FINITE DIFFERENCES AND NUMERICAL ANALYSIS
CONTENTS INTRODUCTION A BRIEF HISTORY OF SEISMOLOGY EXERCISES STRESS AND STRAIN THE STRESS TENSOR 2 1 1 EXAMPLE: COMPUTING THE TRACTION VECTOR 2 1 2 PRINCIPAL AXES OF STRESS 2 1 3 EXAMPLE: COMPUTING THE PRINCIPAL AXES 2 1 4 DEVIATORIC STRESS 2 1 5 VALUES FOR STRESS THE STRAIN TENSOR 2 2 1 VALUES FOR STRAIN 2 2 2 EXAMPLE: COMPUTING STRAIN FOR A SEISMIC WAVE THE LINEAR STRESS?STRAIN RELATIONSHIP 2 3 1 UNITS FOR ELASTIC MODULI THE SEISMIC WAVE EQUATION INTRODUCTION: THE WAVE EQUATION THE MOMENTUM EQUATION 3 3 1 POTENTIALS PLANE WAVES 3 4 1 EXAMPLE: HARMONIC PLANE WAVE EQUATION POLARIZATIONS OF P AND S WAVES SPHERICAL WAVES METHODS FOR COMPUTING SYNTHETIC SEISMOGRAMS† THE FUTURE OF SEISMOLOGY?† EQUATIONS FOR 2-D ISOTROPIC ?NITE DIFFERENCES† 3 10 EXERCISES RAY THEORY: TRAVEL TIMES SNELL’S LAW RAY PATHS FOR LATERALLY HOMOGENEOUS MODELS 4 2 1 EXAMPLE: COMPUTING X(P) AND T(P) 4 2 2 RAY TRACING THROUGH VELOCITY GRADIENTS TRAVEL TIME CURVES AND DELAY TIMES 4 3 1 REDUCED VELOCITY 4 3 2 THE ?(P) FUNCTION LOW-VELOCITY ZONES SUMMARY OF 1-D RAY TRACING EQUATIONS SPHERICAL-EARTH RAY TRACING THE EARTH-?ATTENING TRANSFORMATION THREE-DIMENSIONAL RAY TRACING† RAY NOMENCLATURE 4 9 1 CRUSTAL PHASES 4 9 2 WHOLE EARTH PHASES 4 9 3 PKJKP: THE HOLY GRAIL OF BODY WAVE SEISMOLOGY 4 10 GLOBAL BODY-WAVE OBSERVATIONS 4 11 EXERCISES INVERSION OF TRAVEL TIME DATA ONE-DIMENSIONAL VELOCITY INVERSION STRAIGHT-LINE ?TTING 5 2 1 EXAMPLE: SOLVING FOR A LAYER-CAKE MODEL 5 2 2 OTHER WAYS TO ?T THE T(X) CURVE ?(P) INVERSION 5 3 1 EXAMPLE: THE LAYER-CAKE MODEL REVISITED 5 3 2 OBTAINING ?(P) CONSTRAINTS LINEAR PROGRAMMING AND REGULARIZATION METHODS SUMMARY: ONE-DIMENSIONAL VELOCITY INVERSION THREE-DIMENSIONAL VELOCITY INVERSION 5 6 1 SETTING UP THE TOMOGRAPHY PROBLEM 5 6 2 SOLVING THE TOMOGRAPHY PROBLEM 5 6 3 TOMOGRAPHY COMPLICATIONS 5 6 4 FINITE FREQUENCY TOMOGRAPHY EARTHQUAKE LOCATION 5 7 1 ITERATIVE LOCATION METHODS 5 7 2 RELATIVE EVENT LOCATION METHODS RAY THEORY: AMPLITUDE AND PHASE ENERGY IN SEISMIC WAVES GEOMETRICAL SPREADING IN 1-D VELOCITY MODELS