(U–Th)/He thermochronometric mapping across the northeast Japan Arc: towards understanding mountain building in an island-arc setting

Topographic relief in arc-trench systems is thought to be formed by plate subduction; however, few quantitative investigations have so far been reported, with respect to the related mountain building process. This study applies apatite and zircon (U–Th)/He thermochronometry (AHe, ZHe, respectively) to Cretaceous granite rocks in the north part of the northeast (NE) Japan Arc to reveal its cooling/denudation history. Weighted mean AHe ages ranging from 88.6 to 0.9 Ma and ZHe ages from 83.9 to 7.4 Ma were determined for 10 rock samples. Using the AHe data, denudation rates were obtained for each sample. On the fore-arc side, denudation rates of < 0.05 mm/year were calculated, indicating a slow denudation process since the Paleogene. However, in the Ou Backbone Range and on the back-arc side, denudation rates at > 0.1–1.0 mm/year were computed, probably reflecting a recent uplift event since ~ 3–2 Ma. These data indicate a clear contrast in thermal and denudation histories between the tectonic units in this study area, similar to that previously reported from the southern part of NE Japan Arc. A comparison of the thermal/denudation histories between the N- and S- traverses, revealed the arc-parallel trend, the uplift model of the volcanic arc, and some minor variations of thermal/denudation histories in each tectonic unit. This study offers some further insights into the understanding of tectonic processes in an island-arc setting.


Introduction
Arc-trench systems, resulting from plate subduction processes, form mobile belts, characterized by orogenesis, volcanism, and earthquakes. Early studies of arc-trench systems were largely based on geomorphology and structural geological studies (e.g., Dickinson and Seely 1979;Uyeda 1982Uyeda , 1983. Mountain building processes at collision zones, e.g., the European Alps and Himalayas, have been investigated quantitatively on the basis of thermochronologic methods (e.g., Wagner et al. 1977;Vernon et al. 2008;Burbank et al. 1996;Blythe et al. 2007). However, similar studies in island-arc settings are somewhat limited (see compilation in Herman et al. 2013), because their inland topography is often too young and/or of too low relief to be investigated by these methods. As a result of recent developments in low-temperature thermochronology, such as improving thermal inverse modeling, based in part on apatite fission track (AFT) data (e.g., Ketcham 2005;Gallagher 2012) and the resurgence and modern understanding of the (U-Th)/He system (e.g., Reiners and Brandon 2006;Ault et al. 2019), thermochronology has Fukuda et al. Earth, Planets and Space (2020) 72:24 been successfully applied to mountainous terrain even in island-arc settings (Sueoka et al. 2016).
We have previously attempted to reconstruct mountain building processes in the northeast (NE) Japan Arc using low-temperature thermochronology (Sueoka et al. 2017;Fukuda et al. 2019). Sueoka et al. (2017) conducted apatite and zircon (U-Th)/He (AHe and ZHe, respectively) thermochronology study across the southern NE Japan Arc, Abukuma Mountains on the fore-arc, the Ou Backbone Range (OBR) and the Iide and Asahi Mountains on the back-arc (hereinafter, the S-traverse). Fukuda et al. (2019) conducted thermal inverse modeling based on the AFT method using the same samples of Sueoka et al. (2017). These studies showed contrasting ages and denudation rates between the fore-arc side, volcanic front, and back-arc side in the S-traverse (Fig. 1). Namely, older ages and slower denudation rates on the fore-arc side, and younger ages and faster denudation rates in the OBR and on the back-arc side. This contrast probably reflects the spatial variation of uplift/denudation rates under the recent strong compressive stress field since the Quaternary.
In this paper, we investigate the thermal/denudation histories in the northern NE Japan Arc, i.e., Kitakami Mountains on the fore-arc side, the OBR, and Taihe and Shirakami Mountains on the back-arc side (hereinafter collectively referred to as the N-traverse see Fig. 1). Previous thermochronometric research reported from the S-traverse offered some geological insights; however, it left open the question as to whether the implications were relevant across the entire NE Japan Arc. Therefore, in this work, we report AHe and ZHe thermochronometric data from across the N-traverse and compare the thermal/denudation histories derived with those from the S-traverse.

