Moment tensor solutions estimated using optimal filter theory for 51 selected earthquakes, 1980–1984

Physics of the Earth and Planetary Interiors, 47 (1987) 67—79 Elsevier Science Publishers B.V., Amsterdam — Printed in The Netherlands

67

Moment tensor solutions estimated using optimal filter theory for 51 selected earthquakes, 1980—1984 Stuart A. Sipkin U.S. Geological Survey, MS 967, Box 25046, DFC, Denver, CO 80225 (U.S.A.) (Received January 2, 1986; revision accepted August 12, 1986)

Sipkin, S.A., 1987. Moment tensor solutions estimated using optimal filter theory for 51 selected earthquakes, 1980—1984. Phys. Earth Planet. Inter., 47: 67—79. The 51 global events that occurred from January 1980 to March 1984, which were chosen by the convenors of the Symposium on Seismological Theory and Practice, have been analyzed using a moment tensor inversion algorithm (Sipkin). Many of the events were routinely analyzed as part of the National Earthquake Information Center’s (NEIC) efforts to publish moment tensor and first-motion fault-plane solutions for all moderate- to large-sized (m b> 5.7) earthquakes. In routine use only long-period P-waves are used and the source-time function is constrained to be a step-function at the source (&-function in the far-field). Four of the events were of special interest, and long-period P, SH-wave solutions were obtained. For three of these events, an unconstrained inversion was performed. The resulting time-dependent solutions indicated that, for many cases, departures of the solutions from pure double-couples are caused by source complexity that has not been adequately modeled. These solutions also indicate that source complexity of moderate-sized events can be determined from long-period data. Finally, for one of the events of special interest, an inversion of the broadband P-waveforms was also performed, demonstrating the potential for using broadband waveform data in inversion procedures.

1. Introduction In the past decade, studies of seismic source processes have come to rely on the analysis of waveform data for most of their information. These analyses mostly, but not entirely, consist of waveform modeling and inversion of waveform data. Until the advent of the Global Digital Seismograph Network (GDSN) in the late 1970s (and other digital networks more recently), this required the digitization of analogue data, a long, laborious process. Owing, in large part, to the availability of high-quality digital data, there has been a great increase in the number of different methods for extracting source parameters from waveform data. To compare (and in some cases, contrast) the results from various modeling and inversion procedures, the convenors of the Symposium on

Seismological Theory and Practice chose a data set of 51 global events that occurred from January 1980 to March 1984 to be analyzed. The hypocentral parameters are listed in Table I. The events range in magnitude from mb = 5.6 to 6.9 and M5 = 5.2 to 7.7, with depths ranging from 2 to 651 km (NEIC). The scalar moments obtained in this study range from 2.0 x 1024 to 4.2 x 1027 dyne-cm (M~= 5.5 to 7.7).

2. Method The Multichannel Signal Enhancement (MSE) algorithm determines an earthquake’s mechanism from a suite of observed seismograms by using methods from the theory of optimal filter design. The moment tensor of the source is regarded as an unknown multichannel filter whose input is a set

68 TABLE I Hypocentral parameters No.

Date

1 1/ 1/80 2 5/25/80 3 6/29/80 4 7/29/80 5 10/10/80 6 10/24/80 7 11/ 8/80 8 11/23/80 9 1/18/81 10 1/23/81 11 7/ 6/81 12 10/28/81 13 11/22/81 14 11/27/81 15 1/ 3/82 16 1/ 9/82 17 8/ 5/82 18 9/ 6/82 19 12/13/82 20 2/13/83 21 4/ 3/83 22 4/ 4/83 23 4/11/83 24 4/18/83 25 5/ 2/83 26 5/26/83 27 6/ 1/83 28 6/ 2/83 29 6/ 9/83 30 6/21/83 31 6/24/83 32 7/12/83 33 8/ 6/83 34 8/17/83 35 9/ 7/83 36 9/12/83 37 10/ 4/83 38 10/ 9/83 39 10/17/83 40 10/22/83 41 10/30/83 42 11/16/83 43 11/24/83 44 11/30/83 45 12/22/83 46 12/30/83 47 1/ 1/84 48 2/ 7/84 49 3/ 5/84 50 3/19/84 51 3/24/84 a From the Monthly

