I N T RO D U C T I O N

One of the central goals of palaeomagnetic research is to describe variations in the geomagnetic field, including its direction and strength. Accurate palaeointensity records play a pivotal role in understanding geomagnetic field behaviour (e.g. de Groot et al. 2015 ;Wang et al. 2015 ;Okayama et al. 2019 ;Asefaw et al. 2021 ) and the evolution of dynamos within the core of the Earth and other planetary bodies (e.g. Biggin et al. 2015 ;Tikoo et al. 2017 ;Bono et al. 2019 ;Mighani et al. 2020 ). Fur ther more, insights into the formation and early history of the solar system can be gleaned from palaeointensity estimates of meteorites (e.g. Fu et al. 2014 ;Wang et al. 2017 ;Fu et al. 2020 ;Weiss et al. 2021 ).

A significant amount of the absolute palaeointensity records was acquired using the Thellier-series palaeointensity experiments, which used heating treatments to replace natural remanent magnetization (NRM) recorded by measured rock samples with a thermal remanent magnetization (TRM) obtained by a known laboratoryapplied field (Thellier & Thellier 1959 ;Coe 1967b ). Widely used Thellier-series method, such as the original Thellier-Thellier double heating protocol (Thellier & Thellier 1959 ), the Coe protocol (Coe 1967b ) and the IZZI protocol (Tauxe & Staudigel 2004 ;Yu et al. 2004 ), hav e sev eral challenges for obtaining reliable palaeointensity data, resulting in a low success rate in these protocols and a limitation in the acquisition of available accurate palaeointensities. For example, global palaeointensity records spanning the past 5 Myr drawn from the PINT 2014.01 database did not exhibit an explicit latitudinal dependency as expected for a geocentric axial dipole (GAD) model (e.g. Lawrence et al. 2009 ;Wang et al. 2015 ;Biasi et al. 2021 ;Tauxe et al. 2022 ). One possible primary reason for this is the low-fidelity palaeointensity data in the database (Wang et al. 2015 ).

Based on empirical and experimental arguments from previous studies over past decades, the thermal alteration of samples (Kosterov & Pr évot 1998 ;Fabian 2009 ;Qin et al. 2011 ;Zhao et al. 2014 ;Kim et al. 2018 ;Wang & Kent 2013, 2021 ) and the multidomain (MD) ef fect (Le vi 1977 ;Riisager & Riisager 2001 ;Xu & Dunlop 2004 ;Biggin 2006 ;Dunlop 2011 ;Shaar et al. 2011 ;Smirnov et al. 2017 ;Tauxe et al. 2021 ), are the two crucial reasons restrict the fidelity of palaeointensity determinations during Thellier-type methods. Great efforts have been made, such as low-temperature demagnetization (LTD) treatments (Schmidt 1993 ;Smirnov et al. 2017 ) and the Repeat thEllier-Series ExperimenT (RESET) palaeointensity method (Wang & Kent 2021 ) to correct the MD effect and hav e gradually improv ed success rates in palaeointensity e xperiments (Biggin & Dekkers 2007 ;Paterson 2011 ;Smirnov et al. 2017 ;Wang & Kent 2021 ).

Thermal alteration of lava samples, including thermophysical (such as variations in magnetic domain state) and thermochemical (such as the formation of new ferromagnetic minerals or the degradation of original ferromagnetic minerals) changes, are commonly occurred in laboratory heating process during Thellier-series palaeointensity experiments, which can bias the palaeointensity estimates (Qin et al. 2011 ;de Groot et al. 2014 ;Wang & Kent 2021 ). The par tial ther moremanence check (pTRM check), first proposed by Thellier & Thellier ( 1959 ), is conducted by giving the sample another pTRM at a pre viousl y experienced lower temperature during palaeointensity measurements to detect possible changes in the magnetic mineralogy. A discrepancy between the previously acquired pTRM and the pTRM obtained during the check process at the same temperature indicates that thermal alteration occurred. In the current studies, pTRM checks as the primar y ther mal alteration indicator widely used in palaeointensity experiments (Monster et al. 2018 ;Abdulghafur & Bowles 2019 ;Grappone et al. 2021 ;Wang & Kent 2021 ). For example, 88 per cent of 25 palaeointensity studies collected from 2003 to 2014 used pTRM checks (see table S1 in Wang & Kent 2021 ). Ho wever , the pTRM check has its inherent weakness, which is only effective in detecting thermal changes within particles whose blocking temperature is lower than the check temperature (Coe 1967a ;Wang & Kent 2021 ), resulting in even passing the pTRM check does not guarantee the thermal stability of the measured samples and the accuracy of obtained palaeointensity estimates.

Great effort has been made to propose different palaeointensity experimental techniques to avoid thermal alteration, such as the multispecimen parallel differential pTRM technique (referred to as the MS method, Hoffman et al. 1989 ;Dekkers & B öhnel 2006 ). The MS method complied with a basic assumption of the first-order symmetr y proper ties of pTRM in MD grains (Dekkers & B öhnel 2006 ) to obtain reliable palaeointensities independent of magnetic domain states (Dekkers & B öhnel 2006 ;Michalk et al. 2008 ;2010 ). Moreover, the MS method uses multiple samples, and each sample conducted one moderate-temperature heating treatment, avoiding laborator y-induced ther mal alterations and reducing the processing time duration (Dekkers & B öhnel 2006 ). Ho wever , the sample conducted in the once-heating step may not avoid thermal alteration, and the MS method still needs the rock magnetic measurements to identify the thermal stability of measured samples.

