# Contribution of hyperspectral analysis in relative dating applied to Miculla petroglyphs (Peru)

Frédéric-Victor Donzé, Laurence Audin, Bernard Schmitt, Audrey Taillefer, Laurent Truche

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Frédéric-Victor Donzé, Laurence Audin, Bernard Schmitt, Audrey Taillefer, Laurent Truche. Contribution of hyperspectral analysis in relative dating applied to Miculla petroglyphs (Peru). Journal of Archaeological Science, 2024, 169, pp.106023. 10.1016/j.jas.2024.106023. hal-04989503

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# Contribution of hyperspectral analysis in relative dating applied to Miculla petroglyphs (Peru)

Frédéric-Victor Donzé<sup>a,*</sup>, Laurence Audin<sup>a</sup>, Bernard Schmitt<sup>b</sup>, Audrey Taillefer<sup>a</sup>, Laurent Truche<sup>a</sup>

## ARTICLE INFO

**Keywords:**

Miculla petroglyphs

Petroglyph dating

Rock varnish

Hyperspectral analysis

## ABSTRACT

The Tacna region in southern Peru hosts archaeological remnants of Pre-Columbian period human occupations, including the Miculla Petroglyphs. Existing methods for dating these petroglyphs present substantial uncertainties and are subject to claims lacking objective validation. This study employs advanced hyperspectral analysis, specifically utilizing the SPECIM IQ camera, to reevaluate existing chronological proposals for these petroglyphs. The employed analytical technique is non-destructive and captures spectral data across an extensive range of wavelengths. This allows for a quantitative assessment of patination levels attributable to solar exposure, in comparison to adjacent intact areas. Data from various petroglyphs were analyzed using SPECIM IQ Studio software and Matlab. The analysis differentiated between “engraved” and “varnished” regions on selected boulders. Reflectance ratios between these areas were compared to provide insights into the potential relative ages of different sets of engravings. The results question pre-existing chronologies based on cultural classification schemes for the petroglyphs. While the study underscores the utility of hyperspectral analysis in refining petroglyph dating, it also indicates that this method cannot replace a multi-method approach without further resolution refinement.

## 1. Introduction

The Tacna region, situated in the southernmost part of Peru, provides evidence of past human occupations in the South American continent (Baitzel and Infante, 2019). The discovery of ancient tools, dating back to the Holocene period and remnants of fire pits at various archaeological sites around Tacna suggests long-term human presence (Lavallée et al., 2011). As societies began to settle, Tacna became a cultural melting pot for different civilizations, such as the Wari, Tiwanaku, and the Inca Empire, each leaving distinctive imprints (Magilligan et al., 2008).

Tacna's location along the 'Andean Corridor', a key trade and cultural exchange route extending from Colombia to Argentina, further underscores its importance (Echevarria Lopez, 2020). The Miculla Petroglyphs, a focal point of early human occupation in the Tacna region, offer a glimpse into the region's rich cultural history (Guffroy, 2009). Situated amidst a desert area, these rock carvings on scattered boulders provide an extensive view into the world of ancient societies that once

thrived here.

Approximately 11,000 years ago, the Earth's climate began to warm, marking the onset of the Holocene. Drawing upon data from multiple sources, including Arnold et al. (2021), Abbott et al. (1997a,b), Baitzel et al. (2019), Guffroy (2009), Latorre et al. (2006), Lavallée et al. (2011), Mächtle and Eitel (2013), Magilligan and Goldstein (2001), Magilligan et al. (2008) and Osorio Soto (2023), a chronology of human presence and activity in southern Peru during the Holocene until the end of Late intermediate period can be proposed (Fig. 1). This chronology also allows for the identification of distinct human groups that inhabited the region during various Holocene periods.

During the transition from the Late Pleistocene to the Early Holocene, the Atacama Desert and the Altiplano experienced wetter climatic conditions (Latorre et al., 1997). Early Andean communities emerged during this period, engaging in trade and initiating the domestication of species, particularly in the coastal inter-Andean valleys. The Early Holocene, approximately 8000 to 5000 BCE (Before Common Era), was marked by initial short-term occupations and potential interactions with

<footnote><sup>a</sup> University Grenoble Alpes, University Savoie Mont Blanc, CNRS, IRD, IFSTTAR, ISTerre, 38000, Grenoble, France</footnote>

<footnote><sup>b</sup> Université Grenoble Alpes, CNRS, IPAG, 38000, Grenoble, France</footnote>

<footnote>* Corresponding author.
E-mail address: frederic.donze@univ-grenoble-alpes.fr (F.-V. Donzé).</footnote>
highland communities. The primary inhabitants during this period were early hunter-gatherers, who may have had contacts with groups residing in elevated regions (Lavallée et al., 2011).

As the Holocene progressed into its middle phase, around 5000 to 4000 BCE, there was a shift towards more intensive and nearly year-round occupation (Baitzel and Infante, 2019), see Fig. 1. The local sourcing of raw lithic materials for tool production during this period could indicate reduced mobility compared to earlier phases.

