Subject Index

A absorption 380 acoustic impedance 111 - of brine reservoir 116 - of encasing lithology 116 - of He reservoir 116 acoustic intensity 391 acoustic wave equation 442 adjusted NMO 343 aliasing 25 aligned fractures 558 - observable anomalies in stacking and

P-wave NMO velocities 558 amplitude and phase spectra 521 amplitude balancing 409 - model based offset-dependent 409 - residual amplitude effects 409 amplitude of reflection signal as a function

of time 37 amplitude preserving DMO 353 - revised DMO 353 amplitude preserving equations 336 - three factors that affect the

amplitudes 336 - - DMO process, spherical divergence,

and sampling interval of the data 336 amplitude response 116 - due to change in pore fluid 116, 117 anelastic effects and absorption

loss 400-407 absorption characteristics 405

- attenuation coefficient 401 - attenuation property 400 - complex slowness vector 403 - complex wave number vector 401 - interference coefficients 403, 404 - propagation and attenuation vectors 401 - pulse broadening (refer to

Fig. l3.l3b) 405,406 - solid friction 400 - specific dissipation constant (l/Q) 401 - vector attenuation 403

- - effects on the AVO 403 anisotropic and isotropic migration 494 - geologic information on lithology

discrimination 494 - results, misplacement of events 494 anisotropic dipping single layer 227 - (elliptical velocity function,

Fig. 6.l3 a) 227 - normal ray emergence angle versus dip

angle 227 - - variation of diffractor velocity versus

dip angle 227 anisotropic Kirchoff migration

technique 493 anisotropic layer 262 - average vertical velocity 262 - horizontal and skew moveout

velocities 262 anisotropic medium 491 - steps in determination of velocity model

(elastic constants) 491 anisotropic solid 184 - plane wave equation 184-193 anisotropic velocity analysis over a

converted wave seismic section 492 anisotropy factor 301 - to distinguish sand from shale 301 anisotropy parameters 129 anisotropy 143, 147 - causes 147 apparent anisotropy 270 - (correlation with) lithology 270 apparent velocity filter 67 - in w-k domain 67 apparent velocity 35, 63 - in the frequency domain 63 - in the space-time domain 63 artifacts due to the assumption of

isotropy 319 asymptotic ray theory 359 - zero order or plane wave

approximation 360

622

attenuation correction 71 auto-correlation function 509 automatic gain control (AGe) 25 average velocity 131 - weighted average velocity 132 AVO cross plot 559 - AVO intercept, gradient and

curvature 559 AVO intercept and gradient inversion 418 - perspective 418-420 AVO interpretation 412-415 - AVO contributions from fractional

changes in density, compressional velocity, and shear velocity 413

- AVO gradient and intercept 412 - - background trend in absence of

hydrocarbon bearing strata 412 - AVO gradient in a HTI medium 420

fluid filled and dry crack (discrimination) 420 idea of crack density 420

AVO response 415 - VplVs ratio, anisotropy (effects) 415 AVO signatures 395 - two principal components 395 AVO analysis 395 - anisotropic correction 395 azimuthal anisotropy 179, 263, 305,

306-309 - horizontal symmetry axis 263 - interval velocity 305, 306 - - direction of symmetry axis 306 - - elastic constants 305, 306 azimuthal anisotropy, HTI medium with

horizontal axis of symmetry 146 azimuthal isotropy 305 - interval velocity 305 - - elastic constants 305 azimuthally anisotropic medium 592 - non-hyperbolic travel time equation,

use 592 azimuthally isotropic or anisotropic

media 303

B back-projected Kirchoff field 488 Backus filter 93 backward time extrapolation of the received

signal 482 beam stack 257 - beam stack semblance 259

a reflection tomography method 259 - - maximizing the beam stack

energy 259 bed resolution 110 - a function of reflection frequency 110

Subject Index

birefringent medium 204 Bond stress transformation matrix 154 box car function 58 bulk and shear moduli 537 bulk density of the fluid mixture 537

