New absolute paleomagnetic intensity data from Cenozoic basalts of Northeast China and exploring rock-magnetic parameters for efficient sample preselection on the Tsunakawa–Shaw paleointensity method

Abstract

Despite being essential in determining absolute paleomagnetic field intensity (API) with high fidelity over Earth science research topics, API determination still suffers little quantitative success. This is due to common nonideal magnetic behaviors in experiments using natural rocks caused by physiochemical changes in the magnetic minerals contained. Although linking rock-magnetic parameters to API results may be fundamental, negligible effort has been made using the Tsunakawa–Shaw (TS) API method despite its potentially high experimental success rate in overcoming nonideal magnetic effects. Here, we explore the relationships between rock-magnetic parameters retrieved using relatively rapid and widely pre-conducted measurements and TS API results from late Cenozoic basaltic rocks. We selected rock-magnetic parameters quantified from strong-field high-temperature thermomagnetic curves, magnetic hysteresis loops, and back-field isothermal remanent magnetization demagnetizations. We provide new data pairs of rock-magnetic parameters and TS API results for 41 basaltic rock samples from 8 sites (cooling units) in Northeast China. Then, by compiling them with published data of similar quality, we compiled 133 pairs of rock-magnetic and TS API data at the sample level (38 sites). Using this data compilation, the following topics of interest were identified: Magnetic coercivity (B_c) and remanence coercivity (B_cr) among the hysteresis parameters, and the thermomagnetic parameter ITC_|m| (an index of thermal change quantifying an average of the differences in saturation magnetization at a full temperature range of during a single heating–cooling run) allow meaningful and efficient discrimination between data subsets divided by “success” or “failure” in the API results. We propose sample preselection criteria for the TS experiment: a minimal set of B_c ≥ 13 mT (or B_cr ≥ 26 mT) and ITC_|m|≤ 0.15. Moreover, extended consideration based on the preselection criteria may allow the screening of potentially biased specimen/sample-level API estimates in the site-averaged determination of such a site with a large within-site API dispersion.

Graphical Abstract

Introduction

The intensity of the ancient Earth’s magnetic field (commonly called “paleointensity”) is a crucial factor for understanding the geodynamo evolution (particularly during the early Earth’s history) (Tarduno et al. 2015; Zhang et al. 2022), deep interior evolution (Bono et al. 2019; Zhou et al. 2022), and its links with surface climate, environment, and possibly other integral parts of the Earth’s system (Courtillot et al. 2007; Knudsen and Riisager 2009; Lee and Kodama 2009; Kitaba et al. 2012, 2017; Suter et al. 2014; Cooper et al. 2021). The absolute estimate of paleointensity (i.e., absolute paleointensity, API) can be used in the numerical dating of volcanic activities, archeological artefacts, and remains (Pérez-Rodríguez et al. 2019; Nitta et al. 2020; Genevey et al. 2021). API can be obtained from the natural remanent magnetization (NRM) retained by the acquisition mechanism of thermoremanent magnetization (TRM) (Nagata 1953; Nagata et al. 1963) in materials such as burnt archeological artefacts, volcanic rocks, and other igneous rocks. The Thellier method, made in blocking temperature space, was proposed by Thellier and Thellier (1959) for determining APIs. Subsequently, several modifications of the method (hereafter referred to as Thellier-type methods) have been suggested and applied (Coe 1967; Coe et al. 1978; Prévot et al. 1985; Aitken et al. 1988; Riisager and Riisager 2001; Yu et al. 2004; Wang and Kent 2013). Thellier-type methods are widely applied. However, owing to the frequent failures in API determination considering the high fidelity of the Thellier-type methods, various alternative methods have been developed and improved, for example, the Tsunakawa–Shaw (Yamamoto et al. 2003), Microwave (Hill and Shaw 2000), Triaxe (Le Goff and Gallet 2004), and Multi-specimen (Dekkers and Böhnel 2006) methods. Such API determination remains complicated because it is a time-consuming experimental procedure, exhibits complicated (nonideal) behaviors in the resultant data, and is highly dependent on the materials used (their magnetic properties that govern TRM acquisition), leading to failure in high-fidelity determination. Moreover, an array of determination criteria using multiple statistics (see Paterson et al. 2014 for the types and definitions) has been applied and has become increasingly stringent in the analysis of individual API results to avoid erroneous API data and identify more reliable API data (Kissel and Laj 2004; Leonhardt et al. 2004; Paterson et al. 2014; Cromwell et al. 2015; Tauxe et al. 2016; Sánchez-Moreno et al. 2020).

Efforts have been made to evaluate the relationships between the API results and fundamental rock-magnetic properties that were mainly retrieved from separate pre-conducted measurements for the efficient preselection of samples for high-fidelity API determination (Calvo et al. 2002; Carvallo et al. 2006; Wang and Kent 2013; Di Chiara et al. 2017; Paterson et al. 2017; Jeong et al. 2021; Pérez-Rodríguez et al. 2022; Fukuma 2023). These pre-conducted measurements, hysteresis measurements of saturation (M_s) and remanent (M_rs) magnetizations, and coercivity (B_c), combined with back-field demagnetization of saturation remanence measurement (allowing determination of remanence coercivity B_cr) (Calvo et al. 2002; Carvallo et al. 2006; Wang and Kent 2013; Chiara et al. 2017; Paterson et al. 2017; Jeong et al. 2021; Fukuma 2023), thermal change in magnetic susceptibility (k) or hysteresis data from before to after heating (Haag et al. 1995; Tanaka and Kono 2002; Smirnov and Tarduno 2003; Mochizuki et al. 2004; Wang and Kent 2013; Kim et al. 2018; Jeong et al. 2021), and thermomagnetic analysis that monitors thermal variation in k or induced saturation magnetization (M_s) (Haag et al. 1995; Tanaka et al. 2007; Pérez-Rodríguez et al. 2022) are the most extensively used and investigated because of the measurement speed and minimal specimen amounts needed. A comparison of the ratio combinations retrieved from the hysteresis data, that is, M_rs/M_s (squareness) and B_cr/B_c (Day et al. 1977), is known to be sensitive to the magnetic domain state, although it is influenced by other factors such as magnetic interactions, mineralogy, and thermal fluctuations (Paterson et al. 2017; Roberts et al. 2018a). Paterson et al. (2017) suggested a measure of relative bulk domain stability (BDS), the BDS value, calculated using M_rs/M_s and B_cr/B_c data. Thermal changes in k or hysteresis parameters and differences between the heating and cooling curves from the thermomagnetic analysis can indicate the thermal stability of magnetic carriers in a specimen. These investigations have primarily been performed together with applying Thellier-type API determination. Unfortunately, no quantitative relationship between the proxies of rock-magnetic properties and API results has been well established as a determinative preselection tool for API data fidelity.

