Measurements of the central frequency, Q, and splitting of various spheroidal and toroidal modes have been made.
- Spheroidal mode frequency and Q estimates (He & Tromp, 1996)
- Radial mode frequency and Q estimates (He & Tromp, 1996)
- Spheroidal mode splitting function coefficients (He & Tromp, 1996)
- Toroidal mode centre frequencies, Q, and splitting function coefficients (Tromp & Zanzerkia, 1995)
Spheroidal mode frequency and Q estimates
The observed and PREM predicted center frequencies are listed in

Tab-delimted text version also available.
Mode | fPREM | f | QPREM | Q | w | r |
0S3 | 468.56 | 468.29+/-0.20 | 417 | 327+/-70 | 13.05 | 1.00 |
0S4 | 647.08 | 646.86+/-0.11 | 373 | 408+/-38 | 9.54 | 1.00 |
0S5 | 840.44 | 840.02+/-0.08 | 355 | 376+/-33 | 7.23 | 1.02 |
0S6 | 1038.23 | 1037.55+/-0.08 | 347 | 356+/-8 | 5.93 | 1.16 |
0S7 | 1231.81 | 1231.04+/-0.09 | 342 | 338+/-8 | 5.18 | 1.46 |
0S8 | 1413.53 | 1412.74+/-0.09 | 337 | 332+/-11 | 4.59 | 1.73 |
0S9 | 1578.30 | 1577.02+/-0.12 | 332 | 332+/-10 | 3.89 | 1.53 |
0S10 | 1726.49 | 1724.55+/-0.13 | 327 | 281+/-7 | 4.05 | 1.17 |
1S2 | 679.86 | 680.34+/-0.21 | 310 | 377+/-97 | 11.43 | 1.00 |
1S3 | 939.83 | 940.02+/-0.05 | 282 | 316+/-11 | 14.89 | 1.00 |
1S4 | 1172.85 | 1172.83+/-0.10 | 271 | 291+/-22 | 18.33 | 1.00 |
1S5 | 1370.27 | 1370.04+/-0.13 | 291 | 314+/-29 | 19.77 | 1.00 |
1S6 | 1522.04 | 1521.53+/-0.28 | 345 | 429+/-51 | 16.59 | 1.03 |
1S7 | 1655.52 | 1654.49+/-0.25 | 372 | 415+/-36 | 14.19 | 1.08 |
1S8 | 1799.31 | 1798.00+/-0.24 | 379 | 456+/-37 | 14.72 | 1.19 |
1S9 | 1963.76 | 1962.11+/-0.38 | 380 | 388+/-40 | 15.80 | 1.28 |
1S10 | 2148.45 | 2146.84+/-0.66 | 378 | 371+/-45 | 15.94 | 1.29 |
2S3* | 1242.19 | 1243.03+/-0.06 | 415 | 387+/-14 | 8.30 | 1.62 |
2S4 | 1379.19 | 1379.74+/-0.20 | 380 | 388+/-45 | 5.16 | 1.32 |
2S5 | 1514.93 | 1515.79+/-0.92 | 302 | 336+/-77 | 5.86 | 1.53 |
2S6 | 1680.84 | 1681.34+/-0.20 | 237 | 237+/-8 | 9.68 | 1.33 |
2S8 | 2049.21 | 2050.11+/-0.19 | 197 | 212+/-3 | 15.91 | 1.25 |
3S1* | 943.94 | 944.44+/-0.08 | 819 | 814+/-54 | 3.21 | 1.00 |
3S2* | 1106.21 | 1106.30+/-0.11 | 366 | 312+/-25 | 10.25 | 1.58 |
3S8* | 2819.64 | 2819.90+/-0.41 | 263 | 247+/-13 | 10.81 | 2.12 |
4S1 | 1412.63 | 1411.45+/-0.15 | 355 | 369+/-17 | 8.68 | 1.01 |
4S2 | 1722.30 | 1721.56+/-0.05 | 434 | 495+/-19 | 6.02 | 1.03 |
4S3 | 2048.96 | 2048.35+/-0.06 | 480 | 547+/-12 | 6.82 | 1.12 |
4S4 | 2279.60 | 2278.57+/-0.28 | 290 | 278+/-22 | 7.33 | 1.24 |
5S3* | 2169.66 | 2169.18+/-0.27 | 292 | 311+/-31 | 7.27 | 1.27 |
5S4 | 2379.52 | 2379.38+/-0.06 | 489 | 526+/-26 | 7.64 | 1.12 |
5S5 | 2703.35 | 2703.54+/-0.12 | 502 | 571+/-33 | 9.39 | 1.14 |
5S6 | 3010.69 | 3011.27+/-0.15 | 506 | 565+/-31 | 11.19 | 1.19 |
5S7 | 3290.76 | 3291.45+/-0.10 | 492 | 542+/-34 | 12.68 | 1.26 |
5S8 | 3525.65 | 3525.93+/-0.18 | 418 | 460+/-34 | 13.20 | 1.40 |
5S12 | 4695.98 | 4695.75+/-0.30 | 385 | 417+/-16 | 22.71 | 1.71 |
6S3* | 2821.72 | 2821.91+/-0.13 | 426 | 451+/-29 | 11.46 | 2.98 |
6S10 | 4210.76 | 4211.27+/-0.17 | 354 | 375+/-5 | 19.78 | 1.64 |
7S4* | 3413.22 | 3411.22+/-0.28 | 333 | 277+/-32 | 11.59 | 1.73 |
7S5* | 3659.75 | 3657.73+/-0.08 | 477 | 491+/-32 | 9.10 | 1.67 |
7S6 | 3958.73 | 3956.81+/-0.11 | 504 | 667+/-84 | 10.45 | 1.67 |
7S7 | 4237.86 | 4233.99+/-0.15 | 415 | 462+/-8 | 12.03 | 1.75 |
8S1* | 2873.36 | 2872.62+/-0.06 | 929 | 984+/-54 | 5.75 | 1.41 |
8S5* | 4166.20 | 4165.38+/-0.08 | 611 | 690+/-63 | 14.05 | 2.15 |
8S7 | 4650.44 | 4645.15+/-0.15 | 351 | 375+/-11 | 17.66 | 1.95 |