h

a

mm

s

Latitude

16 42 40.0 38.815 N 16 33 44.7 37.600 N 7 20 5.5 34.808 N 14 58 40.8 29.598 N 12 25 23.5 36.195 N 14 53 35.1 18.211 N 10 27 34.0 41.117 N 18 34 53.8 40.914 N 18 17 24.4 38.640 N 21 13 51.7 30.927 N 3 8 24.2 22.293 S 4 34 17.8 31.272 S 15 5 20.6 18.752 N 17 21 45.8 42.913 N 14 9 50.5 0.972 5 12 53 51.9 46.984 N 20 32 53.0 12.597 S 1 47 2.7 29.325 N 9 12 48.1 14.701 N 1 40 11.0 39.945 N 2 50 1.2 8.717 N 2 51 34.4 5.723 N 8 18 10.1 10.419 N 10 58 51.3 27.793 N 23 42 37.8 36.219 N 2 59 59.6 40.462 N 1 59 54.7 17.038 S 20 12 50.7 9.512 S 18 46 0.9 51.414 N 6 25 27.4 41.346 N 9 6 45.8 24.176 N 15 10 3.4 61.031 N 15 43 51.2 40.142 N 10 55 54.1 55.867 N 19 22 5.2 60.976 N 15 42 8.6 36.502 N 18 52 13.3 26.535 S 11 25 40.6 26.135 S 19 36 21.5 37.588 N 4 21 35.0 60.665 S 4 12 27.1 40.330 N 16 13 0.1 19.430 N 5 30 34.2 7.481 S 17 46 0.7 6.852 S 4 11 29.2 11.866 N 23 52 39.9 36.372 N 9 3 37.6 33.404 N 21 33 20.5 9.924 S 3 33 51.2 8.136 N 20 28 39.8 40.288 N 9 44 2.6 44.162 N Listings of the National Earthquake

Longitude

Dep.

27.780 W 10 118.840 W 5 139.181 E 15 81.092 E 18 1.354 E 10 98.240 W 72 124.253 W 19 15.366 E 10 142.750 E 33 101.098 E 33 171.742 E 33 110.649 W 10 120.839 E 24 131.076 E 543 21.870 W 10 66.656 W 10 165.931 E 31 140.360 E 176 44.379 E 5 75.135 E 16 83.123 W 37 94.722 E 79 62.764 W 40 62.054 E 64 120.317 W 10 139.102 E 24 174.605 W 179 71.249 W 598 174.111 W 21 139.099 E 10 122.402 E 44 147.286W 37 24.766 E 2 161.287 E 63 147.500 W 45 71.082 E 209 70.563 W 15 70.518 W 16 17.520 W 10 25.451 W 24 42.187 E 12 155.454W 12 128.168 E 179 72.110 E 10 13.529 W 11 70.738 E 214 137.322 E 374 160.455 E 14 123.765 E 651 63.333 F 26 148.289 E 43 Information Center.

01b

M 5

6.0 6.1 5.8 6.1 6.5 6.4 6.2 6.0 6.1 5.7 6.9 6.2 6.2 5.8 5.8 5.7 6.2 6.5 6.0 5.6 6.5 6.6 6.0 6.5 6.2 6.8 6.2 5.9 6.2 6.7 6.1 6.1 6.2 6.6 6.2 6.1 6.4 5.9 6.0 6.5 6.1 6.4 6.4 6.6 6.4 6.6 6.5 6.5 6.7 6.5 6.1

6.7 6.1 6.2 6.5 7.3 7.2 6.9 6.9 6.8 7.0 6.2 6.5 6.5 5.2 7.1 6.0 6.2 7.3 5.9 6.5 7.7