Between 4800 and 3640 BCE, the Mid-Holocene experienced drier climatic conditions, evidenced by the absence of large El Niño-related floods (Magilligan et al., 2008). During this period, close relation between the artifacts found in the Tacna region and the Chilean sites of the Chinchorro was confirmed by Lavallée et al. (2011) (Fig. 1). Both marine and terrestrial resources were exploited. While the specific human groups and activities during this period have not been explicitly detailed in other studies, it is likely that local communities adapted to these drier conditions as the Chinchorro did. The Late Holocene saw increasingly climate variations (Latorre et al., 1997). For example, this period was marked by the rise and fall of the Tiwanaku or Wari civilizations, which was influenced by alternating wet and dry periods (Magilligan et al., 2008), see Fig. 1. Note that the Tiwanaku occupied the Altiplano and exerted significant regional influence, extending all the way to Tacna region (Baitzel and Infante, 2019). By around 1300 CE (Common Era), human activity was characterized by long-term adaptations to the recurring El Niño events in South Coastal Peru. These communities of the Late Intermediate Period, such as the Aymara, which is still present today, are often considered descendants of the Tiwanaku (Fig. 1).

Among the diverse Andean ethnic groups—namely the Chinchorro, Huaracane, Wari, Tiwanaku, Chiribaya, and Aymara, whose respective chronologies are illustrated in Fig. 1—which can be attributed with the creation of the Miculla quilcas? The term ‘quilcas’ is a multifaceted concept in various native Andean languages, signifying ‘graphic expression’ and also serving as a technical category for petroglyphs (Echevarria Lopez, 2020). In the next section, we will first explore the

current state of knowledge regarding the dating of these petroglyphs. We will see that the current chronologies present inconsistencies that obscure a clear understanding of the origins of these artistic creations. Subsequent advancements in technology have expanded the paths for both direct and indirect dating methods. Specifically, we will then present a hyperspectral imaging (HSI) analysis—a technique that captures and processes spectral data across an extensive wavelength range—as a means to potentially refine with the help of other archaeometric methods, the existing, yet conflicting, chronologies of these petroglyphs.

## 1.1. Miculla Petroglyphs

Echevarria Lopez (2020) focused on determining the sequence and chronology of the Miculla archaeological site (Fig. 2). The methodology of the author is grounded in a combination of field survey for visual record and formal analysis, taphonomic logic, culturalist anthropology assessment as well as cross-chronological relationships and relative estimates.

One of the key elements of the methodology is the formal-culturalist

<figure><img src="image_4.png" /><figcaption>Fig. 2. General view of Miculla, District 1 (photo credit F.-V.Donzé).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Compilation of the paleo-climatic dataset obtained from Arnold et al. (2021), Abbott et al. (1997a,b), Latorre et al. (2006), Magilligan and Goldstein (2001) and Magilligan et al. (2008). The green zones correspond to humid periods, and the yellow zones to drier ones. In red, the corresponding artifacts identified by Baitzel et al. (2019) in the Sama Valley, close to the Miculla site (Caplina Valley). In blue, the different ethnic or cultural groups related to the Petroglyphs of Miculla according to Lavallée et al. (2011), Magilligan et al. (2008), and Guffroy (2009). In black, the chronologies proposed by Echevarria Lopez (2020) and Guffroy (2009) for the petroglyphs of Miculla. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
approach, which is based on the idea that similar graphic elements could have been produced following the same behavioral parameters. Therefore, any formal difference in the petroglyphs could be interpreted as the result of different cultural behaviors. This methodology allows to determine whether the quilcas of Miculla correspond to more than one cultural period of graphic production or were produced by more than one social group. To this end, the author incorporates a taphonomic perspective, which considers the processes of decay and preservation affecting the petroglyphs.

The analysis results support the hypothesis that the site was created in more than one chronological period, dating back to at least 4500 BCE, and by different cultural groups (see Fig. 1). The formal contrast between the quilcas indicates that the site experienced a remarkable interregional occupation dynamic. From this study, *Echevarria Lopez (2020)* proposes a classification of the petroglyphs into different groups and the state of conservation and patination are used as temporal indicators to establish a sequence such as:

* Group 1 (4500-2500 BCE): With a strong weathering and patination observed in this group, Echevarria Lopez proposed that these petroglyphs are among the oldest at the site. The abstract, geometric, and semi-naturalist motifs, along with the irregular quality of the lines, may reflect the artistic conventions of the time when they were created.

* Group 2 (3000-1000 BCE): These petroglyphs, dominated by zoomorphic and anthropomorphic designs, show good conservation and less weathering than Group 1, suggesting they are younger. The high quality of manufacturing could indicate advancements in technique over time.

* Group 3 (1200-100 BCE): These petroglyphs are mainly anthropomorphic and to a lesser extent zoomorphic. They show a good state of conservation, suggesting they are not as old as those in Group 1. However, the higher levels of patination in some motifs of Group 2 compared to Group 3 suggest that some of the Group 2 petroglyphs are older.

* Group 4 (200 BCE – 500 CE): The abstract-geometric motifs in this group are found in spaces within panels with motifs from other groups, suggesting they were added later. The difference in patination also suggests that this set of quilcas is later in the sequence.

