Source Mechanisms of Mine-Related Seismicity, Savuka Mine ...africaarray.psu.edu/publications/pdfs/Julia_et_al... · Bulletin of the Seismological Society of America, Vol. 99, No.

Ⓔ

Source Mechanisms of Mine-Related Seismicity,

Savuka Mine, South Africa

by Jordi Julià, Andrew A. Nyblade, Ray Durrheim,* Lindsay Linzer,Rengin Gök, Paul Dirks, and William Walter

Abstract We report full moment tensor solutions for 76 mine tremors with momentmagnitudes (Mw) between 0.5 and 2.6 recorded by a network of 20 high-frequencygeophones in a deep gold mine in South Africa. Source mechanisms convey importantinformation on how in-mine stresses are relaxed, and understanding the nature of suchmechanisms is essential for improving our assessment of rock mass response tomining. Our approach has consisted of minimizing the L2 norm of the differencebetween observed and predicted P, SV, and SH spectral amplitudes, with visuallyassigned polarities, to constrain all six independent components of the seismicmoment tensor. Our results reveal the largest principal stresses in the mine are com-pressive, oriented near vertically, and relaxed through a mix of volumetric closure andnormal faulting, consistent with a gravity-driven closure of the mined-out areas. Pre-vious moment tensor studies in deep mines had suggested that the distribution of seis-mic sources in terms of the volumetric-shear mix was bimodal. A bimodal distributionis compatible with our moment tensor solutions only for moment magnitudes above2.2. Events in the 0:5 <Mw <2:2 moment magnitude range display a continuousdistribution of their volumetric-shear mix.

Online Material: Focal parameters for mine tremors at Savuka.

Introduction

An early debate in mining seismology concerned theneed for invoking nondeviatoric failure mechanisms to ex-plain the radiation patterns generated by mine-induced seis-mic events (see, e.g., Wong and McGarr, 1990, and ref-erences therein). This debate was settled in the early 1990sby McGarr (1992a,b), who convincingly demonstrated thenecessity of an implosive component to fully explain theradiation patterns of 7 events observed in deep, tabular goldmines in two mining districts in South Africa, and by Feignerand Young (1992), who showed a significant volumetriccomponent was required to explain the radiation patternsof 19 microseismic events generated during a mine-by ex-periment at the Underground Research Laboratory (URL)in Manitoba, Canada. In his study of South African sourcemechanisms McGarr (1992b) noted that the distribution ofmoment tensor solutions in the deep mines was bimodal:the mine tremors were either pure shear failures, or had aratio of coseismic closure to average shear slip around 0.71.McGarr (1992b) also noted that the moment tensor solutionsreported by Feigner and Young (1992) had a more con-

tinuous distribution of source mechanisms in terms of theirvolumetric-shear mix.

A number of differences between those two studiescould explain the apparent paradox posed by the source-mix distribution of the focal mechanisms. First, the sizeof the database utilized by Feigner and Young (1992) wassignificantly larger (33 events) than that utilized by McGarr(1992b) (10 events), and this difference makes the first studymore relevant statistically. Second, the mining conditionsunder which the seismic events were induced were radicallydifferent; the deep gold mines described by McGarr (1992b)have a maximum principal stress (in absolute sense) that isnegative (i.e., compressive) and near-vertical, which couldexplain the predominance of implosive sources; the URLin Canada is characterized by a maximum principal stressthat is positive and subhorizontal (Feigner and Young, 1992),which could explain the existence of tensile sources. Third,the moment magnitude range for the deep-mine events is1:9 <Mw <3:3, while the magnitude range for the URLevents is �3:3 <Mw <�2:3. The differences could thusbe the result of a magnitude-dependent distribution for thesource mix. And fourth, the observations utilized in bothstudies to infer the moment tensor solutions were different

*Also at School of Geosciences, University of the Witswatersrand, Wits2050, South Africa.

2801

Bulletin of the Seismological Society of America, Vol. 99, No. 5, pp. 2801–2814, October 2009, doi: 10.1785/0120080334

and could have biased the solutions in different ways;McGarr (1992b) utilized select waveform amplitudes in thetime domain, while Feigner and Young (1992) utilized spec-tral amplitudes with polarities attached.

More recently, a moment tensor study of six shallowevents, with moment magnitudes between 1.6 and 1.8, ina coal mine in Utah revealed a continuous variation of thesource mix (Fletcher and McGarr, 2005). The moment tensorsolutions were obtained from select time-domain amplitudes,as in McGarr (1992b), thus demonstrating that the bimodaldistribution reported in McGarr (1992b) did not reflect anybias introduced by the inversion method. The lack of overlapin the magnitude range, the small size of the data set, and thedifferent mining conditions (shallow versus deep), however,can still explain the observed differences in the source-mixdistributions.

In this study, we report moment tensor solutions for 76well-recorded seismic events, with moment magnitudes inthe 0.5–2.6 range and recorded in a deep gold mine in South

Africa (Savuka mine, Carletonville mining district). Themoment tensor solutions have been obtained by invertingspectral amplitudes with polarity attached and verified in thetime domain with synthetic seismograms. Our results de-monstrate that the source-mix distribution is continuous un-der deep mining conditions in the 0:5 <Mw <2:2 momentmagnitude range. At larger magnitudes our results are lessconclusive but still compatible with a bimodal distributionof the volumetric-shear mix, as reported by McGarr (1992b).

Data

The data set utilized in this study has been obtained froma network of 20 seismic stations deployed underground byIntegrated Seismic Systems International (ISSI) to monitormine-related seismic activity at the AnglogoldAshantiSavuka gold mine, South Africa (Fig. 1). The network con-sists of a combination of three-component sensor types: theG4.5 geophone, with a flat response in velocity between 4

4100040000390003800037000 42000

4100040000390003800037000 42000

-280

00-2

7000

-290

00

-280

00-2

7000

-290

00

Easting (m)

Nor

thin

g (m

)

SAV43

SAV41SAV40

SAV44

SAV61SAV36

SAV77SAV34

SAV27

SAV81

SAV80

SAV09

SAV63

SAV29SAV64

SAV78

SAV79

SAV08

SAV21

SAV35

Carletonville

South Africa

Figure 1. Plan of Savuka mine, South Africa, with the location of the in-mine geophones (circles) and the 100 seismic events (graysquares) considered in this study. The black circles denote the stations utilized for moment tensor inversion and the gray circles indicate thestations that could not be utilized. The thin solid lines delineate the outline of the mine, while the shaded areas represent the areas that weremined during 2007. The hypocentral locations were obtained from ISSI.

