Tree Roots Characterization Through Spectral Analysis and Machine Learning of Ground Penetrating Radar Data

  • Arboriculture & Urban Forestry (AUF)
  • April 2026,
  • jauf.2026.013;
  • DOI: https://doi.org/10.48044/jauf.2026.013

Abstract

Background Spectral analysis of data acquired using ground penetrating radar (GPR) allows for the evaluation of the amplitudes and frequencies associated with reflections generated by subsurface materials and their interaction with electromagnetic waves. This interaction produces a unique response for each material type.

Methods In this study, we tested two widely used time-frequency tools (the short-time Fourier transform [STFT] and power spectral density [PSD]) to characterize the subsurface roots of three distinct tree species: Jacaranda mimosifolia, Libidibia ferrea, and Handroanthus impetiginosus. Furthermore, we developed an artificial neural network (ANN) to distinguish the evaluated species, complementing the spectral analysis. GPR data were collected using a 900 MHz antenna within an area containing all 3 species.

Results Through spectral and ANN analysis of 200 A-scans (single radar traces) per species, we were able to differentiate them in the frequency domain, demonstrating the potential of signal processing techniques for mapping tree roots. Validation was achieved through excavation of the site around L. ferrea (which was suppressed), enabling the accurate identification of each root encountered.

Conclusions Using spectral analysis and ANN, it was possible to differentiate the root system of the 3 species evaluated using GPR data.

Keywords

Introduction

Urban afforestation plays a vital role in promoting environmental quality and enhancing urban resilience. Urban trees help regulate temperature, mitigate air and noise pollution, improve mental well-being, and foster biodiversity (Yin et al. 2024). To fully realize these benefits, it is crucial to understand and manage not only the aboveground components of trees but also their root systems (Cavalari et al. 2024). Urban root systems are interconnected with built infrastructure, and inadequate management can result in pavement uplift, damage to subterranean utilities, and compromised structural stability of the trees. Therefore, investigating tree roots is essential for both tree health and the sustainability and safety of urban environments (Masini et al. 2023).

Effective methods for assessing tree roots are critical for urban forest management (Fantozzi et al. 2024). Root evaluations enable arborists and planners to make informed decisions regarding tree health, risk mitigation, and infrastructure protection. Traditional approaches, such as manual excavation, are invasive, labor-intensive, and potentially harmful to both the tree and its surrounding environment. This underscores the need for accurate, noninvasive techniques capable of evaluating root systems without disturbing the soil (Grabosky et al. 2025).

Ground penetrating radar (GPR) has emerged as a promising technology for noninvasive geophysical investigations, including root detection (Nichols et al. 2017). GPR is increasingly applied in arboriculture due to its ability to map root systems efficiently and nondestructively, providing information about spatial distribution, depth, and diameter (Moraes Amaral et al. 2022; Santos and Filho 2024). The technique operates by emitting electromagnetic pulses into the ground and analyzing the signals reflected from objects with differing dielectric properties (Annan 1996; Daniels 2004). However, interpreting GPR signals remains challenging, particularly in heterogeneous soils where signal clutter, multiple reflections, and noise hinder the accurate identification of roots (Luo et al. 2022; Aboudourib et al. 2024; Rocha et al. 2024).

To improve the interpretability and accuracy of GPR data, advanced signal processing techniques, particularly spectral analysis, are increasingly implemented. Spectral analysis examines the frequency content of GPR signals, allowing the identification of patterns and the differentiation of subsurface features based on their dielectric characteristics (Lai et al. 2010; Santos et al. 2014). This approach improves root detection by reducing noise and enhancing the contrast between roots and surrounding soil (Lantini et al. 2022). When integrated with conventional GPR imaging, timefrequency analysis offers a more robust framework, leading to more reliable assessments in complex urban settings (Guo et al. 2022). Time-frequency analysis is a signal-processing framework that characterizes the temporal evolution of the signal spectral content with high resolution.

Analyzing GPR signals in the frequency domain reveals subtle spectral variations that may not be evident in the time domain, thus improving the discrimination of subsurface structures (Santos et al. 2014). Among the techniques commonly used are the shorttime Fourier transform (STFT), which provides a time-frequency decomposition of the signal (Allen and Rabiner 1977; Owens and Murphy 1988; Tomazic 1996), and power spectral density (PSD), which describes how signal power is distributed over frequency (Welch 1967; Saghfi et al. 2019).