Some examples of quilcas belonging to different groups are presented in Fig. 3.

While the methodology is multi-faceted, incorporating field surveys, formal analysis, taphonomic logic, and culturalist anthropology theory, the defined groups of petroglyphs are circumscribed by the sample and its visual recognition, inherently restricting the generalizability of the findings. The study heavily relies on the level of patination and the state of conservation from a visual point of view as primary temporal indicators. It seems that the absence of quilcas with superimposed motifs also limits the ability to establish a clear temporal sequence and the

spatial proximity does not necessarily establish a cultural or chronological link between petroglyphs. What is currently observable is merely a fraction of the original art, meaning that any proposed chronology is based on incomplete data, which could be misleading. The study also notes drastic changes in the formal language of the petroglyphs between different groups. Such qualitative leaps in form raise questions about the cultural and chronological continuity of these petroglyphs. While *Echevarria Lopez (2020)* provides a comprehensive methodology for establishing a chronology for Miculla petroglyphs, this study suffers from some weaknesses that limit its scientific validity. Especially since previous studies have associated Miculla petroglyphs to more recent epochs.

Flores Espinoza (1979) proposed that the petroglyphs belong to the Late Regional Periods, specifically around 1000-1400 CE. Her justification is based on the similarity of the petroglyphs to the ceramics of the Gentilar, San Miguel, Collao, and Chiribaya styles. Ayca (1987), reported by *Echevarria Lopez (2020)*, suggested that the petroglyphs date to the Late Intermediate Period, specifically the 11th-15th century AD (Anno Domini). He based his proposition on the presence of Chiribaya ceramic and Collao black-on-red pottery in the area. Then, *Gordillo Bergazo & Lopez Hurtado (1987)* proposed that the petroglyphs could be associated with local developments, specifically the Gentilar phase and the Inca era (Inca Chucuito). They also considered the possibility of a Tiwanaku era association. Their justification is based on the presence of Gentilar and Chicuito ceramics and an association with Tiwanaku era sites.

Later on, *Guffroy (2008, 2011)* delves into the complexities of petroglyph traditions in South Peru, specifically focusing on Tradition B and Tradition C. According to this author, Tradition B, which emerged between 200 BCE and 600 CE, is predominantly found along the north and central coasts of Peru, stretching from the valley of the Río Chancay to Nazca. This tradition is characterized by its intricate and often indecipherable geometric figures. The petroglyphs in this category are generally small and depict a range of subjects from humans and supernatural beings to local fauna such as foxes and snakes. On the other hand, Tradition C appears later in the historical timeline, specifically between 700 and 1532 CE according to *Guffroy (2008, 2011)*, and is closely tied to the communication routes and caravan paths in southern Peru. The most significant site representing this tradition is Toro Muerto in the department of Arequipa, which boasts several thousand engraved blocks. These engravings are stereotypically executed but with a level of care, featuring humans engaged in various activities such as dancing and animal husbandry. Additionally, various animals like felines and birds are commonly depicted, along with zigzag lines and some cupules. Regarding Miculla site, *Sekouri (2018)* emphasizes its complexity, which features not only petroglyphs but also other artificial remains such as tombs, apachetas, pathways, irrigated agricultural zones, and dwellings. According to the author, the petroglyphs were created from around 1000 CE until the arrival of the Spanish. This dating is primarily based on indirect evidence, again provided by *Gordillo Bergazo and*

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Examples of petroglyphs associated to group identity (ID), based on the catalog set up by *Echevarria Lopez (2020)*. On the left, quilcas of Group 4 (200 BCE – 500 CE) and on the right, quilcas of group 3 (1200–100 BCE) (photo credit F-V. Donzé).</figcaption></figure>
Lopez Hurtado (1987), who suggest that the dating of the Miculla petroglyphs is supported by the presence of Inca ceramics and archaeological sites associated with the second regionalism in the surrounding areas as mentioned above. These indirect dating methods are corroborated by the presence of tombs with masonry walls at the site, see Guffroy's book (2009). However, the author cautions that this evidence should not be taken as a direct correlation between the petroglyphs and the tombs, given the extensive area that the site covers and its relatively low number of engravings. This timeframe complicates the task of associating these petroglyphs with other elements like geoglyphs, apachetas, and agricultural practices, especially given the extensive area that the site covers. However, one of the most compelling observations is the interaction between irrigated agricultural lands and the petroglyphs. The author still cites Gordillo Bergazo and Lopez Hurtado (1987) who note an irrigation canal extending 1200 m in length that traverses a small area of engraved rocks before terminating in a circular geoglyph within an agricultural zone.

To complete this overview of petroglyph dating, an interesting attempt to do a dating of Bolivian petroglyphs using indirect micro-erosion analysis was been performed by Bednarik (2016). Although it offers wide applications in estimating the ages of many types of geomorphic exposures, micro-erosion analysis has been applied not only to petroglyphs but also to the hammerstones used in their productions, or small spalls recovered from such tools. Bednarik (2016) used this approach at four Bolivian sites and among them to Toro Muerto (in the Mizque valley), not far from Miculla site. This method suggests that a minimum of three traditions by tools have been used on site from 2050 BCE to 1450 AD.

