Shear Wave Velocity in Geoscience: Applications, Energy-Efficient Estimation Methods, and Challenges

Abstract

Shear wave velocity (V_s) is a key geomechanical variable in subsurface exploration, essential for hydrocarbon reservoirs, geothermal reserves, aquifers, and emerging use cases, like carbon capture and storage (CCS), offshore geohazard assessment, and deep Earth exploration. Despite its broad significance, no comprehensive multidisciplinary review has evaluated the latest applications, estimation methods, and challenges in V_s prediction. This study provides a critical review of these aspects, focusing on energy-efficient prediction techniques, including geophysical surveys, remote sensing, and artificial intelligence (AI). AI-driven models, particularly machine learning (ML) and deep learning (DL), have demonstrated superior accuracy by capturing complex subsurface relationships and integrating diverse datasets. While AI offers automation and reduces reliance on extensive field data, challenges remain, including data availability, model interpretability, and generalization across geological settings. Findings indicate that integrating AI with geophysical and remote sensing methods has the potential to enhance V_s prediction, providing a cost-effective and sustainable alternative to conventional approaches. Additionally, key challenges in V_s estimation are identified, with recommendations for future research. This review offers valuable insights for geoscientists and engineers in petroleum engineering, mining, geophysics, geology, hydrogeology, and geotechnics.

1. Introduction

Surface waves, which are generated near Earth’s boundaries, propagate parallel to the surface. These waves can be categorized based on the orientation of ground movement [1,2]. The velocity of shear waves is a crucial feature that characterizes the mechanical features and stiffness of subsurface formations. The velocity of shear waves serves as a pivotal factor in gaining insight into the response of underground formations across diverse geological and geotechnical contexts [3]. Shear waves, alternatively termed S-waves, represent seismic waves that travel horizontally or transversely through the Earth, contributing significantly to our comprehension of subsurface dynamics [4]. They travel slower than primary waves (P-waves) but faster than the surface waves. V_s is essential for elucidating the elastic characteristics of rocks. If we consider an isotropic elastic medium, the relationship between V_s, shear modulus (G), and density ($\rho$) could be expressed as [5]:

$$V_S=\sqrt{{\displaystyle \raisebox{1ex}{$G$}\!\left/ \!\raisebox{-1ex}{$\rho $}\right.}}$$

(1)

Based on the above equation, it can be seen that the V_s is directly related to the square root of shear modulus and inversely related to the square root of density.

Shear wave velocity is indeed a critical factor within geoscience, with lots of applications [6,7,8,9,10,11,12,13,14,15,16,17,18]. Earthquake engineering [6,7], characterization of geotechnical sites [8,9], reservoir evaluation [10,11], and analysis of groundwater resources [12,13] are conventional applications of shear wave velocity. Furthermore, new applications of V_s data encompass exploration for geothermal energy [14], assessment of landslide hazards [15], utilization in carbon capture and storage (CCS) projects [16], evaluation of geohazards in offshore environments [17], and exploration into the depths of the Earth’s subsurface [18]. In this research, a concise overview has been given to those applications.

Despite the numerous applications of V_s, there are some crucial challenges in predicting shear wave velocity in geoscience. For instance, issues such as a lack of adequate data, spatial and temporal variability, non-unique relationships, anisotropy and inhomogeneity, difficulty in integration of multiple data sources, different machine learning and AI techniques, interpretability, uncertainty quantification, and the need for standardization and collaboration can be mentioned. Those challenges are also elaborated in this research.

Precise determination of V_s holds paramount importance in both geoscience and geotechnical engineering. Conventional approaches to predicting V_s, such as laboratory analyses, tend to be labor-intensive, costly, and frequently unfeasible for expansive studies [19]. Therefore, researchers have been exploring energy-efficient and cost-effective ways of predicting shear wave velocity, taking advantage of advancements in geophysical and geotechnical data analysis techniques. For this purpose, geophysical methods, remote sensing techniques, and machine learning algorithms have been utilized to measure/predict the V_s [20,21,22].

In this research, an inclusive overview has been given to the different applications, energy-saving estimation techniques, and challenges related to accurate V_s prediction in geoscience and geoengineering fields. The objective of the research is to collate and integrate the most important aspects of V_s application and prediction from a multidisciplinary viewpoint. Thus, in this research, the different V_s applications and potential challenges have been elaborated in several disciplines, including petroleum engineering, geotechnics, hydrogeology, earthquake engineering, geology, mining engineering, etc.

2. Conventional Applications

The significance of shear wave velocity spans different disciplines within geoscience and geotechnical engineering, with its applications ranging from earthquake engineering to groundwater resource assessment. In earthquake engineering, V_s serves as a cornerstone in seismic hazard evaluation and the designation of earthquake-resistant structures [6,23]. Studies have explored its correlation with ground motion amplification, facilitating ground motion prediction and site response analysis [24]. V_s also aids in seismic site classification, crucial for assigning sites with appropriate design parameters [25]. In geotechnical site characterization, V_s plays a pivotal role in evaluating soil stiffness, liquefaction potential, and seismic site response [26]. It assists in soil characterization for design purposes, informing foundation design and slope stability analysis [27,28,29,30].

Reservoir characterization benefits significantly from V_s, particularly in hydrocarbon exploration, where it provides insights into lithology of formations. V_s aids in identifying lithological variations within reservoirs [31], estimating porosity [32], evaluating fluid content [33], and analyzing mechanical properties [34]. Shear wave velocity is vastly utilized in groundwater resource assessment to determine the properties and characteristics of aquifers [11]. It provides valuable information about the subsurface conditions and helps in understanding groundwater potential, flow behavior, and storage capacity [12]. Groundwater resource assessment utilizes V_s for aquifer characterization, groundwater flow modeling, seawater intrusion assessment, and groundwater resource mapping. V_s helps in assessing the properties of aquifers, like porosity and permeability [35] and hydraulic conductivity [36], facilitating groundwater flow modeling and mapping groundwater resources in different geological formations [12].

Conventional approaches of V_s prediction are commonly impractical for large-scale investigations due to their time-consuming and expensive nature. Therefore, there is a growing need for alternative approaches to estimate V_s accurately and efficiently, especially in the context of expansive geotechnical and geological investigations [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36].

3. New Applications

The emerging applications of shear wave velocity (V_s) prediction span various domains within geoscience and geotechnical engineering, showcasing its versatility and significance in contemporary research. In geothermal energy exploration, V_s prediction serves crucial roles in reservoir characterization [37], fracture detection [38], resource potential mapping [39], and enhanced geothermal system (EGS) development [40]. By estimating V_s, researchers can assess the mechanical properties, fluid content, and heat transfer capabilities of subsurface formations, aiding in optimizing geothermal well design and operation [37,38,39,40].

Landslide hazard assessment benefits from V_s prediction, enabling landslide susceptibility mapping [41], early warning systems [42], slope stability analysis [43], and modeling of landslide-induced ground motion [44]. V_s estimation facilitates the evaluation of mechanical properties and slope stability, contributing to effective mitigation strategies and risk management [41,42,43,44].

