Seismic source mechanisms for quarry blasts: modelling observed Rayleigh and Love wave radiation patterns from a Texas quarry

Transcription

1 Geophys. J. Int. (2004) 156, doi: /j X x Seismic source mechanisms for quarry blasts: modelling observed Rayleigh and Love wave radiation patterns from a Texas quarry Keith L. McLaughlin, 1 Jessie L. Bonner 2 and Terrance Barker 3 1 SAIC, Centre for Monitoring Research, Suite 1450, 1300 N 17 St. Arlington VA 22209, USA. scatter@cmr.gov 2 Weston Geophysical Corporation, 4000 S. Medford Dr Suite 10W, Lufkin, TX 75901, USA. bonner@westongeophysical.com 3 SAS Institute, San Diego Office, Suite 200, Telesis Court, San Diego, CA 92121, USA. terry.barker@sas.com Accepted 2003 August 10. Received 2003 August 7; in original form 2002 October 16 SUMMARY A theoretical understanding of the mechanisms by which quarry blasts excite seismic waves is useful in understanding how quarry blast discriminants may be transported from one region to another. An experiment in Texas with well-placed seismic stations and a cooperative blasting engineer has shed light on some of the physical mechanisms of seismic excitation at short periods (0.1 3 Hz). Azimuthal radiation patterns of the Hz Rayleigh and Love waves are diagnostic of two proposed mechanisms for non-isotropic radiation from quarry blasts. Observations show that the Love and Rayleigh wave radiation patterns depend upon the orientation of the quarry benches. Two possible mechanisms for non-isotropic radiation are (1) the lateral throw of spalled material and (2) the presence of the topographic bench in the quarry. The spall of material can be modelled by vertical and horizontal forces applied to the free surface with time functions proportional to the derivative of the momentum of the spalled material. We use wavenumber integration synthetics to model the explosion plus spall represented by seismic moment tensor sources plus point forces. The resulting synthetics demonstrate that the magnitude of the SH (Love) compared with the SV (fundamental Rayleigh or Rg) in the short period band (0.5 3 Hz) may be explained by the spall mechanism. Nearly all of the available mass must participate in the spall with an average velocity of 2 5 m s 1 to provide sufficient impulse to generate the observed Love waves. Love wave radiation patterns from such a mechanism are consistent with the spall mechanism. We modelled the effects of the topographic bench using 3-D linear finite-difference calculations to compute progressive elastic wavefields from explosion sources behind the quarry bench. These 3-D calculations show SH radiation patterns consistent with observations while the SV radiation patterns are not consistent with observations. We find that the radiation patterns from the explosion behind the 3-D bench cannot be modelled by a modified moment tensor. The 3-D effects of the bench are more complicated than the representation by a moment tensor with a single reduced horizontal couple. The 3-D finite-difference synthetics exhibit strong azimuthal asymmetry and polarity reversals in the outgoing P-SV waves (P, S and Rg) radiated behind the bench for V p /V s ratios between 2 and 3. Both mechanisms may contribute to the non-isotropic radiation patterns but the spall mechanism is the simplest physical mechanism that explains the bulk of the observations. Adjustments to the time functions for the horizontal force, the vertical force and the explosion source may further refine the remaining differences between prediction and the observations. Key words: quarry blasts, source mechanisms, surface waves. GJI Seismology INTRODUCTION Identification of large industrial blasts is an important seismological problem. In order to properly document natural activity, earthquake seismologists wish to identify and exclude blasts from their catalogues. It is also necessary to identify blasts that could be mistaken for (or hide) a clandestine underground nuclear explosion. Several empirical methods may successfully discriminate large industrial blasts from earthquakes (Smith 1989, 1993; Hedlin et al. 1990; Su et al. 1991; Gitterman & van Eck 1993). Most methods rely upon the effects of delay firing upon the seismic spectra (Willis 1963; Smith 1989; Hedlin et al. 1990). Delay firing imposes spectral scalloping upon the spectra and gives spectra corner frequencies lower than those of microearthquakes with the same magnitude. The spectra C 2004 RAS 79

