A revised weight of evidence model for potential assessments of geothermal resources: a case study at western Sichuan Plateau, China

Efficient exploration of geothermal resources is the basis of exploitation and utilization of geothermal resources. In recent years, Geographic Information System (GIS) has been increasingly used for the exploration owing to its power ability to integrate and analyze multiple sources of data related to the formation of geothermal resources, such as geology, geophysics, and geochemistry. Correctly understanding the con-trol effect of evidence factors on geothermal resources is the premise and basis of whether the prediction results of evidence weight model are accurate. Traditionally, the conventional weight of evidence model assume that each evidence factor exerts a uniform controlling effect on the formation and distribution of geothermal resources. However, recent research indicates significant variations in the controlling ability of factors such as faults and granites, influenced by factors like activity levels and crystalline ages. Yet, studies addressing this differential control are lacking. To address this gap, we propose a series of weight of evidence models using abundant geological, geophysical, and geothermal data from the western Sichuan plateau, a high-temperature geothermal hotspot in China. This study aims to investigate the impact of varying controlling abilities of evidence factors on the evaluation model, with faults and granites as a case. Performance metrics include prediction rate, success rate index, receiver operating characteristic curve (ROC) and prediction rate of geothermal well. The findings of this research reveal that the weight of evidence model developed through the methodology outlined in this study exhibits superior performance compared to the conventional weight of evidence model. This superiority is evidenced by higher prediction rates, success indices, prediction rate of geothermal wells, and larger AUC values of ROC. Among these models, the weight of evidence model considering both fault and gran-ite classification have the best performance in model evaluation indicators, with a prediction rate of 22.528 and a success index of 0.015408 in the very high potential area. The prediction rate and success index of the high potential area are 3.656 and 0.0025, respectively, and the prediction rate and success index of the middle potential area are 1.649 and 0.001128, respectively, and the AUC value is 0.808, indicating that the model has good accuracy. In terms of geothermal well prediction, the total prediction rate of geothermal favorable areas based on fault and granite classification evidence weight


Background
Geothermal energy, which originates from the heat stored in earth's interior, is characterized by cleanliness, stability, and wide spatial distribution, as well as huge reserves (Cao et al. 2022), and has become a popular object of research in the world nowadays (Duo and Zheng 2008;Wang 2016;Xu et al. 2016).According to statistics from the World Geothermal Congress, as of the end of 2019, a total of 88 countries had engaged in the direct utilization of geothermal energy, with an installed capacity of approximately 107,727 MWt and a compound annual growth rate of 8.7% (Lund and Toth 2021), and 29 countries had engaged in geothermal power generation, with an installed capacity of 15,950 MW and an annual power generation of 95,098 GW (Toth et al. 2022).China, situated within the geothermal belt adjacent to the Pacific Rim in the east and the Mediterranean-Himalayan geothermal belt in the southwest, boasts abundant geothermal resources (Wang et al. 2019a, b).It is estimated that the shallow geothermal energy resources annually exploitable in 336 cities above the prefecture level in China amount to approximately 7 × 10 8 tons of standard coal.Hot dry rock resources located at depths ranging from 3 to 10 km represent a substantial energy reservoir, estimated at 86 × 10 18 tons of standard coal.Harnessing a mere 2% of this vast resource would yield energy equivalent to 4040 times the total energy consumption of the nation.These findings underscore the immense potential of deep geothermal energy as a sustainable and abundant energy source, capable of significantly satisfying China's energy needs (Wang et al. 2017).These substantial geothermal reserves underscore China's potential to harness geothermal energy as a sustainable and renewable energy source, contributing to its energy security and environmental sustainability goals..The robust development of geothermal resources holds promise for mitigating environmental hazards associated with conventional fossil fuels and facilitating the transition towards a more sustainable energy landscape in China (Wang et al. 2020;Wang and Lu 2022).
Efficient exploration of geothermal resources is the basis of exploitation and utilization of geothermal resources.Geological surveys, geophysical exploration, and geochemical analysis of thermal fluids are the three main primary applied to explore geothermal resources (Kana et al. 2015).As the exploration process progresses from regional to local scales, a large number information is generated through geological, geochemical, and geophysical surveys, among others.Therefore, it is imperative to integrate and interpret these diverse datasets to pinpoint the precise locations and extents of areas warranting further investigation or exploratory drilling.This holistic approach to data analysis and interpretation is crucial for identifying geothermal potential area and optimizing geothermal resource exploration efforts (Noorollahi et al. 2008).The advancement of computer technology has led to the gradual adoption of GIS (Geographic Information System)-based multi-source data fusion analysis methods in geological exploration.This approach involves quantifying geological, remote sensing, geophysical, and geochemical data through specific methodologies to generate corresponding potential distribution maps (Yu 2016).GIS models, characterized by their simplicity and versatility, enable rapid analysis and comparison of extensive datasets, thus minimizing manpower and material resource consumption.Consequently, these methods have found widespread application in mineral resource prediction and geological hazard assessment (Zhu et al. 2003;Li et al. 2009).In recent years, there has been a growing trend towards applying such techniques in the realm of geothermal exploration.
There are many geothermal potential models based on GIS, such as fuzzy logic model (Coolbaugh et al. 2007), index overlay model (Noorollahi et al. 2008), weight of evidence model (Tüfekçi et al. 2010).The weight of evidence model, initially proposed by a Canadian mathematician and geologist, has emerged as a pivotal evaluation tool in geothermal exploration (Agterberg 1992), whose widespread adoption is attributed to its ability to minimize the impact of subjective factors on predictive outcomes by deriving weights solely from data sources.For instance, Tüfekçi et al. (2010) proposed a weight of evidence model to delineate the geothermal potential areas in western Anatolia, Turkey, and delineated five geothermal targets successfully, among which Aydın and Denizli areas are already under development.Based on the related data of the Fujian Province, Yu (2016) established a weight of evidence model to assess its potential areas, and the results showed that the areas of Fuzhou, Zhangzhou, Longyan, Xiamen is favorable for the concentration of geothermal resources.Abuzied et al. (2020) predicted the geothermal resource potential along the coast of the Gulf of Suez through the weight of evidence model and found that the geothermal favorable areas are mainly located in Ras Matarma, Ras Badran, Abu Rudies, Belayim, Abu Durba, El-Tur and the southwestern coastal areas of the Gulf of Suez, most of which are located at fault junctions.In addition, Zhou et al. (2021) delimited 10 excellent geothermal constituencies and 3 geothermal prospective areas in Fuzhou, with the method of the weight of evidence model.A similar work utilizing the weight of evidence model to evaluate the geothermal resource potential can be found in the Chuan-Tibet Railway carried out by Chen (2021).
During the construction of the weight of evidence model, a thorough comprehension of the control mechanisms through which evidence factors govern geothermal resources is imperative.Numerous research findings indicate that various factors, have significantly distinct effects on geothermal resources.For example, Wang et al. (1999) suggested that geothermal resource may occurs in the areas with strong fault activity.Faulds et al. (2012) deemed there exists direct relationship between the distribution of high-temperature geothermal systems and the density and strain rate of Quaternary faults in the western Basin of the United States.Besides, Li et al. (2019) underscores that the relationship between hydrothermal activities and fault activity is very close by studying the characteristics of geothermal distribution and the relationship of fracture distribution in the Jianchuan-Deqin area of the Sling-block in Sichuan and Yunnan Province.However, granitic rocks formed in different periods have distinct radiogenic characteristics (Artemieva et al. 2017), consequently, their impact on geothermal resources varied.As suggested by previous research (Zhao and Luo 1995;Yang 2016;Li and Li 2017;Song et al. 2020), the granitic formed since the Yanshanian are closely linked to geothermal resources.During model construction, past studies assumed uniform control effects of individual factors on geothermal resource formation.For example, granite from varied periods or faults with differing activity strengths were considered to exert equivalent influences on geothermal resource formation.Such assumptions may introduce discrepancies between model predictions and actual outcomes.To date, limited attention has been directed towards investigating the impact of varying control exerted by evidence factors on the assessment outcomes of weight of evidence models.Consequently, this study aims to address this gap, offering a more comprehensive understanding of geothermal resource potential evaluations.