Over the past two decades, applications of the Tsunakawa–Shaw (TS) API method have gradually increased. The TS method is the most advanced version of the Shaw method (Shaw 1974). It determines an API in the coercivity space by performing progressive altering field (AF) demagnetization (AFD) for each of the natural remanent magnetization and laboratory-induced remanent magnetizations of a specimen, with the implementation of anhysteretic remanent magnetization (ARM) correction (Rolph and Shaw 1985), double heating test (Tsunakawa and Shaw 1994), and low-temperature demagnetization before each progressive AFD (Yamamoto et al. 2003). It has achieved successful determinations in historical lava rocks, burnt archeological materials, and geologically ancient volcanic and granitic rocks, even with nonideal magnetic behaviors (non-single-domain-dominated) (Yamamoto et al. 2003; Mochizuki et al. 2004, 2006, 2011, 2013, 2021; Oishi et al. 2005; Yamamoto and Tsunakawa 2005; Yamamoto and Hoshi 2008; Tsunakawa et al. 2009; Ahn et al. 2016; Kato et al. 2018; Kitahara et al. 2018, 2021; Yamamoto and Yamaoka 2018; Ahn and Yamamoto 2019; Okayama et al. 2019; Singer et al. 2019; Yoshimura et al. 2020; Lloyd et al. 2021), and in materials with artificially laboratory-aged TRM (Yamamoto et al. 2022). Empirically, in these TS API determinations for NRMs of historical volcanic rocks and laboratory-aged TRMs, no significant determination bias due to cooling rate effects has been identified. For the applicability and usability of the TS method, exploring and evaluating potential links between the API results and rock-magnetic properties retrieved from separate rapid measurements is required for time-saving in laborious experiments and enhancing API data fidelity.

These TS API studies have provided data on rock-magnetic properties such as strong-field high-temperature thermomagnetic (M_s-T) curves and hysteresis data (Yamamoto et al. 2003, 2015; Mochizuki et al. 2004, 2006, 2011, 2013; Yamamoto and Tsunakawa 2005; Ahn et al. 2016; Kitahara et al. 2018, 2021; Yamamoto and Yamaoka 2018; Ahn and Yamamoto 2019; Yoshimura et al. 2020). Notably, thermomagnetic curve data were previously used to roughly assess the thermal stability of magnetization by visual inspection, identify magnetic minerals as remanence carriers, and detect the occurrence of hump-shaped behaviors in the heating curve. The “hump” can indicate the presence of titanomaghemite, which is a low-temperature by-product after the initial emplacement of volcanic rock bodies (Grommé et al. 1969; Marshall and Cox 1971; Özdemir and Dunlop 1985) and is suspected to cause unwanted effects by acquisition of chemical remanence that replaces or overprints the primary TRM, i.e., failure in or erroneous API determination (Yamamoto and Tsunakawa 2005; Gee et al. 2010; Paterson et al. 2010). However, quantifying rock-magnetic properties, particularly the thermal stability from thermomagnetic curves, and ascertaining its association with TS API results require further investigation.

This study explored the quantifiable relationships between (rapidly obtainable) rock-magnetic parameters and TS API results, and criteria with rock-magnetic parameters for efficient sample preselection using in the TS method. First, we conducted rock-magnetic experiments and API determinations by the TS method on late Cenozoic basalt samples from Northeast (NE) China volcanic fields. We present new paired data from the TS API, M_s-T curves, and magnetic hysteresis experiments. Second, we compiled a large-volume dataset from new and previously published data of the same quality for late Cenozoic basalts bearing titanomagnetite. Here, we use BDS, M_rs/M_s, B_cr/B_c, B_cr, and B_c data, and parameter data quantified from thermomagnetic curves, that is, ITC₅₀ and ITC_|m| (“Ms-T curves and ITC parameters” section), which are measures of thermally induced magnetic change during a heating–cooling cycle (thermal stability). These parameters are called ‘ease-of-use’ rock-magnetic parameters. Using the compiled dataset, we found meaningful relationships between the rock-magnetic parameters and individual acceptance (success or failure) of the associated TS API estimates. These relationships represent a guideline for effective, time-saving sample preselection before the API experiment and high fidelity of the API estimate after the API experiment using the TS method.

Materials

Cenozoic basalts of NE China volcanic fields

There are several Cenozoic volcanic fields (Changbaishan volcanic field [CVF], Longgang volcanic field [LVF], Jingpohu volcanic field [JVF], and Yitong volcanic field; Fig. 1) in NE China where basaltic products (calc-alkaline and alkali basalts) are widely distributed between the Late Cretaceous and Late Quaternary, mainly concentrated in the Miocene and Quaternary (Wang et al. 1988; Liu 1987; Liu et al. 2001; Wei et al. 2013). We sampled 56 oriented block samples of basaltic rocks from 8 sites (≈cooling units) in the CVF, LVF, and JVF (Fig. 1); the sampling was conducted through a 2014–2016 Korean-Chinese cooperative research project studying the Baekdusan (Changbaishan) volcano and its surrounding volcanic fields. Sites 14175, 14192, 14181, 14182, and 14183 belong to the CVF, site 14201 belongs to the LVF, and sites 14222 and 14226 belong to the JVF. Brief information on the sampling sites and associated age constraints is summarized in Table 1.

Fig. 1

Schematic map showing the distribution of Cenozoic volcanics in Northeast (NE) China and locations of sampling sites of Cenozoic basalt rocks. The sampling campaign was conducted through a 2014–2016 Korean-Chinese cooperative project of Baekdusan (Changbaishan) volcano. Distributions of the volcanic rocks, faults, and graben boundaries are from Liu et al. (2001). CVF Changbaishan volcanic field, LVF Longgang volcanic field, JVF Jingbohu volcanic field, YVF Yitong volcanic field, Tan-Lu F. Tan-Lu fault, Fu-Mi F. Fushun-Mishan fault, Yi-Yi F. Yitong-Yilan fault

Table 1 Brief information on the sampled sites and associated age constraints of the Northeast (NE) China volcanic field analyzed in this study

Several oriented cylindrical specimens and several nonoriented tiny fragment specimens were prepared from each of the collected block samples and used to determine paleomagnetic directions, API estimates, M_sT curves, and measurements of the magnetic hysteresis parameters. The context regarding paleomagnetic directions is briefly addressed in this study (“API determination results” section) because of minimal interest.

Cenozoic basalts with previously published data

This study used previously published data (TS API and rock-magnetic data) for the late Cenozoic basalts of the Ethiopian Afar and Baengnyeong Island (South Korea) from Ahn et al. (2016) and Ahn and Yamamoto (2019), respectively. The geological background and samples from these two areas are briefly introduced.

Many piles of basaltic lavas with Plio-Pleistocene ages are found in the Afar Depression, which lies at the East African triple junction of the Red Sea, Gulf of Aden, and Ethiopian rifts. Geologically recent tectonic activities have exposed thick sequences of basaltic lava piles along high cliffs formed by normal faulting. Ahn et al. (2016) introduced good exposures of a thick basaltic lava sequence ~ 350 m tall along high cliffs in the Dobi area, Ethiopian Afar (11.84°N, 41.67°E) and collected 112 oriented block samples from 29 successive lava flows (each likely corresponding to a cooling unit) for paleomagnetic investigation. The ages of the collected basaltic samples were estimated to be in the early Matuyama reversed chron, covering the early Olduvai normal subchron, ~ 2.4–1.9 Ma.

