Telford - Applied geophysics.pdf

Contents

Preface to the Second Edition / x v Excerpts from Preface to the FirstEdition/xvii Mathematical Conventions / xix 1.

Introduction / 1

2.4.3.

2.5. Field Operations / 23

2.5.1. 2.5.2. 2.5.3. 2.5.4. 2.6.1.

Gravity Methods/6

2.1.

2.1.1. 2.1.2.

General/6 History of Gravity Exploration / 6

2.2. Principles of Gravity/ 7

2.2.1. 2.2.2. 2.2.3. 2.2.4. 2.2.5.

Newton's Law of Gravitation / 7 Acceleration of Gravity / 7 Gravitational Potential/7 Potential-Field Equations / 9 Derivatives of the Potential / 9

2.3. Gravity of the Earth / 10

2.3.1. 2.3.2. 2.3.3. 2.3.4.

Figure of the Earth / 1 0 Gravity Reduction / 1 1 Densities of Rocks and Minerals / 1 5 Density Estimates from Field Results / 1 8

2.4. Gravity Instruments/ 19

2 A.I. 2.4.2.

2.6.2. 2.6.3. 2.6.4.

In trod action / 6

General/19 Absolute Measurement of Gravity/20

Land Surveys / 23 Drift Correction / 24 Marine Surveys / 24 Airborne Gravity / 26

2.6. Gravity Data Processing/ 26

Reference / 5

2.

Relative Measurement of Gravity / 20

2.6.5. 2.6.6. 2.6.7.

Noise, Regionals, and Residuals / 26 Graphical Residualizing / 27 Surface-Fitting Residualizing Methods / 27 Empirical Gridding Methods/27 Second Vertical Derivative Methods/32 Wavelength Filtering / 32 Field Continuation / 32

2.7. Gravity Interpretation / 34

2.7.1. 2.7.2. 2.7.3. 2.7.4. 2.7.5. 2.7.6. 2.7.7. 2.7.8. 2.7.9.

General/34 Gravity Effect of a Sphere/35 Gravity Effect of a Horizontal Rod/36 Gravity Effect of a Vertical Cylinder/37 Gravity Effect of a Thin Dipping Sheet/39 Gravity Effect of Horizontal Sheets, Slabs, Dikes, and Faults/40 Applying Simple Models to Actual Anomalies / 44 Gravity Effects of Complex Shapes/44 The Direct and Inverse

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Contents Problems of Interpretation / 46 Excess Mass / 47 Overburden Effects / 48 Maximum-Depth Rules / 48

2.7.10. 2.7.11. 2.7.12.

2.8. Field Examples / 48 2 9. Problems / 52 References / 60

3.

Magnetic Methods / 62

3.1.

Introduction/62

3.1.1. 3.1.2.

General/62 History of Magnetic Methods/62

3.2. Principles and Elementary Theory / 63

3.2.1. 3.2.2. 3.2.3. 3.2.4. 3.2.5.

Classical versus Electromagnetic Concepts / 63 B-H Relations: The Hysteresis Loop / 64 Magnetostatic Potential for a Dipole Field/65 The General Magnetic Anomaly / 66 Poisson's Relation / 67

3.3. Magnetism of the Earth / 67

3.3.1. 3.3.2. 3.3.3. 3.3.4. 3.3.5. 3.3.6. 3.3.7. 3.3.8.

Nature of the Geomagnetic Field/67 The Main Field/68 The External Magnetic Field / 72 Local Magnetic Anomalies / 72 Magnetism of Rocks and Minerals / 72 Remanent Magnetism/73 Magnetic Susceptibilities of Rocks and Minerals / 73 Magnetic Susceptibility Measurements / 73

3.4. Field Instruments for Magnetic Measurements / 75

3.4.1. 3.4.2. 3.4.3. 3.4.4.

General/75 Flux-gate Magnetometer / 75 Proton-Precession Magnetometer / 77 Optically Pumped Magnetometer / 78

3.4.5. 3.4.6. 3.4.7.

Gradiometers / 80 Instrument Recording / 80 Calibration of Magnetometers / 80 3.5. Field Operations / 80 3.5.1. General / 80 3.5.2. Airborne Magnetic Surveys/81 3.5.3. Shipborne Magnetic Surveys / 83 3.5.4. Ground Magnetic Surveys / 83 3.5.5. Gradiometer Surveys / 84 3.6. Magnetic Effects of Simple Shapes / 84

3.6.1. 3.6.2. 3.6.3. 3.6.4. 3.6.5. 3.6.6. 3.6.7. 3.6.8. 3.6.9. 3.6.10.

