The Thermal Evolution of Western Norway Based on Multi‐Sample Models of an Elevation Transect: Implications for the Formation of High‐Elevation Low‐Relief Surfaces on an Elevated Rifted Continental Margin

The post‐Caledonian thermal and geomorphological evolution of onshore Western Norway is poorly understood, including the formation and age of the high‐elevation low‐relief surfaces seen across the Norwegian landscape. We present new apatite fission track (AFT) and (U‐Th‐Sm)/He analyses from an elevation transect (ET) covering ∼1,800 m vertical distance below a high‐elevation low‐relief surface in the inner Nordfjord. The AFT ages increase with elevation from 159 ± 11 Ma to 256 ± 21 Ma and apatite (U‐Th‐Sm)/He ages increase with elevation from 80 ± 4 Ma to 277 ± 15 Ma. In order to test different possible thermal evolutions, we present the first multi‐sample thermal history models from Norway using HeFTy combining both AFT and (U‐Th‐Sm)/He ages along the ET, refining available thermal history models for the area considerably. The best modeling results are found for a thermal evolution with slow cooling throughout the Mesozoic and increased cooling rates from the Late Cretaceous until present, indicating a Cenozoic age for the low‐relief surface at the top of the transect. The models also allow for cooling to surface conditions in the Late Jurassic, but such an evolution must have been followed by rapid burial by 1.5–3 km Cretaceous sediments, and by re‐exhumation in the Cenozoic, indicating that the low‐relief surface cannot represent a simply uplifted Jurassic or Cretaceous peneplain. We compare our results with multi‐sample models from the wider North Atlantic region, supporting previous findings of Cenozoic exhumation and landscape forming processes within that region.


Introduction
Elevated passive continental margins (EPCM) are important features which occur on all continents and have been studied for decades, but the geodynamic mechanisms and processes behind their formation and maintenance remain controversial (e.g., Green et al., 2018).Low temperature thermochronological methods, such as apatite fission track (AFT) and apatite (U-Th-Sm)/He analysis, are tools that have long been used to constrain the cooling and denudation history of EPCMs, delivering important constraints for passive margin evolution (e.g., Wildman et al., 2019).
The EPCMs of the North Atlantic region (Greenland, British Isles, Norway) represent prime examples where the tectono-morphological evolution is highly debated: the core of the debate centers around whether the high altitude, low relief landscapes on both sides of the North Atlantic are remnants of uplifted peneplains of various ages (e.g., Green et al., 2013Green et al., , 2022;;Hall et al., 2013;Japsen et al., 2006Japsen et al., , 2018;;Lidmar-Bergström et al., 2013), or whether the highland plateaus are the result of glacial erosion in the Quaternary following long-lasting erosion and isostatic uplift subsequent to the Caledonian orogeny (Nielsen et al., 2009(Nielsen et al., , 2010;;Pedersen et al., 2018).Interestingly, low temperature thermochronology has been used to support both of the two contrasting models.AFT data have been interpreted to either show repeated phases of uplift, peneplanation and reburial since the Caledonian orogeny until the present (Green et al., 2022;Japsen et al., 2018).Quite differently, the data have been interpreted to show continuous cooling without reheating since the Caledonian orogeny (Johannessen et al., 2013;Leighton, 2007;Nielsen et al., 2009).One reason for these highly differing interpretations is the degree of freedom when modeling thermal histories based on single sample AFT data, where a wealth of different thermal histories still fit to the measured data, in particular hampering the understanding of the cooling and exhumation history during the Cenozoic.
One approach to reduce the degree of freedom and to derive more constrained thermal histories based on low temperature thermochronology is to sample elevation transects (ET), where the vertical spatial separation between the samples from an undisturbed rock column is used to constrain the thermal evolution of the entire transect (e.g., Fitzgerald et al., 1995;Gleadow & Fitzgerald, 1987;Gallagher et al., 2005;Fitzgerald & Malusà, 2019).In addition, AFT data can be combined with other low thermochronological methods, such as (U-Th-Sm)/He analysis of zircon or apatite (e.g., Reiners & Brandon, 2006;Wildman et al., 2019).Inverse thermal modeling of several samples in an ET together (multi-sample modeling) reduces the risk of overinterpreting the thermal history of a sample, which can be a problem with single-sample modeling (Gallagher et al., 2005;Johnson & Gallagher, 2000), and it makes it possible to get a better understanding of the cooling history in an area with limited direct constraints and where traditional age-elevation plots give little information.
In the North Atlantic region, multi-sample inverse thermal modeling of ETs including both AFT and (U-Th-Sm)/ He ages has been conducted for the British Isles using the QTQt software (Cogne et al., 2016).These authors document a rapid exhumation pulse (1-2.5 km) during the Paleogene, which they couple with uplift and exhumation due to the arrival of the proto-Iceland mantle plume.Jess et al. (2018Jess et al. ( , 2019) ) present multi-sample inverse models of AFT and (U-Th-Sm)/He data with QTQt from the West Greenland passive margin, deriving contrasting thermal evolutions for different segments of the margin, indicating that some areas did experience considerable exhumation during the Cenozoic, whereas others probably did not.Recently, Danišík and Kirkland (2023) presented multi-sample modeling of zircon-and apatite (U-Th-Sm)/He data using the software HeFTy from West Greenland, proposing that limited (<3.5 km) erosion did occur in their study area during the Cenozoic.
Multi-sample thermal history modeling of ETs has not been conducted previously for the East Greenland or Norwegian ECPMs, resulting in only relatively loosely constrained thermal histories based on AFT and (U-Th-Sm)/He data (e.g., Green et al., 2022;Hansen & Reiners, 2006;Japsen et al., 2014;Johannessen et al., 2013;Ksienzyk et al., 2014;Redfield, Braathen, et al., 2005;Redfield, Osmundsen, & Hendriks, 2005;Rohrman et al., 1995).In this study, we present new AFT data and apatite (U-Th-Sm)/He data from a steep, structurally intact ET in Western Norway, located below a prominent low-relief surface at the top of the Skåla mountain (Figures 1 and 2).We present single sample modeling and the first multi-sample inverse thermal history modeling for the Skåla transect and for a previously published transect of Green et al. (2022) using a new release of the software HeFTy.We aim to test previously proposed differing thermal histories for the west-Norwegian margin and to propose more tightly constrained thermal models which can contribute toward solving the debate on the origin of EPCMs in the North Atlantic region.