Baengnyeong Island (37.92°N, 124.67°E; 45 km²), the subject region of Ahn and Yamamoto (2019), is located off the furthest northwest point of South Korea. Most of the island surface is occupied by Proterozoic metasedimentary rocks (slate, phyllite, and quartzite), and in the northeastern part of the island, covering ~ 4 km², intrusive and extrusive basaltic rocks called the Jinchon Basalt are exposed, which is the subject of the paleomagnetic study. The Jinchon Basalt rocks are products of late Cenozoic alkali magmatism, likely caused by dramatic changes in stress regimes under the interplay between the India and Eurasia collision and the subduction of the Pacific Plate beneath the eastern margin of Eurasia (Choi et al. 2006). Ahn and Yamamoto (2019) collected seven oriented block samples from each of two exposure sites (B1 and B2) along the northeast coast for paleomagnetic investigation. The ages of the samples were in the Early Pliocene, at approximately 4‒5 Ma.

Methods

NE China basalts

Magnetic hysteresis parameters, BDS, and first-order reversal curves (FORCs)

The hysteresis parameter data were acquired from the hysteresis loop and back-field measurements with a tiny fragment of tens of milligrams at room temperature in ambient air using a Princeton Measurements Corporation (PMC) MicroMag 3900 Vibrating Sample Magnetometer (VSM) at the Korea Institute of Geoscience and Mineral Resources (KIGAM). Each hysteresis loop was measured by applying magnetic fields up to 1.0 T, and the measured data were corrected for paramagnetic and diamagnetic contributions using a high‐field slope correction. This enabled the determination of M_s, M_rs, and B_c. B_cr was determined from the back-field demagnetization of the saturation remanent magnetization. Then, the hysteresis ratio combinations M_rs/M_s and B_cr/B_c were calculated. The hysteresis ratio combinations were used to calculate the BDS value as follows (Paterson et al. 2017):

$${\text{BDS}}\, = \, - \,0.{39}00\,\left\{ {{\text{log}}_{{{1}0}} \left( {\text{X}} \right)\, - \,0.{6}0{62}} \right\}\, + \,0.{6353}\, \, \left\{ {{\text{log}}_{{{1}0}} \left( {\text{Y}} \right)\, + \,{1}.{2}0{18}} \right\}$$

where X represents B_cr/B_c data and Y represents M_rs/M_s data. All the acquired data are provided in Additional file 1: Table S1. The B_cr, B_c, B_cr/B_c, M_rs/M_s, and BDS values were used to explore possible relationships with the TS API results. These hysteresis parameters are associated with an effective bulk magnetic domain state that may control the thermal change of remanence capacity, thus, “BDS” (Paterson et al. 2017).

For a limited number of samples, FORC diagrams were constructed at room temperature, processing data with FORCinel (Harrison and Feinberg 2008) to more definitively diagnose the magnetic domain states (Roberts et al. 2014, 2018b). The measurement and processing parameters are provided in Additional file 2: Figure S1.

M_s-T curves and ITC parameters

Thermomagnetic curve data were acquired from M_s-T analysis with a tiny fragment of tens of milligrams in a vacuum environment (1–10 Pa) using a Natsuhara Giken NMB-89 magnetic balance at the Marine Core Research Institute (MaCRI), Kochi University. During analysis, the specimen was heated from ~ 20 to 580 °C (or 610 °C or 700 °C) and then cooled to 50 °C, with an average heating/cooling rate of ~ 15 °C/min in a constant applied field of 0.3 T (or 0.5 T). The running time for a single cycle was ~ 1.5 h. The measured thermomagnetic curve data, displaying temperature variation in saturation magnetization (M_s vs. T) during the heating–cooling cycle, were reprocessed by a spline smoothing fitting to each of the heating and cooling run data to place data points at every 1 °C interval between 50 °C and 580 °C (or 610 °C or 700 °C).

Two different indices of thermal change, herein called ITC₅₀ and ITC_|m|, were prepared to quantify the change in M_s after the heating–cooling run using the reprocessed data. The ITC₅₀ value was calculated as follows:

$${\text{ITC}}_{{{5}0}} \, = \,\left( {{\text{m}}_{{{5}0}} \, - \,{\text{M}}_{{{5}0}} } \right)/{\text{M}}_{{{5}0}}$$

where m₅₀ and M₅₀ are the induced current values in proportional response to the M_s values on the cooling and heating curves at 50 °C, respectively. The ITC_|m| value is given by:

$${\text{ITC}}_{|{\text{m}}|}= {\sum }_{{\text{i}}=1}^{{\text{N}}}|({\text{m}}_{{\text{i}}}-{\text{M}}_{{\text{i}}})| / (\mathrm{N M_{{{5}0}}})$$

where m_i and M_i are the values corresponding to the induced saturation magnetizations on the cooling and heating curves at the same i-th temperature, which ranges from 50 to 580 °C (or 610 °C or 700 °C) at 1 °C intervals; N is the number of the total data pairs of the feedback current values, proportional to the strong-field magnetization; and M₅₀ is the current (induced saturation magnetization) value on the heating curve at 50 °C. These indices were designed similar to the alteration indices introduced by Hrouda et al. (2002) and Hrouda (2003). The calculated ITC data are presented in Additional file 1: Table S1 and were used to explore the relationships with the TS API results.

API determination

All API experiments were performed at the MaCRI, Kochi University.

For cylindrical specimens cored from basaltic rock samples, all of which had associated hysteresis and thermomagnetic curve data, each API experiment using the TS method was conducted following a procedure similar to that of most TS-based paleointensity studies (Ahn and Yamamoto 2019). Remanence measurements, AFD treatments, and ARM acquisition were performed using a DSPIN automated system (Natsuhara Giken). AFD treatments were performed with 38 (or 34) steps in the peak AFs from 2 to 180 (or 140) mT. Three ARMs for each specimen were imparted by a direct current (DC) bias field of 50 μT with peak AFs of 180 mT, in which the bias field directions were (sub-)parallel to the characteristic directions of NRM or the laboratory-induced TRM directions. To impart the laboratory TRMs, the specimens were heated to 580 °C in a vacuum (mostly < 50 Pa), maintained for 15 min (for the first TRM acquisition, TRM1) and 60 min (for the second TRM acquisition, TRM2), and then cooled to room temperature for ~ 3 h, using a TDS-1 thermal demagnetizer with a built-in DC field coil (Natsuhara Giken). The DC field was mainly set to 50 μT (occasionally 10, 25, or 30 μT). A low-temperature demagnetization was conducted before starting the progressive AFD treatment of the remanent magnetization.

The TS API experimental result per specimen was evaluated using a minimal set of the following determination criteria [similar to those described in Ahn and Yamamoto (2019)], and an API value was estimated by determining the slope of the linear segment defined for the NRM-TRM1* diagram when the ARM correction was validated by the unity slope of the linear segment of the TRM1–TRM2* diagram:

• 1. A primary NRM component should be isolated by progressive AFD on the Zijderveld diagram (anchored MAD_anc < 10°, where MAD represents the maximum angular deviation; that is, a measure of precision when the best-fit line for the selected component is determined).