General/ 84 The Isolated Pole (Monopole) / 85 The Dipole/87 Two-Dimensional Features/88 Dipping Dike (Prism) / 92 Dipping Sheet/97 Horizontal Sheet (Plate) /100 Semiinfinite Horizontal Sheet: Fault Approximation /100 Contact between Beds of Different Susceptibilities /103 Demagnetization /104

3.7. Processing and Interpretation / 106

3.7.1. 3.7.2. 3.7.3. 3.7.4. 3.7.5. 3.7.6. 3.7.7. 3.7.8. 3.7.9. 3.7.10. 3.7.11.

General/106 Crude Interpretation and Structural Aspects /106 Data Processing Operations: The Fourier Transform /107 Derivatives /107 Continuation /107 Spectral Analysis / 108 Reduction to the Pole / 109 Use of Master Curves for Dikes of Great Depth Extent / 109 Matched Filtering / 112 Werner Deconvolution / 112 Depth Estimates / 113

3.8. Field Examples / 114

3.8.1.

Ground Surveys / 114

3.8.2.

Airborne Surveys / 117

3.9.

Problems/124

References / 134

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Contents

4.

Seismic Methods/136

4.1.

In trod action / 136

4.1.1. 4.1.2. 4.1.3.

Importance of Seismic Work/ 136 History of Seismic Exploration /137 Outline of the Seismic Reflection Method /139

4.2. Seismic Theory/ 140

4.2.1. 4.2.2. 4.2.3. 4.2.4. 4.2.5. 4.2.6. 4.2.7. 4.2.8.

Theory of Elasticity / 140 Wave Equation and Its Solutions /143 Body Waves: P and S Waves /147 Surface Waves /149 Energy of Waves / 149 Wave Motion/151 Partitioning of Energy at an Interface /155 Seismic Velocity / 158

4.3. Geometry of Seismic Wavepaths / 162

4.3.1. 4.3.2. 4.3.3.

Reflection Paths in a Constant Velocity Layer /162 Velocity Gradient and Raypath Curvature /167 Geometry of Refraction Paths/169

4.4. Characteristics of Seismic Events / 175 Distinguishing Features of 4.4.1. Events /175 Reflections and 4.4.2. Refractions /175 4.4.3. Diffractions /176 4.4.4. Multiples /178 4.4.5. Surface Waves /182 4.4.6. Effects of Reflector Curvature /182 4.4.7. Types of Seismic Noise / 184 4.4.8. Attenuation of Noise / 185 4.5. Reflection Field Methods and Equipment/ 186

4.5.1. 4.5.2. 4.5.3.

Field Methods for Land Surveys /186 Field Layouts/ 187 Field Equipment for Land Surveys /192

4.5.4. 4.5.5.

Marine Equipment and Methods / 202 Measurement of Velocity / 207

4.6. Refraction Field Methods and Equipment/209

4.6.1. 4.6.2. 4.6.3. 4.6.4. 4.6.5. 4.6.6.

Comparison of Refraction and Reflection Methods / 209 In-Line Refraction / 209 Broadside Refraction and Fan Shooting/210 Engineering Surveys on Land/211 Marine Refraction Work / 212 Refraction Data Reduction / 212

4.7. Data Processing/ 214

4.7.1. 4.7.2. 4.7.3. 4.7.4. 4.7.5. 4.7.6. 4.7.7. 4.7.8. 4.7.9. 4.7.10. 4.7.11. 4.7.12. 4.7.13. 4.7.14.

Data Reduction / 214 Introduction to Digital Processing: Fourier Transforms / 216 Convolution / 217 Correlation/222 Phase Considerations / 226 Frequency Filtering / 226 Velocity Analysis / 229 Common-Midpoint Stacking/229 Apparent-Velocity (ApparentDip) Filtering / 229 The p-r Transform / 230 Relative-Amplitude Processing / 230 Migration or Imaging/230 Measures of Coherence / 232 Other Types of Processing / 233

4.8. Basic Geological Concepts in Petroleum Exploration / 233

4.8.1. 4.8.2.

Basic Concepts / 233 Objectives of Interpretation / 235

4.9. Refraction Interpretation / 235

4.9.1. 4.9.2. 4.9.3. 4.9.4. 4.9.5.

Interpretation of Refraction Records / 235 Refraction Interpretation Methods / 237 Delay-Time Methods / 237 Wavefront Methods / 240 Engineering Applications / 242

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Contents

4.10. Reflection Interpretation / 243

4.10.1. 4.10.2. 4.10.3. 4.10.4. 4.10.5. 4.10.6. 4.10.7. 4.10.8.