Geothermal resources characteristics in the western Sichuan Plateau
The western Sichuan plateau, which spans a region between 27° 58′ N and 34° 20′ N and 97° 22′ E and 102° 29′ E (Fig. 1), is located at the eastern end of the Tibet Plateau Fig. 1 Location of the study area and geology-tectonics map (modified from 1:1.5 million geological map of Tibetan Plateau and its surrounding areas and Metcalfe 2002;Zhang et al. 2012;Replumaz et al. 2014;Tang et al. 2017;Qin et al. 2021) in the Songpan-Ganzi orogenic belt.It is an essential component of China's high-temperature Yunnan-Tibet geothermal zones (Liao and Zhao 1999), as well as one of the country's main distribution areas for high-temperature geothermal resources (Zhang et al. 2021).
Since the onset of the Cenozoic era, the west Sichuan Plateau has experienced significant uplift and deformation attributed to the persistent northward subduction of the Indian plate.This geological process has led to the formation of a network of faults, characterized by both North-South and NW-trending orientations.Notable among these faults are the Xianshuihe fault, the Ganzi-Litang fault, and the Jinshajiang fault, which serve as the primary trunk faults in the western Sichuan region.These faults, deeply embedded in the crust, exert substantial control over the tectonic evolution of the area (Gao et al. 2015;Qu et al. 2019;Qin et al. 2021).The above faults have strong activity, high slip rate and frequent seismic activity.For example, the Litang 7.5 earthquake in 1948 and Luhuo 7.9 earthquake in 1976 are related to the activities of the Litang fault and the Xianshuihe fault, respectively (Wang et al. 2008a, b;Zhang et al. 2017).Multiple eras of magmatic activity, from the Jinningian to the Xishanian, have been linked to the faults of region.As a result, several granite outcrops of the Precambrian, Triassic, Jurassic, Cretaceous, and Neogene geological eras are exposed on the surface.The Triassic magmatic rocks have the broadest spread of all of these (Fig. 1c).
The complex tectonic activity and geological in the western Sichuan plateau offers conducive conditions for the genesis of high-temperature geothermal resources.Current data reveal the identification of 248 sites exhibiting hydrothermal activity in the region, with nearly 60% of these sites hosting hot springs surpassing 40 °C.Remarkably, 11 hot springs exhibit output temperatures exceeding the boiling point for the altitude at which they are situated (Zhang et al. 2017).Numerous geothermal areas in the western Sichuan Plateau have relatively high heat storage temperatures, according to the results of geochemical research, which include Rekang geothermal area with a temperature range of 200-225 °C (Tian et al. 2018), the Cuopu geothermal area with a temperature range of 175-200 °C (Tian et al. 2019), the Laoyulin geothermal area with a temperature range of 232-235 °C, the Hailuogou and Caoke geothermal area with a temperature range of 201-205 °C (Zhang 2018), the Ganzi geothermal area with a temperature range of 180-210 °C (Fan et al. 2019), and the Litang geothermal area with a temperature range of 152-195 °C (Zhang et al. 2019).Zhang et al. (2017) partitioned the western Sichuan plateau into three geothermal belts running from east to west, namely Dege-Batang-Xiangcheng, Ganzi-Xinlong-Litang, and Luhuo-Daofu-Kangding (Table 1).Based on analysis of geothermal data, the geothermal systems were divided into Batang and Kangding types in the study area (Zhang et al. 2017).In these geothermal systems, meteoric water undergoes circulation along the fault, and then, the water is heated by the deep heat sources, and rises to surface form hot springs (Zhang et al. 2017).Tang et al. (2020) based on a combination of the Curie depth, distribution of radioactive elements, and existing measured heat flow data to estimate the southeastern margin of the Tibet Plateau heat flow distribution, which suggest that the heat flow distribution on the area follows a high in the southwest and low in the northeast pattern, with the western Sichuan plateau falling within the high heat flow area.Notably, the high heat flow concentration locations include Kangding, Litang, Batang, Dege, Jiulong, and Xiangcheng, with the greatest heat flow reaching 88 mW/m 2 .
The geothermal resources within the study area predominantly consist of medium to high-temperature resources.According to Qu et al. (2019), the total estimated geothermal reserves amount to approximately 4.26 × 10 16 kJ, with an exploitable geothermal fluid volume of 1.29 × 10 7 m 3 /a and a corresponding heat energy of 2.56 × 10 12 kJ/a.Specifically, high-temperature geothermal potential is assessed at around 2.37 × 10 16 kJ, translating to a 30-year power generation capacity of 2501.2MW as reported by Wang (2018).These findings underscore the abundant and promising nature of geothermal resources in western Sichuan, indicative of favorable prospects for high-temperature geothermal exploration.
Although there are abundant geothermal resources in the western Sichuan Plateau, the potential distribution characteristics of geothermal resources in the region are still unclear due to the harsh natural environment and high exploration cost.Therefore, this study formulated a series of weight of evidence models leveraging extensive geothermal, geological, and geophysical datasets from the west Sichuan Plateau, a vital region for high-temperature geothermal resources in China.By employing granites with varied active faults and invasion ages as case studies, the impact of diverse evidentiary factors on the outcomes was assessed.The findings not only enhance the precision and dependability of geothermal resource prediction models, but also offer crucial insights for the

