# Thermal modeling and heat flow density interpretation of the onshore Northwest Java Basin, Indonesia

- Setya D. H. Putra
^{1}, - Suryantini
^{1, 2}and - Wahyu Srigutomo
^{3}Email authorView ORCID ID profile

**4**:12

**DOI: **10.1186/s40517-016-0052-x

© The Author(s) 2016

**Received: **18 May 2016

**Accepted: **6 September 2016

**Published: **22 September 2016

## Abstract

Studies pertaining to heat flow density distribution in Indonesian tertiary sedimentary basins have been conducted intermittently throughout more than two decades. Even so, all of these studies have always concentrated on the basic compilations of thermal gradient, thermal conductivity, and terrestrial heat flow datasets or the study of basin thermal history rather than on the investigations into their present thermal regime. In addition, syntheses on the possible causes to the observed heat flow density distribution in these basins have been largely determined only on the basis of its correlation with geological and geophysical evidences. One basin experiencing this particular problem is the onshore Northwest Java Basin, where knowledge of the present-day subsurface temperature structure is virtually absent and interpretation of heat flow distribution has been mainly qualitative. For these reasons, in this study we have attempted to quantitatively characterize the present subsurface temperature distribution and surface heat flow density of the onshore Northwest Java Basin using a simple numerical thermal modeling approach, based on the most recent heat flow datasets. Taking into account a conductive heat transfer process, the modeling exercise is aimed at deriving a 3-D subsurface temperature distribution. The temperature distribution is translated into the predicted surface heat flow distribution. The modeled temperature field reveals its dependence on the geometrical aspects of the basin’s basement. Comparison between the computed and the observed heat flow densities, taking into account the uncertainties of both, suggests that advective heat transport by groundwater flow may be present, in addition to conduction. The modeling results are thus capable of demonstrating the importance of a quantitative approach in studying the present thermal state of a sedimentary basin.

### Keywords

Heat flow density Onshore Northwest Java Basin Subsurface temperature Thermal modeling## Background

Therefore, in this study, we attempt to perform the first numerical modeling study of the 3-D thermal structure of the onshore Northwest Java Basin by taking into account a conductive heat transfer. The procedure is based on heat flow density dataset gathered by Suryantini (2007) and a number of publicly available data. The influence of lithology and basement geometry on the thermal structure of the basin is discussed by examining the spatial variation of the modeled temperature distribution. We also compare the observed HFD values with those calculated from the modeled temperature distribution to aid in interpreting the spatial variation of their differences. These differences are then interpreted by attributing them to other subsurface heat transfer-related phenomena, such as advective redistribution of heat by groundwater flow (e.g., Kilty and Chapman 1980) and refraction of conductive heat (e.g., Beardsmore 2005). We demonstrate that the modeling results enable the identification of prominent thermal signatures in relevance to the geological elements of the onshore Northwest Java Basin and provide insight into its present-day thermal regime.

## Methods

As mentioned previously, in this study, we aim to generate a conductive subsurface temperature distribution of the onshore Northwest Java Basin, and thus its conductive heat flow density distribution through a numerical modeling procedure. Thermal parameters and geological data are collated based on previous studies concerning their compilation and earlier interpretation. The latter data are utilized to produce a basin fill and basement geometry model to be assigned thermal conductivity values, to construct a subsurface 3-D thermal conductivity model. The numerical modeling is based on a finite difference approximation of the heat conduction equation, to which the thermal conductivity model becomes the primary input. The modeled heat flow density is then compared against the observed one in a similar fashion to that of Cacace et al. (2013), the resulting difference(s) of which is subsequently interpreted in terms of its relationship with the basin’s thermal and hydrological regimes. A flowchart is presented in Fig. 2 to provide the overall picture of the research methodology employed in this study. The data, assumptions, procedures, and results relevant to each component of the workflow are elaborated in much more detail in the following sections.

### Geological setting of the onshore Northwest Java Basin

### Heat flow density distribution

#### Heat flow density datasets

The primary data used in this study are based on the most recent compilation of heat flow density, thermal gradient, and thermal conductivity values of the west Java region, each of which was obtained from hydrocarbon wells by Suryantini (2007). Several additional values were also obtained from the collection of open-access world heat flow datasets maintained in the website (http://www.heatflow.und.edu) to make up for a few spatial gaps in the central and western parts of the study area (Fig. 5). The latter data originated from the compilation of thermal gradients by the Indonesian Petroleum Association (IPA) and South East Asia Petroleum Exploration Society (SEAPEX) which were published earlier by Rutherford and Qureshi (1981) and HFD values published by Thamrin (1985).