C CDP survey 75 - 6-fold coverage 75 - stacking charts 76 centre of the crystal 143 characteristic equation 193 characteristic frequency of a seismic

event 115 Christoffel equation (wave equation) 168,

181, 182, 186 - for orthorhombic system 186 Christoffel matrix 181 CMP stacked traces 77 CMP stacking 88-90 - problem in stacking due to structural

dip 89 - - Fig. 3.33a,b (example) 90 - stacked record section 88 - stacked trace 88 - the exploding reflector model 88 - vertical stacking, common-depth-point

stacking, or up hole stacking 88 coherence 79 coherent arrivals 35 coherent noise 5 - ringing, singing or water

reverberations 5 - surface waves 34 comb function 58 common depth point (CDP) gather 276 - for P and SV waves 276 Common depth point (CDP) stacking 94 - CDP stacked trace 94 common symmetry systems 145 - orientation of symmetry planes 145 complex trace analysis 117-119 - apparent polarity 117, 118 - instantaneous frequency 117 - instantaneous phase 118 - natural separation of amplitude and

phase information 117 - reflection strength 117, 118 - weighted average frequency 117, 118 compliance and stiffness matrices 146 composite waveform 115 - effect of bed thickness 115 compound anisotropy 565 - orthorhombic symmetry 570 compressive stress 561 - maximum 561

Subject Index

- least 561 concept of migration 481 - using the solutions of scalar wave

equation in 3-D and 2-D 481 constant offset to zero offset,

transformation 329 - as a mapping problem 329 constructive interference 548 converted wave 494 - exploration potential 494 convolution 477, 501, 503, 508 - for continuous time data 503, 508 - for discrete-time data 503 - short convolution operator 501 - three-dimensional 477 convolutional model of seismogram 53 - convolution, section multiple train and

reflectivity function 53 corrections 325 - normal moveout 325 - dip moveout 325 cracked rock regime 578 - delineation 578

3-D velocity model 580 anisotropic velocity conditions, evidence of 580 crack-induced anisotropy 575 travel time deviations (anomalies) 581 use of velocity anomalies 578

cross plot 542 - velocity-porosity 542 - - kerogen contents of Shales 542 cross-correlation function 508 - normalized cross correlation 512 cross-plot of anisotropy factor and vertical

velocity 303 - for identifying lithology 303 cross-sections 93 - time sections 93 - depth sections 93 - migrated section 93 - record section 94 - seismic section 94 - geological cross-section 94 crystallographic axes 143 cumulative S wave splitting 205 cusp 97 cyclic layering 494 - sand/anisotropic shale 494

D 3-D AVO technique 558 - for principal directions of fractures 558 - to map crack density 558 3-D data 543

623

- 3-D data display 544 - 3-D seismic exploration 545 - 3-D seismic imaging 545

tremendous potential for exploration, field development and production 545

- deep-water facies analysis 546 - high spatial resolution 546 - (solving) reservoir related problems 545 3-D laterally varying anisotropic

media 320 - numerical algorithm ANRAY86 for ray

tracing 320 4-D seismic monitoring 545

see 4-D seismic reservoir monitoring 535

4-D seismic reservoir monitoring 535 4-D seismic surveys 541

see 4-D seismic reservoir monitoring 535

datumning 447 decibel value 55 deconvolution 505 - deconvolution filter 516 degenerate shear waves 202 delta function 52 depositional environment 541 - depositional energy 541 - rate and source 541 depth section 102 - prepared from depth traces 102 detection of thin bed 103 - detection limit 103 determination of lithology 43 - use of colocated P and shear wave

stacks 43 determination of velocities (elastic

constants) using qP_qP and qP_qSV data 492

different types of data gathers 76 - CHP gather 77 - CMP gather 77 - CRP gather 77 - CSP gather 77 diffraction arrivals 94 diffraction hyperbola 232, 426 diffraction stack migration 425 digital and electric analog filters 68 - comparison of performance 68 digital filtering 512 - digital seismogram 512 - filter coefficients 512 - low pass filter 513 digital function 517 - frequency and phase characteristic 517 digital recording 26, 28, 60