In summary, none of these studies provides irrefutable scientific evidences for the dating of Miculla petroglyphs. This lack of consensus can be attributed to a variety of factors that contribute to the complexity and ambiguity surrounding the site's chronology. While some scholars have employed only stylistic comparisons to date the petroglyphs, others have relied on indirect evidence such as associated ceramics and tombs. These differing approaches used independently inherently lead to disparate conclusions, further complicating the matter.

## 1.2. Possible dating based on the level of patination

In light of Hyperspectral analysis (HSI) — a technique that collects and processes spectral data over a broad range of wavelengths — we propose that this method, which can provide spectral information on the level of patination, could be used as a valuable tool for assessing relative dating (Calvini et al., 2019). The process of patination involves the development of a thin layer called “rock varnish” on exposed rock surfaces (Potter and Rossman, 1977). This varnish is a manganese (Mn) and iron (Fe) oxide-rich layer that can encapsulate traces of other elements like clay minerals. Over time, these layers accumulate incrementally, making them a potential tool in dating petroglyphs. Despite the development of several methodologies, they still fail to explain differences in varnish growth rates in various climates (Dorn et al., 2024). Many hypotheses propose to explain the formation of rock varnish predominantly from subaerial settings, such as direct sunlight, air exposure, photo-oxidation, or the presence of cyanobacteria. However, these approaches often do not apply well in places without light, such as underground or under rock overhangs, where temperatures and chemical conditions are different. Moreover, they do not adequately cover why rock varnish might grow faster in moist or cooler climates, where different chemical reactions and biological activities speed up its formation. Even in very dry deserts, the ways minerals are carried by water and wind can vary significantly, which also affects how fast varnish forms.

To overcome these limits, a promising approach is called the polygenetic model (Chaddha et al., 2024). This approach looks at the formation of rock varnish as a combination of many different biological and geological processes, in order to quantify its complex evolution across

various environments. This model provides insights on how living organisms and natural chemical processes work together to form rock varnish. Although this method shows potential, it is still complex and takes a lot of time to apply.

What we propose here is not to replace such a complex approach, but to use it in a complementary way, by employing the relative spectral reflectance of rock varnish to measure different levels of patination (Dorn and Oberlander, 1982). While high-resolution HSI equipment covering the whole visible and near-infrared ranges (VNIR + SWIR) allows for detailed characterization of the varnish's mineralogical and chemical composition, the use of a less expensive camera restricted to the VNIR range can still yield quantitative data on the level of patination. This is what we will present in the next sections.

## 2. Materials and methods

The methodology behind hyperspectral analysis is rooted in the principles of spectroscopy. Every material absorbs, reflects, and emits light in a unique way across different wavelengths, thereby producing a characteristic 'spectral signature.' Hyperspectral sensors capture these spectral signatures by dividing the electromagnetic spectrum into many contiguous bands, sometimes into hundreds or even thousands. This level of detail far exceeds that of traditional multispectral sensors, which divide the spectrum into only a few wider bands.

The raw data obtained from hyperspectral sensors is often represented as a three-dimensional cube, with two spatial dimensions (length and width of the observed area) and one spectral dimension (wavelength). Each pixel in this cube contains a complete spectrum of the light reflected from the corresponding area on the ground surface, providing information about the materials present there. Therefore, the use of hyperspectral analysis offers an interesting tool for unlocking a wealth of detailed information hidden within the spectral signatures of materials.

### 2.1. Data acquisition using SPECIM IQ camera

We used the portable and lightweight SPECIM IQ camera. At the core of this camera is its hyperspectral sensor. This sensor captures the visible and very near-infrared (VNIR) light reflected from the object or scene under observation and separates it into about two hundred spectral bands. The medium spectral resolution of the camera allows it to capture the unique 'spectral signature' of each material in the scene. The SPECIM IQ camera recording of the full hyperspectral image is based on an internal line scanner process, i.e., the push broom principle. It covers the entire wavelength range of 400-1000 nm at a spectral resolution of 7 nm. Its characteristics are summarized in Table 1 (Behmann et al., 2018).

<caption>**Table 1**</caption>

Characteristics of the SPECIM IQ hyperspectral imaging system and its context RGB camera (Behmann et al., 2018).

<table><thead><tr><th></th><th>SPECIM IQ</th></tr></thead><tbody><tr><td>Sensor type</td><td>CMOS</td></tr><tr><td>Spectral range</td><td>400-1000 nm</td></tr><tr><td>Spectral resolution</td><td>7 nm</td></tr><tr><td>Spectral bands</td><td>204</td></tr><tr><td>Image size</td><td>512 × 512 px</td></tr><tr><td>Focal length</td><td>21 mm</td></tr><tr><td>Field of view (fixed lens)</td><td>31 × 31°</td></tr><tr><td>Imaged wall @ 1m</td><td>55 × 55 cm</td></tr><tr><td>Spatial resolution @ 1m</td><td>1.07 mm</td></tr><tr><td>Focus range</td><td>15 cm - infinity</td></tr><tr><td>Weight</td><td>1.3 kg</td></tr><tr><td>Context RGB image</td><td></td></tr><tr><td>Image size</td><td>1280 × 960 px</td></tr><tr><td>Imaged wall @ 1m</td><td>110 × 82 cm</td></tr><tr><td>Spatial resolution @ 1m</td><td>0.85 mm</td></tr></tbody></table>
Simultaneously with the hyperspectral imaging, a 1.2 Megapixels RGB context image with slightly better resolution is also recorded as a context image, taken from virtually the same point of view (2.5 cm above the HSI lens) and with exactly the same illumination. This provides a comprehensive view of the field of study.

