715b3e0c87100a36d78646f8afec2746 minerals-15-00873.pdf fb01f7f4fed5fa41368d11355ea12723a0b98d16 minerals-15-00873.pdf 9d3dfe01444fd5a5df728329882f1a6a9aeff9f37590f3e70b409e95d9a8bd19 minerals-15-00873.pdf Title: Exploring Smoothing and Interpolation in Thellier-Type Paleointensity Determinations Subject: Smoothing and interpolation of zero-field (Z) and infield (I) heating steps in Thellier-type paleointensity determinations have been tested. Paleomagnetic samples of different materials were artificially magnetized with an applied field of 50 T. Six samples were measured following the standard double-heating Coe-variation experimental protocol, and the obtained results were used to test several mathematical functions to smooth the experimental data. The best smoothed results were obtained using a Five Parameters Logistic (5PL) function that resulted in field estimates of good quality, although not better than those obtained experimentally. Therefore, the smoothing of de- and remagnetization data appears unnecessary. In addition to smoothing, the tested functions can be used to interpolate additional Z and, indirectly, also I steps. Interpolation using cubic Hermite splines (without any smoothing) displays a better performance than interpolation (and smoothing) using the 5PL function. A new single-step heating method is presented, combining experimental and interpolated de- and remagnetization steps. The new method would not be applicable for retrieving reliable ancient field intensities on its own, but it could save measuring time under some circumstances. Keywords: paleomagnetic intensity; Thellier; smoothing; interpolation; single-step Author: Lluís Casas, Marc Ortiz and Roberta Di Febo Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25; modified using OpenPDF 1.4.2 CreationDate: Tue Aug 19 12:08:56 2025 CEST ModDate: Tue Aug 19 12:20:19 2025 CEST Custom Metadata: yes Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 19 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 10777814 bytes Optimized: no PDF version: 1.5 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- FYJUFU+CMSY10 Type 1 Builtin yes yes yes 83 0 BEOVSN+VnURWPalladioL Type 1 Custom yes yes yes 84 0 BECHVZ+URWPalladioL-Bold Type 1 Custom yes yes yes 85 0 CFRYYK+URWPalladioL-Roma Type 1 Custom yes yes yes 86 0 GGYXJS+EURM10 Type 1 Builtin yes yes yes 87 0 IFRTMK+URWPalladioL-Ital Type 1 Custom yes yes yes 88 0 GIGFZE+CMR10 Type 1 Builtin yes yes yes 141 0 KCMCPF+PalatinoLinotype TrueType WinAnsi yes yes no 189 0 QFLWGV+CMEX10 Type 1 Builtin yes yes yes 243 0 KCMDAH+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 217 0 KCMCPF+PalatinoLinotype TrueType WinAnsi yes yes no 218 0 PDXFNG+PazoMath-Bold Type 1 Builtin yes yes yes 363 0 MPUDFL+PazoMath Type 1 Builtin yes yes yes 364 0 ZGFDNZ+EURB10 Type 1 Builtin yes yes yes 365 0 KCMCPF+PalatinoLinotype TrueType WinAnsi yes yes no 287 0 KCMCPF+PalatinoLinotype TrueType WinAnsi yes yes no 407 0 KCMCPD+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 408 0 KCMCPF+PalatinoLinotype TrueType WinAnsi yes yes no 463 0 KCMCPF+PalatinoLinotype TrueType WinAnsi yes yes no 519 0 KCMCPF+PalatinoLinotype TrueType WinAnsi yes yes no 537 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2025-09-10 03:08:13 CEST RepresentationInformation: minerals-15-00873.