Geological Setting and Previous Models for the Thermal Evolution of Western Norway
Our ET is located in the inner Nordfjord area in Western Norway, close to the present-day drainage divide and in the hinterland of the rifted North Sea and Norwegian Sea margins (Figure 1).The bedrock geology of Western Norway is dominated by the Proterozoic Western Gneiss Region (WGR) and overlying Caledonian nappes, which were emplaced on top of the WGR during the Caledonian orogeny (Corfu et al., 2014;Hacker & Gans, 2005;Roberts & Sturt, 1980;Røhr et al., 2004).During the collapse of the Caledonian orogen, extension was first taken up along large-scale, low-angle detachment faults belonging to the Nordfjord-Sogn Detachment Zone (NSDZ), forming Devonian sedimentary basins in the hanging wall (Figure 1; Fossen, 1992;Fossen & Dunlap, 1998;Krabbendam & Dewey, 1998;Osmundsen et al., 1998Osmundsen et al., , 2023)).By the end of the Permian, rifting of the North Sea and Norwegian Sea (Figure 1) and rift flank uplift were initiated (Roberts et al., 1995).Steep brittle faults formed, accommodating further extension (Fossen, 1992;Peron-Pinvidic & Osmundsen, 2020).A renewed period of rifting occurred in the Late Jurassic-Early Cretaceous (Bartholomew et al., 1993;Steel & Ryseth, 1990).Onshore, paleomagnetic dating, 40 Ar-39 Ar dating and K-Ar fault gouge dating have revealed periods of increased fault activity and fault reactivation during the Carboniferous-Permian, Late Triassic-Jurassic, Early Cretaceous and Late Cretaceous-early Paleogene (Braathen et al., 2004;Eide et al., 1997;Fossen et al., 2021;Hestnes et al., 2022;Ksienzyk et al., 2016;Scheiber & Viola, 2018;Tartaglia et al., 2022;Torsvik et al., 1992).studies, some also combined with (U-Th-Sm)/He data, identified offsets of ages across major faults and suggested a fault-dissected margin with downfaulting toward the offshore rift and footwall uplift of the rift shoulder (Figure 1; Johannessen et al., 2013;Ksienzyk et al., 2014;Leighton, 2007;Redfield et al., 2005aRedfield et al., , 2005b)).Based on geomorphological, thermochronological and offshore stratigraphic observations, three contrasting models of the thermal and topographic evolution have been proposed for Western Norway during the past decade.All three models are characterized by fast cooling and large-scale exhumation from the Caledonian collapse until the Carboniferous-Early Triassic (e.g., Dunlap & Fossen, 1998), but following this early fast cooling, the thermal evolutions differ: 1.One model suggests that the Caledonian topography was never reduced to sea level and that mountains existed throughout the Mesozoic, only slowly being lowered by erosion, reflected in slow cooling of the crust (Nielsen et al., 2009).In the Eocene-Oligocene, climatic changes caused an increase in erosion rates, resulting in fast cooling and exhumation until the present (e.g., Nielsen et al., 2009).Such an evolution is in accordance with the single sample AFT time-temperature models of ETs of Johannessen et al. (2013), which interpreted low Jurassic-Cretaceous cooling rates and accelerated cooling in the latest Cretaceous-Paleogene south of the Sognefjord (Figure 1).This study suggested sustained elevated topography throughout the Mesozoic and the Cenozoic based on thermal models combined with earlier published AFT and vitrinite reflectance data from the region (Johannessen et al., 2013).Similarly, Leighton (2007) used both single sample and multisample thermal AFT models (after Gallagher et al., 2005) of Southern Norway to infer fast cooling until the Triassic or Jurassic, slow cooling in the late Mesozoic and early Cenozoic, followed by rapid cooling initiated in the Neogene and lasting until the samples reached surface levels.2. A second model is characterized by significant topography in Western Norway in the Jurassic, inferred from the deposition of alluvial conglomerates in the offshore basins, and continued sediment supply to the offshore  et al., 2022;Johannessen et al., 2013;Leighton, 2007) and locations where Jurassic sediments are preserved onshore (Fossen et al., 1997;Sommaruga & Bøe, 2002).
until the Mid Jurassic, when the North-and Norwegian Sea became fully marine, and rift episodes and rift shoulder uplift (Mørk & Johnsen, 2005;Redfield, Osmundsen, & Hendriks, 2005;Redfield & Osmundsen, 2013;Steel, 1993;Sømme, Helland-Hansen, & Martinsen, 2013;Sømme, Martinsen, & Lunt, 2013).Late Jurassic sediments deposited on top of the basement in Western and Mid-Norway imply that by Late Jurassic times, at least the coastal region of Norway was exposed to the surface (<40°C), followed by burial and reheating (Fossen, 1998;Sommaruga & Bøe, 2002).A Middle-Late Jurassic (ca.160 Ma) basement paleosurface dipping ca.5°to the west is identified in seismic data offshore Western Norway, supporting the existence of a Jurassic peneplain eroded to sea level (e.g., Fossen et al., 2017).The exhumation of the basement to the surface in the Late Jurassic, followed by burial to 30-50°C in the Cretaceous, is in accordance with single-sample AFT thermal models for coastal areas of Western Norway south of Sognefjorden (Figure 1; Ksienzyk et al., 2014).3. Finally, geomorphological studies combined with thermochronological data and offshore observations have inferred the development of several peneplains, followed by reburial and subsequent exhumation, during Mesozoic and Cenozoic times (e.g., Japsen et al., 2018;Lidmar-Bergström et al., 2013;Lidmar-Bergström & Näslund, 2002).Based on a regional AFT sample set, including several ETs and boreholes, Green et al. (2022) interpreted multiple phases of exhumation, peneplanation and burial for the Breheimen region and Western Norway (Figure 1): (a) Carboniferous (311-307 Ma) exhumation and cooling from >110°C to the surface leading to an (b) Early Permian peneplain, (c) Early Triassic burial down to >110 and 90°C with renewed exhumation starting around 245 Ma leading to a (d) Middle Triassic peneplain, (e) Middle Jurassic burial down to >110°C and renewed exhumation starting around 170-167 Ma leading to a (f) Middle Jurassic peneplain, (g) Early to Late Cretaceous burial from >110 to 50°C and renewed exhumation starting around 102-92 Ma leading to a (h) mid-Cretaceous peneplain, (i) Late Cretaceous and Paleogene burial followed by Early Miocene exhumation, finally leading to (j) the formation of an Early Miocene peneplain.
We sampled ∼5 kg of rock for each sample and crushed it down to grain sizes <315 μm.To extract the apatites, we used standard separation techniques, including Wilfley table, Frantz magnetic separator, and heavy liquids (LST = litium heteropolytungstate and DIM = diiodomethane).The mineral concentrates were sieved and only apatite grains >100 μm were used for further analyses.

Apatite Fission Track (AFT)
AFT analyses were performed at the Department of Earth Science, University of Bergen (Norway).The apatites were mounted in epoxy before grinding and polishing them to reveal the central parts of the apatite grains.To reveal spontaneous fission tracks, each sample was etched in 5 M nitric acid for 20 s at 20 ± 0.5°C.The samples were irradiated at the Technical University Munich (Germany) in the FRM II research reactor with a neutron flux of 1 × 10 6 neutrons cm 2 .The neutron flux was monitored by the use of dosimeter glasses IRMM 540R (15 ppm U).To reveal the induced tracks in the mica detectors, they were etched at room temperature for 20 min with 40% hydrofluoric acid.
All samples were analyzed using the External Detector Method (EDM).The EDM method measures induced tracks on an external detector to calculate the uranium content of each grain in the area where spontaneous tracks were counted (Gallagher et al., 1998).We used two different automated microscope systems: an Olympus BX51 microscope/FT-stage software setup (Dumitru, 1993), and a newer Zeiss AxioImager Z2s microscope/Autoscan software setup.
As expected, the EDM results of the two systems overlap well within their uncertainties.We have used only the data acquired with the former setup for further analysis and modeling, but the results from both systems and further information on the comparison can be found in Hestnes et al. (2024).
Fission tracks were counted at 1,250× magnification whilst etch pit diameters (Dpar; Donelick et al., 2005) and confined track lengths were measured at 2,000× magnification.The Dpar is measured parallel to the crystallographic axis and used as a measure for the bulk chemical composition of the apatite grain (Fitzgerald & Malusà, 2019).We did five Dpar measurements for each grain counted and for each grain where one or more track lengths were measured.A zeta calibration factor (Hurford & Green, 1983) of 260.7 ± 5.8 Ma (Hestnes) was used when calculating the fission track ages.
We calculated all fission track ages using the Isoplot R online software (Vermeesch, 2018).All ages and other values are given with uncertainties of 1 sigma.
Track length measurements were corrected with a calibration factor of 1.020561 and a Dpar calibration factor of 1.200328 after Ketcham et al. (2015).

Apatite (U-Th-Sm)/He Analysis
(U-Th-Sm)/He analyses were performed at the Geoscience center, University of Göttingen (Germany).For each sample, we handpicked 4-5 apatite crystals under binocular and petrographic microscopes.During the picking, we targeted apatites free of cracks and inclusions, and with well-defined external geometries.However, it was not possible to detect chemical zonation, which is common for apatites of the studied formations.Each apatite was photographed, dimensions measured and individually packed in a platinum capsule.The platinum capsules were then degassed under high vacuum by heating with infrared diode laser to determine the 4 He content.The extracted gas was purified with a SAES Ti-Zr getter at 450°C and analyzed with a Hiden triple-filter quadrupole mass spectrometer equipped with a positive ion counting detector.Re-extraction was performed for every sample to ensure a quantitative helium extraction.After the He-analysis, the platinum capsules were retrieved to further analyze the U, Th and Sm content.The apatite crystals were dissolved in nitric acid and spiked with calibrated 230 Th and 233 U solutions.The actinide concentrations were determined by the isotope dilution, and the Sm, Ca, P and REE concentrations were determined by an external calibration method using an iCAP Q ICP-MS equipped with an APEX microflow nebulizer.The long-term averages of the standards Durango and Limburg apatites are given in Hestnes et al. (2024).To all the extracted apatite ages, we applied an alpha ejection correction (F T correction) following the procedure of Farley et al. (1996).