Conventional measurements of rock magnetic properties before and after heating steps serve as another indicator to detect thermal changes (Smirnov & Tarduno 2003 ;Carvallo et al. 2006 ;Qin et al. 2011 ;Paterson et al. 2017 ;Kim et al. 2018 ;Wang & Kent 2021 ). For instance, Qin et al. ( 2011 ) identified the M rs,480 • C / M rs,25 • C as the alteration index to select palaeointensity samples without thermal changes. Jeong et al. ( 2021 ) compared hysteresis properties before and after heating treatments to detect the possible thermal changes to recover the geomagnetic field intensities from the Hawaii 1960 historical lava samples. Paterson et al. ( 2017 ) established a link between magnetic behaviour and palaeointensity estimates and identified the bulk domain stability (BDS) trend to reveal the remanence stability of measured samples. These findings show that comprehensive rock magnetic analyses have great prospects for tracking thermal changes.

In this study, we proposed a new method, thermal rock magnetic cycling (TRMC), which conducted critical rock magnetic properties at ele v ated temperatures during multiple heating-cooling cycles to provide deeper insight into the thermal alteration of bulk samples and individual magnetic components with different Curie temperatures in measured samples. We conducted the TRMC method on a Galapagos lava sample GA 84.6 (Wang & Kent 2013 ;2021 ). The variation in hysteresis properties revealed that the corrected Arai plot of GA 84.6c contained two linear segments with different palaeointensity values, but both were biased by thermophysical alteration. To further test the ef fecti veness of the above method, we utilized the TRMC method to e v aluate the thermal stability of a historical lava sample (HS 2) from Mt Lassen during high-temperature heating experiments, which helped us to detect thermal changes and interpret the changes in the TRM unblocking spectrum of palaeointensity specimen. As a new method, the TRMC experiment can track thermal alteration details, which can help us assess the thermal stability of palaeointensity specimens, interpret palaeointensity estimates in previous studies and preselect palaeointensity samples in new palaeofield strength studies.

M AT E R I A L S A N D M E T H O D S

Lava samples

Lava samples from the GA-X site on Floreana Island in the Galapagos Archipelago ( Fig. S1 ) provide a valuable low-latitude record of the Santa Rosa Excursion event during the Matuyama chron. This event has been dated to 925.7 ± 4.6 ka based on 40 Ar/ 39 Ar age determinations (Balbas et al. 2016 ) and has an associated palaeointensity record of 4.23 ± 1.29 μT (Wang & Kent 2013 ;2021 ). Although the pTRM check of the critical specimen GA 84.6c from the GA-X site passed, it failed to provide a reliable palaeointensity record. For this study, we chose sister specimens of GA 84.6 for electron probe micro-anal yser (EPMA) anal ysis and comprehensi ve thermal rock magnetic cycling (TRMC) measurements. These specimens were cut from 10-mm-diameter half-cylinder specimens cut along the edge of palaeointensity specimen GA 84.6c (Wang & Kent 2013, 2021 ;Fig. S2 ). We also measured conventional rock magnetic curves at room temperature on these fresh specimens to verify the consistency of hysteresis behaviour in GA 84.6 sister specimens using the Day plot ( Fig. S3 ).

To further test the ef fecti veness of our TRMC method for palaeointensity interpretations, we conducted the proposed experiment on another historical lava specimen, HS 2-8C. On 19 May 1915, a small eruption occurred at Mt Lassen in nor ther n California. The geomagnetic field strength at the eruption site was 54 μT (Coe et al. 2004 ). Coe et al. ( 2004 ) collected samples from the 1915 Mt Lassen dacite flow to obtain the hysteresis behaviour from rock magnetic experiments and extract the expected palaeointensity record using the Thellier method. Their results indicated that the primary magnetic carriers within sample HS 2 were non-single-domain (non-SD) titanomagnetite grains and obtained a relati vel y accurate palaeointensity of 45 μT (Coe et al. 2004 ). Additionally, Coe et al. ( 2004 ) also observed that the room-temperature remanences and coerci vities slightl y changed after repeated heating-cooling treatments, especially after heating from 400 to 600 • C. These findings prompted us to use the new TRMC method to evaluate the impact of thermal changes on palaeointensity estimates within the 1915 Mt Lassen sample.

Rock magnetic measurements and EPMA analysis

To identify the composition and size distribution of magnetic carriers within the Galapagos lava sample, we measured low-temperature ther mal fluctuation tomog raphy (LT-TFT, Jackson et al. 2006 ) curves on a fresh specimen GA 84.6v from 10 to 320 K for every 10 K using the Quantum Designs Magnetic Properties Measuring System (MPMS) in the Institute for Rock Magnetism (IRM), the University of Minnesota. Another specimen, GA 84.6u, was chosen for EPMA analysis and back-scattered electron (BSE) imaging using an electron probe microanalyser at Wuhan Sample Solution Anal ytical Technolo gy Co., Ltd, Wuhan, China. The anal ysis w as conducted using the JXA-8230 model from JEOL with a 1 μm beam diameter and either 15 or 20 kV accelerating voltage. After two heating-cooling cycles with a target temperature of 607 • C, the same microscopic analysis was conducted on specimen GA 84.6w to detect potential thermal alteration. BSE imaging was also conducted on a fresh specimen and an after-heated specimen from sample HS 2, which may detect the thermal changes after high-temperature heating treatments.

In addition, we conducted low-field thermal magnetic susceptibility measurements ( κ-T curves) in Argon on a powdered bulk sample of GA 84.6 using an AGICO KLY-3 Kappabridge equipped with a high-temperature furnace at the Palaeomagnetism and Geochronology Laboratory at the Institute of Geology and Geophysics, Chinese Academy of Sciences. In order to gain more insights into the thermal alteration characteristics, we conduct high-temperature rock magnetic measurements on additional fresh ∼20 mg specimen GA 84.6w on a high-temperature measurements system in the Institute for Rock Magnetism (IRM), the University of Minnesota. We calculated the low-field susceptibility ( к LF ) from the hysteresis loops measured at ele v ated temperatures from room temperature to 607 • C for every 20 • C. Then, we repeat the 25 • C to 607 • C measurements after the first heating treatment, which allows us to compare the к LF values of the initial state to the after-heated state.

