Geomagnetic paleointensity dating of mid-ocean ridge basalts from the neo-volcanic zone of the Central Indian Ridge

Describing the evolution of the neo-volcanic zone in the spreading ridge is essential for understanding the dynamics and environments of abyssal basins. However, the absolute dating of ocean floor basalts is generally difficult. As a characteristic age indicator, absolute intensity of past geomagnetic field (absolute paleointensity, API) is useful to date ocean floor basalts. In this study, we adopted the Tsunakawa–Shaw method to measure APIs of whole-rock seafloor basalts collected from a conical cone on the Central Indian Ridge and performed rock magnetic experiments. We conducted the experiments on a total of 18 specimens (two or three specimens from each of eight lava sites). Six specimens from two lava sites with different morphologies (pillow and sheet), three for each, passed the acceptance criteria. API means at site level are 33.0 ± 1.0 and 35.8 ± 1.7 μT, respectively. The similarity of API site means suggests that they erupted within a short period. These site-level API means are approximately 0.7 to 0.8 times the present geo-magnetic intensity of 46.0 μT at the sampling sites. The accepted specimens show higher Curie temperature, lower initial intensity of natural remanent magnetization, higher ratio of saturation remanence to saturation magnetization (M rs /M s ), and signal of harder magnetic mineral than rejected ones. Our primary comparison between the two site-level API means and the 1590–present high-resolution IGRF-13 + gufm1 model constrains that the eruption timing of the conical cone to be < 1590 CE. When we compared the two site-level API means with the paleointensity curves calculated from the BIGMUDI4k.1 and ArchKalmag14 k.r, we found that they overlap in the period of − 7575 to −1675 CE or − 25 to 1590 CE, which may be the eruption timing of the conical cone. We concluded that timing of recent volcanic eruption in abyssal environment could be investigated by using appropriate rock magnetic selection and care-fully examined API.


Introduction
Volcanic activities in the mid-ocean ridges mainly occur in a focused area of the sea-floor spreading axis, known as neo-volcanic zones (NVZs).They are characterized by young volcanic features and symmetric magnetic anomalies (e.g., Macdonald et al. 1984;Smith and Cann 1990;Okino et al. 2015).The evolution of NVZs contributes to both long-term phenomena, like the formation of abyssal basins, and short-term ones, such as neotectonic activity, global material cycles, and the persistence of the deep-sea ecosystem.However, understanding of the evolution with absolute dating has not been achieved.This is because a detailed age, especially less than 10 4 years, cannot be determined from the record of geomagnetic reversals recognized from magnetic anomalies and radiometric dating.The observation of lava superposition and/or chemical composition transition can only provide the relative age of seafloor lava.Reconstructions of variations in absolute intensity of past geomagnetic field (absolute paleointensity, API) recorded in in-situ lavas, combined with global geomagnetic models, may provide age estimates.However, precise measurements of API using mid-ocean ridge basalts (MORBs) have not yet been established.
Because glass hosting remanent magnetization-carrying minerals in its interior is thought to protect the magnetic minerals from weathering, many previous studies used submarine basaltic glass from the quenched margins of MORBs to obtain high-quality APIs (e.g., Juarez et al. 1998;Pick and Tauxe 1993a,b;Mejia et al 1996;Gee et al. 2000;Carlut and Kent 2000;Riisager et al. 2003;Carlut et al. 2004;Bowles et al. 2006).For example, Bowles et al. (2006) conducted API measurements for age determination using near-axis MORB glasses collected from the East Pacific Rise at 9°-10°N.They found an age difference of 150 to 200 years between the old and new lavas using a contrast in APIs.
Non-glass MORBs have also been used for API measurement; however, there are only a few studies (Dunlop and Hale 1976;Grommé et al. 1979;Prévot et al. 1983).Grommé et al. (1979) confirmed that basalts containing titanomagnetite that had been low-temperature oxidized by seafloor weathering gave significantly low paleointensities using pillow lavas collected from the seafloor younger than 0.7 Ma.Prévot et al. (1983) showed that the linearity in the natural remanent magnetization (NRM)-thermal remanent magnetization (TRM) diagram and the partial TRM (pTRM) check test in the Thellier method could not detect the titanomagnetite alteration (change in the Curie point) during heating using MORBs collected from the FAMOUS area at 37°N of the Mid-Atlantic Ridge, which formed approximately 2000-6000 years and 10000-100000 years ago.Carlut and Kent (2002) used "zero-age" MORBs erupted in 1993 collected from the East Pacific Rise to measure APIs and identified the problem of overestimated API owing to the effects of multi-domain (MD) grains and laboratory cooling rates.In summary, when we measure APIs from nonglass MORBs, we obtain APIs that are too strong or weak because of several problems associated with magnetic minerals (alteration during heating, low-temperature oxidation, and MD grains).It is expected that there is frequently no glass left in MORBs, so it is better to be able to measure APIs even in the non-glass parts of MORBs.
The use of MORBs as targets for API measurements is valuable because it avoids the risk of overestimation by thermochemical remanent magnetizations (TCRMs).Titanomagnetite in subaerial lava often forms ilmenite lamellae by high-temperature oxidation because of relatively slow cooling (Haggerty 1991).Divided titanomagnetite into SD sizes by ilmenite lamellae is suitable for API study (Shcherbakov et al. 2019).However, Kilauea 1960 lavas in Hawaii often show overestimated API although the lavas include titanomagnetite with ilmenite lamellae (e.g., Yamamoto et al. 2003).One possible cause is TCRM acquired during the formation of ilmenite lamellae below Curie temperature (Yamamoto 2006).However, ilmenite lamellae are rare in MORBs because they are often rapidly cooled on the seafloor (Petersen et al. 1979).
Recently, the Tsunakawa-Shaw method (Yamamoto et al. 2003) has been used in various studies (e.g., Kato et al. 2018;Kitahara et al. 2018Kitahara et al. , 2021;;Ahn and Yamamoto 2019;Yoshimura et al. 2020;Mochizuki et al. 2021;Biasi et al. 2021;Yamamoto et al. 2022;Pérez-Rodríguez et al. 2022).This is the latest version of the Shaw method and has following functions; anhysteretic remanent magnetization (ARM) correction, double heating technique, and low-temperature demagnetization.The ARM correction can correct laboratory heating alteration or magnetic anisotropy by using ARM acquired before and after heating.The low-temperature demagnetization can demagnetize MD grains' magnetization.The method would work for the non-glass part of MORBs including MD grains of titanium-poor titanomagnetites.In this study, we applied the Tsunakawa-Shaw method to whole-rock MORBs from a volcanic conical cone on the Central Indian Ridge (CIR) to measure the APIs and estimate the eruption age by comparing the APIs with geomagnetic field models.