Geomorphology and geology
The basic components of an island arc have been described as comprising; a trench, fore-arc, volcanic front, and back-arc basin (e.g., Dickinson and Seely 1979). As such, the NE Japan Arc can be classified as a typical island arc because with respect to the cross-arc direction, its inland topographies appear in such a geomorphic arrangement (e.g., Ota et al. 2010) (see cross section in Fig. 1). In this paper, following the definition of Koike et al. (2005), we divide the NE Japan Arc into three tectonic units: the fore-arc side, the OBR, and the backarc side, with the OBR regarded as the volcanic front.
In the northern NE Japan Arc, clear geological differences are observed between the fore-arc side and the back-arc side of the OBR. Cretaceous granitic rocks at approximately 120-100 Ma (e.g., Yokoyama et al. 2016) are widely exposed only in the Kitakami Mountains on the fore-arc side. In contrast, green tuffaceous rocks and volcanic ejecta formed around and after the Miocene, cover most of the basement rocks in the OBR and on the back-arc side. More than 30 Quaternary volcanoes are distributed around the OBR and the back-arc side; whereas, no Quaternary volcanism has been reported from the fore-arc side (Fig. 1).
The tectonic history of NE Japan has been investigated using various methods such as structural geology, stratigraphy, and volcanology (e.g., Sato 1994;Nakajima et al. 2006;Nakajima 2013;Yoshida et al. 2013). Prior to ~ 21 Ma, the NE Japan Arc was located at the edge of the Asian continent. Between ~ 21 and 13.5 Ma, the opening of the Sea of Japan occurred due to spreading of the back-arc basin (e.g., Otofuji et al. 1985;Jolivet et al. 1994), forming the NE Japan Arc. Following its formation as an island arc, a compressional stress field developed and has been dominant in the NE Japan Arc since ~ 8 Ma (e.g., Nakajima 2013). From ~ 3 to 2 Ma to present, the inland topographic relief was formed (Yonekura et al. 2001) under an intense compressional stress field derived from subduction of the Pacific and Philippine Sea plates (Takahashi 2006(Takahashi , 2017. This E-W compressive stress regime reactivated ancient normal faults formed during the opening of the Sea of Japan as reverse faults (Sato 1994;Okamura et al. 1995;Okada and Ikeda 2012). Therefore, major topographic structures (e.g., faults, mountains) are generally distributed in an N-S direction along the NE Japan Arc.

Samples
We collected 20 Cretaceous granite samples along an N-traverse to apply AHe and ZHe dating (Fig. 1), and obtained AHe/ZHe data for 10 samples. To avoid possible reheating from recent volcanisms, sample localities were located > 10 km away from Quaternary volcano centers and high-temperature zones. Geothermal gradients measured in boreholes generally drop to background levels at ~ 10-20 km from Quaternary volcanic centers in Japan (Umeda et al. 1999). Based on this evidence, any thermal effects on our data from Quaternary volcanoes are disregarded for discussion in this work.

(U-Th)/He thermochronometry
Low-temperature thermochronology is a powerful tool to reveal thermal history. In particular, AHe and ZHe thermochronology data, because of the range of their temperature sensitivity, are useful for reconstructing cooling and denudation histories in the shallow crust (e.g., Reiners and Brandon 2006). In general, the typical closure temperatures for AHe thermochronometer are in the range 50-100 °C (Ault et al. 2019), and for ZHe a b Fig. 1 a Index map of the study area of the N-traverse. Numbered localities are our sampling sites. (U-Th)/He ages obtained in this study are also shown. Quaternary volcanoes: Committee for Catalog of Quaternary Volcanoes in Japan (1999); Active fault traces: Nakata and Imaizumi (2002); Hot Fingers: Tamura et al. (2002); Geothermal gradients: Tanaka et al. (2004); FT age: ages without sample codes indicating data from previous studies: Ganzawa (1987) on the back-arc side, and Goto (2001) on the fore-arc side; Boundaries: the lines showing the eastern and western limits of the OBR, defined by Koike et al. (2005). b Geomorphic cross section of study area. The cross sections were drawn along the 5 light blue lines in Figure (a). These figures were drawn using Generic Mapping Tools (GMT; Wessel and Smith 1991) and 50-m mesh digital elevation model (DEM) of the Geospatial Information Authority of Japan (GSI) is 100-200 °C (Guenthner et al. 2013;Ault et al. 2019); therefore, thermal histories from depths of ~ 2-7 km can be reconstructed under common geothermal gradients (~ 30 °C/km). However, He diffusivity may vary as a result of various factors, such as, the grain size and the cooling rate (e.g., Reiners and Brandon 2006;Ault et al. 2019), and also the degree of α-radiation damage (e.g., Shuster et al. 2006;Guenthner et al. 2013;Cherniak 2019). The variation of He diffusivity in individual grain impacts on the nominal closure temperature and thus their ages, which introduces complexities in the interpretation of such ages for reconstructing thermal histories. Hence, an evaluation of the reproducibility of grain ages is essential for interpreting He thermochronometric data.