2 80 K. L. McLaughlin, J. L. Bonner and T. Barker Table 1. Chemical lime, Chemlime, blasts. Date No of Total Powder Rock Quarry Delay holes ANFO factor moved face direction (t) (t) 1994 June SW face NW to SE 1994 June SW face NW to SE 1994 July SE face SW to NE then appear to be deficient in high frequencies. However, non-delay fired quarry detonation seismic spectra are also observed to be deficient in high-frequency energy compared with microearthquakes (Smith 1993). It has been postulated that spall contributes to lowfrequency seismic energy and the general tendency for quarry blasts to appear deficient in high-frequency energy (Barker et al. 1993a). This hypothesis has not been rigorously tested and questions remain as to the physical mechanisms by which blasts excite regional waves and whether discrimination procedures can be transported to regions without prior experience. Therefore, carefully monitored blasts offer an opportunity to study the physics of seismic wave excitation and propagation while furthering our theoretical understanding of seismic discrimination. It has long been observed that groups of seismograms from a single quarry at a fixed receiving station will often exhibit similar waveforms. Most microearthquake network operators learn to spot particular industrial sources by location and waveform characteristics. In fact, it has been suggested that waveform correlation methods and pattern recognition algorithms can be used to routinely identify blasting operations at known industrial sites (Harris 1991). However, in time, seismograms are recorded from the same industrial operation that differ significantly in waveform characteristics and do not correlate well with previous events. Stump et al. (2001) discuss how variations in the blasting practices can create this variability, while this paper and Bonner et al. (2003) show that different locations of the blast within the quarry may also cause differences in waveforms observed at regional distances. It is just these variations in waveform characteristics we wish to exploit to shed light upon the physical mechanisms of seismic excitation by the blasting operations. In order to use the information contained in the variability of waveforms from a quarry, an experiment must be able to separate the effects of the delay firing, location within the quarry and orientation of the quarry face. A cooperative quarry operator and good azimuthal coverage are beneficial. Goforth & Bonner (1995) noted that the character of seismograms from central Texas quarries was correlated with the orientation of the active quarry face as the quarry operations migrated within the quarry. In a subsequent study with good azimuthal coverage of a few blasts, Bonner et al. (1996) inferred Rg radiation patterns from phase matched filtered Rg waveforms. They found Rg was enhanced behind the bench and attenuated for paths crossing the quarry floor. Delitsyne (1996) studied intermediate period Love waves from quarry blasts in Siberia. They found that the Love-wave polarities on opposing quarry faces were reversed and blasts in the quarry floor produced small Love waves compared with Rg. They concluded that the Love-wave polarity reversals and amplitude dependence were consistent with a spall mechanism for Love waves generation from the quarry faces and opening of a vertical tension crack for blasts in the quarry floor as suggested by the master crack model of Konya & Walter (1990). Previous modelling studies of simultaneously detonated explosions have shown that spall is an important factor in the generation of surface waves. Spall is defined as the tensile failure of the near surface layers (Eisler & Chilton 1964; Stump 1985). For a contained explosion, the initial compressive shock wave reflects off the free surface as a tensile wave, which causes subsurface strata to fail in tension. Vertical spall may be represented as a cylindrically symmetric source delayed in time from the explosion (Stump 1985) or as a circular horizontal tension crack that opens and closes in the vertical direction (Day & McLaughlin 1991; Stevens et al. Figure 1. Overhead view of the Chemlime quarry near Clifton, Texas. The 1994 June 28 and July 12 blasts (dashed lines labelled 1 and 2) were located in the West pit (W) and were delay fired towards the SSE. The 1994 July 17 blast (dashed line labelled as 3) was also in the West pit, however, the blast was delay-fired towards the ENE. The rock crusher (C) and the East pit (E) are also shown. The white circle shows the location of the video camera that produced the image in Fig. 2. This photo was taken in 1997 and the hashed region to the south of the July 17 blast shows the limestone section mined during the years following the experiment. Overhead imagery courtesy of the United States Geological Survey.

3 Seismic source mechanisms for quarry blasts ). Only in recent studies has the effect of spall from mining explosions been investigated, including the formulation of a linearelastic model for cast blasts (Anandakrishnan et al. 1997) that has been developed into the MineSeis code (Yang 1998). Recently, Bonner et al. (2003) showed that the linear-elastic model could explain short-period Rayleigh-wave generation from cast blasts in northern Arizona. In this paper, we attempt to model quarry blast data of Bonner et al. (1996) to infer physical excitation mechanisms for shortperiod fundamental Rayleigh (Rg) and Love (SH) waves. The Love Figure 2. Videographic snapshots of the 1994 June 28 Chemlime blast.