Geological setting and sampling
The CIR near the Rodriguez ridge-ridge-ridge triple junction is classified as a slow to intermediate rate spreading system, with full spreading rates of 35.5 mm/year at 10°S and 47 mm/year at 25°S (the Mid-Ocean Ridge VELocity, MORVEL: DeMets et al. 2010).In this study, we use the prefix CIR-SX following Briais's (1995) ridge segment classification.The ridge axis of the CIR segment 1 (CIR-S1) to segment 4 (CIR-S4) has an axial valley of less than 10 km in width.The CIR is divided into segments by fracture zones and non-transform discontinuities (NTDs) (Parson et al. 1993;Briais 1995).Almost at the center of the axial valley, the neo-volcanic zone, which is interpreted as the area of the most recent volcanic activity, consists of a small ridge (several hundred meters in relative height, 1-5 km wide, and more than 10 km long) parallel to the axial valley.The ridge is a series of small hills mainly composed of pillow lavas.Previous sea-surface magnetic anomaly surveys have identified the Brunhes-Matuyama boundary along the off-ridge of CIR-S1 and CIR-S2 (Honsho et al. 1996;Sato et al. 2009;Okino et al. 2015).The axial valley in CIR-S2 seems asymmetric, which suggests the NVZ recently jumped eastwards (Okino et al. 2015).Several hydrothermal fields in the NTDs between CIR-S1 and CIR-S2 also contribute to the magnetic anomalies (Fujii et al. 2016;Fujii and Okino 2018).
In this study, we used basalts from a volcanic conical cone in the NVZ of CIR-S2 (Fig. 1).The basalts were collected using the manned submersible Shinkai 6500 during the R/V Yokosuka cruise of YK05-16 in 2006 and were archived at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC).Rock sampling by Shinkai 6500 was conducted along a survey line from the conical cone of the current ridge axis to the eastern rift-valley wall of CIR-S2 during the 6K#926 dive.This site is located within the eastern portion of the axial valley in the middle of the segment.A sheet lava flow was observed at the top of the conical cone.The basalts are all fresh, gray basalts with inconspicuous phenocrysts, many of which have glass rims (Additional file 1: Fig. S1).The basalts of sites 6K#926R01 and 6K#926R02 were collected from scree fields that appear to be fragments of pillow lava at the base of the conical cone.
The basalts of sites 6K#926R03 through 6K#926R07 were collected from pillow lavas.The basalts of sites 6K#926R05 through 6K#926R07 were pillow lava with broken surfaces and exposed cross-sections.The basalt of site 6K#926R08 was collected from a sheet lava at the top of the conical cone.