624

- alias filter 28 - analog to digital converter 28 - formatter 28 - gain control amplifier 28 - multiplexer 28, 29 - preamplifier 28 - playback 28

analog display 28 deformatter 28 demultiplexer 28 digital to analog converter 28

- bit, byte, word 60 - multiplexed data 61 digitization methods 27 dip moveout and true amplitude

imaging 353-358 dip moveout 83-88, 345 - dip moveout (DMO) correction 89 - remnant moveout 87 - steps in implementation 345 dip-corrected NMO as two cascaded

processes 342 dip-domain DMO 352 - correction for reflection-point

smear 352 - DMO impulse response

(generation) 352-353 - impulse response curve 352, 353 dip-moveout processing 347 - for depth-variable velocity 347 - use of ray-tracing 347 - goal of DMO processing 349 - ideal DMO processing 353 dipping reflector 325, 340 - conflicting zero-offset slopes 344 - - triplication in (to, y) plot 343 - ray path for separated source receiver

and coincident source receiver 340 - stacking velocity 325 - zero offset section (Yi' to) 340 direct detection of hydrocarbons 535 dispersion and anisotropy 188 - geometrical representation 188 dispersion equation 187 - for slowness (inverse velocity)

surface 184, 187 - for wave vector surface 187 - Kronecker delta 187 dispersion relation 183 see also dispersion equation 187 dispersion 406 - frequency-dependent velocity 406 displacement reflection coefficient 362 displacement transmission coefficient 362 distortions in anisotropic medium 394

Subject Index

- by focusing and defocusing of seismic energy 394

- radiation pattern vs. reflection coefficient for P waves 399-400

divergence effect 391 see geometrical spreading 391-404

Dix-type hyperbolic fit 271 Dix (1955) formula 245 - see Dix equation 244 Dix equation 244 - generalized form, non-vertical ray

path 250-251 - vertical ray path 246-250 - - interval velocity 244 DMO, in terms of time dip 343 - in dip domain 350-353 DMO algorithms 357 - amplitude vs. offset (AVO) studies 357 - relative performance 357 - processing of synthetic-dipping reflector

data 357 - true amplitude (correct) DMO 357 - - final migrated image, steeply dipping

events 357 DMO impulse response 339, 346, 348 - for constant and varying isotropic

velocity 346-348 - under conditions of aniso­

tropy 348-350 - triplication in the DMO impulse

response 348 DMO mapping 347 - it's practical use 347 - - in dip-decomposition procedure 348 DMO operator 326 DMO ray path geometry 354 - for finite offset, and zero offset 354 DMO-NMO algorithm 333 DMO-NMO process 335 - as a two-step process 335 double Taylor series 122 downward depropagation 447 - downward continuation 447, 448-451 - wave tracking 447,451-453 - snapshot of the wave at a given instant of

time 447 dynamic correction, reflected wave 241 - travel time for multi-layer isotropic

media 241 - time-distance relationship, parametric

forms 242 dynamic range 55

Subject Index

E earth's reflectivity 356 effect of phase velocity surface on the

variation of Rapp(i) from Ripp(i) 368 effect of transverse isotropy 293 - on velocity and intercept time (P and SV

waves) 293-296 effective parameters 168 - for seismic signatures in HTI media

168 effective reflection coefficient 3 eigen value problem 360 - eigen values 360 - eigen vectors 360, 361 elastic constitutive equations 201 elastic constitutive relations 151 elastic stiffness constants matrix 169 - for VTI and HTI media 169 elastic stiffness constants 156 - in a rotated coordinate 156 elastic stiffness tensors for different

symmetry systems 147 ellipsoidal wave front 331 - an envelope of circular wave fronts 331 elliptical anisotropy 267, 373

see elliptically anisotropic medium 139, 266

- reflection and transmission coefficients for P incidences 373

- vertical and horizontal phase (and ray) velocities 267

- migrator's equation 139, 141 elliptically anisotropic medium 139, 266 emergence angle 225 - see angle of emergence 223 emerging wavefront properties 221 empirical relationship 539 - density and P-wave velocity 539 - P-wave velocity to porosity 539 - time average equation 539 - velocity, porosity and clay content 539 enhanced oil recovery (EOR) 540 equality of phase 215 equivalent cavity 16 equivalent wavelet 99 explicit filters for depth migration 464 - basis of explicit filter operators 465 - isotropic laterally varying earth

model 466-469 - numerical wave field extrapolation 464 - phase-shift method of wavefield