4 82 K. L. McLaughlin, J. L. Bonner and T. Barker Table 3a. Linear gradient velocity model. H V p V s Density (m) (m s 1 ) (m s 1 ) (kg m 3 ) Linear gradient from Linear gradient from V p V p V p Half-space 8000 V p Table 3b. Modified linear gradient velocity model. Figure 3. Location of the Chemical Lime quarry in central Texas and local stations used in the analysis of the explosion seismograms. Stations B4 and B6 were inoperable during the experiment. Table 2. Original velocity model of Bonner et al. (1996) on top of Prewitt (1969) velocity model. H V p V s Density (m) (m s 1 ) (m s 1 ) (kg m 3 ) V p V p V p Half-space 8000 V p H V p V s Density (m) (m s 1 ) (m s 1 ) (kg m 3 ) Linear gradient from Linear gradient from V p V p V p Half-space 8000 V p and the delay firing was directed either to the southeast or northeast as indicated in Fig. 1. This intershot spacing, D, and burden, B, are consistent with standard shooting practices that move between 1000 and times more rock than ANFO by weight, and use scaled burdens, B = B/W 1/3, between 0.5 and 2 m kg 1/3 (Langefors & Kihlstrom 1963). The total yields of the three blasts were 3.16, 2.97 and 2.21 t of ANFO. and Rayleigh waves have been extracted by phase-matched filtering of recordings made at several azimuths around a quarry in central Texas. Three blasts conducted behind two perpendicular quarry benches were recorded. Two mechanisms are explored for nonisotropic radiation as suggested by Barker et al. (1993a,b). These two mechanisms are the near-source scattering of explosion waves behind quarry faces and the spallation of the rock into the open-pit of the mine. OBSERVATIONS Description of quarry blasts Three blasts were recorded from the Chemical Lime Quarry, Chemlime, in Central Texas summarized in Table 1, illustrated in Fig. 1 and previously described in Bonner et al. (1996). Each shot consisted of between 28 and 42 holes of approximately 165 lb each (W = 76 kg) of ANFO spaced approximately D = 4 5 m apart and approximately B = 4 5 m behind the quarry face. We refer to D as the intershot spacing and B as the burden. The shots were fired with nominal delays of 27 ms in a single line from either north-northwest to south-southeast or from southwest to northeast. The total duration of the first two shots was approximately 1.1 s (Fig. 2) and approximately 0.7 s for the second smaller shot. The quarry face is approximately 10 m high and the three shots were fired behind two different faces of the quarry (the southwest and the southeast), Data The objective of our study was to compare local ( 10 km) recordings of short-period surface waves with numerical modelling results from different quarry blast sources. The short-period surface waves excited by a surface source at this distance in simple geological structures are the largest recognizable phases and are readily modelled using established methods. For example, the Rg recorded at 10 km distance for the June 28 blast had spectral magnitudes that were 30 db larger than the P-wave arrivals. This fact is related to the complexities of delay firing that deliberately seeks to reduce amplitudes of ground vibrations. Thus, while a complete analysis might model Table 4. Modified velocity model with discrete layers for wavenumber integration synthetics. H V p V s Density Q µ (m) (m s 1 ) (ms 1 ) (kg m 3 ) V p V p V p Half-space 8000 V p

5 Seismic source mechanisms for quarry blasts 83 Figure 5. Rayleigh wave (Rg) radiation pattern inferred for the June 28 blast located behind the southwest bench and delay fired from the northwest toward the southeast. Compare the Rg radiation pattern with the Love wave radiation pattern at the top of Fig. 4. The pit and blast orientation is shown for reference, the timescale is in seconds from the origin of the blast and increases toward the centre. In the centre of the plot, the outline of the maxima of the Rg waves is presented. Figure 4. Love wave (SH) radiation patterns inferred for the June 28 (top) and July 17 (bottom) blasts located behind the southwest and southeast benches, respectively. The pit and blast orientation is shown for reference, the timescale is in seconds from the origin of the blast and increases toward the centre. In the centre of the plot, the outline of the maxima of the short-period Love waves is presented. the entire waveform, we did not have the signal-to-noise ratio for a thorough study of the P-waves. In addition, short-period body-wave waveforms are notoriously unpredictable. No established methodology exists to simultaneously invert the body-waves for structure and general source complexity. In contrast, for some regions, shortperiod surface waves can be inverted with minimal source assumptions to obtain layered structures that reproduce the observed wave propagation. The resulting surface wave excitation (eigenfunctions) may then be exploited to model the source. The seismic recordings used for this study and Rayleigh-wave matched-filter processing are described in Bonner et al. (1996). Between 6 and 7 stations (Fig. 3) recorded each shot on threecomponent Sprengnether 6000, 2 Hz geophones connected to Refraction Technologies (RefTek) 72-0A dataloggers. Sample rates Figure 6. Amplitude Rg/SH ratios for blasts June 28 (squares) and July 12 (asterisks) along the southwest quarry face (striking NW SE). Stations 1, 2, 7 and 8 to the northeast and southwest (perpendicular to the quarry face) have Rg/SH ratios 1. While stations 3, 5, 9 and 10 to the southeast and northwest (parallel to the quarry face) have Rg/SH ratios <1.