T her mal rock magnetic c y cling (TRMC) experiment

We performed the ne wl y de v eloped TRMC e xperiment on a Galapagos lava specimen GA 84.6v to track the thermal alteration in detail. We used a Lake Shore vibrating sample magnetometer (VSM 8604) at the China University of Geosciences (Wuhan, Fig. S4 ), equipped with a Model 86-OVEN high-temperature oven to measure hysteresis loops, back-field direct current demagnetization (DCD) curves and first-order reversal curves (FORCs, Pike et al. 1999 ;Roberts et al. 2014 ) at ele v ated temperatures from 25 • C to each target temperature (100

To track the thermal alteration after the first heating to 575 • C, we repeat the specimen heating from room temperature to 575 • C (Fig. 1 ). The above TRMC procedure for specimen GA 84.6v included nine heating-cooling cycles and required over 300 hr of experimental time (Fig. 1 ).

During the TRMC experiment (Fig. 1 ), all rock magnetic curves were measured in a maximum applied field of 1.5 T. Critical parameters such as saturation magnetization ( M s ), saturation remanent magnetization ( M rs ) and magnetic coercivity ( B c ) were extracted from corrected hysteresis loops using high-field linear slope correction. The DCD measurement procedure was modified to obtain high-resolution DCD curves, and remanent coercivity ( B cr ) was extracted from these curves. We also calculated the low-field susceptibility ( к LF ) from the hysteresis loops after each heating-cooling cycle. The coercivity distribution of GA 84.6v was derived from DCD curves using the cumulative log Gaussian (CLG) model (Robertson & France 1994 ;Heslop et al. 2002 ) and skew-normal distribution model (MAX UnMix web application, Maxbauer et al. 2016 ) to analysis the magnetic constituents contained in the measured specimen. FORC measurements used a field increment of 2 mT and an averaging time of 1 s, and the software package FORCinel v3.06 (Harrison & Feinberg 2008 ) was used to calculate the FORC diagrams. We additionally used an Agilent molecular pump to reduce the inner furnace pressure from 101.325 kPa (atmospheric pressure) to about 10 -7 kPa during the TRMC experiment ( Fig. S4c ). At the same time, a flow of 99.99 percent high-purity inert argon gas was inserted at a rate of 80 to 130 cc/min into the sample space to avoid severe oxidation of the measured specimen ( Fig. S4e ).

Considering the relati vel y high thermal stability of the 1915 Mt Lassen sample, we perform a simplified TRMC procedure on specimen HS 2-8C. We modified the measured temperature intervals from 25 to 50 • C and selected a target temperature range from 100 to 600 • C at 100 • C intervals, which reduced the experimental time to less than 80 hr. We also used the VSM 8604 equipped with high-temperature measurement instruments (e.g. model-86 OVEN, Agilent molecular pump, as shown in Fig. S4 ) at the China University of Geosciences (Wuhan) to measure hysteresis loops, DCD curves, and FORCs from room temperature to each target temperature (100 • C, 200 • C, 300 • C, 400 • C, 500 • C, 600 • C and 600 • C). This entire set of TRMC experiments consists of seven heating-cooling cycles, and all rock magnetic curves were measured in a maximum applied field of 1.5 T.

R E S U LT S

3.1 T her mal alteration analysis for Galapagos lava sample GA 84.6

Magnetic carriers and thermophysical alteration

The results of EPMA analysis and BSE imaging of specimen GA 84.6u reveal micron-sized iron oxide particles (Figs 2 a, b and S5 ) dominantly composed of titanomagnetite, with a maximum titanium content of almost 0.6 ( Table S1 ). These particles commonly display e xtensiv e e xsolution features, with ilmenite divided into regions with particle sizes of less than 10 μm, or even 1 μm, as a result of deuteric oxidation (Fig. 2 b). This produced low-titanium magnetite particles ( Table S1 ). The Curie temperature near 580 • C from the temperature dependence of magnetic susceptibility ( к-T ) curves (Fig. 2e) and the Verwey transition near 120 K ( Fig. S6 ) also indicates that the dominant magnetic carrier within GA 84.6 is magnetite or low-titanium magnetite in agreement with previous studies by Wang & Kent ( 2013, 2021 ).

After subjecting the specimen to two heating-cooling cycles with a target temperature of 607 • C, the composition and size distribution of iron-oxides in the heated specimen GA 84.6w is nearly the same as in the GA 84.6u in the BSE image (Figs 2 c, d and S5 ). This consistency suggests that no significant thermochemical alteration occurred, such as oxidation induced by high-temperature treatments. This finding is consistent with the reversible heatingcooling curves of the thermomagnetic experiment for GA 84.6s (Wang & Kent 2013 ) shown in Fig. 2 (g). The minimal changes in induced magnetizations suggest that the thermal alterations are predominantly thermophysical than thermochemical, as evidenced by the irreversible к-T (Fig. 2 e) and к LF -T curves (Fig. 2 f).

