291:
The ideal TRM is one that can record the magnetic field in such a way that both its direction and intensity can be measured by some process in the lab. Thellier showed that this could be done if pTRM's satisfied four laws. Suppose that A and B are two non-overlapping temperature intervals. Suppose
73:
that was much more intense than remanence acquired in the Earth's field without heating; that heating rocks in the Earth's magnetic field could magnetize them in the direction of the field; and that the Earth's field had reversed its direction in the past.
783:
216:. Because numerous experiments have been done modeling different ways of acquiring remanence, pTRM can have other meanings. For example, it can also be acquired in the laboratory by cooling in zero field to a temperature
62:(1600), a report of a series of meticulous experiments in magnetism. In it, he described the quenching of a steel rod in the direction of the Earth's field, and he may have been aware of the Chinese work.
718:
202:
204:, cooling to room temperature and measuring the remaining remanence in between each heating step. The series of remanences can be plotted in a variety of ways, depending on the application.
457:
419:
936:
965:
904:
875:
673:
644:
587:
536:
370:
319:
117:
212:
If a rock is later re-heated (as a result of burial, for example), part or all of the TRM can be replaced by a new remanence. If it is only part of the remanence, it is known as
276:
243:
146:
831:
809:
609:
558:
501:
479:
341:
1144:
967:. Then it is easy to verify that reciprocity, independence and additivity hold. It only remains for linearity to be satisfied for all the Thellier laws to be obeyed.
723:
978:
developed a physical model that showed how real magnetic minerals could have the above properties. It applies to particles that are
32:). This remanence can also be very stable, lasting without significant change for millions of years. TRM is the main reason that
684:
28:) from the Earth's field. TRM can be much larger than it would be if exposed to the same field at room temperature (see
159:
1124:
1087:
1054:
1025:
424:
386:
912:
941:
880:
851:
649:
620:
563:
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346:
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93:
119:
of the minerals carrying it. A TRM can also be partially demagnetized by heating up to some lower temperature
877:
that is independent of magnetic field for small fields. No irreversible changes occur at temperatures below
53:
252:
219:
122:
841:
Suppose that a sample has a lot of magnetic minerals, each of which has the following property: It is
1079:
979:
52:
in water. While quenching it was oriented in the Earth's field to get the desired polarity. In 1600,
814:
792:
592:
541:
484:
462:
324:
1202:
1192:
1116:
321:
is a pTRM that is acquired by cooling the sample to room temperature, only switching the field
1197:
1112:
1104:
1161:
906:. If the resulting TRM is heated in zero field, it becomes superparamagnetic again at an
29:
8:
1152:
1165:
1120:
1105:
1083:
1072:
1050:
1021:
842:
246:
88:
778:{\displaystyle \scriptstyle M_{{\text{A}}\cup {\text{B}}}=M_{\text{A}}+M_{\text{B}}}
1169:
1011:
33:
991:
149:
1173:
1186:
1046:
66:
36:
are able to deduce the direction and magnitude of the ancient Earth's field.
1140:
975:
87:
It has long been known that a TRM can be removed if it is heated above the
44:
As early as the eleventh century, the
Chinese were aware that a piece of
1074:
The Road to
Jaramillo: Critical Years of the Revolution in Earth Science
58:
278:, then cooling the rest of the way to room temperature in zero field.
70:
49:
1017:
720:
is acquired by turning the field on in both temperature intervals,
982:, having a uniform magnetization that can only rotate as a unit.
789:
If these laws hold for any non-overlapping temperature intervals
17:
48:
could be magnetized by heating it until it was red hot, then
156:, in which the sample is heated to a series of temperatures
148:
and cooling back to room temperature. A common procedure in
45:
713:{\displaystyle \scriptstyle M_{{\text{A}}\cup {\text{B}}}}
249:), applying a magnetic field and cooling to a temperature
65:
In the early 20th century, a few investigators found that
970:
836:
538:
can be removed by heating through temperature interval
945:
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623:
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487:
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222:
162:
125:
96:
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898:
869:
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803:
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667:
638:
603:
581:
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503:is not much larger than the present Earth's field.
495:
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364:
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313:
270:
237:
196:
140:
111:
1184:
197:{\displaystyle \scriptstyle T_{1},T_{2},\ldots }
1009:
1102:
1010:Stacey, Frank D.; Banerjee, Subir K. (1974).