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-09-09 12:07:57 CEST Size: 10777814 Format: PDF Version: 1.5 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 632 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: ViewerPreferences: HideToolbar: false HideMenubar: false HideWindowUI: false FitWindow: true CenterWindow: false DisplayDocTitle: false NonFullScreenPageMode: UseNone Direction: L2R ViewArea: CropBox ViewClip: CropBox PrintArea: CropBox PageClip: CropBox PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Item: Title: Materials and Methods Children: Item: Title: Materials Item: Title: Smoothing and Interpolation Methods Item: Title: Results and Discussion Children: Item: Title: Standard Double-Heating Coe Method Item: Title: Smoothed Data in Standard Double-Heating Coe Method Item: Title: Interpolated Data in Single-Step Heating Method Item: Title: Conclusions Item: Title: References Info: Title: Exploring Smoothing and Interpolation in Thellier-Type Paleointensity Determinations Author: Lluís Casas, Marc Ortiz and Roberta Di Febo Subject: Smoothing and interpolation of zero-field (Z) and infield (I) heating steps in Thellier-type paleointensity determinations have been tested. Paleomagnetic samples of different materials were artificially magnetized with an applied field of 50 T. Six samples were measured following the standard double-heating Coe-variation experimental protocol, and the obtained results were used to test several mathematical functions to smooth the experimental data. The best smoothed results were obtained using a Five Parameters Logistic (5PL) function that resulted in field estimates of good quality, although not better than those obtained experimentally. Therefore, the smoothing of de- and remagnetization data appears unnecessary. In addition to smoothing, the tested functions can be used to interpolate additional Z and, indirectly, also I steps. Interpolation using cubic Hermite splines (without any smoothing) displays a better performance than interpolation (and smoothing) using the 5PL function. A new single-step heating method is presented, combining experimental and interpolated de- and remagnetization steps. The new method would not be applicable for retrieving reliable ancient field intensities on its own, but it could save measuring time under some circumstances. Keywords: paleomagnetic intensity; Thellier; smoothing; interpolation; single-step Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25; modified using OpenPDF 1.4.2 CreationDate: Tue Aug 19 12:08:56 CEST 2025 ModDate: Tue Aug 19 12:20:19 CEST 2025 ID: 0xd71b96c4d38667981b9752b7349c9272, 0xd3fd674cc51a9f3a487ae8e16d210ccc Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: FYJUFU+CMSY10 FontSubset: true FirstChar: 0 LastChar: 48 FontDescriptor: FontName: FYJUFU+CMSY10 Flags: Symbolic FontBBox: -29, -960, 1116, 775 FontFile: true ToUnicode: true Font: BaseFont: QFLWGV+CMEX10 FontSubset: true FirstChar: 0 LastChar: 17 FontDescriptor: FontName: QFLWGV+CMEX10 Flags: Symbolic FontBBox: -24, -2960, 1454, 772 FontFile: true ToUnicode: true Font: BaseFont: BEOVSN+VnURWPalladioL FontSubset: true FirstChar: 128 LastChar: 225 FontDescriptor: FontName: BEOVSN+VnURWPalladioL Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: BECHVZ+URWPalladioL-Bold FontSubset: true