In carbon capture and storage (CCS) projects, V_s prediction finds utilizations in storage formation characterization [45], caprock integrity assessment [46], reservoir monitoring, leakage detection [47], site selection, and risk assessment [48]. By estimating V_s, researchers can evaluate subsurface properties, containment integrity, and potential CO₂ leakage pathways, enhancing the safety and efficacy of CCS initiatives [45,46,47,48].

Geohazard assessment in offshore environments relies on V_s prediction for seabed stability assessment [49], identification of submarine landslide hazards [50], offshore infrastructure design [51], and seismic hazard analysis [52]. V_s estimation aids in evaluating mechanical properties, detecting geohazards, and optimizing offshore infrastructure performance and safety [49,50,51,52].

Deep Earth exploration benefits from V_s prediction in mantle convection studies [53], seismic discontinuity identification [54], anisotropy studies [55], and core structure investigations [56]. Researchers can infer the seismic structure, understand mantle dynamics, and investigate phenomena, such as seismic anisotropy and core–mantle coupling, using shear wave velocity estimation [53,54,55,56].

4. Energy-Efficient and Cost-Effective Approaches

In this section, a concise description is given to the most energy-efficient and cost-effective methods of V_s measurement or prediction. As already mentioned, those methods include the geophysical methods, remote sensing technique, and machine learning algorithms. In what follows, those methods are described.

4.1. Geophysical Methods

Geophysical methods have emerged as valuable tools for shear wave velocity estimation, providing economical and environmentally friendly alternatives to conventional laboratory experiments and field measurements. In what follows, the applicable geophysical methods used for V_s prediction are elaborated.

4.1.1. Seismic Refraction Techniques

Originally developed for large-scale seismic studies, such as earthquake and seismotectonic research, seismic refraction is now extensively used for near-surface applications. Controlled seismic signals help map subsurface structures, supporting hydrogeological, engineering, and environmental studies [44,57].

Seismic refraction is a commonly applied geophysical technique for estimating V_s via analyzing the times of travel of S-waves and P-waves in the subsurface. In other words, both of these waves are determined by analyzing how fast they travel through different subsurface layers, based on the arrival times recorded at various points. This technique enables the construction of depth-dependent V_s profiles, aiding in geological and geotechnical investigations [58]. For instance, Sarkar et al. (2021) applied multichannel analysis of surface waves (MASW) alongside seismic refraction tomography (SRT) to achieve high-resolution V_s profiling in the Bhutan Himalaya, demonstrating its efficiency and cost-effectiveness [58].

As it was mentioned before, seismic waves include P-waves, which propagate faster and travel through both solids and liquids, and S-waves, which move more slowly and only through solids. While P-waves are more commonly used in refraction surveys due to their higher velocity and ease of detection, S-waves provide valuable insights into unconsolidated materials [45,59]. This method measures the duration for seismic waves to propagate through subsurface layers and reach multiple receivers at different distances from the source [59]. As it can be seen in Figure 1, the data obtained can identify velocity discontinuities, which help in predicting geological boundaries and material types.

4.1.2. Surface Wave Analysis

Surface wave analysis is a widely used geophysical technique for estimating V_s by measuring the dispersion characteristics of surface waves, particularly Rayleigh waves (R-waves). These waves are sensitive to subsurface V_s variations and can be measured at the surface without requiring intrusive methods. This makes surface wave analysis an affordable and non-destructive approach for characterizing the sites of projects. Nazarian was of the first who introduced the spectral analysis of surface waves (SASW) technique, which has since been commonly applied [60]. Boore (2006) reviewed progress in surface wave analysis and emphasized its potential for V_s estimation, while also highlighting challenges in extracting reliable dispersion curves and selecting appropriate inversion methods [61]. The technique typically involves three key stages: initially, seismic data are acquired, followed by dispersion curve estimation and, finally, inversion to derive the V_s profile.

One of the main advantages of R-wave-based techniques is that these waves dominate when generated by a vertical source, allowing effective V_s estimation. Steady-state testing was the initial approach, in which a monochromatic surface wave was produced by a vertically acting vibrator. Early studies determined wavelength and phase velocity by measuring phase differences between receivers [54,55,62,63]. However, early methods were limited by monochromatic sources and depth approximation assumptions. The introduction of spectral methods, such as SASW, enabled broader frequency analysis, improving depth resolution but requiring complex data processing.

Despite its advantages, surface wave analysis has several limitations. The inversion process is highly complex and influenced by the ambiguity of the solution, meaning different models can represent the data with equal accuracy. Additional uncertainties arise from experimental data errors, model assumptions (e.g., 1D isotropic elastic models), and parameterization choices. While a single best-fitting V_s profile may suffice for some applications, deeper layers are more challenging to resolve due to decreasing sensitivity at greater depths [2].

Lateral variations in seismic properties also pose challenges, as surface wave methods typically assume a 1D subsurface structure. These methods are most effective when applied to sites with minimal lateral heterogeneity and relatively flat ground surfaces. Additionally, higher modes in surface wave propagation can complicate the analysis. If not properly accounted for, they can be misinterpreted as fundamental modes, leading to errors in the velocity profile. However, simultaneous inversion of fundamental and higher-order modes can enhance the reliability of results by incorporating additional independent constraints [2]. Since no standardized procedures exist for handling higher modes, customized analyses by experienced professionals are often required [2,56].

Given these considerations, careful data acquisition and expert interpretation are essential for accurate V_s estimation using surface wave analysis. While commercially available software simplifies processing, improper use by non-experts can lead to significant errors, reducing trust in non-destructive techniques within parts of the earthquake engineering community [2].

4.1.3. Seismic Tomography

Seismic tomography is a robust imaging technique that reconstructs three-dimensional models of the Earth’s inner structure through seismic wave travel times and waveforms analysis. Similar to medical CT scans, this method utilizes seismic waves produced by earthquakes or explosions to infer subsurface structures. In a homogeneous Earth, seismic rays would propagate along straight paths; however, due to the planet’s complex layering, waves undergo reflection and refraction at material boundaries, altering their paths [64]. By recording seismic wave energy at multiple stations, researchers can detect anomalies in wave velocity, revealing variations in subsurface properties (Figure 2).

This technique has been widely applied to shear wave velocity estimation. Travel time tomography and waveform inversion are commonly used to develop detailed subsurface velocity models. For instance, Li et al. (2012) employed a simultaneous inversion of surface wave dispersion data together with receiver functions to construct a high-resolution three-dimensional V_s model, demonstrating seismic tomography’s effectiveness in capturing velocity variations in complex geological settings [65].

Other studies have also highlighted the capability of seismic tomography and related geophysical techniques in V_s estimation. Pilz et al. (2012) [66] presented a one-step inversion method to derive 3D S-wave structures using high-frequency correlation functions from ambient seismic noise. The approach, tested through simulations and real-world data, successfully mapped local subsurface heterogeneities. Manu-Marfo et al. (2019) [67] used ambient noise tomography to develop a 3D model of V_s and Moho topography for the Tyrrhenian Basin. Results revealed a broad low-velocity zone in the uppermost mantle, reflecting past tectonic evolution. The findings support an exhumed mantle basement beneath the Vavilov Basin and ongoing Africa–Eurasia convergence.

In essence, while all three techniques involve the use of seismic waves to probe the Earth’s subsurface, they differ in their methods of wave generation, propagation, and analysis, leading to different types of insights into Earth’s structure and properties.