1145:"Some theoretical aspects of rock magnetism"
452:{\displaystyle \scriptstyle M_{\text{B}}(H)}
414:{\displaystyle \scriptstyle M_{\text{A}}(H)}
343:on while the temperature is in interval A;
214:partial thermoremanent magnetization (pTRM)
1107:Rock Magnetism: Fundamentals and Frontiers
931:{\displaystyle \scriptstyle T_{\text{UB}}}
833:, the sample satisfies the Thellier laws.
1103:Dunlop, David J.; Ă–zdemir, Ă–zden (1997).
1013:The Physical Principles of Rock Magnetism
960:{\displaystyle \scriptstyle T_{\text{B}}}
899:{\displaystyle \scriptstyle T_{\text{B}}}
870:{\displaystyle \scriptstyle T_{\text{B}}}
668:{\displaystyle \scriptstyle M_{\text{B}}}
639:{\displaystyle \scriptstyle M_{\text{A}}}
582:{\displaystyle \scriptstyle M_{\text{B}}}
531:{\displaystyle \scriptstyle M_{\text{A}}}
365:{\displaystyle \scriptstyle M_{\text{B}}}
314:{\displaystyle \scriptstyle M_{\text{A}}}
112:{\displaystyle \scriptstyle T_{\text{C}}}
1185:
1040:
1096:
1034:
281:
1139:
1069:
971:The NĂ©el model for single-domain TRM
837:A simple model for the Thellier laws
286:
77:
1133:
13:
271:{\displaystyle \scriptstyle T_{2}}
238:{\displaystyle \scriptstyle T_{1}}
141:{\displaystyle \scriptstyle T_{1}}
82:
14:
1214:
845:until the temperature reaches a
1063:
1003:
826:{\displaystyle \scriptstyle B}
804:{\displaystyle \scriptstyle A}
604:{\displaystyle \scriptstyle B}
553:{\displaystyle \scriptstyle A}
496:{\displaystyle \scriptstyle H}
474:{\displaystyle \scriptstyle H}
445:
439:
407:
401:
372:has a similar definition. The
336:{\displaystyle \scriptstyle H}
207:
1:
997:
22:thermoremanent magnetization
7:
985:
10:
1219:
39:
20:rock cools, it acquires a
1174:10.1080/00018735500101204
1080:Stanford University Press
154:stepwise demagnetization
1041:Temple, Robert (2006).
1070:Glen, William (1982).
961:
932:
908:unblocking temperature
900:
871:
827:
805:
779:
714:
669:
640:
605:
583:
554:
532:
497:
475:
453:
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272:
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198:
142:
113:
1113:Cambridge Univ. Press
962:
933:
901:
872:
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555:
533:
498:
476:
454:
416:
367:
338:
316:
273:
240:
199:
143:
114:
1049:. pp. 169–171.
942:
913:
881:
852:
847:blocking temperature
815:
793:
724:
685:
650:
621:
593:
564:
542:
513:
485:
463:
459:are proportional to
425:
387:
347:
325:
296:
253:
220:
160:
123:
94:
30:isothermal remanence
1166:1955AdPhy...4..191N
1153:Advances in Physics
1043:The Genius of China
957:
956:
928:
927:
896:
895:
867:
866:
823:
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493:
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471:
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449:
448:
411:
410:
362:
361:
333:
332:
311:
310:
282:Ideal TRM behavior
268:
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235:
234:
194:
193:
138:
137:
109:
108:
953:
938:that is equal to
924:
892:
863:
843:superparamagnetic
771:
758:
744:
736:
705:
697:
661:
632:
575:
524:
436:
398:
358:
307:
287:The Thellier laws
247:Curie temperature
105:
89:Curie temperature
78:In paleomagnetism
1210:
1178:
1177:
1149:
1137:
1131:
1130:
1110:
1100:
1094:
1093:
1077:
1067:
1061:
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1038:
1032:
1031:
1007:
966:
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935:
934:
929:
926:
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922:
905:
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873:
868:
865:
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861:
832:
830:
829:
824:
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808:
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802:
784:
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781:
776:
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769:
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745:
742:
737:
734:
719:
717:
716:
711:
708:
707:
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703:
698:
695:
675:are independent.
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645:
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244:
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201:
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186:
185:
173:
172:
147:
145:
144:
139:
136:
135:
118:
116:
115:
110:
107:
106:
103:
1218:
1217:
1213:
1212:
1211:
1209:
1208:
1207:
1183:
1182:
1181:
1160:(14): 191–243.
1147:
1138:
1134:
1127:
1101:
1097:
1090:
1068:
1064:
1057:
1039:
1035:
1028:
1020:. p. 105.