#### General description of heat flow density distribution

The HFD in the onshore Northwest Java Basin features considerably high values (Fig. 6a, b) with an average of 94.05 ± 26.42 mW/m^{2}, compared to that of average continental heat flow which is only about 65 mW/m^{2} (Stein 1995; Pollack et al. 1993). Although there have been different views pertaining to whether the basins situated behind the Sumatra–Java volcanic arcs are of non back-arc (e.g., Uyeda and Kanamori 1979) or back-arc basins (e.g., Koesoemadinata et al. 1994; Suryantini et al. 2006), Matsubayashi and Nagao (1991) viewed the crust beneath these areas as being a “semi-continent” one, which has HFD similar in characteristics to the basin and Range provinces. The average HFD within this province is actually ~85–90 mW/m^{2} (Wisian and Blackwell 2004), slightly lower than the mean HFD of the onshore Northwest Java Basin, where the latter may be affected by a small number of wells with very high HFD (see discussion below and in “Discussion” section).

There are two major ranges into which heat flow densities fall in most parts of the basin, i.e., 75–90 and 90–105 mW/m^{2}, respectively (Fig. 6b). High to extremely high values (105 to > 120 mW/m^{2}) along with the lowest ones (<75 mW/m^{2}) are also distributed in several isolated localities. The higher HFD values are mostly found in the southern part of the basin, the cause of which Suryantini et al. (2006) attributed to the possible location of the boundary between the coastal plain of Jakarta and the Bogor Zone folded units. Although the HFD distribution does not appear to correlate with the superficial lithology of the basin (Fig. 6a), in general, it coincides with the basin geometry and geological structures. The high to anomalously high values, for example, are located in either area of very shallow basement (well SUM244 in the Tangerang High) or close to large faults (e.g., wells JNG-1, JRR-1, JRR-2 southeast of Ciputat Sub-basin, and PJN-P1, PJB-P1 south of Pasirputih Sub-basin), and areas located on both (well RDH-2 in the Rengasdengklok High). On the other hand, the lowest heat flow values (60–75 mW/m^{2}) are located around areas of basement low (e.g., wells SUM245 in the Ciputat Sub-basin, KRW-1 and SKD-1 in the Pasirputih Sub-basin), as well as nearby fault (well TGB-1).

The aforementioned facts suggest that the HFD distribution in the basin might be controlled by both basement topography, i.e., through heat refraction (e.g., Beardsmore 2005; Thakur et al. 2012; Rawling et al. 2013) due to the basement-to-sedimentary fill thermal conductivity contrast and the presence of heat transfer by moving groundwater (Kilty and Chapman 1980) which may recharge or discharge along the basin’s bounding faults (Ehlers and Chapman 1999), or both. However, there are also high HFD values that are not directly located in the vicinity of faults nor are they situated over a shallow basement, i.e., wells CLU-5, SNT-1, and PCT-1 (northern Pasirputih Sub-basin, east, and southeast of Pamanukan High, respectively), though Suryantini (2007) interpreted based on gravity studies that several concealed faults possibly exist beneath areas around SNT-1. Moreover, there are not any anomalously high or low heat flow densities in Pamanukan High region where most data are situated near major faults. We will examine this matter of complication in the following sections by the use of numerical modeling of conductive heat transfer in the basin. The modeled temperature field allows for the conductive component of the HFD values to be recovered (Cacace et al. 2013), which in turn enables a subsequent comparison to be made with the observed heat flow values.