Experimental procedures for He content measurement
The mineral separation of apatite and zircon was carried out at Kyoto Fission-Track Co., Ltd., using conventional methods. Samples were crushed into small pieces manually with a stainless mortar and pestle, and also using a rod mill. This was followed by magnetic separation, performed using a neodymium magnet (NEOMAX) for removing magnetic minerals. The target minerals were concentrated by density separation using sodium phosphate tungstate (SPT: 3.07 g/cm 3 : Danhara et al. 1992) and diiodomethane (CH 2 I 2 : 3.33 g/cm 3 ) as the heavy liquid.
(U-Th)/He analyses were conducted at the University of Melbourne. Three or four suitable grains were handpicked under a binocular microscope using the following criteria: grain width of 75 up to 200 µm, transparent and authigenic shapes, and no visible inclusions. Grain geometries were recorded using ImageJ software because these parameters are used to calculate the F T correction (Farley et al. 1996) for calibrating the alphaejection in each crystal. After measuring grain sizes, one or a few grains of apatite and a single grain of zircon were put into small acid-treated platinum capsules.
Experimental protocols of He content measurement were based on House et al. (2000) using a laser extraction system. Single grains were outgassed for 4 He under vacuum using a laser set on a wavelength of 820 nm with fiber-optic coupling to the sample chamber. Conditions of laser ablation heating were ~ 900 °C for 5 min for apatite, and for ~ 1300 °C for 20 min for zircon. A hot blank measurement was also conducted to ensure total degassing of 4 He after each gas extraction. He concentrations were determined using isotope dilution against a pure 3 He spike, calibrated against an independent 4 He standard. In cases where 4 He content of a single grain was too low, aliquots of multiple grains were analyzed for accumulating a detectable content.
Second, dissolving the degassed grains and analyzing parent isotopes were performed after all Pt packets were removed from the sample stage. For dissolving apatite grains, whole Pt capsules were immersed into HNO 3 to measure 238 U, 235 U, 232 Th, and 147 Sm concentrations using solution ICP-MS. While in zircon, degassed grains were removed from their Pt capsules and transferred to where they were spiked with 233 U and 229 Th and digested in small volumes (0.3-0.5 ml) at 240 °C for 40 h in HF. Standard solutions containing the same spike amounts as samples were treated identically, as were a series of unspiked reagent blanks. A second bombing in HCl for 24 h at 200 °C ensured dissolution of fluoride salts. Zircon solutions were then dried down, dissolved in HNO 3 and diluted in H 2 O to 5% acidity for analysis of 238 U, 235 U and 232 Th by solution ICP-Mass Spectrometry. For checking analytical accuracy, we simultaneously measured age standard samples as unknown samples. In this case, we used Durango apatite (McDowell et al. 2005) and Fish Canyon Tuff zircon (Gleadow et al. 2015) as standards.

Dating results
AHe and ZHe dating results are shown in Tables 1 and 2, respectively. All He dating results are also displayed in Fig. 1a. Moreover, as mentioned previously, we also measured Durango apatite and Fish Canyon Tuff zircon as secondary standards, which yielded ages of 32.3-30.0 Ma, and 29.9-28.1 Ma, respectively (Tables 1 and  2). These results are consistent with reference ages within the ± 2σ uncertainty level (Durango: 32.1 ± 1.7 (1σ) Ma: McDowell et al. 2005;FCT: 28.01 ± 0.04 (1σ) Ma: Phillips and Matchan 2013), which verified the accuracy of measurements in this study.