These advancements in geophysical methods underscore their practical applications in geoscience and geotechnical engineering. Techniques such as seismic refraction, seismic tomography, and surface wave analysis provide efficient, non-invasive, and environmentally friendly means for V_s estimation. However, each method has its limitations, which must be considered when selecting the most suitable approach.

Table 1. Advantages and disadvantages of different geophysical methods.

Technique	Advantages	Disadvantages	Depth Range	Spatial Resolution
Seismic Refraction	Provides depth-dependent shear wave velocity profile High-resolution estimation of Vs Cost-effective and efficient Non-intrusive and minimal site disturbance	Requires controlled seismic sources Limited to near-surface applications Sensitive to geophone spacing and array design	Under 100 m	high
Surface Wave Analysis	Estimates shear wave velocity variations with depth Cost-effective and efficient Minimal disturbance to the site	Requires long-wavelength surface waves Extracting reliable dispersion curves is tough Appropriate inversion methods are crucial	10–100 m	intermediate
Seismic Tomography	Provides detailed subsurface velocity models Captures Vs variations in complex settings High-resolution estimation of Vs	Requires seismic data from multiple receivers Computational complexity Sensitivity to initial model assumptions	Meters to a few kilometers	low

summarizes the key advantages and disadvantages of these techniques in V_s prediction. In this table, we can also see the depth range and spatial resolution of each method. Surface wave analysis offers intermediate spatial resolution for estimating shear wave velocity. It is not as high as some other techniques, like seismic refraction [68,69]. Surface wave analysis is most commonly used for estimating shear wave velocities in the near-surface environment, typically within the first 10 to 100 m [70]. Seismic tomography’s spatial resolution for estimating V_s can vary depending on the data acquisition and processing methods. Generally, it is not very high in comparison with other methods. However, it can still provide a useful representation of the subsurface structure. The depth of seismic tomography typically ranges from a few meters to a few kilometers. It is also used to image deeper structures, even to the Earth’s core, but the resolution and detailed imaging capabilities generally decrease with the depth [71].

Recent advancements in geophysical methods for estimating V_s are significantly enhancing subsurface characterization. For example, advancements in seismic interferometry have allowed for the reconstruction of subsurface velocity structures using passive seismic noise. This technique reduces the need for active sources and enhances the resolution of shallow subsurface imaging [72]. In addition, the compilation of uniformly processed global shear-wave-splitting data has provided a more consistent and extensive database for interpreting shear wave velocity structures, aiding in the assessment of subsurface anisotropy and heterogeneity [73].

Key future directions include the following: (1) Combining machine learning algorithms with established geophysical techniques, such as surface wave analysis and seismic tomography, is improving the accuracy and efficiency of V_s estimations. For instance, hybrid models that integrate full-waveform inversion with deep learning are being developed to enhance seismic imaging and subsurface characterization [74]. (2) Development of advanced inversion techniques: Innovative inversion methodologies, such as probabilistic neural network tomography, are enabling more accurate and rapid estimation of shear wave velocities from surface wave dispersion data, facilitating large-scale subsurface imaging [75]. (3) Enhanced data acquisition technologies: The deployment of advanced geophysical tools, including high-frequency surface wave methods and continuous monitoring systems, is improving the spatial resolution and temporal coverage of shear wave velocity measurements, leading to more detailed subsurface models [76]. These innovations are poised to transform geotechnical and seismological practices by offering more accurate, efficient, and non-invasive methods for subsurface characterization.

Seismic interferometry and comprehensive global datasets can also be mentioned as the two main breakthroughs of geophysical methods for estimating shear wave velocity. Advancements in seismic interferometry have allowed for the reconstruction of subsurface velocity structures using passive seismic noise [77]. This technique reduces the need for active sources and enhances the resolution of shallow subsurface imaging [72]. The compilation of uniformly processed global shear-wave-splitting data has provided a more consistent and extensive database for interpreting shear wave velocity structures, aiding in the assessment of subsurface anisotropy and heterogeneity [73].

4.2. Remote Sensing

Remote sensing is a technique for detecting and analyzing an area’s physical properties from a distance by measuring reflected and emitted radiation, typically using satellite or airborne sensors. This method captures large-scale images of the Earth’s surface, providing visibility beyond what is possible from ground-based observations. For example, satellite cameras can record ocean temperature variations, while sonar systems on ships generate images of the ocean floor without direct access. Figure 3 illustrates the concept of remote sensing.

A major benefit of remote sensing is its application in geological mapping. Unlike conventional methods that are often constrained by limited coverage, remote sensing allows for large-scale data acquisition through satellite imagery and satellite gravity measurements [78,79,80,81,82,83]. Satellite gravity maps the distribution of gravity anomalies to estimate rock density, functioning similarly to terrestrial gravimeters but deployed in orbit [84,85,86,87]. Meanwhile, satellite imagery provides high-resolution and frequently updated surface condition data, offering a dynamic alternative to relatively static gravity-based mapping [88]. When combined with V_s measurements at depths of up to 30 m (V_s30), remote sensing enhances geological assessments by correlating surface conditions with subsurface properties [89]. Since V_s30 serves as an indicator of rock stiffness, it can be theoretically linked to rock density derived from gravity measurements, improving the accuracy of geological models [89].

Beyond geological mapping, remote sensing techniques have proven valuable in geotechnical applications, particularly in estimating shear wave velocity (V_s) [21]. By analyzing surface features and soil composition captured through airborne or satellite imagery, researchers can establish correlations between spectral characteristics, reflectance patterns, and V_s values. For example, Wróbel et al. (2022) integrated surface wave analysis and borehole measurements with airborne imagery, demonstrating the cost-effectiveness and accuracy of this approach in V_s estimation [90]. Similarly, Holland et al. (2005) developed a methodology for estimating sediment density and V_s gradients in subsurface formations by formulating mathematical relationships between remote sensing data and geotechnical parameters [91]. These researchers highlighted the potential of remote sensing for rapid and cost-efficient V_s assessments over large spatial extents.

The benefits of remote sensing in V_s prediction include its non-intrusive nature, reduced need for extensive fieldwork, and capability to effectively span extensive regions [21]. Additionally, remote sensing facilitates temporal monitoring, allowing researchers to analyze changes in V_s over time. However, the precision of V_s estimations is influenced by the resolution and quality of the imagery, as well as the availability of ground truth data for calibration. Atmospheric and geometric distortions may introduce uncertainties, and correlations between surface features and V_s can vary depending on regional geological conditions, necessitating site-specific validation.

Table 2. Advantages and disadvantages of the remote sensing technique.

Technique	Advantages	Disadvantages
Remote Sensing	Cost-effective and energy-efficient Provides spatially extensive information Non-intrusive and reduces fieldwork requirements Enables monitoring of temporal variations	Relies on correlations with surface features Requires ground truth data for calibration and validation Uncertainties due to atmospheric and geometric effects Correlations may vary with regional geological conditions

summarizes the key benefits and limitations of remote sensing in V_s forecasting.