Thermal History Modeling
Thermal history modeling combining both AFT and (U-Th-Sm)/He data was done using the HeFTy v2.1.7 software (Ketcham, 2005).During the AFT modeling, we used the annealing model of (Ketcham et al., 2007b), etch pit diameters (Dpar) were used as kinetic parameters (Donelick et al., 2005), and the confined track lengths were corrected by c-axis projection (Ketcham et al., 2007a).The radiation damage accumulation and annealing model after (Flowers et al., 2009) was used during the modeling of (U-Th-Sm)/He data.
We applied traditional single sample-modeling, but the recently released v2.1.4version of the HeFTy software also includes new capabilities for multi-sample modeling, where samples with known relationships to each other are combined into one model (Ketcham et al., 2018).For ETs, the modeling is done in time-depth (t-Z) space, which is then converted to time-temperature (t-T) space using a 1D thermal model (Ketcham, 2022).The highestelevation sample of the ET functions as the control sample, and the other samples in the transect displace relative to it.We used the weighted mean path for each sample in the ET to compare the multi-models.The stratigraphic relationship between the samples is set to Nonconformity since the ET consists of crystalline basement not affected by depositional systems and the inheritance between samples is set to Parallel, which specifies that all samples underwent the same unroofing history.
The multi-sample modeling function also allows testing for topographic development and tilting.Tilting allows the vertical distance between samples to change and is defined as degrees of rotation around the control sample.Topographic development is specified using a number between 0 and 1, where 0 is no topographic development (same topography at the start and end of the model run) and 1 represents full topographic development from a peneplain (peneplain at start of model, present-day topography at end of model).In the case of an ET, where all samples are collected at the Earth's surface, full topographic development implies that the temperature difference between samples will be controlled by the geothermal gradient at the start of the model but by the atmospheric temperature gradient at the end of the model, thus allowing samples to converge at temperatures.Both topographic development and tilting occur over finite time intervals, which can be independent.Initiation and cessation are controlled by constraint boxes; thus, one pair of constraint boxes allows for variation in the beginning and ending of tilting, and another set (or possibly the same pair) allows the program to vary the timing of topographic development.Currently, the software only allows for one episode of tilting, but topographic development can be distributed across multiple constraints.If no ending constraint is specified for topography or tilting, it is assumed to be present-day.All single and multi-sample models were run using the controlled random search algorithm (Ketcham, 2022).The new versions of HeFTy also differ from previous versions (v1) in calculating a combined goodness of fit (GOF) that incorporates all statistical tests used, rather than using minima and averages of individual GOFs.This was done to make test results more consistent with their informal classifications of "acceptable" and "good" (Ketcham, 2005).An acceptable model is one that does not fail a 95% confidence test (GOF > 0.05), and a good model fits better than expected for a random sample from the set of correct solutions (GOF > 0.5), marking a resolution limit.Modeling scenarios that result in good fits may be considered as fitting the data better than acceptable ones, but that should not be considered the only criterion in interpretation, as GOF calculations rely upon the fidelity of the individual measurement uncertainties, which are often underestimated (e.g., Flowers et al., 2022).Notably, an acceptable fit to an alternative geological hypothesis means that the data do not rule out that hypothesis, and consistency with independent data may make such a hypothesis preferable to one that fits the data somewhat better.

AFT Ages
We collected 12 samples along the slope of the Skåla mountain (1,841 masl), one sample for every 100-150 m (Figure 2).The elevation difference is 1,778 m (Figure 2a), while the horizontal distance between the lowermost and topmost samples is 4,347 m (Figures 2b and 3).The topmost sample of Skåla comes from a pronounced lowrelief surface (Figures 2c and 2d), which is commonly interpreted as representing a peneplain formed close to the sea level (Lidmar-Bergström et al., 2013).The Skåla mountain consists of a homogenous monzonitic augen gneiss that shows a variably developed ductile foliation (Figures 2e and 2f).No indications of brittle fault zones or pronounced lineaments, representing the surface expression of faults-and fracture zones or tectonic boundaries, have been observed along the transect, and the ET is therefore considered to be structurally intact.
The apatites from our samples show varying quality.Many apatites are zoned and/or cracked and many were not suited for AFT analysis due to a high density of dislocations.For each sample, we chose 20-40 crystals for analysis.Table 1 and Hestnes et al. (2024) show the results of all EDM analyses.
The ages obtained show a general increase with elevation, where the lowermost sample yields a central age of 159 ± 11 Ma, and the uppermost sample has an age of 256 ± 21 Ma (Figure 4a, Table 1).The average uranium content of the analyzed samples is generally low and varies between 3 and 12 ppm (Figure 5a, Table 1).The mean Dpar values vary from 1.57 ± 0.12 μm to 1.84 ± 0.12 μm (Figure 5b and Table 1).
We measured confined track lengths for eight of the samples (Figure 2); single track length information for each sample can be found in Hestnes et al. (2024).For sample VAH_08, VAH_10, VAH_14 and VAH_17 we did not observe any confined track lengths due to the generally low U content (Table 1).The mean track lengths (MTL) vary from 11.36 ± 1.87 μm to 12.52 ± 1.52 μm (Figure 4b and Table 1).There is a weak trend of increasing mean track length with elevation, but all analyses overlap within 1σ uncertainty (Figures 2 and 4b).With higher elevation, the track length distributions narrow (Figure 2).The kernel distributions of the track lengths show a weak bimodal shape with the trend decreasing toward the higher elevations (blue line in track length histograms, Figure 2).

Apatite (U-Th-Sm)/He Ages
We chose four samples along the Skåla ET for (U-Th-Sm)/He analysis (Figure 4c).Four apatite crystals were dated per sample, with the single grain results shown in Figure 4c and Table 2. From the 16 analyzed crystals, two apatites from sample VAH_15 showed U and Th concentrations below the detection limit, resulting in large uncertainties (1σ > 30%).These two ages are marked gray in Table 1 and are not included in the sample unweighted average age, shown in any figures or used for further analysis.The remaining 14 single grain ages range from 80 ± 4 Ma to 277 ± 15 Ma with the youngest ages at the base of the ET and the oldest ages at the top (Figure 4c).For each sample, the dispersion of single grain ages is expressed by the 1σ sample standard deviation.
For the four samples in this study, the 1σ sample standard deviation is 13.9% (VAH_06), 1.9% (VAH_09), 25.3% (VAH_15) and 8.8% (VAH_18).Because of the known partial annealing/retention zones for AFT (∼120-60°C) and (U-Th-Sm)/He (∼70-40°C, depending on chemical composition, cooling rate and radiation damage density; Reiners & Brandon, 2006), AFT ages are generally expected to be older than (U-Th-Sm)/He ages in a sample where both analyses were performed.For the four samples in this study dated with both methods, all except VAH_18 reveal a central AFT age, which is older than the (U-Th-Sm)/He ages (Figures 4a and 4c).

Thermal History Modeling
In the following, we present our modeling approach as well as the results from the thermal history modeling of the Skåla ET as and the Jotunheimen transect of Green et al. (2022).