Model establish
Analyzing the relationship between evidence components and geothermal training points, performing an independence test, and constructing the model are some of the steps in the weight of evidence model construction process for geothermal resource evaluation(Tüfekçi et al. 2010) (Fig. 2).Through classification and statistical analysis based on predetermined rules, the weight of evidence model seeks to convert the measured values of various aspects that affect the occurrence of geothermal resources into informative values.The calculation method is as follows (Van Western 1997): where N i represents the number of geothermal training points in the ith category of evi- dence factor X i ; N represents the total number of geothermal training points in the study area; S i represents the number of grids in the ith category of evidence factor X i ; S repre- sents the total number of grids in the study area.
The weights of evidence factors can be determined by follows (Agterberg 1992): (1) (2) W + = ln P(B|D) P(B|D) , where B and B are the number of grids containing and not containing the evidence fac- tor, respectively; D is the number of geothermal training points; whereas, D is the num- ber of points that are not geothermal training points.
The relevance of the chosen evidence factors to the geothermal training points must be assessed prior to building the weight of evidence model.For each layer of evidence, the contrast C should be analyzed (Yu 2016): where C indicates the level of correlation between the evidence factor and the geothermal training points.C > 0 indicates that the evidence factor supports geothermal formation, while C < 0 indicates that the evidence factor is not favorable for geothermal formation.When C = 0, there is no correlation between the evidence factor and geothermal formation.The weight of the evidence factor can be determined by selecting the maximum C value.
However, the weight computation may be influenced by the weak significance of particular C values.The significance of C value can be increased through studentized method (Yu 2016;Abuzied et al. 2020): where S 2 (W + i ) and S 2 (W − i ) are the variances of W + i and W − i , respectively.S(C) is the standardized value of C, and Studentized(C) is the studentized value of C.
After determining the information value and the weight of each evidence factor, the total information value of all evidence factors can be calculated using the following formula (Yu 2016):

Data resources
Drawing upon regional geological comprehension of geothermal resource origins in western Sichuan, along with available published data and established exploration methodologies, six primary influencing factors concerning geothermal resources within the (3) western Sichuan Plateau are selected.These factors include fault, granite, land surface temperatures (LST), Bouguer gravity, aeromagnetic anomaly, and Gutenberg-Richter b values.Then, a weight of evidence model is constructed utilizing these factors.
Applying a Mono-window algorithm to accessible Landsat 8 pictures yielded the land surface temperature (for the calculation procedure, see "Land Surface Temperature (LST)" section).The Bouguer gravity was obtained from the 1:3,000,000 gravity series map of the Tibetan Plateau and its surrounding regions, and the aeromagnetic data were obtained from1:2,500,000 aeromagnetic series map of the Chinese land area.The National Data Center for Earthquake Science and the China Earthquake Networks provided the seismic data, respectively.Other data were acquired from published literature (Tang et al. 2017;Qin et al. 2021).According to Geothermal Hot Springs History of China: Southwest Volume, there are 196 hot springs and geothermal wells of various varieties on the western Sichuan Plateau (Wang 2018).There are 184 hot springs of these, mostly in the regions of Kangding, Litang, Batang, Ganzi, Rural, and Xiangcheng.For simplicity of analysis, this study makes the assumption that hot springs within a 1 km radius are part of the same geothermal system, and the 15.3 × 10 4 km 2 study area is divided into 150,591 evaluation units, each measuring 1 km × 1 km.Generally, the same geothermal system may have multiple surface heat displays within a certain range.To prevent redundant statistical analysis of hot spring manifestations from identical geothermal systems, which could skew predictive model outcomes, this study adopts a criterion where hot springs within a 1 km radius are considered part of the same geothermal system.A dataset comprising 103 distinct natural hot springs representing various geothermal systems is chosen as training points and inputted into the analytical model (Fig. 3). Figure 3 shows that the distribution of geothermal training points is uneven in the study area.There are almost no geothermal training points in Shiqu, Seda, Yajiang and Jiulong, while there are a certain number of geothermal training points in other areas.

Fault
Faults, recognized as crucial thermal control structures, significantly influence the genesis of geothermal resources, particularly in the context of uplifted mountain hydrothermal geothermal systems (Qiu et al. 2022).The extensive distribution of faults presents favorable pathways for geothermal fluid migration, while the thermal energy generated through frictional shear within extensive and deep fault zones contributes supplementary heat to geothermal resources (Zhu and Shi 1990;Ai et al. 2021).Since the Cenozoic era, the collision between the Indian Plate and the Eurasian Plate has led to the formation of numerous NW-trending faults across the western Sichuan Plateau (Fig. 4a).Previous studies have pinpointed three main faults in the research area: the Ganzi-Litang fault, the Xianshui River fault, and the Jinsha River fault.These faults remain active in the present day and have considerable cutting depth (Wang et al. 2008a, b;Zhang et al. 2017).A few secondary faults also have relatively high strike-slip rates, such the Batang fault as 8.7 ± 2.1 mm/a (Zhang et al. 2017).The medium-high temperature hot springs are intensively exposed along the faults, indicating that the faults in the study area are important transport channels for hot fluids and heat.
Buffer analysis was conducted on the faults using the ARCGIS geographic information system to analyze a quantitative correlation between faults and geothermal training points.Figure 4b illustrates the outcome, indicating that geothermal training points predominantly occur in grid cells proximate to the faults.The number of geothermal training points decreases with increasing distance from the faults, as seen in Fig. 4c.According to statistical analysis, over 65% of the geothermal training points are located less than 4 km from the faults.