Recent advancements in remote sensing techniques for estimating shear wave velocity have enhanced subsurface characterization. Key breakthroughs include seismic interferometry: Utilizing passive seismic noise correlations, seismic interferometry reconstructs subsurface velocity structures without the need for active sources. This method has been applied to image seismic scattering and velocity structures, particularly in volcanic regions [72]. Ambient noise tomography: By analyzing background seismic signals, this technique maps underground geological structures, providing insights into subsurface velocity variations [77]. Looking ahead, the future of remote sensing for V_s estimation is poised to benefit from the integration of multimodal data fusion and advanced machine learning algorithms, enabling more accurate and comprehensive subsurface imaging. Frequency–velocity convolutional neural networks (CNNs): These networks enable rapid, non-invasive 2D V_s imaging of near-surface geomaterials by analyzing normalized dispersion images. They offer flexibility in experimental configurations and have demonstrated effectiveness in imaging soil-over-bedrock interfaces [92].

Deep neural networks (DNNs) integrated with rock physics modeling: This approach combines theoretical rock physics models with DNNs to predict V_s across various frequency bands. It has shown superior accuracy compared to traditional empirical formulas, with prediction errors within 200 m/s in real field data applications [93].

For example, one of latest advancements in remote sensing and AI for V_s is the investigation conducted by Meng et al. Their study highlighted the growing role of artificial intelligence in enhancing the analysis of remote sensing data and emphasized how techniques like SAR altimetry and 3D imaging radar altimetry, combined with AI tools, have improved the detection and characterization of oceanic phenomena, like internal solitary waves. The integration of AI-driven approaches with remote sensing technologies represents a promising direction for future research in geophysics, as similar methodologies could be applied to V_s estimation by incorporating more advanced machine learning models and deep learning architectures. These developments align with the need for transformer-based models and physics-informed graph neural networks (GNNs) to further enhance the accuracy and reliability of shear wave velocity predictions across diverse geological conditions [94].

4.3. Machine Learning and Data-Driven Techniques

Lately, there has been growing emphasis on machine learning and data-driven methods for their potential in predicting shear wave velocity in various geotechnical and geophysical applications [95]. These methods provide economical and environmentally friendly substitutes for traditional techniques. This section reviews some major previous studies that utilized ML and data-driven approaches for V_s prediction, highlighting their methodologies, performance, and notable findings.

In 2007, Rezaee and colleagues [11] utilized neuro-fuzzy systems, artificial neural networks, and fuzzy logic to predict V_s based on log data from conventional wells in a sandstone reservoir located in the Carnarvon Basin, Australia. The models were trained on two wells and validated on a third, demonstrating high reliability. The similar performance of different intelligent methods confirmed their effectiveness for complex reservoir characterization. Rajabi (2010) [95] applied genetic algorithms and fuzzy logic together with neuro-fuzzy techniques to predict compressional, shear, and Stoneley wave velocities from well log data in the Sarvak carbonate reservoir, Iran. Using 3030 data points, the models were trained and tested, with fuzzy logic showing the lowest prediction errors. The results demonstrated the reliability of intelligent techniques for reservoir characterization. Asoodeh and Bagheripour (2012) [96] introduced a hybrid committee machine approach to forecast sonic wave velocities using log data of conventional wells. This approach combines fuzzy logic, artificial neural networks (ANNs), and neuro-fuzzy algorithms to improve predictive capabilities. Additionally, by incorporating a genetic algorithm combined with a pattern search technique, the model’s accuracy in predictions was further enhanced. Applied to the Asmari Formation in Iran, the approach outperformed individual intelligent systems in reliability and effectiveness.

Maleki et al. (2014) utilized the support vector machine (SVR) for predicting the V_s values in the southern part of Iran [97]. Their methodology utilized seismic data, geological attributes, and information from previous borehole logs. The SVR model exhibited promising accuracy and demonstrated the potential of data-driven approaches in capturing V_s variations. Bagheripour et al. (2015) [98] proposed a method based on the support vector regression (SVR) approach to predict V_s utilizing well log data, addressing limitations in direct measurements. By leveraging structural risk minimization, SVR outperformed neural networks and empirical models in accuracy. The method was successfully applied to carbonate reservoirs in Iran’s gas fields, offering a fast and cost-effective solution. In 2015, other scholars also presented a novel ant colony–fuzzy inference system (ACOFIS) for V_s prediction, integrating fuzzy reasoning with ant colony optimization. Applied to the Cheshmeh–Khosh oilfield, the method outperformed conventional approaches, improving prediction accuracy. ACOFIS also showed potential for estimating other reservoir rock properties [99]. Ataee et al. (2018) [100] studied the correlation between V_s and various soil index parameters, including SPT, soil moisture, fine content, depth, and liquid limit, by employing the ANN method and multiple regression analysis. The study, based on data from Mashhad, Iran, proposed new prediction equations for V_s and found that the ANN method provided more accurate predictions with lower estimation errors and higher correlation coefficients compared to multiple regression analysis.

Anemangely et al. (2019) [101] developed a model for V_s prediction in the Ahvaz field using well log data and feature selection via the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). Chosen optimization algorithms (PSO, GA, and COA) together with the least square support vector machine (LSSVM) showed the LSSVM-COA model to be the most accurate and reliable, outperforming empirical and regression models. After validation of the model in the Ab-Teymour field, its generalizability and high accuracy for V_s estimation were demonstrated. Wang and Peng (2019) [102] proposed another method for estimating V_s using the mean impact value (MIV) and extreme learning machines (ELMs), applied to well log data of two wells located in China’s Ordos Basin. The method identified the most significant logs for V_s estimation and outperformed traditional models like ANN-LM with regard to the precision of prediction and computation time. The proposed ELM-MIV model was shown to be a highly efficient and precise tool for estimating shear wave velocity, with potential for integration into software systems for rapid log acquisition.

Azadpour et al. (2020) [103] combined machine learning and rock physics to improve V_s prediction in some carbonate reservoirs. Through adjustments to Gassmann’s fluid substitution model and introducing a factor exponent, the approach enhanced accuracy. Using inversion-based estimation and Gaussian process regression, the method outperformed conventional models, reducing prediction errors significantly. Lian et al. (2020) [104] integrated machine learning with rock physics modeling to improve the seismic interpretation accuracy. By generating synthetic well logs and testing RF, MLP, and SVR algorithms, the approach enhanced P- and S-wave velocity predictions. The proposed method outperformed conventional rock physics modeling, significantly increasing prediction accuracy. In another study, machine learning techniques were applied, particularly artificial neural networks, to predict V_s for geomechanical modeling in wells lacking direct measurements. The approach outperformed traditional linear models, especially in hydrocarbon-bearing intervals. It was then used to calculate in situ stresses and safe mud weight windows, with predictions closely matching actual drilling events [105]. Wang et al. (2020) [106] presented a hybrid model combining long short-term memory (LSTM) together with particle swarm optimization (PSO) networks to estimate V_s using traditional logs. By employing grey relational analysis to select sensitive logs and optimizing the LSTM model’s hyperparameters, the approach enhanced prediction accuracy and robustness. Tested with real petrophysical data, the model outperformed conventional methods, offering a solution for V_s prediction in oil and gas reservoir studies.