Interpretation Techniques / 243 Modeling: Synthetic Seismograms / 245 Evidences of Faulting / 248 Fold and Flow Structures / 250 Reefs/257 Unconformities and Seismic Facies Patterns / 262 Use of Velocity Information / 262 Hydrocarbon Indicators / 262

4.11. Specialized Methods / 264

4.11.1. 4.11.2. 4.11.3. 4.11.4. 4.11.5. 4.11.6. 4.11.7. 4.12.

Profiling/264 Three-Dimensional Methods/267 Use of Channel Waves / 270 Vertical Seismic Profiling / 270 Shear Waves in Exploration / 271 Variation of Amplitude with Offset/271 Cross-Hole Methods / 271

Problems/273

5.4. Typical Values of Electrical Constants of Rocks and Minerals / 289

5.4.1. 5.4.2. 5.4.3.

References / 292

6.

Methods Employing Natural Electrical Sources / 293

6.1. Self-Potential Method/ 293

6.1.1. 6.1.2. 6.1.3. 6.1.4.

6.2.1. 6.2.2.

Electrical Properties of Rocks and Minerals/ 283

5.1. Classification of Electrical Methods/283

6.2.3. 6.2.4. 6.2.5. 6.2.6. 6.2.7.

5.2. Electrical Properties of Rocks and Minerals/ 283

5.2.1. 5.2.2. 5.2.3. 5.2.4.

Electrical Potentials / 283 Electrical Conductivities / 284 Magnetic Permeability / 287 Polarization Potentials / 287

5.3. Measurement of Electrical Properties of Rocks and Minerals / 288

5.3.1. 5.3.2.

Laboratory Measurement of Resistivity/288 Measurement of Dielectric Constant / 288

Origin of Potentials / 293 Self-Potential Field Equipment / 296 Field Procedure / 296 Interpretation of Self-Potential Data/297

6.2. Telluric and Magnetotelluric Methods/302

References / 280

5.

Resistivities of Rocks and Minerals / 289 Dielectric Constants of Rocks and Minerals / 291 Magnetic Permeability of Minerals / 292

6.2.8.

Origin and Characteristics of Magnetotelluric Fields and Telluric Currents/302 Elementary Electromagnetic Theory/306 Attenuation of EM Fields / 307 Boundary Conditions / 309 Magnetotelluric Fields / 309 Field Equipment and Operations/311 Interpretation of Telluric Data/314 Interpretation of Magnetotelluric Data / 317

6.3. Field Examples / 327

6.3.1. 6.3.2.

Self-Potential/327 Tellurics and Magnetotellurics / 327

6.4.

Problems/335

References / 342

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Contents

7.

Electromagnetic Methods / 343

7.1. 7.2.

Introduction and Historical Background / 343

7.2.2. 7.2.3. 7.2.4. 7.2.5. 7.2.6. 7.3.

7.4.

Vector and Scalar Potentials/343 Description of EM Fields; Biot-Savart Law/344 Field in the Frequency Domain / 345 Combination of FD Fields / 350 Mutual Inductance / 353 Fields in the Time Domain / 355 General/361 Power Sources / 361 Transmitter Loops / 362 Receiver Coils / 362 Receiver Amplifiers / 362 Indicators/363 Compensating Networks / 363

EM Field Systems for Ground Surveys / 364

7.4.1. 7.4.2. 7.4.3. 7.4.4. 7.4.5. 7.4.6.

General/364 Frequency-Domain Systems; Dip-Angle Measurements / 364 FD Systems for PhaseComponent Measurements / 370 Time-Domain EM Ground Systems / 372 Measurement of H / 376 Assessment of EM Ground Methods/377

7.5. Airborne EM Systems / 377

7.5.1. 7.5.2. 7.5.3. 7.5.4. 7.5.5. 7.5.6. 7.5.7. 7.5.8.

General/377 Quadrature Method / 377 Turair System / 377 Airborne VLF/378 Phase-Component Measurements / 378 Transient (Input) Method / 379 Cryogenic EM System / 383 Assessment of Airborne EM/383

7.7.

Interpretation / 383

7.7.8. 7.7.9. 7.7.10. 7.7.11.