2802 J. Julià, A. A. Nyblade, R. Durrheim, L. Linzer, R. Gök, P. Dirks, and W. Walter

and 2000 Hz and a sensitivity of 2:8 V=m=sec; the G14 geo-phone, with flat response in velocity between 12 and2000 Hz and a sensitivity of 80 V=m=sec; and the G28 geo-phone, with a flat response in velocity between 28 and2000 Hz and a sensitivity of 15 V=m=sec. The seismic sta-tions are operated at sampling rates ranging from 2000 to10,000 samples per second, with timing synchronizedthrough common Global Positioning System time keeping.Except for one surface sensor, the sensors are deployed atdepth along the two gold-bearing horizons being mined:the Ventersdorp Contact Reef (VCR) and the Carbon LeaderReef (CLR). The VCR is mined at depths of around 3000 m,with Ventersdorp Lavas in the hanging wall and a thin layerof shale in the footwall. The CLR is mined at depths ofaround 3500 m and is separated from the shallower VCRby an ∼500 m thick layer consisting predominantly ofquartzite.

Data Selection

A total of 11,224 mine tremors, with local magnitudesbetween �3:4 and 4.4, were cataloged by ISSI during 2007through the Savuka mine in-mine network. This large catalogincludes events induced by mine activity at the Savuka mineitself, as well as events induced in nearby mines. Good azi-muthal coverage is critical for accurately mapping the seis-mic radiation patterns of the recorded mine tremors, so aselection was made for those events with locations fallingnear or within the volume covered by the in-mine network.Furthermore, the moment tensor inversion procedure em-ployed in this study assumes the propagating medium is awhole space of constant wave speed. This is a reasonableassumption, as the seismic waves from the selected eventsare expected to propagate through the quartzite layer sepa-rating the two gold-bearing horizons. Nonetheless, to ensurethat the selected seismic phases propagate at constant wavespeed, Wadati diagrams were constructed for each eventfrom ISSI, hand-picked P- and S-travel times. Wadati dia-grams are representations of S–P versus P travel timesand, for media of constant wave speed, follow a straight linewith a slope that is directly related to the VP=VS ratio of themedium (Wadati, 1933). For each event, a search was run forthe largest subset of stations that yielded slopes with asso-ciated VP=VS ratios between 1.55 and 1.70, which are appro-priate for quartzites at shallow depths (Christensen, 1996).Outliers were removed from the data set.

To illustrate this Wadati filter, Figure 2 displays aWadatidiagram for an Mw 1:8 event recorded at as many as 16 sta-tions. Note how stations SAV34 and SAV64 have beenrejected due to inconsistent S–P or P-travel times. The cor-responding waveforms are shown on a recorded section inFigure 3, along with the manual travel-time picks reportedby ISSI. Except for the S-wave arrival at station SAV64,all the recordings show clear P- and S-wave arrivals. Wethink the discrepancy highlighted by the Wadati diagramsfor SAV64 is the result of an unclear S-wave onset in the

recordings; for SAV34, the discrepancy could be causedby either a misidentification of the S-wave arrival in the northcomponent or a deviation from propagation at uniformwave speed.

Sensor Orientation

Sensor orientations were verified by comparing theo-retically rotated waveforms with empirically rotated wave-forms (Fig. 4). Theoretical rotations were performed throughthe rotation angles calculated as

tanφ � �yS � y0�=�xS � x0�;cosϕ � �zS � z0�=��xS � x0�2 � �yS � y0�2

� �zS � z0�2�1=2;(1)

where �xS; yS; zS� and �x0; y0; z0� are the station and sourcecoordinates, respectively, with x being north, y being east,and z being up, and ϕ and φ are the takeoff angle and azi-muth, respectively. The empirical rotation angles, on theother hand, were obtained from the eigenvectors associatedwith the eigenvalues of the covariance matrix

Var�x� Cov�x; y� Cov�x; z�Cov�x; y� Var�y� Cov�y; z�Cov�x; z� Cov�y; z� Var�z�

24

35 (2)

2007/01/03 18:31:21.223 Mw = 1.8Vp/Vs = 1.59±0.09 δt0 = -0.443±0.011 r=0.94

0.3

0.2

0.1

0.0

0.0

0.0-0.2-0.4 0.4

tP - t0 (s)

t S -

t P (

s)

SAV64SAV34

Figure 2. Wadati diagram for event 2007.01.03.18.31.21.223.The reference time on the horizontal axis is the trigger time fromone of the recording stations, randomly selected by ISSI to label theevent. Note that two stations, SAV34 and SAV64, have been left outof the Wadati line. The VP=VS ratio, origin time correction, andregression coefficient from the least-squares fit to the data points(not including the rejected stations) is shown in the plot. Confidencebounds are given at the 95% confidence level.

Source Mechanisms of Mine-Related Seismicity, Savuka Mine, South Africa 2803

defined by Montalbetti and Kanasewich (1970), whereVar�x� � P�xi � x��2=�n � 1�, Cov�x; y� � P��xi � x��×�yi � y��=�n � 1�, with * denoting the average within theP-wave window of the in-mine recordings and n denotingthe number of data points. Realize that this polarization filteronly yields the directions of the P, SV, and SH axes andcannot resolve the sense of motion due to the symmetryof the covariance matrix with respect to reflections aboutthe origin of coordinates.

The sensor orientation could only be verified for 13 sta-tions out of the 20 in the network, as 7 of them had at leastone component failing for the entire recording period, whichprevented the rotation into the local ray-coordinate system.Additionally, we observed that the theoretically and empiri-cally rotated waveforms did not compare well for 7 of those13 stations. Fortunately, corrections could be obtained for 4of them through rotations around the vertical axis, yielding atotal of 10 stations available for moment tensor inversion(Table 1). However, an ambiguity of 180° around the vertical

axis is still possible. Indeed, we observed that waveforms re-corded at stations SAV79 and SAV81 were, for some events,more consistent with the moment tensor solutions when ro-tated by 180°. Therefore, these stations were also not used toconstrain focal mechanisms.

A final event selection was done after sorting the eventsby the number of recording stations with verified sensor ori-entations, in descending order, and selecting the top 100. Thehypocentral locations and origin times for the selected eventsare listed in Ⓔ Table E1 (available in the electronic editionof BSSA).

