Quantitative Elemental Oxides Analysis of Rock Cuttings Using Laser-Induced Breakdown Spectroscopy Coupled with Bayesian Optimization and Support Vector Machine

Abstract

Fast elemental analysis in the wellsite is crucial across the energy sector, where timely and accurate geological information drives operational efficiency and safety. In geothermal projects, rapid geochemical characterization aids in identifying reservoir quality and alteration zones, optimizing drilling locations, and reducing nonproductive time. For carbon storage, a quick assessment of rock mineralogy ensures suitable cap rock integrity, which is essential for environmental safety. In hydrocarbon exploration and production, immediate elemental data enable real-time lithology evaluation, improving well placement, reducing drilling risks, and lowering operational costs. Overall, integrating advanced machine learning with portable, on-site Laser-Induced Breakdown Spectroscopy (LIBS) technology provides fast, reliable elemental data that support adaptive and cost-effective resource development in these critical operations. In retrospect, this paper explores and evaluates the application and coupling of the Bayesian optimization process for hyperparameter tuning with support vector machine, with the objective of quantifying major oxide elements present in rock cuttings samples from LIBS. The main objective of using this process is to automatically optimize the model performance while minimizing the manual iterative and random trial and testing of the hyperparameters. In this investigation, over 1000 samples were prepared to develop the predictive model, where X-ray fluorescence was used as the reference method for obtaining concentration. The model performance was evaluated using multiple metrics, achieving an R-squared value in the range of 0.93 to 0.97, indicating the model’s reliability and accuracy when dealing with high-dimensionality and nonlinearity that are exhibited in the data set.

Introduction

Mud logging units have been a standard feature in the oil and gas industry since their commercial introduction in the late 1930s; until today, they are one of the main direct monitoring methods during the drilling process. One of the primary objectives of a mud logger is to describe the formation’s lithology versus the depth based on the liberated rock cuttings that are collected from the shale shaker. Once the basic visual inspection of the rock cuttings had started, the scope of the current rock cutting analysis capabilities has expanded as additional analytical instruments were introduced, bringing more information, such as mineralogy and elemental composition, into the hands of the geologist. From the elemental composition of the rock cutting alone, numerous correlations and ratios can be derived regardless of the lithology, stratigraphic age, geographic location, or depositional environment. These correlations can support the identification of hydrocarbon-bearing zones and aid in mapping stratigraphic columns for more informed decision-making during exploration and development. Beyond hydrocarbon exploration, elemental analysis of rock cuttings is vital in sustainability-focused applications such as carbon storage when assessing the caprock integrity and mineral trapping capacity, as well as geothermal projects when identifying hydrothermal alteration zones. ,

The addition and advancement of analytical technology, such as X-ray Fluorescence (XRF) and Inductively Coupled Plasma (ICP), enable the acquisition of around 42 and 55 elements, respectively, in the periodic table. Although ICP is the gold standard, XRF has been used extensively in the field for the rapid geochemical analysis of rock cuttings. XRF has seen acceptance and adoption for field use due to industry familiarity, robustness, ease of deployment, and cost. Another analytical technique is Laser-Induced Breakdown Spectroscopy (LIBS), where a high-powered pulsed laser beam is tightly focused on the sample to ablate the targeted material from the sample’s surface creating a plasma; as the plasma cools, excited atoms and ions emit element-specific photons, which are captured by the spectrometer; both the emission line and counts are recorded for analysis. Theoretically, all elements in the periodic table can be detected by LIBS; it is especially effective in analyzing lighter elements with low ionization potentials, such as lithium and boron. It performs adequately for metallic elements but is less effective for high-ionization elements, such as sulfur and phosphorus. Besides LIBS’s ability to detect all elements, LIBS’s superiority and uniqueness also stem from its rapidness, where, in comparison with XRF and ICP, measurements can be done in a matter of seconds. , For these reasons, LIBS serves as an attractive analytical technique for various applications.

Although the usage of LIBS in the oil and gas industry is still at its infancy, before the introduction of a high caliber XRF to the field, LIBS was used by Saudi Aramco and Haliburton for obtaining elemental measurements in the well site in the early mid 2000s; however, at the time, the calibration techniques used were highly affected by the matrix and deemed inefficient for an unknown sample material. , The introduction of a hand-held/remote LIBS system has been one of the main drivers to significantly increase LIBS usage in various industries for quick on-site analysis. Notably, the Chemistry Camera (ChemCam) instrument that contains LIBS was deployed by NASA for Mars exploration back in 2011. As a matter of fact, Los Alamos National Lab reported completing its millionth measurement using LIBS on Mars. In the context of application in the energy industry, LIBS was used for shale rock characterization, − pipeline chemical inspection, geosteering, crude oil grade discrimination, and subsurface CO₂ leakage detection. These studies illustrate LIBS’s capacity to provide swift and diverse applications within the energy sector.