6 84 K. L. McLaughlin, J. L. Bonner and T. Barker Figure 7. Diagram of recursive grid refinement used in finite-difference calculations. Eight levels of refinement were used with one grid on each level resulting in an arrangement of nested grids. The quarry and explosion sources are located in the finest grid (level 8). Table 5. Recursive refinement grid tree. Level dx, dy, dt (s) No of cells Grid dimensions V max /V min F max Grid-cycles dz (m) (m, m, m) (m s 1 ) (Hz) (4 s duration) , , / , , / , 9920, / , 4960, / , 2480, / , 1240, / , 620, / , 310, / Total were 100 or 125 samples s 1 and the data were corrected for the instrument response (both phase and amplitude) since the bandwidth (0.2 3 Hz) for short-period fundamental Rayleigh waves (Rg) was affected by the instrument corner frequency. Seismic velocity models Analysis of the Rg resulted in a three-layer shear wave velocity model (Table 2) for the upper crust. While only the upper few Table 6. 3-D finite-difference calculations. Run Quarry present Velocity Multiple/ Burden Quarry face model single shot Shot location Shot-0 No Original Single Shot-0a No Linear gradient Single Shot-0b No Linear gradient Single with V p /V s = 1.67 in upper layers Shot-1 Yes Original Multiple fired 5 m South delay west-to-east Shot-1a Yes Original Single location 1 5 m South Shot-1b Yes Original Single location 2 5 m South Shot-1c Yes Linear gradient Single location 1 5 m South Shot-1d Yes Linear gradient Single location 2 10 m South Shot-1e Yes Linear gradient Single location 2 5 m South with V p /V s = 1.67 in upper layers Figure 8. Diagram of quarry models and shot locations used to simulate 3-D wave propagation. The line of multiple shots 5 m behind the bench is indicated by filled circles. Two single shot locations 1 and 2 are labelled.

7 Seismic source mechanisms for quarry blasts 85 kilometres of the models are truly relevant to the short-period surface wave eigenfunctions, the finite-difference models were extended to larger distances and greater depths than the surface waves require to suppress internal reflections from body waves. Thus, for the purposes of computation, this model was placed over a regional crustal model from Prewitt (1969). The 5 km of low-velocity sediments that comprise the Fort Worth Basin of west-central Texas are underlain by granites and other Greenvillian age rocks. Early calculations showed some anomalous phases resulting from the thick high Poisson ratio layer with V p = 5000 and V s = 1320 m s 1. This layer was then replaced by a layer with linear velocity gradients from the high V p /V s ratio of 2.6 at a depth of 1 km to a V p /V s ratio of approximately 1.67 at a depth of 5.2 km consistent with a decreasing Poisson ratio with depth (see Tables 3a and b). A fourth model is tabulated with discrete layers used for calculating wavenumber integration synthetics (Table 4). Observed Rayleigh and Love wave radiation patterns Figs 4 and 5 show the waveforms and inferred radiation patterns of short-period Rayleigh (Rg) and Love (SH) waves extracted from the Chemlime shot seismograms. The radiation patterns show clear correlation with the quarry faces orientation. Love waves (Fig. 4) exhibit minima at azimuths perpendicular to the quarry faces and maxima parallel to the quarry faces. Rayleigh (Fig. 5) waves (Rg) are enhanced behind the quarry face; to the southwest for shots 1 and 2 and to the southeast for shot 3. The radiation pattern dependence upon the quarry face orientation is clearly demonstrated by comparison of the patterns for shots 1 and 2 (oriented NW SE) compared with shot 3 (oriented SW NE). In addition, the radiation patterns show a tendency for Rg and Love amplitudes to be larger in the directions of the delay fire: to the southeast for shots 1 and 2 and to the northeast for shot 3. Figure 9. Comparisons of finite-difference calculations (squares) for an explosion source in a layered half-space with wavenumber integration synthetics (dots) at a distance of 1000 m low-pass filtered at 3.5 Hz (top) and 2.5 Hz (bottom). The appropriate source time function has been convolved with the wavenumber integration Green explosion functions.