5.8 6.9 6.7 6.4 7.0 6.2 7.3 6.2 6.3 6.8 6.9 6.7 7.6 6.2

7.5 7.0 7.1

Region Azores Is. Calif—Nevada border reg. Near S. coast of Honshu, Japan Nepal Algeria Cent. Mexico Near coast of N. Calif. S. Italy Near coast of Honshu, Japan Sichuan Province, China Loyalty Is. reg. Easter Island reg. Luzon, Philippine Is. E. USSR—N.E. China border reg. Cent. Mid-Atlantic Ridge New Brunswick Santa Cruz Is. S. of Honshu, Japan W. Arabian Peninsula S. Xinjiang, China Costa Rica N. Sumatra Near coast of Venezuela S. Iran Cent. Calif. Near W. Coast of Honshu, Japan Tonga Is. Peru—Brazil border reg. Andreanof Is., Aleutian Is. Hokkaido, Japan reg. Taiwan reg. S. Alaska Aegean Sea Near E. coast of Kamchatka S. Alaska Afghanistan—USSR border Near coast of N. Chile Near coast of N. Chile N. Atlantic Ocean S. Sandwich Is. reg. Turkey Hawaii Banda Sea Chagos Archipelago reg. N.W. Africa Hindu Kush reg. Near coast of Honshu, Japan Solomon Is. Mindanao, Philippine Is. Uzbek SSR Kuril Is.

69

of Green’s functions and whose output is a set of theoretical seismograms. The input Green’s functions are taken as known, and the algorithm determines the filter (moment tensor) that makes the output agree as well as possible, in a least squares sense, with the observed seismograms. The moment tensor acts as both a signal-enhancement filter and a noise-rejection filter; features of the seismograms that are not included in the Green’s functions (for example, arrivals generated by unmodeled near-receiver or near-source structure) are regarded as noise and have little effect on the solution. Furthermore, the waveform amplitudes as not normalized as in some other inversion schemes, since this would vitiate important information regarding the relative locations of the nodes and antinodes of the source mechanism. We use two variants of the MSE algorithm. In the first variant, all the elements of the moment tensor are constrained to have a step-function (s-function in the far-field) time-history, differing only by constant factors, while in the second variant these elements are allowed to be independent functions of time. This second representation provides information about the time-history of the rupture process, and is helpful for identifying multiple earthquakes and for studying such processes as changes in fault orientation or in slip direction, In both variants, the solutions are constrained to be purely deviatoric, but are not required to be double-couples. The ‘time-dependent’ version of the algorithm was applied to three events of special interest, which were also suspected of being complex events due to their large non-double-coupie components. The Green’s functions used here are those for the far field of a point-source, and include the effects of reflection at the free surface and attenuation. The Green’s functions are computed using the WKBJ method. These algorithms are presented in more detail in Sipkin (1982, 1986). The centroidal depth is one of the source parameters determined in the inversion procedure. Since the surface reflected phases pP and sP are included in the P-waveforms (for shallow events) the interference of these waveforms should be an accurate indicator of source depth. For long-period data the surface reflected phases cannot be separated from the direct phase, and thus methods in

which they are individually identified and measured cannot be used. Nábèlek (1984) has suggested that constraining the time-function to be a step-function will result in the centroidal depths being biased to too great a depth. This observation is true if no time shifts are introduced to align the real data and the Green’s functions. As shown by Doombos (1982) and by the synthetic examples in Sipkin (1986), however, proper alignment of the data will result in unbiased depth estimates. Doornbos (1985) has also shown how the time delays thus obtained may then be used to invert for the centroid time shifts. The linear constraint that the moment tensor is purely deviatoric has been imposed by reparameterizing the normal equations. Although it may be possible to resolve statistically significant isotropic components using normal mode data (Silver and Jordan, 1982), they are not readily resolvable using body-wave data (Dziewonski and Woodhouse, 1983). Since the solutions are not, however, constrained to be pure double-couples there are an infinite number of ways they can be decomposed into a ‘best’ double-couple and a remainder. We have chosen the decomposition proposed by Knopoff and Randall (1970) in which the moment tensor is decomposed into a double-couple and a compensated linear-vector dipole (CLVD), both of which share the same principal axis system. This is a more satisfying decomposition than one in which the best douple-couple and the remainder require stress fields with different orientations. Using the Knopoff and Randall decomposition, the contribution of the CLVD component to the total moment is 2 I ~‘ mm I/ I ~max I’ where A ~ is the eigenvalue with the smallest absolute value and A max is the eigenvalue with the largest absolute value.