Reproducibility of grain ages
To calculate the weighted mean age of samples, more than three intra-sample analyses were used, employing IsoplotR (Vermeesch 2018). We verified whether grain ages within the error range of ± 3σ were consistent or not with a weighted mean age ranging within ± 95% confidence interval. When single grain ages did not overlap within the weighted mean age of a sample, the grain ages were rejected as outliers and the weighted mean age without such outliers was recalculated.
The accumulation of α-radiation damage and other parameters can impact strongly on 4 He retention in apatite and zircon; thus, such effects should be taken into account for interpretation of thermochronologic data (see also a review in Ault et al. 2019). Recent studies concerning the effects of radiation damage have also been investigated in the AHe system (e.g., Shuster et al.   2T Fukuda et al. Earth, Planets and Space (2020) 72:24 N/A denotes a weighted mean age was not adopted because of poor reproducibility a F T is the a-ejection correction after Farley et al. (1996) b Effective uranium concentration (U ppm + 0.235 Th ppm) (Shuster et al. 2006) c Grain morphology: 0T = no terminations, 1T = one termination, 2T = two terminations (Brown et al. 2013  Cherniak 2019). However, our samples were expected to have been less affected by radiation damage, because they are Cretaceous granites which yield younger He ages and lower uranium and thorium content than found in similar rock types in most major orogens world-wide. If the radiation damage effect is negligible, then the age obtained can be interpreted as a cooling ages reflecting a thermal history. For verifying the reproducibility of (U-Th)/He grain ages and the effect of possible radiation damage, plots of age versus effective uranium (eU) ppm (a proxy for radiation damage) (Shuster et al. 2006;Flowers et al. 2009) were constructed for each locality (Figs. 2 and 3). If the plot showed a positive or negative correlation within 3σ, the sample was considered to have a dispersed age, owing to radiation damage, or possibly some other factors (e.g., see Table 3 in Wildman et al. 2016). If grain ages were over-dispersed and did not correlate with eU, we calculated the arithmetic mean ages from all grains including possible outliers even for such poor age reproducibility samples. As an overview of radiation damage accumulation in our samples, eU in apatite reaches 100 ppm at most (Fig. 2), and that in zircon ranges below 900 ppm (Fig. 3). This observation leads us to the conclusion that radiation damage in our samples is unlikely to have had a major effect on ages and/or T c , considering from He diffusion changing for slow cooling samples in Fig. 3 in Ault et al. (2019). Regarding AHe ages (Fig. 2, Table 1), most of the samples reproduced well; whereas, FST04 had the wide age dispersions. While, in ZHe ages (Fig. 3, Table 2), the grain ages for samples FST06 and 10 were grouped into two clusters. Age dispersion of AHe of FST04 within the error range of ± 3σ in such localities has no correlation with eU, suggesting the little influence of radiation damage on these grain ages. On the other hand, only ZHe grain ages in FST10 appear to show a negative correlation within ± 3σ against the eU values (Fig. 3). However, these samples indicate improbable effects to cause age dispersion or clustering from radiation damage, inferring age dispersion arises from other possible factors, such as zonation of parent nuclides (e.g., Meesters and Dunai 2002), implantation from neighbor minerals (e.g., Spiegel et al. 2009), and fluid inclusions of radiometric He traps (Danišík et al. 2017). Thus, we did not employ weighted mean ages for these three samples.

Results of weighted mean ages
Weighted mean ages for AHe data at nine localities and for ZHe data at five localities were obtained (Table 3).
The weighted mean ages that we adopted for AHe range from 88.6 to 0.9 Ma (Tables 1 and 3, Fig. 4c); while those for ZHe ages range from 83.9 to 9.9 Ma (Tables 2 and 3, Fig. 4c). Fitzgerald et al. (2006) suggested that the true ages should be between weighted mean ages and minimum ages. We plotted the minimum ages for poorly reproduced samples together with the arithmetic mean ages (Fig. 4). In this figure, the mean AHe age of FST04, and ZHe ages of FST06 and 10 were displayed in gray color just for reference, although they have less reliable data than the others. AHe ages are younger than or comparable to the corresponding ZHe ages considering the uncertainty of 95% confidence intervals. These results are consistent because of an expected age relationship resulting from the range of closure temperatures between the two systems. Moreover, two thermochronologic studies were previously conducted in this study area; AFT ages of 100.0-82. Effective uranium (eU) ppm versus AHe grain ages (with errors indicated by ± 3σ). Two horizontal green lines show the upper and lower limits of the weighted mean ages, namely the + 95% and − 95% confidence intervals. No green lines imply that the weighted mean age was not considered meaningful because of poor reproducibility on the fore-arc side, and ZFT ages of 53.4-21.8 Ma (Ganzawa 1987) on the back-arc side (Fig. 1a). Results of our He dating show reasonable age relationships compared to these data. As to the AHe ages in Fig. 4c, older ages range from 88.6 to 43.7 Ma on the fore-arc side (FST07, 08, 09), while younger ages range from 6.2 to 0.9 Ma in the OBR (FST06, 10, 11, 12) and between 4.9 and 3.2 Ma on the back-arc side (FST03, 05) These results indicate a strong age contrast between the fore-arc side and west of the OBR.