9S3* | 3554.98 | 3557.08+/-0.18 | 777 | 625+/-62 | 11.89 | 2.14 |
9S14 | 6768.24 | 6763.73+/-0.46 | 484 | 469+/-6 | 24.14 | 1.74 |
11S4* | 4766.87 | 4766.11+/-0.03 | 701 | 810+/-19 | 14.35 | 2.08 |
11S5* | 5074.41 | 5072.83+/-0.10 | 665 | 661+/-52 | 13.39 | 1.79 |
12S8 | 6137.16 | 6132.17+/-0.18 | 567 | 562+/-16 | 16.06 | 1.55 |
12S12 | 7455.08 | 7448.99+/-0.43 | 570 | 456+/-10 | 22.33 | 1.78 |
13S1* | 4495.73 | 4494.83+/-0.33 | 735 | 648+/-73 | 14.72 | 2.30 |
13S2* | 4845.26 | 4845.72+/-0.11 | 878 | 891+/-18 | 16.92 | 2.54 |
13S3* | 5193.82 | 5193.54+/-0.07 | 908 | 970+/-34 | 12.63 | 1.69 |
16S5* | 6836.40 | 6830.57+/-0.08 | 581 | 593+/-27 | 25.61 | 2.42 |
16S7* | 7474.13 | 7472.18+/-0.34 | 800 | 452+/-13 | 18.56 | 1.58 |
17S1* | 6129.05 | 6123.83+/-0.88 | 716 | 597+/-47 | 7.14 | 0.89 |
17S12 | 9151.29 | 9145.47+/-1.99 | 462 | 414+/-58 | 29.49 | 2.01 |
17S13 | 9435.95 | 9428.13+/-0.29 | 554 | 553+/-10 | 28.44 | 1.91 |
18S3* | 6891.92 | 6886.27+/-0.10 | 851 | 865+/-85 | 19.69 | 2.00 |
18S4* | 7240.99 | 7238.49+/-0.08 | 943 | 1003+/-71 | 19.77 | 1.83 |
21S6* | 8850.77 | 8849.46+/-0.34 | 740 | 575+/-74 | 26.46 | 1.94 |
21S7* | 9173.79 | 9172.14+/-0.50 | 800 | 658+/-98 | 27.74 | 1.97 |
21S8* | 9496.96 | 9495.01+/-0.47 | 667 | 573+/-44 | 29.09 | 1.99 |
23S4* | 8941.57 | 8937.42+/-0.21 | 809 | 904+/-100 | 24.16 | 1.88 |
23S5* | 9289.58 | 9290.07+/-0.20 | 899 | 934+/-79 | 24.40 | 1.78 |
27S1* | 9485.85 | 9493.79+/-0.50 | 648 | 818+/-84 | 28.87 | 2.35 |
Radial mode frequency and Q estimates
The observed and PREM predicted center frequencies are listed in

Mode | fPREM | f | QPREM | Q |
---|---|---|---|---|
1S0 | 1631.34 | 1631.64+/-0.01 | 1499 | 1835+/-154 |
2S0 | 2510.48 | 2509.77+/-0.02 | 1241 | 1721+/-183 |
3S0 | 3271.19 | 3272.59+/-0.03 | 1083 | 1217+/-50 |
4S0 | 4105.77 | 4106.55+/-0.01 | 969 | 1252+/-53 |
5S0 | 4884.20 | 4888.48+/-0.02 | 920 | 1181+/-78 |
6S0 | 5740.28 | 5742.03+/-0.01 | 913 | 1130+/-85 |
8S0 | 7424.14 | 7429.76+/-0.03 | 852 | 899+/-39 |
9S0 | 8262.65 | 8269.67+/-0.06 | 840 | 1265+/-67 |
Spheroidal mode splitting function coefficients
For each mode the first line contains the coefficients and the second line the error estimates. The tabulated coefficients Ast and Bst are related to the complex splitting-function coefficients cst defined by



Tab-delimted text version also available.
Mode | A20 | A21 | B21 | A22 | B22 | A40 | A41 | B41 | A42 | B42 | A43 | B43 | A44 | B44 | A60 | A61 | B61 | A62 | B62 | A63 | B63 | A64 | B64 | A65 | B65 | A66 | B66 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0S3 | 502 | 457 | 401 | -600 | -1047 | -5 | 102 | -4 | -72 | 270 | -13 | -21 | 17 | 123 | |||||||||||||
413 | 526 | 738 | 767 | 678 | 189 | 344 | 340 | 376 | 364 | 385 | 386 | 389 | 389 | ||||||||||||||
0S4 | 836 | -47 | 259 | -432 | -521 | -26 | -9 | 67 | -124 | 144 | 35 | 150 | -9 | 169 | -41 | 19 | -23 | 57 | 20 | -14 | 19 | -4 | -34 | 11 | 5 | -21 | -6 |
179 | 169 | 338 | 260 | 274 | 124 | 185 | 195 | 228 | 165 | 240 | 238 | 243 | 240 | 64 | 118 | 123 | 126 | 123 | 127 | 127 | 126 | 128 | 130 | 130 | 130 | 131 | |
0S5 | 645 | -271 | -24 | -527 | -689 | 48 | 2 | -40 | -15 | 4 | -40 | 47 | -15 | 38 | -4 | -11 | 25 | 2 | -15 | -2 | 12 | -11 | -4 | -9 | 0 | 4 | -8 |
128 | 104 | 188 | 170 | 175 | 70 | 114 | 117 | 125 | 108 | 134 | 135 | 136 | 133 | 36 | 64 | 67 | 71 | 67 | 70 | 71 | 71 | 71 | 72 | 72 | 72 | 72 | |
0S6 | 390 | -170 | 222 | -885 | -777 | -69 | 30 | 270 | 82 | -191 | 21 | 132 | 46 | 207 | -72 | -88 | 29 | -15 | 105 | -26 | 88 | 62 | 37 | 116 | -4 | 12 | 38 |