8 86 K. L. McLaughlin, J. L. Bonner and T. Barker Fig. 6 shows the ratios of Rg/SH amplitudes for shots 1 and 2 along the southwest bench. Rg/SH amplitudes are between 1 and 4 for stations 1, 2, 7 and 8, which are located to the northeast and southwest. Rg/SH amplitudes are less than 1 for stations 3, 5, 9 and 10, which are located to the southeast and northwest. Several stations were not operational during the July 12 event (shot-2) but the consistency of the Rg/SH ratios for the two shots along the same bench provides confidence that the Rg/SH patterns are reproducible for events on the same quarry face. MODELLING Modelling the quarry bench with 3-D finite-difference simulations Finite-difference calculations with recursive grid refinement First, we wished to examine the near-source scattering problem by placing explosions behind a quarry bench. Barker et al. (1993b) suggested the topographic bench introduces a far-field seismic radiation pattern to an isotropic moment tensor (explosion) source. They further hypothesized that the radiation pattern could be modelled by an effective non-isotropic moment tensor source. The method of elastic finite differences with recursive grid refinement (see McLaughlin & Day 1994) was used to model 3-D wave propagation in this problem with a large range of scales. The quarry was modelled with a fine grid of 5 m cells enclosed in a succession of coarser grids as illustrated in Fig. 7. Eight levels of refinement were used with a refinement factor of 2 between successive levels. Each grid was composed of 63 wide by 63 long by 31 deep cells. The coarsest grid had a grid spacing of 640 m while the finest grid had a spacing of 5 m (see Table 5). This procedure allows us to model details of the quarry pit ata5mresolution in a small region and the far-field wave propagation of 1 5 Hz waves to greater distance with coarser grids. Table 5 demonstrates the utility of the recursive grid refinement procedure compared with a uniform grid. In order to grid the same volume that was gridded at the coarse 640 m spacing with a fine spacing of 5 m would have required cells instead of the cells, which is a great saving in both memory and computation. However, since the fine grid does not extend outward from the quarry, each Figure 10. Snap shots of the vertical velocity from simulation shot-1 at T = 3 s. (top left) and T = 2 s. (top-right) and total horizontal velocity at T = 2s. (bottom-centre). Note the peanut shaped radiation pattern for the total horizontal component and the phase reversals of the vertical component.

9 Seismic source mechanisms for quarry blasts 87 Figure 11. Vertical, radial, and transverse synthetic seismograms at a distance of 2 km from simulation shot-1. Seismograms have been lowpass filtered at 2 Hz. transition from fine grid to coarse grid results in trapping the high frequencies that do not propagate into the coarser grid. The resulting waves recorded in the coarser grids at greater and greater distance can only accurately support waves with frequencies lower than the Fmax listed in the Table 5. Therefore, some care must be taken to use only those portions of the synthetics that faithfully record the outgoing waves with appropriate bandwidth (lowpass filtered) before high-frequency reflections arrive from either the bottom or outer boundaries of the coarser grids. Numerical calculation series Several numerical experiments are summarized in Table 6. First, an explosion source was placed in the upper 10 m of a laterally ho- Figure 12. Delay fired shot-1 radiation patterns are the maxima of the envelopes of the seismograms of Fig. 11. In the upper plot, the delay-firing direction is marked by the D arrow, and the spall direction is marked with the arrow labelled S. mogeneous layered half-space with no quarry present (shot-0). This control calculation was compared with a wavenumber integration code (Apsel 1979) for testing and validation. Next, the quarry pit (Fig. 8) was inserted into the finest grid (level 8 with 5 m resolution)

10 88 K. L. McLaughlin, J. L. Bonner and T. Barker Figure 13. Vertical, radial, and transverse synthetic seismograms at a distance of 2 km from simulation shot-1a. Seismograms have been lowpass filtered at 2 Hz. by setting the elastic moduli of the appropriate cells to zero (shot-1). This implicitly forces the free surface boundary condition upon the topographic representation of the quarry pit. The explosion sources are inserted into the calculation by specifying the diagonal moment tensor components of appropriate cells with the relevant time delays. Each source was given a time function with a 0.25 s rise time in order to remove spurious high frequencies from the calculation. This is equivalent to applying a lowpass filter to the resulting synthetic seismograms. Both single shots ( N m total explosion moment) and multiple shots ( N m total explosion moment) with delay firing were simulated. Most simulations were run Figure 14. Shot-1a radiation patterns are the maxima of the envelopes of the seismograms of Fig. 13. In the upper plot, the delay-firing direction is marked by the D arrow, and the spall direction is marked with the arrow labelled as S. to between 3 and 4 s duration requiring between 48 and 72 hr of CPU time on an SGI R8000 (100 MHz) workstation. Three velocity components were saved on the free surface at every 160 or 640 m and every 0.01 or 0.04 s. Several calculations were performed with the linear gradient velocity model (Table 3) instead of the original model of Bonner et al. (1996) (shot-0a, shot-1c and shot-1d). No significant differences were seen in the results from the calculations with the linear gradients. One calculation (shot-1e) was performed