Modeling Approach: Transferring Geological Evolution Into Thermal Models
In order to test whether our newly acquired thermochronological data from the Skåla transect and the Jotunheimen profile from Green et al. (2022) are compatible with previously proposed thermal and exhumation histories for Western Norway (Green et al., 2022;Japsen et al., 2018;Johannessen et al., 2013;Ksienzyk et al., 2014;Rohrman et al., 1995), we set up three differing sets of modeling scenarios based on available geological information and assumptions: two end-member cases (Figures 6a and 6c) and an intermediate case (Figure 6b).Note that in addition to these three possible thermal evolutions, we tested a variety of additional model setups to explore alternative possible thermal histories that fit our data, but we think that the three set-ups presented here well illustrate the degree of freedom the data allow.
We based the initial constraints of all our models on higher-temperature thermochronology data from previous studies in the region: within the WGR, mica 40 Ar/ 39 Ar ages (interpreted to represent cooling through ∼450-400°C) are ∼400-375 Ma (Hacker, 2007;Root et al., 2005;Walsh et al., 2007Walsh et al., , 2013;;Warren et al., 2012;Wiest et al., 2021;Young et al., 2011), and models of 40 Ar/ 39 Ar K-feldspar data indicate cooling of the WGR through 400°C around 390-330 Ma and through 200°C around 310-230 Ma (Walsh et al., 2013).For this study, we assume an initial steady-state geothermal gradient of 15°C/km for Western Norway, as also used by Green et al. (2022).We also investigated models with an initial steady-state gradient of 25°C/km and a gradient that varies in time from 25°C/km until 250 Ma to 15°C/km from 250 to 0 Ma by changing the basal heat flux.Neither of the latter scenarios significantly changed the model output.We used relatively broad initial constraints in our models based on the mica 40Ar/39Ar ages; time = 400-330 Ma and depth = 26-30 km (∼400-450°C; Figure 6a).
The end constraint in the single-sample models is based on the annual average surface temperature, that decreases with increasing elevation from 5°C to 6°C.In multi-sample modeling, the surface temperature of each sample is determined by combining the Mean Sea Level (MSL) temperature and the atmospheric lapse rate (°C/km).In the inner Nordfjord, the MSL temperature is set to 5°C based on present-day average annual temperatures and the atmospheric lapse rate to 5.5°C/km based on the changes in temperature with altitude in the region.
If no further external constraints are added than those mentioned above, HeFTy will look for paths that fit the data assuming continuous cooling between the initial and end constraints.If the program is required to test additional events, such as burial and reheating, additional constraints need to be added.To model the three main geological hypotheses proposed for Western Norway as described in Section 2, we use the following external constraints (Figure 6): Geochemistry, Geophysics, Geosystems  Note.Term, Crystal terminations; Dim, Crystal dimensions; Tot, Total crystal length; Pri, Length of crystal prism; W, Width of crystal.Amount of helium is given in nano-cubic-cm in standard temperature and pressure.Amount of radioactive elements are given in nanograms.Ejection correct.(Ft): correction factor for alpha-ejection (according to Farley et al., 1996;Hourigan et al., 2005).Uncertainties of helium and the radioactive element contents are given as 1σ. in relative error %.Uncertainties of the radioactive element concentrations are ca.10% (due to the high uncertainty in the crystal mass estimation).Uncertainty of the single grain age is given as 1σ in % and in Ma and it includes both the analytical uncertainty and the estimated uncertainty of the Ft.Uncertainty of the sample average age is 2 standard error.as (SD)/(n)1/2; where SD = standard deviation of the age replicates and n = number of age determinations.At the calculation of the ejection correction factor (Ft) the shapes of the crystals were approached by hexagonal prismatic faces truncated by pyramidal faces and a minor base plate {0001}.The number of terminations of the crystals were also considered at the calculation of the proportion of the surface that is affected by the alpha-ejection.For mass calculations we used the specific gravity of 3.2 g/cm 3 .
1. To test for continuous cooling throughout the post-Caledonian period, we use only the initial and end constraints described above (Figure 6a) and topographic development from the start of the model.2. To test for Jurassic cooling to surface or close to surface temperatures (e.g., Fossen, 1998;Sommaruga & Bøe, 2002), we add a constraint box close to the surface in the Late Jurassic (160-150 Ma, blue solid box, Figure 6b).By adding an additional constraint box (blue stippled rectangle, Figure 6b), we test possible reburial.By reducing the size of the constraint box and manually moving it to different temperatures and ages, we test for the boundary conditions of timing and depth of reburial accepted by the data input.The topographic development is set to start from the initial constraint.3. To test for repeated episodes of exhumation, peneplanation and reburial, we added constraint boxes according to the model suggested for the Jotunheimen transect by Green et al. (2022, their Figure 8a).Based on the estimated paleotemperatures for the high elevation samples of the transect and the suggested peneplains for the region, the following events were interpreted (Figure 6c): development of a sub-Permian Peneplain (300-280 Ma), burial to 130-120°C in the Middle Triassic (250-240 Ma), followed by cooling/exhumation and the formation of a Late Triassic peneplain (235-220 Ma), renewed burial to ∼90-80°C in the Middle Jurassic (175-160 Ma), and renewed cooling/exhumation leading to a Late Jurassic peneplain (165-150 Ma), burial to ∼65-60°C in the mid-Cretaceous (105-90 Ma), the development of a Late Cretaceous peneplain (95-85 Ma), burial to ∼40-35°C in the Early Miocene (24-20 Ma) with subsequent start of cooling/exhumation to surface conditions.As suggested by Green et al. (2022), it is not assured that all cooling episodes led to cooling to surface temperatures.Therefore, we allowed the "peneplain" constraint-boxes to stretch from the surface to 2 km depth.The topographic development is set to start from the initial constraint.
The general setup is the same for all models (Figure 6a) except that topographic development and tilting can be defined in the multi-sample model.We tested for minor Permian tilting related to rift activity, but this caused no obvious change to the modeling results.Tilting is therefore not included in the models we present here and is not discussed further.

Skåla Elevation Transect
In order to illustrate the difference between traditional single-sample models and multi-sample models, we modeled each sample of the Skåla ET both individually and together in a multi-sample model, using the simplest of the three modeling approaches (Figure 6a).

Single Versus Multi-Sample Models
For single-sample modeling, it is possible to model all AFT and (U-Th-Sm)/He single ages from each sample together, except for sample VAH_18, where the AFT age is younger than the (U-Th-Sm)/He single ages and the model does not find acceptable paths if both AFT and (U-Th-Sm)/He ages are used as input.For multi-sample modeling, it is possible to model 10 out of 12 AFT ages, and 10 out of 14 single (U-Th-Sm)/He ages together (Figures 4 and 7; we started with trying to model all samples together, and successively removed problematic samples, i.e., if no acceptable paths were found).One approach to model all data points together could be to increase the uncertainty on problematic input samples until the data points can be modeled together, but we prefer not to do this in order to explore the degree of freedom the data points allow as they are.Note that AFT samples 8, 10, 14 and 17 do not have measured track lengths and they thereby contribute less to constraining thermal histories.
There are many potential reasons why some data points do not fit into a common thermal model.The two AFT ages which do not fit into the multi-sample model are VAH_07 and VAH_18, which are both younger than the AFT ages above and below (Figure 4).Both show low U and weakly zoned grains, which can contribute to excess dispersion, and have ages that contrast with adjacent samples (VAH_08 and VAH_19) over fairly short distances without there being a recognized intervening structure.The VAH_18 AFT age is younger than all four AHe ages, three of which reproduce well, so we considered the latter to be more reliable.The four (U-Th-Sm)/He ages which do not fit into a common model come from the oldest grain in VAH_6, the two grains of VAH 15, and the oldest grain in VAH_18.Grain zonation could possibly contribute to the relatively large dispersion in (U-Th-Sm)/He single grain ages for these samples, together with other factors leading to (U-Th-Sm)/He single grain age dispersion in slowly cooled terrains (e.g., Recanati et al., 2021 and references therein).We explored the influence of grain zonation on the (U-Th-Sm)/He dates for these samples by using the zonation modeling function in HeFTy, which shows that the two old grains in VAH_06 and VAH_18 easily can become as young as the three other dates in the two samples by inserting a weak zonation with a U-and Th-rich core and a U-and Th-poor rim, which was partly observed in the apatite grain mounts.For the two ages from sample VAH_15, one has to assume an opposite zonation for the two grains in order to converge the ages, and since we do not know which zonation is more common, both ages are excluded from thermal history modeling.In total, the multi-sample models include 20 out of 26 data points covering two thermochronological methods, which is much more than in previously published thermal models from the region.For comparison, the single-sample models are presented with the same input data as the multi-sample models (Figure 7).
All single sample models show relatively fast cooling from the initial constraint until the Permian-Triassic (Figure 7a).From the Triassic onwards, most models show slow cooling until the late Mesozoic and renewed increased cooling during the Cenozoic (Figure 7a).In contrast, the multi-sample model needs to find a common cooling history working for the input data of all samples (Figure 7c).The resulting model shows fast cooling until the Permian (>240 Ma), followed by slow cooling from the Permian until the Late Cretaceous, when renewed increased cooling starts at ca. 80 Ma (Figure 7d).In the multi-sample model, a composite-probability scheme that combines the GOF of each piece of data into a single value is used.