• 2. On the NRM-ARM1* diagram, a single linear segment for slope calculation should be recognized within the coercivity range defining the primary NRM component. The segment should have at least 30% in NRM fraction [we used the statistic FRAC suggested by Shaar and Tauxe (2013)]: FRAC_N ≥ 0.30; the earlier TS API determinations of Ahn et al. (2016) used the NRM fraction statistic equivalent to that designed by Coe et al. (1978). The associated correlation coefficient should not be < 0.995 (r_N ≥ 0.995).

• 3. On the TRM1-TRM2* diagram, a single linear segment should be recognized with FRAC_T ≥ 0.30 and r_T ≥ 0.995. The linear segment slope is unity within experimental errors with 1.05 ≥ slope_T ≥ 0.95 to validate the ARM correction.

No criterion based on other independent measurements, such as hysteresis measurements and thermomagnetic analyses, was included at this level of acceptance evaluation, later referred to as ‘success’ or ‘failure’. The determined specimen-level API values were used in consideration of sample- and site-level API determinations, which discuss their relationships with rock-magnetic parameters.

Additionally, only a minimal set of cylindrical specimens (retrieved from eight block samples from three sites: 14181-B, 14181-E, 14181-F, 14181-G, 14222-B, 14222-D, 14226-C, and 14226-E) were subjected to Thellier-type API experiment by applying the experimental protocol of Coe et al. (1967) (also called ‘Coe-Thellier’’ API experiment/method/protocol), for comparison with correlating TS API estimates. However, because these Coe-Thellier API experiments and results were not of major interest, descriptions of the method and results have been restricted to Additional file 3: Additional information note.

Preparing previously published data and an extended data compilation

In addition to the new NE China basalt data, we collected previously published specimen level, magnetic hysteresis, M_s-T curve, and TS API data for late Cenozoic basalts from Ahn et al. (2016) (Ethiopian Afar) and Ahn and Yamamoto (2019) (Baengnyeong Island) to use a larger amount of data in analyses. All measurements, including the magnetic hysteresis parameters (and BDS), M_s-T curves, and TS API determinations for the previously published data, were conducted at MaCRI, Kochi University. The individual experimental procedures were similar to those for the NE China basalts, as summarized below.

The magnetic hysteresis parameters (and BDS) for the previously published data were measured using a PMC MicroMag 3900 VSM with set operational values similar to those for NE China basalts. Only the maximum applied field varied: 1.8 T and 0.5 T for the Ethiopian Afar and Baengnyeong Island basalts, respectively. The determination of M_s, M_rs, B_c, and B_cr and the calculation of BDS were the same as those for the NE China basalts. The hysteresis data were generally measured once for each block sample, except for a few in which up to four specimens were measured per sample.

All M_s-T curve measurements for the previous data were performed using a Natsuhara Giken NMB-89 magnetic balance identical to that used for the NE China basalts. The M_s-T curves for the Ethiopian Afar were obtained by heating to 700 °C with an average heat rate of ~ 10 °C/min in a constant DC field of 0.5 T under a vacuum (1‒10 Pa). The M_s-T curves for the Baengnyeong Island basalts were obtained under almost the same experimental conditions but under ambient air. The data processing and calculations for ITC₅₀ and ITC_|m| from each of the M_s-T curves were the same as those for the NE China basalts. An M_s-T curve per block sample was obtained. However, the curve data from the block samples revealing the ‘hump-shaped’ behavior during heating (“Type U” of M_s-T curve behavior category in Ahn et al. 2016; 15 samples) were excluded because of the presence of titanomaghemite.

Most TS API determination experiments for the previous data were performed with the same instruments and almost identical conditions to those for the NE China basalts; one differing condition was the maximum heat temperature in the TRM acquisitions, which was set to 610 °C. On the other hand, only four of the Ethiopian Afar TS experiments were performed using a Natsuhara Giken SMD-88 spinner magnetometer and Natsuhara Giken DEM-8601C AF demagnetizer equipped with a coil for ARM acquisition for remanence measurements and demagnetizations. In these cases, each progressive demagnetization comprised 17 AF steps up to 140 mT. A total of 127 specimen-level TS experimental data (belonging to 30 sites) were individually evaluated using the same criteria for specimen-level API determination acceptance as those for the NE China basalts. Our analyses adopted previous acceptance interpretations and API estimates (where accepted) at the specimen level.

Due to the occasional presence of multiple specimen-level data for a single sample, we prepared a ‘sample-level’ data compilation comprising the hysteresis, M_s-T, and TS API data from the new and previous ‘specimen-level’ data. Multiple specimen-level data points for a single sample were averaged to obtain the sample-level data for the given sample. Only three sample-level data pairs could be prepared for samples from sites B1 and B2 in Ahn and Yamamoto (2019) because of the loss of M_s-T measurement data.

Results

New data from NE China basalts

Rock-magnetic results

Forty-one tiny specimens (one specimen per sample) underwent hysteresis loop and back-field-curve measurements. Figure 2a shows hysteresis loops, back-field curves, and the determined B_c, B_cr, B_cr/B_c, and M_rs/M_s values. These specimen-level values were considered equivalent to the sample-level values. B_c, B_cr, B_cr/B_c, M_rs/M_s, and associated BDS values ranged from 5.5–51 mT, 12–79 mT, 1.3–2.6, 0.10–0.51, and 0.21–0.77, respectively; the data and their fundamental statistics are presented in Additional file 1: Table S1 and Table 2, respectively. A biplot of the hysteresis combination ratios, B_cr/B_c and M_rs/M_s (‘Day plot;’ Day et al. 1977), for 41 data and the BDS trend line (Paterson et al. 2017) are shown in Fig. 2b. In the Day plot, the data are plotted in the single-domain (SD) region, pseudo-SD (PSD) region, or the left-side region outside the PSD region; the majority are also aligned along or near the SD + multi-domain (MD) mixing lines, as suggested by Dunlop (2002a, b). The data distribution within a site is well-clustered or dispersed, differing between sites. In addition to the Day plot results, FORC diagrams were generated for samples 14175-F, 14181-G, 14182-B, 14183-C, and 14222-F (Additional file 2: Figure S1). The FORC diagrams of samples 14222-F and 14181-G indicated an SD-like behavior consistent with the interpretation of the bulk domain state using the Day plot. The PSD behavior in the Day plot for sample 14182-B can be attributed to a mixture of SD and vortex (PSD)/MD particles. Sample 14183-C, indicating PSD or SD + MD mixing by the Day plot results, represents the predominance of fine vortex particles in the FORC diagram. The FORC diagram of sample 14175-F indicates coarse vortex/MD particles, whereas the associated Day plot result suggests a PSD or SD + MD mixing behavior.