Recent literature has demonstrated LIBS suitability for geological application. It shows that modern hand-held LIBS instruments can produce meaningful broadband spectra directly from the rocks. These articles highlighted the increase of utilization, adoption, and acceptance of LIBS in field geology, mineral exploration, and geochemical mapping, showcasing that portable LIBS can now provide rapid and robust quantitative analysis for field applications. ,− Initial research indicated that broadband LIBS spectra from unprocessed cuttings preserve adequate chemical information for lithological differentiation through multivariate methods like principal component analysis and partial least-squares (PLS). , Recent study has advanced to quantitative analysis of cuttings utilizing full-spectrum LIBS. Sha et al. (2023) established a multielement LIBS approach for drilled cuttings, demonstrating that suitable spectral preprocessing and multivariate regression may produce precise predictions of various major and minor elements. A growing body of research has concentrated on lithium, where traditional XRF spectroscopy exhibits insensitivity. Min et al. (2024) illustrated that LIBS can accurately quantify lithium concentration in drilled cuttings when paired with baseline correction and machine-learning regressors. Likewise, Qubaisi (2025) demonstrated that hand-held LIBS, calibrated against ICP–OES, can deliver swift, on-site lithium assays across sedimentary drill cuttings. In parallel, advancement in drilling automation suggests the transition toward real-time analysis of cuttings using LIBS technology. Modern systems employ robotics for cuttings preprocessing prior to directing them through integrated LIBS analyzers, producing high-frequency elemental data sets that can be converted into mineralogical profiles, brittleness indicators, total organic content estimates, and synthetic gamma-ray logs to facilitate real-time geosteering and hazard prediction. The incorporation of LIBS into robotic cuttings logging in the Eagle Ford shale has facilitated the concurrent quantification of major oxides and an extensive array of trace elements, transforming routine cuttings into a comprehensive chemostratigraphic data set instead of merely a descriptive sample stream. This integration shows LIBS evolving into a pivotal rule of advanced, data-intensive cuttings analysis. −

Despite the evident utilization of LIBS for various objectives in the industry, like other analytical techniques, the matrix effect is still considered to be an obstacle when determining the element’s concentrations in highly heterogeneous materials such as geologic samples. Ideally, the photon’s emission intensity increases at known spectral lines in relation to the elemental concentration present in a sample; however, other interconnected parameters affect the emission line intensity, like the material and laser pulse properties, and the degree of interaction between the laser and the material, thereby creating results are created that are dependent on the matrix. Primarily, the matrix effect occurs when highly and easily ionizable species/elements dominate the plasma, interfering with the emission behavior of lower ionizable species. This occurrence decreases the detectable concentration of the low ionizable species, underestimating the elemental concentration present in the sample. In addition, during the material ablation process, different materials’ physical properties like thermal conductivity, enthalpy of vaporization, and crystal structure affect the amount of the removed mass from the sample. For example, when ablating silicate minerals such as mica and feldspar, the amount of ablated mass varies due to their different crystal structure and hardness. Additionally, Eppler et al. (1996) observed that sand combined with graphite absorbs four times as much and gives twice as strong a signal in comparison to sand combined with cellulose, yielding different outcomes. He also investigated the matrix effect of known concentrations of lead and barium constants in a variety of soil and sand mixtures. It was found that barium carbonate and lead monoxide have the highest emission intensities in comparison to the other mixtures. As a result, different samples with the same element concentration produce different emission intensities, yielding distinct results.