Spectral Amplitudes

Spectral amplitudes for the P, SV, and SH pulses wereobtained in the time domain from the theoretically rotatedwaveforms through the integrals of squared velocities andsquared displacements according to (Trifu et al., 2000)

0.90.80.70.60.50.40.30.20.10.0 1.0 0.90.80.70.60.50.40.30.20.10.0 1.0

time (s) time (s)

Z

N

E

E

Z

N

E

Z

N

Z

N

Z

N

E

E

N

Z

N N

E

Z

N

E

E

Z

N

E

Z

N

Z

N

Z

N

E

E

N

Z

Z

E

E

Z

Z

E

E

Z

N N

E

SA

V64

SA

V36

SA

V80

SA

V40

SA

V79

SA

V44

SA

V63

SA

V34

SA

V81

SA

V41

SA

V77

SA

V43

SA

V09

SA

V61

SA

V78

SA

V08

P S P S

P S P S

P S P S

P S P S

P S P S

P S P S

P S P S

P S P S

Figure 3. Velocity recordings from the Savuka in-mine network for event 2007.01.03.18.31.21.223, sorted by P-wave travel time. Thetraces have been normalized by their maximum absolute amplitude value for displaying purposes. The P- and S-wave travel-time picksreported by the in-mine network operator are overlain on the traces. Note that half of the recording stations (SAV64, SAV80, SAV63,SAV09, SAV78, SAV44, SAV41, and SAV43) have at least one failing channel.


u � 2S3=4D2

S1=4V2

; (3)

where u is the spectral amplitude, SD2 �RD2�t�dt,

SV2 �RV2�t�dt, D is displacement, V is velocity, and the

integrals are evaluated within finite time windows. FollowingTrifu et al. (2000), Pwaveforms were windowed between theP-wave and the S-wave arrivals and S waveforms were win-dowed between the S-wave arrivals and a time window twotimes the S–P travel-time difference in length. Polarities forthe spectral amplitudes were visually assigned by compar-ing the low-pass filtered instrument response in the time

domain to the observed low-pass filtered P- and S-wavepulses (Fig. 5).

Although the spectral amplitudes are evaluated in thetime domain, they are equivalent to measuring the heightof the spectral plateau in the frequency domain (Urbancicet al., 1996). Consequently, the low-pass filter must go belowthe corner frequency to make the observed pulse shape simi-lar to the shape of the instrument response in the time do-main. Typically, we were successful in assigning polaritiesafter low-pass filtering below 10 Hz using two passes of athird order Butterworth filter. However, difficulties weresometimes experienced with the 14 and 28 Hz geophonesand with stations very close to the source. In such cases,we generally succeeded by low-pass filtering below 20 or40 Hz, which suggests that the frequency content of the fil-tered waveform was still within the flat part of the sourcespectrum. Time shifts between the SV and SH pulse, prob-ably due to anisotropic effects, were observed during thisprocess, but because our moment tensor solutions involveonly spectral amplitudes, the time shifts have no effect onour moment tensor solutions.

Inversion Method

Estimates for the six independent components of theseismic moment tensor were obtained by inverting P, SV,and SH spectral amplitudes with polarities attached. Asexplained before, the ray paths for the selected seismicevents are mostly contained within the ∼500 m thick layerof quartzite separating the two gold-bearing reefs, so the

0.80.60.40.20.0 1.0 0.80.60.40.20.0 1.00.80.60.40.20.0 1.0

time (s)

Theoretical (uncorrected) Empirical Theoretical (corrected)

P

SH

SV

Figure 4. Recordings of event 2007.01.03.18.31.23.223 at station SAV77 in the local ray-coordinate system. The vertical scale is thesame in all plots. The left-hand column shows the theoretically rotated waveforms before applying the correction reported in Table 1. Notethat most of the P-wave energy is wrongly mapped into the SH component. The middle column shows the empirically rotated waveforms,which correctly display most of the P-wave energy in the P component. The right-hand column shows the theoretical rotations on thecorrected components, which compare well with the empirical ones.

Table 1List of Stations

ID South (m) West (m) Down (m) Rotation (°)

SAV08 27950 �39827 1869 ?SAV21 27816 �40454 226 ?SAV27 28676 �39582 2003 ?SAV29 29617 �40545 3649 �90SAV34 28330 �40660 2142 180SAV35 29024 �40247 2285 55SAV36 27958 �40226 2960 okSAV40 27738 �39822 2964 okSAV61 27854 �40568 2010 okSAV77 28220 �39753 3089 90SAV79 28109 �40220 3733 ok*

SAV80 29114 �41600 3657 okSAV81 29000 �41638 3493 ok*

*Not utilized due to orientation ambiguity.


forward problem can be safely formulated for a homogenouswhole space. Following Trifu et al. (2000), the forwardproblem can be expressed as

u � cF∶M; (4)

whereu is thevector of spectral displacements in the local ray-coordinate system, c � 1=�4πρv3R� with v being either theP- or S-wave velocity, R the hypocentral distance, ρ the den-sity, andM is thematrix defining the seismicmoment tensor inthe geographic system. F is the excitation matrix given by

FP �sin2 ϕ cos2 φ 1=2 sin2 ϕ sin 2φ 1=2 sin 2ϕ cosφ

1=2 sin2 ϕ sin 2φ sin2 ϕ sin2 φ 1=2 sin 2ϕ sinφ1=2 sin 2ϕ cosφ 1=2 sin 2ϕ sinφ cos2 ϕ

24

35;

FSV �1=2 sin 2ϕ cos2 φ 1=4 sin 2ϕ sin 2φ cos2 ϕ cosφ1=4 sin 2ϕ sin 2φ 1=2 sin 2ϕ sin2 φ cos2 ϕ sinφ� sin2 ϕ cosφ sin2 ϕ sinφ �1=2 sin 2ϕ

24

35; (5)

FSH ��1=2 sinϕ sin 2φ � sinϕ sin2 φ � cosϕ sinφ

sinϕ cos2 φ 1=2 sinϕ sin 2φ cosϕ cosφ0 0 0

24

35;

where ϕ and φ are, again, the takeoff angle and azimuth,respectively.

Because of the symmetry of the moment tensor M,equation (4) can be rewritten as

uj �Xk

cijfikmk; i � P; SV; SH; j � 1;…; n;

(6)

where n is the number of data points, m1 � M11,m2 � M12 � M21, m3 � M22, m4 � M13 � M31, m5 �M23 � M32, and m6 � M33 and where f1 � F11, f2 �F12 � F21, f3 � F22, f4 � F13 � F31, f5 � F23 � F32,and f6 � F33. Equation (6) defines a linear problem, whichis solved for the moment tensor elements mk with no con-straints (i.e., full moment tensor solution) after a singularvalue decomposition (SVD) of the matrix cijf

ik (see, e.g.,

Menke, 1984). Because the only moment tensor solutionsthat do not require a truncation of the singular value spectrumare capable of independently constraining all moment tensorcomponents, in practice, the moment tensor solutionsreported in this study minimize the difference between ob-servations and predictions in a least-squares sense.

