Seismic Source Mechanisms for Quarry Blasts: Modelling Observed Rayleigh and Love Wave Radiation Patterns from a Texas Quarry

Geophys. J. Int. (2004) 156, 79–93 doi: 10.1111/j.1365-246X.2004.02105.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. Bonner2 and Terrance Barker3 1SAIC, Centre for Monitoring Research, Suite 1450, 1300 N 17 St. Arlington VA 22209, USA. E-mail: [email protected] 2Weston Geophysical Corporation, 4000 S. Medford Dr Suite 10W, Lufkin, TX 75901, USA. E-mail: [email protected] 3SAS Institute, San Diego Ofﬁce, Suite 200, 90188 Telesis Court, San Diego, CA 92121, USA. E-mail: [email protected]

Accepted 2003 August 10. Received 2003 August 7; in original form 2002 October 16 Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021

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 0.2–3 Hz Rayleigh and Love waves are diagnostic of two proposed mechanisms for non-isotropic radiation from quarry blasts. Obser- vations 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 calcu- GJI Seismology lations 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. Wefind 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.

empirical methods may successfully discriminate large industrial INTRODUCTION blasts from earthquakes (Smith 1989, 1993; Hedlin et al. 1990; Su Identification of large industrial blasts is an important seismological et al. 1991; Gitterman & van Eck 1993). Most methods rely upon the problem. In order to properly document natural activity, earthquake effects of delay firing upon the seismic spectra (Willis 1963; Smith seismologists wish to identify and exclude blasts from their cata- 1989; Hedlin et al. 1990). Delay firing imposes spectral scalloping logues. It is also necessary to identify blasts that could be mistaken upon the spectra and gives spectra corner frequencies lower than for (or hide) a clandestine underground nuclear explosion. Several those of microearthquakes with the same magnitude. The spectra

C 2004 RAS 79 80 K. L. McLaughlin, J. L. Bonner and T. Barker

Table 1. Chemical lime, ‘Chemlime’, blasts. locations of the blast within the quarry may also cause differences Date No of Total Powder Rock Quarry Delay in waveforms observed at regional distances. It is just these varia- holes ANFO factor moved face direction tions in waveform characteristics we wish to exploit to shed light (t) (t) upon the physical mechanisms of seismic excitation by the blasting operations. 1994 June 28 42 3.16 0.32 21 157 SW face NW to SE 1994 June 12 40 2.97 0.3 21 246 SW face NW to SE In order to use the information contained in the variability of 1994 July 17 28 2.21 0.32 14 872 SE face SW to NE 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) then appear to be deficient in high frequencies. However, non-delay noted that the character of seismograms from central Texas quar- fired quarry detonation seismic spectra are also observed to be de- ries was correlated with the orientation of the active quarry face as ficient in high-frequency energy compared with microearthquakes the quarry operations migrated within the quarry. In a subsequent (Smith 1993). It has been postulated that spall contributes to low- study with good azimuthal coverage of a few blasts, Bonner et al.

