We project the data points onto a transect x-x’ along the east coast of the Northland Peninsula (Fig. 4.1b) and conduct the modelling in 2 dimensions to reduce the complexity and increase the inversion efficiency. This is a reasonable simplification as our data points strike approximately 300 km within a relative narrow width (< 80 km) and the topographic relief is insignificant in the modelled region. As the trend of the 2D model is generally perpendicular to the proposed direction of allochthon (Rait, 2000) (Fig. 4.1b), the thermochronological data from the footwall basement are more sensitive to heating from the burial of the overlying nappes rather than the true transport direction of the allochthon movement. Thus, here we simulate the emplacement and subsequent erosion of the allochthon as the burial and exhumation of the basement.
Fig. 4.6 2D thermo-kinematic model of the eastern Northland basement, involving the emplacement and erosion of the Northland Allochthon. (a) Initial model setting prior to 30 Ma. (b) Allochthon emplacement. (c) Post-emplacement uplift of the basement and erosion of the allochthon. See section 4.5.3 for more details. Location of the profile is shown in Fig.4.1b.
In the model set-up, the crustal thickness is set to ~25 km (Fig. 4.6a), according to Salmon et al. (2013). The initial thermal structure is set to approximate the present-day geothermal gradient of 40 °C/km (Reyes, 2007). Other thermo-kinematic parameters are as typical in Pecube models (Braun et al., 2012), listed in Table 4.3.
For simplicity no flexural isostasy is considered. The allochthon in eastern Northland
erosion and topographic decay (T1–T4)
basement uplift and exhumatioon (T2–T3) allochthon emplacement (T1)
E
initial set-up prior to 30 Ma
a
is simulated to be emplaced at the time T1 (Fig. 4.6b), which is allowed to vary in the range of 30–15 Ma. The basement AFT ages young towards the northwest, implying an increase, in this same direction, in the original thickness of the allochthon; this must be satisfied in the 2D model. To this end, we set the maximum thickness of allochthon to H in the northwestern boundary of the transect thinning towards the southeast (Fig. 4.6b); while H is allowed to vary from 0 to 10 km. The original extent of the allochthon along the model transect is prescribed to 210 km (Fig. 4.6b), corresponding to the present outcrop of the allochthon in western Northland.
Following allochthon emplacement, the basement of eastern Northland is set to be uplifted and exhumed at rate E during a period from time T2 to T3 (Fig. 4.6c). T2 and T3 are searched in time ranges of 30–0 Ma and T2–0 Ma, respectively, whereas E is allowed to vary between 0.01 and 5 km/Myr and is sampled in a logarithmic space.
Above the basement, the surface relief is set to reduce gradually due to erosion of the allochthon, over a period from T1 to T4 (Fig. 4.6c); T4 is searched between 15 and 0 Ma.
We prescribe a Mesozoic basement exhumation from 150 to 100 Ma at the rate of 0.15 km/Myr, in order to reproduce the oldest ZFT and AFT ages south of Auckland, where no allochthon emplacement has been documented.
Table 4.3 Fixed thermo-kinematic model parameters
Parameter (unit) Value
Crustal density (kg/m3) 2700 Mantle density (kg/m3) 3200
Crustal thickness (km) 25
Thermal diffusivity (km2/Myr) 30 Basal crustal temperature (°C) 1015 Sea-level temperature (°C) 15 Atmospheric lapse rate (°C/km) 6 Crustal heat production (°/Myr) 0 4.5.4 Results
The inversion results are presented in Fig. 4.7, as scatter plots in the parameter space projected onto a surface each defined by two parameters. Each dot represents a forward model, and its colour depicts the model misfit between prediction and
observation. 1D and 2D posterior marginal PDFs are computed for each parameter and for parameter combinations, respectively. Predictions by the expected (weighted mean) and “best-fit” models are summarised in Table 4.4.
Fig. 4.7 Inversion results of the thermo-kinematic model in eastern Northland. Scatter plots present the parameter space projected onto planes defined by pairs of parameters. Each dot depicts a forward model colour coded according to its misfit value. 1D posterior marginal probability density functions (PDFs) are plotted along axes. 2D posterior marginal PDFs are plotted as 67 % (black) and 95 % (grey) confidence contours. Stars represent the “best-fit”
forward model (lowest misfit).
Results suggest that the emplacement of Northland Allochthon occurred since the mid-Oligocene (~30–27 Ma) (T1; Fig. 4.7a), and its maximum thickness was up to
the model predicts a short (~1–6 Myr; Fig. 4.7d) period of basement uplift at the rate of ~0.1–0.8 km/Myr (E; Fig. 4.7c). Finally, the results suggest that the emplaced allochthon has been eroded slowly over a long period until ~3–0 Ma (T4; Fig. 4.7b).
Table 4.4 Free model parameters.
Parameter Code Range Unit Mean ± standard error
(best-fit) Allochthon emplacement T1 30–15 Ma 28.3 ± 1.3 (27.7)
Maximum thickness of
allochthon at T1 H 0–10 km 3.9 ± 1.0 (4.3)
Onset of basement uplift T2 30–0 Ma 22.7 ± 3.0 (22.6) End of basement uplift T3 T2–0 Ma 18.5 ± 4.9 (21.0) Logarithm of basement uplift
rate during T2 – T3 Log (E) -2–0.7 Log
(km/Myr) -0.46 ± 0.37 (-0.19) End of allochthon erosion T4 15–0 Ma 1.6 ± 1.1 (0.09)
Lowest misfit 63
In general, both the mean and the “best-fit” models reproduce the observed data well (Fig. 4.8b), except for the oldest ZFT age in the southeast of the model, which most likely represents a mixed age inherited from multiple detrital sources (Raza et al., 1999). During the Late Oligocene–Early Miocene, the basement rocks in northern Northland are predicted to have undergone heating to over ~120 °C (Fig. 4.8a), interpreted as the result of burial beneath the allochthon (and autochthon) sequences.
The magnitude of heating decreased towards the southeast (Fig. 4.8a), due to the thinning of the allochthon in that direction (Fig. 4.8c).
Fig. 4.8 Prediction of the 2D thermo-kinematic model. (a) Predicted thermal histories of representative samples. Heavy lines represent the mean T-t paths; light lines represent the envelopes of “good-fit” models (misfit < 100); dotted lines represent the “best-fit” models (lowest misfit). (b) Observed (symbols) versus the predicted data by the mean (solid lines) and the “best-fit” models (dotted lines). (c) The current allochthon thickness in western Northland (grey shade) (Isaac et al., 1994) versus the predicted maximum allochthon thickness (at ~27 Ma) in eastern Northland. Solid lines represent the thickness predicted by the mean model with the envelope of “good-fit” models (misfit < 100), whereas the dotted line is thickness predicted by the “best-fit” model (lowest misfit). Box represents the thickness of the allochthon at Parua Bay, predicted by the thermal models (QTQt) of the allochthon (JR11-40c) and autochthon (JR11-40b), assuming 30–40 °C/km geothermal gradient and 5–15 °C surface temperature at time of emplacement.