11 Seismic source mechanisms for quarry blasts 89 with lower P velocities in the upper layers consistent with a V p /V s = 2 in order to test the sensitivity of the results upon the Poisson ratio of the material. Two locations were chosen for the single shots to test the sensitivity to the distance of the shots behind the quarry face (see Fig. 8). One calculation (shot-1d) was conducted with the explosion source 10 m behind the quarry face rather than 5 m behind the quarry face. Fig. 9 compares the single shot in the layered half-space without the quarry (shot-0a) with wavenumber integration synthetics. The wavenumber integration synthetics have been convolved with the appropriate source time function and both sets of seismograms have been low-pass filtered at 3.5 Hz (top) and 2.5 Hz (bottom). Grid dispersion can be seen in the finite-difference calculations above 2.5 Hz. This waveform comparison provides confidence that the finite-difference calculations are propagating waves as expected for periods less than 2.5 Hz. Results of 3-D finite-difference calculations Snap shots of the vertical velocity and the total horizontal velocity are shown in Fig. 10 for the shot-1 simulation. This calculation simulates the delay fire of multiple shots 5 m behind a 10 m high bench. Phase reversals for waves radiated behind the bench are immediately evident. The total horizontal component contains both radial and transverse motion and the individual seismograms must be rotated before we can separate the P-SV and SH components of motion. The rotated synthetic seismograms at a distance of 2 km from the multiple delay simulation (shot-1) are shown in Fig. 11. The seismograms have been low-pass filtered at 2 Hz. Surprisingly there are clear phase reversals of all three components for seismograms behind the bench (to the south) compared with seismograms across the quarry floor (to the north). The maxima of the envelope of each seismogram were measured and the radiation pattern for the vertical, radial and transverse components of motion are shown in Fig. 12. Note that the vertical and radial components of motion are local maxima in directions perpendicular to the quarry face and motions are enhanced in the direction of the delay fire. The transverse motion radiation pattern is aligned parallel to the quarry face and enhanced in the direction of delay firing. In order to separate the effects of the delay fire from the single shot and test the sensitivity of the radiation patterns upon location along the bench, we performed several single point explosion simulations listed in Table 6. It is easier to examine the individual phases of the point sources on the seismograms since they do not have the long source duration. Synthetic seismograms at a distance of 2 km from a single shot located 5 m behind an outside bench corner (shot-1a) are shown in Fig. 13. The radiation patterns are shown in Fig. 14. We do not present detailed shot-1b, shot-1c, shot-1d and shot-1e simulation results. The point-source simulations at location 2 (shot- 1b and shot-1d did not show significantly different results from the shot-1a simulation demonstrating that the effect of the point-source explosion behind the bench is not sensitive to the location along the Table 8. Moment tensor model for the explosion behind the bench. M 0 (N m) Delay duration (s) γ bench and further that the effect continues to a distance at least as far behind the bench as the bench is high. The simulations with linear velocity gradients (shot-0b, shot-1c and shot-1d) demonstrated that results are nearly identical to models without the velocity gradient for seismograms at 1, 2 and 4 km from the source. The fundamental 1 2 Hz Rayleigh and Love waves are not greatly sensitive to details of the velocity model below 1 km at these distances. The simulation with a lower V p /V s ratio in the upper layers demonstrated that the results are not sensitive to the Poisson ratio. The phase reversals are observed for V p /V s ratios between 2 and 3. It is immediately obvious that the Love wave (SH or transverse) radiation patterns of Figs 12 and 14 are similar to the observed radiation patterns of Fig. 4 when we account for the tendency for the patterns to be enhanced in the direction of the delay fire. The P-SV (vertical and radial) radiation patterns of Figs 12 and 14 do show asymmetry of enhanced radiation behind the bench; however, the magnitude of the asymmetry is not equal to the observed data shown in Fig. 5. Modelling spall with wavenumber integration synthetics Next we attempted to model the observed radiation patterns with a simple explosion plus the spall model (Table 7) of Barker et al. (1993a). Green functions were synthesized for the velocity model in Table 4 at a distance of 10 km using wavenumber integration synthetics for the velocity model at a distance of 10 km. The explosion Green functions were then convolved with a 1.1 s long boxcar source function with a total explosion moment of Nm (Table 8). The vertical and horizontal force Green functions were convolved with source functions representing the time derivatives of the vertical and horizontal momentum of t of ballistic rock with a take-off velocity of 4.24 m s 1 at an angle of 45 in the north direction. The spall functions were further convolved with a 1.1 s duration boxcar with unit area to represent the delay duration. We assumed no net change in the height of centre of mass of the material for the first spall model (spall-1) and assumed the centre of mass fell one-half the height of the bench in a second spall model (spall-2). The source functions are shown in Fig. 15 and following Barker et al. (1993a) we write the vertical, F z, and horizontal, F y, forces as F z = m{ż 0 δ(t) + (gt ż 0 )δ(t t d ) and g[h(t) H(t t d )]} [H(t) H(t t r )]/(t r t) (1) F y = mẏ 0 [δ(t) δ(t t d )] [H(t) H(t t r )]/(t r t), (2) where the spall dwell time, t d,isgivenby Table 7. Explosion plus spall models. Model M 0 Delay duration, Total mass, Take-off Take-off angle, Elevation Spall dwell (N m) t r (s) m (tonne) velocity, v 0 (m s 1 ) θ (deg) change, z 0 (m) time, t d (s) spall spall