Time-frequency analysis based on the STFT and PSD plays a fundamental role in the interpretation of GPR signals, particularly in complex and heterogeneous environments. The STFT allows the temporal evolution of spectral content to be examined and facilitates the identification of nonstationary responses, such as those produced by tree roots, amid noise and multiple reflections (Allen and Rabiner 1977; Cohen 1995). On the other hand, the PSD provides a global representation of how signal energy is distributed across the frequency domain, enabling objective comparisons of spectral amplitudes and the extraction of features from materials (Welch 1967). Compared with other time-frequency tools, such as wavelet transforms or more adaptive methods, STFT and PSD offer the advantages of conceptual simplicity, computational efficiency, and providing a good result with GPR signals (Santos et al. 2014).

Another tool to analyze GPR signals, artificial intelligence (AI), particularly artificial neural networks (ANNs), is increasingly employed to address the persistent challenges in GPR signal interpretation (Wang et al. 2022). These methods rely heavily on the quality of extracted signal features. Spectral analysis, by enhancing signal representation, facilitates the capture of relevant temporal and frequency characteristics necessary for accurate classification in complex soil environments (Luo et al. 2022).

ANNs are computational models inspired by the functioning of the human brain, capable of learning complex relationships between input and output data (Bishop 1995). In supervised classification tasks, ANNs can be trained to recognize subtle patterns in highdimensional data (Ripley 1996). The use of ANNs in this context aims to automate the root identification process, reducing the subjectivity inherent in manual interpretation and increasing the robustness of the analysis in complex environments. In this study, spectral analysis techniques and ANNs were applied to distinguish subsurface roots of 3 tree species, Jacaranda mimosifolia D. Don; Libidibia ferrea (Mart. ex Tul.) L.P.Queiroz; and Handroanthus impetiginosus (Mart. Ex DC.) Mattos, in order to reduce uncertainties in tree risk assessment and its management.

Materials and Methods

Study Site and Data Acquisition

The study area was characterized by a permeable surface covered with grass composed of landfill material and fine sand with low clay content and brown to reddish coloration, free of any infrastructural element (pipes or cables) that could impede proper root growth. Three tree species were present: Jacaranda mimosifolia D. Don; Libidibia ferrea (Mart. ex Tul.) L.P.Queiroz; and Handroanthus impetiginosus (Mart. ex DC.) Mattos. Jacaranda mimosifolia was a mature and vigorous specimen, showing no signs of xylophagous infestation. It measured 8 m in height with a diameter at breast height (DBH) of 44 cm. The L. ferrea specimen exhibited a severely inclined trunk and an internal cavity with advanced wood decay. It measured 18 m in height and had a DBH of 58 cm; due to its compromised condition, the tree was removed before the GPR survey, leaving only the stump (Amaral et al. 2022). Handroanthus impetiginosus was another mature tree in apparent good health, standing 18-m tall with a DBH of 46 cm.

Jacaranda mimosifolia, from the Bignoniaceae family, is native to South America and can reach 15-m high and a DBH of 30 cm to 50 cm. Its wood has a density ranging from 0.49 g/cm3 to 0.65 g/cm3, and the wood has a moderate natural durability against insects and fungi, with colors presenting varying from light brown to yellowish, occasionally with gray or purplish tones (Araújo et al. 2022). Anatomically, it is classified as diffuse-porous, with vessels evenly distributed across growth rings, small to medium in size, and occurring solitarily or in radial multiples.

Libidibia ferrea is a Brazilian native species from the Fabaceae family (Lorenzi 1992). It reaches heights of 10 m to 15 m and has a DBH of 40 cm to 60 cm. The wood is highly dense (0.99 g/cm3 to 1.27 g/cm3) (Carvalho 2003), hard, heavy, and exhibits high natural durability (Campos-Filho and Sartorelli 2015). Heartwood and sapwood are distinctly colored: the heartwood is dark brown to blackish, while the sapwood is yellowish-beige (Cury 2001). The wood is diffuse-porous, with medium to large vessels and simple perforation plates.

