topographic responses are much higher frequency and higher amplitude than the flat surface response. Recall that previous studies of ground motion in the presence of surface topography indicated that amplitudes are impacted when the scale length of topography is similar to the seismic wavelength. Indeed the shear waves in our simulations in the frequency band 0.5–8 Hz have wavelengths of 0.4–6.0 km spanning the scale lengths of variations in the topography. In order to further understand the simulated response, we measured the spectral amplitudes of carefully windowed segments of the wavefield for the flat and topographic case. Figure 7a shows such an example where the P, P-coda (energy between the P and Rg phases), and Rg phases are indicated by the color-coded windows for the flat and topographic cases. The smoothed Fourier spectral amplitudes are plotted in Figure 7b. Note that the P wave spectra are nearly identical with the topographic case slightly lower than the flat case. In the topographic case the lower amplitude of the P wave may reflect the energy lost to scattering to Rg. The P wave coda in the topographic case is composed of P-to-P and P-to-Rg scattered energy and has a similar average spectrum as the direct P wave with modulation caused by path-specific scattering, while the amplitude of the P wave coda for flat case is very small in both the time and frequency domains. The Rg phase in the flat case is peaked at about 1.5 Hz and falls off very quickly away from this peak frequency. However, in the topographic case the Rg phase has the low-frequency spectral amplitude of the Rg in the flat case (i.e., peaked between 1 and 2 Hz) plus the high-frequency spectral amplitudes of the P wave. These spectral measurements show how the Rg waves in the topographic case have the low-frequency spectral characteristics of the Rg phase for the flat Earth and high-frequency spectral characteristics of the P wave. Figure 7 demonstrates the dramatic effect topographic scattering has on the Rg spectrum by increasing the high-frequency content. This higher-amplitude Rg energy above the peak frequency for the flat Earth case may contain the high-frequency shear wave energy that converts to regional Sn and Lg as suggested by Myers et al. . Further investigations will be required to understand how this energy propagates and ultimately is observed at distant stations. Finally, note that attenuation would impact these spectra equally and the relative spectral amplitudes between the flat and topographic would be the same.
 The seismograms in Figure 6 show that interaction of shallow explosion generated waves with topography results more motion at the surface and at higher frequencies than the flat Earth case. In this study we are interested in characterizing the seismic response from shallow explosions in the presence of realistic topography with emphasis on the S wave energy. We measured the root-mean-square (RMS) Rg amplitudes as the response in the window defined by group velocities between 4 and 2 km/s centered on Rg. RMS amplitudes were measured along radial profiles on the surface to 12 km distance spaced 1 km in distance and 15° in azimuth and in four frequency bands (1–2, 2–4, 4–6 and 6–8 Hz). The Rg amplitude ratio between the topographic and flat cases (topographic/flat) was measured to account for geometric spreading effects and to emphasize the alteration of the wavefield caused by topography. Similar to the spectral amplitudes in Figure 7b, note that attenuation would impact these spectra equally and the relative amplitudes between the flat and topographic would be the same. The mean Rg amplitude ratios at 1 km distance intervals are plotted in Figures 8a and 8b along with the spread (minimum and maximum) for the vertical and radial components. These plots show that for the lowest-frequency band (1–2 Hz) the Rg amplitudes can be increased or decreased by topographic effects, but amplitudes vary by less than about a factor of two. As the frequency increases we observe amplification on average of the Rg energy over the flat Earth case. The amplification can be quite large, reaching an average factor of about five for the 4–6 and 6–8 Hz bands on the vertical component. The radial component amplitudes in the band 2–8 Hz are increased by a factor of two on average at distances beyond 10 km. We speculate that the difference between Rg amplitude ratios in the topographic and flat case possibly arises from the fact that the high-velocity model used results in Rayleigh wave particle motions with larger amplitudes in the vertical than the radial component. Because the radial component Rg motions are smaller than the vertical the amplification by interaction with topography may be reduced. In Figure 8c we plot the SH/SV amplitude ratio (transverse/vertical) for the topographic case. This shows how topography scatters energy from a shallow explosion onto the transverse component. At 10 km the Rg amplitude on the transverse component above 2 Hz can have on average about 50% of the Rg amplitude on the vertical component. In some cases the energy on the transverse (SH) component can exceed that on the vertical (SV) demonstrating that topographic scattering is an effective mechanism for partitioning energy from explosions from the P-SV polarizations to SH. These plots illustrate how amplitudes of shear waves from explosions are increased by propagation in regions of rough topography and how topography tends to capture energy and propagate it along the surface.