3. Moment tensor solutions For all of the inversions in this study, except one, only long-period data GDSN data was used. The exception was the New Brunswick earthquake on 9 January 1982, for which broadband waveforms, obtained by a simultaneous deconvolution of the long- and short-period waveforms (Harvey and Choy, 1982), were also used. While auto-

70

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#16

#17

#18

#19

#20

#21

#22

#23

#24

#25

//26

1/27

#28

#29

#30

Fig. 1. P-wave solutions with the constraint that the source time-history be a step-function. Solid curves are the nodal surfaces of the moment tensors, dashed lines are the nodal planes of the best double-couples.

71

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mating the inversion procedure for routine use by the NEIC it was determined that, for moderate sized events, automation was feasible only for the analysis of P-waves. For events of special interest, however, SH-waveforms can be included, although this procedure has not been automated. All 51 of the events were analyzed using the algorithm in routine use at the U.S. Geological Survey, in which the time-history at the source is assumed to be a step function. For four of the events, inversions

using both long-period P- and SH-waves had already been done in the course of other studies. For three of the events the time-dependent algorithm was also used. 3.1. Step-function solutions The ‘routine’ (P-wave) solutions are listed in Table II. The solutions are given in two formats, first, in the principal axis system (note that since

72

TABLE II P-wave solutions Event No.

Depth

Principal Axes T Val

a

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 a

25 9 17 16 11 64 11 9 30 8 27 7 23 546 18 9 14 139 6 21 28 73 30 64 11 13 182 591 11 20 30 35 8 80 39 211 50 37 22 14 54 7 134 36 22 212 386 19 651 29 13

Scale factor:

10Ex

26 25 25 25 26 26 27 26 26 26 26 25 25 25 26 24 26 26 25 25 26 26 25 26 25 27 25 25 25 26 26 25 26 26 25 25 27 26 25 26 26 26 26 27 25 27 26 26 27 26 26 dyne-cm.

.

2.65 2.12 4.39 4.20 2.93 4.56 4.15 1.23 3.96 1.27 4.40 7.28 5.98 2.27 4.82 2.36 4.30 2.35 4.68 2.47 4.54 2.79 2.20 3.75 4.35 1.25 7.23 2.42 1.48 1.12 1.07 7.66 1.47 4.22 4.30 2.17 1.60 1.25 4.24 4.24 2.06 1.09 9.23 1.06 3.55 1.88 6.66 5.05 1.01 2.99 5.06

I a

P

P1

Aim

Val

17 7 2 69 63 19 1 2 53 5 60 6 3 45 6 58 53 3 15 4 64 64 16 4 63 72 17 4 57 84 52 23 11 74 19 87 58 55 30 16 9 39 71 0 11 60 47 37 6 65 48

9 237 244 25 175 226 255 218 273 184 26 107 46 41 49 22 45 44 68 99 10 57 52 291 224 50 132 239 336 234 27 319 1 54 319 154 48 57 49 313 79 342 232 351 21 2 53 119 115 214 276