96 | 62 | 159 | 121 | 117 | 67 | 64 | 95 | 89 | 77 | 107 | 100 | 86 | 92 | 38 | 54 | 58 | 64 | 54 | 70 | 69 | 64 | 69 | 71 | 72 | 67 | 61 | |
0S7 | 269 | -174 | -40 | -626 | -741 | -4 | 44 | 236 | 58 | -59 | 60 | 15 | -118 | 132 | -42 | -1 | 33 | -60 | 73 | -36 | 52 | -29 | 37 | 121 | -59 | -32 | -40 |
67 | 85 | 106 | 80 | 102 | 28 | 48 | 45 | 52 | 52 | 50 | 50 | 49 | 50 | 14 | 26 | 26 | 27 | 27 | 28 | 28 | 27 | 27 | 27 | 27 | 27 | 27 | |
0S8 | 236 | -391 | 42 | -411 | -934 | 0 | 43 | 63 | 80 | -141 | -15 | 214 | -79 | -22 | -39 | 111 | 3 | -176 | 0 | -39 | 224 | 169 | 108 | 339 | 14 | 128 | 33 |
73 | 79 | 105 | 88 | 101 | 34 | 50 | 56 | 55 | 57 | 54 | 56 | 57 | 57 | 17 | 30 | 32 | 31 | 32 | 32 | 32 | 32 | 33 | 31 | 32 | 32 | 32 | |
0S9 | -276 | -279 | -67 | -495 | -807 | 30 | 134 | 35 | -79 | -185 | -131 | 387 | -81 | 37 | -59 | -189 | -20 | -226 | 69 | -62 | 170 | -75 | 145 | 231 | 28 | 287 | 3 |
76 | 78 | 126 | 90 | 107 | 37 | 51 | 60 | 58 | 58 | 61 | 58 | 59 | 60 | 18 | 34 | 35 | 32 | 34 | 34 | 34 | 34 | 35 | 33 | 34 | 35 | 34 | |
0S10 | -473 | -127 | -144 | -57 | -493 | -77 | 65 | 49 | 181 | -23 | -313 | 758 | -158 | 1 | -32 | -78 | 37 | -37 | -54 | -60 | 201 | 119 | -84 | 292 | -34 | 392 | -31 |
79 | 88 | 125 | 96 | 119 | 33 | 55 | 60 | 57 | 58 | 57 | 57 | 59 | 59 | 16 | 31 | 32 | 31 | 32 | 31 | 32 | 31 | 31 | 31 | 31 | 32 | 32 | |
1S2 | -38 | -498 | 696 | -315 | -746 | 37 | 5 | -428 | -292 | -309 | 90 | -24 | 62 | 68 | |||||||||||||
477 | 651 | 619 | 623 | 986 | 179 | 333 | 328 | 345 | 353 | 358 | 357 | 359 | 361 | ||||||||||||||
1S3 | 43 | -45 | 68 | -383 | -646 | -19 | 82 | -30 | -17 | -15 | 14 | -7 | 6 | -4 | -1 | -4 | -16 | 1 | 20 | -1 | -2 | 2 | 0 | 0 | 0 | 0 | 0 |
104 | 104 | 113 | 138 | 173 | 42 | 76 | 81 | 94 | 94 | 93 | 92 | 93 | 93 | 22 | 44 | 42 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | |
1S4 | 145 | -223 | 185 | -606 | -843 | -44 | -109 | -62 | -32 | -140 | 12 | 28 | 105 | 12 | -25 | -31 | -53 | -2 | 16 | 14 | 14 | -17 | 9 | -12 | -3 | 1 | 5 |
156 | 128 | 175 | 210 | 239 | 107 | 137 | 163 | 244 | 235 | 256 | 259 | 286 | 284 | 70 | 123 | 112 | 138 | 135 | 143 | 144 | 149 | 149 | 149 | 150 | 149 | 149 | |
1S5 | 154 | -22 | 177 | -1078 | -577 | -45 | -243 | 75 | 56 | -96 | 61 | 151 | 97 | -83 | -24 | 1 | -21 | 17 | -49 | 7 | -8 | 20 | 3 | -13 | -4 | -8 | 3 |
161 | 116 | 185 | 192 | 216 | 97 | 128 | 144 | 166 | 159 | 192 | 174 | 207 | 206 | 50 | 88 | 92 | 101 | 99 | 101 | 101 | 103 | 104 | 104 | 104 | 105 | 105 | |
1S6 | 414 | 182 | -36 | -1392 | -607 | -61 | -240 | -34 | 382 | 184 | 77 | -7 | -85 | 81 | 13 | -222 | -330 | -10 | -152 | 57 | -138 | -95 | 331 | 53 | -320 | 39 | -94 |
258 | 158 | 319 | 357 | 264 | 131 | 188 | 211 | 211 | 200 | 229 | 220 | 246 | 255 | 65 | 112 | 126 | 128 | 125 | 130 | 127 | 129 | 129 | 131 | 132 | 133 | 134 | |
1S7 | 599 | -8 | -28 | -1172 | -644 | 3 | -114 | -9 | 135 | -272 | 102 | 42 | 188 | 82 | -1 | -159 | -44 | -114 | 18 | 90 | -40 | -32 | 52 | -35 | 57 | -12 | -16 |
201 | 111 | 259 | 302 | 191 | 103 | 127 | 169 | 155 | 152 | 162 | 173 | 179 | 188 | 52 | 90 | 101 | 100 | 98 | 101 | 98 | 102 | 100 | 102 | 103 | 103 | 104 | |
1S8 | 760 | -70 | -64 | -1120 | -699 | -63 | -34 | 25 | 227 | -194 | 36 | 95 | 168 | -10 | -35 | -201 | -111 | -51 | 0 | -17 | -21 | -37 | 103 | 84 | 85 | -17 | -56 |
166 | 85 | 266 | 245 | 194 | 107 | 105 | 168 | 152 | 126 | 159 | 168 | 165 | 180 | 62 | 83 | 107 | 102 | 96 | 102 | 98 | 101 | 108 | 105 | 109 | 112 | 114 | |