#### Numerical modeling of subsurface temperature distribution

^{2}s

^{−1}) of the material (lithology), respectively. The characteristic length scale can be envisaged as the approximate distance that any thermal perturbations may propagate to for a given amount of time. The value of thermal diffusivity is commonly in the order of ~10

^{−6}m

^{2}s

^{−1}; however, it can be made a function of thermal conductivity (\(\lambda\), W m

^{−1}K

^{−1}), i.e., \(\kappa \sim \lambda /(2.3 \times 10^{6} )\) (Beck 1988). The value of \(\tau\) can thus be used to estimate either the duration of the heat diffusion process or the length of the influenced zone after a thermal event has taken place at a certain time (Stuwe 2007). The latter is of importance in justifying the aforementioned assumption, since we would like to calculate the depth range influenced by a thermal perturbation associated with the last tectonic event, i.e., uplift at the late Miocene–Pliocene. The appropriate \(\tau\) is thus about 5–6 my BP (Hall and Morley 2004). Taking the average thermal conductivity of the overall Northwest Java Basin to be 1.87 W m

^{−1}K

^{−1}(cf. Table 2 of Matsubayashi and Nagao 1991), \(\kappa \sim \; 9. 7\; \times \; 10^{ - 7} {\text{m}}^{ 2} \;{\text{s}}^{ - 1}\), the characteristic length scale calculated using Eq. 1b is about 34.11–37.37 km, respectively. This suggests that with respect to the approximate crustal thicknesses of areas within the Sunda Shelf, i.e., ~20 km (Ben-Avraham, 1973), the late Miocene–Pliocene tectonic thermal perturbation must have completely equilibrated through the crust, thus justifying the steady-state assumption.

#### Governing equation and numerical solution

^{−3}), specific heat capacity (J kg

^{−1}K

^{−1}), and radiogenic heat production (W m

^{−3}), respectively. The right-hand term of Eq. 2a can be dropped to yield the equation of steady-state heat conduction for a heterogeneous medium:

Since, in a heterogeneous medium, the thermal conductivity is bound to vary spatially (as indicated by the subscripts of each thermal conductivity component), Eq. 2b is non-linear and a closed form analytical solution like that tabulated by Carslaw and Jaeger (1959) for simplified geometries cannot be derived (Nagihara 2003). Instead, the solution is found using a numerical method. In this study, we use a finite difference approximation (Haenel et al. 1988) to solve Eq. 2b for the 3-D conductive temperature distribution, based on a set of material thermal property distribution and boundary conditions (Beardsmore and Cull 2001). For the sake of simplicity, a Gauss–Seidel scheme (Chapra 2011) is adopted to solve for the sets of resulting linear finite difference system of equations (e.g., Kilty and Chapman 1980) of temperature at each grid node, where a fixed number of 1000 iterations is used for each modeling run, ensuring sufficiently small temperature residuals.

#### Subsurface thermal properties

Bulk thermal conductivities of all formations present in the study area

Formation | Lithology | λ (W m |
---|---|---|

Cisubuh | Shale | 1.73 ± 0.03 |

Parigi | Limestone | 2.39 ± 0.09 |

Upper Cibulakan | Shale, limestone | 1.88 ± 0.18 |

Lower Cibulakan | Calc sand, marl, shale, limestone | 2.21 ± 0.17 |

Jatibarang | Volcanic | 2.42 |

Basement | Metamorphic | 2.79 |

*H*

_{0}= 3.1 μW m

^{−3}and

*D*= 7.8 km. The subsurface geometry of the basin fill, basement, and structures are based on geological cross section of Kingston (1988) as well as a basement depth map utilized by Suryantini (2007). The 3-D thermal conductivity model constructed using values in Table 1 and subsurface geometry is displayed as a pair of cross sections in Fig. 8.

#### Model domain setup

^{o}× 5

^{o}, larger than the smallest extent of the basin. Owing to these limitations, a constant heat flow value and its uncertainty are employed at the base of the model domain instead of a constant temperature. The basal heat flow and its uncertainty are obtained by subtracting the total radiogenic heat production of the model domain volume from the average surface HFD and its uncertainty (e.g., Limberger et al. 2014). The topography is set to zero meter above sea-level everywhere within the model domain, including the extended area (Fig. 7). Although the initial surface temperature assumed by Suryantini et al. (2006) is 26.67 °C, which conforms to that of the surface air temperature by Hijmans et al. (2005) (http://www.worldclim.org), the average value calculated from the Suryantini (2007) complete HFD dataset is 28 °C. Since some studies have indicated that the ground surface temperature is slightly above that of the surface air (e.g., Smerdon et al. 2006), the latter was imposed as a uniform constant temperature on the top boundary. A complete list of the numerical model domain parameters as well as boundary conditions is given in Table 2.