Calculation and interpretation of denudation rates
Little radiation damage effects were observed in our samples; thus, we interpret AHe ages as cooling ages reflecting thermal histories. The AHe closure temperature at every locality is applicable to interpret such thermal histories, except for one over-dispersed age sample (FST04) ( Table 3). Thus, we computed the individual closure temperatures of the AHe system for each sample, based on the Dodson (1973) method for calculating denudation rates. The closure temperature, T c , varies depending on the cooling rate, dT/dt, in addition to the dimension of the diffusion domain (the mean half width of each sample was adopted in this study; Table 1

), a;
where E a is the activation energy (= 151.46 kJ/mol), R is the gas constant (= 8.314 J/K mol), A is the geometric factor (= 55 for sphere), τ is the time constant, D 0 is the diffusivity at infinite temperature (= 50 cm 2 /s), T s is the surface temperature (= 10 °C, every locality), t AHe is the AHe age of the sample. The calculation of closure temperatures was performed by repeatedly substituting dT/dt, τ, and T c until a stable value of closure temperature was obtained (up to ten times). Errors of T c were propagated from those of AHe ages and grain sizes. The results of the calculation of closure temperatures are shown in Table 3. On the fore-arc side, lower temperatures at ca. 50-55 °C (FST07, 08, 09) were calculated. On the other hand, higher temperatures at ca. 60-80 °C were calculated at the OBR (FST06, 10, 11, 12) and on the back-arc side (FST03, 05). The obtained closure temperatures were used to estimate mean denudation rates through geologic timescale by the following equation: where dD/dt indicates the mean denudation rate since t AHe , G denotes the geothermal gradient.
In the NE Japan Arc, geothermal gradients vary drastically with locality and the values used were extracted from Tanaka et al. (2004) and GSJ (2009) as shown in Table 3. In this study, thermal gradients were assumed to be constant temporally because it is difficult to evaluate their temporal and spatial variations over one-ten million years. Values of geothermal gradients were adopted at 20-40 °C/km on the fore-arc side, and 40-60 °C/km at the OBR and on the back-arc side based on the database of Tanaka et al. (2004). Alternatively, geothermal gradients at every locality were read on the iso-geothermal gradient map drawn at intervals of 10 °C/km published by GSJ (2009). In this calculation, we adopted averages between the upper and lower limits of contours from sampling localities were included. Their uncertainties were assigned by the contour interval. Errors of    Fig. 4 Comparison of thermal/denudation histories between the S-traverse and N-traverse. Vertical blue lines in the graphs show the boundary between the fore-arc side and the OBR/back-arc side. Numbers on the map denote the sample localities in the N-and S-traverse corresponding to the sample codes in the graphs (a, c). Pink lines show hot fingers (Tamura et al. 2002). The map was drawn using GMT (Wessel and Smith 1991) and 30 arc-second grid of the General Bathymetric Chart of the Oceans (GEBCO). Active fault traces in red lines are cited from Nakata and Imaizumi (2002). a AHe/ZHe ages and denudation rates plot along the S-traverse. Weighted mean ages and minimum ages within ± 95% confidence intervals were plotted using data from Sueoka et al. (2017) after Fitzgerald et al. (2006). Gray data for ZHe show less reliable because their grain ages are over-dispersed. b Mean denudation rates and their uncertainties along the S-traverse. These rates were reported from Sueoka et al. (2017) using geothermal gradients of Tanaka et al. (2004). Data calculated using the database of GSJ (2009) were computed in this study. c AHe/ZHe ages and denudation rates plot along the N-traverse. Weighted mean ages and minimum ages within ± 95% confidence intervals were plotted after Fitzgerald et al. (2006). Gray data are less reliable because their grain ages are over-dispersed. d Mean denudation rates and their errors along the N-traverse. These rates were calculated using geothermal gradients from Tanaka et al. (2004) and GSJ (2009). FST04 was not calculated because its weighted mean age was not adopted denudation rates were propagated from those of the ages, geothermal gradients, and grain sizes. The computed denudation rates are shown in Table 3 and Fig. 4d. On the fore-arc side, slower rates at < 0.05 mm/year were calculated because of older AHe ages (FST07, 08, 09). Hence, AHe thermochronometers on the fore-arc side should indicate the mean denudation rates from Cretaceous, before the uplift of mountains. On the other hand, faster rates at > 0.1-1.5 mm/year were detected at the OBR and on the back-arc side. Such high denudation rates should be derived by a faster cooling rate calculated from closure temperatures (60-80 °C) and younger AHe ages (6-1 Ma). Consequently, a clear contrast in denudation rates is identified between the forearc side and the west of the OBR. In particular, younger AHe ages at ~ 3-1 Ma (FST03, 10, 12) should have been affected by the strong E-W compression since 3-2 Ma. AHe ages ~ 6-5 Ma (FST05, 06, 11) have also affected but only partial age resetting is considered to have occurred under such compression since ~ 3-2 Ma. As to other possibilities for explaining the young ages, Quaternary volcanisms or recent local heating was also considered to explain the younger AHe ages. Although we managed to eliminate thermal disturbances from major Quaternary volcanism as possibilities for age resetting, it is difficult to reject these possibilities completely because the NE Japan Arc has a complex tectonic history. However, we consider that AHe ages at ~ 6-5 Ma and their calculated denudation rates should be adopted as the upper limit of denudation rates.
In calculating the denudation rates, we assumed the linear and horizontal isotherms. However, isotherms should be perturbed by some factors during mountain building process, for instance, the amplitude of surface topography, the faster uplift/denudation, the ancientry of mountain, and so on (Stüwe et al. 1994). These factors can potentially cause an erroneous calculation of denudation rates. We did not consider these effects because (a) the mountains in the study area generally have moderate widths of ca. 40-80 km and lower elevations ranging from a few hundred to ~ 1500 m, (b) we obtained slower denudation rates of 0.01-1.5 mm/year, and (c) the onset of uplift of mountains has initiated since the last few Ma. We, thus, regarded them as negligible effects on isotherm advection according to these backgrounds in this study.