The c factor in equations (4) and (6) does not includeany corrections for anisotropy or attenuation. As noted

before, time shifts were observed between the SV and SHamplitudes, which we attribute to anisotropic propagationeffects due to horizontal layering. The SV and SH compo-nents coincide with the S1 and S2 components in a trans-versely isotropic medium, which may delay the pulses withrespect to each other but will not introduce any pulse dou-bling (Backus, 1962). Because the inversions are performedin the frequency domain, where phase information isdropped (except for polarity), we do not believe thatanisotropy strongly maps into our solutions. Attenuation, onthe other hand, could potentially have a stronger effect. As

shown later, our reported moment tensor solutions correctlypredict the polarities of the observed amplitudes, so ourmechanism types should not be strongly affected by attenua-tion effects. On the other hand, attenuation corrections wouldmake the observed amplitudes bigger, and our moment ten-sor sizes could be somewhat underestimated.

Formal uncertainties for the components of the seismicmoment tensor are not reported in this study. In theory, thelinearity of the forward problem defined by equation (6)allows for the matrix of covariance of the spectral amplitudesto be easily propagated into uncertainties of the moment ten-sor components (e.g., Menke, 1984). Fletcher and McGarr(2005), for instance, assign a standard deviation to the ob-served amplitudes equal to 20% of the observed amplitudeand propagate the uncertainties into the moment tensor solu-tions. This approach is successful in conveying the relativeaccuracy among the moment tensor components, but we findit is somewhat arbitrary and statistically misleading. A mean-ingful matrix of covariance for the spectral amplitudesshould include uncertainties in the amplitude measurementas well as uncertainties in the velocities of the propagatingmedium, sensor orientations, and event locations. Our ap-proach has been to conduct numerical experiments in an at-tempt to falsify those observations that are critical to ourstudy. As shown later, we will be interested to know how


well constrained the isotropic part of our moment tensorsolutions are. The observed spectral amplitudes will thenbe reinverted for a purely deviatoric source in order to assessthe necessity of an isotropic component in the moment tensorsolutions. This new suite of inversions will be conductedthrough the same system defined in equation (6) with theadditional constraint that the trace of the moment tensorbe zero,

m1 �m3 �m6 � 0: (7)

Moment Tensor Solutions

We have applied the inversion of spectral amplitudeswith polarity attached described in the previous section tothe 100 events selected for this study, after assuming a wholespace of VP � 6:0 km=sec, VS � 3:70 km=sec, and ρ �

2:69 g=cm3. Only those moment tensor solutions that cor-rectly predict P, SV, and SH polarities for all the waveformswere accepted (the polarity requirement was relaxed forsmall amplitudes, which probably represent null measure-ments), and the quality of the solutions was assessed throughthe condition number and the correlation between observedand synthetic amplitudes. The accepted moment tensor solu-tions, totaling 76, and the corresponding condition numbersand correlation coefficients are listed in Ⓔ Table E2 (avail-able in the electronic edition of BSSA).

The condition number is defined as the ratio between thesmallest and largest singular values in the SVD and is a mea-sure of how robustly constrained the moment tensor compo-nents are. A condition number of 1 indicates that all momenttensor components are equally well constrained, while a con-dition number of 0 indicates that there is at least one com-ponent not resolved and that the solution is nonunique. Forour accepted moment tensor solutions the condition numbersrange between 0.04 and 0.19, just one to two orders of mag-nitude smaller than the ideal value. As discussed later, thereported moment tensor solutions define a consistent radia-tion pattern that agrees well with the stress pattern of themine, suggesting this range of values reflects that the solu-tions are well constrained. The reported condition numbersshould then be taken as a measure of the relative robustnessamong the solutions.

The correlation coefficients were obtained from thecross correlation between observed and synthetic waveformsand are a measure of the similarity between observations andpredictions. Synthetic seismograms were computed from thespectral amplitudes as

u�t� � uδ�t � R=v�; (8)

where u�t� is the displacement vector in the time domain, u isthe spectral amplitude from equation (4), δ�t� is a unit-areaDirac’s delta function, v is either the P- or S-wave velocity,and R is the hypocentral distance, then differentiated toobtain velocities and finally convolved with the instrumentresponse. The correlation coefficients were obtained as

cor � �1=3��C�uobs;P; usyn;P� � C�uobs;SV; usyn;SV�� C�uobs;SH; usyn;SH��; (9)

where uobs stands for observation, usyn for synthetic, andwhere

C�f; g� � max�Z

f�t� τ�g�t� dt�=

�Zf�t�g�t� dt

�;

(10)

where τ is the time shift, after low-pass filtering both obser-vations and synthetics generally below 10 Hz (20 or 40 Hzfor the 14 and 28 Hz instruments). Note that a coefficient of1.0 implies a perfect agreement between observations and

0.40.30.20.10.0 0.5

time (s)

Impulse Response (+)

-P

-SV

+SH

Figure 5. Assignment of polarity for the P, SH, and SV am-plitudes recorded at station SAV61 and corresponding to event2007.02.01.18.08.14.177. The top trace is the instrument responsein the time domain (positive polarity) normalized to unit amplitude,and the traces below are the P, SH, and SV components, respec-tively. All traces have been low-pass filtered below 10 Hz. The si-milarity of the impulse response to the P and S pulses demonstratesthat the frequency content of the pulses is within the flat part of thesource spectrum and suggests the polarities are negative, positive,and negative for the P, SH, and SV amplitudes, respectively.


predictions, while larger and smaller values indicate the am-plitudes have been either overpredicted or underpredicted,respectively. The correlation coefficients corresponding toour accepted moment tensor solutions range between 0.54and 1.18, and we found that even coefficients as small as0.54 give a satisfactory visual match between observationsand predictions. As with the condition numbers, the valuesof the correlation coefficient should be used as a measure ofthe relative goodness of fit of the solutions. In the following,we discuss a few moment tensor solutions in detail.

Event 2007.02.21.18.21.56.591 (Mw 1:6)

Figure 6 displays the moment tensor inversion resultsfor this event, along with the coverage of the focal sphere.Spectral amplitudes for this event were measured for P, SV,and SH arrivals recorded at six in-mine seismic stations andthe polarities were visually assigned for each of them, asdescribed before. The coverage of the focal sphere is char-acteristic of mining environments and reflects the lack ofstation coverage ahead of the advancing mine stopes. The

measured P- and S-wave amplitudes, however, had bothpositive and negative polarities, which suggests that morethan one energy lobe in the radiation pattern has beensampled. The moment tensor solution obtained for this eventis mxx � �1:25 × 1011 Nm, mxy � 0:74 × 1011 Nm,myy � 0:09 × 1011 Nm, mxz � 1:20 × 1011 Nm, myz �0:55 × 1011 Nm, and mzz � �2:66 × 1011 Nm and has alarge condition number around 0.16 and a correlation coeffi-cient around ∼0:70, which is in the middle-to-low portion ofthe observed range and offers a satisfactory visual matchbetween predictions and observations.