Fig. 2

Summary of results of the magnetic hysteresis properties from Vibrating Sample Magnetometer measurements of the NE China basalts. a Hysteresis loops (raw and corrected) and back-field curve for a representative sample (14222-F). The determined B_c, B_cr, B_cr/B_c, and M_rs/M_s values are given. b Biplot of M_rs/M_s vs. B_cr/B_c (the so-called Day plot) in logarithmic space for the NE China basalt samples. Each circle symbol corresponds to the result from each block sample. The circles with the same color represent the results of samples from the same site. The diamond or cross symbol inscribed in each circle symbol indicates the “success” or “failure” Tsunakawa–Shaw (TS) absolute paleomagnetic field intensity (API) determination (Table 3), respectively. The theoretical curves for the mixtures of single-domain (SD) and multi-domain (MD) particles (three gray long-dashed lines) and SD and SP (10 nm in size) particles (two gray solid lines). The boundaries for the SD and pseudo-SD (PSD) regions suggested by Dunlop (2002a, b), and the bulk domain stability (BDS) trend line (pink solid line) with labels of some BDS values (diamond symbols) suggested by Paterson et al. (2017) are also shown. For the five data points with the sample labeling, the corresponding First-order reversal curve diagrams are provided in Additional file 2: Figure S1

Table 2 Summary of statistics of individual rock-magnetic parameters obtained in the NE China basalt samples

Forty-four tiny specimens (generally one specimen per sample, except for three samples) underwent M_s-T analysis (under a vacuum). Figure 3 shows the heating–cooling curves for the 15 sample examples. The heating curves showed a predominant magnetic mineral phase(s) with variable Curie temperatures (T_cs; ~ 100 °C to 580 °C) from sample to sample, presumably associated with titanomagnetite with variable degrees of Ti substitution. Based on the T_c of the predominant mineral phase, the analyzed samples can be classified into Category I, with ≥ 400 °C in T_c of the predominant phase (107 in total), and Category II, which involves the others (26 in total) (Additional file 4: Table S2). ITC₅₀ and ITC_|m| were calculated for each M_s-T curve (Fig. 3). Each specimen-level value was regarded as its sample-level representative value; however, for three samples, two were averaged as a sample-level value. These resultant sample-level ITC₅₀ and ITC_|m| values ranged from near zero–3.2 and near zero–1.2, respectively. The absolute ITC₅₀s (hereafter, |ITC₅₀|) and ITC_|m| values were used to explore the relationships with the paleointensity results (“Results from the extended data compilation” section). The sample-level indices and individual fundamental statistics are listed in Additional file 1: Table S1 and Table 2, respectively.

Fig. 3

Examples of strong-field high-temperature curves (M_s-T curves) between the room temperature and 700 °C. Red and blue lines for each result indicate heating and cooling curves, respectively. The indices of thermal change, ITC₅₀ and ITC_|m|, are also given

API determination results

Before describing the API experimental results, we briefly introduce the results of the NRM demagnetization behavior obtained from the NRM AFD step in the Tsunakawa−Shaw (TS) experiments. The results of one representative specimen from each site are shown in Additional file 5: Figure S2. Each demagnetization result generally displayed one or two directional remanence components. The low AF level (secondary) remanence component was removed by the pre-treatment with low-temperature demagnetization and/or by up to 4–26 mT AF. Generally, it represented a small portion of the total NRM. However, the specimens from sites 14175, 14182, and 14201 showed a relatively large proportion of the low AF level component. Furthermore, a few specimens encountered difficulty in characteristic remanent magnetization (ChRM) isolation owing to a strong overlap of the two remanence components (not shown), particularly at site 14201. The high-AF level remanence component for most specimens was well defined (i.e., small MAD values) and directed toward the origin (Additional file 5: Figure S2) and was thereby considered as ChRM. The ChRM directions isolated from multiple specimens per site were similar and yielded a site-mean direction with high precision (not shown). Thus, specimen-level ChRMs are recognized individually as primary (paleomagnetic) remanence components. However, for site 14201 the ChRM directions could be grouped into two: ~ 190° in declination and ~ −50° in inclination, and ~ 350° in declination and ~ −55° in inclination (not shown).

Forty-two specimens underwent the TS API determination protocol. One specimen was taken from each sample, except for sample 14181-E (two specimens), and four to seven samples were collected from each site. The results for the three specimens with passed or failed API determination are shown in Fig. 4. Individual interpretations of the experimental results are summarized in Table 3. Successful specimens generally exhibited common characteristics with well-defined straight lines on the NRM-TRM1* diagrams and a uni-vector component directed to the origin on the Zijderveld orthogonal plots (Fig. 4a). Conversely, the failed specimens showed convex upward or downward and high-level interval-scattered NRM-TRM1* diagrams with or without a nonunity slope and/or convex upward TRM1-TRM2* diagrams (Fig. 4b and c). Twenty-seven specimens (~ 66% of the total) allowed for successful API determination, ranging from 6.3 to 66.2 μT. Three or more specimen-level API determinations were obtained from five sites (14181, 14182, 14192, 14222, and 14226), enabling them to be taken adequately for their site averages. Calculated site averages ranged from 7.4 to 61.3 μT (corresponding to 1.2 × 10²²–10.1 × 10²² Am² in virtual axial dipole moment), with the standard deviations ranging from 5.7 to 40.4% of the respective average (Additional file 6: Table S3).

Fig. 4

Examples of specimen-level TS API results. a Specimen 14222-F-14 (successful in API determination), b Specimen 14175-F-1BL (failed in API determination), and c Specimen 14183-C-1A4 (failed in API determination). As the result of a single API experiment result, NRM vs. TRM1* diagram (left panel) and TRM1 vs. TRM2* diagram (right panel) are shown, where black symbols show selected data intervals for determining the linear segments (associated to API determination). Inset of a Zijderveld diagram on each NRM vs. TRM1* diagram shows the altering field demagnetization result of NRM, where filled (open) symbols indicate projection onto the horizontal (vertical) plane. Statistical values used in the API determination are also given

Table 3 Summary of specimen-level Tsunakawa–Shaw (TS) absolute paleomagnetic field intensity (API) results for the NE China basalt samples

Association between rock-magnetic parameters and API results

We briefly document several characteristics of the relationships between rock-magnetic parameters and TS API results from the NE China basalts. The NE China results likely indicate that the samples bearing SD-like particles, even those mixed with vortex/PSD particles, perform successfully in TS determination; however, those with only a vortex (PSD) or mixtures of vortex and MD particles fail. Moreover, the samples with ‘intermediate’ values in M_rs/M_s (~ 0.1 to 0.3) or BDS (~ 0.2 to 0.6) show considerable contrast in the performance of TS determinations. The site 14222 samples that involved Ti–rich titanomagnetites with SD-like behavior and good thermal stability had high success rates in specimen-level TS experiments and good within-site consistency of the TS APIs. The site 14226 samples bearing Ti–rich titanomagnetites with varying domain states and thermal alterations could allow a high success rate of specimen-level determinations and good within-site consistency. All samples from site 14175 that were thermally unstable failed to successfully determine TS API. The site 14181 samples with SD-like to coarser particles and few thermal alterations performed very well in the API determinations at the specimen level, but resulted in unwantedly scattered API values between the specimens.

Results from the extended data compilation

Our extended data compilation (made from the new NE China and two previously reported late Cenozoic basalt data) comprised 133 sample-level data pairs (acquired from the specimen-level datasets of 153 hysteresis parameter, 136 M_s-T parameter, and 168 TS API data), including B_c, B_cr, B_cr/B_c, M_rs/M_s, BDS, |ITC₅₀|, and ITC_|m| parameter data, and TS API data with success or failure acceptance. This data compilation is suitably large; therefore, the relationships between rock-magnetic and TS API data are expected to be observable. Of the 133 data pairs, 90 (68%) represented successful TS API results. The individual sample-level parameter values and their fundamental statistics are listed in Additional file 4: Table S2 and Table 4, respectively. Using this data compilation, we compare the hysteresis and M_s-T parameters (“Comparisons between hysteresis and thermomagnetic curve parameters” section) and the distributions of two data subsets for individual rock-magnetic parameters subdivided by the ‘success’ and ‘failure’ acceptance in TS API determination (“Comparisons of distributions in rock-magnetic parameter between ‘successful’ and ‘failed’ TS API data” section).