Numerical properties of the entire model domain

Parameter | Value (s) |
---|---|

Areal extent (km | 252 × 112 |

Depth (km) | 8 |

Top of domain at (masl) | 0 |

Number of nodes | 127 × 57 × 51 |

Number of cells | 126 × 56 × 50 |

Grid resolution (km | 2 × 2 × 0.1 |

Top boundary = Surface temperature ( | 28 |

Lateral boundary = Heat flow (mW m | 0 |

Bottom boundary = Basal heat flow (mW m | 104.86 (maximum); 78.44 (average); 52.02 (minimum) |

We use a system of finite difference pattern as described by Beardsmore and Cull (2001). In their scheme, temperature is solved at each node, whereas the values of thermal conductivity and radiogenic heat production must be assigned to the cells prior to the temperature calculations. In other words, the discretization approach we adopt in this study makes use of a node-based scheme (Murthy et al. 2006), i.e., the grid system is mesh centered (Faust and Mercer 1980). To explore the uncertainties in the resulting modeled temperature distribution, the numerical modeling is carried out three times; each one is based on the original, maximum, and minimum value of formation thermal conductivity and basal heat flow density.

## Results

### Synthetic results

The comparison between 1-D temperature profile extracted from the 3-D finite difference-modeled temperature distribution and vertical temperature calculated using Eq. 4 is displayed in Fig. 9c. It can be observed that the result derived using numerical solution matches that of analytical one. Therefore, our numerical conductive heat transfer modeling procedure is considered reliable and is subsequently employed to the onshore Northwest Java Basin.

### Modeled temperature fields

^{2}(Table 2). As for the results of the modeling using the maximum and minimum formation thermal conductivities and basal heat flow values, we use them only in the validation procedure (“Synthetic results” section) as well as for calculating the maximum and minimum HFD (“Modeled surface heat flow density” section).

Figures 10 and 11 demonstrate that the conductive temperature shows an alternating pattern, i.e., higher subsurface temperatures are observed in sub-basinal areas, and conversely, lower subsurface temperatures can be seen to occur in basin high areas. This pattern is more explicitly exhibited in areas crossing the Tangerang High, Ciputat Sub-basin, and Rengasdengklok High. The high temperature reaches > 300 °C beneath Ciputat Sub-basin and the low one is 180 °C beneath Tangerang and Rengasdengklok Highs at maximum depth. Specifically, except for the three aforementioned areas, the alternating pattern did not actually make a significant appearance until a depth of 3000–4000 m is reached.

### Modeled surface heat flow density

^{2}. Such calculations require only the near-surface temperature gradient of the model domain (here denoted by \(\frac{{{\text{d}}T}}{{{\text{d}}z}}\)) and the harmonically averaged thermal conductivity at each lateral grid node position. While the former can be readily extracted from the 3-D temperature distribution, the latter is calculated using an equation of the form (Beardsmore and Cull 2001):

In addition, the calculation of surface HFD values are also performed using the temperature distributions that have been modeled using the maximum and minimum thermal conductivity and basal heat flow values. These HFD values will be employed in the procedure explained in “Discussion” section.

## Discussion

The phenomenon demonstrated by the temperature-at-depth maps (Fig. 10; “Modeled temperature fields” section) can be explained by examining the characteristic of the subsurface geology, i.e., in terms of the depths where the lateral distribution of lithology starts to change significantly. Except for beneath the Tangerang High–Ciputat Sub-basin–Rengasdengklok High regions, the lateral lithology within other areas (eastern Pasirputih Sub-basin, Pamanukan High, and Jatibarang Sub-basin) is more or less similar, i.e., they are comprised of sedimentary units at shallower depths. This occurs until a uniform depth of around 3–4 km is reached beneath these regions. About and below this depth range, the lateral distribution of lithology is alternated between the basement and sediments.

The above suggests that the thermal conductivity contrast between the sedimentary basin filling and the crystalline basement is more significant than that between the sedimentary formations themselves, such that areas with thicker sedimentary piles have their isotherms bent upward, thus implying higher geothermal gradients. The reverse occurs for those of shallower basements (Fig. 11). This means that the conductive temperature distribution is sensitive to the basement’s geometry.