Testing Geological Hypotheses With Multi-Sample Models
When systematically testing the three different hypotheses with the different constraint boxes as shown in Figure 6, only two of the three hypotheses give good/acceptable model paths during multi-sample modeling: 1. Modeling hypothesis 1 assumes cooling following the Caledonian collapse with no possibility to reheat (Figure 6a).The model produces both good and acceptable paths (Figures 8a-8d).The result for the topmost sample of the transect (the control sample) shows fast cooling until the Permian, followed by somewhat slower cooling until a distinct change in cooling occurs in the mid Triassic at ∼3 km depth (Figure 8a) and temperatures of ∼50-40°C (Figure 8b).The sample remains at these conditions until Late Cretaceous times, when the cooling rate suddenly increases again (Figure 8a).The topmost sample thus enters the PAZ in the late Carboniferous and the lowermost sample leaves the PRZ in the Paleocene-Early Eocene (Figure 8c).The model still produces good paths when using a constraint box, which forces the change from slow to fast cooling into the Paleocene, but the increase in cooling rate cannot be pushed to later than ∼60 Ma.In this scenario, the samples still leave the PRZ and the PAZ by the Paleocene-Early Eocene, as described above.2. Modeling hypothesis 2 assumes fast cooling to shallow crustal levels (<2 km) in the Late Jurassic (165-150 Ma), followed by reburial in the Cretaceous (Figure 6b).The model only produces acceptable paths but no good paths (Figures 8e-8h).The best-fit path for the top of Skåla (VAH_19) shows fast cooling until the Early Permian followed by slower cooling until the Late Jurassic (Figure 8e).In the Late Jurassic, the top of Skåla reaches ∼30°C before quickly starting to reheat to ∼50°C (Figure 8e).During the cooling in the Late Jurassic, all samples of the transect leave the PAZ, and the three topmost samples leave the PRZ (Figure 8g).With a geothermal gradient of 15°C/km, it would mean that the top of Skåla would be at ∼2 km depth in late Jurassic times followed by reburial to ∼3 km depth in the Cretaceous.The three lowest samples of the transect re-enter the PAZ, giving a weak bimodal shape to the modeled track lengths (Figure 8h).We also tested if the model would allow for shallower and/or later reburial by changing the constraints of reheating.This exercise shows that the reheating must reach temperatures between 40 and 60°C (∼3-4 km depth) for the model to work, and the model gives paths which have a higher GOF if the reheating happens in Early Cretaceous times and not later.We also tested whether the cooling event in the Late Jurassic had to be followed by reheating by removing the reheating constraint from the model (Figure 7b).By doing this, the model stopped producing paths, showing that reheating is needed.3. Modeling hypothesis 3 as proposed by Green et al. (2022) assumes repeated episodes of cooling, peneplains and reheating (Figure 6c).The model does not find any paths that fit the data under these conditions.

Jotunheimen Elevation Transect of Green et al. (2022)
Other studies in Western Norway have also sampled ETs (Andriessen, 1990;Green et al., 2022;Johannessen et al., 2013;Leighton, 2007;Rohrman et al., 1995), but only Green et al. (2022) have made their AFT raw data available for thermal modeling, and none of the studies include multi-sample time-temperature inverse modeling.
The study by Green et al. (2022) contains an extensive elevation profile in Jotunheimen, consisting of 12 samples with the lowest samples at 5 masl and the highest at 2090 masl collected over a horizontal distance of 17.5 km (Figures 1 and 3).The topmost sample (GC970-7) of the Jotunheimen transect comes from a low relief surface interpreted as a peneplain.(U-Th-Sm)/He data are not available from the Jotunheimen transect.Following the same multi-sample modeling procedure as for the Skåla transect, we modeled the Jotunheimen profile in order to see whether the data allow for similar cooling histories.The models for the Jotunheimen ET were run with the same setup and input data as for the Skåla ET, except for the kinematic parameter input.For the Jotunheimen data set, Cl (wt%) was used as the kinematic parameter.
We first tried the same approach as for the Skåla transect, combining as many samples as possible into one thermal model.However, for this transect, only six out of 12 samples (Figure 4d) can be combined into a multi-sample inverse model that produces either good and/or acceptable thermal history paths (Figures 3 and  9; other combinations produce no paths).We then also modeled two minor sections of the entire profile together-the four top most samples and the four bottom-most samples of the ET, which occur within similar lithologies that are not dissected by faults/lineaments (Figures 3 and 9m and 9n).The results of both the combined model and the different section models are shown in Figures 9a-9n, and the results are described in the following.
When modeling the six samples of the Jotunheimen transect together with the different constraint boxes as shown in Figure 6, all the three hypotheses give good/acceptable model paths: 1. Modeling hypothesis 1, assuming cooling with no reheating (Figure 7a), results in a model producing good and acceptable paths (Figures 9a-9d).The best-fit model shows fast cooling, where the top of the transect enters the PAZ in the Late Carboniferous-Early Permian and changes to slower cooling in the Permian (Figure 9b).Since the Jotunheimen transect does not contain (U-Th-Sm)/He data, the PRZ zone is not shown in Figure 9.
The model shows relatively slow cooling until the Eocene-Oligocene, followed by a slight increase in cooling until present.The lowermost sample leaves the PAZ in the Early Cretaceous (Figure 9c).From the point when the lowermost sample leaves the PAZ, we only know that the samples need to reach surface temperatures by the present time and that the samples are not reheated into the PAZ again.2. Modeling hypothesis 2, assuming Late Jurassic cooling to surface conditions followed by reheating (Figure 7b), results in a model producing only acceptable paths (Figures 9e-9h).The best-fit model shows fast cooling, where the top of the transects enters the PAZ in the late Permian, followed by a Permian-Triassic change from fast to slow cooling (Figure 9e).For the topmost sample of the transect, the model shows slow cooling until the Late Jurassic, before a change back to very fast cooling occurred in the Middle Jurassic.The cooling to surface temperatures was followed by Early Cretaceous reheating, and the topmost sample reached a temperature of ∼50°C.The three lowermost samples re-enter the PAZ, creating bimodal modeled track length plots (Figure 9g).Maximum reburial later than the Early Cretaceous is incompatible with the model and reheating temperatures must have exceeded 40°C for the model to produce acceptable paths.With a geothermal gradient of 15°C, about ∼2.5 km of burial is required on top of the Jotunheimen transect in the Early Cretaceous to make the model work (Figures 9e and 9f).The reheating is followed by renewed cooling in the middle Cretaceous.3. Modeling hypothesis 3, assuming pulses of uplift, peneplanation and reburial (Figure 7c), results in a model producing acceptable paths (Figures 9i-9l).The best-fit model of the uppermost sample shows cooling to ∼30°C in the Permian (Figure 9j).The first reheating events in the Permian-Triassic show a fast trend of ∼3°C Myr 1 , whereas the later events in the Triassic-Jurassic, Cretaceous and Cenozoic events show first slow reheating (∼0.2-0.8°CMyr 1 ) followed by faster reheating (∼2-10°C Myr 1 ; Figure 9j).For the Early Triassic reheating, the samples are buried deeper than the PAZ, and only for the last reheating in the Oligocene-Miocene, the samples do not re-enter the PAZ (Figure 9k).The Triassic, Jurassic, Cretaceous and Neogene cooling events all showed a similar trend with fast cooling of ∼2-8°C Myr 1 (Figure 9j).The path envelopes show that acceptable paths are produced up to surface-level temperatures (Figure 9i).The modeled track length distributions show a bimodal character for all samples where the trend is weaker with elevation (Figure 9l).
Modeling the top-and bottom-section of the profile individually, only acceptable paths are produced, and the topmost block does not produce any paths for hypothesis 3 (Figures 9m and 9n).The shape of the modeled paths for hypotheses 1 and 2 is similar to the combined model.

Track Length Distributions
Confined track lengths provide important information to constrain the thermal history of individual samples (Gleadow et al., 1986).The widening of the track length histogram and the increase in 1σ for lower elevations for .The track length distribution plots show the same scale, where the x-axis shows length (0-20 μm) and y-axis show frequency (0.0-0.50).(e) Modeling hypothesis 2: Time-depth model of GC970-09 with constraints defining near-surface cooling/exhumation in the Late Jurassic, followed by reburial.(f) Timetemperature model of (e).(g) Time-temperature best-fit paths of the included samples of the Jotunheimen transect for the model in panels (e, f).(h) Modeled track length distributions as in panel (d).(i) Modeling hypothesis 3: Time-depth model of GC970-09 with constrains defining episodes of repeated cooling/exhumation and reheating/burial.(j) Time-temperature model of (i).(k) Time-temperature best-fit paths of the included samples of the Jotunheimen transect for the model in panels (i, j).(l) Modeled track length distribution as in panel (d).(m) Modeling only the top most structural block consisting of four samples of the Jotunheimen transect with hypothesis 1 (left) and 2 (right).Both hypotheses only produced acceptable paths, whereas the third hypothesis did not produce any paths.(n) Modeling the lowest coherent structural block of four samples of the Jotunheimen transect with hypotheses 1 (left), 2 (right) and 3 (bottom).All three hypotheses only produced acceptable paths.the samples of the Skåla transect (Figures 2 and 4b, Table 1) indicates that the lower samples resided longer within the PAZ.Alternatively, it could indicate that the lower samples of the Skåla transect experienced some reheating.The weak bimodality seen for the track lengths from the kernel distribution (Figure 2) also indicates either slow cooling through the PAZ or some degree of reheating (Gleadow & Brown, 2000), which is also indicated from the modeled track length distributions (Figure 8).