Zhang et al. (2021) [107] utilized the DNN method to estimate the V_s spatial distribution to assess the liquefaction of soil. The hybrid approach showed improved performance, thereby highlighting the potential benefits of integrating ML in V_s estimation. Jeong et al. (2021) [108] introduced a method based on conditional variational autoencoders (CVAEs) to reconstruct shear slowness data from other well logs, like neutron porosity, compressional slowness, gamma ray, and bulk density. Compared to bi-LSTM and LSTM models, the CVAE method provided superior results. Olayiwola and Sanuade (2021) [109] compared three models, including LSSVM, adaptive neuro-fuzzy inference system (ANFIS), and ANN, for predicting V_p and V_s by using wireline log data. R², or coefficient of determination, can be calculated by subtracting the unexplained variation from the total variation, then dividing the result by the total variation. R² tells us how much better the model is at predicting the data compared to just using the average of the data. This indicator was used in that research. The LSSVM model outperformed the others, achieving high accuracy, with R² or coefficient of determination values of 0.9706 for V_p and 0.9991 for V_s. Based on their research, the approach can aid geoscientists and engineers in reservoir characterization and drilling operations. Miah (2021) [110] developed a data-driven model using coupled simulated annealing (CSA) and LSSVM to predict V_s. The study identified the V_p as the most influential parameter for estimating V_s, followed by shale volume, bulk density, and porosity. The proposed model, with a high correlation coefficient (R² = 0.96), outperformed existing correlations and could be applied for accurate prediction of rock mechanical properties together with wellbore failure analysis, improving drilling safety and reducing exploration costs.

Kim (2022) [111] introduced a hybrid ML approach for generating synthetic shear sonic (DTS) logs, addressing the limited availability of DTS data. The approach combined supervised learning models (LSTM, SVR, and DNN) with data clustering and PSO to enhance prediction accuracy and optimize hyperparameters. The results showed that this integrated method outperformed non-clustered models, providing a more reliable and efficient solution for generating synthetic DTS logs. Wong et al. (2022) [112] explored the use of the ML technique for estimating sonic wave travel time in hydrocarbon exploration, addressing obstacles and benchmarks. They compared regression methods, including curve-fitting artificial neural and multiple linear regression (MLR) networks, for effective travel time prediction. The aim was to connect machine learning experts with oil and gas engineers to enhance prediction accuracy.

Mehrad et al. (2022) [113] proposed a high-accuracy model for predicting V_s in carbonate reservoirs using well log data. By applying the CNN and multilayer extreme learning machines (MELMs) with optimization algorithms, the MELM-COA model showed better generalizability and faster learning times compared to CNN. The proposed method outperformed traditional empirical equations and is recommended for similar fields with larger datasets. Laalam et al. (2022) [114] estimated the V_s values in the Williston Basin by using the random forest regression. For this purpose, they used a combination of remotely sensed geophysical data along with geological information. The model achieved promising results, demonstrating the potential of ML techniques in inferring V_s values. Zhang et al. (2022) [115] predicted the V_s values by the convolutional neural networks (CNNs) technique for a study conducted in Ordos Basin. They trained the model using a large dataset comprising seismic data, geological information, and well-logging data. The CNN-based model showed better performance than the traditional approaches, indicating the effectiveness of deep learning techniques in capturing complex relationships within the data. Jiang et al. (2022) [116] presented a deep learning approach to predict shear wave velocity from conventional logging data in tight sandstone formations, offering insights into efficient subsurface characterization.

Feng et al. (2023) [93] enhanced shear wave velocity prediction by integrating theoretical rock physics models into deep learning. By generating a comprehensive labeled dataset through forward simulation, the model improved physical interpretability and generalization. The proposed deep neural network outperformed traditional empirical formulas, achieving prediction errors below 5% in real-world applications. Zhang et al. (2023) [117] introduced a Gaussian process regression (GPR) approach to estimate the V_s in sandstone reservoirs by utilizing V_p and geological information of the reservoir. Unlike deep learning, GPR effectively handles small datasets while also quantifying uncertainty. Field tests showed that GPR outperformed conventional methods, providing more accurate and reliable S-wave velocity predictions. Kheirollahi et al. (2023) [118] focused on estimating V_s in carbonate reservoirs, where conventional S-wave logs usually were unavailable due to high costs. Various predictive models, including MLR, ANN, and ELM, were tested using conventional well logs. The feed-forward neural network model, with an optimal design found through grid search optimization, achieved the greatest precision, with R-values of 0.99 for training and 0.96 for testing datasets, and is proposed for V_s prediction in other wells. Cova and Liu (2023) [119] introduced a new method for V_s prediction utilizing the bidirectional gated recurrent unit (GCN-BiGRU) combined with a graph convolutional network. Their model captured both spatial and temporal dependencies in well log data and enhanced prediction accuracy by incorporating a self-learning graph neural network and feature generation techniques. The GCN-BiGRU outperformed other machine learning methods and empirical formulas, such as Castagna’s velocity formula, LSTM, and SVR, in predicting S-wave velocity based on the North Sea open dataset.

Akinyemi et al. (2023) [120] applied seven machine learning algorithms (LR, RFR, KNN, SVR, BPANN, CatBoost, and XGBoost) to estimate the shear and compressional sonic logs (DTS and DTP) from conventional wireline information from the Niger Delta Basin. The best performance for DTP prediction was achieved with CatBoost (R² = 90%) and for DTS prediction with CatBoost (R² = 95%). The models showed strong performance, with R² values exceeding 80% for DTP and 90% for DTS, and blind testing validated their accuracy, confirming the potential for estimating geomechanical parameters in wells lacking sonic log data. Mustafa et al. (2023) [121] developed ML models to predict V_s in shale formations using wireline logs, addressing the high cost of direct measurements. Six machine learning techniques were tested, with ANN outperforming the others, achieving the highest accuracy (R² = 0.96) and lowest errors. The proposed models offer a fast, reliable, and cost-effective solution for estimating S-wave velocity, aiding in the derivation of rock mechanical properties. Khalilidermani and Knez (2023) [122] improved V_s estimation for hydrocarbon reservoirs using well log data from the Aboozar limestone oilfield in Iran. Various methods, including empirical correlations, linear regression, and machine learning (multivariate linear regression and gene expression programming), were tested against actual V_s measurements. The gene expression programming (GEP) model delivered the most accurate predictions (R² = 0.972), outperforming traditional empirical methods. The study provided a new correlation for precise V_s estimation, applicable to the Aboozar oilfield and similar geological formations.

Fu et al. (2024) introduced a neural network method for V_s prediction in locations lacking this data, aiming to enhance the accuracy of subsurface oil and gas distribution models [123]. By incorporating an attention module to assign weights to input data, followed by processing through a LSTM network, the approach achieved a mean absolute error (MAE) of 38.89 in Well B, outperforming the standard LSTM network’s MAE of 45.35. Gomaa et al. (2024) [124] presented an ANN model for accurately estimating V_s utilizing widely available data, like porosity, bulk density, Vp, and gamma ray. The model, developed using 2350 data points, demonstrated exceptional precision, with a strong coefficient of determination of 0.958, making it a practical tool for well design without the need for specialized software. This method provided a more efficient and budget-friendly solution to traditional methods of estimating V_s.