## 2.2. Hyperspectral data analysis

Once captured by the SPECIM IQ camera, we first analyzed a set of hyperspectral reflectance data obtained from various petroglyphs with SPECIM IQ Studio, the software provided with the camera. This platform has been used to remove the noisy parts of the hyperspectral signal, which correspond in our case to the wavelengths lower than 425 nm and higher than 700 nm. Above 700 nm in the near-infrared, there is an increased noise amplitude, which is due to the inherent sensitivity of the sensor used in the imaging process. As we will be using derivatives of the spectrum, we have limited its range to where the peak-to-peak noise is less than 1%. Regarding the contribution of rock grain size on sunlight reflectance at low emission angles, this is a multifaceted issue. The size and orientation of the rock grains play a critical role in determining how light interacts with the surface, affecting specular reflection, scattering, and absorption. This, in turn, can alter at the pixel scale the spectral signature captured in the imaging process. However, the specific effects of rock grain size on sunlight reflectance at low emission angles are complex to consider, as they require millimeter-scale measurements of the rock texture. Therefore, while the influence of grain size and orientation is acknowledged, their effect cannot be evaluated in this type of study. Once the retained spectral signatures of the untouched varnished rock and engraved rock are obtained, we save them in files to be used as input data for Matlab analyses. These analyses involve the comparison between the first and second derivatives, their first integrals of the hyperspectral signatures, as well as their ratio between the untouched varnished rock and engraved rock signatures to highlight their differences in the relative intensity of reflection at different wavelengths.

## 2.3. Data set

The boulders at the Miculla site on which the petroglyphs were engraved, are of alluvial and colluvial origin (Guffroy, 2009; Echevarria Lopez, 2020). Engraved on medium sized blocks of generally dark red granodiorite, the petroglyphs are found scattered both at the bottom of the ravine and on the surrounding terraces (Guffroy, 2009). In all instances, they are hard rocks. The hardness of the rocks is a significant factor, as most of the petroglyphs were produced by a direct percussion technique on natural patina, applied to rocks of varying morphologies and sizes, whether semi-buried or suspended on the slopes of the hills (Echevarria Lopez, 2020).

The petroglyphs are located in different sectors throughout the site. However, the exact number of these groups can vary depending on the methodology of the study and the extent of the explored area. We have selected some petroglyphs, all of them located in the sector close to the museum (Fig. 2).

To accommodate the limited time available on site, we focused our study on a carefully selected sample of petroglyphs that offered a range of visual patinas (see Fig. 4). Our selection included Boulder N°9, which features zoomorphic motifs; Boulders N°1 and N°12, which display both anthropomorphic and zoomorphic motifs; and Boulder N°. 21, characterized by its long-line form. For Boulders N°1, 9, and 12, we further diversified our sample by choosing motifs that faced different directions relative to the sun (Fig. 5). This was done to evaluate how these varying orientations might affect their respective hyperspectral signatures.

# 3. Results

Hereafter, we present key information to reproduce our technical approach, comparable to what we did on Neolithic paintings (Schmitt et al., 2023). The measurement process includes seven steps:

* Reference Panel: After selecting the field of view of the HSI camera, a white reference panel (Spectralon® 99%, 10 × 10 cm) is positioned next to the engraved wall within the instrument's field of view. This allows the capture of the spectral characteristics of the rock surface

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Selected petroglyphs for the study petroglyphs (photo credit F.-V.Donzé). The numbering refers to a database produced by the authors.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Boulder N°1-Zone 1</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Boulder N°9 (Zone 1 bottom square; Zone 2 top square)</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Boulder N°12-Zone 2</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Boulder N°1 (Zone 2 bottom square; Zone 3 top square)</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Boulder N°12-Zone 1</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Boulder N°21-Zone 1</figcaption></figure>

**Fig. 5.** Field of view of the HSI camera for the selected petroglyphs, the white reference panel (is positioned next to the engraved boulder in the field of view of the instrument to allow to capture the spectral characteristics of the rock surface lighting. The letter Z refers to the numbering of the selected "Zone".

lighting simultaneously with the image (simultaneous white reference), as shown in Fig. 5.

* **Focusing:** The hyperspectral camera is then manually focused on the target using the viewfinder camera, a small RGB camera situated just above the spectral camera. The focus is achieved by highlighting sharp edges.

* **Context Image:** To overlay the spectral and viewfinder camera images, their parallax is corrected either automatically or manually.