Grain densities, magnetic susceptibility, and NRM measurements
Four cubic specimens were cut from each of the eight lava block samples collected from the eight sites.Bulk grain densities were measured for each sites using one or two  (c, d) Sites 6K#926R01 and 6K#926R02, scree field, (e, f) Sites 6K#926R03 and 6K#926R04, fresh pillow lava, (g) Site 6K#926R05 (also 6K#926R06 and 6K#926R07), broken pillow lava, (h) sheet lava near the peak of the conical cone.B/M: Brunhes-Matuyama boundary; 1r.1, 2, 2Ay: magnetic isochron of C1r.1n, C2n, C2An.1n, respectively out of the four specimens at the Atmosphere and Ocean Research Institute (AORI) of the University of Tokyo using a high-precision microbalance with a resolution of 0.01 mg and a gas pycnometer (AccuPyc 1330 Pycnometer).Magnetic susceptibility was then measured for all specimens using a ZH Instruments SM 150 L susceptibility magnetometer at AORI.The initial NRM intensity was also measured for all the specimens using an automatic spinner magnetometer with an alternating field (AF) demagnetizer (DSPIN, Natsuhara Giken) installed at AORI.

Rock magnetism
We cut chip samples for rock-magnetic measurement from 16 out of 18 specimens showing relatively strong initial NRM intensity, before API measurements (Additional file 1: Fig. S2).We conducted thermomagnetic analyses for 16 fragments of the 16 chip samples using a magnetic balance at Kyushu University (Natsuhara Giken MNB-2000M1).The chip samples were heated to 700 °C in a vacuum (< 5 Pa) and a magnetic field of 100-500 mT.We also conducted magnetic hysteresis measurements on 15 fragments of the 16 chip samples and first-order reversal curve (FORC) measurements on 5 fragments of the 16 chip samples using an alternating gradient magnetometer (PMC MicroMag 2900) at the National Institute of Polar Research.Hysteresis loops were measured in the coercivity range of − 0.5 to 0.5 T. In FORC measurements, B c was from 0 to 150 mT (except for 6K#926R08, 0 to 400 mT), B u was − 60 to 60 mT.The maximum applied magnetic field was 1.0 T and the averaging time at each measurement point was 100 ms.FORCinel software (Harrison and Feinberg 2008, version 3.06) was used for analysis, and the VARIFORC algorithm of Egli (2013) was used for smoothing (Sc0 = 4, Sb0 = 3, Sc1 = Sb1 = 7).The regions with low coercivity and those around B u = 0 were smoothed out small, whereas the other regions were smoothed out large.