RE?ECTION AND TRANSMISSION COEF?CIENTS 6 3 1 SH-WAVE RE?ECTION AND TRANSMISSION COEF?CIENTS 6 3 2 EXAMPLE: COMPUTING SH COEF?CIENTS 6 3 3 VERTICAL INCIDENCE COEF?CIENTS 6 3 4 ENERGY-NORMALIZED COEF?CIENTS 6 3 5 DEPENDENCE ON RAY ANGLE TURNING POINTS AND HILBERT TRANSFORMS MATRIX METHODS FOR MODELING PLANE WAVES† ATTENUATION 6 6 1 EXAMPLE: COMPUTING INTRINSIC ATTENUATION 6 6 2 T?AND VELOCITY DISPERSION 6 6 3 THE ABSORPTION BAND MODEL† 6 6 4 THE STANDARD LINEAR SOLID† 6 6 5 EARTH’S ATTENUATION 6 6 6 OBSERVING Q 6 6 7 NON-LINEAR ATTENUATION 6 6 8 SEISMIC ATTENUATION AND GLOBAL POLITICS REFLECTION SEISMOLOGY ZERO-OFFSET SECTIONS COMMON MIDPOINT STACKING SOURCES AND DECONVOLUTION MIGRATION 7 4 1 HUYGENS’ PRINCIPLE 7 4 2 DIFFRACTION HYPERBOLAS 7 4 3 MIGRATION METHODS VELOCITY ANALYSIS 7 5 1 STATICS CORRECTIONS RECEIVER FUNCTIONS KIRCHHOFF THEORY† 7 7 1 KIRCHHOFF APPLICATIONS 7 7 2 HOW TO WRITE A KIRCHHOFF PROGRAM 7 7 3 KIRCHHOFF MIGRATION SURFACE WAVES AND NORMAL MODES LOVE WAVES 8 1 1 SOLUTION FOR A SINGLE LAYER RAYLEIGH WAVES DISPERSION GLOBAL SURFACE WAVES OBSERVING SURFACE WAVES NORMAL MODES EARTHQUAKES AND SOURCE THEORY GREEN’S FUNCTIONS AND THE MOMENT TENSOR EARTHQUAKE FAULTS 9 2 1 NON-DOUBLE-COUPLE SOURCES RADIATION PATTERNS AND BEACH BALLS 9 3 1 EXAMPLE: PLOTTING A FOCAL MECHANISM FAR-?ELD PULSE SHAPES 9 4 1 DIRECTIVITY 9 4 2 SOURCE SPECTRA 9 4 3 EMPIRICAL GREEN’S FUNCTIONS STRESS DROP 9 5 1 SELF-SIMILAR EARTHQUAKE SCALING RADIATED SEISMIC ENERGY 9 6 1 EARTHQUAKE ENERGY PARTITIONING EARTHQUAKE MAGNITUDE 9 7 1 THE B VALUE 9 7 2 THE INTENSITY SCALE FINITE SLIP MODELING THE HEAT ?OW PARADOX 9 10 EXERCISES EARTHQUAKE PREDICTION 10 1 THE EARTHQUAKE CYCLE 10 2 EARTHQUAKE TRIGGERING 10 3 SEARCHING FOR PRECURSORS 10 4 ARE EARTHQUAKES UNPREDICTABLE? 10 5 EXERCISES INSTRUMENTS,NOISE,AND ANISOTROPY 11 1 INSTRUMENTS 11 1 1 MODERN SEISMOGRAPHS 11 2 EARTH NOISE 11 3 ANISOTROPY† 11 3 1 SNELL’S LAW AT AN INTERFACE 11 3 2 WEAK ANISOTROPY 11 3 3 SHEAR-WAVE SPLITTING 11 3 4 HEXAGONAL ANISOTROPY 11 3 5 MECHANISMS FOR ANISOTROPY 11 3 6 EARTH’S ANISOTROPY 11 4 EXERCISES