12 90 K. L. McLaughlin, J. L. Bonner and T. Barker Figure 15. Quarry blast source functions: explosion (top), horizontal spall force (middle), and vertical spall force (bottom). Note that the total duration of the spall signal is the sum of delay duration and spall dwell time. [ t d = ż 0 + ( ẏ z 0g ) ]/ 1/2 g, (3) where g is the acceleration of gravity, m is the spall mass, t r is the ripple fire duration, and the initial horizontal and vertical velocities are given by (ẏ 0, ż 0 ) = v 0 (sin θ,cos θ), (4) where ν 0 is the initial spall velocity, and θ the ballistic angle with respect to the horizontal. Note that the delay duration spreads out the spall forces over time and the total spall duration is the sum of the spall dwell time and the delay duration. Samples of the spall model seismograms and the radiation patterns are shown in Fig. 16. It is clear that the largest phases on these seismograms are the fundamental Rayleigh and Love waves. Therefore, the maxima of the envelopes of the bandpassed synthetic seismograms were computed to form the radiation patterns seen in Fig. 17. No attempt was made to simulate the spatial extent of the delay fire (approximately 200 m long) upon the radiation patterns. We can see from these seismograms that the approximate SV/SH amplitude ratios are consistent with observations that give maximum Rg/SH ratios perpendicular to the quarry face. Of course, the spall model predicts a null perpendicular to the quarry face while observations favour a weak but measurable Love wave in that direction. Consistent with the central Texas observations, the P-SV (vertical and radial) amplitudes are maximum behind the bench; however, the amplitude enhancement in the spall model is less than the observations. The asymmetry of the spall radiation pattern arises out of the interference between the horizontal force, the vertical force, and the isotropic (explosion) moment components of the source; the radiation patterns of the vertical point force and the explosion point source are cylindrically symmetric while the horizontal force introduces cylindrical asymmetry. It may be possible to further adjust the three time functions to better model the observed Rg radiation pattern asymmetry. We do not present the details of the second spall model (spall-2) except to say that including the introduction of a net fall in the centre of mass did not greatly change the radiation patterns from those in Fig. 17 since it only introduces another cylindrically symmetric radiation pattern. Modelling the bench face with a modified moment tensor source Barker et al. (1993b) postulated that the effects of the bench upon the seismic radiation from a quarry blast explosion might be modelled by a modified moment tensor. They argued that the couple perpendicular to the quarry face is effectively reduced by the presence of the free-surface boundary condition analogous to the spall model of Day & McLaughlin (1991) or the model of Stevens et al. (1991) for an explosion within a mountain. Following this suggestion, we convolved the individual Green function components for M xx, M yy and M zz with 1.1 s duration boxcars such that M yy = γ M 0 and M xx = M zz = M 0. Seismograms were computed for selected azimuths and the radiation patterns in Fig. 18 were computed from the maxima of the envelopes of the bandpass filtered synthetic seismograms. We can see from these synthetic radiation patterns that the transverse (Love wave) radiation is a four-lobed pattern with nodes parallel and perpendicular to the quarry face. The maximum Love waves from such a source are at 45-degree azimuths to the quarry face. The vertical and radial synthetics are maximum perpendicular to the quarry face. These predicted radiation patterns do not appear to reflect what we see from the 3-D linear finite-difference calculations or the Chemlime observations. It is clear that the theoretical radiation from an explosion behind a bench is more complicated that the simple model suggested in Barker et al. (1993b). The simple model of a reduced moment tensor component is not consistent with either the data or the more complete 3-D finite-difference calculations. CONCLUSIONS We modelled observed short-period fundamental Rayleigh (Rg) and Love (SH) waves from a quarry in central Texas. Short-period fundamental Rayleigh waves and Love waves non-isotropic radiation patterns depend on quarry face orientation. Two physically based models served as working hypotheses for the quarry-blast non-isotropic radiation patterns. The first model assumes that the ballistic throw (spall) of material by the quarry blast can be modelled by simple forces applied to the horizontal free surface (Barker