Paleointensity measurements
For the API measurement experiments, we used two or three specimens from each of eight site, 18 specimens in total.We conducted API experiments on the specimens in 7 cc non-magnetic plastic cubes and applied the Tsunakawa-Shaw method (Yamamoto et al. 2003).This is an advanced version of the Shaw method (Shaw 1974) with the addition of an ARM correction (Rolph and Shaw 1985), a double-heating technique (Tsunakawa and Shaw 1994), and low-temperature demagnetization (Ozima et al. 1964;Mochizuki et al. 2004;Smirnov et al. 2017), which can demagnetize the MD component of low-Ti titanomagnetite.The Shaw-type method uses coercivity spectra obtained from alternating field (AF) demagnetization to minimize the frequency of heating.We used the DSPIN at Kyushu University to measure the NRM, TRM, and ARM with stepwise AF demagnetization for the Tsunakawa-Shaw method.For low-temperature demagnetization, the specimens were first soaked in liquid nitrogen in a non-magnetic dewar for 10 min, then left for 30 min at room temperature while being air-dried in a nearly zero magnetic field shield.Sixteen specimens were subjected to stepwise AF demagnetization at 2-10 mT intervals with AF steps of up to 180 mT (~ 40 steps in total).For TRM acquisition, specimens were heated to 610 °C in vacuum (< ~ 10 Pa) and cooled in a DC magnetic field of 30 µT.The peak temperature was held for 15 min for the first heating (TRM1) and 30 min for the second heating (TRM2) and then cooled to room temperature over 1 h.The ARM was acquired by superimposing a 180 mT peak AF on a 50 µT DC bias magnetic field before and after the heating step.The ARMs before and after the first heating and ARM after the second heating are referred to as ARM0, ARM1, and ARM2, respectively.The ARM correction was performed using the following equations: We adopted the following acceptance criteria, the same as those used in recent API studies using the Tsunakawa-Shaw method (e.g., Yamamoto et al. 2022).
1.Primary components are separated from the NRM by the stepwise AF demagnetization.The maximum angular deviation (Kirschvink 1980) is smaller than 10°.2. One segment within the coercivity range of the primary NRM component that provides a linear relationship in the NRM-TRM1* diagram.This segment spans at least 30% of the initial NRM (f N ≥ 0.30).The correlation coefficient of the segments is not smaller than 0.995 (r N ≥ 0.995).3.One segment also gives a linear relationship on the TRM1-TRM2* diagram.This segment spans at least 30% of the initial TRM1 (f T ≥ 0.30).The correlation coefficient of the segments is not smaller than 0.995 (r T ≥ 0.995).The slope of the segment coincides with the line with a slope of 1 within the experimental error (1.05 ≥ slope T ≥ 0.95), proving that the ARM correction is valid.The highest coercivity of the segment is fixed to be the same as that of the NRM-TRM1* diagram.

Grain densities, magnetic susceptibility, and NRM measurements
The grain density, magnetic susceptibility, and initial NRM intensity were summarized in Table 1.The grain densities of the specimens from all sites show 2.93-2.99(g/cm 3 ), which are typical values for basalts.The magnetic susceptibility and initial NRM intensities range 0.0008-0.0066(SI) and 1.73-23.22(A/m), respectively.

Rock magnetism
Four representative results of the thermomagnetic analysis are shown out of the 16 results (Fig. 2a-d) (see Additional file 1: Fig. S3 for the other results).The 16 chip Fig. 2 Results of rock magnetic measurements.a-d Typical thermomagnetic curves heated in vacuum (Red line: heating procedure, blue line: cooling procedure).e AF demagnetization curves of NRM and ARM.f-h Typical hysteresis loops before (red) and after (blue) paramagnetic correction.The paramagnetic correction was performed based on the assumption that the titanomagnetite is saturated at 0.5 T. i Relation between the hysteresis ratios of the ratio of coercivity of remanence to coercivity (B cr /B c ) and the ratio of saturation remanence to saturation magnetization (M rs /M s ) for the chip samples.j-n FORC diagrams of representative specimens, each of which is drawn from 169 FORCs with the maximum applied magnetic field was 1.0 T samples show major curie temperature (T c s) between 170 and 340 °C, with another minor T c s between 450 and 600 °C.Fifteen chip samples exhibited the intersections in the heating and cooling curves (Fig. 2a, b, and d).Only one chip sample from site R07 exhibited a completely reversible thermomagnetic curve (Fig. 2c).Three chip samples from sites R01 through R03 showed very slight signs of bumping in areas higher than 450 °C, common in low-temperature oxidized samples (Fig. 2b).The differences between the curves before and after the intersection varied from sample to sample.The initial NRM intensities up to 20 A/m is consistent with the magneticanomaly-derived absolute magnetization in these regions (Fujii et al. 2016;Fujii and Okino 2018).The magnetic susceptibility results have a positive correlation with the initial NRM intensities (Additional file 1: Fig. S4).The relationship implies that samples with larger amount of ferromagnetic minerals, which might be produced in slower magma cooling, carry stronger values of NRM.Furthermore, the slope of the NRM-susceptibility diagram shows sharper in lower susceptibility values, probably indicating that magnetization acquisition is efficient in the early stage of crystallization.
The results of the NRM stepwise AF demagnetization can be divided into two groups (Fig. 2e).The first is the magnetically hard group, with median destructive fields (MDFs) ranging from 52 to 77 mT (red in Fig. 2e).The second is a magnetically soft group with MDFs ranging from 17 to 32 mT (blue in Fig. 2e).The similar character is observed in the demagnetization curves of ARM (Fig. 2e).
Typical magnetic hysteresis loops are shown in Fig. 2f-h.There are two types of loops: wide (Fig. 2f,  g) and narrow (Fig. 2h). Figure 2i shows a biplot of the hysteresis parameters for the 15 chip samples from eight sites.All data points are distributed in the single domain (SD) region based on the day plot (e.g., Day et al. 1977), with the ratio of saturation remanence to saturation magnetization (M rs /M s ) exceeding 0.5.The M rs /M s for all the samples exceeded 0.5, the theoretical upper limit for a randomly oriented uniaxial grain ensemble.This is a common observation in MORBs (e.g., Gee and Kent 1995;Carlut and Kent 2002).These results are either due to an overestimated value when the M s value is not fully saturated (Fabian 2006) or to the presence of multiaxial SD grains (Mitra et al. 2011).See Additional file 1: Fig. S5 for all the hysteresis loops.
The FORC diagrams of 6K#926R01, 6K#926R03, 6K#926R04, 6K#926R07, and 6K#926R08 show closed teardrop contours with some magnetostatic interactions (B u within ± ~ 20 mT) and the negative region along the negative part of B u axis, which means that the chip samples mainly include SD grains (Fig. 2j-n).The FORC diagrams of 6K#926R03 and 6K#926R08 indicate elongated coercivity distributions at B u = 0.In particular, the FORC diagram of 6K#926R08 indicates a sharp ridge along the B c axis (> 400 mT), similar to central ridges observed in the marine sediments (e.g., Egli et al. 2010).