To address the matrix effect issue, the utilization of matrix-matched samples during the calibration process is essential in attempting to quantify the element’s concentration. Construction of the calibration curve is done by plotting a region of interest for the selected element emission line to observe the intensity or area under the curve versus the concentration of the element. This method, which is referred to as univariate, assumes a linear relationship between the plasma emission intensity line and concentration; however, it has been demonstrated that this approach is not suitable when dealing with nonhomogeneous systems that exhibit a matrix effect, such as soils or rocks. In the literature, multiple spectral normalization techniques were demonstrated, most commonly by dividing the spectrum by the dominant elements in the sample. For example, normalizing the stainless steel alloy spectrum with iron. However, in the context of geological samples, there is not a single element within rocks or soil samples with a constant concentration value; nevertheless, normalization of the spectra with silica is often used. , Regardless of whether normalization was applied, it does not eliminate the matrix effect but rather reduces or smooths the spectral fluctuations that result from the sample and laser physical condition. Furthermore, Ciucci et al. (1999) introduce the concept of a calibration-free method in quantifying the elements via LIBS, overcoming the matrix effect. This method assumes the following: (1) constant elemental composition of both the sample and plasma, ensuring uniform elemental composition; (2) the energy level adheres to Boltzmann distribution, where the plasma is in local thermodynamic equilibrium; (3) ionization state is governed by Saha–Boltzmann equilibrium relation; (4) the spectral emissions are minimally dense, allowing the self-absorption phenomena to be disregarded; and (5) the plasma path of observation is spatially consistent. Although this method is evidently used, its elemental predictability is still deemed insufficient when analyzing geological samples. ,

Regardless of whether calibration was applied, spectral interferences between the elements in geological samples are still present, and the usage of multivariate and advanced data-driven models is recommended for quantitative LIBS analysis, specifically in heterogeneous samples. , Multivariate models’ strength comes in their ability to detect the behavior of the entire inputted variables and correlated to the outputs, so instead of focusing on one emission line signal as a single variable and correlated to the corresponding element, multivariate models take into account the behavior of the entire LIBS spectra and correlated to the element of choice, creating a calibration curve fit for purpose. The PLS regression (PLSR) multivariate model is the most commonly used for LIBS quantification. It has been used in numerous applications, such as metal alloy, molten salt fuel, and soil nutrient. Moreover, support vector machine (SVM) was also used as a multivariate model for LIBS quantifications of Molybdenum in geological ores. Even though PLSR utilization is common across various applications, it is better suited for data sets with linear behavior. A comparative analysis of PLSR and SVM of slag samples shows the superior performance of the SVM model, where the R-squared values increased for all major elemental oxides. Another comparison is done on 16 sedimentary rock samples with SVM having better performance. This indicates that SVM is better at capturing the complex relationship between the spectra and the concentrations in the data set compared to PLSR.

While multivariate models such as SVM clearly provide better performance for complex geological samples, their effectiveness greatly depends on the proper selection of the hyperparameters, such as the regularization parameter and Kernel function. This sensitivity is well documented in machine learning literature and libraries, most notably Scikit-Learn, which explicitly emphasize on the impact of the hyperparameter on the model’s performance. Most LIBS studies employ manual selection, fixed default values, or basic grid searches for the hyperparameters, typically integrating SVM into traditional chemometric workflows without a clear approach to global optimization. ,, Such approaches are computationally inefficient and prone to local minima and can yield suboptimal regression models, particularly when modeling thousands of spectral variables. This reflects a gap in current LIBS methodology, which is that while nonlinear regressors are demonstrably more suitable for full-spectrum LIBS quantification, they are rarely implemented with systematic, globally optimized hyperparameter tuning.

Bayesian optimization provides a systematic and effective approach to this problem. In contrast to grid or manual search, Bayesian optimization utilizes a probabilistic surrogate model and an acquisition function to explore hyperparameter space, facilitating the swift identification of high-performing SVM configurations in high-dimensional, nonlinear problems. Bayesian-optimized SVM has proven effective in various applications, consistently surpassing conventionally tuned Support Vector Regression (SVR) and alternative regression methods. − In the field of LIBS, the application of Bayesian optimization is notably restricted. The limited studies focus on applying Bayesian Optimization to experimental conditions, including laser energy, focusing distance, or detection geometry for sensitive surface-contamination detection, as well as to deep-learning architectures, rather than to SVR-based models. − Currently, no established LIBS quantification framework integrates full-spectrum data with Bayesian-optimized SVR models. This represents a significant methodological gap, which is LIBS quantification studies increasingly dependent on nonlinear models yet lack the necessary optimization strategies to fully utilize their predictive capabilities. This study addresses the existing gap by developing a Bayesian-optimized SVR approach tailored for full-spectrum, multioxide LIBS regression, thereby offering a more accurate and robust modeling framework for geological materials.

