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Table 7 Weighting and bias coefficients of the best ANN models (new gas geothermometers: GasG1 to GasG8)

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

Neuron IW(m,k) b1(m,1) LW(m,n) b2(n)
Input variable 1 Input variable 2 Input variable 3 Input variable 4 Input variable 5 Bias Weight Bias
GasG1 (k = 3, m = 18, n = 1)      
 1 − 10.4966 − 1.1378 0.8463    9.5785 − 1.7731 − 1.0356
 2 22.0807 − 12.9076 19.0550    − 10.6989 − 0.4489  
 3 − 14.8833 4.3913 − 0.1612    8.5887 4.2903  
 4 − 51.9879 − 0.3416 5.9872    19.3727 − 0.2385  
 5 16.7261 − 4.8153 − 0.0926    − 9.4315 4.2683  
 6 4.3149 3.8523 − 5.4022    − 0.5974 0.8856  
 7 10.5391 − 20.9557 33.7107    2.5871 − 0.2241  
 8 − 2.0890 1.1073 20.2039    7.9015 0.3611  
 9 0.5418 1.3637 − 2.3029    0.0489 − 3.3014  
 10 − 5.6519 0.9427 4.8160    1.3659 − 10.5466  
 11 1.1402 − 3.2332 2.6054    − 4.1995 1.5774  
 12 5.2141 − 0.5295 − 4.0756    − 1.3200 − 7.5987  
 13 3.6485 − 19.4886 − 0.8257    12.7539 5.0275  
 14 − 4.4414 0.0312 0.4327    4.3220 6.0399  
 15 − 3.5400 − 0.7734 3.5304    1.4321 − 2.7057  
 16 − 4.0591 19.9584 0.6652    − 13.0292 5.0045  
 17 5.5351 − 1.0741 − 5.2122    − 1.3846 − 4.8823  
 18 2.7430 1.2762 0.3413    1.2202 − 0.9442  
GasG2 (k = 3, m = 15, n = 1)      
 1 − 74.7200 − 29.3826 71.2961    − 9.1189 0.1740 − 0.4764
 2 − 51.6547 21.8776 5.1177    13.0007 − 0.3961  
 3 − 0.5704 − 8.5959 11.2749    1.0424 − 11.5175  
 4 − 2.8170 − 5.8255 2.3507    6.9290 0.1195  
 5 138.9491 − 164.2573 14.7326    − 2.4335 − 0.2194  
 6 10.0731 10.0604 3.4971    − 0.7834 − 10.0376  
 7 8.2489 8.4971 2.0266    − 0.4685 20.6834  
 8 − 6.9094 4.3475 2.2922    0.6182 0.5344  
 9 − 0.6145 − 8.8942 11.4466    0.9874 11.3964  
 10 − 6.5749 − 7.2235 − 1.1089    0.2658 10.8816  
 11 − 109.4214 3.9406 18.2203    − 19.5511 − 0.2835  
 12 68.6847 − 37.4115 − 78.8355    0.2217 0.1522  
 13 − 7.8109 1.3878 − 6.8636    − 9.5630 − 14.2420  
 14 8.0752 − 1.1217 7.0651    10.1010 − 13.8272  
 15 − 20.7201 10.9331 − 12.9707    − 8.4363 − 0.2044  
GasG3 (k = 3, m = 18, n = 1)      
 1 0.2605 − 2.8324 0.7405    − 4.6395 0.0965 − 0.6741
 2 − 4.1589 5.9679 0.2775    5.0844 0.4591  
 3 1.2094 13.6531 3.8001    − 6.2841 0.1207  
 4 − 18.5398 0.6195 0.5262    10.0722 − 0.5122  
 5 2.7557 − 5.8167 2.0639    − 6.4099 0.0843  
 6 − 2.5005 − 0.3730 − 2.0823    − 0.7033 − 2.6769  
 7 − 8.7356 3.4340 1.9566    5.5936 − 0.4428  
 8 − 3.9373 − 0.2286 3.8324    1.0464 − 0.6335  