Geochemistry, Geophysics, Geosystems
For hypothesis 2, where the samples are reheated after Late Jurassic exhumation, the modeled track length distributions (blue line in Figures 8h and 9h) show a weak bimodal shape for the lowermost samples, similar to the trend seen in the measured track lengths (Figure 2).This is to be expected since reheating the apatites will cause already existing track lengths to partially anneal and shorten (Gleadow et al., 1986).For the best-fit paths of the Skåla transect, the reheating into the PAZ would only have affected the three lowermost samples down to ∼60-70°C (Figure 8g).The best-fit paths of the Jotunheimen transect, all except the topmost sample reheat into the PAZ up to ∼80°C (Figure 9g).The modeled bimodal track length distribution is therefore most obvious for the lowermost Jotunheimen transect samples (Figure 9h).

Single Versus Multi-Sample Thermal Models
When performing inverse modeling in HeFTy, it is important to be aware that the modeling software does not produce one right answer but attempts to investigate all possible paths given a variety of constraints.It is also important to note that the information of thermochronological data is limited and the thermal evolution is likely more complex than the resolution of a thermal model (Gallagher, 2021;Green & Duddy, 2021a).In an ongoing debate about the quality of thermal history models, people argue that the modeling software might produce unrealistic scenarios if not applied carefully (Gallagher, 2021;Green & Duddy, 2021a, 2021b).However, with multi-sample inverse modeling, we limit the possibility for data noise and the software to over-fit the data into a model.In addition, by using two different thermochronometers, we can better constrain the denudation rates and timing of rate changes (Figure 8; Valla et al., 2010).
In the multi-sample model, even though the external constraints are the same, the samples are also constrained by the neighboring below and above samples, making the search "window" narrower.The single sample models clearly give broader and more varying path envelopes than the multi-sample model.In addition, without adding additional external constrains, the resulting best-fit paths might not correlate well with the different samples during single sample modeling (Figure 7b), whereas they necessarily correlate with the multi-sample model (Figure 7d).
The multi-sample modeling tool allows testing for other external constraints, such as the start of topographic development and tilting.Both of these constraints will change the position of the samples relative to the isotherms.For example, the topographic constraint added in the multi-sample models (Figures 7c and 7d), will transition the samples from being 26°C apart under a steady-state geothermal gradient to being ∼9°C apart under the atmospheric lapse (assuming a geothermal gradient of 15°C/km).With no topographic development, they stay ∼9°C apart (except as altered by the thermal lag).This is in part because the thermal solution in HeFTy is 1D and does not yet include the reduction of topographic wavelength effects on isotherms with depth (e.g., Mancktelow & Grasemann, 1997).Including HeFTy's simplified representation of topographic development partially bridges this gap by making isotherms effectively horizontal early in the model, when samples are deep.In Figure 7d, the majority of change in the relationship between the samples in temperature through the Mesozoic is most likely due to the thermal lag, and not due to a significant change in topography.The thermal lag is an effect from fast cooling, as seen in the Carboniferous-Permian, and the abrupt change to slow cooling, as in the Permian (Figure 7d).In such a setting, it will take a while for the samples to cool due to thermal buffering.

Comparing the Skåla and Jotunheimen Elevation Transects
The Skåla and Jotunheimen ETs are located relatively close to each other on the western side of the present-day drainage divide (Figure 1).For this reason, we expect a similar cooling history for both transects.The total elevation difference, the horizontal distance, and the number of samples varies between the profiles (Figure 3).In the previously interpreted thermal history for the Jotunheimen transect, Green et al. (2022) converted AFT and MTL data to depths through time by either assuming or using measured geothermal gradients for the region.The methods employed by Green et al. (2022) as described by Green et al. (2013Green et al. ( , 2018) ) are the subject of an ongoing debate (Gallagher, 2021;Green & Duddy, 2021a, 2021b;Green et al., 2019;Jess et al., 2019Jess et al., , 2020)).Diving into the technical aspects of this debate is outside the scope of this paper, and only the results of our multi-sample modeling approach are discussed in the following.
For the modeling of both Hypotheses 1 and 2, both transects show quick cooling from the initial constraint in the Devonian until about Permian or Jurassic times (depending on the tested model) (Figures 8 and 9), which we relate to Caledonian collapse, extensive denudation and active deformation along major extensional shear zones, such as the NSDZ (Figure 1; Fossen & Dunlap, 1998), and subsequent regional brittle fault systems related to offshore rifting and rift flank uplift (Figure 1; Fossen, 2010;Fossen et al., 2021).
Modeling hypothesis 1 (Figure 6a) reveals a similar trend for both the Skåla and the Jotunheimen transect of entering the PAZ in the late Carboniferous-early Permian (Figures 8c and 9c).Even though the Jotunheimen transect reaches higher altitudes (2,090 masl) than the Skåla transect (1,841 masl), the uppermost samples of the Geochemistry, Geophysics, Geosystems 10.1029/2023GC010986 HESTNES ET AL.
Jotunheimen transect could not be modeled together with the lower samples and the highest sample included in the multi-sample model is at a lower elevation (GC970-9, 1,510 masl).The topmost sample of the Skåla transect is located at cooler temperatures than the topmost modeled sample of the Jotunheimen transect (stippled line, Figure 9c), which might simply be explained by the difference in altitude between the two samples.A difference between the two ETs is that the track length distributions of the individual samples from Green et al., 2022 (Figure 9), mostly show "steady cooling" pattern from top to bottom, whereas the lower Skåla data feature track length distributions implying they stayed in the PAZ longer and also cooled later (Figure 2).The lack of (U-Th-Sm)/He-data in the Jotunheimen transect, which in the Skåla transect shows ages down to the Late Cretaceous, might be the reason why the Jotunheimen transect shows continuous cooling and does not show a clear Late Cretaceous change from slow to fast cooling (Figure 9c).Therefore, the difference in the models might not represent a true geological difference in cooling history.
For the modeling of hypothesis 2 (Figure 6b), both models show similar best-fit paths, with Late Jurassic cooling to near-surface temperatures, followed by burial in the Early Cretaceous to 40-70°C.Similar to hypothesis 1, the topmost sample of the Skåla transect is generally at cooler temperatures than the topmost modeled sample of the Jotunheimen transect (Figure 9g), which might be due to the elevation difference between the two samples.Both models also leave the PAZ in the Late Modeling hypothesis 3 (Figure 6c) is only possible for six out of 12 samples of the combined Jotunheimen model, and the four samples of the bottom block-it does not fit the data of the four top-most Jotunheimen samples (Figure 9) and not the samples from Skåla.The hypothesis of repeated uplift, peneplanation and reburial is mainly inferred from the presence of mapped paleo-surfaces throughout Scandinavia (e.g., Green et al., 2022;Lidmar-Bergström et al., 2013).The paleosurfaces are interpreted to represent regional erosion surfaces formed close to the sea level and are used as key constraints in the models.The formation process behind and the age of these paleo-surfaces are, however, highly debated (Chalmers et al., 2010;Egholm et al., 2009Egholm et al., , 2017;;Hall et al., 2013;Japsen & Chalmers, 2022;Nielsen et al., 2009Nielsen et al., , 2010)).As recommended by Gallagher (2021), if good and certain geological constraints are not present, one needs to assess how the data fit a thermal model both with and without the constraints.Based on the lack of well-constrained evidence for repeated peneplains in the inner Nordfjord, and the fact that the Skåla data do not fit such a hypothesis 3 model, we argue that such an evolution is less likely based on the presented low-temperature thermochronological data and thermal modeling.
When sampling ETs for thermochronological studies, especially when the aim is to combine the samples in a multi-sample model, the choice of location is important.The Skåla transect, represented by a single lithology and being structurally intact, shows the expected increasing age with elevation and most samples can be fitted into the same multi-model.For the Jotunheimen transect, there is a larger scatter in age with elevation (Figure 4d) and the reason why only six of 12 samples fit a common model could be the sampling strategy that crosses both different lithologies, regional shear zones and valleys possibly representing faults (Figure 3).Sampling across major valleys or lineaments could sample blocks with different tectonic histories that should be taken into account during modeling (Fitzgerald & Malusà, 2019).