Granite
The heat produced through the decay of radioactive elements, namely uranium (U), thorium (Th), and potassium (K), per unit volume of rock and per unit time, is termed as the radioactive heat generation rate of the rock (Shen and Yang 1989).Numerous studies have demonstrated that granitic rocks, considered as the primary contributor to radioactive heat generation, serve as a latent heat source for geothermal systems (Rybach et al. 1978;Fernàndez et al. 1998;Wyborn 2010;Vidal and Genter 2018;Zhang et al. 2020a, b, c).Under the influence of the northward subduction and extrusion of the Indian plate, large-scale magmatic activities occurred in many periods in western Sichuan and eastern Tibet, forming many granite bands (Fig. 5a).The distribution of granite was predominantly influenced by oceanic subduction and continental collision associated with plate tectonics.Pre-Mesozoic granite was primarily distributed within post-basin uplifts and island arc fold belts.Granite formations since the Meso-Cenozoic era have chiefly occurred within island arcs and back-arc basins near the hinterland uplifts.Magmatic activity within the research area is primarily concentrated during the Triassic (220-230 Ma), Jurassic (160-190 Ma), Cretaceous (71-94 Ma), and Cenozoic (13-41 Ma) periods (Tang et al. 2017).Multiple stages of granitic intrusive rock formation occurred from the Jinningian to the Xishanian stage along fault lines.Triassic intrusive rocks are predominantly distributed in the Yidun Island arc and Songpan-Ganzi fold belt, comprising mainly monzonitic granite, granodiorite, and diorite lithologies.Jura-Cretaceous intrusive rocks are mainly found in the northwest of the Yidun Island arc and north of Danba.Cenozoic intrusive rocks are primarily located in Genie Mountain in the western part of the Yidun Island arc and Zheduoshan Mountain in the eastern part of the Xianshuihe fault, and the Zheduoshan intrusive rock is regarded as originating from the strike-slip movement along the Xianshuihe fault (Tang et al. 2017).
A distance diagram was produced after performing buffer analysis on the granite mass (Fig. 5b), and it is crystal evident that the majority of the geothermal training points are located in grid cells that are close to the granite.The number of geothermal training points and the distance from the granite have a negative link, according to the statistical histogram of granite and geothermal training (Fig. 5c).In particular, 69 geothermal training stations, or 67% of the total, are situated within 10 km of the granite.

Land surface temperature (LST)
As the ascent of deeply seated heat along fractures can induce thermal anomalies at the Earth's surface, surface temperature measurements can be employed to identify areas exhibiting geothermal anomalies (Wang et al. 2019a, b).Rapid and efficient identification of potential geothermal regions can be achieved through remote sensing techniques, which detect surface temperature anomalies.Particularly in regions with abundant geothermal resources but intricate ground conditions, such as the Qinghai-Tibet Plateau, remote sensing inversion of surface temperature enables swift delineation of geothermal anomaly areas, offering guidance for regional geothermal resource exploration.
A recent study by Ren et al. (2021) using Landsat 8 thermal infrared imagery to infer LST anomalies in the Xunwu region of Jiangxi Province resulted in the identification of 11 geothermal anomaly areas, demonstrating the successful application of remote sensing-based LST inversion techniques to geothermal exploration.In order to identify three geothermal opportunities, Xin et al. (2021) built LST for the Shijiazhuang area using Landsat 8 band 10 imagery.They then coupled this field with geological and geophysical data to find Sigou Village in Pingshan County, Gaocheng-Wuji, and Mayu-Huanmadian.
The Mono-window algorithm is commonly employed in surface temperature inversion procedures, requiring only three parameters: surface emissivity, atmospheric transmittance, and atmospheric average temperature.This method yields highly accurate surface temperature calculations.With precise parameter estimation, the accuracy of this method is within < 0.4 °C.Even with moderate errors in parameter estimation, the average error is approximately 1.1 °C, significantly lower than the errors introduced by atmospheric correction methods.Its calculating principle is as follows (Qin 2001): (10) where T s is the LST; T a is the average atmospheric temperature; T b is the brightness temperature; C and D are intermediate variables; a and b are regression coefficients; τ is the atmospheric transmittance; ε is the surface emissivity.
Terrain correction is necessary in regions characterized by substantial terrain variations to mitigate LST anomalies induced by solar radiation discrepancies.By employing an empirical statistical approach to adjust the radiative energy received by slope pixels to a horizontal orientation, the influence of topography can be effectively mitigated.The calculation formula is as follows (Zhai et al. 2015): where z represents the solar zenith angle, φx represents the solar azimuth angle, S repre- sents the pixel slope angle, φn represents the pixel aspect angle, L T represents the uncor- rected radiance value of the land cover, m and b are the regression coefficients obtained from analysis, L H represents the corrected radiance value of the land cover, and L T rep- resents the theoretical radiance value of the land cover in a flat terrain without topographic variations.
Utilizing a series of 14 Landsat 8 images captured between June and August from 2019 to 2020, the Mono-window algorithm and topographic correction inversion were employed to assess the LST distribution across the western Sichuan Plateau (Fig. 6a).The LST across the entire region ranged from − 10.2 to 49.0 °C.Over 99.30% of the area exhibited surface temperatures exceeding 15 °C, with concentrations observed mainly in river valleys, urban centers, and areas with low vegetation cover.A mere 0.01% of the region displayed temperatures below 0 degrees Celsius, primarily situated in high-altitude regions characterized by year-round snow and ice coverage.Analysis of the statistical table in Fig. 6b reveals that more than 90% of the geothermal training points were located in areas where LST ranged between 20 and 30 °C, underscoring a strong correlation between the distribution of LST and geothermal training points.