Comparison of shorter-term denudation/uplift rates along the N-traverse
For creating current topographic landforms, the surface materials are subjected to vertical movements. As geomorphic fundamental, the relationships between uplift and denudation can simply be expressed as the following equation (England and Molnar 1990); Bedrock uplift is caused by tectonic and isostatic displacement/deformation, while exhumation (denudation) occurs as a result of tectonic denudation (e.g., normal faulting, crustal thinning), as well as erosion and weathering. Hence, bedrock uplift and denudation are independent processes even though they can interact with each other. In perspective, denudation should become faster as bedrock uplift increases, because topographic reliefs and slopes grow accompanied by bedrock uplift. However, bedrock uplift and denudation reach steady state, and then topographic reliefs do not change through time, a situation termed dynamic equilibrium (e.g., Ohmori 1985).
Shorter-term (< ~ 10 5 year) denudation rates have been obtained in the N-traverse based on geomorphic and geologic approaches. As an overall trend, uplift and denudation rates on the shorter-term along the N-traverse range from ~ 0.1 to 1.0 mm/year. A comparison between short-and long-term denudation/uplift rates is discussed separately in the three tectonic units described below. Furthermore, geodynamic modeling were concerned using a finite element method based on rheology for the entire NE Japan Arc (e.g., Shibazaki et al. 2008Shibazaki et al. , 2016. Shibazaki et al. (2016), provide an estimate of long-term uplift rates assuming some boundary conditions and geophysical parameters. We also compared our denudation rates from thermochronometric data with those modeling results.

Fore-arc side
Denudation rates of ~ 0.3-0.4 mm/year over ~ 10 1 year were calculated based on the amount of sedimentary loads in catchments (Fujiwara et al. 1999). Uplift rates were estimated at ~ 0.2 to ~ 0.4 mm/year over ~ 10 5 year based on the elevations and emergent ages of the fluvial/ marine terraces (e.g., Tajikara and Ikeda 2005;Okuno et al. 2014). Moreover, geodynamic modeling, using the finite element method (Shibazaki et al. 2016), provided uplift rates up to 0.4 mm/year on a 10 6 years timescale. Denudation rates at < 0.05 mm/year were obtained based on our thermochronometric data, indicating one order of magnitude discrepancy in rates between short-and long term (described later).

Ou Backbone range
Denudation rates of 0.3-0.4 mm/year over ~ 10 1 year were calculated based on the amount of sedimentary loads in catchments (Fujiwara et al. 1999). Uplift rates at < 0.6 mm/ year were obtained over ~ 10 5 year based on the elevations and emergent ages of the fluvial/marine terraces (e.g., Tajikara and Ikeda 2005), and uplift rates of ~ 0.5-0.7 mm/ Surface uplift = Bedrock uplift − exhumation (denudation).
year from displacements across the eastern margin faults of Kitakami lowland and the western margin faults of Yokote basin on 10 5−6 years timescales (Awata 1988;Ikeda et al. 2002;Doke et al. 2012). Geodynamic modeling using the finite element method (Shibazaki et al. 2016) offered uplift rates of ~ 0.4-1.0 mm/year on a 10 6 years timescale. Our denudation rates in this study were estimated at ~ 0.2-1.4 mm/year, which are consistent with the independently derived short-term rates outlined above.