Further insight can be gained from the eigenvalues (σi)and eigenvectors (ei) associated to the moment tensor solu-tion. The eigenvalues are indicative of the compressional(negative) or tensional (positive) character of the principalstresses, and the direction is given by the correspondingeigenvectors (e.g., Lay and Wallace, 1995). For this momenttensor solution, we obtain σ1 � �3:35 × 1011 Nm,σ2 � �1:22 × 1011 Nm, and σ3 � 0:74 × 1011 Nm, ande1 � �0:49; 0:04;�0:87�, e2 � ��0:72; 0:57;�0:38�, ande3 � ��0:49;�0:82;�0:31�. The largest principal stress is

-5.0e-08

0.0e+00

5.0e-08

-5.0e-08 0.0e+00 5.0e-08

Mi=1.3e+11 Nm Md=2.1e+11 Nm

0.0 0.5

SAV29 fc=20Hz

0.0 0.5

SAV34 fc=10Hz

0.0 0.5

SAV35 fc=10Hz

0.0 0.5

SAV36 fc=20Hz

0.0 0.5 1.0

SAV61 fc=10Hz

0.0 0.5

SAV77 fc=20Hz

Pred

icte

d am

plitu

de (

ms)

Observed amplitude (ms)

Time (s) Time (s)

P

SV

SH

P

SV

SH

P

SV

SH

-0.012 s

0.010 s

0.015 s

0.005 s

0.021 s

0.021 s

0.007 s

0.023 s

0.023 s

0.010 s

0.016 s

0.002 s

0.001 s

0.019 s

0.019 s

0.020 s

0.007 s

0.020 s

Figure 6. Moment tensor inversion results and coverage of the focal sphere for event 2007.02.21.18.21.56.591. The upper left-handdiagram compares predicted and observed spectral amplitudes for P, SV, and SH components. The lower left-hand diagram shows the P-wave radiation pattern for the isotropic and deviatoric moment tensors, along with the coverage of the focal sphere (overlying the deviatoricsymbol). The waveforms on the right-hand side are shown to compare the corresponding observed (black curves) and predicted (gray curves)P, SV, and SH amplitudes in the time domain. The event origin time is at t � 0 sec, and the synthetic waveforms have been shifted by theamount noted above each trace, to facilitate the comparison with the observations. The time shifts between observed and synthetic waveformsare due to inaccuracies in the event location, assumed wave speed, and/or anisotropic effects. Note that only spectral amplitudes wereinverted, so the observed time shifts did not influence our moment tensor solutions. The waveforms are shown in velocity.


thus compressive and oriented near vertically (deflectionfrom the vertical is ∼29°), consistent with the stress condi-tions expected in a deep mine.

All moment tensors can be decomposed into isotropicand deviatoric components, with the isotropic eigenvaluegiven by tr�σi�=3, where tr�σi� � σ1 � σ2 � σ3 is the trace,and the deviatoric eigenvalues given by σ�

j � σj � tr�σi�=3(e.g., Jost and Herrman, 1989). For this particular momenttensor solution tr�σi� � �3:83 × 1011 Nm, representativeof an implosive volumetric source. The deviatoric eigenvaluesare σ�

1 � �2:07 × 1011 Nm, σ�2 � 0:06 × 1011 Nm, and

σ�3 � 2:01 × 1011 Nm, which are well approximated by a

double-couple force equivalent (e.g., Jost and Herrmann,1989). The eigenvectors of the deviatoric moment tensorare the same as those for the general moment tensor, so thedouble-couple solution has a subvertical pressure axis anda subhorizontal tension axis characteristic of normal faulting.The decomposition of the moment tensor solution for this

event thus indicates that stresses have been relaxed throughnormal faulting and coseismic closure (McGarr, 1992a).

Event 2007.02.01.01.49.31.639 (Mw 1:1)

More generally, however, we obtain deviatoric momenttensors that do not follow a clear double-couple pattern, andFigure 7 displays the moment tensor inversion results and thecoverage of the focal sphere for one such event. All P-waveamplitudes are negative, although a polarity could not be as-signed for SAV35 due to its small amplitude, and polaritiesof both signs are found among the S-wave amplitudes. Themoment tensor solution obtained for this event ismxx � �2:48 × 1010 Nm, mxy � 1:47 × 1010 Nm, myy ��1:98 × 1010 Nm, mxz � 1:50 × 1010 Nm, myz � �1:78×1010 Nm, andmzz � �4:33 × 1010 Nm and has a large con-dition number of ∼0:18 and a correlation coefficient of 0.88,

-7.9e-09

0.0e+00

7.9e-09

-7.9e-09 0.0e+00 7.9e-09

Mi=2.9e+10 Nm Md=3.4e+10 Nm

0.0 0.5

SAV29 fc=10Hz

0.0 0.5

SAV34 fc=20Hz

0.0 0.5

SAV35 fc=20Hz

0.0 0.5

SAV36 fc=20Hz

0.0 0.5 1.0

SAV40 fc=20Hz

0.0 0.5

SAV61 fc=20Hz

0.0 0.5

SAV77 fc=20Hz

Pred

icte

d am

plitu

de (

ms)

Observed amplitude (ms)

Time (s)

Time (s)

P

SV

SH

P

SV

SH

P

SV

SH

P

SV

SH

0.009 s

0.022 s

0.015 s

0.022 s

0.023 s

0.003 s

0.026 s

0.022 s

0.023 s

0.016 s

0.043 s

0.041 s

0.011 s

0.036 s

0.035 s

0.022 s

0.029 s

0.010 s

0.021 s

0.047 s

0.046 s

Figure 7. Same caption as in Figure 6, but for event 2007.02.01.01.49.31.639. The P-wave and SH-wave spectral amplitudes for stationSAV35 and SAV34, respectively, were not included in the inversion due to difficulties in assigning a polarity, but the corresponding syntheticseismograms predicted by our moment tensor solution are shown as a gray, dotted line.


which, once more, offers a satisfactory visual match betweenobservations and predictions.