Handroanthus impetiginosus, from the Bignoniaceae family, is also native to South America, featuring dense wood (0.90 g/cm3 to 1.07 g/cm3) with pale sapwood and dark yellow to olive or greenish-brown heartwood. The species can reach heights of 20 m to 30 m and a DBH of 30 cm to 60 cm. It is malleable, mechanically resistant, and resistant to rot and insect attacks (high durability)(Carvalho 2003; Moraes Neto 2021). Its anatomy presents diffuse-porous: growth rings are not visible; the vessels are solitary and radial multiples, medium to large, few to moderately numerous; and tyloses and other colored mineral deposits are common.

GPR data were acquired around the former position of the L. ferrea tree using a 900-MHz antenna (Geophysical Survey Systems Inc., Nashua, NH, USA). A 5.0 m × 5.0 m grid was established around the tree with parallel profiles acquired at 0.1-m intervals in both X and Y directions, resulting in a total of 133 profiles. Acquisition parameters were selected to enable high-resolution subsurface root characterization: 1,024-time samples per trace, 0.05-m spacing between A-scans, a 70-ns time window, and the velocity for time-depth conversion was 0.08 m/ns. Data processing and visualization were performed using ANDAS Technology (Santos et al. 2022).

Following GPR data collection, the area surrounding the L. ferrea (5 m × 5 m) was excavated using an air spade (high-pressure air jet), allowing for the visual identification and separation of root systems from each tree. Figure 1a and 1b show the studied area with the 3 trees and the excavation area, respectively, while Figure 1c presents a schematic diagram of the identified roots for each species.

Figure 1.

(a) Trees in the studied area: A – Jacaranda mimosifolia; B – Libidibia ferrea (before removal); C – Handroanthus impetiginosus. (b) Exposed roots. (c) Scheme of the trees and roots in the studied area.

The 3 tree species evaluated in this study exhibit distinct structural root system characteristics that influence their interaction with the subsurface environment and GPR signal responses. All roots excavated were healthy with no apparent signs of biodeterioration by fungi or insects. Libidibia ferrea develops a prominent taproot system, characterized by a thick central root that penetrates deeply into the soil, providing strong anchorage and drought resilience. In contrast, J. mimosifolia typically presents a more diffuse and moderately deep root system, with smaller lateral roots distributed more evenly (Lorenzi 2002). Handroanthus impetiginosus, while also possessing dense wood and robust roots, tends to form a more irregular and fibrous root structure, adapting to varying soil conditions with both vertical and horizontal extensions (Parcianello et al. 2021). These anatomical and morphological differences can affect the contrast in the subsurface, thereby influencing root detectability and classification in GPR surveys.

Short-Time Fourier Transform (STFT)

The Fourier analysis transfers signals from the time domain to the frequency domain, and it is limited to stationary signals whose properties change with time. This transform eliminates the time resolution of the signal which makes it unable to capture signal transitions over time.

Thus, an analysis method adapted for nonstationary signals requires more than the Fourier transform (Cohen 1995; Sejdic et al. 2009). The STFT is a time-frequency technique commonly used for this purpose. The STFT can be defined as follows: STFTsw(t,f)=τs(τ)w(τt)ej2πfτdτ1 and in a discrete form to the time series s(n) formed by b samples: STFTsw(i,p)=n=0bs(n)w(in)ej2πcib2 where i and p = 0, 1, 2, ..., b-1. STFT produces a local spectrum of the signal s(n) around sample i. The entire power spectrum, corresponding to all time points, produces a 2-D representation, time-frequency, called a spectrogram. The spectrogram is a common tool in signal analysis and provides the distribution of signal energy in the time-frequency plane.

Power Spectral Density (PSD)

A sequence of samples can be represented by PSD, a set of spectral coefficients. PSD computes the average power distribution of a time series signal over the frequency domain. PSD deals with random signals most of the time, so it can only be estimated. One of the methods to estimate PSD is called periodogram and can be defined as follows (Welch 1967): PSD=X(f)X(f)*2π3 where X(f) is the Fourier Transform of the signal, X(f)* is the complex conjugate of the Fourier transform, and f represents the frequency domain.

Artificial Neural Networks (ANNs)

ANNs are computational models inspired by biological neural systems and have proven effective for pattern recognition tasks, particularly in processing complex, high-dimensional data (Ripley 1996). In geophysical applications such as GPR, ANNs provide a robust framework for signal classification, especially in heterogeneous subsurface environments. By learning nonlinear relationships between input features and class labels, ANNs can enhance classification accuracy and improve model generalization (Bishop 1995).