13 Seismic source mechanisms for quarry blasts 91 Figure 16. Seismograms derived from spall model 1 (Fig. 15). et al. 1993a). The second hypothesis posits that non-planar free surfaces (quarry face and pit) introduce non-isotropic radiation patterns (Barker et al. 1993b). Both mechanisms may contribute to the non-isotropic radiation patterns but the spall mechanism is the simplest physical mechanism that explains the bulk of the observations. The spall mechanism synthetics predict the gross Love-wave radiation pattern and the magnitude of the Rg/SH ratio in the short period band (0.5 2 Hz). Nearly all of the available mass must participate in the spall with an average ballistic velocity of 2 5 ms 1 to provide sufficient impulse to generate the observed Love waves. Adjustments to the time functions for the horizontal force, the vertical force and the explosion source may further refine remaining differences between prediction and observations. Figure 17. Radiation patterns, 0 2 Hz, for the model spall-1 with the spall direction S and delay-fire direction D shown in the upper plot.

14 92 K. L. McLaughlin, J. L. Bonner and T. Barker 3-D finite-difference calculations show Rg and SH radiation patterns roughly consistent with observations. However, we find that radiation patterns from an explosion behind the 3-D bench are not represented by a modified moment tensor as suggested by Barker et al. (1993b). Barker et al. postulated that the effect of the quarry bench might be modelled by simple modification of the explosion moment tensor. Their simple model of a reduced horizontal couple is neither consistent with the data nor the more complete 3-D finitedifference calculations. There may not be a simple way to simulate the perturbative effects of the 3-D quarry structure on layered Green functions by perturbing the fundamental source. This work demonstrated that controlled experiments at a cooperating quarry could be combined with numerical modelling to test competing seismic source hypotheses. Unfortunately, a single shot behind the bench was not available from the Chemline quarry. Stump et al. (2003) confirmed that a Mueller Murphy (1971) source model, empirically developed from near-source data for nuclear explosions, matched the spectral ratios observed from small, contained chemical explosions detonated in coal mines. Provided a cooperative quarry operator can be found, future experiments might include shots at different distances behind the bench and shots in the quarry floor to supplement the work of Stump et al. (2003). Experiments may then measure the relative importance of vertical spall, horizontal spall, and the geometric effects of the quarry bench. ACKNOWLEDGMENTS We wish to thank Gene Herrin for suggesting the SMU Maxwell/S- CUBED collaboration and Steve Day for providing useful theoretical insights into source modelling. We also want to thank Tom Goforth, Delaine Reiter and James Lewkowicz for insightful comments regarding the manuscript preparation. In addition, we express our gratitude to Brian Stump and Alan Beck for reviewing and improving the manuscript. Work at Maxwell/S-CUBED was sponsored by US Dept of Energy, Office of Non-proliferation and National Security, Office of Research and Development ST486 under Phillips Laboratory Contract no F C Additional research was sponsored by the Department of Energy s Small Business Innovative Research Programme under Contract no DE-FG02-00ER REFERENCES Figure 18. Radiation patterns, 0 2 Hz, for the reduced moment tensor source, M yy = γ (M xx = M zz = M 0 ), γ = 0.2. This model explains neither the finite-difference calculations nor the observed data. Anandakrishnan, S., Taylor, S.R. & Stump, B.W., Quantification and characterization of regional seismic signals from cast blasting in mines: a linear elastic model, Geophys. J. Int., 131, Apsel, R.J., Dynamic Green s functions for layered media and application to boundary-value problems, PhD thesis, University of California, San Diego. Barker, T.G., McLaughlin, K.L. & Stevens, J.L., 1993a. Numerical models of quarry blast sources, S-CUBED Report, SSS-TR Barker, T.G., McLaughlin, K.L., Stevens, J.L. & Day, S.M., 1993b. Numerical models of quarry blast sources: effects of the bench, S-CUBED Report, SSS-TR Bonner, J.L, Herrin, E.T. & Goforth, T.T., Azimuthal variation of Rgfrom Central Texas quarry blasts, Seism. Res. Letts, 67, 43. Bonner, J.L., Pearson, D.C. & Blomberg, S., Azimuthal variation of short-period Rayleigh waves from cast blasts in northern Arizona, Bull. seism. Soc. Am., 93, Day, S. & McLaughlin, K., Seismic source representations For Spall, Bull. seism. Soc. Am., 81,

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