FirstChar: 3 LastChar: 237 FontDescriptor: FontName: BECHVZ+URWPalladioL-Bold Flags: Symbolic FontBBox: -152, -301, 1000, 935 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: CFRYYK+URWPalladioL-Roma FontSubset: true FirstChar: 2 LastChar: 237 FontDescriptor: FontName: CFRYYK+URWPalladioL-Roma Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: GGYXJS+EURM10 FontSubset: true FirstChar: 11 LastChar: 27 FontDescriptor: FontName: GGYXJS+EURM10 Flags: Symbolic FontBBox: -32, -243, 1060, 720 FontFile: true ToUnicode: true Font: BaseFont: IFRTMK+URWPalladioL-Ital FontSubset: true FirstChar: 45 LastChar: 246 FontDescriptor: FontName: IFRTMK+URWPalladioL-Ital Flags: Symbolic FontBBox: -170, -305, 1010, 941 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: PDXFNG+PazoMath-Bold FontSubset: true FirstChar: 68 LastChar: 68 FontDescriptor: FontName: PDXFNG+PazoMath-Bold Flags: Symbolic FontBBox: -10, -266, 829, 695 FontFile: true ToUnicode: true Font: BaseFont: MPUDFL+PazoMath FontSubset: true FirstChar: 68 LastChar: 68 FontDescriptor: FontName: MPUDFL+PazoMath Flags: Symbolic FontBBox: -40, -283, 878, 946 FontFile: true ToUnicode: true Font: BaseFont: GIGFZE+CMR10 FontSubset: true FirstChar: 40 LastChar: 61 FontDescriptor: FontName: GIGFZE+CMR10 Flags: Symbolic FontBBox: -40, -250, 1009, 750 FontFile: true ToUnicode: true Font: BaseFont: ZGFDNZ+EURB10 FontSubset: true FirstChar: 22 LastChar: 27 FontDescriptor: FontName: ZGFDNZ+EURB10 Flags: Symbolic FontBBox: -30, -247, 1178, 723 FontFile: true ToUnicode: true Pages: Page: Sequence: 1 Annotations: Annotation: Subtype: Link Rect: 104, 177, 152, 186 Annotation: Subtype: Link Rect: 34, 165, 130, 174 Annotation: Subtype: Link Rect: 36, 75, 152, 84 Annotation: Subtype: Link Rect: 34, 63, 89, 72 Annotation: Subtype: Link Rect: 34, 774, 139, 810 Annotation: Subtype: Link Rect: 515, 774, 560, 810 Annotation: Subtype: Link Rect: 100, 665, 111, 678 Annotation: Subtype: Link Rect: 274, 665, 285, 678 Annotation: Subtype: Link Rect: 414, 146, 420, 155 ActionDest: 51 Annotation: Subtype: Link Rect: 193, 118, 200, 127 ActionDest: 51 Annotation: Subtype: Link Rect: 529, 90, 536, 99 ActionDest: 51 Annotation: Subtype: Link Rect: 421, 27, 560, 37 Annotation: Subtype: Link Rect: 34, 308, 87, 327 Page: Sequence: 2 Annotations: Annotation: Subtype: Link Rect: 387, 666, 394, 675 ActionDest: 51 Annotation: Subtype: Link Rect: 468, 526, 475, 535 ActionDest: 51 Annotation: Subtype: Link Rect: 449, 512, 456, 521 ActionDest: 51 Annotation: Subtype: Link Rect: 481, 470, 488, 479 ActionDest: 51 Annotation: Subtype: Link Rect: 315, 415, 322, 424 ActionDest: 51 Annotation: Subtype: Link Rect: 456, 359, 463, 368 ActionDest: 51 Annotation: Subtype: Link Rect: 463, 359, 470, 368 ActionDest: 51 Annotation: Subtype: Link Rect: 217, 345, 224, 354 ActionDest: 51 Annotation: Subtype: Link Rect: 225, 345, 237, 354 ActionDest: 51 Annotation: Subtype: Link Rect: 349, 262, 361, 271 ActionDest: 51 Annotation: Subtype: Link Rect: 500, 234, 512, 243 ActionDest: 51 Annotation: Subtype: Link Rect: 314, 220, 326, 229 ActionDest: 51 Annotation: Subtype: Link Rect: 447, 206, 459, 215 ActionDest: 51 Annotation: Subtype: Link Rect: 286, 192, 298, 201 ActionDest: 51 Annotation: Subtype: Link Rect: 210, 178, 222, 187 ActionDest: 51 Annotation: Subtype: Link Rect: 386, 164, 