frequency seismic energy and the general tendency for quarry blasts (1996) inferred Rg radiation patterns from phase matched filtered Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021 to appear deficient in high-frequency energy (Barker et al. 1993a). Rg waveforms. They found Rg was enhanced behind the bench and This hypothesis has not been rigorously tested and questions remain attenuated for paths crossing the quarry floor. Delitsyne (1996) stud- as to the physical mechanisms by which blasts excite regional waves ied intermediate period Love waves from quarry blasts in Siberia. and whether discrimination procedures can be transported to regions They found that the Love-wave polarities on opposing quarry faces without prior experience. Therefore, carefully monitored blasts of- were reversed and blasts in the quarry floor produced small Love fer an opportunity to study the physics of seismic wave excitation waves compared with Rg. They concluded that the Love-wave po- and propagation while furthering our theoretical understanding of larity reversals and amplitude dependence were consistent with a seismic discrimination. spall mechanism for Love waves generation from the quarry faces It has long been observed that groups of seismograms from a and opening of a vertical tension crack for blasts in the quarry floor single quarry at a fixed receiving station will often exhibit simi- as suggested by the master crack model of Konya & Walter (1990). lar waveforms. Most microearthquake network operators learn to Previous modelling studies of simultaneously detonated explo- spot particular industrial sources by location and waveform char- sions have shown that spall is an important factor in the generation acteristics. In fact, it has been suggested that waveform correlation of surface waves. Spall is defined as the tensile failure of the near methods and pattern recognition algorithms can be used to routinely surface layers (Eisler & Chilton 1964; Stump 1985). For a con- identify blasting operations at known industrial sites (Harris 1991). tained explosion, the initial compressive shock wave reflects off However, in time, seismograms are recorded from the same indus- the free surface as a tensile wave, which causes subsurface strata trial operation that differ significantly in waveform characteristics to fail in tension. Vertical spall may be represented as a cylindri- and do not correlate well with previous events. Stump et al. (2001) cally symmetric source delayed in time from the explosion (Stump discuss how variations in the blasting practices can create this vari- 1985) or as a circular horizontal tension crack that opens and closes ability, while this paper and Bonner et al. (2003) show that different 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.

C 2004 RAS, GJI, 156, 79–93 Seismic source mechanisms for quarry blasts 81

1991). Only in recent studies has the effect of spall from mining short-period Rayleigh-wave generation from cast blasts in northern explosions been investigated, including the formulation of a linear- Arizona. elastic model for cast blasts (Anandakrishnan et al. 1997) that has In this paper, we attempt to model quarry blast data of Bonner been developed into the MineSeis code (Yang1998). Recently, Bon- et al. (1996) to infer physical excitation mechanisms for short- ner et al. (2003) showed that the linear-elastic model could explain period fundamental Rayleigh (Rg) and Love (SH) waves. The Love Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021

Figure 2. Videographic snapshots of the 1994 June 28 Chemlime blast.

C 2004 RAS, GJI, 156, 79–93 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)(ms−1) (kg m−3) 300 3000 1000 1500 700 3100 1180 1600 4200 Linear gradient from Linear gradient from 2500 3468–5000 1320–3000 ∗ 14 000 6140 V p.6 2500 ∗ 11 900 6720 V p.6 2500 ∗ 8900 7100 V p.6 3000 ∗ Half-space 8000 V p.6 3100

Table 3b. Modiﬁed linear gradient velocity model.

H V p V s Density Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021 (m) (m s−1)(ms−1) (kg m−3) 300 2000 1000 1500 700 2100 1180 1600 4200 Linear gradient from Linear gradient from 2500 Figure 3. Location of the Chemical Lime quarry in central Texas and local 2350–5000 1320–3000 stations used in the analysis of the explosion seismograms. Stations B4 and ∗ 14 000 6140 V p.6 2500 B6 were inoperable during the experiment. ∗ 11 900 6720 V p.6 2500 ∗ 8900 7100 V p.6 3000 Table 2. Original velocity model of Bonner et al. (1996) on top of ∗ Half-space 8000 V p.6 3100 Prewitt (1969) velocity model.

H V p V s Density (m) (m s−1)(ms−1) (kg m−3) and the delay firing was directed either to the southeast or northeast 300 3000 1000 1500 as indicated in Fig. 1. This intershot spacing, D, and burden, B, are 700 3100 1180 1600 consistent with standard shooting practices that move between 1000 4200 5000 1320 2500 ∗ and 10 000 times more rock than ANFO by weight, and use scaled 14 000 6140 V p.6 2500 / − / ∗ burdens, B = B/W 1 3, between 0.5 and 2 m kg 1 3 (Langefors & 11 900 6720 V p.6 2500 ∗ Kihlstrom 1963). The total yields of the three blasts were 3.16, 2.97 8900 7100 V p.6 3000 ∗ and 2.21 t of ANFO. Half-space 8000 V p.6 3100 and Rayleigh waves have been extracted by phase-matched filtering Data of recordings made at several azimuths around a quarry in cen- The objective of our study was to compare local (∼10 km) record- tral Texas. Three blasts conducted behind two perpendicular quarry ings of short-period surface waves with numerical modelling results benches were recorded. Two mechanisms are explored for non- from different quarry blast sources. The short-period surface waves isotropic radiation as suggested by Barker et al. (1993a,b). These excited by a surface source at this distance in simple geological two mechanisms are the near-source scattering of explosion waves structures are the largest recognizable phases and are readily mod- behind quarry faces and the spallation of the rock into the open-pit elled using established methods. For example, the Rg recorded at 10 of the mine. 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 com- plexities of delay firing that deliberately seeks to reduce amplitudes OBSERVATIONS of ground vibrations. Thus, while a complete analysis might model