Table 4 Summary of statistics of the respective sample-level rock-magnetic parameters and TS API estimates in the expended data compilation

Comparisons between hysteresis and thermomagnetic curve parameters

To date, M_rs/M_s and BDS have been the most meaningfully addressed in the literature reporting Thellier-type API determinations with similar purposes to this study. When considering our data compilation, the success or failure in TS determination does not appear to correlate strongly with either M_rs/M_s or BDS (Fig. 5). This consideration will also be addressed quantitatively in “Comparisons of distributions in rock-magnetic parameter between ‘successful’ and ‘failed’ TS API data” section. This preliminary observation highlights the fundamental need to explore possible links between other rock-magnetic parameters and TS API results.

Fig. 5

Day plot (in logarithmic space) for all data (N = 133) of the Data Compilation prepared in this study. Each circle symbol corresponds to the result from each block sample. The diamond and cross symbols indicate data with “success” and “failure” TS API determination (Table 3), respectively. The gray long-dashed lines, gray solid lines, boundary lines of x = 2, x = 5, and y = 0.5, and pink solid line with pink diamond symbols are the same as those in Fig. 2b

Furthermore, we must check whether the M_s-T parameters are worth considering as an alternative because these hysteresis parameters are influenced by the magnetic domain state and other factors (magnetic interactions, mineralogy, thermal fluctuations) (Paterson et al. 2017; Roberts et al. 2018a). Figure 6 shows the biplots of ITCs (|ITC₅₀|, ITC_|m|) vs. hysteresis parameters (B_c, B_cr, B_cr/B_c, M_rs/M_s, and BDS), with the correlation coefficient R and p value for each biplot. The |ITC₅₀| and ITC_|m| values had little or weak correlations with any hysteresis parameters at the 95% confidence level. This indicates that |ITC₅₀| and ITC_|m| are predominantly influenced by other major factors (potentially thermally induced magnetic changes) that differ from those acting on the hysteresis parameters.

Fig. 6

Biplots of M_s-T curve parameter (ITC50, ITC|m|) vs. hysteresis parameter (B_cr, B_c, B_cr/B_c, M_rs/M_s, BDS) with variable combinations. Correlation coefficient value and p value for the two variables of each biplot are shown. All biplots show little or very weak correlations

Comparisons of distributions in rock-magnetic parameter between ‘successful’ and ‘failed’ TS API data

Figures 7 and 8 compare box plots, frequency histograms, histograms of relative frequencies in %, and cumulative distributions in relative % between the “success” and “failure” data subsets for individual hysteresis parameters and individual thermomagnetic curve parameters, respectively. Additionally, Welch’s t-test was used for quantifiable comparisons between subsets. The t-statistics and p values for each parameter are listed in Table 5.

Fig. 7

Comparisons of distributions in the respective hysteresis parameters, B_cr (a), B_c (b), B_cr/B_c (c), M_rs/M_s (d), and BDS (e), between the TS API “success” and “failure” data subsets. The box plot, frequency histogram, relative frequency histogram, and cumulative distribution are shown for each parameter. In the box plot, the boxes denote the interquartile ranges (IQRs), the whiskers denote the 95% (≈1.5 × IQR) ranges, the solid lines in the boxes are the median values, and the blue diamond symbols represent values that lie outside the 95% ranges. In the frequency histogram, distribution of the “failure” data subset is omitted for presentation clarity. For reference, distribution of all data of the Data Compilation is plotted in the frequency diagram

Fig. 8

Comparisons of distributions in the respective M_s-T parameters, ITC₅₀ (a) and ITC_|m| (b), between the TS API “success” and “failure” data subsets. See Fig. 7 for detailed descriptions of these diagrams

Table 5 Summary of the Welch’s t-test results of the TS API ‘success’ and ‘failure’ data subsets for the respective rock-magnetic parameters

For the cases with hysteresis parameters, B_cr, B_c, M_rs/M_s, and BDS (Fig. 7a, b, d, and e) allow us to recognize differences in mean and distribution between the two “success” and “failure” data subsets through Welch’s t-test at a 95% confidence level. However, B_cr/B_c failed to differentiate between subsets (Fig. 7c; Table 5). The differentiation is more visible in B_cr and B_c than in M_rs/M_s or BDS, displaying characteristics such as higher B_cr, B_c, M_rs/M_s, and BDS values and more successful results in TS API determination.

For the ITC cases, both |ITC₅₀| and ITC_|m| appeared to have lower values in |ITC₅₀| and ITC_|m| with more successful TS API results (Fig. 8). However, Welch’s t-test results strongly suggest that only ITC_|m| can discriminate between the ‘success’ and ‘failure’ data subsets at the 95% confidence level.

Comparison between inter-sample dispersion of API determinations and rock-magnetic parameters for sites

In paleointensity studies, multiple specimens or samples in a site/cooling unit undergo API determination; in turn, these multiple API determinations require within-site consistency to ensure their reliability and fidelity. However, paleomagnetists have often experienced considerable within-site dispersion of API determinations between specimens/samples, which is problematic. In our data compilation, the majority of sites with three or more specimen/sample-level TS API estimates (16 of 21 sites) had reasonably small dispersions of API estimates (< 20% in % of the standard deviation of the respective site average) (Additional file 7: Table S4). Conversely, sites 14181, DB15, DB12, DB(-1)B, and DB(-6) showed large within-site standard deviations (> 20%).

We explored the relationships between the within-site standard deviation (in % of the site average) and site average and its standard deviation (in % of the site average) for the different rock-magnetic parameters of B_c, B_cr, M_rs/M_s, BDS, and ITC_|m|. Figure 9 shows the relationships with the correlation coefficients and p values. Most respective site averages and standard deviations of the parameters had no significant correlation with the within-site TS API standard deviations. Alternatively, the B_c standard deviations in % had a weak but statistically significant correlation with the within-site API standard deviations in % (positive correlation with R = 0.508 and p = 0.026). B_c individuals within the five sites with large within-site API standard deviations (> 20%) ranged from 12 to 51 mT (Additional file 4: Table S2), exhibiting no distribution bias.

Fig. 9

Comparisons between TS API within-site standard deviation (%) and site-average (a) and within-site standard deviation (%) (b) of respective rock-magnetic parameters (B_cr, B_c, M_rs/M_s, BDS, and ITC_|m|). For each biplot of comparison, the correlation coefficient R and p value with a fit linear regression line (black line) are given. Light-blue, green, and orange circles indicate data points from Ethiopian Afar basalts (Ahn et al. 2016), Baengnyeong Island basalts (Ahn and Yamamoto 2019), and NE China volcanic field basalts (this study), respectively

Furthermore, as a referential comparison considering the API determination fidelity, we further explored whether the average and standard deviation (in %) of the rock-magnetic parameters individually had no significant relationship with the TS API estimates at the site level (Fig. 10). Consequently, all the parameter statistics, except for the ITC_|m| within-site standard deviation, indicated no meaningful correlation with the TS API site averages (low R and p > 0.05). The apparent (positive) correlation between the ITC_|m| standard deviations and API site averages (R = 0.491 and p = 0.038) depended on the single data point for site 14226 with the highest ITC_|m| standard deviation (119%) and the highest API site-average (61.3 μT) values; considering the single data exclusion, the correlations become statistically insignificant. This result rules out that our TS API estimates can be biased depending on the magnetic properties of the sample in general.