extrapolation 465 - computational domain for design of

optimum wave propagators 467 - problem of finite length filter

design 467

625

- the question of stability versus accuracy 468

- anisotropic earth model 469 - accuracy of the extrapolators 470 - depth migration 470 - - using a LS table of extrapolators 470 - exact downward continuation

operator 469 exploding reflector concept 353 - kinematics of zero-offset

migration 353 exploding reflector model (ERM) 140,

445,481, 482 field reconstruction and imaging 446

- one way wave equation 445 - for anisotropic medium 140 explosion 15 extrapolation of wavefield 498 - creating from a given section a new

section 498 - filter operator convolved with trace to

prevent waveform distortion 499 - mathematical statement of

extrapolation 498

F far-field point source radiation

pattern 394 - seismic source directivity 394 - spherical divergence 394 Fermat's principle 241 filter effect 68 - by timing errors in stacking 68 filtering effects 62 finite difference migration 439-442 fluid-filled porous solid 114 - longitudinal velocity 114 focusing and defocusing of energy 136 - in an anisotropic medium 136 Fourier analysis 519 Fourier synthesis 519 Fourier theorem 518 Fourier transform 65, 478 - one dimensional 65 - two dimensional 65 - - two Nyquist frequencies 66 fracture anisotropy, background

anisotropy 568 - (separation) 568-571 fracture anisotropy (modeling) 572 - use of synthetic seismogram 572-575

shear wave splitting by calculation of multiple scattering and crack diffraction 572

fracture characterization in azimuthally anisotropic medium 590-592

626

- combined application of V nmo and VH 590

- multiple offset VSP technique (use of) 590

- (determination of) cracks filled with cement or clay 592

- (determination of) gas filled open fractures 592

- (determination of) strike of the fractures 592

fracture orientation in marine seismic studies 581

- amplitude variation with angle (AVA) 581

- fractogram(s) display 583, 584 - reflection amplitude behavior over a

fractured medium 582 - residual geometrical spreading

effects 583 - use of P-wave AVO 581 fracture parameters 560 - crack aspect ratio 560 - fluid content 560 - fracture density 560 fractured media 574 - attenuation factor Q-l 574 fractured reservoir 12 - mapping and characterization 12 fractured rock 559 - aspect ratio (crack shape) 560 - elastic and seismic properties 559-561 - - elastic stiffness tensor 560 - - effective compliance tensor 559 fracture-induced anisotropy 557 - exploration value 557-592 frequency domain migration 442-445 - frequency shift effect 444 - of stacked and prestack data 445 frequency filters 68 - low pass, high pass or band pass 68 frequency selective absorption 16, 55 function-theoretical consideration 243

G gas sands 380 - AVO anomalies 380 - AVO characteristics 380 - AVO gradient and intercept 412-415 - classification 380 gas saturation 387 - (relation to) the ratio of the P to SH

reflection coefficient 387 geologic information on lithology

discrimination 494 geometrical spreading (or spherical

divergence) 15, 16,55,357,391-394,583

Subject Index

- offset dependent geometrical spreading effect 394

geophones 21 - damping 21 - - critical damping 23 - high fidelity of the geophone 23 - natural frequency 21 - response 23 geothermal reservoir (Coso geothermal

reservoir, California) 575, 576 - bulk density, and strike of fractures,

determination 575-578 - shear-wave splitting, detection,

polarization diagram, rose diagrams (for) frequency 576, 577

- time delays (of split shear waves) 576 - tomographic inversion results, crack

density 578 granular materials 538 - frame shear modulus against frame bulk

modulus 538 - - correlation coefficient 538 - sands and sandstones 538 Green's function 473, 474, 476, 501 - for a non-planar surface 476 - Green's displacement dyadic 484 - Green's stress tensor 484 - Green's traction tensor 488 - Kirchoff approximation 477 - useful properties 474 group velocity 190, 262 - as velocity of modulation on a wave 190 - for azimuthally anisotropic media 262 - for azimuthally isotropic media 262

H high frequency filtering 68 high resolution 3-D seismic survey (for

geotechnical applications) 595 - 3-D seismic acquisition system

(SEISCAT) 594 - - migrated picture of the diapir 595 - - prestack migration processing 595 high resolution approaches 596-599 - cross-well and single well seismic

data 596 - fracture controlled transport system 598 - - strong evidence, reflection data 598 - high-frequency imaging system 598 - seismic methodologies for imaging gas-

filled fractures 597 higher frequencies 103 - for increased resolutions 103 homomorphic deconvolution 506 - cepstrum domain 506 horizontal and vertical resolution 103-107