Description of quarry blasts Table 4. Modified velocity model with discrete layers for wavenumber integration synthetics. Three blasts were recorded from the Chemical Lime Quarry, ‘Chem- µ lime’, in Central Texas summarized in Table 1, illustrated in Fig. 1 H V p V s Density Q −1 −1 −3 and previously described in Bonner et al. (1996). Each shot consisted (m) (m s )(ms) (kg m ) of between 28 and 42 holes of approximately 165 lb each (W = 300 3000 1000 1500 50 76 kg) of ANFO spaced approximately D = 4–5 m apart and ap- 700 3100 1180 1600 50 proximately B = 4–5 m behind the quarry face. We refer to D as 1200 3468 1320 2000 50 the intershot spacing and B as the burden. The shots were fired with 1000 3978 1880 2000 75 nominal delays of 27 ms in a single line from either north-northwest 1000 4488 2440 2000 100 1000 5000 3000 2500 200 to south-southeast or from southwest to northeast. The total du- ∗ 14 000 6140 V p.6 2500 300 ration of the first two shots was approximately 1.1 s (Fig. 2) and ∗ 11 900 6720 V p.6 2500 300 approximately 0.7 s for the second smaller shot. The quarry face ∗ 8900 7100 V p.6 3000 300 is approximately 10 m high and the three shots were fired behind ∗ Half-space 8000 V .6 3100 500 two different faces of the quarry (the southwest and the southeast), p

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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 method- ology exists to simultaneously invert the body-waves for structure and general source complexity. In contrast, for some regions, short- period surface waves can be inverted with minimal source assump- tions 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 Figure 6. Amplitude Rg/SH ratios for blasts June 28 (squares) and July 12 matched-ﬁlter processing are described in Bonner et al. (1996). (asterisks) along the southwest quarry face (striking NW–SE). Stations 1, Between 6 and 7 stations (Fig. 3) recorded each shot on three- 2, 7 and 8 to the northeast and southwest (perpendicular to the quarry face) component Sprengnether 6000, 2 Hz geophones connected to have Rg/SH ratios ≥1. While stations 3, 5, 9 and 10 to the southeast and Refraction Technologies (RefTek) 72-0A dataloggers. Sample rates northwest (parallel to the quarry face) have Rg/SH ratios <1.

C 2004 RAS, GJI, 156, 79–93 84 K. L. McLaughlin, J. L. Bonner and T. Barker Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021 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 Fmax Grid-cycles dz (m) (m, m, m) (m s−1) (Hz) (4 s duration) 1 640 0.04 123 039 39 680, 39 680, 19 200 6140/3684 0.16 100 2 320 0.02 123 039 19 840, 19 840, 9600 6140/3684 0.31 200 3 160 0.01 123 039 9920, 9920, 4800 4824/2808 0.63 400 4 80 0.005 123 039 4960, 4960, 2400 3964/1864 1.25 800 5 40 0.0025 123 039 2480, 2480, 1200 3533/1392 2.5 1600 6 20 0.001 25 123 039 1240, 1240, 600 3100/1180 5.0 3200 7 10 0.000 625 123 039 620, 620, 300 3000/1000 10.0 6400 8 5 0.000 3125 123 039 310, 310, 150 3000/1000 20.0 12 800 Total 984 312 25 500 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 Figure 8. Diagram of quarry models and shot locations used to simulate / = South with V p V s 1.67 3-D wave propagation. The line of multiple shots 5 m behind the bench is in upper layers indicated by filled circles. Two single shot locations 1 and 2 are labelled.