In this study, a feedforward neural network was implemented using TensorFlow (Abadi et al. 2015) (Python language) to classify roots from 3 tree species based on spectral features extracted from GPR data. The input layer consisted of 4 features: GPR amplitude, STFT amplitude, PSD amplitude, and the dominant frequency obtained from PSD analysis. The network architecture included 1 hidden layer with 25 neurons using the ‘ReLU’ (Rectified Linear Unit) activation function, and an output layer with 3 neurons (1 per species: –1 to J. mimosifolia, 0 to Libidibia ferrea, and 1 to Handroanthus impetiginosus) using the ‘softmax’ activation function. A total of 600 A-scans were used (200 for each species), with 30% reserved for testing and 70% for training. The model was trained in over 200 epochs, and performance was evaluated using classification accuracy and confusion matrices.

Results

From the 3D GPR data, it was possible to construct the depth slices (C-scans) for the evaluation of the mapped root system. In Figure 2, we have slices ranging from 0.06 m to 0.45 m of depth, where the main roots appear between 0.11 m and 0.34 m, spreading in all directions of the evaluated area. With only the data in the time domain, it is not possible to differentiate the tree species to which the root belongs, only to make an inference from the location of the specimen. Thus, we selected depths (0 m to 0.45 m) with greatest number of roots to perform the spectral analysis.

Figure 2.

GPR depth slices around the L. ferrea tree (lilac/purple lines are the mapped roots in the subsoil).

To illustrate the process, Figure 3a shows the GPR slice at a depth of 0.14 m, where at 3.8 m along Y direction (dashed black line) we have the presence of root branches of the evaluated species J. mimosifolia (A – black line), L. ferrea (B – blue line) and H. impetiginosus (C – green line). From the GPR data it was possible to obtain the amplitude distributions for the STFT (Figure 3b) and PSD (Figure 3c). Each timefrequency tool allows a different visualization of the marked roots, showing that each of them can provide different information for each species. From the example we see that for branch A, in STFT and PSD signal processing, the roots appear little or not at all in the images, showing a small amplitude. On the other hand, roots B and C are well highlighted in all processing.

Figure 3.

As per Figure 2, depth slice in 0.14 m of depth. (a) GPR data (A – J. mimosifolia; B – L. ferrea; C – H. impetiginous). Dashed line: selected GPR profile in X = 3.8 m. (b) STFT data. (c) PSD data (slice in 900 MHz).

Figure 4 presents the selected GPR profile (B-scan) at X = 3.8 m (black dashed line in Figure 3a), where diffraction hyperbolas associated with subsurface roots from the 3 studied species are observed, J. mimosifolia in black, L. ferrea in blue, and H. impetiginosus in green (Figure 4a). In a similar manner, amplitude distributions derived from the STFT (Figure 4b) and the PSD (Figure 4c) were extracted from the GPR data. Figure 5 illustrates representative examples of GPR signals (A-scans) and their corresponding spectral transformations for each of the 3 root classes. The original GPR signals (Figure 5a) demonstrate differences in waveform structure, with L. ferrea exhibiting the highest initial amplitudes and more persistent oscillations compared to J. mimosifolia and H. impetiginosus. In contrast, H. impetiginosus presents a damped signal with lower amplitude and reduced duration, suggesting a weaker dielectric contrast.

Figure 4.

(a) GPR profile extracted at 3.8 m along Y direction (black dashed line in Figure 3a). (b) Corresponding STFT profile. (c) Corresponding PSD profile. Colored dashed lines and arrows: positions of J. mimosifolia (black), L. ferrea (blue), and H. impetiginosus (green). Dashed white line: 900-MHz central frequency.

Figure 5.

Example of signals selected to J. mimosifolia (black line), L. ferrea (blue line), and H. impetiginosus (green line). (a) GPR raw A-scans. (b) STFT amplitudes. (c) PSD amplitudes (dashed red line: 900-MHz central frequency).

The STFT amplitude plots (Figure 5b) further highlight these distinctions in the time-frequency domain. The L. ferrea signal displays higher energy concentrations in the early nanoseconds, while H. impetiginosus shows a notably lower energy distribution throughout the signal. The J. mimosifolia response presents an intermediate behavior, with moderate amplitude peaks distributed across the time axis. These patterns reinforce the visual contrast observed in the raw GPR traces and indicate species-specific spectral energy distributions.