Dehghani et al. (2024) evaluated the effectiveness of different ML techniques in estimating the shear wave transit time, highlighting the potential of these techniques in geophysical applications [125]. Joshi et al. (2024) [126] developed an artificial intelligence model, VelProfES, designed to predict subsurface V_s profiles without relying on traditional geophysical techniques. The model, trained on bore log and V_s data from Japan’s Kyoshin network, used simple parameters, like layer thickness, SPT-N values, and soil type. The VelProfES model, enhanced with synthetic data from CTGANs, provided accurate predictions with minimal error, in contrast to traditional polynomial and empirical models. Yilmaz et al. (2024) presented a deep-learning-based approach for predicting V_s30 at strong motion station locations using three-channel earthquake records [127]. Leisi and Shad Manaman (2024) described an innovative seismic and well-logging data integration workflow to predict the shear velocity volume using an artificial neural network [128].

These studies underscore the importance of integrating machine learning techniques with traditional geophysical methods to enhance the accuracy and efficiency of S-wave velocity estimation, thereby advancing our understanding of subsurface formations. Estimating V_s is crucial for accurately characterizing subsurface formations, particularly in clastic rocks. Traditional methods often rely on empirical relationships, such as Castagna’s equation [129], which correlates V_p to V_s. Recent advancements have integrated ML methods with traditional geophysical models to enhance the precision of V_s predictions. In the context of V_s estimation, machine learning approaches have shown promise. For instance, combining LSTM with attention mechanisms has enhanced feature extraction from well log data, leading to more precise estimations [130]. Incorporating geographical information, like latitude and longitude, into ML models has also shown the improvement in V_s predictions. This approach accounts for regional geological variations, enhancing the model’s robustness and accuracy [131]. Another latest breakthrough of V_s prediction by AI techniques is the application of XAI techniques, such as SHapley Additive exPlanations (SHAP), which has provided insights into the decision-making processes of ML models. This transparency is crucial for validating model predictions and understanding the influence of different input features on V_s estimation [131].

Looking ahead, the future of AI-based methods in V_s prediction is poised to see further advancements, driven by continued improvements in model complexity, data integration, and computational power, potentially leading to even more accurate and efficient prediction capabilities. For example, combining ML models with FWI techniques is one of the promising methods that aims to leverage the strengths of both data-driven and physics-based approaches for more accurate and efficient subsurface characterization [74]. Additionally, future models will likely incorporate uncertainty quantification methods to assess the reliability of V_s predictions. This development will aid in risk assessment and decision-making processes in geotechnical engineering and seismic hazard analysis [132].

As we can see, according to the literature review, the interest of utilizing ML approaches in V_s prediction has increased in recent years.

Table 3. Error estimation metrics comparison of AI models for shear wave velocity prediction.

Reference	AI Model	Error Estimation
Rezaee et al. (2007) [11]	NFS	MSE = 0.001
Rajabi (2010) [95]	GA, FL, NF	MSE = 0.0153, 0.0084, 0.0184
Asoodeh and Bagheripour (2012) [96]	FL, ANN, NF	MSE = 0.0081, 0.0068, 0.0078
Maleki et al. (2014) [97]	SVR, BPNN	R2 = 0.97, 0.94
Bagheripour et al. (2015) [98]	SVR	R2 = 0.9716
Nourafkan et al. (2015) [99]	ACOFIS	MSE = 0.0033, R2 = 0.9590
Anemangely et al. (2019) [101]	LSSVM-COA, LSSVM-PSO, LSSVM-GA	R2 = 0.929, 0.877, 0.868
Wang and Peng (2019) [102]	ELM, ANN	RMSE = 0.0795, 0.0913
Azadpour et al. (2020) [103]	ML	R2 = 0.941
Lian et al. (2020) [104]	SVM, RF, MLP	Average R2 for ML models = 0.64
Khatibi and Aghajanpour (2020) [105]	NN	R2 = 0.9555
Olayiwola and Sanuade (2021) [109]	LSSVM	R2 = 0.9991
Miah (2021) [110]	LSSVM-CSA	R2 = 0.96
Wong et al. (2022) [112]	ANN, MLR	R2 = 0.86 (ANN), 0.36 (MLR)
Mehrad et al. (2022) [113]	CNN, MELM, LSSVM	R2 = 0.825, 0.826, 0.815
Laalam et al. (2022) [114]	XGBoost, RFR, LR, AdaBoost, BRR	R2 = 0.55 to 0.92, XGBoost outperforms others
Zhang et al. (2022) [115]	CNNs	R2 = 0.957
Kheirollahi et al. (2023) [118]	MLR, ELM, ANN	R2 = 0.99 (ANN), 0.96 (MLR, ELM)
Cova and Liu (2023) [119]	GCN-BiGRU	R2 = 0.947
Akinyemi et al. (2023) [120]	LR, KNN, SVR, RFR, XGBoost, CatBoost, BPANN	R2 = 0.92 to 0.94 (CatBoost had best result)
Khalilidermani and Knez (2023) [122]	GEP	R2 = 0.972
Mustafa et al. (2023) [121]	ANN	R2 = 0.96
Fu et al. (2024) [123]	NN	MAE = 38.89, LSTM MAE = 45.35
Gomaa et al. (2024) [124]	ANN	R2 = 0.58
Dehghani et al. (2024) [125]	ANN, LR, RF, LB, SVM	R2 = 0.8780, 0.8471, 0.8470, 0.9495, 0.8583, 0.7975
Leisi and Shad Manaman (2024) [128]	ANN	RMSE = 0.94

summarizes the performance of various machine learning models used for predicting shear wave velocity across the studies mentioned in the literature review. The table presents the error estimation metrics (R², MSE, MAE, and RMSE) for each model, providing insights into the technological evolution of AI-based approaches in V_s estimation. According to this table, the performance of AI models in shear wave velocity estimation has improved significantly over the years. Early studies used relatively simpler methods, such as neuro-fuzzy systems and ANN, with performance metrics like R² values around 0.94 and MSE between 0.008 and 0.015. However, modern techniques, such as LSSVM, XGBoost, CNN, and hybrid models, show much stronger results, with R² values approaching 0.9991 and MAE and RMSE values decreasing significantly, reflecting technological advancements in model design, data quality, and algorithm optimization.

Numerous studies have investigated methods for estimating V_s, evaluating their effectiveness through real data, and offering important findings for petroleum studies. However, despite these progressions, challenges remain in selecting appropriate ML algorithms and interpreting their results. ML models often depend on statistical relationships, which may not always align with geological realities, leading to potential inaccuracies. Additionally, the performance of these models is highly sensitive to data quality and the selection of relevant features. To address these challenges, future studies should aim at creating sophisticated predictive models that prioritize key geological features. Incorporating domain-specific knowledge into ML algorithms can enhance their interpretability and reliability. Moreover, employing robust validation techniques and integrating multiple data sources can improve the generalizability of these models across different geological settings. In

Table 4. Advantages and disadvantages of machine learning and data-driven approaches.

Technique	Advantages	Disadvantages
ML and Data-Driven Approaches	Captures complex relationships in data Offers high prediction accuracy Can handle non-linear relationships Utilizes available data effectively Allows for incorporation of multiple data points	Requires large, labeled datasets May suffer from overfitting Interpretability of results may be challenging Performance dependent on data quality

, the major merits and demerits of these techniques in predicting shear wave velocity are presented.