The eigenvalues for the seismic moment tensor for thisevent are σ1 � �6:36 × 1010 Nm, σ2 � �1:77 × 1010 Nm,and σ3 � �0:67 × 1010 Nm, and the corresponding eigen-values are e1 � �0:47;�0:46;�0:75�, e2 � ��0:72; 0:30;�0:63�, and e3 � ��0:51;�0:84; 0:20�, which again reveala compressive and subvertical maximum principal stress (de-flection from vertical is ∼41°). The trace of the momenttensor is �8:80 × 1010 Nm, suggestive of an implosivevolumetric contribution and consistent with the negativepolarities observed for all P-wave amplitudes. The deviatoriceigenvalues are σ�

1 � �3:43 × 1010 Nm, σ�2 � 1:16×

1010 Nm, and σ�3 � 2:27 × 1010 Nm, which clearly do

not match the double-couple pattern. The deviatoric mo-ment tensor can further be decomposed into major andminor double couples (e.g., Jost and Herrmann, 1989);for this particular event, one possible decompositionwould be

�3:431:16

2:27

24

35

��1:16

1:160:00

24

35�

�2:270:00

2:27

24

35

(11)

in 1010 Nm. This decomposition would explain theobserved radiation pattern through two normal faults, witha common P axis and two corresponding T axes formingan angle of 90°, and a coseismic volumetric closure.

The deviatoric moment tensor can be decomposed inmultiple ways and the choice of the decomposition type isarbitrary (see, e.g., Jost and Herrmann, 1989). Anothercommon choice is the decomposition into a compensatedlinear vector dipole (CLVD) and a double couple, whichcan be useful in identifying pillar failures (the force equiva-lent is the compression CLVD combined with an isotropicimplosion that annihilates the P-wave compressions in thedirections perpendicular to the principal axis of the CLVD)(e.g., Sileny and Milev, 2006, 2008). The decompositionutilized in equation (11) was the one favored in McGarr(1992a,b), and it has been chosen here for consistency withthose studies.

Discussion and Conclusions

The 76 moment tensor solutions obtained in this studyreveal that the largest (in an absolute sense) principal stressesare generally negative (i.e., compressional) and orientedsubvertically (see Ⓔ Table E3, available in the electronicedition of BSSA). This is in agreement with the expectedprincipal stresses in the deep mine being mainly causedby gravitational forces attempting to close the mined-out

areas. Indeed, in-situ measurements in the East Rand Pro-prietary mine (ERPM), also in the Witswatersrand basin,show that the maximum principal stress is compressionaland oriented at an angle between the vertical and the normalto the gold-bearing horizon (which dips around 30° to thesouth-southwest in the ERPM area) (Pallister et al., 1970).If a decomposition of the deviatoric moment tensor intotwo double couples as in equation (11) is chosen, then thesolutions listed in Table E3 indicate that deep-mine stressesare relaxed through a combination of coseismic volumetricclosure and normal faulting.

We have obtained isotropic (mI), deviatoric (mD), total(mT) scalar moments, and moment magnitudes from ourmoment tensor solutions. Assuming that the eigenvaluesof the general moment tensor are given by σ1, σ2, and σ3,then the scalar moments are defined as (Bowers and Hudson,1999)

mI � j1=3 tr�σi�j;mD � max�jσ�

j j�; and mT � mI �mD;(12)

respectively, where tr�σi� � σ1 � σ2 � σ3 and σ�j � σj�

tr�σi�=3. The moment magnitude is obtained from the totalscalar moment as (Hanks and Kanamori, 1979)

Mw � 2=3�log10�mT� � 9:1�; (13)

where mT is expressed in newton meter. The values for thescalar moments and moment magnitudes can be found inⒺ Table E4 (available in the electronic edition of BSSA).

A careful inspection of our moment tensor solutions(Ⓔ Table E4) reveals that a total of 66 solutions have a sig-nificant isotropic moment representing more than 10% of thetotal moment (computed as mI=mT × 100). Before drawingany conclusions about the volumetric-shear mix, however, itis important to assess how well constrained the volumetriccomponents are, and, as explained before, this is investigatedby rerunning the moment tensor inversions after imposing apurely deviatoric moment tensor solution (equation 7). Thisis illustrated in Figure 8 through event 2007.03.04.06.16.04.098, where low-frequency synthetic seismograms pre-dicted by the full and constrained moment tensor solutionsare compared to the corresponding observed traces. Bothmoment tensor solutions correctly predict the polarities forthe P, SV, and SH amplitudes, and the correlation coeffi-cients between observed and predicted amplitudes are simi-lar, 0.86 for the full solution and 0.77 for the constrainedsolution. The condition number of the full moment tensorsolution is around 0.15.

The results of this exercise reveal that 47 solutionsrequire a nonzero trace to fully explain the polarities forthe observed amplitudes, while the polarities for theremaining 19 events can be explained just as well througha purely deviatoric source. As expected, the match between


observed and predicted amplitudes is generally better for thefull moment tensor solutions (correlation coefficients rangebetween 0.54 and 1.18) than for the constrained solutions(correlation coefficients range between 0.42 and 1.32), asthe full solutions have an additional degree of freedom com-pared to the constrained solution. Occasionally, the changein the correlation coefficient is big enough that it could beused to favor one solution over the other but, in general, weobserve that the change is not significant. The conditionnumber for the solutions with an uncertain volumetric com-ponent ranges between 0.05 and 0.17, similar to the rangeobserved for the full moment tensor solutions for the wholedata set. As argued before, we think that this range of valuesreflects well-constrained moment tensor solutions, as thesimilarity suggests uncertain volumetric contributions arethe result of uncertainties in the amplitude measurementsrather than an insufficient coverage of the focal sphere.The deviatoric P-wave radiation patterns for these momenttensor solutions are displayed in Figure 9, superimposed onthe Savuka mine plan.