* **Integration Time:** The integration time is adjusted (in the range of 1–500 ms). The viewfinder camera image provides an evaluation for the integration time of the spectral camera, but manual optimization is always performed to use 80–90% of the detector's capacity, while being cautious about saturation, especially in the white reference target.

* **Recording:** After these initial adjustment steps, the image recording process is triggered. First, a dark reference image representing the sensor background noise and read noise, without incoming light, is recorded automatically. Then, the line scanner starts the actual data acquisition.

* **Validation & Reference Selection:** After the full 512 × 512 pixels image is scanned, the focus and possible saturation or underexposition are checked in the data validation view with a synthetic RGB image derived from the hyperspectral image cube and minimum and maximum intensity pixel histograms. If the image is validated, part of the white area of the Spectralon reference target (typically 2000–8000 pixels depending on camera-wall distance) is then selected by thresholding the intensity of the image followed by a pixel connectivity algorithm.
* Calibration: After removal of the dark background, the calibration process converts the image cube into 'reflectance factor' units by dividing the spectra of all pixels by an average spectrum of the selected area of the Spectralon reference. All the data are automatically stored, including the raw and calibrated hyperspectral data cubes, the dark and white reference spectra, an RGB preview of the HSI data, and the RGB context image.

As mentioned previously, with SPECIM IQ Studio, we can identify and label the unique spectral signatures of specific areas, namely the “engraved” and untouched “varnished” zones located on each selected boulder. This process of setting classes involves labeling pixels in the hyperspectral images that correspond to these zones of interest. Each class represents a specific material characteristic of a particular area, and each pixel labeled as that class provides an example of the zone’s spectral signature. The results of this classification can be visualized in several ways. In this instance, the classified hyperspectral image is displayed in the photo visualization, with each pixel colored according to its classified material: one color for the “engraved” areas and another for the untouched “varnished” areas (Fig. 6). This provides a clear visual representation of the location of each material in the image.

Spectral plot can be displayed for any pixel in the image, showing the measured spectral signature for that pixel and how it compares to the spectral signatures of the defined classes. This allows for a detailed examination of the spectral information upon which the classification is based and can aid in interpreting and validating the results of the classification. Subsequently, an optimized and unique hyperspectral curve is obtained, which we fit with a 7th degree polynomial in Matlab to ensure a negligible calculation bias. Thus, for each zone of each selected boulder, we define two distinct classes: one corresponding to the “engraved” areas and a second one corresponding to the untouched “varnished” areas. For the eight different selected zones presented in Fig. 5, we obtain 16 hyperspectral classes, as presented in Fig. 7.

### 3.1. Results of the hyperspectral analyses

Once these representative polynomial hyperspectral curves are obtained, we can easily obtain their first and second derivatives (Fig. 8). Derivative analysis of hyperspectral data can provide detailed information about the spectral characteristics of the data, including the positions of absorption bands and the presence of specific spectral features. This analysis could potentially identify subtle changes in the spectral data that might correspond to different periods of alteration or different engraving techniques.

The first derivative of a hyperspectral signal provides information about the rate of change in reflectivity across the spectrum, or in simpler terms, the slope of the spectral curve at each point. This can highlight inflection points or changes in the trend of the spectral response that are indicative of different material properties. For instance, a sudden increase or decrease in reflectivity at a particular wavelength range, which might suggest the presence of a specific mineral or chemical compound, can be accentuated in the first derivative.

The second derivative, on the other hand, provides information on the curvature or the rate of change of the slope of the spectral curve. This can be particularly useful for distinguishing materials with similar overall spectral shapes but different detailed spectral features. Materials that might appear similar when comparing raw reflectivity could exhibit distinct second derivative spectra, revealing subtle differences in their spectral features (Tsai and Philpot, 1998).

### 4. Discussions

Looking at the first and second derivative curves (Fig. 8), we can see that the hyperspectral signatures exhibit large variabilities for data from the same set, i.e. the same boulder but with different orientations. Let us consider for example the green curves (Fig. 8 top left) corresponding to the first derivative of the two zones of Boulder 9. This large variability

<figure><img src="image_14.png" /><figcaption>**Fig. 6.** Boulder N°21 (top) and boulder N°14 (bottom) as examples of selected areas for which two classes of materials are defined in order to differentiate the engraved areas (yellow color) from the untouched “varnished” areas (green color). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. 7. The sixteen-hyperspectral classes corresponding, eight for the different “engraved” areas (left) and eight for the different untouched-“varnished” areas (right) extracted from the eight zones (Fig. 5) of the four selected boulders (Fig. 4).</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 8. First derivatives (top) and second derivatives (bottom) of the hyperspectral curves.</figcaption></figure>

means that two petroglyphs of same style located on the same rock block with different orientations relative to the sun could be interpreted first as a different evolution rate in terms of varnishing process. Moreover, their second derivatives tighten and exhibit maxima and minima for the same range of wavelength. This means that the nature of this evolution is common to all these petroglyphs, probably because all boulders are

made of the same dark granodiorite.