 9 2.1539 0.4060 3.8254    1.0421 − 3.2267  
 10 0.5414 12.1314 0.1324    − 0.6745 0.5703  
 11 2.4237 9.6744 0.8198    − 1.0205 − 0.4172  
 12 2.1196 0.1036 − 0.6293    − 1.2896 − 1.8327  
 13 − 3.1159 − 1.4763 0.4641    − 5.7187 − 0.1605  
 14 0.8259 1.6177 9.0616    1.9310 1.2339  
 15 3.6085 − 2.0623 − 2.2694    5.3824 − 0.1270  
 16 − 13.5662 1.6842 − 2.0641    3.1308 − 0.3221  
 17 1.0129 4.8087 0.1825    4.8000 − 0.2732  
 18 4.7110 6.9895 − 4.6717    − 2.6020 − 0.2882  
GasG4 (k = 3, m = 34, n = 1)      
 1 0.8413 1.0481 4.5492    − 4.3604 0.5430 0.7175
 2 1.6852 − 1.1809 4.0247    − 4.2626 − 0.6184  
 3 − 3.1846 3.0345 0.6129    4.2989 0.4547  
 4 − 2.4474 − 2.2656 3.1111    3.6910 − 0.1940  
 5 − 1.7082 4.3553 1.0333    3.4071 − 2.2762  
 6 − 4.8797 6.0548 0.1265    2.8825 1.9591  
 7 0.4419 4.7801 0.6585    − 1.5392 2.1423  
 8 1.9559 3.0935 − 4.7555    − 1.7757 3.0085  
 9 − 0.3619 − 5.2932 6.4612    1.1353 3.5850  
 10 1.5416 − 1.9525 4.7684    − 2.3951 2.4549  
 11 − 4.0310 − 2.8368 8.6461    2.0696 − 3.2083  
 12 1.3875 2.8019 2.1562    − 0.2151 − 2.1271  
 13 − 6.2492 − 0.8381 4.9963    − 0.5368 2.3720  
 14 − 5.4812 − 2.5508 0.2280    1.4242 2.2546  
 15 1.2885 3.7342 − 3.5705    − 1.3129 − 3.2678  
 16 0.6120 6.8702 1.6604    0.4849 5.1290  
 17 − 8.0473 7.0992 3.3462    − 0.6557 6.2486  
 18 − 6.5842 4.8933 4.9639    − 0.5687 − 5.3591  
 19 2.0680 − 2.0030 3.2922    0.5423 1.8140  
 20 − 2.7406 9.8262 8.5937    2.1876 0.6365  
 21 7.7279 2.7843 − 10.4992    0.5845 1.5671  
 22 − 10.3807 11.2299 1.2403    − 0.8739 − 3.2182  
 23 − 2.5572 − 7.6695 − 0.8698    − 1.1968 2.8984  
 24 6.7225 − 3.9473 2.0077    2.1102 − 4.8149  
 25 12.5036 3.5952 − 5.8924    2.4635 0.5574  
 26 1.1006 − 0.6048 − 4.1736    2.9012 − 0.9523  
 27 − 3.2534 5.5943 − 2.5071    − 0.9127 2.2162  
 28 6.1765 2.4106 − 1.4982    5.4936 7.1628  
 29 − 8.6020 4.5660 − 3.5287    − 3.1652 − 3.1148  
 30 2.2915 − 3.0145 − 2.4441    3.5085 0.0843  
 31 − 5.0789 − 1.0713 − 4.5243    − 7.5724 − 3.3251  
 32 − 1.0222 2.7998 − 5.5370    − 3.9064 − 2.1729  
 33 − 10.9591 − 4.7211 4.3928    − 8.6022 3.8019  
 34 6.5221 1.8689 2.3093    8.0946 − 5.0940  
GasG5 (k = 3, m = 15, n = 1)      
 1 4.6610 9.3354 − 2.9977    − 10.1278 1.2400 − 1.9220
 2 − 2.0011 3.1019 4.6559    1.5880 2.0416  
 3 − 1.3652 − 6.8953 0.2085    − 4.3337 − 3.5757  
 4 2.2086 6.9970 − 0.7490    4.9651 − 3.5151  
 5 15.0925 12.5673 − 1.6365    − 2.8091 − 0.6210  
 6 − 0.2917 − 4.4285 − 4.8459    − 2.2553 1.9381  
 7 − 1.4554 − 3.8719 0.6722    0.5524 − 3.7513  