1S9 | 938 | -211 | -319 | -1130 | -938 | -110 | -21 | 10 | 350 | -307 | 122 | 114 | -2 | 82 | -33 | -69 | -8 | -63 | 38 | -26 | -34 | -105 | 131 | 22 | 55 | 7 | -49 |
239 | 123 | 300 | 349 | 257 | 110 | 147 | 190 | 166 | 167 | 184 | 187 | 197 | 199 | 55 | 99 | 109 | 105 | 106 | 106 | 105 | 105 | 105 | 106 | 108 | 107 | 107 | |
1S10 | 980 | -65 | -615 | -1111 | -685 | 0 | 32 | 241 | 94 | -100 | 105 | -165 | -8 | 49 | 0 | -38 | -33 | -47 | -34 | -17 | -10 | -11 | 30 | -42 | 18 | -10 | 9 |
273 | 214 | 454 | 442 | 349 | 104 | 170 | 199 | 178 | 186 | 191 | 190 | 198 | 200 | 51 | 97 | 101 | 99 | 99 | 100 | 99 | 99 | 100 | 99 | 101 | 100 | 101 | |
2S3* | 1952 | -141 | 104 | -816 | -793 | 153 | -147 | 17 | -32 | 1 | 57 | 69 | -134 | 142 | -37 | 28 | -100 | -84 | 11 | 16 | -22 | -16 | 32 | 3 | 56 | -8 | 14 |
67 | 79 | 80 | 143 | 102 | 29 | 56 | 53 | 57 | 58 | 57 | 57 | 56 | 57 | 14 | 28 | 28 | 28 | 28 | 28 | 28 | 28 | 28 | 28 | 28 | 28 | 28 | |
2S4 | 101 | -309 | 6 | -827 | -813 | -81 | -34 | 69 | 95 | 50 | 135 | 33 | -115 | 207 | -1 | -1 | -52 | -7 | -10 | 25 | -17 | -20 | -5 | -4 | -6 | -33 | -42 |
192 | 161 | 228 | 223 | 221 | 100 | 150 | 174 | 181 | 166 | 178 | 167 | 166 | 176 | 52 | 94 | 99 | 101 | 99 | 99 | 98 | 101 | 101 | 101 | 102 | 98 | 98 | |
2S5 | 438 | -881 | -134 | -655 | -650 | -27 | -18 | 12 | -93 | 0 | 123 | 152 | 208 | -57 | 20 | -52 | 11 | -125 | 60 | -11 | -19 | 26 | -38 | -28 | -7 | -49 | 62 |
444 | 636 | 767 | 744 | 764 | 142 | 279 | 282 | 282 | 281 | 279 | 281 | 280 | 283 | 68 | 136 | 136 | 136 | 136 | 136 | 136 | 136 | 136 | 136 | 136 | 136 | 136 | |
2S6 | -221 | -594 | 586 | -48 | -1639 | 129 | -276 | 22 | -47 | -33 | -179 | 170 | 63 | 66 | 83 | -209 | -194 | -164 | -30 | 100 | 331 | 6 | -18 | 98 | -1 | 148 | -47 |
181 | 172 | 245 | 179 | 238 | 119 | 136 | 167 | 181 | 195 | 176 | 177 | 161 | 178 | 65 | 103 | 105 | 118 | 116 | 120 | 123 | 125 | 124 | 122 | 122 | 118 | 118 | |
2S8 | -307 | -668 | 598 | 449 | -1513 | 420 | -260 | -121 | -515 | 314 | 207 | 64 | -118 | 876 | 166 | -215 | -167 | -241 | -1 | -74 | 370 | -30 | 106 | 253 | -100 | 189 | 124 |
99 | 79 | 147 | 154 | 118 | 44 | 67 | 80 | 74 | 71 | 78 | 79 | 82 | 84 | 22 | 41 | 42 | 42 | 42 | 42 | 43 | 42 | 43 | 42 | 42 | 43 | 43 | |
3S1* | 99 | 25 | -53 | -134 | 120 | ||||||||||||||||||||||
88 | 38 | 30 | 271 | 277 | |||||||||||||||||||||||
3S2* | 3706 | -214 | -30 | 418 | -502 | -145 | -473 | -126 | -862 | -153 | -217 | -140 | -44 | 172 | |||||||||||||
171 | 223 | 211 | 297 | 261 | 133 | 205 | 161 | 227 | 215 | 151 | 155 | 241 | 257 | ||||||||||||||
3S8* | 526 | -237 | 315 | -735 | -1209 | 73 | -187 | -128 | 30 | -163 | 109 | 88 | -90 | 48 | 69 | -243 | -67 | -101 | -38 | 56 | 122 | -76 | -82 | -66 | 45 | -74 | 65 |
150 | 176 | 230 | 220 | 222 | 57 | 104 | 109 | 106 | 107 | 107 | 109 | 111 | 109 | 28 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | |
4S1 | 285 | -281 | -103 | -62 | -265 | ||||||||||||||||||||||
102 | 108 | 113 | 236 | 235 | |||||||||||||||||||||||
4S2 | 4 | -141 | 151 | 237 | -456 | 120 | 25 | 4 | -26 | -6 | 207 | -10 | 88 | 140 | |||||||||||||
76 | 61 | 54 | 81 | 88 | 32 | 57 | 49 | 57 | 60 | 64 | 64 | 67 | 67 | ||||||||||||||
4S3 | 44 | 90 | 121 | -201 | -362 | 50 | -81 | -81 | -123 | -46 | 67 | 17 | 136 | 168 | 16 | -10 | 9 | 59 | 44 | 0 | -8 | 97 | 81 | -40 | 49 | 46 | -2 |
60 | 39 | 37 | 49 | 53 | 35 | 44 | 55 | 68 | 71 | 62 | 58 | 57 | 51 | 20 | 39 | 40 | 31 | 34 | 37 | 39 | 36 | 37 | 38 | 39 | 43 | 43 | |