Paleointensity measurement
The results of the API experiments for a total of 18 specimens, two or three from each of the eight sites, are summarized in Table 1.All NRM directions show a single component toward the origin of the orthogonal projection (Fig. 3; Table 1), and all maximum angular deviations of the NRM are less than 0.8.The representative results of the Tsunakawa-Shaw method are shown in Fig. 3a, b.Six specimens from two sites (6K#926R07 and 6K#926R08) passed the acceptance criteria of the Tsunakawa-Shaw method.The specimen-level APIs are 32.3 to 34.1 µT for 6K#926R07 (site-level mean is 33.0 ± 1.0 µT [N = 3, 1σ]), 33.9 to 37.2 µT for 6K#926R08 (site-level mean is 35.8 ± 1.7 µT [N = 3, 1σ]).The standard deviations are 3.0% and 4.7% of the mean, respectively, indicating highly precise APIs.See Additional file 1: Fig. S6 for the other accepted results.This is the first API measurement ever obtained from MORB using the Tsunakawa-Shaw method.The remaining 12 specimens are rejected by the acceptance criteria.All of them are rejected because the slope of the TRM1*−TRM2 diagram (slope T ) exceeded the range of 1.00 ± 0.05 (Table 1; Fig. 3).See Additional file 1: Fig. S7 for the other rejected results.The acceptance rate for the API measurements in this study is 33.3%.The amount of change in ARM between before and after the LTD treatment was of − 3.6 to 2.9%.

Characteristics of paleointensity results and the cause of acceptance/rejection
In this subsection, we discuss the characteristics of the parameters of the API results and the causes of acceptance or rejection.The standard deviations of the site-level API means are small (< 5%).This is probably because the MORBs did not acquire TCRM, unlike subaerial basalts, thereby preventing the mixture situation of accurate and overestimated API results.Based on the results of FORC and thermomagnetic analyses, we can estimate that the analyzed MORBs are dominated by titanium-rich SD grains with no MD grains.There was no significant difference between ARM0 and ARM1 (slope A1 ranged from 0.822 to 0.958), indicating little thermal alteration by heating.This suggests that on-axis submarine basalts were suitable for API experiments.We interpreted these factors as successful API measurement using the Tsunakawa-Shaw method.The Coe-Thellier method (Coe 1967) may also be applicable to API measurements for MORBs in future studies.
The variation in the slope N values from specimens from sites 6K#926R01 to 6K#926R06 (1.023-1.543)was larger than those of specimens from sites 6K#926R07 and 6K#926R08 (1.078-1.239;Fig. 3c; Table 1).The slope T of specimens from sites 6K#926R01 to 6K#926R06 (1.106-1.205)was clearly different from those of specimens from sites 6K#926R07 and 6K#926R08 (0.951-1.041;Fig. 3d; Table 1).The trend of slope T suggests that the mechanism by which MORBs are rejected in the API experiments may be common.The mechanism is likely unusual alteration process; the coercivity spectrum of TRM decreased after the second heating, even though the ARM coercivity spectrum did not change.