McGarr (1992b) reported a bimodal distribution of thevolumetric-shear mix for 10 events with moment magnitudesin the 1.9–3.3 range recorded in two deep mines in SouthAfrica. The distribution peaked at values of 0.0 and 0.71for the volumetric to shear-slip ratio (�ΔV=ΣAD), withno events having ratios between 0.0 and 0.5. FollowingMcGarr (1992b), the volumetric closure (�ΔV) and the aver-age shear slip (ΣAD) are calculated as

ΔV � tr�σi�=�λ� 2μ�;ΣAD � �jσ�

1 j � jσ�2 j�=2μ; (14)

where tr�σi� is the trace of the moment tensor, σ�1 and σ�

2 arethe eigenvalues of the major and minor double couples of thedeviatoric moment tensor, λ and μ are Lamé’s elasticconstants, and A and D represent the fault area and averageslip, respectively. We have assumed that λ� 2μ � 1:63×1011 Pa and μ � 3:76 × 1010 Pa for the Witswatersrandquartzite (McGarr, 1992b). The �ΔV, ΣAD, and�ΔV=ΣAD values for the 76 moment tensors can be found

0.0 0.5

SAV29 fc=40Hz

0.0 0.5

SAV34 fc=20Hz

SAV35 fc=20Hz

0.0 0.5

0.0 0.5

SAV36 fc=20Hz

0.0 0.5 1.0

SAV61 fc=20Hz

0.0 0.5

SAV29 fc=40Hz

0.0 0.5

SAV34 fc=20Hz

SAV35 fc=20Hz

0.0 0.5

0.0 0.5

SAV36 fc=20Hz

0.0 0.5 1.0

SAV61 fc=20Hz

-0.007 s

-0.004 s

-0.010 s

-0.010 s

0.007 s

-0.008 s

-0.014 s

0.006 s

0.007 s

-0.010 s

0.015 s

-0.002 s

-0.018 s

0.008 s

-0.014 s

-0.007 s

-0.004 s

-0.010 s

-0.010 s

0.007 s

-0.008 s

-0.014 s

0.006 s

0.007 s

-0.010 s

0.015 s

-0.002 s

-0.018 s

0.008 s

-0.014 s

Time(s)

Time(s)

Time(s)

Time(s)

FULL MOMENT TENSOR DEVIATORIC MOMENT TENSOR

Mi= 1.5e+10 Nm Md= 3.6e+10 Nm Md= 3.8e+10 Nm

Figure 8. Observations (black curves) and synthetic seismograms (gray curves) for event 2007.03.04.06.16.04.098 corresponding to afull moment tensor solution (left-hand set of panels) and a purely deviatoric moment tensor solution (right-hand set of panels). The eventorigin time is at t � 0 sec, and the synthetic waveforms have been shifted by the amount noted above each trace. Note that both solutionssatisfactorily explain the P-wave amplitudes in all recordings. The isotropic component of the full moment tensor solution is explosive andrepresents ∼29% (mI=mT × 100) of the total moment tensor.


4100

040

000

3900

038

000

3700

042

000

4100

040

000

3900

038

000

3700

042

000

-28000-27000 -29000

-28000-27000 -29000

Northing (m)

SA

V43

SA

V41 SA

V40

SA

V44

SA

V61

SA

V36

SA

V77

SA

V34

SA

V27

SA

V81

SA

V80

SA

V09

SA

V63

SA

V29

SA

V64S

AV

78

SA

V79

SA

V08

SA

V21

SA

V35

Zone

5

Zone

4

Zone

3

Zone

1

Zone

2

2007

/01/

0203

:39:

30.2

87

2007

/01/

1218

:53:

44.0

41

2007

/01/

2912

:03:

49.7

84

2007

/02/

0621

:54:

44.7

99

2007

/02/

0819

:08:

01.1

93

2007

/02/

1418

:59:

21.1

64

2007

/01/

2406

:15:

38.7

3620

07/0

1/28

13:4

7:49

.558

2007

/02/

1612

:28:

52.0

10

2007

/02/

2107

:17:

10.6

78

2007

/01/

1719

:05:

47.9

76

2007

/02/

0519

:04:

19.6

1320

07/0

2/14

05:0

7:21

.708

2007

/02/

1502

:25:

46.8

11

2007

/02/

1912

:10:

02.8

68

Zone

1Zo

ne 2

2007

/02/

0600

:39:

45.7

79

2007

/02/

1418

:46:

17.7

30

2007

/11/

1518

:34:

11.1

11

2007

/11/

1603

:19:

10.9

09

2007

/11/

2419

:35:

52.4

87

2007

/11/

2918

:57:

44.9

86

2007

/01/

0600

:35:

47.3

8920

07/0

1/07

23:2

9:52

.426

2007

/02/

1501

:18:

34.0

61

2007

/01/

0318

:31:

21.2

23

2007

/01/

0321

:20:

47.1

05

2007

/01/

0616

:22:

37.0

98

2007

/02/

0218

:37:

59.3

08

2007

/02/

1318

:45:

58.1

25

2007

/02/

1402

:03:

11.7

89

2007

/02/

1402

:27:

07.1

6720

07/0

2/21

18:4

6:22

.671

2007

/11/

1718

:12:

22.5

57

2007

/11/

2207

:10:

06.6

57

2007

/01/

3119

:14:

31.3

09

2007

/01/

0518

:28:

16.7

0620

07/0

1/11

18:2

5:29

.772

2007

/01/

1318

:10:

01.0

94

2007

/01/

1718

:42:

13.7

37

2007

/01/

2418

:57:

49.9

56

2007

/01/

2518

:18:

51.5

17

2007

/01/

2618

:14:

21.9

04

2007

/01/

2717

:16:

16.3

03

2007

/01/

2917

:56:

34.2

12

2007

/01/

3119

:11:

56.2

65

2007

/02/

0101

:49:

31.6

39

2007

/02/

0118

.08.

14.1

77

2007

/02/

0905

:28:

14.6

68

2007

/02/

0918

:07:

31.5

04

2007

/02/

1013

:06:

02.3

16

2007

/02/

1318

:49:

35.9

53

2007

/02/

1618

:44:

27.2

8220

07/0

2/21

18:2

1:56

.591

2007

/03/

0509

:27:

58.5

98

Zone

3

Zone

4

Zone

5

Figure9.

Spatiald

istributionof

thedeviatoricfocalm

echanism

sforthe

Savuka

mineeventsconsidered

inthisstudy(onlythoseeventswith

awell-constraineddeviatoricparthave

been

included).The

blacksymbolsrepresentthose

eventswith

asignificantvolum

etriccomponent(m

orethan

10%

ofthetotalscalarm

oment);the

gray

symbolsrepresentthose

eventswith

anear-

deviatoric

solutio

n(lessthan

10%

ofthetotalscalar

mom

ent).The

mineplan

isthesameas

inFigure

1,with

activ

eareashighlig

hted.


in Ⓔ Table E5 (available in the electronic edition of BSSA).Note that negative values of the source-mix ratio indicate anexplosive volumetric component, null values indicate apurely deviatoric source, and positive values indicate an im-plosive volumetric component. A quick inspection of the ra-tios reveals a more or less continuous variation of volumetricclosure to average shear-slip ratios (�ΔV=ΣAD), withvalues ranging between �0:4 and 0.9, and peaking around0.2 and 0.6 (Fig. 10). The moment tensors with an uncertainvolumetric contribution include all the explosive sources.