Aeromagnetic anomaly
The basics underlying the utilization of aeromagnetic anomalies for geothermal exploration lies in the detection of variations in the magnetic properties of rocks.Diverse rock compositions exhibit distinct magnetic characteristics, which are quantified and documented through aeromagnetic survey data acquisition.The magnitude of the aeromagnetic anomaly reflects changes in the Earth's magnetic field brought on by the magnetism of sediments and rocks (Yakubu et al. 2020;Jiao et al. 2022).Therefore, aeromagnetic anomaly can be helpful in locating areas of subsurface heat activity, hidden (11) granites, and fault tectonic.In the area of geothermal anomaly, geological phenomena such as subsurface magmatic events and hydrothermal circulation can induce alterations in the magnetic properties of rocks, thereby generating magnetic anomalies.As per prior investigations, positive magnetic anomalies may indicate the existence of magmatic intrusions, whereas negative magnetic anomalies may indicate the presence of fracture or hydrothermal activity zones (Jiang 2013;Zhang et al. 2020a, b, c).
The western Sichuan Plateau has aeromagnetic anomalies that range from − 149 to 199 nT, as shown in Fig. 7a.Positive aeromagnetic anomalies are prevalent across a wide range of west Sichuan Plateau.According to the statistical histogram of aeromagnetic anomalies and geothermal training points, approximately 48% of the total training points primarily cluster within regions exhibiting low positive aeromagnetic anomalies ranging from 0 to 20 nT (Fig. 7b).Furthermore, aeromagnetic anomalies ranging from 20 to 40 nT and from − 40 nT to 0 nT collectively represent 20% and 22% of the total geothermal training points, respectively.This underscores a clear correlation between the spatial distribution of geothermal training points and the occurrence of low-value aeromagnetic anomalies within the western Sichuan Plateau.

Bouguer gravity
Bouguer gravity is a measure of the gravitational force observed after making adjustment for topography, Bouguer and normal field corrections (Liu 2007).Bouguer gravity may be used to detect underground tectonic activity and changes in the Earth's crust because the Bouguer gravity value is exclusively determined by the distribution of mass beneath the surface of the planet.Elevated Bouguer gravity values could indicate uplifted basement areas, fostering heat accumulation due to disparate thermal conductivities between the basement and overlying strata.Such conditions may give rise to localized temperature anomalies (Xiong and Gao 1982).On the contrary, areas exhibiting diminished Bouguer gravity values could potentially signify zones of hydrothermal activity (Wu 2013).
Figure 8a illustrates the Bouguer gravity anomalies across the western Sichuan Plateau, ranging approximately from − 515 to 290 mGal.Evidently, these anomalies exhibit a consistent decline from the southeast towards the northwest, implying a progressive thickening of the crust from the Sichuan Basin to the Qinghai-Tibet Plateau.Notably, areas with low gravity anomalies correlate with the presence of igneous

Seismicity
Tectonic activity often manifests as earthquakes.Previous research has indicated a connection between geothermal activity and earthquake incidence.Geothermal activities are commonly found in seismic zones, where seismic events occur frequently, and seismic occurrences are prevalent in geothermal gradient zones (Li et al. 2019;Tang et al. 2020;Liu et al. 2021).A crucial indication to estimate seismic activity is the b-value in the Gutenberg-Richter law (Ren 2012), which represents the level of local seismic activity, can be calculated using the formula below: (16) lg N = a − bm, where m is the earthquake magnitude; N is the annual average occurrence times of magnitude greater than m; a is the constant related to the frequency of earthquake occurrence; b is the proportion of earthquake frequency of different magnitude.
This analysis focuses on earthquakes with magnitudes more than 2.0 and hypocenter depths less than 20 km that occurred in the western Sichuan Plateau between 1990 and 2020 (Fig. 9a).Gutenberg-Richter b values were determined through the application of the Gutenberg-Richter relation and the least squares method.Seismic activity in the region is concentrated in areas such as Ganzi-Kangding-Jiulong, Ganzi-Litang, and Batang, aligning with the Xianshui River fault, Ganzi-Litang fault, and Batang fault, respectively.A comparison between the data depicted in Fig. 9 b and c reveals that geothermal training points predominantly cluster in areas characterized by low b values.Furthermore, 90 of the geothermal training points, constituting 87% of the total, fall within the range of 0 < b < 1.This finding indicates a significant spatial correlation between the distribution of small to medium-sized earthquakes and geothermal training points.

Conditional independence
To mitigate the interference among the layers of evidence, the impact of certain factors on geothermal distribution is repeatedly assessed, resulting in deviations in the model's predicted outcomes.Consequently, a correlation analysis of the evidence layers is necessary using ARCGIS.When the |R| is below 0.3, it indicates that the two factors are independent of each other (Chen et al. 2020).The covariance and correlation coefficient matrices for the evidence factors are shown in Table 2 and Table 3. Aeromagnetic anomaly and LST have the lowest absolute value of the correlation coefficient, which is 0.01313.The distance between granite and the aeromagnetic layer exhibits the highest absolute value of the correlation coefficient, however |R|= 0.29309 is still less than 0.3.Each layer of evidence is hence conditionally independent.

Different weight of evidence models
The processing of evidence factors significantly influences the accuracy and reliability of geothermal resource potential predictions generated by weight of evidence models.The conventional weight of evidence model assumes that each evidence factor has the same influence on the formation of geothermal resources.However, it overlooks the varying influence exerted by the distinct attributes of these evidence factors, thereby impacting the precision of geothermal resource predictions.This issue could lead to inaccuracies in the forecasts of geothermal resource potential.This section conducts a comprehensive comparative analysis of various prediction models, encompassing the conventional weight of evidence model, the weight of evidence model considering fault classification, the weight of evidence model considering granite classification, and the weight of evidence model considering both fault and granite classification.The analysis utilizes prediction rate, success index, ROC curve, and prediction rate test of geothermal wells as the comparative evaluation criteria, elaborately discussed in the work by Chung and Fabbri (1999), Tüfekçi et al. (2010), and Yu (2016).

