Resources: Normal-Mode Observations

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 $\mu$ Hz under f and f_PREM under Q and Q_PREM.The splitting width, w, is the frequency difference between the highest and lowest frequency singlets. The splitting ratio, r, is the ratio of the observed splitting width to the splitting width predicted due to the effects of rotation and hydrostatic ellipticity. Core-sensitive modes are labeled by an asterisk.

Tab-delimted text version also available.

Mode	f_PREM	f	Q_PREM	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 $\mu$ Hz under f and f_PREM,and the observed and predicted quality factors are listed under Q and Q_PREM.

Mode	f_PREM	f	Q_PREM	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 A_st and B_st are related to the complex splitting-function coefficients c_st defined by $c_{st}=(-1)^t(2\pi)^{1/2}(A_{st}-iB_{st})$ for t>0, $c_{st}=(4\pi)^{1/2}A_{st}$ for t=0, and $c_{st}=(2\pi)^{1/2}(A_{s\vert t\vert}+iB_{s\vert t\vert})$ , for t<0. The coefficients are listed in unit of 10^-6. Core-sensitive modes are indicated by an asterisk.

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 A_st and B_st are related to the complex splitting function coefficients c_st defined by $c_{st}=(-1)^t(2\pi)^{1/2}(A_{st}-iB_{st})$ for t>0, $c_{st}=(4\pi)^{1/2}A_{st}$ for t=0, and $c_{st}=(2\pi)^{1/2}(A_{s\vert t\vert}+iB_{s\vert t\vert})$ , for t<0 (Li et al., 1991). The center frequencies are listed in $\mu$ Hz and the coefficients are listed in unit of 10^-6.

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.