Thus, in this paper, we are investigating the combination of LIBS technology with the SVM machine learning model for quantitative analysis of sedimentary rock cutting samples. A series of around a thousand samples were compressed into pellets, and for each sample, spectra were recorded by LIBS. In this investigation, we are focusing on the major element oxides of the rock cuttings as most elements in rocks and soils naturally occur as stable oxide compounds, making an oxide-based reporting standard for interpreting bulk mineral composition and facilitating comparisons across geological samples. For each sample, the spectra are set to be the input variable. The SVM’s hyperparameters were tuned by using the Bayesian optimization algorithm. Then, 5-fold cross-validation was performed to enhance the performance. Afterward, the model performance was evaluated based on the R-squared, root-mean-squared error, and mean absolute error (MAE). The model performance reveals the R-squared value in the range of 0.93 to 0.97, showcasing the model’s reliability and accuracy across various elemental oxides.

Methodology

Although theoretically the relationship between the intensity signal is linearly correlated with the concentration, as mentioned above, other matrix-related parameters affect the results, leading to nonlinearity. Consequently, the utilization of nonlinear multivariate models is essential in capturing those behaviors to establish a robust calibration curve for rapid elemental quantifications. SVM is a statistical method based on the Vapnik-Chervonenkis theory. − The algorithm was initially used for classification problems; however, Drucker et al. (1996) extended it to solve regression problems. Since SVM can handle multicollinearity, high dimensionality, and nonlinearity, it serves as a suitable tool when dealing with LIBS data. The SVM expression is described as follows and is in a simplified visual representation in Figure .

$$f(x)=⟨w,x_i⟩+b$$ 1

where, for a given data set ${\{(x_i,y_i)\}}_{i=1}^{\mathrm{n}},\chi \times \mathbb{R}$ , the spectrum is denoted as x _i with y _i being the corresponding element concentration. w is the weight vector and b is the bias. To find the equation above, we do the following:

$$\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{z}\mathrm{e}:\frac{1}{2}{\parallel w\parallel }^2+C\sum _{i=1}^n({\xi }_i+{\xi }_i^{*})$$ 2

$$\mathrm{S}\mathrm{u}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{o}:\{\begin{array}{l}{y}_i-⟨w,x_i⟩-b\le \epsilon +{\xi }_i\\ ⟨w,x_i⟩+b-y_i\le \epsilon +{\xi }_i^{*}\\ {{\xi }_i,\xi }_i^{*}\ge 0\end{array}$$ 3

1.

Schematic of linear SVM demonstrating a simplified case of the concept.

The constant C > 0 is the regularization parameter that governs the trade-off between simplifying the model f(x) and penalizing deviations exceeding ε in the loss function. To solve the above equations with the constraints, we convert them into a Lagrange dual problem described in detail by Smola and Schölkopf (2004). Once solved, the SVM prediction problem is expressed as follows:

$$f(x)=\sum _{i=1}^n({\alpha }_i-{\alpha }_i^{*})K(x_i,x)+b$$ 4

where α _i ,α _i * are the Lagrange multipliers and K(x _i ,x) is the kernel function to measure the similarity between the points to map the inputs in high dimensions. As we are dealing with high-dimensional data, the kernel function will help us to fit the data and find similarities without the need to explicitly transform them into the corresponding dimension. There are numerous kernel function formulations; however, in this study, we subjected the workflow to the linear, polynomial, radial basis function (RBF), and sigmoid kernels, shown, respectively, below:

$$K(x_i,x)=⟨x_i,x⟩$$ 5

$$K(x_i,x)={(\gamma ⟨x_i,x⟩+r)}^d$$ 6

$$K(x_i,x)=\exp (-{\gamma \parallel x_i-x\parallel }^2)$$ 7

$$K(x_i,x)=\tanh (\gamma ⟨x_i,x⟩+r)$$ 8

To find the optimum values and combinations of the regularization constant, epsilon, and kernel that yield the best calibration model, we used Bayesian optimization to tune these parameters. Bayesian optimizations build a probabilistic/surrogate model that captures the relationship between the hyperparameters to a performance score for the objective function and then uses Bayes’ theorem to optimize and select the next set of hyperparameters combinations by optimizing an acquisition function. Unlike other hyperparameter optimization techniques, such as grid and random search, Bayesian optimization’s strength comes in its ability to efficiently learn from previous iterations and trials to make an educated guess about the next set of hyperparameters. In this paper, we want to find the set of hyperparameter combinations that yield the highest cross-validation score; as such, the Bayesian optimization for hyperparameters is expressed as follows:

$$\begin{array}{l}{\theta }^{+}=\arg \max f(\theta ),\theta \in D\\ \end{array}$$ 9

where f(θ) is the objective score to maximize the average cross-validation’s R-squared value and θ is the hyperparameter combination set from the search space D. To decide on the next set of hyperparameters, we applied the expected improvement as the acquisition function displayed below:

$$\mathrm{E}\mathrm{I}(\theta )=\mathbb{E}[\max (f(\theta )-f({\theta }^{+}),0)]$$ 10

where f(θ⁺) is the best recorded score

$$\begin{array}{l}{\theta }_{t+1}=\arg \max \mathrm{E}\mathrm{I}(\theta )\\ \theta \in D\end{array}$$ 11

To put it simply, for each combination of parameters, 5-fold cross-validation (CV) was applied to assess the model’s generalization and to avoid overfitting. In this process, the training data are split into five equal folds, with one of them used as the testing/validation fold, and then the performance is calculated by the R-squared. This process is iterated five times, alternating each fold to be used as the testing/validation fold. Afterward, the model’s R-squared is averaged from all five iterations (Figure ). As this process is coupled with the Bayesian optimization, a hundred different combinations of hyperparameters were tested, and in each of those combinations, an averaged R-squared was calculated from its corresponding cross-validation results. While the R-squared is the primary chosen criterion for the model selection, the root-mean-square error (RMSE) and MAE were also calculated on the testing data set to further evaluate the accuracy of the model.

$$R^2=1-\frac{\sum _{i=1}^n{(y_i-{ŷ}_i)}^2}{\sum _{i=1}^n{(y_i-\mathrm{y̅})}^2}$$ 12

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{n}\sum _{i=1}^n{(y_i-{ŷ}_i)}^2}$$ 13

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{n}\sum _{i=1}^n|y_i-{ŷ}_i|$$ 14

2.

Schematic of the five-fold cross-validation process.

Data Acquisition and Preparation

Data Acquisition

In preparation for the measurements, sample preparation is a crucial step in ensuring representative results. 1300 sedimentary rock cutting samples with various matrices and trace elements were used to cover a wide range of concentrations. The samples were sieved, rinsed with water, washed with 99% Isopropyl Alcohol, and then vacuum-dried to speed up the drying process. Next, each sample was ground and then pressed into a 13 mm diameter pellet for 15–30 min with an applied pressure of 1000–5000 psi, depending on the rock cuttings’ friability. Afterward, the major elemental oxides were obtained using SpectroSCOUT Energy Dispersive XRF from Spectro AMETEK and recorded in weight percentage (wt %). The SpectroSCOUT system quantifies elemental concentrations based on characteristic XRF lines and automatically converts the measured elemental intensities into their corresponding oxide forms using built-in calibrations. The instrument’s software applies matrix-matched calibrations and stoichiometric oxide calculations, for example, Si → SiO₂, producing final oxide concentrations directly in wt % for each sample. These oxides were used as the concentration data for this study.

To acquire and record the spectra, a commercial hand-held LIBS analyzer (SciAps Z-903) was used on the prepared samples. This system uses a pulsed Neodymium-doped yttrium aluminum garnet (Nd­(revert): YAG) as its excitation source, with a pulse energy of 5–6 mJ per pulse, running up to 50 Hz repetition rate, and 1 ns pulse duration. The analyzer’s three spectrometers can capture 190–950 nm, covering a broad range of elements’ plasma emission light from the ultraviolet to near-infrared regions. In addition, the system has an onboard argon-purge feature that displaces ambient air, minimizing background noise and unwanted spectral lines, improving the signal-to-noise ratio by stabilizing the plasma, and protecting the optics from contamination such as dust or moisture that might degrade the system.

During the process of acquiring the samples spectrum, the instrument fired seven individual laser shots, sized around 100 μm per shot, each directed at a different position on the sample surface. This multishot rastering approach is standard for SciAps LIBS analyzers and is essential for inhomogeneous surfaces because a single LIBS pulse can create a small crater and alters the local surface chemistry; repeated shots at the same location can lead to unstable plasma conditions, increased ablation depth, and reduced reproducibility. By sampling seven separate locations, the analyzer mitigates surface heterogeneity effects such as pores, inclusions, grain boundaries, or dust particles. The seven spectra collected from the seven positions are then averaged by the instrument’s software to produce a single, stable, and representative spectrum for each sample. Afterward, all the data are exported from the analyzer software as CSV files in preparation for model building, as shown in Figure .