Rock-magnetic difference between accepted and rejected paleointensity results
The shared characteristics of the specimens that passed the API acceptance criteria, compared to the samples that did not, were (1) high T c (Fig. 2c, d; Table 1), (2) low initial NRM intensity (Table 1), (3) high MDF of NRM and ARM (Fig. 2e; Table 1), and (4) high M rs /M s (> 0.7; Fig. 2i) and wide hysteresis loops (Fig. 2f, g).The accepted specimens from sites 6K#926R07 and 6K#926R08 show relatively high T c s of 233 °C to 331 °C, whereas the rejected specimens from the other sites show relatively low T c s of 172 °C to 226 °C.These results indicate that the remanence carriers in the accepted and rejected specimens were relatively low-and high-Ti titanomagnetite, respectively.The previously reported geochemical composition of TiO 2 /FeO is consistent across the sites (Sato et al. 2015;Neo 2011) (Additional file 2: Table S1; Additional file 1: Fig. S8), independent of the trend of T c s.We found no systematic differences in the FORC diagrams between the accepted and rejected specimens.All accepted specimens contained hard magnetic minerals, as indicated by the high MDF of NRM and ARM.The specimens from sites 6K#926R07 and 6K#926R08 indicate M rs /M s values greater than 0.7, whereas all the rejected specimens had M rs /M s values less than 0.7.These results suggest that high T c , low initial NRM intensity, high MDF of the NRM, and high M rs /M s could be useful for the pre-selection of MORB specimens for API experiments.
On the other hand, an exceptional feature of more elongated ridge along the B c axis (> 400 mT) with a higher coercivity peak (~ 70 mT) in FORC diagram was found in the chip sample from site 6K#926R08 (Fig. 2n).This may be associated with the sheeted morphology of the site.Considering the feature of the FORC diagram with high MDF and T c of the 6K#926R08 chip sample, it suggests the possible presence of elongated or needle-shaped low Ti titanomagnetite grains in the chip sample.

Paleointensity dating
The two site-level API means (33.0 ± 1.0 and 35.8 ± 1.7 µT) are very close to each other (Fig. 3e).Because the two lavas with different morphologies (6K#926R07: pillow lava, 6K#926R08: sheet lava) showed similar APIs, they may have erupted almost simultaneously.This is consistent with the geological observations and petrological descriptions.However, they are slightly distinguishable at one standard deviation (1σ) level.Based on the rate of change in geomagnetic intensity (0.015-0.067 µT/ year) estimated from the IGRF-13 (Alken et al. 2021) and gufm1 (Jackson et al. 2000) models from 1590 to 2023 CE, there may be a time difference of (35.8-33.0µT)/0.015or 0.067 (µT/year) = 42-187 years between the two lavas.
The site-level API means are approximately 0.7-0.8times the present geomagnetic intensity of 46.07 μT calculated using IGRF-13 (Alken et al. 2021) at the study site (latitude − 24° 53' , longitude 69° 58').Additionally, considering their standard deviations (1σ), the API means can be distinguished from the present geomagnetic intensity.This means that these lavas erupted at somewhat earlier time than the present.To estimate the upper limit of the eruption timing of the studied lavas, we compared the site-level APIs with the model made up of the IGRF-13 model with the gufm1 model (Jackson et al. 2000), which allows high-precision reconstruction of the API variation from the present back to 1590 CE (Fig. 4).The geomagnetic intensity from 1590 to 2023 CE always exceeds 40 µT (Fig. 4; Additional file 3: Table S2).The minimum intensity in 1590 CE was 40.43 µT.This value does not overlap with the range of standard deviations of our sitelevel API means.Therefore, it is constrained that the conical cone erupted before 1590 CE.In addition, the conical cone erupted after ~ 0.77 Ma because the sampling sites locate between the both Brunhes-Matuyama boundary identified in the sea-surface magnetic anomalies (Fig. 1) (Okino et al. 2015).We can robustly estimate that the conical cone erupted before 1590 CE and after ~ 0.77 Ma.
Next, we further consider to improve the age constraint by comparing with the CALS3k.4(Korte and Constable 2011) (Additional file 4: Table S3), BIGMUDI4k.1 (Arneitz et al. 2019) (Additional file 5: Table S4), and ArchKalmag14k.r (Schanner et al. 2022) (Additional file 6: Table S5) models (Fig. 4).The latest two models include new archeointensity data from African continent (e.g., Tarduno et al. 2015;Osete et al. 2015;Casas et al. 2016), which is relatively close to the CIR.They also include only data from archeologic and volcanic materials, avoiding the smoothing effect of sediment data.Therefore, we consider that the two latest geomagnetic models are more suitable than the CALS3k.4model for dating the conical cone using our API data.
Over the last 4000 years, which is the temporal limitation of the BIGMUDI4k.1 model, we find five overlapping age intervals between the both of two site-level API means and the BIGMUDI4k.1 paleointensity curve at the standard deviation level (orange zones in Fig. 4a).The overlap is in the time interval from − 25 CE to 1635 CE.Combined with the above-mentioned robust age constraint of ~ 0.77 Ma to 1590 CE, it suggests that the conical cone may have erupted within a period of − 25 to 1590 CE.Over the last 14,000 years, which is the temporal limitation of the ArchKalmag14k.rmodel, we find four overlapping age intervals between the both of two site-level API means and the ArchKalmag14 k.r paleointensity curve at the standard deviation level (light purple zones in Fig. 4b).Combined with the primary robust