Trac king thermoph ysical alteration using the TRMC method

We extracted critical hysteresis parameters ( M s , M rs , B c and B cr ) from the rock magnetic curves obtained during the TRMC experiment ( Fig. S7 ). The M s of GA 84.6v remained constant at each measured temperature across the different cycles, indicating again that no significant thermochemical alteration occurred in the measured specimen (Fig. 3 The variations in the parameters described above indicate that thermophysical alteration of the measured specimen occurred throughout the heating treatment during the TRMC experiment. For target temperatures below 450 • C, the measured specimen undergoes thermophysical alteration involving domain structure changes, reducing the remanence carrying capacity. After GA 84.6v was heated to 450 • C, the M rs and B c began to increase. Severe thermal alteration occurs after heating to 550 • C due to changes in domain state (PSD to more SD behaviour), leading to a sharp enhancement of the remanence carrying capacity . Additionally , room-temperature κ LF values exhibit a reduced trend after 400 • C heating treatments ( F ig. S8 ), w hich may originate from domain state changes after high-temperature heating treatments. We obtained two components (low-coercivity component, LC, and high-coercivity component, HC) unmixed from DCD curves using skew-normal distribution and CLG distribution models (Figs S9 and S10). Fig. 4 shows the critical hysteresis parameters ( B crL , B crH , SIRM L %, SIRM H % obtained from the skew-normal model; B crL , B crH , SIRM L , SIRM H obtained from the CLG model) of each magnetic component contained in GA 84.6v. When the target temperature was below 500 • C, both values of SIRM L and SIRM H decreased (Fig. 4 ). Therefore, the reduced remanence of the measured specimen in this lower temperature range ( < 500 • C) originating from domain structure changes in the LC and HC. Considering the room temperature SIRM H increases sharply, and the value of SIRM H % is enhanced to 70 per cent when the target temperature exceeds 500 • C, we suggest that HC minerals mainly dominate the hysteresis properties of the bulk specimen, especially after the high-temperature heating process higher than 500 • C (Fig. 4 ).

FORC measurements were conducted simultaneously during the TRMC experiment. For target temperatures below 450 • C, FORC diagrams from the first to the fifth cycles displayed a consistent vertical spread along the B μ -axis and a low-coercivity signal (Fig. 5 ), indicating that subtle thermophysical alterations during low-temperature heating were not discernible in the FORC diagrams. A slight increase in coercivity was observed after heating the specimen to 450 • C, resulting in more SSD-like behaviour in the FORC diagrams (Fig. 5 ). For target temperatures exceeding 450 • C, FORC diagrams, measured at room temperature, revealed a closed-contour peak with e xtensiv e v ertical and horizontal spreads (Fig. 5 ). This suggests strong thermal changes, leading to a shift in the domain state towards a more SD-like behaviour, as evidenced by the rapid movement of hysteresis parameter ratios from the PSD to more SD-like behaviour in the Day diagram (Fig. 5 ).

Consequently, thermophysical alteration is primarily driven by changes in the domain structure of the bulk specimen when target temperatures remain below 450 • C, resulting in a reduced remanence carrying capacity. Upon reaching a target temperature of 450 • C, the remanence carrying capacities of GA 84.6v start to increase sharpl y, largel y attributed to the thermal alteration of the HC. Moreover, as the measured temperature approached 550 • C-near the Curie temperature of most meta-stable magnetic particles within GA 84.6v-the hysteresis parameters stabilized, indicating the thermal stability of magnetic carriers with higher Curie temperatures.

T her mal alteration analysis for 1915 Mt Lassen sample HS 2

In the historical lava specimens of HS 2, primary titanomagnetite exhibits constant near-homogeneous features in the fresh specimen (Fig. 6 a) and the after-heated specimen (Fig. 6 b). For another lava specimen, HS 2-8C, we extracted critical hysteresis parameters ( M s , M rs , B c and B cr ) from rock magnetic curves ( Fig. S12 ) during the TRMC experiment to detect thermal changes within the measured specimen. Considering changes in the saturation magnetization are considered to best detect thermochemical alteration, the temperature dependence of M s is shown in Fig. 7 (a). Additionally, the TRMC results of the Galapagos lava sample indicated that M rs values are valuable markers of variations in the remanence carrying capacity and domain state of the measured samples, which should be regarded as the most important parameter to analyse. Thus, we prioritized establishing the temperature dependence of M rs in Fig. 7 (b). Other hysteresis properties ( B c and B cr ) are shown in Fig. S13 . Fig. 7 (a) shows that the M s of HS 2-8C remains constant at a giv en temperature ov er different heating-cooling c ycles, indicating that no significant thermochemical alteration occurred. The M rs measured after heating to target temperatures of 100-300 • C (room temperature measurements made at the second to fourth cycles) are relati vel y close to the initial value (Fig. 7 b). When the target temperature reaches 400 • C, the room-temperature M rs (5th cycle) begins to increase and reaches a maximum value after the first heating to 600 • C (7th cycle, Fig. 7 b). We determined that specimen HS 2-8C has remarkable thermal stability for target temperatures below 400 • C. Slight thermal-physical changes occurred in the specimen after heating to target temperatures reaching 400 • C. The value of M rs subsequently increased as a result of domain structure changes, weakly enhancing the remanence carrying capacity of HS 2-8C. The above thermal change details also lead to relati vel y constant values of hysteresis ratios ( M rs / M s , B cr / B c , Fig. 7 c) and room temperature κ LF curve ( Fig. S8 ).

Additionally, we can determine the thermal stability of each magnetic component with a distinct Curie temperature in HS 2-8C by monitoring the difference in properties obtained at two adjacent measured temperatures in each cycle, which is defined as M -h). This consistency indicates that the weak thermophysical alteration after high temperatures cannot be detected by FORC diagrams. We also showed all the FORC diagrams in Figs S14 and S15.

In summary, for specimen HS 2-8C, slight thermophysical alteration occurred when target temperatures reached 400 • C, resulting in an increased remanence carrying capacity. We also isolated the thermal stable magnetic component with the Curie temperatures between 25 and 350 • C. Based on the above thermal alteration analysis for specimens GA 84.6v and HS 2-8C, the TRMC is a powerful method that can track the cause and the process of thermal alteration of bulk specimens and utilizes critical hysteresis properties measured at ele v ated temperatures to assess the thermal stability of individual magnetic components with different Curie temperatures within each specimen. These findings are expected to e v aluate the thermal stability of palaeointensity specimens and help palaeointensity interpretations, which are less detailed in previous studies.