The different trends between the first derivative curves prevent us from extracting information that could enable us to date these petroglyphs relatively. Indeed, if we can already observe that the same type of motifs of the same boulder exhibit variabilities overlapping with all other petroglyphs of different motifs with different level of varnish, this
leads to a dead end. Thus, we needed to find another way to analyze this
set of curves, e.g. smoothing these variabilities and get coherent infor-
mation regarding the different petroglyph styles and orientations.

To do so, we considered the integrals of hyperspectral curves, and
saw that we could gain direct insights into the total light absorption or
reflection across a selected wavelength range for a given zone. We
compared the ratios between the value of the integral of the engraved
areas and the value of the integral of the intact-varnished areas for each
zone in order to minimize the variations due to different orientations of
petroglyphs on the same boulder. As illustrated in Fig. 9, the results
allow us to make two key observations: First, the variability between
same style petroglyphs situated in different zones of the same boulder is
now both minimal and coherent, meaning that these zones are closely
related. Second, we finally could identify variations in the levels of
weathering or patination, which in turn reveal consistent and relative
signatures among different sets of engravings of different styles found on
separate boulders.

Thus, the engraved areas of the rock art that show a total reflectance close to their surrounding intact-varnished areas, which correspond to a ratio value close to one, like the two zones of Boulder 9 presented on the extreme right part of the graph presented in Fig. 9. This small difference of reflectance might indicate that these petroglyphs were exposed for the longest time to the sunlight and probably be the older ones of our selection. At the opposite, the highest ratio value obtained for the petroglyph present on boulder 21 might indicate that this petroglyph has been exposed to the sun for less time and thus, it is probably the younger one.

Regarding Boulders 1 and 12, the engravings are well grouped

according to their respective zones. Despite the low difference in
amplitude, could the engravings found on Boulder 12 be older than
those on Boulder 1 according to our criterion based on the ratio of the
derivatives? Indeed, older layers, or those exposed to the atmospheric
environment longer, might show different reflectance characteristics
compared to newer layers. Since environmental changes that affect the
varnish's growth and makeup can also change the evolution of its optical
properties, we have limited our study to this single site. Assuming
consistent environmental conditions across these surfaces is a strong
assumption because post-engraving disturbances (such as water flow,
human activity, or animals) could differentially remove, damage, or
hide varnish, making it appear younger or older than it actually is.
Moreover, there is no standard calibration for converting reflectance
ratios directly into absolute dates without extensive site-specific cali-
bration involving other dating methods to establish a baseline. This is
why we used the ratios between the value of the integral of the engraved
areas and the value of the integral of the intact-varnished areas. While
relative reflectance analysis does reduce some variability due to shared
exposure conditions, discrepancies in microtopographical and material
characteristics, in and outside engraving, could still introduce
uncertainty.

4.1. *Comparison between petroglyphs*

Let us first turn our attention to the petroglyphs found on Boulders
N°1 and N°12. According to the classification proposed by Echevarria
Lopez (2020), the Quilcas on Boulder N°1 exhibit a delineated
morphology characterized by sinuous and elongated shapes. These
feature anthropomorphic motifs with headdresses in Zones 1, 2, and 3,
are unique to motifs found in Group 3. Still according to Echevarria
Lopez, Group 3 is estimated to date from 1200 to 100 BCE. Concurrently,
the simple zigzag line found in Zone 1 aligns with an abstract and
geometric aesthetic, and is posited to belong to Group 4, which is esti-
mated to date from 200 BCE to 500 CE. Echevarria Lopez (2020) also
notes that the two types of patterns on boulder N°1 exhibit different
patina. However, our analyses reveal that the petroglyphs on the two
differently oriented faces of the same boulder show the same range of
total relative reflectance.

Guffroy (2009) contends that these motifs are part of the same tradition, identified as Tradition C, sharing numerous similarities with petroglyphs in Locumba and extending across the border into the Arica region at the site of El Rosario. According to Guffroy (2009), these petroglyphs are closely associated with ancient caravan routes in northern Chile. While certain iconographic and contextual elements, such as dancers and the fusion of zigzag patterns with human figures, suggest a lineage with Toro Muerto, the majority of motifs depict the lifestyles of local societies in a naturalistic style. This aesthetic is more closely aligned with the petroglyphs of the central coast and diverges from the formal tradition found between Nazca and Arequipa, seemingly corresponding with the Aymara cultural groups. Both occupation evidence and iconographic analysis indicate a late chronological attribution for these petroglyphs, dated between 1000 and 1532 CE (Guffroy, 2009).