 To illustrate the elemental effect of topography on the response in the time domain we considered propagation to the west-northwest for the case shown in Figure 4. We selected a profile where the topography is relatively simple and only a small valley disrupts the nearly flat surface. Figure 9 shows the vertical component ground velocities plotted in record section for the flat (black) and topographic (red) cases along with the elevation along the profile. In this record section amplitudes are normalized by the square root of the distance, so surface waves should have constant amplitude as they spread cylindrically and there is no attenuation. A small valley near the source generates a converted P-to-Rg phase, Rgtopo, that propagates as a precursor to the direct Rg phase and travels with the same velocity. Also note that a Ptopo phase is generated that follows the direct P wave. Group velocities are indicated by the solid lines for speeds of 6, 5, 4 and 2 km/s. Dashed lines indicate the Rg group velocity, approximately 3 km/s, and the same velocity but advanced by about 0.5 s for the precursor, Rgtopo. The topographically generated Rg phase travels with the same velocity and amplitude decay as the direct Rg and is a clear example of P-to-Rg scattering that dominates the response in the presence of topography (Figures 4, 5, and 6). This demonstrates that P-to-Rg scattering is an effective mechanism for generating shear wave energy from shallow explosion sources and propagating that energy as the surface waves.
4.2. Effect of Location on the Response
 Rugged topography causes a complex pattern of scattering and mode conversion therefore the response is strongly sensitive to the location of the event. Figure 10 shows the vertical ground velocity at 1.0 and 2.0 s after the event using four different reported locations, specifically those reported by LLNL and Wen and Long [2010, hereafter WL] for the 2006 and 2009 events (Figure 1a and Table 1). These events are separated from each other by only 2–5 km, however they are situated in different topographic environments as shown in Figure 1a: the 2006 LLNL location is very near the suspected tunnel entrance at low elevation at the head of the canyon; the 2006 WL location is about halfway up the slope of the west-sloping, north-south striking ridge; the 2009 LLNL location is under the east-sloping face of a north-sloping valley surrounded by higher elevation on three sides; and the 2009 WL location is beneath a south-sloping face at high elevation at the head of the canyon and above the suspected tunnel entrance. The resulting ground motions assuming explosion sources at 600 m beneath the local surface topography are quite different with each event having a different pattern of surface motions. The closest event pairs: 2006 LLNL and 2006 WL; and 2006 LLNL and 2009 WL separated by about 2 km have very different responses, especially at 2.0 s after the event, indicating that the variations of topography near these event locations cause significant scattering of the ground motions. While the specific patterns of motions are different for the four event locations the general character such as the generation of Rgtopo phases and the shift to higher frequencies is consistent with the results shown earlier.
 So far we have considered only the response at the surface. We now demonstrate the response propagating within the Earth corresponding to ray parameters (takeoff angles) for distant propagation by considering the motions at the marker point locations below the source shown in Figure 3. We measured the RMS amplitude of the velocity time series decomposed into P-, SV- and SH- ray coordinates assuming propagation along straight rays. In the following we will refer to P, SH, and SV as the components of motions separately from seismic phases. In this case we did not window arrivals but simply measured the RMS amplitude of the entire rotated trace. Figure 11 shows the amplitudes plotted in stereographic lower-hemisphere projections (azimuth and takeoff angle) for the three components of motion below the source for both the flat and topographic cases (using the 2009 LLNL location). Marker points were located at 15° increments in azimuth and for takeoff angles (measured from the vertical) of 15°–90° in 15° increments, so the inner and outer rings of Figure 11 correspond to takeoff angles of 15° and 90°, respectively. No correction for geometric spreading was applied because the points are equidistant from the source. However, the RMS values were normalized to make the maximum SV amplitude 1.0 for flat case. The relative amplitudes within and between the components and for both the flat and topographic cases were preserved. We found differences between the topographic and flat (reference) cases were more apparent when we considered motions in the frequency band 2–8 Hz, which is the band used for the amplitude measurements shown in Figure 11.