4S4 | -21 | -26 | 258 | -481 | -896 | 40 | 87 | 39 | -283 | -90 | 263 | 218 | -255 | 79 | -32 | -212 | 234 | -96 | -34 | -57 | -291 | -52 | 38 | 20 | 128 | 42 | -50 |
168 | 141 | 195 | 206 | 204 | 100 | 128 | 149 | 163 | 157 | 193 | 153 | 170 | 165 | 55 | 95 | 106 | 104 | 107 | 104 | 102 | 104 | 106 | 108 | 107 | 100 | 103 | |
5S3* | 358 | -272 | 186 | -560 | -694 | -35 | 165 | -27 | 11 | -53 | 23 | 50 | -38 | 238 | 3 | -5 | -13 | 6 | -49 | 45 | -29 | 22 | 21 | 44 | 77 | 26 | 40 |
211 | 165 | 178 | 221 | 220 | 96 | 155 | 163 | 177 | 161 | 186 | 179 | 177 | 170 | 49 | 101 | 98 | 80 | 90 | 97 | 98 | 94 | 94 | 98 | 97 | 100 | 100 | |
5S4 | -45 | -149 | 32 | -80 | -342 | -23 | -9 | -45 | -29 | 113 | 60 | -25 | 53 | 47 | -4 | 84 | -25 | 13 | 65 | 2 | 45 | 48 | 9 | 5 | 25 | 12 | -41 |
58 | 30 | 37 | 61 | 44 | 26 | 33 | 43 | 44 | 40 | 42 | 44 | 44 | 42 | 12 | 23 | 24 | 25 | 23 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | |
5S5 | -28 | -71 | 146 | -295 | -610 | -34 | -119 | -68 | -46 | 67 | 176 | 91 | 14 | 134 | -18 | 12 | -19 | 29 | -61 | 45 | 31 | 0 | -39 | -55 | -25 | 14 | -17 |
70 | 42 | 70 | 84 | 50 | 31 | 45 | 54 | 53 | 47 | 47 | 52 | 54 | 52 | 15 | 27 | 29 | 29 | 28 | 30 | 30 | 29 | 29 | 29 | 30 | 30 | 29 | |
5S6 | -41 | -88 | 344 | -487 | -701 | -30 | -172 | -43 | 91 | 26 | 155 | 42 | -138 | 198 | 5 | -30 | -42 | 45 | -49 | -25 | 16 | -29 | 9 | -7 | -20 | 35 | -30 |
63 | 39 | 76 | 82 | 60 | 30 | 40 | 48 | 46 | 45 | 47 | 47 | 50 | 50 | 15 | 27 | 29 | 28 | 28 | 29 | 29 | 29 | 29 | 28 | 29 | 28 | 28 | |
5S7 | -95 | 6 | 285 | -546 | -715 | -5 | -239 | -8 | -14 | 7 | 179 | 115 | 32 | 64 | -20 | -113 | -5 | -43 | -53 | -23 | 82 | 1 | 21 | -15 | -126 | 118 | -18 |
59 | 32 | 59 | 65 | 40 | 34 | 43 | 56 | 50 | 50 | 49 | 52 | 48 | 49 | 17 | 31 | 33 | 32 | 33 | 33 | 33 | 34 | 33 | 32 | 32 | 32 | 33 | |
5S8 | 67 | -11 | 233 | -531 | -862 | -204 | -162 | -43 | 76 | 57 | 113 | 106 | 50 | 223 | -58 | -138 | -81 | 9 | -72 | 120 | 75 | -3 | 64 | 40 | -28 | 50 | -42 |
106 | 61 | 112 | 130 | 114 | 50 | 71 | 86 | 83 | 79 | 79 | 81 | 86 | 81 | 25 | 47 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 47 | 47 | 47 | 47 | |
5S12 | 292 | -89 | 628 | -405 | -1174 | 80 | -423 | -380 | 214 | 81 | 246 | 34 | -22 | 113 | 0 | -218 | -37 | -196 | -83 | -112 | 166 | -52 | 25 | -16 | -36 | 36 | 50 |
92 | 74 | 115 | 99 | 112 | 61 | 65 | 87 | 73 | 74 | 85 | 82 | 87 | 91 | 35 | 45 | 60 | 50 | 51 | 51 | 52 | 55 | 55 | 56 | 52 | 56 | 55 | |
6S3* | 1760 | 114 | 199 | -305 | -612 | 287 | -290 | -134 | -80 | 66 | 104 | 28 | 168 | -46 | 36 | -39 | -176 | 67 | 101 | 50 | -104 | 32 | -2 | 59 | -15 | 2 | 99 |
95 | 91 | 90 | 87 | 90 | 49 | 78 | 83 | 101 | 102 | 103 | 98 | 81 | 88 | 26 | 47 | 50 | 46 | 47 | 52 | 50 | 50 | 50 | 52 | 51 | 52 | 53 | |
6S10 | 290 | -56 | 494 | -485 | -1124 | -17 | -221 | -225 | 148 | 52 | 120 | 261 | -21 | 290 | -58 | -138 | -122 | -118 | -106 | -37 | 241 | -1 | 158 | 85 | 71 | 85 | 168 |
62 | 43 | 93 | 67 | 70 | 59 | 47 | 71 | 56 | 62 | 79 | 64 | 64 | 58 | 40 | 38 | 54 | 47 | 48 | 51 | 44 | 44 | 52 | 48 | 51 | 42 | 43 | |
7S4* | 388 | 736 | 519 | -882 | -732 | -123 | -295 | -430 | 3 | -18 | 91 | 83 | -252 | -256 | -16 | -172 | 25 | 77 | 162 | 48 | 29 | -39 | -99 | 3 | 54 | -251 | 35 |
214 | 190 | 226 | 268 | 227 | 159 | 220 | 245 | 261 | 267 | 277 | 259 | 219 | 274 | 86 | 153 | 161 | 154 | 154 | 164 | 163 | 170 | 165 | 167 | 163 | 148 | 156 | |
7S5* | 462 | -87 | 204 | -446 | -485 | -33 | -74 | -41 | -97 | -42 | 62 | 101 | -38 | -7 | -9 | -44 | -129 | -41 | 5 | 19 | -20 | 23 | -17 | 11 | 16 | 30 | -23 |