Conclusions
The Tsunakawa-Shaw method was first applied to MORBs collected from the volcanic conical cone in the NVZ of CIR-S2, providing the six APIs of 32.3-37.2µT from six specimens (three specimens each from two lava sites, 6K#926R07 and 6K#926R08).Although the FORC diagram results did not differ significantly among the chip samples, specimens with high T c , low initial NRM intensity, high MDFs of NRM and ARM, and large values of the hysteresis ratios of M rs /M s tended to be accepted in the API experiments.Using this trend, we should be able to increase the success rate of API measurements from MORBs.Although the lavas at the two sites had different morphologies (pillow vs. sheet lava), their site-level API means were similar.Therefore, these lavas are suggested to erupt within a short period.The primary comparison between our two API site means and the 1590-present high-resolution IGRF-13 + gufm1 model constrains the eruption timing of the studied conical cone to be < 1590 CE.Considering the overlapping between the two sitelevel API means and paleointensity curves calculated from the BIGMUDI4k.1 and ArchKalmag14k.r models, we can estimate that the conical cone may have erupted in − 7575 CE to − 1675 CE or − 25 CE to 1590 CE.Although we could not determine the unique eruption timing of the NVZ conical cone of CIR-S2, we demonstrated that the measuring APIs provides a helpful information for investigating the history of volcanic eruptions and lava emplacements in the abyssal environment.

Fig. 4
Fig. 4 Comparison of our two site-level API means (blue and green lines) with the geomagnetic intensity curves over (a) 4 ka and (b) 14 ka calculated from the IGRF-13 (Alken et al. 2021) + gufm1 (Jackson et al. 2000) (black curve), CALS3k.4(Korte and ConsTable 2011) (white line), BIGMUDI4k.1 (Arneitz et al. 2019) (yellow line), and ArchKalmag14 k.r (Schanner et al. 2022) (gray line) geomagnetic models.Colored areas along geomagnetic intensity curves indicate the standard deviation range.The black dashed vertical line indicates the upper limit of eruption timing of the conical cone on the CIR-S2 constrained by the IGRF-13 + gufm1 model.The Orange (light purple) areas indicate overlapping time interval between the two site-level API means and the BIGMUDI4k.1 (ArchKalmag14k.r)geomagnetic intensity curve

Table 1
Rock magnetism properties, density, and paleointensity results of lava samples collected by YK05-16 6K#926 Column headings: NRM meas., intensity for NRM before low-temperature demagnetization; χ, magnetic susceptibility; B cr /B c : the ratio of coercivity of remanence to coercivity; M rs /M s : the ratio of saturation remanence to saturation magnetization; lower T c , lower curie temperature; H L , H H , low and high limit of the interval of AF steps chosen for the determination of a characteristic direction or a linear segment; MAD, maximum angular deviation of a primary component in NRM; MDF, median destructive field for NRM stepwise AF demagnetization; slope