Subject Index

- horizontal extent to be observable on a seismic record 105

- - Fresnel zones for high and low frequencies 105, 106

- vertical resolution 104 - - resolvable limit 104 horizontal moveout interval velocity 304 horizontal slowness 234, 277 HTI media 166, 179,390 - isotropy plane 390 - symmetry axis plane 390 - linearized form of group (ray)

velocity 179-181 - - (in) natural coordinate frame and

survey frame 180 HTI model 166 - fracture plane 166 - split shear waves 167 - symmetry axis plane 166, 167 Huygen's principle 160, 476, 498 - mathematical statement of

extrapolation 498 - rigorous mathematical statement 476 hydrocarbon detection 415 - use of fluid factor 415 hydrocarbon indicator (HCI) 42 hydrocarbon traps 6 - by sedimentary structures 6 - true stratigraphic traps 7 - palaeogeomorphic traps 7 - unconformity traps 7 hyperbolic velocity analysis 252-257, 261 - basis 252-253

cross-correlation 253 - - maximization of selected

functions 253 - hyperbolic moveout trajectories 255 - velocity spectra 254, 255-257

ideal reservoir rocks 536 ideal seismogram 49 identification 'headers' 70 identification of primary reflection

events 79 image of two events 56 - with same reflectivity (horizontal and

dipping reflectors, Fig. 3.9) 56 image ray 231 - image ray time 231 - minimum time point on the surface 232 image wavelet 356 - zero phase image wavelet on migrated

section 356 imaging 446, 463 - Claerbout imaging principle 446

627

- condition in slant frame coordinate 463 imaging condition 489 imaging of stacked seismic data 479-481 impedance 373 implicit differentiation 189 impulse response 47 - of any linear system 47 - of the water layer 93 instantaneous intercept time 'to' 278 instantaneous velocity 278 interpreting the 3-D data 590 interval and stacking velocities 287 - under conditions of anisotropy 287-288 - - elliptical velocity functions 287 - from roots mean square velocity

(VRMS) 131 interval velocity 130-133 intrinsic anisotropy 270 intrinsic attenuation 406-407 inverse filter 516

see deconvolution filter 516 inverse Fourier transformation 489 inversion algorithms and model

assessment 322-323 inversion procedure 263 - elastic constants, estimation 263 - orientation of symmetry axis,

estimation 263 isotropic Kirchoff migration scheme 493 isotropic solid 181 - plane wave equation 181-184 isotropy plane 166, 167

see fracture plane 166, 167 isotropy 96 - ray path, coincident source-receiver

positions 96 iterative model based optimization 300 - to determine elastic stiffness

coefficients 300

J Jacobian 355 Jacobian matrix 313, 318

K kinematics of DMO equations 331-334 Kirchoff elastic wave migration 483-486 - simultaneous migration of p-

and S-waves 483-486 Kirchoff integral solutions of wave

equation 425 - diffraction summation process 425 Kirchoff migration 483, 494 - in anisotropic inhomogeneous

media 494 - to generate the migrated image 483

628

Kirchoff-Helmholtz integral 487 - for forward extrapolation of the

displacement field 487 KRK integral 482, 483 - applicable to unstacked seismic

data 483 - extrapolation of both sources and

receivers 483

L Lames constants 159 lateral velocity variation 259 - velocity estimation by beam stack 259 lattice 143 layer stripping method 300, 315 layered medium 287 - with elliptical velocity functions 287 layering induced anisotropy 159 - VTI media 159 leading split shear wave arrival 198 linear CDP survey 30 linear operation 48 linear system 507 - it's impulse response 507 - time-invariant system 507 link 12 - between wavefront characteristics and

subsurface medium properties 12 lithological change indicator (LCI) 42 lithology discrimination 309 lithology indicator 301, 542 - V plV s ratio 542 lithology 272, 384 - three velocity parameters and their

ratios, correlation with 272 local stacking operator 258 long-path multiples 3

M marine seismic sources 18-20 - bubble effect 18 - far-field wave shapes 20 - air guns 18 - implosion 19 - sparker 18 - water guns 18 - gas guns 18 marine seismic surveys 43 - depth controllers 44 - hydrophones 23, 24, 43 - navigation system 43 - radio positioning 45 - satellite positioning methods 45 - streamer 23, 43 method of inversion 308 - for weak-anisotropy approximation 308