1008:
1004:
1000:
988:
973:
950:
946:
943:
940:
939:
921:
917:
914:
911:
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768:
764:
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741:
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629:
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619:
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594:
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568:
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561:
543:
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521:
517:
514:
511:
510:
486:
483:
482:
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461:
460:
433:
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422:
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355:
351:
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261:
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157:
131:
127:
124:
121:
120:
102:
98:
95:
92:
91:
85:
83:Demagnetization
80:
54:William Gilbert
42:
34:paleomagnetists
12:
11:
5:
1216:
1206:
1205:
1203:Ferromagnetism
1200:
1195:
1193:Rock magnetism
1180:
1179:
1132:
1125:
1095:
1088:
1062:
1055:
1033:
1026:
1001:
999:
996:
995:
994:
992:Rock magnetism
987:
984:
972:
969:
949:
920:
888:
859:
838:
835:
821:
799:
787:
786:
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754:
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731:
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628:
612:
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571:
548:
520:
504:
491:
469:
447:
444:
441:
432:
409:
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403:
394:
354:
331:
303:
288:
285:
283:
280:
264:
260:
231:
227:
209:
206:
192:
189:
184:
180:
176:
171:
167:
150:paleomagnetism
134:
130:
101:
84:
81:
79:
76:
41:
38:
9:
6:
4:
3:
2:
1215:
1204:
1201:
1199:
1196:
1194:
1191:
1190:
1188:
1175:
1171:
1167:
1163:
1159:
1155:
1154:
1146:
1142:
1136:
1128:
1126:0-521-32514-5
1122:
1118:
1114:
1109:
1108:
1099:
1091:
1089:0-8047-1119-4
1085:
1081:
1076:
1075:
1066:
1058:
1056:0-671-62028-2
1052:
1048:
1047:Andre Deutsch
1044:
1037:
1029:
1027:0-444-41084-8
1023:
1019:
1015:
1014:
1006:
1002:
993:
990:
989:
983:
981:
980:single-domain
977:
968:
947:
918:
909:
886:
857:
848:
844:
834:
819:
797:
765:
761:
752:
748:
738:
729:
699:
690:
680:
677:
655:
626:
616:
613:
597:
569:
546:
518:
508:
505:
489:
467:
442:
430:
404:
392:
382:
379:
378:
377:
375:
374:Thellier laws
352:
329:
301:
279:
262:
258:
248:
229:
225:
215:
205:
190:
187:
182:
178:
174:
169:
165:
155:
151:
132:
128:
99:
90:
75:
72:
68:
67:igneous rocks
63:
61:
60:
55:
51:
47:
37:
35:
31:
27:
23:
19:
1198:Geomagnetism
1157:
1151:
1135:
1106:
1098:
1073:
1065:
1042:
1036:
1012:
1005:
974:
907:
846:
840:
788:
678:
615:Independence
614:
506:
380:
373:
290:
213:
211:
153:
86:
64:
57:
43:
25:
21:
15:
1141:NĂ©el, Louis
1115:. pp.
507:Reciprocity
245:(below the
208:Partial TRM
1187:Categories
998:References
976:Louis NĂ©el
679:Additivity
59:De Magnete
56:published
739:∪
700:∪
381:Linearity
191:…
71:remanence
50:quenching
1143:(1955).
1018:Elsevier
986:See also
589:through
16:When an
1162:Bibcode
40:History
18:igneous
1123:
1119:–224.
1086:
1053:
1024:
560:, and
69:had a
1148:(PDF)
681:: If
481:when
292:that
1121:ISBN
1084:ISBN
1051:ISBN
1022:ISBN
811:and
646:and
421:and
376:are
46:iron
1170:doi
1117:223
383::
152:is
26:TRM
1189::
1168:.
1156:.
1150:.
1111:.
1082:.
1078:.
1045:.
1016:.
923:UB
617::
509::
1176:.
1172::
1164::
1158:4
1129:.
1092:.
1059:.
1030:.
952:B
948:T
919:T
891:B
887:T
862:B
858:T
820:B
798:A
785:.
770:B
766:M
762:+
757:A
753:M
749:=
743:B
735:A
730:M
704:B
696:A
691:M
660:B
656:M
631:A
627:M
611:.
598:B
574:B
570:M
547:A
523:A
519:M
490:H
468:H
446:)
443:H
440:(
435:B
431:M
408:)
405:H
402:(
397:A
393:M
357:B
353:M
330:H
306:A
302:M
263:2
259:T
230:1
226:T
188:,
183:2
179:T
175:,
170:1
166:T
133:1
129:T
104:C
100:T
24:(
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