Conventional weight of evidence model
Following attribute values of evidence grid layers, six distinct evidence grid layers undergo categorization, as detailed in "Methodology and data sources" section.The distance to fault and granite raster layers are partitioned into 12 groups, with intervals of 2000 m and 2500 m, respectively.Similarly, the LST and B-value layers are classified into 12 categories using the Jenks classification method.Additionally, the Bouguer gravity raster layer and the aeromagnetic raster layer are divided into 12 categories at intervals of 10 nt and 20 mGal.Formulas 1 to 8 are utilized to calculate the information value and weight parameters for each evidence layer, as outlined in Tables 4 and 5.The weight calculation results in Table 5 reveal that faults and granites, with weights of 0.216 and 0.26, respectively, collectively contribute to approximately half of the overall weights.This observation suggests that faults and granites are the primary governing factors influencing the formation of geothermal resources in the western Sichuan Plateau.Therefore, this study will select fault and granite classification as exemplary cases to explore their impact on the prediction results of the evidence weight model, so as to analyze the influence of the difference control effect of evidence factors on the prediction results of the evidence weight model.Using ARCGIS, the information values of raster layers were added together based on the assigned weights to each evidence layer, resulting in the distribution of information quantity values illustrated in Fig. 10a for the western Sichuan Plateau.The total information value ranges from − 1.512 to 0.817 across the study area.The Ganzi-Xinlong, Kangding, Dege-Litang, and Batang-Derong regions predominantly exhibit high information values, whereas the northern Shiqu-Seda, southern Daocheng, southern Jiulong, and the Yajiang-Xinlong-Daofu region exhibit predominantly low information values.
In order to visually display the geothermal potential across different information values, it is important to categorize the information value into multiple levels for geothermal potential zoning.In this study, the information values are categorized into various grades based on the cumulative frequency of geothermal training points (Zhang et al. 2020a, b, c).According to the aforementioned principles, the overall geothermal information value of the study area is categorized into five grades: extremely low, low, moderate, high, and extremely high.The corresponding information value ranges for each grade are as follows: − 1.512 to − 0.444 for extremely low potential, − 0. 444 to 0 for low potential, 0 to 0.270 for moderate potential, 0.270 to 0.392 for high potential, and 0.392 to 0.817 for extremely high potential (Fig. 11).Utilizing the aforementioned classification method, a geothermal potential distribution map of the western Sichuan Plateau was generated, depicted in Fig. 10b.The extremely high potential zones are scattered across various regions including Kangding, Batang, Litang, Derong, Ganzi, and Xiangcheng, with a concentration observed around Kangding.High to moderate potential zones predominantly surround the extremely high potential zones, whereas extremely low potential zones are primarily situated in areas such as Shiqu and Yajiang-Xinlong-Daofu.Low potential zones are widely dispersed throughout the study area.Generally, regions exhibiting significant surface heat manifestations, such as Kangding and Litang, demonstrate relatively substantial geothermal potential.Additionally, areas with fewer geothermal training spots, such as Danba, Seda, Derong, Daofu, and Luhuo, also display certain geothermal anomalies.).The distribution of information value revealed by the recently developed weight of evidence model is depicted in Fig. 13a, demonstrating an information value range from − 1.096 to 0.801 across the research region.While low information value sites are scattered throughout the research area, high information value regions exhibit strip-shaped patterns along Ganzi-Kangding-Jiulong, Baiyu-Litang, and Batang-Derong.The geothermal potential is stratified into five levels according to the distribution of geothermal information values (Fig. 14): extremely low potential (− 1.096 to − 0.523), low potential (− 0.523 to 0), moderate potential (0 to 0.301), high potential (0.301 to 0.480), and extremely high potential (0.480 to 0.801).As depicted in Fig. 13b, the geothermal

The weight of evidence model considering granite classification
Figure 15 illustrates the relation between geothermal training sites and pre-and post-Yanshanian granite plutons.Data analysis indicates a decrease in the occurrence of geothermal hotspots with increasing distance from the granite plutons.Within the pre-Yanshanian granite, geothermal hotspots are predominantly clustered within a 10 km radius.Conversely, the distribution of geothermal hotspots in post-Yanshanian granite layers appears more uniform, lacking a discernible concentration trend.
The weight of evidence model, akin to fault classification methodology, was employed incorporating granite classification.Distances from granite formations of varying ages were divided into 12 classes at 2500 m intervals (see Figs. 4,6,7,8,9), while conventional weight of evidence modeling was applied to the remaining raster layers of evidence.The information value distribution across the study area, as depicted in Fig. 16a, spans from − 1.035 to 0.8.Areas with high information value are predominantly concentrated in Kangding, Batang, Litang, Daofu, and Ganzi-Derge, while regions with low information value exhibit a dispersion pattern similar to that observed in the conventional weight of evidence model.The information value is categorized into five tiers: extremely low potential (− 1.035 to − 0.351), low potential (− 0.351 to 0), moderate potential (0 to 0.223), high potential (0.223 to 0.352), and extremely high potential (0.352 to 0.801) (Fig. 17).The spatial distribution of geothermal potential zones, as presented in Fig. 16b, shows minimal deviation from the conventional weight of evidence model, suggesting that faults exert a more significant influence on geothermal resources compared to granite formations.The spatial distribution of areas with medium and high geothermal potential remained largely in line with the conventional weight of evidence model.However, the extent of extremely high potential areas was further constrained, predominantly located in Kangding, Litang, Batang, Dege-Ganzi, and other regions.Apart from

The weight of evidence model considering both fault and granite classification
This section will focus on developing a model that integrates the categorization methods discussed in "The weight of evidence model considering fault classification" and "The weight of evidence model considering granite classification" section.Fault layers are depicted in Fig. 12, while granite layers are illustrated in Fig. 15.The distribution pattern of information across the study area remains consistent with the weight of evidence model incorporating fault classification, suggesting that faults exert a more significant influence on geothermal resources compared to granite formations.The total information value was divided into various categories, including extremely low potential (− 0.847 to − 0.444), low potential (− 0.444 to 0), moderate potential (0 to 0.281), high potential (0.281 to 0.592), and extremely high potential (0.592 to 0.838) (Fig. 19), a geothermal potential level with the weight of evidence model considering both fault and granite classification was obtained (Fig. 18b).The spatial distribution of geothermal potential zones closely resembles that of the weight of evidence model incorporating fault classification, highlighting the strong correlation between geothermal resource formation and faults in the western Sichuan Plateau.The majority of the study area is classified as having low potential, with areas of extremely low potential predominantly located in Shiqu and northern Yajiang.Along the Ganzi-Kangding-Jiulong, Baiyu-Litang, and Batang-Derong regions, potential with high and moderate geothermal potential can be identified.Areas with extremely high geothermal potential are primarily clustered in Kangding, with additional scattered occurrences in Batang, Litang, and Ganzi-Dege (Fig. 19).