 As expected the flat case shows no azimuthal dependence, the P and SV amplitudes only vary with takeoff angle and the SH amplitudes were essentially zero. The variation of the amplitude of the P and SV components with takeoff angle in the flat case illustrates the amplitude dependence of pP and pS with ray parameter for the assumed half-space model. The plane wave reflection coefficients for P waves incident on the free surface are (always) maximal for incidence of 0° for P reflection (pP) and (for our assumed model) 45° for SV conversion/reflection (pS) at an angle of 24° [Aki and Richards, 2002]. The P response is greatest at 15° and the SV response is greatest at 30° in Figure 11b corresponding to the nearest marker point positions for these peaks in the pP and pS reflection amplitudes. Note that the color scales are the same for the amplitude plots in Figures 11a and 11b with some saturation of SV amplitudes for topographic case.
 The amplitudes for the topographic case (Figure 11b) vary due to the interaction with the nonplanar free surface in 3-D and show patterns of increased and decreased amplitudes relative to the flat case. P and SV amplitudes are increased to the west-southwest and east-northeast (Figure 11b). To emphasize the differences between the topographic cases and the reference flat solutions, we plot the log10 RMS amplitude ratios (topographic/flat) in Figure 11c where the P and SV ratios compare the topographic to the flat case and the third panel shows the SH amplitude ratio for the topographic case to SV for the flat case. Note that the amplitude ratio plots have different scales because of the different ranges of values being plotted. We will describe several aspects of these measurements.
 First, the P-polarized amplitudes show little variation in the presence of topography with most amplitude ratios about 1.0. Most of the variation for the topographic case is for waves propagating along the surface (takeoff angles of 90°) that interact with the rough surface topography and either increase or decrease the amplitude relative to the flat case. The weak P wave and large surface wave noted in the surface motion images at southeastern azimuths (Figures 4 and 5) is seen as the reduced P wave and enhanced SV amplitudes at 90° takeoff (horizontal) angles and azimuths 135°–165° (Figure 11c). However, the high-amplitude surface wave pulse is poorly represented by the RMS amplitude. The lack of variation for downward propagating P waves is not surprising because the first arriving direct P wave does not interact with the surface and the only contribution to waves with this ray parameter and polarization are surface reflections such as pP that are backscattered with similar ray parameters as the direct wave. Similar results were found by Frankel and Leith . Second, larger variations are seen with the SV- and SH-polarized waves. The amplitude ratios of SV-polarized waves show variations of a factor of two or more (±0.3 in log10 units) at takeoff angles of 30° and 45°, corresponding to teleseismic ray parameters. Specifically, there is a pattern of amplification to the west-southwest and the east-northeast and deamplification to broad azimuthal swaths to the north and south for the P-polarized motions. This pattern can be seen in the SV-polarized RMS amplitudes as well (Figure 11b). Amplification appears to be related to P-SV reflection/conversion along the concave ridges that bound the north-south oriented valley above the event (Figure 1a). The largest SV amplitudes are seen to the west where the P-SV reflection and conversion is focused by the ridge to downward propagating ray parameters. We will highlight similar effects with the other event locations. Third, for horizontally propagating (takeoff angles of 90°) SV-polarized waves have larger amplitudes at all azimuths. Recall that SV-polarized waves at the surface correspond to vertical components of motion. From the time series (Figure 6) and amplitude ratio plots (Figure 8) plots one can see that the S wave consistently has higher amplitude for the topographic case relative to the flat case. Fourth and finally, the amplitudes of SH-polarized waves are increased for all azimuths and takeoff angles in the presence of a topographic free surface. Interestingly the SH amplitudes are largest for the vector ray parameters corresponding to amplified SV, that is the west-southwestern and the east-northeastern azimuths for takeoff angles of 30° and 45° (Figure 11b). This further supports the idea that three-dimensional topography and topography varying across the raypath can act to homogenize the energy with different shear wave polarizations.