398, 173 ActionDest: 51 Annotation: Subtype: Link Rect: 317, 150, 324, 159 ActionDest: 51 Page: Sequence: 3 Annotations: Annotation: Subtype: Link Rect: 529, 449, 541, 458 ActionDest: 51 Annotation: Subtype: Link Rect: 544, 449, 556, 458 ActionDest: 177 Annotation: Subtype: Link Rect: 235, 393, 247, 402 ActionDest: 51 Annotation: Subtype: Link Rect: 544, 365, 556, 374 ActionDest: 177 Annotation: Subtype: Link Rect: 249, 323, 261, 332 ActionDest: 51 Annotation: Subtype: Link Rect: 338, 295, 350, 304 ActionDest: 51 Annotation: Subtype: Link Rect: 197, 254, 209, 263 ActionDest: 51 Annotation: Subtype: Link Rect: 387, 240, 399, 249 ActionDest: 51 Annotation: Subtype: Link Rect: 460, 226, 472, 235 ActionDest: 177 Annotation: Subtype: Link Rect: 480, 128, 492, 137 ActionDest: 51 Page: Sequence: 4 Annotations: Annotation: Subtype: Link Rect: 245, 561, 252, 573 ActionDest: 113 Annotation: Subtype: Link Rect: 485, 299, 492, 311 ActionDest: 24 Annotation: Subtype: Link Rect: 520, 257, 527, 269 ActionDest: 24 Annotation: Subtype: Link Rect: 484, 229, 491, 241 ActionDest: 24 Annotation: Subtype: Link Rect: 487, 176, 494, 185 ActionDest: 51 Annotation: Subtype: Link Rect: 532, 174, 539, 186 ActionDest: 24 Page: Sequence: 5 Annotations: Annotation: Subtype: Link Rect: 189, 304, 201, 313 ActionDest: 177 Annotation: Subtype: Link Rect: 188, 181, 200, 190 ActionDest: 177 Annotation: Subtype: Link Rect: 287, 139, 299, 148 ActionDest: 177 Annotation: Subtype: Link Rect: 405, 123, 412, 135 ActionDest: 114 Annotation: Subtype: Link Rect: 452, 67, 459, 79 ActionDest: 114 Page: Sequence: 6 Annotations: Annotation: Subtype: Link Rect: 191, 347, 203, 356 ActionDest: 177 Annotation: Subtype: Link Rect: 196, 153, 208, 162 ActionDest: 177 Annotation: Subtype: Link Rect: 209, 112, 221, 121 ActionDest: 177 Annotation: Subtype: Link Rect: 285, 84, 297, 93 ActionDest: 177 Page: Sequence: 7 Annotations: Annotation: Subtype: Link Rect: 401, 349, 408, 361 ActionDest: 273 Annotation: Subtype: Link Rect: 436, 296, 448, 305 ActionDest: 177 Annotation: Subtype: Link Rect: 448, 296, 460, 305 ActionDest: 177 Annotation: Subtype: Link Rect: 408, 130, 420, 140 ActionDest: 177 Page: Sequence: 8 Annotations: Annotation: Subtype: Link Rect: 259, 756, 266, 768 ActionDest: 274 Annotation: Subtype: Link Rect: 312, 756, 319, 768 ActionDest: 273 Annotation: Subtype: Link Rect: 305, 643, 316, 651 ActionDest: 51 Annotation: Subtype: Link Rect: 423, 457, 434, 465 ActionDest: 51 Annotation: Subtype: Link Rect: 225, 180, 232, 192 ActionDest: 274 Annotation: Subtype: Link Rect: 501, 166, 508, 178 ActionDest: 273 Page: Sequence: 9 Annotations: Annotation: Subtype: Link Rect: 486, 756, 493, 768 ActionDest: 273 Page: Sequence: 10 Annotations: Annotation: Subtype: Link Rect: 367, 669, 374, 681 ActionDest: 42 Annotation: Subtype: Link Rect: 334, 592, 345, 601 ActionDest: 51 Annotation: Subtype: Link Rect: 331, 427, 338, 439 ActionDest: 42 Annotation: Subtype: Link Rect: 508, 399, 515, 411 ActionDest: 273 Annotation: Subtype: Link Rect: 513, 357, 527, 369 ActionDest: 24 Annotation: Subtype: Link Rect: 195, 204, 202, 216 ActionDest: 275 Annotation: Subtype: Link Rect: 549, 176, 556, 188 ActionDest: 275 Annotation: Subtype: Link Rect: 410, 134, 417, 146 ActionDest: 274 Annotation: Subtype: Link Rect: 439, 134, 446, 146 ActionDest: 275 