Introduction / 383 General Interpretation Procedure/385 Ground Systems; FDEM over Dipping Sheet/385 Ground Systems; TDEM over Dipping Sheet/409 The Sphere Model in FD and TD Ground Systems/436 Layered Structure: EM Depth Sounding / 441 Interpretation of Airborne EM Data/450 Turair/454 Airborne VLF / 454 Phase-Component AEM / 456 Resistivity Mapping / 460

7.7.12.

Input AEM/464

7.7.3. 7.7.4. 7.7.5. 7.7.6. 7.7.7.

EM Equipment/ 361

7.3.1. 7.3.2. 7.3.3. 7.3.4. 7.3.5. 7.3.6. 7.3.7.

EM Field Procedures / 383

1.1.1. 7.7.2.

Electromagnetic Theory / 343

7.2.1.

7.6.

7.8.

Field Examples / 477

7.9.

Problems / 504

References / 519

8.

Resistivity Methods / 522

8.1.

Introduction / 522

8.2.

Elementary Theory/ 522

8.2.1. 8.2.2. 8.2.3. 8.2.4. 8.2.5. 8.3.

Potentials in Homogeneous Media / 522 Single Current Electrode at Depth / 523 Single Current Electrode at Surface / 523 Two Current Electrodes at Surface / 524 Current Distribution / 525

Effect of Inhomogeneous Ground / 527

8.3.1. 8.3.2. 8.3.3. 8.3.4.

Introduction / 527 Distortion of Current Flow at a Plane Interface / 527 Distortion of Potential at a Plane Interface / 527 Surface Potential due to Horizontal Beds / 529

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Contents

8.3.5. 8.3.6. 8.3.7. 8.4.

8.6.4. 8.6.5. 8.6.6. 8.6.7. 8.6.8.

9.3.4.

Power Sources / 532 Meters/534 Electrodes and Wire / 535

General/535 Apparent Resistivity / 535 Electrode Arrays (Spreads) / 535 Resistivity Field Procedures / 538 Introduction / 539 Resistivity Modeling / 539 Vertical Sounding; Two Horizontal Beds / 539 Vertical Sounding; Multiple Horizontal Beds / 544 Lateral Mapping; Vertical Contact / 554 The Vertical Dike / 559 Mapping Three-Dimensional Anomalies / 561 Measuring Overburden Depth and Resistivity / 562

8.8

9.3.3.

9.3.5. 9.3.6. 9.3.7.

Field Examples/565

9.4.1. 9.4.2. 9.4.3. 9.4.4.

9.5. Interpretation / 591

9.5.1. 9.5.2. 9.5.3. 9.6.

Field Examples / 602

9.7. Problems/ 604 References / 609

10.

Radioactivity Method / 611

10.1.

Introduction / 611

10.2.1.

Induced Polarization / 578 Introduction / 578

9.2. Sources of the Induced Polarization Effects/578

9.2.1. 9.2.2. 9.2.3. 9.2.4.

Plotting Methods / 591 General Interpretation / 595 Theoretical and Model Work/596

10.2.2. 10.2.3. 9.1.

General/584 Field Equipment / 584 Field Procedures / 588 Noise Sources / 589

10.2. Principles of Radioactivity/ 611

Problems/570

References / 577

9.

General/581 Time-Domain Measurements / 581 Frequency-Domain Measurements / 582 Relative Phase Shift and Phase Components / 582 Magnetic Induced Polarization (MIP) Measurements / 583 Relation between Time- and Frequency-Domain IP Measurements / 583 IP Response Examples / 583

9.4. IP Field Operations / 584

Interpretation / 539

8.6.1. 8.6.2. 8.6.3.

8.7.

9.3.1. 9.3.2.

Electrode Layouts and Field Procedure / 535

8.5.1. 8.5.2. 8.5.3. 8.5.4. 8.6.

9.3. Induced Polarization Measurements / 581

Equipment for Resistivity Field Work/532

8.4.1. 8.4.2. 8.4.3. 8.5.

Potential Due to Buried Sphere / 530 Effect of Anisotropic Ground / 531 Effect of Topography / 532

General/578 Membrane Polarization / 579 Electrode Polarization / 579 Equivalent Electrical Circuits / 581

10.2.4. 10.2.5. 10.2.6. 10.2.7. 103.

Constituents of the Nucleus/ 611 Nuclear Disintegrations / 612 Radioactive Decay Processes / 614 Radioactive Equilibrium / 617 Units/618 Radioactivity of Rocks and Minerals / 619 Age Determination Using Radioisotopes / 619

Instruments /620

10.3.1. 10.3.2.

Introduction / 620 Geiger-Muller Counter / 620

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Contents

10.3.3. 10.3.4. 10.3.5.