Geological Implications of the Inverse Thermal Models and Consequences for the Age of High-Altitude Low-Relief Surfaces in the Study Area
Fast cooling and exhumation of the rock column from the Caledonian collapse until the Carboniferous-Permian is reflected in all models of this study, as also previously shown by 40 Ar/ 39 Ar geochronology and low temperature thermochronology (Hacker, 2007;Johannessen et al., 2013;Ksienzyk et al., 2014;Leighton, 2007;Rohrman et al., 1995;Root et al., 2005;Walsh et al., 2007Walsh et al., , 2013;;Warren et al., 2012;Young et al., 2011).Green et al. (2022) suggest that by Late Carboniferous times, the landscape was reduced to a peneplain extending across Fennoscandia (Figures 9i-9k;Green et al., 2022).The oldest samples included in either the Skåla or the Jotunheimen thermal models postdate such an event, and low temperature thermochronology is not able to resolve this early history.If a sub-Permian peneplain existed, it must have been reburied to heat the samples to temperatures higher than the PAZ (Figure 9k).
The onset of Permian rifting affected a wide region of the Norwegian continental lithosphere.The Oslo rift was active in the latest Carboniferous and Permian (e.g., Larsen et al., 2008;Neumann et al., 1992) and the first phase of rifting in the North Sea and the Norwegian Sea was initiated in the Permian (Faerseth, 1996;Theissen-Krah et al., 2017).During the Permian-Triassic phase of rifting, the main deformation took place just offshore mainland Norway, and the resulting tectonic rift flank uplift has been interpreted from the offshore sedimentary record (Müller et al., 2005;Steel, 1993).
Offshore, large amounts of sediments accumulated in the North Sea and Norwegian Sea during the Triassic and Jurassic, implying that the topography in the source areas was considerable during that time (e.g., Müller et al., 2005;Mørk & Johnsen, 2005;Steel, 1993).Early Jurassic relief of about 1.6 km was suggested by Sømme, Helland-Hansen, and Martinsen (2013), Sømme, Martinsen, and Lunt (2013) based on sediment volumes stored in point-sourced depocenters along the margin.The second phase of rifting offshore in the Jurassic-Early Cretaceous led to extensive thinning of the margin in the Norwegian Sea (Osmundsen et al., 2021).This second phase of rifting is thought to be more localized in the offshore region (Fossen et al., 2021), but brittle faults still remained active throughout the Mesozoic, also in the inner Nordfjord area (Hestnes et al., 2022).The Late Jurassic-Early Cretaceous rifting was followed by post-rift subsidence in the offshore region from the Early Cretaceous (e.g., Brekke, 2000).
According to the hypothesis 1 models (Figures 8a and 9a), the top of Skåla and Jotunheimen remained at ∼3 km depth (∼60-50°C) from the Permian until the Cretaceous.In such a scenario, the constant and depth throughout the Permian to Cretaceous time in the inner Nordfjord could indicate that the area was little affected by the large-scale Jurassic-Early Cretaceous rift phase seen offshore, and the area could have remained a high altitude landscape with slowly developing river valleys until the Late Cretaceous.Offshore Nordfjord, Bauck et al. (2021) showed offshore canyon incision in the Late Jurassic-Early Cretaceous and during two periods in the Late Cretaceous.The canyon incision was at least 800 m deep into uplifted fault block crests.Since the bathymetry diminishes toward the mainland, the study could say nothing about how the Nordfjord itself is connected to these offshore valleys.We speculate here that the E-W oriented Nordfjord, following the major ductile NSZ, could have acted as a river drainage network already since the Mesozoic stretching inland toward the present-day drainage divide.Similarly, the drainage system of Sognefjorden has been suggested to have existed already in the Late Jurassic (Sømme, Helland-Hansen, & Martinsen, 2013;Sømme, Martinsen, & Lunt, 2013) and the incision of Sognefjorden has been suggested to have been active at least throughout the Cenozoic (Anell et al., 2010;Nesje & Sulebak, 1994).
Alternatively, according to the hypothesis 2 models (Figures 8e and 9e), the top of Skåla and Jotunheimen could have been exhumed close to the surface (as a result of increased rift shoulder uplift and subsequent erosion due to the offshore rift phase) already in the Late Jurassic followed by 1.5-3 km of reburial in the Cretaceous.South of Sognefjorden along the coast, vitrinite reflectance data from Late Jurassic sediments overlaying the basement show values of 0.28%-0.29%R0, indicating a burial temperature of less than 50°C (Fossen et al., 1997).From this study, the burial of a maximum of 1 km was suggested.Later, new vitrinite reflectance analyses from the same sediments showed values of 0.38% and burial of more than 2 km depth (Japsen et al., 2018), which is similar to the interpreted burial depth of Jurassic sediments of 1.8-2.3km from the Trondheim region (Figure 1b; Sommaruga & Bøe, 2002).The extent of the post-Late Jurassic sedimentary cover in Western Norway is not known-our thermochronological models at least indicate that such a cover could have extended across the inner Nordfjord and Sognefjorden region if the area was exhumed to near-surface temperatures in the Late Jurassic (Figures 8e-8g and 9e-9g).Other geological constraints do not give a unique answer regarding the situation of Western Norway in the Cretaceous either, and the topographic evolution during this time is debated.The Cretaceous has been suggested to be (a) a period of moderate topography (∼500 m) (Gabrielsen et al., 2010;Sømme, Helland-Hansen, & Martinsen, 2013;Sømme, Martinsen, & Lunt, 2013), (b) a regional peneplain with sediment accumulation (Japsen et al., 2018;Lidmar-Bergström et al., 2013), or (c) dominated by topography even higher than today (Nielsen et al., 2009).Our model from the inner Nordfjord shows that at least within the study region, the top of the Skåla and Jotunheimen transects remained at depths of more than 2 km for most of the Cretaceous (Figures 8 and 9).Bringing the samples to the surface from >2 km depth requires exhumation by removal of overlaying rocks, indicating that the low-relief surfaces at the top of the transects cannot be explained by simple surface uplift of Jurassic or Cretaceous peneplains.
Following the change in the cooling rate in the latest Cretaceous-Paleogene, the thermochronological data provide little information about the cooling path below the temperature of the PAZ and PRZ.Our data show that the lowest sample of the Skåla transect remained within the PAZ until at least the Late Cretaceous and in the PRZ until the Early Paleogene (Figures 8c and 8g), indicating ∼1-2 km of overburden must have been removed during the Cenozoic, as is also suggested from other thermochronological studies further south (e.g., Johannessen et al., 2013;Ksienzyk et al., 2014).This implies that the low-relief surface at the top of the Skåla mountain either has to be a Cenozoic feature or a Late Jurassic peneplain which was buried and re-exhumed from below a sedimentary cover.

Summary and Conclusions
In this study, we present new AFT and apatite (U-Th-Sm)/He ages from an ET up the Skåla mountain in the inner Nordfjord, Western Norway.This ET is structurally intact and yields late Permian to Late Jurassic AFT ages and Triassic to Late Cretaceous (U-Th-Sm)/He ages; both thermochronometers show a positive age-elevation relationship.We present the first consistent multi-sample thermal history models from Western Norway for the Skåla and the nearby Jotunheimen ET (Green et al., 2022) using the HeFTy v2.1.4software, which results in more robust temperature/depth-time models than those derived from single-sample modeling, complementing similar models from the British Isles and West Greenland (Cogne et al., 2016;Danišík & Kirkland, 2023;Jess et al., 2018Jess et al., , 2019)).We tested three different possible thermal evolutions for the Skåla-Jotunheimen area, aiming at constraining the cooling and exhumation histories and possible formation ages for the low-relief surfaces at the top of the transects.
(a) Unconstrained thermal modeling with only initial and final constraints fixed yielded thermal histories with the best fit to the data: the models show fast cooling from Devonian initial conditions until the Triassic, followed by slow cooling throughout the Jurassic and Cretaceous, and a renewed increase in cooling occurring in the latest Cretaceous/Paleogene.(b) Thermal histories with an acceptable fit to the data are found for both transects for a thermal evolution that brings the uppermost samples surface conditions in the Late Jurassic: in this model, fast cooling until the Permian is followed by moderate cooling to surface conditions in the Late Jurassic, before the samples have to be reburied to 50-70°C in the Cretaceous, followed by cooling to surface conditions throughout the Cenozoic.(c) Finally, testing for four episodes of cooling and reburial as suggested by Green et al. (2022) does not lead to acceptable paths for the Skåla transect, whereas acceptable paths could be found for the Jotunheimen transect, which notably does not include (U-Th-Sm)/He data and which therefore allows for more degrees of freedom.
The debate concerning the topographic evolution of Western Norway centers around whether today's high altitude low-relief surfaces are remnants of peneplains formed at sea level (e.g., Japsen et al., 2018) or whether the lowrelief surfaces are the result of high-altitude glacial erosion during the Quaternary (e.g., Pedersen et al., 2018).Our modeling results indicate that (a) the low-relief surfaces at the top of the transects cannot represent a Late Jurassic or Cretaceous peneplain simply uplifted to high-altitudes, (b) if a Late Jurassic peneplain developed in the area, it had to be reburied by 1.5-3 km of Cretaceous sediments, unburied and then uplifted, and (c) our results do not reveal any details about the thermal evolution once the samples have cooled below the PAZ and PRZ in the latest Cretaceous/Paleogene; formation and uplift of an early Miocene peneplain can therefore not be ruled out, nor can the formation of the low-relief surfaces by Quaternary glaciations.Our study supports the findings from the British Isles showing a pulse of exhumation in the latest Cretaceous-early Paleocene (Cogne et al., 2016).This supports the general picture of considerable erosion and exhumation, and thereby reshaping and final modeling of the landscape during post-rift times in the Cenozoic, which seems to be a common feature for elevated passive continental margins in the northern Atlantic realm.