Annotation: Subtype: Link Rect: 373, 106, 380, 118 ActionDest: 275 Page: Sequence: 11 Annotations: Annotation: Subtype: Link Rect: 180, 682, 191, 691 ActionDest: 51 Page: Sequence: 12 Annotations: Annotation: Subtype: Link Rect: 328, 630, 336, 642 ActionDest: 495 Annotation: Subtype: Link Rect: 466, 575, 473, 587 ActionDest: 497 Annotation: Subtype: Link Rect: 526, 575, 533, 587 ActionDest: 497 Annotation: Subtype: Link Rect: 466, 452, 478, 461 ActionDest: 177 Annotation: Subtype: Link Rect: 478, 452, 490, 461 ActionDest: 177 Annotation: Subtype: Link Rect: 275, 410, 287, 419 ActionDest: 177 Annotation: Subtype: Link Rect: 387, 368, 399, 377 ActionDest: 177 Annotation: Subtype: Link Rect: 399, 368, 411, 377 ActionDest: 177 Annotation: Subtype: Link Rect: 426, 157, 433, 169 ActionDest: 495 Page: Sequence: 13 Page: Sequence: 14 Annotations: Annotation: Subtype: Link Rect: 180, 721, 191, 729 ActionDest: 51 Annotation: Subtype: Link Rect: 509, 93, 516, 107 ActionDest: 497 Page: Sequence: 15 Annotations: Annotation: Subtype: Link Rect: 324, 466, 336, 475 ActionDest: 177 Annotation: Subtype: Link Rect: 473, 199, 480, 211 ActionDest: 510 Page: Sequence: 16 Annotations: Annotation: Subtype: Link Rect: 338, 418, 345, 430 ActionDest: 510 Annotation: Subtype: Link Rect: 314, 220, 325, 228 ActionDest: 51 Page: Sequence: 17 Annotations: Annotation: Subtype: Link Rect: 307, 547, 319, 556 ActionDest: 177 Annotation: Subtype: Link Rect: 525, 129, 560, 140 Annotation: Subtype: Link Rect: 165, 116, 362, 127 Page: Sequence: 18 Annotations: Annotation: Subtype: Link Rect: 200, 496, 237, 507 Annotation: Subtype: Link Rect: 162, 472, 199, 482 Annotation: Subtype: Link Rect: 117, 446, 155, 456 Annotation: Subtype: Link Rect: 82, 395, 119, 405 Annotation: Subtype: Link Rect: 358, 369, 395, 380 Annotation: Subtype: Link Rect: 501, 343, 539, 354 Annotation: Subtype: Link Rect: 162, 319, 199, 329 Annotation: Subtype: Link Rect: 131, 267, 168, 278 Annotation: Subtype: Link Rect: 323, 228, 361, 239 Annotation: Subtype: Link Rect: 204, 204, 242, 214 Annotation: Subtype: Link Rect: 403, 177, 441, 188 Annotation: Subtype: Link Rect: 135, 153, 173, 163 Annotation: Subtype: Link Rect: 439, 126, 476, 137 Annotation: Subtype: Link Rect: 480, 101, 518, 112 Annotation: Subtype: Link Rect: 372, 75, 409, 86 Page: Sequence: 19 Annotations: Annotation: Subtype: Link Rect: 184, 744, 221, 754 Annotation: Subtype: Link Rect: 204, 719, 242, 729 Annotation: Subtype: Link Rect: 370, 692, 408, 703 Annotation: Subtype: Link Rect: 59, 668, 96, 678 Annotation: Subtype: Link Rect: 59, 642, 96, 652 Annotation: Subtype: Link Rect: 152, 604, 190, 614 Annotation: Subtype: Link Rect: 271, 578, 309, 588 Annotation: Subtype: Link Rect: 505, 501, 542, 512 Annotation: Subtype: Link Rect: 433, 475, 471, 486 Annotation: Subtype: Link Rect: 519, 450, 557, 461 Annotation: Subtype: Link Rect: 95, 425, 132, 435 Annotation: Subtype: Link Rect: 247, 399, 284, 410 Annotation: Subtype: Link Rect: 397, 373, 435, 384 Annotation: Subtype: Link Rect: 222, 348, 259, 358 Annotation: Subtype: Link Rect: 59, 310, 96, 320 Checksum: 34a8cc3b Type: CRC32 Checksum: 715b3e0c87100a36d78646f8afec2746 Type: MD5 Checksum: fb01f7f4fed5fa41368d11355ea12723a0b98d16 Type: SHA-1 Checksum: 9d3dfe01444fd5a5df728329882f1a6a9aeff9f37590f3e70b409e95d9a8bd19 Type: SHA-256