Scintillation Meter / 621 Gamma-Ray Spectrometer / 622 Miscellaneous Instruments / 627

10.3.6.

Calibration of Instruments / 628

11.7. Elastic-Wave (Acoustic) Methods/665

11.7.1. 11.7.2. 11.7.3.

10.4. Field Operations / 628

11.7.4.

10.5. Interpretation / 629 10.6. Field Examples / 634 10.7.

11.8. Nuclear Methods / 673

11.8.1. 11.8.2. 11.8.3. 11.8.4.

Problems/637

References / 644

11.

Geophysical Well Logging/645

11.1.

In troduction / 645

11.1.1. 11.1.2. 11.1.3. 11.1.4.

11.3. Self-Potential (SP) Logging/654 Sources of SP/654 11 .3.1. 11.3.2. Instrumentation / 655 11 .3.3. Uses of SP Curves in Oil-Well Logging/656 11.3.4. Uses of SP Curves in Mineral Logging/658 11 .3.5. Geological Interpretation of SP/658 11.4. The Dipmeter/ 659

Nuclear Processes / 673 Gamma-Ray Logging/675 Density Log/676 Neutron Logging/677

11.9. Gravity, Magnetic, and Thermal Methods / 681

11.9.1.

Uses of Well Logging / 645 History of Well Logging / 645 General Aspects of Well Logging / 646 Rock Property Measurements / 647

11.2. Resistivity Methods / 648 11.2.1. Introduction to Resistivity Logging/648 11 .2.2. Normal Resistivity Logging / 649 11 .2.3. Lateral Arrangement / 650 11 .2.4. Microlog / 650 11 .2.5. Focused-Current Logs / 651 11 .2.6. Induction Log / 652 11 .2.7. Resistivity Logging in Mineral Search/654

Elastic Waves in Boreholes / 665 Sonic Log/667 Amplitude and Full-Waveform Logs/670 Borehole Televiewer / 672

11.9.2. 11.9.3. 11.9.4.

Gravity and Magnetic Field Logging/681 Susceptibility Log / 681 Nuclear Magnetic-Resonance Log/682 Thermal Logging / 683

11.10. Well-Log Interpretation / 683

11.10.1. General/683 11.10.2. Combining Measurements from Several Logs / 683 11.11.

Field Examples / 684

11.11.1. Analysis of an Oil Sand / 684 11.11.2. Analysis of Carbonate Section/684 11.11.3. Coal Identification / 684 11.11.4. Evaporites/685 11.11.5. Sulfur/687 11.11.6. Slate and Chert / 687 11.11.7. Mineral Exploration / 687 11.11.8. Borehole Methods in the USSR/689 11.12.

Problems/690

References / 698

12.

Integrated Geophysical Problems/700

11.5. Electromagnetic Wave Propagation Method/ 663

12.1.

11.6. Induced Polarization Logging / 665

12.2. Examples and Problems / 701

Introduction / 700

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Contents

Appendix A. Mathematical Background / 727 A. 1. Determinants / 727

A.12.1. A.12.2. A.12.3.

A.2.

Matrices/ 728

A3.

Vector Analysis / 729

A.3.1. A.3.2. A.3.3. A.3.4.

A. 12. Laplace Transforms / 741

Basic Theory / 729 Vector Products / 730 The Vector Operator V /731 Vector Theorems / 731

A A.

Curvilinear Coordinates / 733

A.5.

Taylor's Series; Maclaurin's Series/735

A. 6.

Binomial Expansion / 736

A. 7.

Complex Numbers / 736

A.8.

Method of Least Squares/ 737

A.9.

Fourier Series and Transforms/ 738

Basic Theory/741 Calculation of Laplace Transforms / 742 Transforms of the Error Function and its Derivatives / 742

A. 13. Linear Systems / 743 References / 744

Appendix B. Location Determination / 745 B. 1. Direction Determination / 745 B.2. Distance Measurement / 745 B.3. Elevation Measurement/ 745 B.4. Angle Measurement / 746

A.9.1. A.9.2. A.9.3.

Fourier Series / 738 Fourier Integral; Fourier Transforms / 738 Digital Functions; z Transforms / 740

A. 10. Convolution / 740 A.11.

Correlation / 741

A.I 1.1. A.11.2.

Cross-Correlation / 741 Autocorrelation / 741

B.5. Doppler Measurement of Velocity/746 B. 6. Radionavigation / 746 B. 7. Acoustic and Inertial Positioning / 748 B.8. Satellite

Positioning/749

Reference / 750

Index/751

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