4.

Workflow of the process.

An example of the LIBS spectrum of one of the samples is displayed in Figure . In this figure, several emission lines of the elements were highlighted for visualization. In this study, the entire LIBS spectrum was used for each sample rather than on a selected peak. This ensured that all spectral information and trends were included in the analysis.

3.

Example of the LIBS Spectrum (intensity versus wavelength). Prior to taking the sample spectra, we used XRF to find the major elemental oxides, which serve as the ground truth or actual concentration in building the model. In this sample, the concentrations results showed 56.258 (wt %) SiO₂, 16.780 (wt %) Al₂O₃, 2.487 (wt %) CaO, 2.110 (wt %) TiO₂, 1.979 (wt %) K₂O, and <1 (wt %) of SO₃, Fe₂O₃, and MgO.

Data Preparation

Prior to model initialization, multiple data preparation techniques were used on the experimental results to enhance the model robustness and performance. Exploratory data analysis process was utilized to statistically understand, clean, and visualize the data, uncovering anomalies, outliers, patterns, and relationships between the data sets. Next, a logarithmic transformation, specifically ln­(1 + y), was calculated for all the targeted variables (concentration). This process addresses the data skewed distribution by reducing the impact of extreme values through variance stabilizations, thereby leading to better convergence during model training. In addition, using this type of logarithmic transformation over a natural log can better handle values near or equal to zero without resulting in an undefined output.

As for the input variables (LIBS Spectrum), background subtraction and Savitzky-Golay smoothing were used to reduce the noise and enhance peak visibility. Then, a standard scaler shown in the equation below was applied to transform the spectrum to have a standard deviation of one and a mean of zero. This process is crucial in ensuring equal contributions and the importance of each feature of the input variables by minimizing bias and equalizing the spread. For example, Figure illustrates one of the spectra used as input data; as shown, the intensity values vary significantly in magnitude. Consequently, high-intensity regions will disproportionately dominate the model learning process by giving importance to this region, leading to misinterpretation and bias and potentially ignoring important smaller intensity regions.

$$X_{\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{d}}=\frac{X-\mu }{\sigma }$$ 15

Moreover, as shown in Figure , the data set was split into 70% training and 30% testing before standardization to prevent data leakage. This process needs to be performed prior to preventing the influence of the testing data on the model training. If the standardization was applied before splitting, the mean and standard deviation were calculated on the entire data set, including the testing set, which should be used for blind performance evaluation. In that case, the model might yield overoptimistic performance. By applying a standard scaler separately, the testing data set integrity is preserved to provide an unbiased assessment of the model’s performance.

After preprocessing, a full spectrum strategy per sample was adopted instead of a single isolated peak for input selection. This approach was used due to the heterogeneity exhibited in geological materials that often contain overlapping emissions lines and matrix-dependent variations in shapes and intensity. By providing the entire spectrum to the model, the analysis is not restricted to preselected peaks and can capture subtle spectral variations across the full wavelength range, including weak emissions that may fall below the typical manual selection thresholds. This approach reduces the subjectivity associated with manual peak selection and aligns with multivariate practices, where data-driven algorithms naturally handle high dimensional inputs. As a result, the SVR model can learn more complete and robust relationships between the LIBS spectra and XRF oxide concentrations.

Results and Discussion

In the following section, we will discuss the main observations of this investigation, which are divided into (a) model performance evaluations, (b) model optimization progressions over the iterations, and (c) challenges and limitations encountered during implementation.

Model Performance Interpretations

The workflow displayed in Figure was applied to the data to construct eight models for SiO₂, Al₂O₃, CaO, TiO₂, K₂O, SO₃, Fe₂O₃, and MgO. During the tuning process, the model performance was assessed via the average R-squared of the cross-validation. Once the best hyperparameters are selected, the model is trained, and its performance is evaluated on the testing data, where a summary of the testing performance is shown in Table .