51 | 57 | 61 | 56 | 52 | 39 | 56 | 62 | 75 | 77 | 74 | 76 | 65 | 68 | 21 | 39 | 38 | 42 | 41 | 42 | 42 | 42 | 41 | 42 | 42 | 42 | 41 | |
7S6 | 202 | 13 | 77 | -373 | -567 | -73 | -50 | 74 | -62 | -30 | 94 | 231 | -125 | 51 | -41 | -41 | -65 | -4 | -18 | 37 | 43 | -30 | -36 | 5 | 40 | -6 | 9 |
61 | 38 | 61 | 54 | 66 | 44 | 53 | 60 | 66 | 73 | 75 | 67 | 57 | 58 | 22 | 38 | 40 | 43 | 45 | 45 | 44 | 44 | 45 | 44 | 44 | 43 | 42 | |
7S7 | 297 | -47 | 325 | -533 | -684 | -91 | -118 | -94 | 20 | 26 | 70 | 150 | -29 | 192 | -73 | -46 | -69 | -82 | -35 | 91 | 269 | -7 | 23 | 122 | 126 | -92 | -1 |
66 | 42 | 64 | 51 | 78 | 59 | 48 | 63 | 52 | 63 | 76 | 51 | 68 | 62 | 39 | 41 | 50 | 52 | 61 | 57 | 53 | 49 | 67 | 51 | 54 | 48 | 46 | |
8S1* | 379 | 146 | 109 | -24 | -175 | ||||||||||||||||||||||
22 | 61 | 50 | 33 | 39 | |||||||||||||||||||||||
8S5* | 943 | -182 | 357 | 26 | -441 | -21 | 256 | -458 | -513 | -35 | 90 | -40 | -203 | 159 | 62 | 13 | -60 | -90 | 81 | 48 | -116 | 67 | 7 | 128 | 121 | 51 | 14 |
60 | 58 | 54 | 73 | 61 | 39 | 65 | 62 | 68 | 67 | 69 | 67 | 54 | 64 | 20 | 36 | 37 | 38 | 38 | 40 | 40 | 40 | 39 | 40 | 39 | 35 | 36 | |
8S7 | 361 | -204 | 634 | -1034 | -1012 | -101 | -227 | -49 | -297 | 326 | 36 | 182 | -286 | -143 | -25 | -19 | -217 | -59 | -156 | -27 | 64 | -164 | -19 | 115 | -41 | 30 | -34 |
49 | 40 | 63 | 61 | 69 | 48 | 52 | 66 | 60 | 67 | 70 | 63 | 60 | 67 | 32 | 48 | 47 | 53 | 50 | 61 | 57 | 53 | 57 | 52 | 55 | 45 | 49 | |
9S3* | 1038 | -153 | 47 | 377 | 230 | -225 | -41 | -197 | 8 | -2 | -79 | 128 | -36 | 136 | -22 | 90 | 53 | -49 | -61 | 0 | 92 | -16 | 22 | -16 | 35 | -2 | 29 |
118 | 141 | 139 | 121 | 140 | 49 | 95 | 96 | 104 | 105 | 100 | 101 | 78 | 78 | 25 | 47 | 48 | 49 | 49 | 47 | 48 | 46 | 47 | 50 | 50 | 49 | 49 | |
9S14 | 10 | 66 | 135 | -740 | -1043 | -97 | -343 | 18 | -154 | 1 | -5 | 3 | -20 | 256 | 0 | -58 | -135 | -148 | -136 | -11 | 105 | -103 | 127 | -101 | 16 | -48 | 188 |
90 | 52 | 98 | 134 | 126 | 61 | 42 | 85 | 69 | 62 | 83 | 82 | 96 | 107 | 35 | 38 | 59 | 48 | 39 | 45 | 50 | 53 | 48 | 48 | 54 | 52 | 47 | |
11S4* | 998 | 48 | 39 | -42 | -530 | 145 | -144 | -155 | -176 | 310 | -83 | -34 | -54 | -71 | -179 | 0 | -32 | -40 | -206 | 81 | 173 | -43 | -83 | 98 | 153 | 49 | 106 |
19 | 20 | 22 | 27 | 26 | 25 | 23 | 22 | 55 | 57 | 43 | 49 | 35 | 41 | 20 | 23 | 25 | 34 | 39 | 35 | 36 | 41 | 47 | 43 | 39 | 21 | 26 | |
11S5* | 733 | 48 | 206 | -50 | -273 | -16 | -50 | -46 | -230 | 53 | -158 | 67 | -112 | 123 | -55 | -87 | -36 | -26 | -24 | -5 | 38 | -23 | -25 | 19 | -19 | 87 | -11 |
63 | 56 | 48 | 62 | 52 | 35 | 54 | 55 | 64 | 65 | 62 | 65 | 47 | 58 | 17 | 31 | 33 | 34 | 34 | 35 | 35 | 35 | 35 | 35 | 35 | 34 | 33 | |
12S8 | 54 | -34 | 280 | -468 | -728 | -128 | -185 | 96 | 184 | -45 | 102 | 64 | 11 | 331 | -11 | -16 | -24 | -50 | -40 | -72 | 145 | 23 | -57 | -17 | -36 | 28 | -1 |
49 | 33 | 50 | 49 | 68 | 40 | 43 | 49 | 44 | 49 | 58 | 51 | 58 | 49 | 24 | 35 | 40 | 38 | 39 | 44 | 40 | 42 | 42 | 38 | 40 | 34 | 38 | |
12S12 | 255 | -275 | 584 | -323 | -581 | -26 | -199 | -97 | 50 | -98 | 44 | -37 | -129 | 214 | 1 | -32 | -52 | -36 | 3 | -32 | 145 | 41 | 47 | 38 | -91 | 42 | -51 |
65 | 55 | 89 | 73 | 99 | 33 | 43 | 52 | 47 | 49 | 52 | 52 | 55 | 54 | 17 | 29 | 32 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 31 | 30 | 30 | |
13S1* | 1243 | 348 | -872 | 56 | -224 | ||||||||||||||||||||||
96 | 333 | 214 | 143 | 77 | |||||||||||||||||||||||