Therefore, we can conclude that while machine learning offers promising avenues for S-wave velocity estimation in clastic rocks, careful consideration of algorithm selection, feature importance, and model validation is essential to achieve accurate and reliable predictions.

5. Challenges of V_s Measurement

Predicting shear wave velocity in geoscience is an important task with various challenges. Based on the conducted research, a number of major challenges were detected and categorized by the authors. In what follows, those major challenges are discussed.

5.1. Data Availability and Quality

A significant hurdle in estimating V_s lies in the adequacy and reliability of data. Obtaining extensive data collections of shear wave velocity measurements from diverse geological settings can be difficult due to factors such as limited accessibility, cost, and logistical constraints [113]. To improve data availability, platforms like IRIS [133] and OpenTopography [134] can facilitate data sharing among researchers and institutions. Additionally, OSGeo [135] offers open-source tools for managing and analyzing geospatial data, which can be critical for enhancing the quality and accessibility of data used in shear wave velocity studies. Furthermore, standardizing measurement techniques and data reporting is essential for ensuring consistency and comparability across studies [113]. Initiatives like the IRIS Data Management Center and databases like the ShearWave Velocity Database could play a key role in promoting data standardization. These efforts, coupled with the establishment of standardized reporting guidelines, are helpful for improving the quality and availability of shear wave velocity data [136].

5.2. Spatial and Temporal Variability

Shear wave velocity exhibits significant spatial and temporal variations due to geological heterogeneity, soil compaction, weathering, and other factors. These variations pose challenges in accurately predicting shear wave velocity across different locations and time periods. Capturing the inherent variability of V_s and understanding its effect on prediction accuracy are critical for reliable assessments of site-specific seismic hazards [65]. Integrating high-resolution spatial data from platforms like LiDAR or UAV-based surveys (e.g., OpenTopography Data) can help capture fine-scale surface variations [134]. Temporal variability can be monitored by conducting periodic seismic surveys (e.g., MASW) to track changes due to seasonal soil moisture variations. Additionally, applying geostatistical methods (e.g., Kriging) for spatial interpolation and leveraging machine learning models can improve predictions of V_s across variable terrains and time periods [137].

5.3. Non-Unique Relationships

The relation between the V_s parameter and other geophysical or geological parameters is often not unique. Multiple combinations of parameters can result in similar shear wave velocity values, leading to challenges in accurately predicting V_s based on limited data inputs. Resolving the non-uniqueness of these relationships requires the integration of diverse data and robust development of inversion and modeling techniques [11]. To address this, various techniques focus on reducing the uncertainty and finding more reliable solutions. These include incorporating additional constraints, using different inversion approaches, and refining models based on statistical analysis [138].

5.4. Anisotropy and Inhomogeneity

Geological formations commonly exhibit anisotropy (directional dependence) and inhomogeneity (variations within a region). These characteristics significantly affect shear wave velocity predictions. Anisotropic properties can result from sedimentary layering, preferred orientation of minerals, or stress-induced fabric [139], while inhomogeneity can arise from variations in grain size, compaction, or saturation. Accounting for anisotropy and inhomogeneity requires advanced models and methods to accurately predict shear wave velocity in complex geological settings [110,140]. This issue can be addressed by a combination of advanced modeling techniques, including joint inversion of seismic data, and consideration of geological and rock physics properties is essential [141].

5.5. Integration of Multiple Data Sources

The incorporation of multiple data sources is crucial for improving shear wave velocity predictions. Combining geotechnical measurements, seismic data, remote sensing, and geological information enhances the understanding of subsurface conditions and improves the reliability of shear wave velocity estimation. However, effectively integrating different data types and extracting their complementary information remains a challenge, requiring sophisticated data fusion and integration algorithms [110]. To address this challenge, the main solution can be using data fusion techniques.

5.6. Interpretability and Uncertainty Quantification

Interpreting and communicating the results of V_s predictions are crucial for decision-making in geoscience. Additionally, understanding the uncertainties linked to the predictions and quantifying their influence on risk assessments are critical for accurate hazard evaluation. Efforts to develop interpretable models and establish robust uncertainty quantification frameworks are necessary to enhance the practical applicability of shear wave velocity predictions [142]. The main solution for this problem is to apply machine learning models with built-in interpretability tools, such as SHAP or LIME, to explain model predictions. Additionally, Bayesian approaches or Monte Carlo simulations can be used to quantify uncertainty in predictions by incorporating prior knowledge and propagating errors through the model, providing more robust and reliable V_s estimates [132].

5.7. Standardization and Collaboration

Establishing standardized protocols for shear wave velocity measurement, data collection, and reporting is crucial for improving data quality, comparability, and reproducibility. Collaboration among researchers, industry professionals, and policymakers is essential for addressing common challenges, sharing knowledge and resources, and advancing the field collectively [143]. The solution can be developing and implementing standardized protocols for V_s measurement, data collection, and reporting. This can be achieved through collaboration among researchers, industry professionals, and policymakers to establish common guidelines, improve data comparability, and ensure reproducibility across studies and projects.

5.8. Scale Effects

The V_s predictions may be affected by the scale at which the analysis is conducted. Extrapolating results from laboratory-scale measurements to field-scale conditions or vice versa can introduce uncertainties [144]. Therefore, it is important to employ multi-scale modeling approaches that integrate both laboratory-scale measurements and field-scale conditions. By calibrating laboratory measurements with field data and applying appropriate scaling techniques, we can reduce the uncertainties that arise when extrapolating results between different scales. This approach helps ensure more reliable predictions across varying spatial scales.

As mentioned in the above paragraphs, the V_s predictions in the subsurface formations encounter diverse challenges, especially stemming from the uncertainties in the geological, geotechnical, and structural properties of rocks and soils. Thus, for future works, it is recommended to develop strategies capable of mitigating such challenges.

6. Discussion

The V_s prediction in geoscience and geoengineering is a crucial and challenging task with substantial implications for various applications, including reservoir characterization, seismic hazard analysis, and geotechnical engineering. Despite significant progress, challenges remain in achieving high-accuracy and reliable V_s predictions across diverse geological settings [145]. In this discussion, we will delve into the key findings from the conducted research.

Conventional techniques, such as laboratory-based experiments and field measurements, have been foundational in understanding the physical properties of subsurface materials. These methods, although accurate, are time-consuming, labor-intensive, and often impractical for large-scale studies. However, they remain indispensable in certain contexts, especially for calibrating alternative methods or for specific high-precision tasks. The limitations of these traditional techniques have driven the need for more efficient and cost-effective approaches, with geophysical methods, remote sensing, and machine learning algorithms emerging as the primary alternatives.

Geophysical techniques, such as seismic refraction, surface wave analysis, and seismic tomography, have revolutionized the way V_s is estimated in geoscience. These methods offer significant advantages, including non-intrusiveness, high spatial resolution, and relatively low environmental impact. Seismic refraction, for example, is highly effective in constructing depth-dependent V_s profiles, which are essential for understanding subsurface structures [59]. Surface wave analysis, while traditionally challenging due to the complexity of data inversion, offers an efficient way to estimate shear wave velocity in near-surface environments [61]. Seismic tomography, especially in its advanced forms, like ambient noise tomography, has enabled high-resolution imaging of subsurface velocity variations, even in areas with limited access [65].