D I S C U S S I O N

Using the TRMC method to track thermal changes for palaeointensity interpretations

Galapagos lava sample GA 84.6

To better understand the total thermal changes that occur during palaeointensity determinations, we examined the palaeointensity results for GA 84.6c (Wang & Kent 2013 ;2021 ). We found that the original Arai diagram displays two-slope behaviour (Fig. 8 a). Based on our TRMC results for GA 84.6v, the value of M s remains constant at a given measured temperature across the different cycles (Fig. 3 and c). Based on the original Arai diagram of GA 84.6c, the remanence carrying capacity of the measured specimen appears relati vel y stable, with a slight reduction after heating to temperatures below 500 • C. This leads to a decline in the pTRM-gaining ability of GA 84.6c in this lower temperature range, causing the NRM unblocked to exceed the pTRM imparted by the experimental field. This results in an overestimated palaeointensity value of 28.33 μT (Fig. 8 a).

When the target temperature reaches 500 • C, a pronounced increase in M rs at room temperature measurements indicates changes in domain states (moving from PSD to more SD-like behaviour). This leads to a sharp increase in remanence carrying capacity (Figs 3 b and 5 ). In the original Thellier-Coe palaeointensity measurements, this thermophysical alteration shallower the NRM-pTRM slope and underestimated palaeointensity fitting by the hightemperature range ( ≥500 • C, Fig. 8 a).

After the original Thellier-Coe experiment, Wang & Kent ( 2021 ) developed the RESET method, which involves subjecting a measured specimen (GA 84.6c) to a total TRM (tTRM) from the Curie temperature in a known laboratory field. The same palaeointensity procedure is then repeated (Fig. 8 b), and a corrected Arai diagram is created by plotting the NRM remaining against the tTRM unb locking (F ig. 8 c). The thermal changes of the measured specimen after the original Thellier-Coe experiment will lead to variations in the obtained tTRM unblocking spectrum, which may lead to non-linear corrected Arai plots and biased palaeointensities. The TRMC results showed that the M rs of GA 84.6v increased by 13.1 per cent after the second heating to 575 • C (Fig. 3 b), which indicates that the carrying capacities for remanent magnetization of the bulk specimen were enhanced. For LC and HC, the remanence carrying abilities are decreased and increased, respecti vel y, deri ved from the significantly increased SIRM H along with a decrease in SIRM L after the second 575 • C heating treatments (Figs 4 e and f). Therefore, the enhanced M rs of the bulk specimen originated from HC with a thermal altered state, which reduced the ef fecti ve grain size of magnetic carriers (PSD to more SSD behaviour) to promote remanence carr ying capacities. Fur ther more, a more than 30 per cent decrease in susceptibility of GA 84.6c after the original palaeointensity experiment (Wang & Kent 2013 ) also may demonstrate domain state changes for enhancement of remanence carrying capacities.

In the RESET-corrected Arai diagram (Fig. 8 c), The LC minerals with lower Curie temperatures ( < 500 • C) displayed a reduction of remanence carrying capacities, leading to the acquisition of pTRM decrease during the tTRM obtained process after the original Thellier-Coe experiment (Fig. 8 c). This process promotes NRM remaining to exceed the tTRM unblocking in this temperature intervals (0-500 • C) and biased palaeointensity to a higher value of 26.57 μT (Fig. 8 c). The thermal changes sharply enhanced the ability of HC to record remanent magnetization, such as the pTRM, which caused a shallower NRM-tTRM slope in this higher temperature range (500-575 • C, Fig. 8 c). Consequently, the corrected Arai plot of GA 84.6c yielded two linear segments with distinct palaeointensity values (Fig. 8 c), but both were biased by thermophysical alteration. The above findings are consistent with the TRM blocking spectrum of GA 84.6 shown in Wang & Kent ( 2013 ), which is mainly manifested as a minor decreased pTRM efficiency in 300-500 • C intervals and a sudden increase in pTRM recording capability in higher temperature segment (500-550 • C).

We isolated a stable magnetic component with a Curie temperature above 550 • C using the TRMC experiment (Fig. 3 b), which may preserve a primary TRM. We estimated palaeointensity by fitting the corresponding segments (550-575 • C) on the corrected Arai plot and obtained a result of 4.50 μT (Fig. 8 c). Although the palaeointensity value is consistent with the mean value for site GA-X (4.23 ± 1.29 μT, Wang & Kent 2013 ), the value may still be biased because it was obtained by fitting only two data points to calculate the palaeointensity.

1915 Mt Lassen sample HS 2

We track the entire sequence of thermal changes in a historical lava specimen (HS 2-8C) from Mt Lassen using the TRMC method to interpret the TRM unblocking spectrum of specimen HS 2-2C during palaeointensity experiments. Coe et al. ( 2004 ) collected samples from the 1915 Mt Lassen dacite flow to extract the expected palaeointensity record using the Thellier method. Their results indicated that nonlinear NRM-TRM curves, such as concave and Sshaped, are typical in Arai plots of the 1915 Mt Lassen samples (Coe et al. 2004 ). Although there is a large deviation in the palaeointensity v alues deri ved from low-temperature or high-temperature interv als, the slope calculated by connecting the initial and final data points from the Arai plots provided a more accurate average palaeointensity value of 52 μT (Coe et al. 2004 ). For the specimen HS 2-2C, the slope of the line connecting the endpoints provided a relati vel y accurate palaeointensity value of 45 μT (Coe et al. 2004 ).