1. Prediction Performance of the Methodology Applied on the Testing Data Set for the Samples, with Their Corresponding Model’s Parameters Identified via the Bayesian Optimization Process.

	performance metrics			model’s parameters
component	R 2	RMSE	MAE	C	epsilon	kernel
SiO2	0.970	5.037	2.481	16.701	0.018	RBF
TiO2	0.948	0.077	0.040	5.041	0.003	RBF
Al2O3	0.946	1.594	0.825	74.882	0.025	RBF
Fe2O3	0.949	0.501	0.248	74.882	0.025	RBF
MgO	0.948	0.865	0.466	74.882	0.025	RBF
CaO	0.957	3.006	1.873	74.882	0.025	RBF
K2O	0.938	0.296	0.145	5.041	0.003	RBF
SO3	0.951	3.188	1.786	38.629	0.013	RBF

According to the performance metrics displayed in the table above, the combined model achieved strong performance across the testing data set, yielding R-squared values above 0.93 for all the elemental oxides. This shows that the combination of approaches can reliably predict elemental oxides across diverse ranges of spectral behavior. To further assess the quality of the model, both the RMSE and MAE were calculated for each oxide. The RMSE helps in identifying prediction outliers and capturing the overall precision of the model but is highly sensitive to larger outliers, where it penalizes larger errors by giving them more weight. As for MAE, it provides an easily interpretable measure of the averaged error magnitude, where it treats all of the errors equally. The RMSE values range from as low as 0.077 for TiO₂ to 5.037 for SiO₂, which is expected as Silica has greater variability in sedimentary rocks due to its abundance. This can be seen in Figure , where the Silica variability in the data went to approximately 95 wt % in comparison to Titanium with a variability of around 2% wt. Similarly, the MAE ranges spanned from 0.04 (TiO₂) to 2.481 (SiO₂).

5.

Plot of the actual concentration data (XRF) versus the model prediction (LIBS) for all oxides used during the analysis in wt %. The R ² values in the graphs are for the testing data set.

Furthermore, elemental oxides with low RMSE and MAE values such as TiO₂, Al₂O₃, and Fe₂O₃ reflect the technique precision when applied to elements with relatively well-defined emission lines and characteristics in the LIBs spectral range. These elements might exhibit relatively lower overlapping signals, which allow the model to efficiently learn the behavior and relationship between the LIBS spectra and concentration. As a result, the prediction errors are minimized, producing both a low RMSE and MAE. In contrast, elements with higher error performance metrics, such as SiO₂ and CaO, can be credited to their higher abundance and natural variability. In addition, these elements are often present in complex mineral structures that might produce overlapping signals, introducing noise or ambiguity into the signal, which collectively raises the RMSE and MAE values.

Generally, the utilization of those three metrics gives a holistic assessment of the model’s performance, capturing its overall fit and its ability to dependably and precisely predict the concentrations across the data. Specifically, the RMSE and MAE trends across each element show that the model performance is influenced by other factors beyond the machine learning model itself but also the abundance and spectral behavior of the elements in the samples. This behavior can be seen in SO₃, Al₂O₃, and Fe₂O₃ plots in Figure . Despite the model’s strong overall performance, these plots reveal a quantitative bias at the higher concentration ranges. Even though the accuracy is relatively high (R ² ≈ 0.95), the results show a deviation from the 1:1 line (black line). This behavior can be attributed to several factors. First, LIBS spectra become increasingly nonlinear at elevated elemental abundances due to self-absorption and partial saturation of strong emission lines. Together, these effects compress the spectral response, causing the emission intensity to rise much more slowly than the actual concentration at elevated levels. When the relationship between intensity and concentration becomes flattened in this way, the spectral signal carries less incremental information, and the model’s apparent sensitivity to further increases in concentration is reduced. − Second, the calibration data set contains relatively fewer samples at elevated levels than the mid to lower ranges, indicating that these concentrations are underrepresented in model training. The SVR model, despite Bayesian optimization, most accurately matches the densely populated low to mid ranges, exhibiting somewhat more systematic deviation in sparsely inhabited high concentration regions. Collectively, these effects explain the slight underprediction observed at the upper end of the SO₃, Al₂O₃, and Fe₂O₃ concentration ranges while not substantially impacting the overall model performance.

Model Optimization Progression and Parameters

The Bayesian optimization process revealed distinct optimization profiles for each elemental oxide, as shown in Table . The selected regularization parameters varied significantly across the oxides. The combinations of model parameters were reflected in the iteration profiles of the process in Figure , which demonstrate the score per iteration. Within the specified hyperparameter, Fe₂O₃, CaO, Al₂O₃, and MgO emerged relatively quickly, achieving their optimal scores within the first four iterations. K₂O and TiO₂ also converged rapidly at iteration seven. In contrast, both SiO₂ required considerably more exploration time, with the best score converged at the sixtieth iteration. SO₃ occupied a moderately intermediate position, reaching its best score by the thirty-eighth iteration. In addition, across all of the kernels that were tested, RBF was deemed to be the most suitable for all of the elemental oxides. This confirmed its capabilities for handling nonlinear relationships exhibited between the LIBS spectrum and its corresponding concentrations, as well as its ability to generalize the spectrum’s high dimensionality across the inputted space.