0.00 —0.63 0.27 0.07 0.10 0.00 0.05 0.03 0.00 —0.02 —0.02 0.14 —1.05 0.13 —0.29 —0.73 0.13 —0.01 —0.34 0.29 0.62 —0.12 —0.13 —0.68 0.71 —0.08 0.97 0.21 —0.01 0.19 0.00 0.17 0.00 0.21 0.00 0.01 0.02 —0.15 0.00 —0.05 —0.13 0.30 —0.20 0.00 0.19 —0.04 0.00 0.06 —0.13 0.10 0.39

a

P1

Azm

Val

73 55 85 6 22 24 89 37 22 84 6 82 22 27 80 27 32 58 17 83 20 26 13 85 7 16 5 4 9 5 13 25 73 16 19 2 30 25 57 65 80 35 7 22 22 14 28 43 35 22 34

205 137 5 279 32 127 108 310 35 341 286 243 137 162 278 168 193 139 333 335 150 235 318 127 121 201 224 149 232 10 279 61 131 229 55 36 207 190 201 83 231 217 122 81 286 116 178 346 210 7 56

—2.65 —1.50 —4.66 —4.27 —3.03 —4.56 —4.20 —1.27 —3.96 —1.25 —4.38 —7.43 —4.93 —2.40 —4.54 —1.64 —4.42 —2.33 —4.33 —2.77 —5.16 —2.67 —2.08 —3.07 —5.07 —1.17 —8.21 —2.64 —1.46 —1.31 —1.07 —7.83 —1.47 —4.43 —4.30 —2.18 —1.62 —1.10 —4.24 —4.19 —1.93 —1.40 —9.03 —1.06 —3.75 —1.84 —6.66 —5.11 —0.88 —3.09 —5.45

a

P1

Azm

4 34 4 20 15 59 1 53 29 2 30 5 67 33 7 15 16 32 67 6 15 1 69 1 26 8 72 85 31 4 35 54 13 1 63 3 9 22 13 18 5 32 18 68 65 26 29 25 54 10 21

101 331 154 187 296 350 345 125 137 93 193 16 308 271 139 266 293 312 198 189 246 325 192 21 28 293 331 12 136 100 180 192 269 320 187 306 302 291 311 218 348 102 30 260 135 213 286 230 17 101 161

73

Event

M

0

a

No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

2.65 1.81 4.52 4.24 2.98 4.56 4.17 1.25 3.96 1.26 4.39 7.35 5.45 2.34 4.68 2.00 4.36 2.34 4.51 2.62 4.85 2.73 2.14 3.41 4.71 1.21 7.72 2.53 1.47 1.21 1.07 7.75 1.47 4.33 4.31 2.17 1.61 1.18 4.24 4.22 2.00 1.24 9.13 1.06 3.65 1.86 6.66 5.08 0.95 3.04 5.25

Best Double Couple NP1

% DC

NP2

Strike

Dip

Rake

Strike

Dip

Rake

146 9 289 266 358 349 30 276 271 228 267 152 114 55 184 29 60 93 181 234 2 79 160 66 102 41 214 333 198 195 223 9 45 66 21 35 63 59 86 356 123 137 110 60 136 333 65 269 173 216 294

75 62 85 26 36 34 89 54 26 85 16 82 46 28 80 38 41 66 33 83 35 50 31 86 20 39 28 41 16 41 16 31 73 46 31 42 44 32 60 65 81 35 28 49 39 22 30 43 50 40 39

9 —21 —179 75 50 —43 0 —139 149 178 70 180 —122 165 —1 137 145 —1.58 —58 —1 127 125 —65 2 70 115 —102 —84 55 97 32 —146 —179 113 —129 88 136 144 167 —179 177 8 76 —120 —54 128 160 10 —139 126 154

54 109 199 102 224 117 300 158 29 319 108 242 336 159 274 155 178 354 324 324 139 212 312 336 303 190 47 145 54 6 101 249 315 214 244 218 188 181 183 265 214 40 306 281 272 112 173 172 54 352 45

81 72 89 65 63 68 90 58 77 88 75 90 52 83 89 65 68 70 62 89 63 51 62 88 72 55 63 49 77 50 82 73 89 48 66 48 61 72 79 89 87 86 63 49 59 73 80 83 60 59 74