Subject Index

method to recover elastic constants in the laboratory 317-319

- least squares inversion method 318 - inversion results 319 - stability and convergence 318 mid-point-offset (x,y) coordinate 224 migrated image wavelet 55 migrated image, removal of distortions

caused due to static shifting 495-501 - accurate datum correction 497

cases of nonplanar datum and velocity variation 498 in terms of wavefield extrapolation 497

- input data , zero-offset time section 495

- point diffractor, two horizontal reference surfaces 496

- - depth migration 496 - - zero offset time section 496 - static correction 495 migration in inhomogeneous, anisotropic

media 487 - for converted and non-converted

waves 487-494 migration of seismic data 478 - 3 D migration 480 - to extrapolate converging waves 478 migration process 480 - as an input-output relationship 480 migration 62, 94, 429, 486 - in the space domain, geometric

techniques 429-432 - (in the) wave number domain 432-438 - Kirchoff acoustic wave (P wave only)

migration 486 - Kirchoff elastic wave (P and S waves

both) migration 486 - - enhanced migrated picture 486 - migrated section 440, 446 - - field reconstruction and imaging

446 - migration aperture 427 - migration equation (under conditions of

isotropy and anisotropy) 431 - wavefront method (Schneider 1971) 96 mode converted (P-S) reflection 34 modulated wave 190 multicomponent seismology 299 multiple offset VSP data for quasi-P and

SH-waves 303 - for retrieving elastic stiffness

coefficients 303 multiple reflections - short- or long-path multiples 2 multipulse seismogram 197

Subject Index

N NMO and CMP stacking 325 - dip filter 325 - dip selectivity 325 NMO Correction 325 - non-zero offset data to true zero offset

data (transformation) 325 NMO inverse 351 NMO stretch 78 NMO velocity after Forel and Gardner's

DMO correction 337 - independent of structural dip (refer also

to Fig. 3.33 a, b, p. 90) 337 noise 35 - ambient noise 36, 38 non-hyperbolic moveout 239, 259 - by a low-velocity anomaly 259 - P-wave moveout for long spread in T. I.

media 239 non-linear inversion problem 309 - linear approximation 309

damped least square formulation 309 Jacobian matrix formulation 309

non-periodic layered structure 161 - effective elastic constants 163 - long wavelength approximation 165 normal incidence ray 223, 228, 231 - angle of emergence 223 - - for the coincident source-receiver

position 224 normal incidence travel time 229 normal moveout velocity (VNMO) 123,

127, 128, 171, 207, 221, 232, 236, 238 - azimuthal variation 171 - in Common Depth Point (CDP)

surveys 207 - isotropic layers 236-238 - normal incidence ray 232 - reconstruction of velocity field in

anisotropic media 238-240 - surface emerging wavefront

(relationship) 221-232 - transversely isotropic (T.I.)

medium 232-236 normal moveout 79-82 - adjusted NMO 87 - based on Fermat's principle 82 - hyperbolic equation 80 - on the basis of Pythagoras theorem 82

o objective-oriented interpretation tools

(earth resources management) 546-555 - anisotropy property of a shale

formation 552

data conditioning for the VSP record 553

629

S-wave birefringence on crosshole and VSP record 554 recording geometry at Chevron Experimental Well Site, California 554

- clay diapir river schelde (near Antwerp, Belgium) 593-596

- coal seam, detection 546 - - synthetic seismogram, the reflectivity

method 549-551 - methane production (Cedar Hill Field,

New Mexico) 584-590 - overpressured zone, detection 551 - - velocity-depth curve, knee form 551,