13S2* | 1342 | -53 | -26 | 190 | 230 | 272 | -295 | -310 | 80 | 283 | 139 | 59 | 37 | 147 | |||||||||||||
31 | 39 | 42 | 42 | 51 | 16 | 28 | 23 | 32 | 32 | 31 | 29 | 13 | 30 | ||||||||||||||
13S3* | 778 | 265 | -81 | -84 | -139 | 51 | -44 | -174 | -46 | 16 | -177 | 141 | 45 | -20 | 7 | -102 | 71 | -9 | -9 | -28 | 0 | -11 | -41 | -41 | -24 | 3 | 41 |
27 | 27 | 40 | 41 | 43 | 23 | 32 | 34 | 62 | 60 | 44 | 46 | 36 | 46 | 15 | 20 | 23 | 29 | 28 | 28 | 28 | 29 | 29 | 30 | 26 | 24 | 22 | |
16S5* | 1099 | -57 | 188 | -285 | -524 | -84 | -376 | -46 | 46 | -63 | -213 | 15 | 12 | -80 | -4 | -28 | 21 | 30 | -42 | -22 | -26 | 21 | 1 | 5 | 4 | 42 | -8 |
41 | 45 | 52 | 49 | 45 | 30 | 52 | 53 | 60 | 61 | 53 | 60 | 46 | 57 | 16 | 30 | 30 | 32 | 31 | 32 | 33 | 34 | 34 | 33 | 33 | 29 | 30 | |
16S7* | 553 | 67 | 3 | -223 | 60 | 0 | -65 | 65 | 211 | 80 | 229 | -46 | 32 | -97 | -29 | -8 | 26 | 4 | 37 | -45 | 25 | -7 | 34 | -62 | -48 | 29 | 14 |
80 | 52 | 81 | 81 | 78 | 35 | 54 | 61 | 56 | 57 | 56 | 60 | 58 | 58 | 17 | 32 | 34 | 33 | 34 | 32 | 34 | 34 | 34 | 33 | 34 | 33 | 33 | |
17S1* | -130 | -154 | 69 | -11 | -53 | ||||||||||||||||||||||
144 | 185 | 152 | 228 | 260 | |||||||||||||||||||||||
17S12 | 465 | -209 | 265 | -413 | -1017 | 107 | -175 | 109 | -9 | 75 | -266 | 7 | 229 | 249 | 48 | -107 | -7 | -327 | 77 | 60 | 108 | 79 | 26 | 0 | 85 | 41 | 18 |
254 | 241 | 358 | 322 | 368 | 97 | 158 | 185 | 164 | 185 | 184 | 178 | 181 | 183 | 47 | 91 | 93 | 92 | 92 | 93 | 90 | 92 | 92 | 92 | 93 | 92 | 92 | |
17S13 | 371 | -104 | 318 | -438 | -849 | 158 | -139 | -17 | -20 | -7 | -136 | 163 | -23 | 162 | 55 | -120 | -23 | -259 | 40 | 48 | 262 | 62 | 40 | 69 | 1 | 111 | 60 |
44 | 38 | 63 | 47 | 63 | 42 | 36 | 55 | 41 | 47 | 61 | 49 | 48 | 54 | 28 | 32 | 44 | 36 | 33 | 39 | 38 | 42 | 40 | 39 | 43 | 31 | 36 | |
18S3* | 771 | 39 | 211 | -307 | -381 | 177 | -142 | -158 | -197 | 17 | -79 | -32 | 27 | 154 | 10 | -3 | 125 | -42 | -3 | -9 | 28 | 141 | 29 | -47 | -11 | 62 | -71 |
39 | 59 | 62 | 61 | 66 | 23 | 49 | 49 | 55 | 57 | 56 | 55 | 38 | 38 | 13 | 25 | 23 | 25 | 26 | 27 | 27 | 25 | 25 | 27 | 27 | 25 | 23 | |
18S4* | 886 | 191 | -18 | -141 | -196 | 70 | -95 | -197 | 98 | 71 | 48 | 125 | -106 | 15 | -26 | -129 | -63 | 42 | 20 | 1 | 27 | -47 | 9 | 3 | -25 | -16 | 115 |
35 | 44 | 36 | 35 | 34 | 19 | 30 | 31 | 39 | 40 | 39 | 39 | 31 | 32 | 10 | 17 | 19 | 20 | 20 | 20 | 20 | 19 | 20 | 20 | 20 | 17 | 17 | |
21S6* | 974 | -37 | 0 | -65 | -220 | 33 | -54 | 83 | 25 | 281 | -27 | 46 | -122 | 287 | 6 | -57 | 26 | -28 | -22 | -23 | 20 | -4 | 67 | -21 | -1 | -31 | 48 |
107 | 72 | 88 | 99 | 98 | 70 | 99 | 107 | 123 | 127 | 132 | 116 | 97 | 89 | 35 | 65 | 65 | 69 | 71 | 72 | 70 | 72 | 71 | 72 | 72 | 62 | 65 | |
21S7* | 805 | -12 | -60 | 144 | -103 | 56 | -344 | 146 | 127 | 117 | -54 | 167 | -143 | 225 | 28 | -31 | -75 | -173 | -119 | 8 | -77 | -96 | 80 | 186 | 32 | 33 | 28 |
121 | 91 | 93 | 162 | 157 | 86 | 106 | 108 | 156 | 151 | 151 | 151 | 138 | 151 | 45 | 77 | 74 | 88 | 87 | 88 | 89 | 91 | 92 | 91 | 90 | 85 | 87 | |
21S8* | 753 | 106 | 13 | -26 | -188 | -150 | -19 | -58 | -174 | 14 | 142 | 241 | -87 | 136 | 19 | 8 | -17 | -56 | -59 | 202 | -144 | 66 | 234 | 87 | 46 | 60 | 23 |
102 | 84 | 92 | 140 | 128 | 61 | 93 | 98 | 109 | 107 | 110 | 115 | 115 | 101 | 31 | 57 | 58 | 60 | 61 | 59 | 61 | 62 | 61 | 60 | 62 | 60 | 60 | |
23S4* | 768 | -11 | -28 | -320 | -427 | -40 | 82 | -35 | -85 | -71 | -78 | 36 | 46 | -85 | 9 | 2 | 23 | -29 | -20 | -17 | 4 | 4 | -3 | -3 | 0 | 54 | -3 |