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kilometres of the models are truly relevant to the short-period surface wave eigenfunctions, the ﬁnite-difference models were extended to Observed Rayleigh and Love wave radiation patterns larger distances and greater depths than the surface waves require Figs 4 and 5 show the waveforms and inferred radiation patterns to suppress internal reﬂections from body waves. Thus, for the pur- of short-period Rayleigh (Rg) and Love (SH) waves extracted from poses of computation, this model was placed over a regional crustal the Chemlime shot seismograms. The radiation patterns show clear model from Prewitt (1969). The 5 km of low-velocity sediments correlation with the quarry faces orientation. Love waves (Fig. 4) that comprise the Fort Worth Basin of west-central Texas are under- exhibit minima at azimuths perpendicular to the quarry faces and lain by granites and other Greenvillian age rocks. Early calculations maxima parallel to the quarry faces. Rayleigh (Fig. 5) waves (Rg) showed some anomalous phases resulting from the thick high Pois- are enhanced behind the quarry face; to the southwest for shots 1 −1 son ratio layer with V p = 5000 and V s = 1320 m s . This layer and 2 and to the southeast for shot 3. The radiation pattern depen- was then replaced by a layer with linear velocity gradients from dence upon the quarry face orientation is clearly demonstrated by the high V p/V s ratio of 2.6 at a depth of 1 km to a V p/V s ratio of comparison of the patterns for shots 1 and 2 (oriented NW–SE) approximately 1.67 at a depth of 5.2 km consistent with a decreas- compared with shot 3 (oriented SW–NE). In addition, the radiation ing Poisson ratio with depth (see Tables 3a and b). A fourth model patterns show a tendency for Rg and Love amplitudes to be larger

is tabulated with discrete layers used for calculating wavenumber in the directions of the delay ﬁre: to the southeast for shots 1 and 2 Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021 integration synthetics (Table 4). 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.

C 2004 RAS, GJI, 156, 79–93 86 K. L. McLaughlin, J. L. Bonner and T. Barker

Fig. 6 shows the ratios of Rg/SH amplitudes for shots 1 and 2 pattern to an isotropic moment tensor (explosion) source. They fur- along the southwest bench. Rg/SH amplitudes are between 1 and ther hypothesized that the radiation pattern could be modelled by an 4 for stations 1, 2, 7 and 8, which are located to the northeast and effective non-isotropic moment tensor source. The method of elastic southwest. Rg/SH amplitudes are less than 1 for stations 3, 5, 9 finite differences with recursive grid refinement (see McLaughlin & and 10, which are located to the southeast and northwest. Several Day 1994) was used to model 3-D wave propagation in this problem stations were not operational during the July 12 event (shot-2) but with a large range of scales. The quarry was modelled with a fine grid the consistency of the Rg/SH ratios for the two shots along the same of 5 m cells enclosed in a succession of coarser grids as illustrated bench provides confidence that the Rg/SH patterns are reproducible in Fig. 7. Eight levels of refinement were used with a refinement for events on the same quarry face. 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 MODELLING Table 5). This procedure allows us to model details of the quarry pit ata5mresolution in a small region and the far-field wave propaga- Modelling the quarry bench with 3-D tion of 1–5 Hz waves to greater distance with coarser grids. Table 5 finite-difference simulations

demonstrates the utility of the recursive grid refinement procedure Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021 compared with a uniform grid. In order to grid the same volume that Finite-difference calculations with recursive grid refinement was gridded at the coarse 640 m spacing with a fine spacing of 5 m First, we wished to examine the near-source scattering problem by would have required 2.5 × 1011 cells instead of the 9.8 × 105 cells, placing explosions behind a quarry bench. Barker et al. (1993b) sug- which is a great saving in both memory and computation. However, gested the topographic bench introduces a far-field seismic radiation 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.