Analysis of differences in weight of evidence model evaluation metrics
In the preceding subsection, four distinct weight of evidence models were developed to thoroughly assess the geothermal resource potential across the western Sichuan Plateau.This section aims to investigate the impact of treatment methods applied to evidence factors on prediction outcomes.Specifically, it focuses on analyzing differences among prediction rates, success indices, ROC curves, and prediction rate of geothermal well of each weight of evidence model, elucidating how disparities in evidence factor handling influence the predictive performance of the weight of evidence models.
As depicted in Table 6, within each individual weight of evidence model, both prediction rates and success indices demonstrate an increasing trend with higher geothermal potential area grades.Notably, the success indices for moderate, high, and extremely high potential areas surpass the prior probability, indicating the effectiveness of the four weight of evidence models constructed in this study and their alignment with the actual distribution of geothermal resources.Regarding moderate potential area, the weight of evidence model considering fault classification exhibits the highest prediction rate and success index, recorded at 1.864 and 0.001275, respectively, while the lowest values are observed in the weight of evidence model considering both fault and granite classification, at 1.649 and 0.001128, respectively.Furthermore, the weight of evidence model considering granite classification achieves the highest prediction rate and success index for high potential areas, reaching 3.678 and 0.0025, respectively, whereas the weight of evidence model considering fault classification records the lowest values, at 2.341 and 0.001601, respectively.
Notably, for the extremely high potential area, the weight of evidence model considering both fault and granite classification demonstrates the highest prediction rate and success index, at 22.528 and 0.015408, respectively, whereas the conventional evidence weight model records the lowest values, at 5.728 and 0.003918, respectively.The cumulative prediction rate of geothermal favorable areas for the weight of evidence model considering both fault and granite classification is the highest, totaling 27.833, followed by the weight of evidence model considering granite classification, which totals 15.382.Meanwhile, the cumulative prediction rate for the weight of evidence model considering fault classification is 13.366, whereas the conventional weight of evidence model yields the lowest cumulative prediction rate at 10.774.Overall, the predictive performance of the weight of evidence models improves to a certain extent following the classification of faults and granites.
The AUC values of ROC curves of all models are shown in Fig. 20.According to the ROC curve (Fig. 20), the weight of evidence model considering granite classification has the highest AUC value at 0.814, followed closely by the model considering both faults and granite classification with an AUC value of 0.808.The AUC value for the weight of evidence model considering fault classification is slightly lower at 0.805, and the conventional weight of evidence model has the lowest AUC at 0.802.Overall, the AUC values for all four models exceed 0.7, demonstrating the high accuracy of the weight of evidence models developed in this study.The models developed using the methods in this paper outperform the conventional weight of evidence model, indicating that these methods effectively enhance the predictive performance of the weight of evidence models.Generally, drilling a geothermal well typically incurs very high costs, necessitating extensive geological and geophysical studies to determine the optimal well location before drilling and construction.Therefore, the accuracy of the model can be assessed by predicting the geothermal potential level at the well location.This study tested the model's accuracy using data from 12 wells in western Sichuan Plateau to evaluate its performance in predicting geothermal potential (Fig. 1c).The model's actual predictive effect was assessed by calculating the prediction rate for geothermal wells in each potential zone.The statistical findings of this evaluation are presented in Fig. 21.In terms of the number of predicted geothermal wells, for the extremely high potential area, the weight of evidence model considering fault classification predicts the highest number with 4 wells, followed by the conventional weight of evidence model with 3 wells.The weight of evidence models considering granite classification and both fault and granite classification each predict 2 wells.For high potential areas, the weight of evidence model considering both fault and granite classification predict the highest number of wells (7), followed by the weight of evidence model considering fault classification (5), and both the weight of evidence model considering granite classification and the conventional weight of evidence model predict 3 wells each.In the moderate potential area, the conventional weight of evidence model and the weight of evidence model considering granite classification predict the highest number of wells (6), while the weight of evidence model considering both fault and granite classification predict 3 wells, and the weight of evidence model considering fault classification predicts 2 wells.No geothermal wells were identified in the very low potential areas by any of the models.
However, both the weight of evidence considering fault classification model and the weight of evidence considering granite classification predict a geothermal well in the low potential area, which is inconsistent with the study's expectations.Existing research indicates that the formation of geothermal resources in the western Sichuan Plateau is closely related to the distribution of faults and granite.Considering only a single factor may cause the model to overemphasize its influence, leading to prediction bias and the identification of geothermal wells in low potential areas by the weight of evidence considering fault classification or granite classification models.
In terms of prediction rate, the conventional weight of evidence model has the poorest performance, with a total prediction rate for geothermal favorable areas of 14.4617.The weight of evidence model considering granite classification has a prediction rate of 18.1225, and the weight of evidence model considering fault classification has a rate of 20.0977.The weight of evidence model considering both faults and granite classification performs the best, with a total prediction rate for geothermal favorable areas reaching 47.0526, significantly higher than the other models.
Based on the aforementioned data, the weight of evidence model considering fault and granite classification exhibited successful predictions for the majority of geothermal wells within a smaller area.In summary, the weight of evidence model considering both fault and granite classification outperformed models that considering solely on fault or granite classifications.Consequently, the weight of evidence model considering both fault and granite classification can more precise identify geothermal target zones.
Conventional modeling approaches generally yield models with lower predictive accuracy compared to the methods in this study.Among the three alternative models explored, the weight of evidence model considering both fault and granite classification demonstrates the best prediction performance.The Kangding, Litang, Batang, and Ganzi-Dege regions have been identified as the most promising areas for geothermal exploration in western Sichuan, based on predictions generated by the weight of evidence model considering both fault and granite classification.As a result, these areas warrant focused attention for detailed geothermal resource exploration.Additionally, further investigation is warranted, as regions with less hot spring displays, such as Jiulong, Daofu, Luhuo, and Derong, also demonstrate significant geothermal potential (Fig. 22).