There are at least two major features of Fig. 12 that deserve detailed discussions. The first one is that the distribution of modeled surface heat flow density values bears a resemblance with the overall lateral pattern of basement depth. Higher heat flow values are concentrated within areas of basement highs (e.g., Pamanukan and Rengasdengklok Highs) and lower ones are clustered within sub-basinal areas (e.g., Ciputat Sub-basin). This is a direct manifestation of the control of thermal conductivity on the thermal regime, i.e., high heat flow is attributed to high thermal conductivity and, therefore, to locations where thermally conductive rocks (i.e., the basement) are dominant, and vice versa.

A more careful observation leads to the discovery of another HFD pattern, i.e., there are areas where heat flow density values are lower or higher but are not directly positioned above sub-basins or basin highs, but rather, their edges. Two most noticeable examples to this are the low heat flow in the central part of Tangerang High and an exceptionally high heat flow in the southern part of the Rengasdengklok High (between Ciputat and Pasirputih Sub-basins). This demonstrates that the effect of heat refraction (Beardsmore 2004; Thakur et al. 2012; Rawling et al. 2013; “General description of heat flow density distribution” section), i.e., where heat flows more preferably along thermally conductive zones rather than it does along insulating ones, prevails on these regions. This explains why the computed HFD in the southern Rengasdengklok High is high compared to that of other areas within the basin. There is a short lateral transition between a basin low region (Ciputat Sub-basin), a basin high area (Rengasdengklok), to another basin low (Pasirputih Sub-basin), allowing heat from the low areas to be strongly imparted to the shallow but narrow basement beneath this region. In a reversed manner, the very low modeled HFD in central Tangerang High is probably due to it being situated between two narrow basement highs.

As a final attempt to analyze and interpret the HFD distribution of the onshore Northwest Java Basin, we perform comparisons between the observed HFD with their associated uncertainty (Fig. 6a) and the calculated HFD (Fig. 12) with their predicted uncertainty. A similar procedure has been attempted by Cacace et al. (2013) for an area in northern Germany. In principle, any deviations of the observed HFD values from the modeled ones that are beyond the range of uncertainty of the latter should be mostly attributed to the redistribution of conductive heat by groundwater flow.

*max*and

*min*correspond to the maximum and minimum observed or modeled HFD. For the observed HFD, the maximum and minimum HFD values are equal to the well HFD values plus and minus their uncertainty (Fig. 6a), respectively. The maximum and minimum predicted HFD can be directly obtained by applying Eq. 6 to the 3-D temperature distributions generated from the modeling runs using maximum and minimum values of thermal conductivity and basal heat flow (“Model domain setup” section).

^{−2}when calculated using Eq. 7a than there are resulting from Eq. 7b. The anomalously high and low observed HFD values (i.e., those yielding negative values when inserted into calculations using Eq. 7a and 7b, respectively) are subsequently interpreted in terms of mode of heat transfer, while the extremely high ones are attributed to a geological cause. These interpretations are addressed in more detail through the following discussions.

Some univariate statistics of the heat flow density differences

Statistics | Values for | |
---|---|---|

Differences between calculated and measured HFD maxima (Eq. 7a) | Differences between calculated and measured HFD minima (Eq. 7b) | |

