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Table 9 Statistical metrics used for evaluating the prediction efficiency of gas geothermometers (new and existing)

From: GaS_GeoT: A computer program for an effective use of newly improved gas geothermometers in predicting reliable geothermal reservoir temperatures

Statistical metric Calculation equation Equation number Reference
Percent difference (DIFF%) \(DIFF\% = \left[ {\left( {\frac{{BHT_{CALC\left( i \right)} - BHT_{m\left( i \right)} }}{{BHT_{m\left( i \right)} }}} \right) \times 100} \right]\) (6) García-López et al. (2014)
Root mean square error (RMSE) \(RMSE = \sqrt{{\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left( {BHT_{m\left( i \right)} - BHT_{CALC\left( i \right)} } \right)^{2} }}\) (7) Willmott et al. (2009)
Mean absolute error (MAE) \(MAE = \frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left| {BHT_{m\left( i \right)} - BHT_{CALC\left( i \right)} } \right|\) (8) Wang and Lu (2018)
Mean absolute percentage error (MAPE) \(MAPE = \left( {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left| {\frac{{BHT_{m\left( i \right)} - BHT_{CALC\left( i \right)} }}{{BHT_{m\left( i \right)} }}} \right|} \right) \times 100\) (9) Li and Shi (2010)
Difference coefficient (Theil's U) \(Theil^{\prime}s U = \frac{{\sqrt{{\mathop \sum \nolimits_{i = 1}^{n} \left( {BHT_{m\left( i \right) - } BHT_{GaS\_GeoT\left( i \right) } } \right)^{2} }}}}{{\sqrt{{\mathop \sum \nolimits_{i = 1}^{n} \left( {BHT_{m\left( i \right) - } BHT_{GasGeo\_Lit\left( i \right) } } \right)^{2} }}}}\) (10) Álvarez del Castillo et al. (2012)
  1. BHTm(i) is the bottom-hole temperature measured in a geothermal well; BHTCALC(i) is the temperature calculated by any gas geothermometer; BHTGaS_GeoT(i) is the temperature calculated by the new gas geothermometers (GasG1 to GasG8); BHTGasGeo_Lit(i) is the temperature calculated by the existing gas geothermometers (Table 3), and n is the total number of gas samples