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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 Figure 12. Delay fired shot-1 radiation patterns are the maxima of the Fmax listed in the Table 5. Therefore, some care must be taken envelopes of the seismograms of Fig. 11. In the upper plot, the delay-firing to use only those portions of the synthetics that faithfully record direction is marked by the ‘D’ arrow, and the spall direction is marked with the outgoing waves with appropriate bandwidth (lowpass filtered) the arrow labelled ‘S’. before high-frequency reflections arrive from either the bottom or outer boundaries of the coarser grids. mogeneous layered half-space with no quarry present (shot-0). This Numerical calculation series ‘control’ calculation was compared with a wavenumber integration Several numerical experiments are summarized in Table 6. First, an code (Apsel 1979) for testing and validation. Next, the quarry pit explosion source was placed in the upper 10 m of a laterally ho- (Fig. 8) was inserted into the finest grid (level 8 with 5 m resolution)

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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. 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 by setting the elastic moduli of the appropriate cells to zero (shot-1). marked by the ‘D’ arrow, and the spall direction is marked with the arrow This implicitly forces the free surface boundary condition upon the labelled as ‘S’. topographic representation of the quarry pit. The explosion sources are inserted into the calculation by specifying the diagonal moment to between 3 and 4 s duration requiring between 48 and 72 hr of tensor components of appropriate cells with the relevant time de- CPU time on an SGI R8000 (100 MHz) workstation. Three velocity lays. Each source was given a time function with a 0.25 s rise time components were saved on the free surface at every 160 or 640 m in order to remove spurious high frequencies from the calculation. and every 0.01 or 0.04 s. Several calculations were performed with This is equivalent to applying a lowpass filter to the resulting syn- the linear gradient velocity model (Table 3) instead of the original thetic seismograms. Both single shots (2.5 × 109 N m total explosion model of Bonner et al. (1996) (shot-0a, shot-1c and shot-1d). No moment) and multiple shots (1.0 × 1011 N m total explosion mo- significant differences were seen in the results from the calculations ment) with delay firing were simulated. Most simulations were run with the linear gradients. One calculation (shot-1e) was performed

C 2004 RAS, GJI, 156, 79–93 Seismic source mechanisms for quarry blasts 89

with lower P velocities in the upper layers consistent with a V p/V s Table 8. Moment tensor model for the explosion behind the = 2 in order to test the sensitivity of the results upon the Poisson bench.