Mean (mW m | 0.53 | 13.30 |

Standard deviation (mW m | 34.32 | 21.95 |

Median | 7.75 | 11.83 |

Standard deviation/mean | 64.62 | 1.65 |

Skewness | −2.28 | 2.26 |

HFD difference < 0 mW m | 17 | 12 |

In relevance to the interpretation concerning the effect of groundwater flow, we provide the distribution of shallow groundwater flow zones across the basin, which were originally constructed by Kloosterman (1989) for the areas adjacent to and surrounding Rengasdengklok High, Pasirputih Sub-basin, Pamanukan High, and Jatibarang Sub-basin, and by Lubis et al. (2008) for the Ciputat Sub-basin (the capital city of Jakarta region). The differences between the two HFD maxima (Eq. 7a; Fig. 13a) are in agreement with the groundwater regime. The wells RDH-2 (northern Rengasdengklok High), CLU-5 (northern Pasirputih Sub-basin), PRD-1, GTR-1/2/3, PCT-1 (western Jatibarang Sub-basin) all are anomalous according to Eq. 7a, i.e., the observed HFD plus their uncertainties are higher than the maximum predicted HFD. This is due to them being located in or adjacent to regional groundwater discharge areas, such that the observed HFD is higher than what would be expected from a purely conductive or “background” HFD (e.g., Kilty and Chapman 1980; Cacace et al. 2013). Other wells with anomalous HFD, i.e., SUM244 (Tangerang High), JNG-1 (Ciputat Sub-basin), CKR-1 (Rengasdengklok High), JRR-1/2, and PJB-1 PJN-P1 (western and southern Pasirputih Sub-basin) are not covered by the groundwater regime information. For well SUM244, this might be due to heat refraction (due to it being situated adjacent to the southern part of Rengasdengklok High; see Fig. 11) that is higher in magnitude than that can be accommodated by the maximum modeled HFD, given the extremely rugged basement. Well CKR-1 is adjacent to a relatively large basement fault, thus the influence of deep fluid circulation is likely. For the other wells, such as those located in the southeastern edge of the Pasirputih Sub-basin, magmatic activities may fulfill the necessary condition for generating the tremendously high observed HFD, i.e., up to 171.70 and 219 mW m^{−2} (Fig. 6a), well above a typical conductive HFD value right over active volcanic areas of Southeast Asia, i.e., about 140 mW m^{−2} (Nagao and Uyeda 1995). These wells are indeed relatively close to the volcanic arc south of a major thrust fault and are not within a groundwater recharge area. Well JNG-1 is neither located in an area where significant heat refraction occurs nor is it within a groundwater discharge area. In addition, it is not located in close proximity to any nearby basement fault that may facilitate deep groundwater circulation and advective heat transport, so it remains uncertain of what effect may be responsible for the anomalously high HFD. A possible explanation would be that the near-surface fault located just to the west of JNG-1 cuts through the confining layer in the area, thereby providing a path for hotter, deeper, groundwater to ascend through to a layer containing shallower groundwater body.

At the other end of the spectrum, we can observe in Fig. 13b that there are also wells whose minimum observed HFD values are actually lower than their modeled minima. Although, these wells are mostly situated in groundwater recharge or mixed recharge-discharge zones, such that their HFD is lowered due to the absorption of heat by fluid flow (Kilty and Chapman 1980), there are also wells which show similarly lower-than-predicted HFD, but are not directly within recharge areas, or even adjacent to discharge areas. Examples are WNJ-1, BJR-1, CJT-1, and MLD-1 (a group of wells on the northern part of Pamanukan High). Recalling Fig. 12, this could again be due to the effect of heat refraction whose magnitude is even higher than that can be accounted by the modeled HFD, i.e., conductive heat flow beneath the area is diverted to the nearby crest of Pamanukan High. It is also possible that a more dominant advective–convective heat transfer occurs in the form of groundwater recharge in deeper sections of this area, as evidenced by the presence of faults in the proximity of these wells.

## Conclusions

Finally, to summarize, a simple finite difference thermal modeling approach employed in the present study that is based on steady-state conduction and available data has been able to aid in interpreting surface HFD distribution in the onshore Northwest Java Basin for the first time. It is now recognized that despite the absence of any surface warm or hot springs within the basin, the thermal regime itself is not necessarily completely dictated by conduction. Comparisons between the observed and modeled HFD values reveal that subsurface groundwater flow regime appears to play a crucial role in creating the present observed HFD pattern. In addition to the consequences of groundwater flow regime, heat refraction effect may still prevail in areas where advective heat transfer cannot be proven to account for the anomalous HFD values. For further work, it is expected that (1) more quality HFD data be collected from both newly drilled hydrocarbon and shallow water boreholes in areas within the basin where HFD data are sparse, and (2) deep groundwater flow field be characterized so that advective heat transfer component can be included in future thermal modeling studies.

## Declarations

### Authors’ contributions

SDHP ran the finite-difference temperature modeling, and conducted the study on heat flow density interpretation of the onshore Northwest Java Basin. S and WS contributed to the development of conceptual and numerical thermal models of the basin, respectively. All authors read and approved the final manuscript.

### Acknowledgements

The authors are very grateful to two anonymous reviewers for their constructive comments, all of which have culminated in significant improvements of this paper.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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