58 | 114 | 79 | 77 | 67 | 34 | 65 | 65 | 77 | 78 | 77 | 75 | 73 | 70 | 19 | 36 | 37 | 38 | 38 | 38 | 38 | 38 | 38 | 38 | 38 | 30 | 33 | |
23S5* | 698 | 31 | 269 | 39 | -428 | 62 | -45 | -57 | -27 | 17 | -122 | 29 | 163 | 184 | -18 | -29 | -61 | 23 | 0 | 0 | 4 | 13 | 11 | 3 | -8 | -29 | 40 |
56 | 64 | 67 | 71 | 95 | 38 | 58 | 66 | 80 | 80 | 77 | 81 | 73 | 69 | 20 | 38 | 38 | 40 | 41 | 41 | 41 | 41 | 41 | 41 | 41 | 39 | 39 | |
27S1* | 742 | 769 | 694 | -263 | -176 | ||||||||||||||||||||||
118 | 360 | 270 | 70 | 86 | |||||||||||||||||||||||
Toroidal mode frequencies, Q, and splitting function coefficients
Center frequencies f, quality factors Q, and degree 2 splitting function coefficients for the 11 toroidal modes (Tromp & Zanzerkia, 1995). For each mode the first row contains the results for a starting model that consists of rotation and ellipticity plus SKS12WM13, and the second row lists the associated standard deviations. To demonstrate that the splitting coefficients are reasonably robust, we list the results for a starting model that consists of rotation and ellipticity only in the third row. The fact that we have roughly half as many recordings for modes 0T4 and 0T5 as we do for the other modes is reflected in the relatively poor agreement between the splitting coefficients obtained for the different starting models. The tabulated coefficients Ast and Bst are related to the complex splitting function coefficients cst defined by




Also available as tab-delimited text file.
Mode | f | Q | A20 | A21 | B21 | A22 | B22 |
---|---|---|---|---|---|---|---|
0T4 | 765.83 | 195 | 57 | 102 | 184 | -20 | -664 |
0.44 | 48 | 304 | 412 | 348 | 388 | 389 | |
765.86 | 196 | -101 | 34 | -145 | 393 | -512 | |
0T5 | 928.87 | 192 | 178 | -498 | -3 | -52 | -631 |
0.40 | 37 | 253 | 395 | 318 | 412 | 284 | |
929.17 | 179 | 68 | -370 | -276 | 221 | -29 | |
0T6 | 1079.17 | 215 | 252 | -561 | 66 | -328 | -993 |
0.20 | 10 | 170 | 208 | 220 | 216 | 242 | |
1079.23 | 240 | 257 | -516 | 15 | -330 | -953 | |
0T7 | 1220.97 | 194 | 263 | -198 | 216 | -157 | -1244 |
0.37 | 15 | 322 | 373 | 437 | 407 | 419 | |
1221.01 | 194 | 214 | -197 | 234 | -162 | -1143 | |
0T8 | 1356.43 | 186 | 25 | -558 | 113 | 156 | -1169 |
0.35 | 29 | 236 | 286 | 293 | 309 | 326 | |
1356.87 | 187 | 143 | -513 | -145 | 456 | -723 | |
0T9 | 1487.14 | 189 | 114 | -518 | 56 | 213 | -1367 |
0.23 | 18 | 181 | 170 | 230 | 195 | 234 | |
1487.46 | 190 | 158 | -195 | -285 | 211 | -873 | |
1T1 | 1235.06 | 230 | 48 | -95 | -148 | 443 | 18 |
0.67 | 25 | 46 | 474 | 212 | 243 | 287 | |
1235.49 | 206 | 97 | -2 | -204 | 329 | 230 | |
1T2 | 1319.07 | 283 | -415 | -112 | 14 | 229 | -294 |
0.32 | 20 | 86 | 294 | 266 | 247 | 256 | |
1319.28 | 321 | -318 | -76 | -68 | 197 | -279 | |
1T3 | 1438.37 | 255 | -115 | -59 | 98 | -404 | -519 |
0.50 | 53 | 313 | 428 | 516 | 488 | 437 | |
1438.35 | 257 | -89 | -3 | 111 | -563 | -546 | |
1T4 | 1585.20 | 287 | 86 | -191 | 75 | -567 | -823 |
0.70 | 81 | 302 | 523 | 537 | 423 | 482 | |
1585.32 | 309 | 101 | -53 | -258 | -23 | -538 | |
1T6 | 1925.29 | 252 | 376 | -240 | 156 | -1040 | -1066 |
0.38 | 36 | 213 | 201 | 284 | 285 | 305 | |
1925.41 | 248 | 193 | -150 | -146 | -731 | -907 |
References
- He, X., & Tromp, J., 1996.
Normal-mode constraints on the structure of the mantle and core.
J. Geophys. Res. 101, 20,053-20,082. - Tromp, J., & Zanzerkia, E., 1995.
Toroidal splitting observations from the great 1994 Bolivia and Kuril Islands earthquakes.
Geophys. Res. Lett. 22, 2297-2300.