165 —150 —5 97 115 —116 179 —44 68 5 96 8 —61 63 —170 60 55 —26 —109 —173 67 56 —104 176 97 71 —84 —95 99 84 104 —63 —17 68 —69 92 55 63 31 —25 9 125 97 —60 —116 76 61 133 —48 64 54

No. Sta *

100 41 89 97 93 100 98 95 100 97 99 96 65 89 88 38 94 99 85 79 76 91 88 64 72 87 76 84 98 71 100 96 100 91 100 99 98 76 100 98 87 57 96 100 90 96 100 98 74 93 86

7 8 8 9 9 5 9 8 10 9 4 9 9 7 8 9 8 11 11 8 17 9 13 12 9 13 12 13 16 18 16 14 14~ 19 16 15 16 16 17 5 18 19 8 10 13 8 11 8 5 12 17

74 N

4

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10

14

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51

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2 35 16/

12 25

Fig. 2. Azimuthal equidistant projections showing the epicenters and best double-couple solutions. Diamonds: h <70 km, squares: 70 km 300 km.

75

TABLE III P, SH solutions Event No.

Depth

2 16 19 25

9 9 6 11

Event

M

0

a

No.

2 16 19 25 a

2.28 2.20 4.46 4.16

Principal Axes T Ex a

Val

25 24 25 25

2.59 2.20 4.55 3.70

i a

P1

Aim

Val

3 68 7 64

67 62 52 174

—0.62 0.01 —0.18 0.92

Best Double Couple NP1

a

~i

Azm

Val

83 8 3 17

178 173 142 302

—1.96 —2.20 —4.37 —4.62

NP2

Strike

Dip

Rake

Strike

Dip

Rake

21 10 139 155

87 26 38 30

—6 108 —95 126

112 169 325 294

84 65 52 67

—177 81 —86 71

P1

Azm

7 20 83 20

336 266 255 38

% DC

No p

Sta SH

52 99 92 60

9 7 10 6

8 9 11 9

a

Scale factor: 10Ex dyne-cm.

Mammoth Lakes

(a)

(No 2)

P

(b)

SH

New Brunswick (No 16)

P

SH

®E~E

(c) Yemen (No 19) P

(d) SH

P

Coalinga (No 25) SH

Fig. 3. P, SH-wave solutions. (a) Mammoth Lakes (event No. 2), (b) New Brunswick (event No. 16), (c) Yemen (event No. 19), (d) Coalinga (event No. 25). Solid curves are the nodal surfaces of the moment tensors, dashed lines are the nodal planes of the best double-couples.

I U~J~ i 76

(a)

Mammoth Lakes (No 2)

(b)

Yemen (No 19)

(c)

Coalinga (No 25)

____

Fig. 4. No. (event Relative 2), (b) moment Yemen Time vs.(event time (s) No. (top)19), and(c) percent Coalinga double-couple (event No. (solid) Time 25). Time (s) and isCLVD number (dashed) of seconds vs. time after (bottom). the Time nominal (s) (a) ., Mammoth origin time. Lakes

the moment tensors are not constrained to be pure double-couples the intermediate (I) eigenvalues are not necessarily equal to zero), and second, as

the orientations of the two conjugate nodal planes (NP1 and NP2) of the best double-couple solution. The conventions for strike, dip, and rake

Yemen (No19)

Coalinga (No25)

N

N

/

14 E

i\,

E

0 1~

/

T~ 0~

(a)

(b)

Fig. 5. Principal axis positions on the focal sphere as functions of time. (a) Yemen (event No. 19), (b) Coalinga (event No. 25). Numbers correspond to number of seconds after the origin time. Dashed lines correspond to times during which the moment is less than 0.25 Mm~.