Conclusion
This study introduces a series of weight of evidence models that consider variations in evidence factors, specifically focusing on the influence of fault and granite types on the predictive outcomes of the weight of evidence model for the first time.Drawing upon the research result above, several key conclusions can be drawn: 1. Spatial correlation analysis of evidence factors and geothermal training points reveals a negative correlation between geothermal training points and fault or granite distances, alongside significant correlations with high surface temperatures, low aeromagnetic anomalies, high Bouguer gravity anomalies, and low Gutenberg-Richter b values.Among these factors, fault and granite presence emerge as the primary controlling factors influencing the formation of geothermal resources in the western Sichuan Plateau.2. Comparing the prediction rates, success indices, and ROC curves of the conventional weight of evidence model with the other three models developed in this study, the prediction rates for moderate, high, and extremely high potential in the conventional model are 1.733, 3.313, and 5.728, respectively, with corresponding success indices of 0.001186, 0.002266, and 0.003918.The AUC value of the ROC curve is 0.802.In contrast, the weight of evidence model considering fault classification predict rates of 1.864, 2.341, and 9.161 for moderate, high, and extremely high potential, with success indices of 0.001275, 0.001601, and 0.006266, respectively.Similarly, the weight of evidence model considering granite classification yields prediction rates of 1.716, 3.768, and 9.898, along with success indices of 0.001174, 0.002577, and 0.00677, for moderate, high, and extremely high potential, respectively.Finally, the weight of evidence model considering both fault and granite classification achieve prediction rates of 1.649, 3.656, and 22.528 for moderate, high, and extremely high potential, with corresponding success indices of 0.001128, 0.002500, and 0.015408.The predictive performance and accuracy of the three models developed in this study have improved, with the weight of evidence model considering both fault and granite classification exhibiting the most favorable prediction outcomes.3.Among the prediction rate of geothermal wells, the conventional weight of evidence model has the lowest performance, with the prediction rate of 14.4617 for favorable geothermal areas.In comparison, the weight of evidence model considering granite classification achieved a prediction rate of 18.1225, while the weight of evidence model considering fault classification reached 20.0977.However, the evidence weight model considering both fault and granite classifications demonstrated the best performance, achieving a total prediction rate of 47.0526 for geothermal favorable areas.In summary, it is crucial to comprehensively account for the differential control effects of evidence factors on geothermal resources when employing weight of evidence models for geothermal prediction.4. Utilizing the prediction outcomes from the weight of evidence model considering both fault and granite classification, four primary geothermal favorable zones were delineated: Kangding, Litang, Batang, and Ganzi-Dege, characterized by abundant surface heat manifestations.Moreover, areas exhibiting subdued geothermal activity, such as Jiulong, Daofu, Luhuo, and Derong, also demonstrated significant geothermal potential.These findings underscore the importance of directing future exploration efforts towards geothermal resources in these areas.
While this study has yielded significant results, it is important to acknowledge its minor limitations in some key points.Firstly, the grading methodology applied to the evidence factors directly influences the calculated information quantity.Enhancing the precision of the model necessitates accurate and objective categorization of the evidence layers.Secondly, limited by the harsh natural environment and the fact that there is a lack of boreholes available for temperature measurement, there is a significant lack of research on deep-seated temperatures or heat flow in the west Sichuan Plateau.This study only uses hot springs as a geothermal training point.However, the exploration and evaluation of geothermal resources cannot do without deep temperature data, we will continue to monitor the drilling situation in the western Sichuan region and update our model accordingly to obtain more reliable results.Finally, the study confines its forecast results to geothermal favorable areas, rather than pinpointing potential locations for high-temperature geothermal resources.This limitation arises from the assumption that hot springs with varying temperatures exert uniform effects throughout the model construction process.Nonetheless, prioritizing the exploration of higher temperature geothermal resources remains paramount in exploration endeavors.Addressing these issues can enhance the efficiency of exploring high-temperature geothermal resources in China.

Fig. 2
Fig.2The geothermal resource evaluation roadmap of weight of evidence model based on GIS(Tüfekçi et al. 2010)

Fig. 3
Fig. 3 Spatial distribution of geothermal training points in study area

Fig. 4
Fig. 4 Spatial distribution of faults in the western Sichuan (a) (modified from Qin et al. (2021)) and geothermal training points distance to faults map (b) and geothermal training points distance from faults histogram (c)

Fig. 6
Fig. 6 Distribution of LST in western Sichuan (a) and LST-geothermal training points histogram (b)

Fig. 7
Fig. 7 Aeromagnetic map of western of Sichuan and aeromagnetic-geothermal training points histogram

Fig. 8
Fig. 8 Distribution of Bouguer gravity map of western Sichuan (a) and Bouguer gravity-geothermal training points histogram (b)

Fig. 9
Fig. 9 Spatial distributions of earthquake epicentral in western of Sichuan (a) and Gutenberg-Richter b value map (b) and b value-geothermal training points histogram (c)

Fig. 10
Fig. 10 Amount of information in conventional weight of evidence model (a) and geothermal favorable map (b)

Fig. 12
Fig. 12 Geothermal training points distance to Pleistocene faults map (a) and geothermal training points distance from Pleistocene faults histogram (b); distance to Holocene faults map (c) and distance from Holocene faults histogram (d)

Fig. 13
Fig. 13 The weight of evidence model considering fault classification (a) and geothermal favorable map (b)

Fig. 15
Fig. 15 Geothermal training points distance to granite formed pre-Yanshanian map (a) and geothermal training points distance from granite formed pre-Yanshanian histogram (b); distance to granite formed since-Yanshanian map (c) and distance from granite formed since-Yanshanian histogram (d)

Fig. 16
Fig. 16 The weight of evidence model considering granite classification (a) and geothermal favorable map (b)

Fig. 18
Fig. 18 The weight of evidence model of considering both fault and granite classification (a); geothermal favorable map (b)

Fig. 20
Fig. 20 ROC curve of four weight of evidence models and AUC value of ROC curve

Fig. 22
Fig. 22The map of geothermal favorable differentiation in western Sichuan Plateau

Table 1
Zhang et al. 2017)showing the typical warm and hot springs in three geothermal belts of the western Sichuan (data taken fromZhang et al. 2017)

Table 2
Covariance matrix of evidence layers

Table 3
Correlation coefficient matrix of evidence layers

Table 5
Weighting parameters of evidence layers

Table 6
The prediction rate and success index of four weight of evidence models