 8 14.6274 − 18.1442 1.1720    2.4447 − 0.3234  
 9 − 4.1866 2.2442 6.8280    − 2.1283 0.5290  
 10 1.2033 − 3.7615 − 7.3399    1.4214 0.4381  
 11 − 0.9754 − 5.1881 0.8466    0.5475 2.5457  
 12 − 4.1395 − 8.2389 14.8899    − 5.2272 − 0.1067  
 13 4.3414 15.7990 7.7251    − 8.5051 − 0.5169  
 14 3.0032 0.5427 0.7922    2.7043 2.2648  
 15 − 0.2435 3.8179 0.3571    − 2.9697 − 1.0737  
GasG6 (k = 4, m = 13, n = 1)      
 1 − 7.0424 1.0592 0.5872 − 4.9261   − 0.9909 0.6853 − 1.4850
 2 − 7.7923 0.7611 2.4586 11.5728   3.6960 1.0193  
 3 − 4.0733 − 1.6240 1.7513 − 3.4984   − 0.9385 − 0.7838  
 4 − 2.3369 − 9.6032 0.3973 − 0.2256   4.4306 − 0.6460  
 5 4.6053 3.2060 − 6.2870 2.5629   0.3976 − 1.5127  
 6 4.7627 2.8469 − 6.2893 3.3543   0.4991 1.4433  
 7 − 0.7276 5.4561 1.5209 4.0939   2.8770 3.4748  
 8 − 6.3221 5.2401 − 0.0758 − 1.8561   − 3.3356 − 0.7253  
 9 0.0618 3.3627 0.2201 2.8292   − 5.0749 − 3.2557  
 10 1.3088 1.8037 0.9426 6.5565   2.9480 − 2.2063  
 11 5.6895 3.8142 − 3.7349 0.3184   3.0027 − 0.6407  
 12 3.5135 − 3.4591 2.5028 − 4.2444   5.3923 − 1.8108  
 13 − 1.2860 − 6.6278 − 2.7831 − 3.4112   − 2.6695 2.0116  
GasG7 (k = 4, m = 10, n = 1)      
 1 7.9032 − 0.6015 0.7257 − 0.8062   − 4.9130 − 0.4283 − 0.6240
 2 − 2.9711 − 3.8961 − 0.3714 5.0930   2.1358 − 0.4423  
 3 0.6463 − 1.2954 0.1709 7.7610   − 0.2102 6.7284  
 4 4.6109 − 0.1063 − 18.6311 − 1.7928   − 3.7415 − 4.8884  
 5 − 8.3235 2.7237 − 6.0207 − 4.6909   − 1.0212 0.7313  
 6 5.7018 − 4.4436 7.5091 − 5.5924   7.9518 7.8252  
 7 − 5.6660 3.7079 − 8.5863 7.8219   − 8.8848 7.7244  
 8 − 0.5289 1.7097 − 0.2783 − 8.7773   0.0500 6.2932  
 9 5.7362 − 0.4683 − 22.2945 − 1.7934   − 4.4083 4.7232  
 10 8.8670 − 2.9926 − 0.6986 8.4312   6.8119 0.9991  
GasG8 (k = 5, m = 9, n = 1)      
 1 22.4842 − 33.9535 − 29.5633 15.8975 48.5322 20.3047 0.1346 − 1.3893
 2 3.4291 0.5420 1.0172 − 4.9756 4.5659 0.9671 1.6130  
 3 − 14.4388 3.7895 − 7.2506 79.5516 5.1701 − 33.4122 0.2263  
 4 − 43.2597 − 1.2331 − 24.8234 50.0978 − 9.2286 − 14.9195 − 0.6028  
 5 − 2.2463 0.2702 0.2465 2.9529 1.1975 − 1.8629 − 19.6929  
 6 48.8397 − 3.6155 19.3550 − 55.8381 20.4814 10.5299 − 0.2055  
 7 − 2.9234 − 0.2702 − 0.2371 5.0167 − 2.1591 − 0.3359 9.1898  
 8 − 3.2910 − 0.3027 − 0.4428 6.2711 − 2.9274 − 0.4075 − 7.1448  
 9 1.7139 − 0.3069 1.3356 − 4.0765 − 0.0239 2.9979 − 17.7178  
  1. The input variables of each new gas geothermometer are reported in Table 6. The subscripts k, m and n refer to input, hidden and output neurons, respectively