 We observed similar behavior to that described above for the other event locations. We performed the same amplitude measurements and the resulting amplitude ratio (topographic/flat) plots (Figure 11c) for the other three event locations are shown in Figure 12. Note that the P-polarized amplitudes for the topographic cases are broadly consistent with the flat case, with the largest differences occurring for horizontally propagating waves (takeoff angles of 90°). The SV amplitudes for the 2006 LLNL location are reduced for steep takeoff angles (15°–45°) and enhanced for shallower takeoff angles (Figure 12a). The surface above this event is convex and unfavorable for strong SV reflection/conversion and focusing. The 2006 WL event is located under the west-sloping face of a broad north-south oriented ridge. Strong SV deamplification relative to the flat case is seen in the amplitude ratio to the west, however little or no amplification is seen to the east (Figure 12b). The WL location of the 2009 event that shows larger-amplitude P-, SV-, and SH-polarized energy for takeoff angles of 15°–45° for azimuths to the north (Figure 12c). It is likely that reflection and conversion occurs along the south-sloping face and dome-like structure of the mountain directly north of the suspected tunnel entrance (Figure 1a) enhancing P-SV energy. SV-polarized amplitudes are reduced for 30° and 45° takeoff angles for a broad swath of azimuths from the northeast to the south to the northwest for this event. These examples illustrate how different locations and local near-source surface morphology impact the emerging wavefield and demonstrate the how three-dimensional effects strongly impact the response. While ridges and valleys may be idealized as two-dimensional features, the simulated response in 3-D is quite complex. The response beneath dome-like structures and focusing predicted by our calculations require three-dimensional modeling.
4.3. Effect of Topographic Roughness on the Response
 Here we consider the effect of topographic roughness on the ground motion response of a shallow explosion. The topography from the region surrounding the DPRK test site (Figure 1b) was filtered using a Gaussian smoothing operator with a suite smoothing widths ranging from 0.1 km to 50 km. This spans all scale lengths from the actual topography at nearly its native resolution to the very nearly the flat case. We then computed the response with the same wave propagation parameters as considered above. Importantly, the simulations were performed at the same numerical resolution (grid spacing of 25 m) allowing us to resolve frequencies to 8 Hz at 15 points per wavelength. For the source we used an explosion at the LLNL location of the 2009 event and a depth of 600 m below the surface. The wave motions were recorded at marker points along radial lines from the source. Figure 13 shows the computational domain, marker point locations and several examples of the filtered surface topography. To characterize the filtered topography, we show the mean, standard deviation, and extreme values of the surface elevation over the domain as a function of the Gaussian smoothing width, D, in Figure 14. The variation of surface elevation is large for the roughest case (D = 0.1 km) with elevations from about 250–2300 m. This variation is decreased as the topography is filtered. To relate the scale length of topographic features to seismic waves we show the frequencies of waves with wavelengths equal to the various smoothing widths given the constant speeds of 5190 and 3000 m/s for P and S waves, respectively. We see that topographic features on scale lengths of 1–5 km correspond to wavelengths in the frequency band of interest for nuclear explosion monitoring (1.0–5.2 Hz and 0.6–3.0 Hz for P and S waves, respectively). According to the consensus of reported results [e.g., Geli et al., 1988], waves are impacted by topographic effects when their wavelengths correspond to the horizontal scale length of topographic features. Thus low-pass filtering the topography would limit the highest frequency that can be impacted by topographic scattering. However, these studies mostly considered the response of topography to a near vertically incident plane wave. Here we are concerned with how topographic roughness controls the frequency-dependent response to shallow explosions.
 Images of the vertical ground velocity at the surface at 2.0 s after the event are shown in Figure 15. For the smoothest topography with (D = 25 and 10 km) the response is hardly distinguishable from the flat case shown in Figure 4. Slight variations from the simple, azimuthally symmetric response are seen for D = 5 km. Dramatic deviations from the flatter cases are seen in the response as the smoothing width is decreased to D = 2 km and smaller. Energy between the P and Rg wave is present and varies at all azimuths for the D = 2 km smoothing width. Greater complexity is seen when the smoothing width decreases to 1 and 0.1 km, including energy propagating behind the Rg wave due to backscattering. In these cases much more variability in P and Rg amplitudes are seen with azimuth.