77

from Aki and Richards (1980) are followed. The nodal surfaces of the moment tensors and the nodal planes of the best double-couple solutions are shown in Fig. 1. The best double-couple solutions are plotted with their epicenters in Figs. 2a—f. Many of these solutions differ somewhat from those published in the Preliminary Determination of Epicenters, Monthly Listings (NEIC) since, as of March 1983, focal depth is one of the parameters recovered. Prior to this time, the inversions were done with the focal depths fixed. While we have obtained good results even for the smaller events in this data set (events Nos. 16 and 20), in routine practice we have found it difficult to find a sufficient number of usable long-period P-waveforms for events with a bodywave magnitude of less than about 5.7 or 5.8. The P, SH solutions for four of the events are given in Table III and shown in Fig. 3. These four solutions were previously presented in Choy et al. (1983) and Sipkin (1986). 3.2. Time-dependent solutions Solutions for which the elements of the moment tensors were allowed to be independent functions of time were computed for three of the events in a study by Sipkin (1986). These time-dependent mechanisms are shown in Figs. 4 and 5. The synthetic seismograms corresponding to both the step-function and time-dependent solutions are shown in Sipkin (1986). In this study it is also demonstrated that the improvement to the fit between the real and synthetic data is statistically significant even when the increase in the number of degrees of freedom for the time-dependent case is considered. Figure 4 shows the scalar moments as functions of time, and thus represents the source-time functions. The orientations of the principal axes as functions of time are shown in Fig. 5. The dashed line segments represent the changes in orientation for times during which the scalar moment is less than 25% of the maximum. The solid line segments thus represent the changes in orientation during the release of significant moment. There is no apparent change in source orientation for event No. 19. All three events are complex, exhibiting either source multiplicity

(events Nos. 2 and 19) or a change in source orientation during rupture (event No. 25). For events Nos. 19 and 25 the resulting time-dependent solutions are resolved into a series of (almost) pure double-couples; this is, however, not the case for event No. 2. This has been interpreted by Julian and Sipkin (1985) to imply the existence of non-double-couple mechanisms which are intrinsic to the source process. For events No. 19 and 25, however, the non-double-couple components obtained in the step-function inversions (Tables I and II) are. almost surely due to source complexity that has not been adequately modeled. These results demonstrate, furthermore, that source complexity, even for moderate-sized events (M 6), can be determined from long-period data alone. —

3.3. Broadband solution Broadband waveform data from the New Brunswick earthquake (event No. 16) were also inverted. When using long-period data from shallow-focus earthquakes the pP and sP arrivals modulate the P-waveforms, but are not identifiable as individual phases. This is why, when doing the routine inversions depth must be one of the parameters inverted for. With the broadband data, however, the onset times of the pP and sP arrivals can be clearly measured, and the focal depth accurately determined. The depth found from the broadband pP—P and sP—P differential travel times is 9 km (Choy et al., 1983). This was also the depth which minimized the misfit to the longperiod data. For this inversion, the focal depth was fixed at 9 km. The real waveform data is shown with the resultant synthetic seismograms in Fig. 6. The mechanism (strike 158°, dip 57°, rake 490) is shown in Fig. 7 with the long-period P-wave and P, SH solution. Figure 6 clearly shows that the polarities and amplitude ratios of P. pP, and sP are predicted quite well by this mechanism. The pulse widths at the European stations (KONO, TOL, and GRFO), however, are too narrow. For the surface reflected phases this is partially due to the fact that they are not well resolved in the displacement waveforms, but instead interfere to produce a broad downswing. The sharp downsw=

=

=

78 1.6E+00~

=

N

42.7°

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I

T

44.7° +

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T T

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—__.....,.i.••... —2.OE+OO 2 OE+00

49.8

Fig. long-period and 7. BroadbandP.P-wave SH-wave (solid), (dotted) long-period best double-couple P-wave (dashed), solutions

-1.5E+O0 9.OE—Ol

63.0°

o - -

- -

-9.OE-01 0

Time (s)

15

Fig. 6. Real (solid) and synthetic (dashed) broadband waveforms for the New Brunswick earthquake (event No. 16).

ing seen on both the real and synthetic waveforms at the two South American stations (BOCO and ZOBO) are due to these stations being at an SV node (Choy et a!., 1983) and thus, only pP is

for the New Brunswick earthquake (event No. 16).

those presented by Náb~lek(1984) (his long-period P, SH solutions are almost identical to those in this study), indicates that there was little frequency dependence in the mechanism. The success of this inversion demonstrates the potential for using broadband waveform data in inversion procedures.

