Skip to main content

Science – Society – Technology

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