The magnitude dependence of the volumetric closure toshear-slip ratios is investigated in Figure 11. The figureincludes the ratios for the 76 events reported in this study,plus the 10 measurements obtained by McGarr (1992b). Thediagram shows that the distribution of volumetric to shear-slip ratios is continuous for moment magnitudes below 2.2. Ifwe remove the poorly constrained events from our database,we observe that the ratios for events with moment magni-tudes below 2.2 still display a more or less continuous rangeof values for the �ΔV=ΣAD ratio. For moment magnitudesabove 2.2 the distribution seems bimodal, as reported byMcGarr (1992b), but this magnitude range is clearly under-sampled by our measurements.

Summarizing, the moment tensor solutions obtained inthis study for 76 mine tremors in South Africa have demon-strated that the distribution of coseismic volumetric closure toshear-slip ratios is continuous in the 0:5 <Mw <2:2momentmagnitude range. A continuous distribution of thevolumetric-shear mix had been previously reported for mine tremors atoverlapping and lower magnitude ranges in shallow minesin Canada and Utah (Feigner and Young, 1992; Fletcherand McGarr, 2005), which suggests the continuous distribu-tion of the volumetric-shear mix is independent of miningconditions. At moment magnitudes above 2.2, our measure-

ments do not have enough overlap with those of McGarr(1992b) to either confirm or call into question their postulatedbimodal distribution. The number of measurements in thismagnitude range is significantly smaller than at lower mag-nitudes and more measurements are required to confidentlyassess the bimodality of the source-mix distribution.

Data and Resources

Seismic waveforms used in this study were obtained aspart of the Mine Seismicity Project of AfricaArray (http://africaarray.psu.edu, last accessed July 2009). Event locationsand local magnitudes were obtained from Integrated SeismicSystems International (ISSI). The moment tensor inversioncodes were developed by J. Julià. Some plots were madeusing the Generic Mapping Tools, version 4.3.3 (http://gmt.soest.hawaii.edu [last accessed July 2009], Wesseland Smith, 1998).

Acknowledgments

AngloGold Ashanti is thanked for sharing the proprietary data forSavuka mine used in this study. We are also indebted to Integrated SeismicSystems International for their role in providing the in-mine data analyzed inthis study. The manuscript has greatly benefited from detailed and insightfulreviews from two anonymous referees, as well as from comments by SteveSpottiswoode and Alex Milev at the Council for Scientific and IndustrialResearch in South Africa. Roger Stewart is thanked for helping producea printable version of the Savuka mine plans. Support for this work has beenprovided by the U.S. Department of Energy, Contract Number DE-FC52-06NA27320.

References

Backus, G. E. (1962). Long-wave elastic anisotropy produced by horizontallayering, J. Geophys. Res. 67, 4427–4440.

3.02.52.01.51.00.5

0.5

0.0

-0.5

1.0

3.5

This study

McGarr [1992b]

Moment Magnitude (Mw)

-∆V

/ΣA

D

Figure 11. Magnitude dependence of the volumetric-shear mixfor deep-mine events in South Africa. The solid squares denote fullmoment tensor solutions with a poorly constrained isotropic com-ponent. The events within the dotted lines have small isotropic com-ponents in the full moment tensor solution and are considered to bewell-constrained deviatoric sources (McGarr, 1992b).

1.00.50.0-0.5-1.0 1.50

5

10

15

-∆V/ΣAD

# of

eve

nts

Figure 10. Histogram of volumetric to shear-slip ratios(�ΔV=ΣAD) for the values listed in Ⓔ Table E5 (available inthe electronic edition of BSSA). Negative and positive valuescorrespond to explosive and implosive volumetric contributions, re-spectively. Note the continuous range of values of the source mix,from �0:4 to 1.0.


http://africaarray.psu.edu




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Department of GeosciencesThe Pennsylvania State University407 Deike BuildingUniversity Park, Pennsylvania [email protected].

(J.J., A.A.N.)

Council for Scientific and Industrial Research and School of GeosciencesUniversity of WitswatersrandJohannesburg, South Africa

(R.D.)

MeerCAT Geophysics and School of GeosciencesUniversity of the WitswatersrandJohannesburg, South Africa

(L.L.)

Lawrence Livermore National LaboratoryLivermore, California 94551

(R.G., W.W.)

School of GeosciencesUniversity of the WitswatersrandWits 2050, South Africa

(P.D.)

Manuscript received 21 November 2008


10/8/09 10:19 AMBSSA, Vol. 99:5, Electronic Supplement to Julià et al.

Page 1 of 1file:///Users/andy/Desktop/julia_et_al-E_supplement.html

Electronic Supplement to Source Mechanisms of Mine-Related Seismicity, SavukaMine, South Africa

by J. Julià , A.A. Nyblade, R. Durrheim, L. Linzer, R. Gök, P. Dirks,and W. Walter

Focal Parameters for Mine Tremors at Savuka

The supplementary material provided here consists of four space delimited ASCII tables containingorigin times, locations, moment tensor solutions, and scalar moments for the mine tremors analyzed inthis study.

Tables

Table E1 [ASCII Text File; 8 KB]. Origin times, hypocentral locations, and local magnitudes for themine tremors analyzed in this study. The origin times are given in local South African time and thelocations are given in a local mine-coordinate system where x is North, y is East, and z is Up. Eventlocations and origin times were reported by Integrated Seismic Systems International (ISSI).

Table E2 [ASCII Text File; 12 KB]. General moment tensor solutions for the 81 events analyzed in thisstudy. The moment tensor components are given in the local mine-coordinate system, where x isNorth, y is East, and z is Up. The last two columns correspond to the condition number of the singularvalue spectrum (cond) and the correlation coefficient between observed and predicted waveforms (c12),respectively.

Table E3 [ASCII Text File; 12 KB]. Eigenvalues (s1, s2, s3) and eigenvectors (e1, e2, e3) for themoment tensor solutions listed in Table E2. Note the eigenvalues have been sorted so that s1 < s2 < s3.

Table E4 [ASCII Text File; 8 KB]. Isotropic (mI), deviatoric (mD), and total (mT) scalar moments,and moment magnitudes (Mw) from the moment tensor solutions listed in Table E2.

Table E5 [ASCII Text File; 4 KB]. Volume closure (-DV), total shear-slip (AD), and volumetric toshear-slip ratio (-DV/AD) for the moment tensor solutions listed in Table E2.

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Source Mechanisms of Mine-Related Seismicity, Savuka Mine ...africaarray.psu.edu/publications/pdfs/Julia_et_al... · Bulletin of the Seismological Society of America, Vol. 99, No.

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