Back-arc side
Denudation rates at ~ 0.4-0.5 mm/year over ~ 10 1 year were calculated based on the amount of sedimentary loads in catchments (Fujiwara et al. 1999). Uplift rates at < 0.6 mm/year were estimated over ~ 10 5 year based on the elevations and emergent ages of the fluvial/marine terraces (e.g., Tajikara and Ikeda 2005;Okuno et al. 2014), and uplift rates at ~ 1 mm/year from displacements across Kitayuri faults at 10 5−6 years timescales (Awata 1988;Doke et al. 2012). Uplift rates of ~ 0.4-0.6 mm/year were based on geodynamic modeling using the finite element method on a 10 6 -year timescale (Shibazaki et al. 2016). Denudation rates at 0.1-0.4 were obtained based on thermochronometric data, which are consistent with other methods for the short term.
On the fore-arc side, the data between 10 6−7 years from thermochronometry and < 10 5 year from other methods have one order of discrepancy. This disagreement can be explained by considering the small amount of uplift/denudation compared to the closure temperature depth of the AHe system (typically ca. > 1-2 km), even though the uplift of the fore-arc side has accelerated since the Quaternary (Ota et al. 2010). Hence, higher denudation/uplift rates should be detected in shorter-term (< 10 5 year) methods. Besides, the total amount of denudation since the Quaternary is thought to be smaller than the closure depth of AHe system. This scenario is also supported by geomorphic evidence; the Kitakami Mountains have lowrelief erosional surfaces regarded as remnants of uplifted peneplains (Nakamura 1963). Namely, following the onset of uplift, the Kitakami Mountains have experienced such a relatively small degree of denudation that the erosional surfaces formed pre-uplift are still preserved. For verifying this explanation, the application of lower-temperature thermochronometers and terrestrial cosmogenic nuclides (TCN) method is desirable.
In contrast, denudation rates from thermochronometers on the 10 6 years timescale are consistent with on the shorter-term (< 10 5 years) denudation/uplift rates for the OBR and on the back-arc side. This observation implies that the regional denudation/uplift rates have been maintained under the E-W compression stress field since the Quaternary.
By comparing our thermochronometric data with geodynamic modeling results, the measured and modeled data indicated are consistent with each other on geologic timescales. Shibazaki et al. (2016) suggested such high uplift rates along the OBR, particularly in the regions of hot fingers, correspond to high-temperature zones, implying that heterogeneous thermal structures strongly control uplift of the OBR under a compressional stress field. Based on our thermochronology results, we obtained faster denudation rates; however, it is noted that we did not collect samples from within these hightemperature zones (Fig. 4). Hence, the uplift mechanism cannot necessarily be attributed to heterogeneous temperature distributions. Further, thermochronometric investigations or parameter tunings are required to elucidate the uplift mechanism.

Comparison of thermal and denudation histories between the N-and S-traverses
Our thermochronometric results indicate an obvious contrast in thermal/denudation histories between each tectonic unit along the N-traverse. A similar contrast was also reported along the S-traverse (Sueoka et al. 2017;Fukuda et al. 2019). Integrating the results of both traverses, arc-parallel mountains in the NE Japan Arc indicate that they generally share a common thermal/ denudation history (Fig. 4). If the formation of topography in an island-arc setting is mainly caused by the subduction of an oceanic plate, then it would be possible for thermal histories of arc-parallel topographies to share common geologic features. This study has demonstrated that from two across-arc traverses, there are common thermal/denudation histories in an arc-parallel direction. Thermal/denudation histories in each tectonic unit are now compared and discussed.

Fore-arc side
Denudation rates are approximately in the same range; these rates along with the N-traverse were estimated at ~ 0.01-0.03 mm/year (Fig. 4d), and data for the S-traverse were ~ 0.02-0.03 mm/year (Fig. 4b). However, the elevation of mountains and the formation age of granites are different; the Kitakami Mountains comprise 120-110 Ma granites > 1200 m in elevation in the N-traverse; while the Abukuma Mountains consist of 110-100 Ma granites with elevations of < 600 m in the S-traverse. Differences in the geomorphic and geologic features between two traverses cannot be explained from thermochronologic data, as inferred total denudation and uplift since the Quaternary should be low as discussed in "Comparison of shorter-term denudation/ uplift rates along the N-traverse" section.