6.

Scores’ results of the Bayesian optimization of each element per iteration. For each iteration, different combinations of the hyperparameters are being tested, and the 5-fold cross-validation score is recorded. The scoring criteria used in this paper is the R-squared.

Moreover, the regularization parameter C and epsilon vary significantly among the oxides in Table The highest recorded value is at 74.882 for Fe₂O₃, CaO, Al₂O₃, and MgO, indicating that these elements required a tighter fit to capture the subtle changes within the data. These elements also shared the same epsilon value of 0.025. This combination helps balance between the prediction rigidity and minor flexibility around the margins, whereas K₂O and TiO₂ have the lowest C and epsilon values at 5.041 and 0.003, respectively. They show that the model has more fitting flexibility but a stricter deviation between the actual and predicted values. Both SiO₂ and SO₃ models’ parameters are moderately in the middle, reflecting that there is a need to manage the high variability and noise of the data. These variations demonstrate the ability to balance fitting and generalization based on the elemental oxide’s specific characteristics. Lower epsilon values were needed when minor variations between the actual and predicted values would significantly affect the model prediction accuracy, while higher regularization parameters were required for rather more complex behavior of the data. The Bayesian optimization process was able to tune the parameters to allow the SVR model to achieve the best performance score across all of the oxides.

Challenges and Limitations

While the combination of the spectra, SVM, and Bayesian optimization demonstrated robust results in quantifying the elemental oxides in the rock cuttings, inherent challenges and limitations must be acknowledged as follows: (1) The performance of the model fundamentally depends on the quality and comprehensiveness of the data set. Even though the data set used in this study covers a wide range of concentrations, the model can only predict within the ranges of the data set and cannot extrapolate beyond the given ranges. To overcome this challenge, the model needs to be updated occasionally to cover values that are outside the data set range. (2) The combinations of the methods can be computationally intensive, especially if dealing with an even larger data set, making their application in the field in near-real time. Employing advanced edge computing strategies or GPU acceleration might be necessary to expedite the computational speed for real-time on-site analysis. (3) The low signal intensities and spectral interferences are inherently challenging in quantifying and predicting the sample’s concentrations. Despite advances in LIBS calibration modeling and preprocessing, the utilization of ICP and XRF provides higher accuracy in comparison to LIBS. (4) XRF was used as the reference method for the LIBS calibration since the study focuses on major earth elements. In this study, using XRF data as the target is sufficient, more cost-effective, and practical in comparison to ICP. However, ICP is considered the better choice to enhance the accuracy of the prediction as well as to cover more elements in the model.

Conclusion

In this investigation, we have successfully demonstrated the application of coupling the LIBS spectra with SVM and Bayesian optimization for the quantitative determination of elemental oxides in rock cuttings. More than a thousand samples were prepared to develop the predictive model for eight major elemental oxides that are commonly seen in rocks or soil samples. XRF was used as the reference method by providing the sample’s concentration values for the model building. Multiple performance metrics were used to assess the model’s accuracy, precision, and robustness. For all of the oxides, the R-squared values were all above 0.93, showing the strong accuracy of the model. The coupling of the Bayesian optimizations played a critical role in tailoring the hyperparameters that were used by SVM via selecting the next best set of parameters smartly based on the results of the optimization iterations and progression. The consistent selection of the RBF kernel across all models indicates a strong nonlinear behavior in the data.

The successful integration of the methods highlights the potential for automating on-site geoanalytical analysis, reducing reliance on time-consuming lab-based methods, supporting continuous data acquisition, and accelerating formation evaluation and decision-making during drilling operations. As LIBS instruments become more portable and machine learning models are further refined, this approach could enhance the efficiency and accuracy of geochemical characterization in the oil and gas sector, ultimately supporting faster, data-driven exploration, and reservoir management strategies. Several enhancements can be explored to improve the model, of which ICP as a reference method has better accuracy and reliability. In addition, inclusion and coupling of multiple supervised machine learning models may offer better performance, specifically with fewer varied elements. Nonetheless, the current results showed a strong capability for using LIBS for rapid field applications.

The authors declare no competing financial interest.