 The variation of the elastic response with topographic smoothness is clearly seen in the ground motion time histories and spectra as well. Figure 16 shows the vertical component response at 12 km at four orthogonal compass directions for seven topographic smoothing widths. Also shown for each set of seismograms are the smoothed Fourier amplitude spectra between 0.5 and 8 Hz for the entire trace. The responses for the cases with topographic smoothing width of 5 km or greater are very similar to the flat Earth case and their amplitude spectra vary at most by 10% in the lower-frequency band (1–2 Hz). Both the time and frequency domain representations show that a drastic change in the response occurs when topographic features of scale length less than 5 km are introduced in the simulations. For the rougher topographic models (D ≤ 2 km) the behavior deviates progressively from the flat response as D decreases. We show the responses at four different azimuths to illustrate how the topography alters the response in a strongly path-dependent fashion. At low frequencies (1–2 Hz) one sees deamplification for the northern (Figure 16a) and western (Figure 16d) azimuths and amplification occurring at southern (Figure 16c) azimuths, while the eastern azimuth (Figure 16b) shows deamplification at about 1 Hz and large amplification at about 2 Hz. Above about 3 Hz the rough topographic models (D ≤ 2 km) tend to demonstrate amplification relative to the smoother cases. These amplifications can be quite large reaching values of 3–4. Note that larger amplifications are observed in the raw (unsmoothed) Fourier spectra. The seismograms show that the direct first-motion P waves are broadly similar with amplitudes reduced for the rough cases suggesting energy is scattered from the direct P wave. The P wave coda energy increases as the topography becomes rougher. Specifically, we notice that the topography seen in Figures 1b or 13 is smoothest for the north azimuth and to a lesser extent the southern azimuth. These azimuths show the weakest amplification relative to the flat case. Conversely the western and eastern azimuths cross ridges and rougher topography. This suggests that the roughness and or the angle the path makes with the slope play a role the scattering efficiency. Most of the variability in the response results from energy between the P and Rg, caused by P-to-Rg scattering, and amplification of the high-frequency energy arriving around Rg.
 The amplitude spectra shown in Figure 16 were computed for the entire response. We measured the amplitudes of Rg using group velocity windows (4–2 km/s) as described above on the vertical component time histories corresponding to different topographic smoothing widths. S wave amplitude ratios (topographic/flat) were computed as in Figure 8 in four frequency bands and were plotted versus distance in Figure 17 for the smoothing widths, D = 0.1, 1, 2, and 5 km. Note that the Rg above 4 Hz are amplified more quickly as a function of distance for the smaller smoothing widths. Amplification above 4 Hz appears to continue to increase beyond 12 km. Amplification of Rg in the 2–4 Hz appears to level at a factor of about 2, after which the energy propagates with normal surface wave spreading. A tendency toward equalization of the Rg energy on the vertical and transverse component is also observed (not plotted).
 In this study we described numerical simulations of the elastic response of a simple Earth model with a realistic rough surface topography to shallow explosions. Wave propagation simulations were performed in three dimensions at high resolution enabling us to capture the response in the band of interest for low-yield nuclear explosion monitoring with body waves (0.5–8 Hz) albeit close to the source. We considered realistic topography of the DPRK nuclear test site and clearly demonstrated that rough topography causes significant alteration of the wavefield relative to the flat Earth case. Specifically topography amplifies shear wave motions along the surface and tends to transfer energy from P-SV polarizations to SH polarizations. These effects are strongly path dependent. P-to-Rg scattering is an effective mechanism for generating shear wave energy from a shallow explosion (P wave) source. The spectral properties of the Rg phase from shallow explosions in the presence of surface topography shows that high-frequency S wave energy can easily be generated by topographic scattering. The spectrum of the Rg phase has the low-frequency character of the flat Earth response plus the high-frequency response similar to the direct P wave, due to P-to-Rg scattering. While P-to-Rg scattering is effective for generating shear wave motions for shallow explosions, the simple homogeneous volumetric structure considered does not generate much Rg coda. We expect that realistic depth-dependent structure, either layered structure or smooth velocity gradients would cause dispersion of the Rg surface wave and enhance Rg-to-Rg scattering as energy is turned toward the surface. The simulations did not consider attenuation, but these effects do not impact the differential measurements we made which compare the topographic to the flat cases.