ratio of the material. Two locations were chosen for the single shots M0 (N m) Delay duration (s) γ to test the sensitivity to the distance of the shots behind the quarry 3 × 1011 1.1 0.2 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. bench and further that the effect continues to a distance at least as far Fig. 9 compares the single shot in the layered half-space without behind the bench as the bench is high. The simulations with linear the quarry (shot-0a) with wavenumber integration synthetics. The velocity gradients (shot-0b, shot-1c and shot-1d) demonstrated that wavenumber integration synthetics have been convolved with the results are nearly identical to models without the velocity gradient appropriate source time function and both sets of seismograms have for seismograms at 1, 2 and 4 km from the source. The fundamental been low-pass filtered at 3.5 Hz (top) and 2.5 Hz (bottom). Grid 1–2 Hz Rayleigh and Love waves are not greatly sensitive to details dispersion can be seen in the finite-difference calculations above of the velocity model below 1 km at these distances. The simulation 2.5 Hz. This waveform comparison provides confidence that the with a lower V p/V s ratio in the upper layers demonstrated that the finite-difference calculations are propagating waves as expected for results are not sensitive to the Poisson ratio. The phase reversals are Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021 periods less than 2.5 Hz. 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 Results of 3-D finite-difference calculations radiation patterns of Fig. 4 when we account for the tendency for Snap shots of the vertical velocity and the total horizontal veloc- the patterns to be enhanced in the direction of the delay fire. The ity are shown in Fig. 10 for the shot-1 simulation. This calculation P-SV (vertical and radial) radiation patterns of Figs 12 and 14 do simulates the delay fire of multiple shots 5 m behind a 10 m high show asymmetry of enhanced radiation behind the bench; however, bench. Phase reversals for waves radiated behind the bench are im- the magnitude of the asymmetry is not equal to the observed data mediately evident. The total horizontal component contains both shown in Fig. 5. radial and transverse motion and the individual seismograms must be rotated before we can separate the P-SV and SH components of Modelling spall with wavenumber integration synthetics motion. Next we attempted to model the observed radiation patterns with The rotated synthetic seismograms at a distance of 2 km from a simple explosion plus the spall model (Table 7) of Barker et al. the multiple delay simulation (shot-1) are shown in Fig. 11. The (1993a). Green functions were synthesized for the velocity model seismograms have been low-pass filtered at 2 Hz. Surprisingly there in Table 4 at a distance of 10 km using wavenumber integration are clear phase reversals of all three components for seismograms synthetics for the velocity model at a distance of 10 km. The explo- behind the bench (to the south) compared with seismograms across sion Green functions were then convolved with a 1.1 s long boxcar the quarry floor (to the north). The maxima of the envelope of each source function with a total explosion moment of 3 × 1011 Nm seismogram were measured and the radiation pattern for the vertical, (Table 8). The vertical and horizontal force Green functions were radial and transverse components of motion are shown in Fig. 12. convolved with source functions representing the time derivatives Note that the vertical and radial components of motion are local of the vertical and horizontal momentum of 20 000 t of ballistic maxima in directions perpendicular to the quarry face and motions rock with a take-off velocity of 4.24 m s−1 at an angle of 45◦ in the are enhanced in the direction of the delay fire. The transverse motion north direction. The spall functions were further convolved with a radiation pattern is aligned parallel to the quarry face and enhanced 1.1 s duration boxcar with unit area to represent the delay duration. in the direction of delay firing. We assumed no net change in the height of centre of mass of the In order to separate the effects of the delay fire from the single shot material for the first spall model (spall-1) and assumed the centre of and test the sensitivity of the radiation patterns upon location along mass fell one-half the height of the bench in a second spall model the bench, we performed several single point explosion simulations (spall-2). listed in Table 6. It is easier to examine the individual phases of the The source functions are shown in Fig. 15 and following Barker point sources on the seismograms since they do not have the long et al. (1993a) we write the vertical, Fz, and horizontal, Fy, forces as source duration. Synthetic seismograms at a distance of 2 km from a single shot located 5 m behind an outside bench corner (shot-1a) Fz = m{z˙0δ(t) + (gt − z˙0)δ(t − td) are shown in Fig. 13. The radiation patterns are shown in Fig. 14. − g[H(t) − H(t − td)]}⊗[H(t) − H(t − tr)]/(tr − t) (1) We do not present detailed shot-1b, shot-1c, shot-1d and shot-1e simulation results. The point-source simulations at location 2 (shot- and 1b and shot-1d did not show significantly different results from the Fy = my˙0[δ(t) − δ(t − td)] ⊗ [H(t) − H(t − tr)]/(tr − t), (2) shot-1a simulation demonstrating that the effect of the point-source explosion behind the bench is not sensitive to the location along the where the spall dwell time, td,isgivenby

Table 7. Explosion plus spall models.

Model M0 Delay duration, Total mass, Take-off Take-off angle, Elevation Spall dwell −1 (N m) tr (s) m (tonne) velocity, v0 (m s ) θ (deg) change, z0 (m) time, td (s) spall-1 3 × 1011 1.1 20 000 4.24 45 0 0.6 spall-2 3 × 1011 1.1 20 000 4.24 45 5 0.9

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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.