Based on our TRMC results for HS 2-8C, a slightly underestimated palaeointensity record of HS 2-2C ma y ha ve originated from the thermal instability of the measured sample. The increase in the remanence carrying capacity of the measured specimen after heating temperatures reached 400 • C during the TRMC experiment (5th cycle, Fig. 7 b) led to the NRM being unblocked lower than the pTRM gained, resulting in a shallower NRM-pTRM slope and relati vel y biased palaeointensity record of 45 μT (Coe et al. 2004 ). Our TRMC results indicate that the measured specimen remains thermally stable when the target temperature is below 400 • C. The demagnetization steps in the Thellier-type experiment show no significant secondary components in the NRM (Fig. 8 d). Therefore, w e ma y derive a more accurate palaeointensity value of 51 μT by fitting the lower-temperature segment ( ≤360 • C) from the Arai plot (F ig. 8 d), w hich is closer to the expected field strength (54 μT). When the target temperature exceeds 400 • C, the increase in M rs at room temperature due to domain configuration changes leads to a slight increase in the remanence carrying capacity. In Thelliertype palaeointensity measurements, this thermophysical alteration results in a shallower NRM-pTRM slope and yields an underestimated value of 47 μT at the high-temperature interval ( ≥390 • C, Fig. 8 d).

Utilizing the TRMC results to examine the Arai plot, we observed that the S-shaped NRM-TRM curve arises from weak thermalphysical changes within HS 2-2C at target heating temperatures above 400 • C. The TRMC experiment comprehensi vel y captures the entire thermal alteration of the 1915 Mt Lassen specimen (HS 2-8C), aiding in interpreting the TRM unblocking spectrum behaviour for specimen HS 2-2C. As MD grains are the primary magnetic carrier within the measured specimen, the MD effect may also contribute to the non-linear Arai plot and biased current palaeointensity v alue. Howe ver, the thermal changes in the measured sample are still a critical factor that cannot be ignored when analysing the fidelity of the palaeointensity estimates. Therefore, as a powerful method, the TRMC experiment can ef fecti vel y identify the entire process of thermal alteration in rock magnetic specimens, which can be used to help interpret changes in the TRM unblocking spectrum during palaeointensity experiments and to obtain more accurate palaeointensity estimates from specimens with par tial ther mal stability.

Assessing the effectiveness of the TRMC method

Our TRMC experiment conducted hundreds of rock magnetic curves, of fering comprehensi ve details about thermal alteration during heating treatment. Rapid hysteresis loop and remanent curve measurements yield diagnostic rock magnetic parameters (e.g. M s , M rs , B c and B cr ) measured at room temperature and can capture the thermal alteration of samples after heating to each target temperature (Figs 3 , 4 and 7 ). These room temperature outcomes aid in e v aluating the thermal stability of measured samples and can help us interpret TRM unblocking spectrum shifts (Fig. 8 ). Moreover, the TRMC experiment also collected hysteresis properties at ele v ated temperatures, revealing changes in the hysteresis behaviour of various magnetic carriers with different Curie temperatures (Figs 3 , 4 and 7 ). Therefore, we can study thermal alteration in each magnetic component with different Curie temperatures in measured samples and identify thermally stable components, such as those with high Curie temperatures ( > 550 • C) present in GA 84.6v (Fig. 3 ). By providing a method for tracking thermal alteration independent of palaeointensity experiments, the TRMC method can explore subtle, unrecognizable thermal alteration processes in less detailed palaeointensity measurements, which can help palaeointensity interpretations (Fig. 8 ).

Although the pTRM check for Galapagos lava specimen GA 84.6c passed, this specimen failed to provide a satisfactory palaeointensity estimate from the RESET method. In our TRMC experiments, we traced the thermophysical change details within the measured specimen GA 84.6v. These findings were then used to help e v aluate the thermal stability and interpret the TRM unblocking spectrum in the palaeointensity results for GA 84.6c. Consequently, the TRMC method proposed here can assess the thermal stability of the rock magnetic specimens during the entire heating treatment, which can help us interpret the TRM unblocking spectrum of the palaeointensity specimens during the Thellier-type method.

The CAL check from the RESET palaeointensity experiment offers a more robust approach for tracking thermal changes and detecting alteration by assessing the linearity of the corrected Arai plot (Wang & Kent 2021 ). Ho wever , during palaeointensity experiments, the CAL check was also blind to those samples with proportional thermal changes, leading to a more linear Arai diagram, such as in GA 84.6c. Our studies indicate that the corrected Arai plot for GA 84.6c yielded two linear segments and distinct palaeointensity values (Fig. 8 c). Ho wever , both values were biased, caused by thermophysical alteration detected by the TRMC experiment. Once thermal alteration occurs, the TRMC method will detect it.

Conventional rock magnetic measurements, conducted before and after heating steps, were also used to monitor thermal changes in GA 84.6 (Wang & Kent 2021 ) and HS 2 (Coe et al. 2004 ). These room-temperature rock magnetic measurements can be used to e v aluate the thermal changes in b ulk samples post-heating b ut do not address the processes of thermal alteration in magnetic constituents with different Curie temperatures in a sample. The TRMC experiment not only detects the thermal changes in a sample after each heating treatment via room temperature measurements but also identifies the thermal stability of each mineral component with varying Curie temperatures through high-temperature measurements (Figs 3 , 4 and 7 ).

Applications and limitations of the TRMC method

A potential pitfall in palaeointensity research is over-reliance on the linearity of the Arai diagram, especially for non-SD samples. This will lead to the thermal changes of samples that escaped in the most conventional check methods, resulting in biases in palaeointensity estimates. For example, while the original Arai plot of GA 84.6c contained two linear segments yielding different palaeointensity values (Fig. 8 a), both were affected by previously undetected thermal alteration revealed by our TRMC experiment. We argue that such thermal alteration can remain hidden in more linear Arai plots. The TRMC method can detect the thermal alteration in detail and helps us gain deeper insight into the thermal stability of measured samples. It also offers a chance to interpret the variations in the TRM unblocking spectrum during palaeointensity experiments and assess palaeointensity estimates derived from relati vel y linear or dual-slope Arai plots frequently encountered in past studies, such as those in the Hawaii glassy volcanic specimen hw 120a4 [fig. 4 Historical lava samples have been extensi vel y investigated in recent decades, such as those from Hawaii (Yamamoto et al. 2003 ;Cromwell et al. 2015 ;Grappone et al. 2019 ;Jeong et al. 2021), Mt Etna (Calvo et al. 2002 ;Biggin & Dekkers 2007 ;de Groot et al. 2013 ;de Groot et al. 2014 ) and the Canary Islands (Calvo-Rathert et al. 2016 ). Although much effort has been made to utilize Thellier-series methods (Herrero-Bervera & Valet 2009 ;Cromwell et al. 2015 ;Jeong et al. 2021 ) to recover the palaeointensity values, the published palaeointensity determinations of some historical lava samples still deviate from the expected field strength.