In the frequency domain (Figure 5c), the PSD curves reveal a dominant frequency range around 0.75 GHz to 1.0 GHz, with L. ferrea showing the highest amplitude, especially around 0.75 GHz. Although all 3 classes share a similar dominant frequency range (dashed red line indicates the 900-MHz central frequency), the amplitude of the spectral peaks differs, supporting the relevance of frequency-domain features in distinguishing root types. Together, these examples illustrate how signal characteristics in the time and frequency domains vary among root types, providing the basis for feature extraction and subsequent classification using ANN.

The boxplots in Figure 6 show a variation in the analysis within each one of the three species. We also used the nonparametric Kruskal-Wallis and Dunn tests to determine if there were statistically significant differences in these variables between the species. Figure 6a shows the distribution of GPR amplitudes.

Figure 6.

Statistical characterization of the input features used in the ANN for root classification, based on GPR data. Three root classes: J. mimosifolia (black), L. ferrea (blue), and H. impetiginosus (green). Differences among classes were assessed using the Kruskal-Wallis test followed by Dunn’s post hoc test (P < 0.05), and statistically distinct groups are denoted by different uppercase letters. (a) GPR amplitudes. (b) STFT amplitudes. (c) PSD amplitudes. (d) PSD frequencies (MHz).

No significant difference was observed between J. mimosifolia and L. ferrea (group A), while H. impetiginosus showed significantly lower amplitudes (group B). This pattern suggests that H. impetiginosus roots produced weaker direct reflections in the radar signal, potentially due to smaller root size, wood density, or contrasting dielectric properties (moisture content). In Figure 6b, STFT amplitudes differed significantly among all 3 classes, with J. mimosifolia, L. ferrea, and H. impetiginosus each occupying separate statistical groups (A, B, and C, respectively). The progressive decrease in amplitude from J. mimosifolia to H. impetiginosus reflects distinct time-frequency energy distributions, indicating that STFT-based features are highly effective in distinguishing root signal characteristics. Figure 6c displays PSD amplitudes. Here, L. ferrea roots presented significantly higher values (group B) than both J. mimosifolia and H. impetiginosus (group A). This may indicate a greater concentration of spectral energy in certain frequency bands, possibly due to morphological or structural differences in the L. ferrea roots that affect radar backscattering behavior. Finally, Figure 6d illustrates the dominant frequencies obtained from PSD analysis. No statistically significant differences were found among the 3 classes (all in group A), although a trend is evident by J. mimosifolia, and L. ferrea showed higher median frequencies (approximately 700 MHz to 900 MHz) compared to H. impetiginosus (approximately 600 MHz). This subtle variation may relate to the composition of the root systems but was not sufficient to yield significant group separation under the applied statistical tests.

The performance of the ANN was evaluated over 200 training epochs, as shown in Figure 7. The accuracy plot (Figure 7a) reveals a rapid increase in performance during the first 30 epochs, with validation accuracy surpassing 95% and remaining stable throughout the remainder of the training. Training accuracy followed a similar trend, indicating strong model generalization and the absence of overfitting. The loss curves (Figure 7b) further support this observation, showing consistent reduction and stabilization of both training and validation loss. The minimal gap between the curves suggests a well-balanced learning process, without signs of memorization of the training data.

Figure 7.

Performance of the ANN developed for the classification of 3 tree root classes based on features extracted from spectral analysis of GPR data (AUC: Areas Under the Curve). (a) Accuracy plot. (b) Loss curves. (c) ROC curves. Jm (J. mimosifolia); Lf (L. ferrea); Hi (H. impetiginosus).

Figure 7c presents the receiver operating characteristic (ROC) curves for the 3 target classes: J. mimosifolia, L. ferrea, and H. impetiginosus. The corresponding areas under the curve (AUC) were 0.93, 0.95, and 1.00, respectively, demonstrating excellent discriminative capability of the model across all classes. Notably, the H. impetiginosus class was classified with perfect performance (AUC = 1.00). These results indicate that the ANN was effective in identifying distinct spectral patterns associated with different species or morphological types of tree roots, highlighting its potential as a nondestructive diagnostic tool in urban environments.