Fig. 10

Comparisons between site-average TS API and site-average (a) and within-site standard deviation (%) (b) of respective rock-magnetic parameters (B_cr, B_c, M_rs/M_s, BDS, and ITC_|m|). For each biplot of comparison, the correlation coefficient R and p value with a fit linear regression line (black line) are given. Representation of the data point colors is the same as that in Fig. 9

Discussion

Exploring ‘ease-of-use’ rock-magnetic parameters for the sample preselection criteria

‘Hysteresis’ parameters

Di Chiara et al. (2017) and Fukuma (2023) documented the threshold value of M_rs/M_s < 0.2 to reject, in advance, samples that potentially result in failure in Thellier-type API determination, based on their dataset from historical lava flows and scoriae, and Paleoproterozoic mafic sills, respectively. Conversely, Carvallo et al. (2006) documented that the hysteresis parameters do not appear to correlate with the success or failure of the Thellier-type API results in a large dataset for igneous rocks. Furthermore, Santos and Tauxe (2019) showed that hysteresis parameters have little relationship with the reliability of API results, although samples with higher M_rs/M_s tend to result in better API determinations in Thellier-type applications and vice versa. Paterson et al. (2017) introduced a BDS threshold value of 0.10 (corresponding to approximately 3.4 for B_cr/B_c and 0.08 for M_rs/M_s), where samples with a BDS < 0.10 are less likely to yield meaningful API determinations.

Let us consider the threshold values of the individual parameters for discriminating the “success” and “failure” TS results in our data compilation. The previously suggested threshold value of 0.1 in BDS cannot play a role because all BDS values are > 0.1. However, it may ensure the minimum magnetic domain stability for the API experiments of all data compilation samples. A threshold value of 0.2 in M_rs/M_s allows a ~ 75% (54 of 72) ratio of the “success” samples to the total screened (hereafter called ‘success rate’) and ~ 40% (36 of 90) ratio of the “success” samples abandoned by the criterion to the “success” total (Fig. 11a), indicating an increasing success rate but a relatively large loss of “success” samples. When adopting 20% at maximum in the “success” samples loss rate, up to ~ 73% in the success rate is permitted by a threshold of 0.16 in M_rs/M_s (Fig. 11a). Conversely, using a threshold value in B_cr or B_c yields a success rate > 80% and a relatively small loss of the “success” samples (< 30%); considering 20% as the maximum “success” samples loss, we can set 26 mT in B_cr and 13 mT in B_c as a threshold of the minimum value (Fig. 11b and c). The highest success rate was observed for middle B_cr and B_c threshold values (Fig. 11b, c), which is related to the significant reduction in increasing rate in the cumulative distribution of the “failed” results (Fig. 7a, b). Consequently, B_cr or B_c can be used as more efficient parameters for sample preselection for TS API determination than BDS or M_rs/M_s.

Fig. 11

Variations in ratio of the number of “success” TS API results of the samples preselected by the respective criterion to the total preselected (“success rate”) and in the number of “success” results abandoned by the criterion to the total of “success” results/samples (“rate of the success samples loss”) with different threshold values in the criterion for M_rs/M_s (a), B_cr (b), B_c (c), and ITC_|m| (d). In each diagram, the horizontal line of 0.2 in rate of the success samples loss and vertical line of the respective rock-magnetic parameter value at 0.2 in rate of the success samples loss are given

Alternatively, FORC analysis, which has been increasingly developed in recent years, has the potential as an alternative discrimination tool for the “success” (good) or “failure” (bad) samples. The problem in BDS and M_rs/M_s is the considerable overlap of the two data distributions in their intermediate ranges (approximately 0.2 < BDS < 0.6, 0.1 < M_rs/M_s < 0.3). Based on our NE China cases, although it is from the limited number of data, the FORC analysis may make discernibly different domain states between samples, even with intermediate BDS or M_rs/M_s values (“Association between rock-magnetic parameters and API results” section). Accordingly, we encourage a future challenge using FORC analysis, as mentioned by Paterson et al. (2017).

‘Thermomagnetic’ parameters

As mentioned previously, the ITC parameters are likely influenced by other factors (thermal magnetic alterations associated with the change in the remanence capacity by experimental heating) that do not govern the behavior of the hysteresis parameters. Hence, this allows us to consider them as another discrimination (i.e., preselection) tool in addition to the hysteresis parameters.

Previous studies have acknowledged several informative documentation using thermal changes in various rock-magnetic properties in a qualitative or quasi-quantitative manner to detect and filter out potentially erroneous (particularly low values) Thellier-type API determinations (to ensure or enhance the fidelity of API data). Nonetheless, using quantified parameters based on M_s-T curves to discuss relations to API results is rare, even in previous literature with Thellier-type API determinations; therefore, there is little parameter with a threshold available for reference. Several studies that used quantified parameters are briefly reviewed. Tanaka et al. (2007) used a measure of the difference between the starting and final M_s or k values in % of the starting value in either M_s-T or k-T curves with the criterion of < 15% for sample preselection for Thellier-type experiments. Qin et al. (2011) proposed a ratio using M_rs, the M_rs after a high temperature (480 °C) normalized by the initial M_rs at room temperature of the pristine sample (M_rs480^o_c/M_rs25^o_c), with the criterion of 0.9 ≤ M_rs480^o_C/M_rs25^o_C ≤ 1.1 to improve the reliability of Thellier-type API determinations. Tanaka and Kono (2002) and Kim et al. (2018) suggested a measure of the k difference (% of the pristine value) between the final values after each heating step during a Thellier-type experiment and the pristine value before the experiment, with the criterion that k differences throughout the experiment should be < 20%. These measures shared a common feature: only the initial and final values during the heating process were used in the calculation.

ITC_|m| is a potential preselection criterion because it shows the tendency of more successful API results with decreasing ITC_|m| values and a positive Welch’s t-test (“Comparisons of distributions in rock-magnetic parameter between ‘successful’ and ‘failed’ TS API data” section). When considering a threshold value of 0.15 in ITC_|m| slightly lower than 20% in the “success” samples loss, it permits ~ 76% in the success rate on our data compilation (Fig. 11d). Notably, the ITC_|m| threshold value of 0.15 is similar to those of the other previously documented parameters for thermal changes in Thellier-type experiments (Tanaka and Kono 2002; Tanaka et al. 2007; Qin et al. 2011; Kim et al. 2018). ITC_|m| offers better performance in preselection efficiency than M_rs/M_s or BDS but appears to be less sensitive than B_cr or B_c efficiency (Fig. 11).