de Groot et al. ( 2014 ) utilized magnetic force microscopy (MFM) to observe variations in magnetic domain structure in lava samples from Mt Etna to investigate the reason for the failure of palaeointensity estimates, which can be underestimated by nearly 50 per cent (Calvo et al. 2002 ;Biggin & Dekkers 2007 ;de Groot et al. 2013 ). They found that the domain str ucture star ts to alter after heating to 120 • C, and the primary domain configurations become almost entirely rearranged in their pTRM state after heating to 250 • C (de Groot et al. 2014 ). A comparable situation exists for palaeointensity studies of historic lava flows from Hawaii. Cromwell et al. ( 2015 ) summarized all published palaeointensity results for the 1960 Kilauea lava flow and found that intensity estimates can deviate substantially from the expected value. Jeong et al. ( 2021 ) further showed that thermal alteration undetected by pTRM checks was one of the leading causes of bias in palaeointensity estimates in the 1960 Ha waii flo w. Based on previous studies and current understanding of thermal alteration in the Mt Lassen specimen HS 2-8C, one of the main reasons for failing to recover the expected field strength is thermal alteration in historical lava samples (de Groot et al. 2014 ;Grappone et al. 2019 ;Jeong et al. 2021 ). Our TRMC method can track the course of thermal changes in rock magnetic specimens, which allows researchers to preselect thermally stable samples for new palaeointensity studies and understand the behaviour of Arai plots from previous palaeointensity experiments.

Although the accuracy of palaeointensity values can be readily assessed for historical lava samples based on the expected palaeointensities, the accuracy of geomagnetic field strength estimates from ancient rock samples, such as from the Precambrian, can only be surmised from experimental results (Halls et al. 2004 ;Smirnov 2005 ;Smirnov & Evans 2015 ). Therefore, there is an urgent need to develop more methods to assess the thermal stability of pre viousl y measured samples. The TRMC experiment proposed here can track the thermal alteration process in detail to preselect thermally stable samples for palaeointensity studies, thereby increasing success rates and helping us e v aluate the fidelity of previous palaeointensity data.

Building on the above discussions, the TRMC method, as a standalone rock magnetic experiment distinct from Thellier-series experiments, re veals comprehensi ve details of thermal alteration in sister specimens. Although this information can help us understand the TRM unblocking spectrum of palaeointensity specimens, the TRMC method also has inherent weaknesses. As a comprehensive rock magnetic experiment, the TRMC method directly tracks the thermal changes of sister specimens to suppose the thermal stability of palaeointensity specimens. Ho wever , rock magnetic sister specimens may not completely represent the properties of the palaeointensity specimen because a lava flow may not be homogeneous (de Groot et al. 2014 ). It is necessary to verify the homogeneity of hysteresis behaviour among rock magnetic specimens prior to the TRMC and palaeointensity experiment. For example, we conducted conventional rock magnetic measurements before the TRMC experiment to verify the consistency in sister specimens of GA 84.6 ( Fig. S3 ).

Among the critical hysteresis parameters, emphasizing analysis of the M rs is crucial due to its sensitivity to stability in the remanence carrying capacity of samples during the TRMC experiment (Figs 3 b and 7 b). Ho wever , there are very different recording mechanisms between M rs (obtained by a saturation field) and TRM (obtained by a weaker magnetic field, Thellier 1977 ). The variation in M rs does not directly reflect the changes in TRM, which is one of the potential limitations of the TRMC method. Considering the above situation, in our TRMC experiment, we usuall y uncovered v ariations in specimens' capacity for remanent magnetization using M rs changes. Then, we analyse the reasons for the changes in the M rs value based on variations in the other properties ( M s , B c and B cr ), such as the magnetic domain state transition. For example, the magnetic domain state of GA 84.6v is more SD behaviour after the heating temperature reaches 500 • C, enhancing its remanence carrying capacity. Based on the above discussions, we can deduce the variation of the sample's carrying capacity for TRM, such as GA 84.6v, which has more SD behaviour in the after-heated state, leading to their increased carrying capacity for TRM. These insights may shed light on the thermal stability of the measured samples and can help us interpret the variations in the TRM unblocking spectrum of palaeointensity specimens. Additionally, the TRMC experiment could not serve as the only standard for e v aluating the fidelity of the palaeointensity estimates currently. It is necessary to combine traditional methods based on the TRM unblocking spectrum of palaeointensity specimens (Valet 2003 ), such as the pTRM check, with the TRMC method, which will help us understand the behaviour of the Arai plots more comprehensi vel y and obtain abundant accurate palaeointensities for interpreting the evolution of the Earth's core dynamo.

The much longer experimental duration of the TRMC method ma y ha ve led to unpredictable laborator y-induced ther mal changes within the sister specimens, limiting the applicability of the TRMC experiments in palaeointensity studies. Therefore, a simplified experimental TRMC procedure is needed. For specimen HS 2-8C, we utilized an optimized TRMC procedure to track thermal changes. We modified the measured temperature intervals from 25 to 50 • C and selected a target temperature range from 100 to 600 • C at 100 • C intervals. This entire set of TRMC experiments takes less than 80 hr. Moreover, based on the FORC diagrams of GA 84.6v and HS 2-8C obtained during the TRMC experiments (Figs 5 and 7 ), we determined that FORC diagrams could not comprehensi vel y detect thermal alteration during ele v ated heating steps. Considering the time-consuming FORC measurements, we only measure FORCs at critical temperature points to verify thermal alteration resulting from domain state changes, reducing the duration of the TRMC experiment to about 24 hr. Additionally, our TRMC method has great tracking of thermal changes in only two lava samples with titanomagnetite particles as the magnetic carrier mineral in this study. To further verify the ef fecti veness of the TRMC method for palaeointensity interpretations, we will select more abundant samples for TRMC experiments in future studies.