Discussion

The relationship between the statistical behavior of the extracted features and the classification performance of the ANN provides important insights into how the spectral analysis can be used to characterize tree roots with the GPR method. While previous studies have largely focused on the detection and spatial mapping of roots (Li et al. 2025; Salako et al. 2025; Santos et al. 2025), the results presented here show that spectral features can also be used to achieve specieslevel discrimination. By combining time-frequency analysis with machine learning, the results provided a more reliable characterization of subsurface root systems.

Amplitude-based features derived from the STFT and PSD exhibited clear and statistically significant differences among the 3 root classes. These differences indicate that each species generates a distinct radar response, which cannot be fully explained by spatial position alone. Unlike traditional time-domain interpretation, where root identification often relies on geometric assumptions or excavation context, the use of spectral features allows discrimination to be based on intrinsic signal characteristics linked to root properties.

The strong performance of the ANN further supports this interpretation. The model quickly achieved high accuracy, with stable loss curves, and high AUC values demonstrating good generalization. The perfect classification achieved for H. impetiginosus is consistent with its pronounced separation in several feature distributions, particularly those associated with STFT and GPR amplitudes. These results suggest that the ANN effectively integrates complementary information from multiple spectral descriptors, even when individual features alone do not provide complete separation.

Although the dominant frequency extracted from the PSD did not differ significantly among species, small trends were observed. This indicates that frequency-related features may be less sensitive when used in isolation but still contribute useful information when combined with amplitude-based descriptors. In contrast, the STFT proved especially effective in capturing differences related to the nonstationary nature of root reflections, emphasizing the importance of time-frequency representations for interpreting complex subsurface targets.

The differences observed in signal amplitudes can be explained by a combination of root size, burial depth, and internal moisture content. Previous studies have shown that target size strongly affects the spectral response of GPR signals, with larger targets producing higher reflection amplitudes and more pronounced spectral signatures (Santos et al. 2014). Burial depth also influences signal attenuation and temporal resolution, potentially introducing uncertainties in root identification. However, such effects can be mitigated through appropriate antenna frequency selection, which could compromise the resolution of subsurface targets (Moore and Ryder 2015). The depth and diameter variations found by excavation were relatively limited (with depth differences of approximately 0.5 m and diameter variations on the order of 0.15 m), suggesting that geometric effects alone cannot fully account for the observed spectral differences.

Under these conditions, root moisture content has a significant influence on the results obtained by the GPR method. Because water has a high dielectric constant relative to dry soil and woody tissues, roots with higher moisture content tend to generate stronger reflections and clearer hyperbolic signatures in GPR data (Annan 2003; Butnor et al. 2003). Differences in moisture distribution between species and within individual root systems therefore play a key role in shaping both amplitude and spectral behavior. Despite the combined influence of size, depth, and moisture, the ANN successfully separated the 3 species, indicating that the selected spectral features retain strong discriminatory power even in the presence of these confounding factors.

Overall, these findings demonstrate that spectral and amplitude-based descriptors derived from GPR data, when combined with machine learning techniques, provide a robust framework not only for root detection but also for species-level characterization of subsurface root systems. This approach represents methodological advancement over traditional GPR-based analyses and offers promising applications in urban forestry, tree risk assessment, and subsurface infrastructure management.

Conclusions

This study presents a novel approach for classifying tree root types in urban environments by combining GPR data with spectral analysis (STFT and PSD) and ANNs. The results demonstrated that signal features extracted from the GPR waveforms varied significantly among the 3 studied species, J. mimosifolia, L. ferrea, and H. impetiginosus, particularly in terms of amplitude and frequency content. These differences were effectively captured by the machine learning model, resulting in high classification accuracy and strong discriminative performance.

The integration of geophysical and spectral data with neural networks offers a promising, noninvasive method for identifying root types and assessing belowground structure in urban trees. This has practical implications for urban forestry, particularly in root detection, species identification, and planning for tree risk assessment and infrastructure management. Nonetheless, further studies are needed to expand the range of root types, environmental conditions, and urban soil contexts. These developments may enhance the applicability of this technique as a practical tool for arborists and urban forestry professionals.

Conflicts of Interest

The authors reported no conflicts of interest.

Acknowledgements

This work was carried out based on the Cooperation Agreement (No. 0070/2019) between IPT and Kerno Geo Soluções and was supported in part by the São Paulo Research Foundation— FAPESP under Grants 2017/22855-9 and 2019/09483-0.

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