Ou backbone range
Denudation rates in the N-traverse are slightly higher (0.2-1.5 mm/year: Fig. 4d) than those in the S-traverse (0.1-1.0 mm/year: Fig. 4b). The elevation and distribution of faults are provided as examples of topographic differences between both traverses. The mean elevation of the OBR along the N-traverse (Fig. 1b) is a little lower than the S-traverse (see Fig. 1b in Sueoka et al. 2017). Moreover, the northern OBR has clear reverse faults along the foot of the mountains, whilst fault traces in the southern OBR are indeterminable near our sampling sites in both traverses. Considering the distribution of the last cooling episodes and denudation rates determined by AFT thermochronology along the S-traverse, Fukuda et al. (2019) implied that an uplift model for the OBR is probably by doming (Hasegawa et al. 2005) and not a tilted pop-up style by reverse faults (Nakajima 2013). Sueoka et al. (2015Sueoka et al. ( , 2016 showed that numerical modeling of slope development can also provide the pattern of denudation rate using the advection diffusion equation (e.g., Hirano 1972). Modeling results illustrated that the denudation pattern of doming model should increase towards the summit, but on the other hand, the tilted pop-up model should increase towards the foot of a mountain. Despite the OBR of N-traverse having obvious reverse faults, denudation rates from our AHe data (from FST06 to 11, and 10) indicate faster rates toward the summit of the OBR (Fig. 4c), thus supporting the doming uplift model. Although FST12 is here also included in the classification as the OBR, its denudation shows a little higher rate than for FST06. The locality of FST12 is around or on the boundary between the OBR and the back-arc side, and was, thus, perhaps also affected by the tectonics of the back-arc side, the Hinotodake mountains.

Back-arc side
There are two differences between both traverses; (a) maximum denudation rates in the N-traverse (0.1-0.4 mm/year: Fig. 4d) are higher than for the S-traverse (0.1-0.25 mm/year: Fig. 4b), and (b) ZHe ages ranging over 80-10 Ma were obtained in the N-traverse (Fig. 4c), while those in the S-traverse ranged over 30-10 Ma (Fig. 4a). One of the fundamental causes of (a) is due to temporal variations in the initiation of uplift on the backarc side. Mountains in the Dewa hills have been uplifted non-simultaneously from ~ 5 to 3 Ma (Moriya et al. 2008). Another cause is differences in elevation; the Iide and Asahi Mountains in the S-traverse have high elevations at > 2000 m, while the Shirakami and Taihe Mountains are at an elevation < 1500 m. These observations can be explained as follows: denudation rates for these mountains were almost in the same range, but the timing of initiation of uplift was not simultaneous as suggested by Moriya et al. (2008). The Iide/Asahi and Shirakami/Taihe Mountains, thus, have different present-day elevations. Although the long-term uplift rates or the timing of initiation of uplift on the back-arc side are poorly understood, AHe ages and denudation rates reflect recent tectonics after a few Ma. In the S-traverse, Fukuda et al. (2019) suggested that denudation rates on the back-arc side indicated different values between thermal inverse modeling of AFT method and previous AHe data (Sueoka et al. 2017). Modeling results offered more precise and faster denudation rates of > 1 mm/year (Fukuda et al. 2019), while such rates based on apparent AHe data indicated 0.1-0.3 mm/year (Fig. 4b). Similar approaches employing thermal inverse modeling based on AFT data are desirable for also the N-profile. Next, moving on to (b), the timing of formation of granites is different; all granites in the N-traverse were formed in the Cretaceous around 120-100 Ma, whilst some granites on the back-arc side of the S-traverse are Cretaceous-Paleogene (100-60 Ma) (e.g., Yokoyama et al. 2016). Another possible explaination for the different ZHe ages between the two traverses is that the amount of subsidence in both traverses should be different during the time of the Sea of Japan opening. Okada and Ikeda (2012) suggested that based on seismic reflection data, the amount of extension and contraction since the Miocene varied from ~ 10 to 60 km even in the backarc side. This variation of subsidence during the opening of the Japan Sea probably affects the different ZHe ages between two traverses.
In summary, the back-arc side has wide tectonic, geologic and topographic variation even within a single arc. These observations imply that arc-along tectonics are probably dominant, such as concentration of deformation around the high-temperature zones, namely hot fingers (Tamura et al. 2002). E-W mountain building on the back-arc side should have, thus, occurred under an N-S component of compressive stress (Fukahata 2016). Meanwhile, across-arc tectonics, such as the E-W compression derived from the oceanic plate subduction, does not prevail on the back-arc side, unlike in the OBR.

Conclusions
Apatite and zircon (U-Th)/He thermochronometric mapping across the northern NE Japan Arc, provides new insights into the tectonic history and the process of mountain building. Moreover, we compared thermochronometric data for the N-traverse produced in this study and that previously published for the S-traverse to evaluate the trends in the thermal/denudation histories across an island arc. Consequently, we verified the contrast of thermal/denudation histories in the N-traverse as well as the previous studies of S-traverse, which implied