= + 2 + 1/2 , td z˙0 y˙0 2z0g g (3) Modelling the bench face with a modified moment tensor source where g is the acceleration of gravity, m is the spall mass, tr is the ripple fire duration, and the initial horizontal and vertical velocities Barker et al. (1993b) postulated that the effects of the bench upon the are given by seismic radiation from a quarry blast explosion might be modelled by a modified moment tensor. They argued that the couple perpen- (y˙ , z˙ ) = v (sin θ,cos θ), (4) 0 0 0 dicular to the quarry face is effectively reduced by the presence of where ν0 is the initial spall velocity, and θ the ballistic angle with the free-surface boundary condition analogous to the spall model of respect to the horizontal. Note that the delay duration spreads out Day & McLaughlin (1991) or the model of Stevens et al. (1991) for the spall forces over time and the total spall duration is the sum of an explosion within a mountain. Following this suggestion, we con- the spall dwell time and the delay duration. volved the individual Green function components for M xx, M yy and Samples of the spall model seismograms and the radiation pat- M zz with 1.1 s duration boxcars such that M yy = γ M0 and M xx = terns are shown in Fig. 16. It is clear that the largest phases on M zz = M0. Seismograms were computed for selected azimuths and these seismograms are the fundamental Rayleigh and Love waves. the radiation patterns in Fig. 18 were computed from the maxima of Therefore, the maxima of the envelopes of the bandpassed synthetic the envelopes of the bandpass filtered synthetic seismograms. seismograms were computed to form the radiation patterns seen in We can see from these synthetic radiation patterns that the trans- Fig. 17. No attempt was made to simulate the spatial extent of the verse (Love wave) radiation is a four-lobed pattern with nodes paral- delay fire (approximately 200 m long) upon the radiation patterns. lel and perpendicular to the quarry face. The maximum Love waves We can see from these seismograms that the approximate SV/SH from such a source are at 45-degree azimuths to the quarry face. amplitude ratios are consistent with observations that give maximum The vertical and radial synthetics are maximum perpendicular to Rg/SH ratios perpendicular to the quarry face. Of course, the spall the quarry face. These predicted radiation patterns do not appear to model predicts a null perpendicular to the quarry face while obser- reflect what we see from the 3-D linear finite-difference calculations vations favour a weak but measurable Love wave in that direction. or the ‘Chemlime’ observations. It is clear that the theoretical radia- Consistent with the central Texas observations, the P-SV (vertical tion from an explosion behind a bench is more complicated that the and radial) amplitudes are maximum behind the bench; however, simple model suggested in Barker et al. (1993b). The simple model the amplitude enhancement in the spall model is less than the ob- of a reduced moment tensor component is not consistent with either servations. The asymmetry of the spall radiation pattern arises out the data or the more complete 3-D finite-difference calculations. 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 CONCLUSIONS source are cylindrically symmetric while the horizontal force intro- We modelled observed short-period fundamental Rayleigh (Rg) and duces cylindrical asymmetry. It may be possible to further adjust Love (SH) waves from a quarry in central Texas. Short-period the three time functions to better model the observed Rg radiation fundamental Rayleigh waves and Love waves non-isotropic radi- pattern asymmetry. We do not present the details of the second spall ation patterns depend on quarry face orientation. Two physically model (spall-2) except to say that including the introduction of a net based models served as working hypotheses for the quarry-blast fall in the centre of mass did not greatly change the radiation patterns non-isotropic radiation patterns. The first model assumes that the from those in Fig. 17 since it only introduces another cylindrically ballistic throw (spall) of material by the quarry blast can be mod- symmetric radiation pattern. elled by simple forces applied to the horizontal free surface (Barker

C 2004 RAS, GJI, 156, 79–93 Seismic source mechanisms for quarry blasts 91 Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021

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 par- −1 ticipate in the spall with an average ballistic velocity of 2–5ms Figure 17. Radiation patterns, 0–2 Hz, for the model spall-1 with the spall to provide sufficient impulse to generate the observed Love waves. direction ‘S’ and delay-fire direction ‘D’ shown in the upper plot. 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.

C 2004 RAS, GJI, 156, 79–93 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 finite- difference 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 coop- erating 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 Downloaded from https://academic.oup.com/gji/article/156/1/79/551395 by guest on 30 September 2021 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 com- ments regarding the manuscript preparation. In addition, we ex- press 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 F19628-95-C-0112. Additional research was sponsored by the Department of Energy’s Small Busi- ness Innovative Research Programme under Contract no DE-FG02- 00ER83123.

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