Suggestion of the preselection criteria

Each hysteresis parameter B_c or B_cr and the M_s-T parameter ITC_|m| can be used as a single efficient preselection criterion, revealing better efficiencies in B_c and B_cr than ITC_|m|. Furthermore, a combination of one hysteresis (B_c or B_cr) parameter and the other M_s-T curve (ITC_|m|) parameters can be used as a more efficient tool for preselection, given that there is no correlation between the hysteresis and M_s-T parameters. We consider two parameter combinations with the above-discussed threshold values as the preselection criteria, that is, B_cr ≥ 26 mT and ITC_|m|≤ 0.15, and B_c ≥ 13 mT and ITC_|m|≤ 0.15 (Fig. 12). One combined set of criteria, B_cr ≥ 26 mT and ITC_|m|≤ 0.15, allows ~ 86% (65 of 76) in success rate in % of the screened “success” total, with ~ 28% (25 of 90) in the “success” samples loss rate (Fig. 12a). The other combined set, B_c ≥ 13 mT and ITC_|m|≤ 0.15, allows ~ 85% (63 of 74) in the success rate and ~ 30% (27 of 90) in the “success” samples loss rate (Fig. 12b). We recommend a minimal set of B_c ≥ 13 mT and ITC_|m|≤ 0.15, or of B_cr ≥ 26 mT and ITC_|m|≤ 0.15 as preselection criteria.

Fig. 12

Comparisons of combinations of one hysteresis (B_c or B_cr) and the other M_s-T curve (ITC_|m|) parameters between the TS API “success” and “failure” data subsets. (a and b) Biplots of B_cr vs. ITC_|m| and B_c vs. ITC_|m|, respectively, with the consideration of when a minimal set comprising two different rock-magnetic parameters is adopted as the “sample priority selection criteria;” the proposed threshold values (B_cr ≥ 26 mT and ITC_|m|≤ 0.15, and B_c ≥ 13 mT, and ITC_|m|≤ 0.15, respectively; “Exploring ‘ease-of-use’ rock-magnetic parameters for the sample preselection criteria” section) of the two variables in each biplot are indicated by black solid lines; the pale yellow shaded zone of each biplot represents the zone distributed by data meeting the respective minimal set of criteria

Within-site dispersion of TS API estimates considering rock-magnetic parameters

Generally, the API determination for a site with high fidelity is achieved by averaging the API results from multiple samples/specimens. As stated in “Comparison between inter-sample dispersion of API determinations and rock-magnetic parameters for sites” section, the successful specimen-level TS API estimates in our data compilation allowed reasonably good within-site consistency in API averaging for most of the analyzed sites. We confirmed that unwanted, considerable API biases in site-averaged determination and within-site dispersion relying on inherent sample magnetic properties are less possible (Figs. 9 and 10).

However, for the sites 14181, DB15, DB12, DB(-1)B, and DB(-6), the individual TS API standard deviations were larger than 20% of the respective site averages, which is problematic in providing high-fidelity API site averages. At these sites, only the average of the whole API estimates is not believed to be an adequate API determination for a site. Specifically, we considered whether potentially biased TS API estimates within a site can be determined using rock-magnetic parameters. From the possible positive relationship between B_c and API within-site standard deviations (in %, Fig. 9), we suspect a possible B_c relevance to individual TS API estimates in the specimens of these sites. When considering this and our preselection criteria, the API estimates with B_c < 13 mT might be biased by potential rock-magnetic artefacts. Therefore, the high API estimate (16.6 μT) of sample DB15-2 (12.8 mT in B_c), the high API estimate (45.1 μT) of sample DB(-1)-3 (12.1 mT in B_c), and the low API estimate (25.9 μT) of sample DB(-6)-3 (12.1 mT in B_c) might be biased (Additional file 4: Table S2). Then, exclusion of these APIs in the site average determinations allows that DB15, DB(-1)B, and DB(-6) would yield API averages (~ 11 μT, ~ 24 μT, and ~ 37 μT, respectively) with better within-site consistency (cf. those listed in Additional file 7: Table S4). Extending another consideration relating to our preselection criteria, the low API estimate (21.0 μT) of sample DB12-2 with ITC_|m|> 0.15 (Additional file 4: Table S2) might be less faithful. Nonetheless, even these extended consideration does not allow the selection of the most likely estimates among the highly dispersed TS APIs for site 14181. Currently, the determined site-averaged API of site 14181 must be discarded due to being considered less faithful.

Conclusions

The TS experiment, which is becoming the most advanced and promising API determination technique, requires a systematic effort to link rock-magnetic parameters to TS API results to improve the quantitative success of API determination and API fidelity, as Thellier-type experiments have been most widely applied to date. Here, we explored the relationships between rock-magnetic parameters and TS API results (success or failure in determination and within-site consistency) using voluminous pairs (133 sample-level pairs from 38 different sites/cooling units) of sample-level rock-magnetic parameters and TS API data from late Cenozoic basaltic rocks. We addressed B_c, B_cr, B_cr/B_c, M_rs/M_s, and BDS values, and |ITC₅₀| and ITC_|m| values quantified from hysteresis measurements and thermomagnetic analysis with measurement rapidity and ubiquitous use.

Comparison of the hysteresis parameters to the API determination success or failure revealed that BDS and M_rs/M_s values more frequently addressed in previous literature were slightly higher for samples with “success” TS API results. Compared with BDS and M_rs/M_s, B_c and B_cr allowed more effective discrimination in distribution between “success” and “failure” samples; samples with lower B_c or B_cr displayed a higher failure rate of TS API determination. Comparison of the ITC parameters to the API determination success or failure revealed a visible relationship between ITC_|m| and TS API success or failure. The success/failure discrimination by ITC_|m| was more efficient than that by BDS or M_rs/M_s but less efficient than that by B_c or B_cr. We interpret that B_cr, B_c, and ITC_|m| were individually available as parameters for the sample preselection criterion, with thresholds of B_cr ≥ 26 mT, B_c ≥ 13 mT, and ITC_|m|≤ 0.15, respectively. Moreover, the hysteresis (B_c or B_cr) and thermal change (ITC_|m|) parameters could be complementarily utilized, given the negligible relationship between them. This may be because ITC_|m| is likely more sensitive to thermally induced magnetic changes. Hence, we suggest a minimal set of B_c ≥ 13 mT (or B_cr ≥ 26 mT) and ITC_|m|≤ 0.15 as the sample preselection criteria for quantitative success.

We also confirmed that the sample/specimen-level TS API estimates adopted through the TS experiment acceptance criteria and their derived site-average API values were generally unbiased or less biased by potential rock-magnetic artefacts. However, samples from sites with large within-site API dispersions might be associated with unwanted biases in individual TS API determination. Extended consideration based on our proposed preselection criteria might allow for the selection of more accurate API estimates from highly dispersed estimates within such a problematic site. However, if more faithful, unbiased API individuals cannot be salvaged, it should remain inconclusive in determining the site-averaged TS API.

In conclusion, the rapid-check rock-magnetic parameters implemented in this study can guarantee efficient acquisition and high fidelity of TS API data. Furthermore, we expect that the B_c (or B_cr) and ITC_|m| parameters will also apply to Thellier-type experiments as efficient preselection criteria.