However, these methods are not without their drawbacks because they are sensitive to lateral variations in subsurface properties, and their accuracy diminishes with increasing depth and heterogeneity [71]. Seismic tomography, while powerful, demands complex data acquisition and processing, which can be computationally expensive and requires expert interpretation [64]. The evolution of hybrid models that integrate machine learning with geophysical techniques holds promise for overcoming some of these limitations. By combining the physics-based strength of geophysical methods with the data-driven flexibility of ML models, we can achieve more robust and accurate V_s predictions that account for both geological complexities and data uncertainties.

Remote sensing techniques, including satellite and airborne geophysical methods, have proven to be invaluable for large-scale V_s estimation. These techniques offer a non-intrusive and cost-effective way to acquire geophysical data across vast spatial extents. Remote sensing has been particularly useful for estimating V_s at depths of up to 30 m (V_s30) and for correlating surface features with subsurface properties [89]. The ability to collect real-time or near-real-time data without the need for fieldwork makes remote sensing an attractive option for environmental monitoring, resource exploration, and geohazard assessment. However, these techniques are highly sensitive to the quality of data acquired, the resolution of imaging, and the calibration to ground truth data. Furthermore, correlations between surface conditions and subsurface properties vary significantly depending on regional geological conditions, which presents a challenge for applying remote sensing methods universally across different geological terrains.

Machine learning and deep learning have fundamentally transformed the landscape of shear wave velocity prediction [146,147,148,149,150,151,152]. AI-based models have demonstrated exceptional capabilities in capturing complex, non-linear relationships within large datasets, providing more accurate and efficient predictions than traditional models [123]. The ability of ML algorithms to learn from diverse data sources, such as seismic measurements, geological logs, and remote sensing data, has led to substantial improvements in V_s estimation. For instance, hybrid models that combine machine learning techniques, such as LSTM networks with FWI, have shown promise in enhancing the precision and speed of seismic imaging and subsurface characterization [74]. Furthermore, AI techniques, such as CNNs, have outperformed classical regression models, providing more reliable and accurate predictions across different geological formations [115].

Nonetheless, AI-based methods face several critical challenges. The most pressing issue is the quality and availability of labeled training data, as ML models often require large, high-quality datasets to achieve reliable predictions. The lack of comprehensive and standardized datasets in geoscience is a significant hurdle, especially in remote or inaccessible regions [113]. Furthermore, while AI models can achieve high predictive accuracy, their interpretability remains a major concern. Geoscientists and engineers must understand how models arrive at their predictions, particularly in applications where decisions may have critical consequences, such as in seismic hazard assessment or infrastructure design. Approaches like XAI and model interpretability techniques such as SHAP and LIME are essential for increasing the transparency and trustworthiness of ML models in geoscience applications [131].

Additionally, the problem of overfitting, where models perform well on training data but fail to generalize across different geological settings, remains a significant challenge. Overcoming overfitting requires robust validation techniques, including cross-validation with diverse datasets, and the integration of domain-specific knowledge into AI models. Moreover, uncertainty quantification is an area that requires further research. As V_s estimation plays a crucial role in decision-making processes for infrastructure development and disaster preparedness, incorporating uncertainty quantification into AI models will enable more reliable risk assessments and better decision-making under uncertainty [132].

The future of V_s prediction lies in the continued integration of AI with traditional geophysical methods and the development of more robust, multi-source predictive models. Combining geophysical techniques, such as seismic tomography and surface wave analysis, with AI algorithms offers a powerful hybrid approach that can deliver both high accuracy and computational efficiency. Furthermore, the advent of new inversion algorithms and data fusion techniques will likely enhance the reliability of V_s predictions in geologically complex areas.

AI and machine learning also have a significant role in the optimization of data acquisition technologies, enhancing the efficiency of data collection in real time, reducing the need for expensive and labor-intensive fieldwork, and improving the quality of predictions with sparse data. Advancements in remote sensing and seismic interferometry will also complement AI-driven techniques, providing richer datasets for training and improving prediction accuracy [72]. The integration of PINNs and other hybrid models that combine domain knowledge with machine learning will enhance both the interpretability and accuracy of V_s estimation in complex geological settings.

Regarding the energy consumption, geophysical techniques for estimating shear wave velocity generally have low energy consumption because they rely on passive ambient noise or low-energy active sources, e.g., sledgehammers or small vibrators [153]. AI techniques can initially require substantial energy for training, but they may offer efficiencies in subsequent data processing and analysis [154]. Remote sensing methods, especially those deployed in space, can be energy-efficient during operation but may have higher initial deployment costs.

However, remote sensing techniques generally consume more energy per unit time, especially due to the power requirements of satellites, aircraft, and data processing. However, remote sensing can be more efficient overall, as it avoids the need for repeated, energy-intensive field campaigns and can cover large areas in one go. The tradeoff is that remote sensing might have higher upfront energy costs but can be more sustainable for large-scale or long-term studies, especially when considering repeated field campaigns that ground-based geophysical methods require [155].

In summary, the advancements in geophysical methods, remote sensing, and AI have the potential to revolutionize V_s prediction in geoscience and geoengineering. By addressing the challenges related to data availability, model interpretability, and uncertainty quantification, these technologies can offer more accurate, energy-efficient, and cost-effective solutions for subsurface characterization. Moving forward, multidisciplinary collaboration and the integration of advanced data fusion techniques will be crucial in overcoming existing challenges and enhancing the practical applications of V_s prediction.

7. Conclusions

Shear wave velocity (V_s) measurement and prediction are crucial for understanding subsurface formations in geoscience and geotechnical engineering. This review explored the advancements, methodologies, and challenges in predicting V_s. Geophysical methods offer cost-effective and eco-friendly options, though they face challenges related to sensitivity, data accessibility, and the need for controlled seismic sources. Remote sensing has proven valuable for estimating V_s over large areas, but data quality, uncertainty in correlations, and regional variability must be addressed for more reliable results.

Machine learning techniques, such as random forest regression, convolutional neural networks, and support vector machines, have shown promise in capturing complex relationships and improving prediction accuracy. However, issues such as data availability, overfitting, and interpretability need further refinement.

Energy efficiency plays a crucial role in V_s estimation methods. Geophysical techniques, using passive noise or low-energy sources, generally consume less energy. While AI techniques require substantial energy for training, they offer efficiencies in subsequent data analysis. Remote sensing methods, although energy-intensive at the outset, can be more sustainable for large-scale or long-term studies compared to ground-based methods requiring repeated fieldwork.

Key challenges in V_s prediction include data quality, spatial and temporal variability, non-unique relationships, and anisotropy. Solutions involve the development of standardized protocols, advanced modeling techniques, and integration of diverse data sources. Effective collaboration among researchers, industry professionals, and policymakers, along with robust uncertainty quantification, is vital for enhancing the practical applications of V_s prediction.

In summary, advancing V_s prediction requires continued multidisciplinary collaboration to address these challenges. By refining existing methods and exploring new approaches, significant progress can be made in improving geoscientific models, contributing to safer infrastructure development and seismic hazard mitigation.