Shifting focus to Boulder N°9, we observe that its patina is more
pronounced than that on boulders N°1 and N°12. To enhance the visi-
bility of these petroglyphs, we employed the DStretch plugin ("ywe"
setting) and present the results in Fig. 10. It should be noted that
DStretch (Harman, 2005) is a software extension for ImageJ designed for
the archaeological analysis of rock paintings and petroglyphs. Utilizing
decorrelation stretch, the software enhances color contrast, making faint
or weathered pictographs more discernible. Upon application, it be-
comes evident that the motifs on Boulder N°9 diverge stylistically from
those previously discussed. What initially appeared to be a cross (Zone 1,
Fig. 5 and left of Fig. 10) now seems to represent a bird with open wings,
similar to a condor as seen in petroglyph N°508 in Guffroy's 2009
publication and found at the Yangas site (Tradition B). Additionally, the

<figure><img src="image_17.png" /><figcaption>Fig. 9. Sorted ratios between the value of the integral of the engraved areas and the value of the integral of the intact-varnished areas for each zone. Closer is the value to 1, higher is the weathering or patination level of the engraved zone, corresponding to a longer exposition to the sun light.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. 10.** On the left, boulder N°9 with RGB color. On the right the same boulder processed using DStretch, together with the “ywe” option. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

symbol resembling a chevron just above (Zone 2, Fig. 5 and left of Fig. 10) appears to be an animal figure schematic, also similar to petroglyphs N°356 and N°371 in Yangas site according to Guffroy.

This site is notable for the engraved art along the central coast, particularly in the upper region of Chaupi Yunga, sharing stylistic and iconographic traits with sites like Cheada, Cochineros, and Huancor. Yangas also has a close relationship with water flow and rising levels, a feature shared by other sites like Miculla, Quebrada de los Boliches, Le Cerro la Cal, and the ravines of Locumba. Despite following an older tradition, the engravings at Yangas suggest a later timeframe, possibly transitioning between the Middle Horizon and the Late Intermediate Period, around 1000 CE (Guffroy, 2009).

Finally, the petroglyph of boulder N° 21 representing a long-line can also be observed from another angle (Fig. 11), showing a more complex composition than previously seen in Fig. 4. The quality of the engraving seems to be lower than the one of the other petroglyphs as the high value of the integration ratio could indicate recent patina of the engraved zone suggestion an even younger age.

**5. Conclusion**

In attempting to assess the relative age of various petroglyphs found on boulders, we propose to complete systematic analyses with Hyper-spectral analysis. This technique offers multiple perspectives but not definitive insights by itself. For example, the motifs on boulders N°1 and N°12 exhibit the same integrated reflectance ratio between engraved and intact area, suggesting a similar patina evolution. Turning to boulder N°9, its more pronounced patina ratio could indicate an older production. Lastly, the petroglyph on boulder N°21 presents a higher patina ratio, suggesting a younger age.

Our research is intended to open the door to the systematic use of HSI to assess a possible relative dating of the petroglyphs, as we have already begun to do with rock paintings (Schmitt et al., 2023). Our intent here was to present the methodology we developed while pointing out that the sheer number of petroglyphs at the Miculla site may lead to a much more precise statistical assessment of their chronology through the use of HSI, which is easily carried out in the field. Our study invites further

<figure><img src="image_19.png" /><figcaption>**Fig. 11.** On the left, boulder N°21 with RGB color shot taken from another angle compared to Fig. 4. On the right, the same boulder from the same angle but processed using DStretch, together with the “yds” option. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
comparative HSI studies with similar sites across the Andean corridor and beyond. Such comparative analyses could improve or constrain the sometimes highly subjective dating of petroglyphs.

The application of HSI in our study demonstrates how easy it is to use as a non-destructive and versatile tool for archaeological research, particularly in the context of rock art relative dating. Now, it is clear that for more accurate absolute dating of Miculla petroglyphs, complementary methods need to be used. According to Neumann et al. (2022) and Dorn et al. (2024), the best strategy for directly dating the petroglyphs involves a combination of several methods to detect and quantify the physical and chemical weathering effects under controlled weather and climate conditions. These methods could include X-ray diffraction, confocal Raman spectroscopy, portable X-ray fluorescence spectrometry, cosmogenic nuclide dating, optically stimulated luminescence (OSL) or thermoluminescence (TL), micro-computed tomography, and Hyperspectral (HSI) analysis, as we did here. However, these methods often require the collection of samples, which is not compatible with a total protection and conservation policy. Thus, a future strategy for dating petroglyphs will be to use high precision VNIR + SWIR HSI devices to detect and quantify accurately the physical and chemical changes caused by weathering. The global method for non-destructive absolute dating of petroglyphs is still in gestation, but we're confident that HSI will be part of it.

### CRediT authorship contribution statement

**Frédéric-Victor Donzé:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Conceptualization. **Laurence Audin:** Writing – review & editing, Investigation, Conceptualization. **Bernard Schmitt:** Writing – review & editing, Methodology. **Audrey Taillefer:** Writing – review & editing, Funding acquisition. **Laurent Truche:** Writing – review & editing.

### Declaration of competing interest

The authors declare that they have no competing interests.

### Acknowledgments

This study was made possible by a collaboration agreement between the regional archives of Tacna and the French Institute of Research for Development (IRD). A photographic test with the multispectral instrument was conducted without any sampling or contact with the petroglyphs at the Miculla archaeological site. This test was done to prepare a more extensive project to contribute to the knowledge about this archaeological site of primary importance for the Tacna region. The authors are particularly grateful to Daniel Zegarra Rivera, Director of the Dirección Desconcentrada de Cultura Tacna - DDC-Tacna, as well as Gary Osorio, Ronald Ramirez, and Jesús Gordillo of the Archivos Regionales de.

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