Figure 1 .
Figure 1.(a) Simplified tectonic map of Western Norway.Inset of Norway in the top left corner with the red square indicating the study area.The black square shows the location of the study area with the Skåla mountain in its center.GSZ = Geiranger Shear Zone; NSZ = Nordfjord Shear Zone; NSDZ = Nordfjord-Sogn Detachment Zone;LGF = Laerdal-Gjende Fault.Regional shear zones modified fromWiest et al. (2021).(b) Overview of elevation transects from Western Norway(Green et al., 2022;Johannessen et al., 2013;Leighton, 2007) and locations where Jurassic sediments are preserved onshore(Fossen et al., 1997;Sommaruga & Bøe, 2002).

Figure 2 .
Figure 2. (a) Oblique view on a hillshaded elevation model of the Skåla mountain showing sample location from the foot of the mountain (63 masl) to the top (1,841 masl).Color of circles indicates apatite fission track (AFT) age (cf.Table 1).Bold outline of circles indicates AFT and/or (U-Th-Sm)/He samples included in multisample inverse modeling.Scale for all track length plots and the kernel distributions (blue lines, Gaussian kernel function and halfwidth 0.5) is the same (length along x-axis: 0-20 μm, frequency along y-axis: 0-0.4).(b) Inset shows distance from the first sample (km) against elevation (masl) along the sampled transect.(c) Picture from the top of Skåla mountain looking southwards showing the low relief surfaces at ca. 1,850 masl interpreted as a peneplain.(d) View toward the NNE to the top of Skåla mountain.Photograph taken from locality VAH_15.(e) Picture of sample location VAH_19 showing a moderately foliated monzonitic gneiss (f) Picture of sample location VAH_06 showing a weakly foliated monzonite.

Figure 3 .
Figure 3. Elevation transects (ETs) from this study and Green et al. (2022) plotted as distance from lowermost sample (km) versus elevation (masl).The samples are color-coded according to their apatite fission track central age.Dashed lines represent valleys/topographic lineaments crossing the Jotunheimen transect.The colored bar at the lower part of the diagram represents the various lithologies of the Jotunheimen ET.The curved dark gray line above the Skåla and the Jotunheimen transect represents interpreted peneplains.The plot highlights the difference between the structurally intact and relatively steep Skåla transect and the Jotunheimen transect characterized by a shallower slope angle and the intersection by topographic lineaments.

Figure 4 .
Figure 4. (a) Apatite fission track (AFT) age (Ma) versus elevation (masl) plot.AFT ages given as central age.There is a general increase in age with elevation.(b) Mean track length (track-in-track) versus elevation.All mean track lengths (MTL) overlap within uncertainty, but there is a weak trend of increasing MTL with elevation.(c) (U-Th-Sm)/he ages versus elevation plot.(U-Th-Sm)/He ages given as single grain ages.(d) AFT age versus elevation plot for the Jotunheimen transect of Green et al. (2022).

Figure 6 .
Figure 6.Set-up of the tested models where blue boxes represent external constraints added.The dashed blue boxes represent constraints where dimensions and values are changed between model runs.Shaded light blue area represents the partial annealing and partial retention zone.(a) Cooling from start to end.(b) Exhumation to nearsurface conditions during the Late Jurassic, followed by possible burial.(c) Repeated episodes of exhumation, peneplanation and reburial.

Figure 7 .
Figure 7. (a) HeFTy time-temperature thermal inverse models of all single samples, which are also included in the multisample model of the Skåla elevation transect.The results are shown as path envelopes (gray = acceptable paths and blue = good paths).(b) Time-temperature diagram showing best-fit paths for each of the single sample models together.(c) HeFTy time-temperature thermal multi-sample inverse model with all included samples plotted individually.The black line shows the best-fit model.The results are shown as path envelopes (gray = acceptable paths and yellow = good paths).The blue box represents the initial constraints.(d) Time-temperature diagram showing the best-fit paths for each sample of the multi-sample model.

Figure 8 .
Figure 8. Multi-sample inverse models of the Skåla transect.The plots only show the upper 12 km/180°C, not showing the initial constraints of 30-26 km depth at 400-330 Ma.The models are based on apatite fission track (AFT) and apatite (U-Th-Sm)/He input from 10 samples (Figure 4a).(a) Modeling hypothesis 1: Time-depth model of the control sample VAH_19, the topmost sample of the Skåla transect.(b) Time-temperature model of (a).(c) Time-temperature best-fit paths of the included samples of the Skåla transect for the model in panels (a, b).The blue squares and yellow diamonds represent AFT central ages and (U-Th-Sm)/He single grain ages for the included samples.(d) Resulting modeled track length distributions (blue line) for each best fit path together with measured track lengths (gray histogram).The goodness of fit in this case represents the individual-sample length GOFs.The track length distribution plots show the same scale, where the x-axis shows length of (0-20 μm) and y-axis show frequency (0.0-0.45).(e) Modeling hypothesis 2: Time-depth model of the control sample VAH_19 with constraints defining near-surface cooling/exhumation in the Late Jurassic, followed by reburial.(f) Time-temperature model of (e).(g) Time-temperature best-fit paths of the included samples of the Skåla transect for the model in panels (e, f).(h) Modeled track length distribution as in panel (d).

Figure 9 .
Figure 9. Multi-sample inverse models of the Jotunheimen transect from Green et al. (2022).The plots only show the upper 12 km/180°C, not showing the initial constraints of 30-26 km depth at 400-330 Ma.The models are based on apatite fission track (AFT) input from six samples (Figure 4d).(a) Modeling hypothesis 1: Timedepth model of the control sample GC970-09.(b) Time-temperature model of (a).(c) Time-temperature best-fit paths of the included AFT central ages (blue squares) of the Jotunheimen transect for the model in panels (a, b).(d) Resulting modeled track lengths (blue line) for each best fit path together with measured track lengths (gray histogram).The track length distribution plots show the same scale, where the x-axis shows length (0-20 μm) and y-axis show frequency (0.0-0.50).(e) Modeling hypothesis 2: Time-depth model of GC970-09 with constraints defining near-surface cooling/exhumation in the Late Jurassic, followed by reburial.(f) Timetemperature model of (e).(g) Time-temperature best-fit paths of the included samples of the Jotunheimen transect for the model in panels (e, f).(h) Modeled track length distributions as in panel (d).(i)Modeling hypothesis 3: Time-depth model of GC970-09 with constrains defining episodes of repeated cooling/exhumation and reheating/burial.(j) Time-temperature model of (i).(k) Time-temperature best-fit paths of the included samples of the Jotunheimen transect for the model in panels (i, j).(l) Modeled track length distribution as in panel (d).(m) Modeling only the top most structural block consisting of four samples of the Jotunheimen transect with hypothesis 1 (left) and 2 (right).Both hypotheses only produced acceptable paths, whereas the third hypothesis did not produce any paths.(n) Modeling the lowest coherent structural block of four samples of the Jotunheimen transect with hypotheses 1 (left), 2 (right) and 3 (bottom).All three hypotheses only produced acceptable paths.

Table 1
AFT Data (AFT Ages Highlighted in Bold) (Galbraith, 2005)er of dated grains; n(TL), Number of measured track lengths; N s , Number of spontaneous tracks; N i , Number of induced tracks; N d , Number of tracks counted on dosimeter glass IRMM 540R; ρ s , Spontaneous track density (1 × 10 5 tracks cm 2 ); ρ i , Induced track densities; ρ d , Track densities on counted dosimeter glass IRMM-540R; P(χ 2 ), p-value of the chi-square homogeneity test(Galbraith, 2005); Dpar, etch pit diameter; MTL, mean track length; Age is given as central age.Sample grain quality: G, Good; F, Fair; P, Poor; d, Dislocation; i, Inclusions; s, Scratches; z, Zones; wz, Weakly zoned.The letters in brackets indicate that the grain feature affect few grains in the sample.HESTNES ET AL.

Table 2
Apatite (U-Th-Sm)/HeData (Uncorrected Values Highlighted in Italics and Ft-Corrected Ages Highlighted in Bold)