4. Conclusions We have presented the waveform inversion results for 51 global events chosen by the convenors of the Symposium on Seismological Theory and Practice. The events range in magnitude from mb 5.6 to 6.9 and M 5 5.2 to 7.7 (NEIC). The scalar moments obtained in this study range from 2.0 X 1024, to 4.2 X 1027 dyne-cm (M~= 5.5—7.7). While we have obtained good results even for the smaller events in this data set, in routine practice we have found it difficult to find a sufficient number of usable long-period P-waveforms for events with a body-wave magnitude of less than about 5.7 or 5.8. The results of a time-dependent inversion performed for three of the events mdicates that source complexity, even for moderatesized events, can be determined using long-period =

=

observed. The width of the direct P arrivals, however, is due to a small precursory sub-event, occurring approximately 1 s before the main rupture (Choy et al., 1983; Nâbêlek, 1984). This percursor can be identified as an inflection in the initial upswing at most of the stations. Since in the inversion, the source was constrained to be a single event with a step-function time-history, this sub-event is, of course, not modeled. For this relatively small event, the consistency of the solutions, both with each other and with

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data alone. Furthermore, these results indicate that, in many cases, departures of the solutions from pure double-couples are caused by source complexity that has not been adequately modeled. Finally, we have demonstrated that, at least in some cases, inversion of broadband data is feasible.

Acknowledgments I thank Russell Needham, who helped to do the inversions for many of the events, and Madeline Zirbes, who did the data retneval and preprocessing. I would also like to thank Bob Engdahl and Russell Needham for their helpful reviews of the manuscript.

References Aki, K. and Richards, P.G., 1980. Quantitative Seismology, Vol. 1. Freeman, San Francisco, 557 pp. Choy, G.L., Boatwright, J., Dewey, J.W. and Sipkin, S.A., 1983. A teleseismic analysis of the New Brunswick earthquake of January 9, 1982. J. Geophys. Res., 88: 2199—2212.

Doornbos, D.J., 1982. Seismic moment tensors and kinematic source parameters. Geophys. J., R. Astron. Soc., 69: 235-251. Doornbos, D.J., 1985. Source solutions and station residuals . from long-penod waveform inversion of deep events. J. Geophys. Res., 90: 5466—5478. Dziewonski, A.M. and Woodhouse, J.H., 1983. An experiment in systematic study of global seismicity: centroid-moment tensor solutions for 201 moderate and large earthquakes of 1981. J. Geophys. Res., 88: 3247—3271. Harvey, D. and Choy, G.L., 1982. Broadband deconvolution of GDSN data. Geophys. J., R. Astron. Soc., 69: 659—668. Julian, B.R. and Sipkin, S.A., 1985. Earthquake processes in the Long Valley Caldera area, California. J. Geophys. Res., 90: 11155—11169. Knopoff, L. and Randall, M.J., 1970. The compensated linear-vector dipole: a possible mechanism for deep earthquakes. J. Geophys. Res., 75: 4957—4963. Nábélek, J.L., 1984. Determination of Earthquake Source Parameters from Inversion of Body Waves. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, 361 pp. Silver, P.G. and Jordan, T.H., 1982. Optimal estimation of scalar seismic moment. Geophys. J. R. Astron. Soc., 70: 755—787. Sipkin, S.A., 1982. Estimation of earthquake source parameters by the inversion of wave-form data: synthetic waveforms. Phys. Earth Planet. Inter., 30: 242—259. Sipkin, S.A., 1986. Interpretation of non-double-couple earthquake source mechanisms derived from moment tensor inversion. J. Geophys. Res., 91: 531—547.