 Future simulation efforts could try to model propagation to the near-regional stations (400–600 km) using topography and simple models of crustal and uppermost mantle structure. These simulations would require very large memory for the computational domains and could not model such high frequencies as described here. Nonetheless this would be worth doing to evaluate the effects of scattering by surface topography and deterministic 3-D volumetric structure on regional seismograms from these nuclear tests.
 The downward propagating P wave motions are not altered as much by topography because the amplitudes are dominated by the direct P wave which does not interact with the surface. Variations in P-polarized amplitudes are caused by P-to-P (i.e., pP) reflections at the surface. Downward propagating SV-polarized motions are more strongly impacted by a nonplanar free surface, with high-frequency (2–8 Hz) motions along the surface amplified (relative to the flat case) on average in all directions. SH-polarized motions tend to increase with SV motions, leading to equipartitioning of shear wave energy on all three components. Surface roughness strongly impacts the response with dramatic changes occurring when topographic features of scale lengths of less than 5 km are included, corresponding to P and S waves of frequencies between 1.0 and 5.2 Hz and 0.3–3.0 Hz, respectively. It appears that surface roughness and the direction of propagation relative to the topographic slope have be factors impacting amplification of seismic waves by topography.
 While this study shows that topography strongly impacts the motions emerging from shallow explosions, we were not able to compare simulation results with actual ground motion data because no data is available so close to the source. It would be possible to develop computational tools to propagate solutions that include complex near-source structure to larger distances assuming simple radial Earth models [e.g., Stead and Helmberger, 1988; McLaughlin and Jih, 1988; Gaffet, 1995]. The wavefields emerging from the source region on the lower hemisphere (Figures 11 and 12) show variability in amplitude above 2 Hz. While this may not strongly impact body wave magnitudes made a 1 Hz, variations in spectral content due to topographic scattering could bias measurements of magnitude using broadband spectra [e.g., Murphy and Barker, 2001] and/or spectral ratios at higher frequencies used to make relative source estimates between the 2006 and 2020 events.
 With the current simulations we are not able to further decompose the motions into various shear wave propagation modes, say to predict amplitudes of regional Sn or Lg. For example Xie et al.  and He et al.  used a slowness analysis method with 2-D simulations to measure horizontal slownesses of shear wave motions and determine Rg, Lg, and mantle S wave amplitudes for various near-source volumetric or topographic structures. Future work could apply similar analysis to the simulations described in this study; however, larger domain sizes in 3-D may be required to allow the various propagation modes, traveling at different speeds to separate. We clearly show that three-dimensional effects and out-of-plane sloping topography are important because the SH amplitudes can reach that of SV within 10 km of the source. The strong path dependence of Rg amplification is likely related to the roughness and spatial variation of the free surface. For example the ground motions shown in Figure 16 illustrate that as realistic short-wavelength topography is introduced in the simulations the paths with greater variation in topography (i.e., rougher paths) and those crossing topographic ridges are more strongly amplified. This suggests that a deeper understanding of topographic scattering is possible with further experiments and should be validated with available data from field experiments. The effect of topography on high-frequency observations of shallow explosions can now be investigated with accurate high-resolution numerical simulations in 3-D.
 A.R. is grateful for support as a Fulbright Scholar from the Council for International Exchange of Scholars and the Commission franco-américaine d'échanges universitaires et culturel, to Michel Campillo for hosting him at the Laboratoire de Géophysique Interne et Tectonophysique, Université Joseph Fourier, Grenoble, France, and to the Lawrence Livermore National Laboratory for granting Professional Research and Teaching leave. We thank Jeff Wagoner for assistance with topographic data from the Shuttle Radar Topography Mission project. We are grateful to LLNL Laboratory Directed Research and Development for support to develop the WPP code. The WPP code is open source and available with documentation from the LLNL Web site [Petersson, 2010]. Simulations were performed on parallel computers operated by Livermore Computing using a Grand Challenge Allocation. Figures were made with the Generic Mapping Tool (GMT) [Wessel and Smith, 1998]. Seismogram plots were made with pssac2, developed by Lupei Zhu and Brian Savage. We are grateful for discussions with Michel Bouchon, William Walter, Stephen Myers, and Michael Pasyanos and to two anonymous reviewers for critical comments on the original manuscript. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. This is LLNL contribution LLNL-JRNL-433892.