C O N C L U S I O N S

In this study, we developed a new comprehensive rock magnetic experiment, termed TRMC, to assess the thermal stability of measured samples and interpret palaeointensity results. We measured the rock magnetic properties of a Galapagos lava sample (GA 84.6) at ele v ated temperatures in multiple heating-cooling c ycles, rev ealing that thermophysical alteration occurred throughout the treatment and led to the two-slope behaviour in the Arai plots for GA 84.6c. We also tracked the thermal changes in a Mt Lassen sample HS 2 using the TRMC method to test the viability of the above method. Results show that the TRMC method can track thermal alteration details in HS 2-8C, which allows us to e v aluate the thermal stability of palaeointensity specimen (HS 2-2C) and helps us interpret the variations in the TRM unblocking spectrum during Thellier-series experiments.

The TRMC method utilizes critical hysteresis properties at elevated temperatures on sister specimens to track thermal changes in bulk samples and individual magnetic components with different Curie temperatures in a sample, which enables accurate palaeointensity estimates from samples with partial thermal stability and can be used to help palaeointensity interpretations. The TRMC method can also be widely used to preselect thermally stable samples in new palaeointensity studies to increase success rates. By conducting TRMC experiments combined with other conventional check methods, the entirety cause and the process of thermal changes within measured samples during palaeointensity experiments are expected to be revealed further, which facilitates abundant accurate palaeointensities to study the behaviour of the geomagnetic field and the evolution of the Earth's core dynamo.

A C K N O W L E D G M E N T S

We thank Pierre Rochette for providing the Galapagos lava samples via Dennis V. Kent and Robert S. Coe for the Mt Lassen sample. We also thank Dennis V. Kent and Robert S. Coe for discussing and initially reviewing this paper. We are grateful to Huafeng Qin for measuring к-T curves. We are grateful to Chen Wen, Yang Wu, Xuelong Jiang, Bincheng Hong, Haijun Li, Jianhong Luo, Xiaowei Chen and Ting Cao for their assistance with the TRMC experiment. We are also grateful to the Institute for Rock Magnetism (IRM) at the University of Minnesota for supporting Huapei Wang with a visiting fellowship, which allowed many of these rock magnetic measurements to be made. This research was supported by the National Natural Science Foundation of China (41874079 and 42030205).

AU T H O R C O N T R I B U T I O N S

Huapei Wang developed the concept for this work and designed the rock magnetic experiments. Junxiang Miao conducted rock magnetic measurements and data analysis. Junxiang Miao and Huapei Wang wrote the paper.

S U P P O RT I N G I N F O R M AT I O N

Supplementary data are available at GJ IRAS online. Wang & Kent ( 2013 ). White dots and black triangles are sampling sites from previous studies of Rochette et al. ( 1997 ) and Kent et al. ( 2010 ) that are not discussed in this paper.

Figure S2. 3-D sketch of the sample cutting strategy and divided sister specimens of GA 84.6. The specimens ("i", "s", "t", "u", "v", "w") are cut from a 10 mm diameter half-cylinder specimen for rock magnetic measurements, cut along the edge of palaeointensity specimen GA 84.6c (25-mm diameter cylinder, ∼10-15 mm height). Another 10-mm diameter cylinder, GA 84.6X, is stored for future palaeomagnetic studies. The rest of the 25-mm diameter cylinder specimen GA 84.6c has been used for previous palaeointensity studies (Wang & Kent 2013, 2021 ). The sample-cutting strategy ensures that the rock magnetic specimens closely resemble the properties of the palaeointensity specimen. Figures and captions are modified from Wang & Kent (2013).

Figure S3. Homogeneity test for sample GA 84.6. We conducted hysteresis loop and remanence curve measurements on sister specimens ("i", "v", "w", "y") of the measured sample and plotted the hysteresis ratios on the Day diagram (a, b). The various GA 84.6 specimens have similar hysteresis behaviour in their initial state. (b) shows a smaller plot area. The percentages on the dashed curve in the Day diagrams are modelled volumes of the MD contribution to SSD-MD mixing curve #3 (Dunlop 2002 ). 99.99 per cent high-purity inert gas Argon maintains at 80-130 cc min -1 stream insert to the furnace.

Figure S5. Back-scattered electron (BSE) images of specimen GA 84.6u (a, c) and the after-heated specimen GA 84.6w (b, d). Micron-sized iron oxide particles with e xtensiv e e xsolution from deuteric oxidation are abundant in the measured specimens. Magnetic mineral compositions and the particle size distribution in GA 84.6 are similar before and after heating treatment. Figure S9. Magnetic coercivity distribution of GA 84.6v during the TRMC experiment. The grey circles were coercivity distribution data, and the orange curve shows the model fit results. The blue and purple curves represent the decomposed two coercivity components of the measured specimen. The blue curves displayed the low-coercivity component (LC), and the purple curves displayed the high-coercivity component (HC). The above magnetic constitute unmixed by DCD curves using the skew-normal distribution model of the MAX UnMix web application (Maxbauer et al. 2016 ).

Figure S10. Magnetic coercivity distribution of GA 84.6v during the TRMC experiment. The above magnetic constitute unmixed by DCD curves using the cumulative log Gaussian distribution model (Robertson & France 1994 ;Heslop et al. 2002 ). The red circles were coercivity distribution data, and the black curves show the model fit results. The red (LC) and oange (HC) curves represent the decomposed two coercivity components of the measured specimen.