553 - geothermal reservoir (Coso,

California) 575-578 - fractures controlling fluid transport

(Conoco borehole test facility,near Newkirk, Oklahoma) 596-599

offset dependent tuning effect and NMO stretch (removal) 559

offset VSP geometry 267, 301 - zero-offset P and SH wave data 303 - zero-offset SH-wave VSP data 301 offset -dependent P-P reflection

amplitude 365 - for anisotropy and isotropy 365 optimum bed thickness 116 - for strong constructive addition of top

and bottom reflected waveforms 116 orthorhombic symmetry system 171 - Thomsen parameters 171-173

p P wave and S wave data 42 - combined interpretation 42 - P wave and S wave stacks 43 paraxial equation 454 - for migrating seismic data 454 - for modeling and migration 455 particle displacement 202 particle motion polarization 193-195 particle velocity polarization 187 perfect fidelity 23 - criterion in frequency domain 23 periodic layered structure 159 phase shift operator 467 - in the frequency-wave number

domain 467 phase spectrum 523 - curved phase (spectrum) 523 - linear phase (spectrum) 523 - pulse forms, delay 523

630

- zero phase (spectrum) 523 phase velocity surface 217 phase velocity vector 289 phase velocity 188,233, 377 - as a function of phase angle, dip angle of

the reflector 233 - directional dependence, reflection

coefficient variation (relationship) 377

phase velocity, energy velocity 191 - relationship through wave vector 191 Pie-slice filtering process 66 pitfalls 322 - due to assumption of isotropy 322 pitfalls in routine reflection processing due

to anisotropy 119-142 - imaging 138-142 - interval velocity 130-133 - moveout correction 121-123 - NMO velocity 127-129 - reflectivity 134-138 - stacking velocity 123-127 - waveform and arrival times 119-121 plane wave vector 137 point diffractor l38, 338, 429 - diffraction curve 429 - in an elliptically anisotropic

medium 138 point scatterer 335 Poisson ratio 379 - Koeffoed's observation 383 polarization singularities 196 polarization transformations 203 - by combining non-degenerate shear

waves 203 porosity 537 post-stack migration 548 P-P reflections coefficient 421 - HTI/HTI media 421 - - computer program 421-423 practical guidelines relating rock/fluid

properties with seismic properties 543 - fluid properties 543

density 543 increase of V p/V s ratio 543 saturation 543 viscosity 543

- rock properties 543 bulk density 543 fractures 543 pore shape 543 porosity 543

pressure 540 - confining pressure 540 - effective pressure 540 - fluid pressure or pore pressure 540

Subject Index

pre-stack migration (or before stack migration picture) 445,483, 548, 594, 596

primary reflections principles of geometrical optics 80 processing reflections, necessity 7 - failure of processing 10 program FERMAT 320 - to invert synthetic multi offset VSP travel

time data 320 propagation vector 195 propagator matrices 198-201 - as transfer function between polarization

of down-going and up-going waves 198 - in VSP measurement 198 - use 198

for reflection analysis 198 for transmission analysis 198 local shear wave birefringence properties 198

pseudo-reflectivity function of the subsurface R(r,co) 488,495

- pseudo-reflectivity matrix 495 - pseudo-reflection coefficient 489 pulse doconvolution 72 - before stacking 72 - - deconvolution operator, design 72-73 pulse waveform 16 pure mode processing 9 pure shear motions 176 P-wave anisotropy 364 P-wave AVO response 389 - azimuthal dependence from a fractured

layer 389 P-wave phase velocity surface 365 P-wave reflection coefficient 371 - effect of transverse isotropy 371 P-wave reflectivity 369 - (at) shale-chalk interfaces 369

Q quasi P-wave reflection 388 - between transversely isotropic

media 388 quasi-longitudinal 174, 176 quasi-transverse 174, 176

R radiation pattern 380, 395-400 - as a function of phase or group angle

with the symmetry axis 395 radius of curvature 221, 222, 229, 230 - for a normal incidence reflection 222 - of the incident and refracted wavefront,

law 221 - of the reflected wavefront 229

Subject Index

- of the reflecting upgoing wave 230 random noise 311 ray parameter 217, 219,220, 233, 234, 250,

347 - common ray parameter 248 ray path in common-shot geometry 499 ray tracing, elliptical velocity function 221 - algorithm 221 ray vector 180 - group velocity in the survey frame 180 - in natural coordinate frame 180 ray velocity 128, 139, 209, 266, 591

see also group velocity 11, 177, 178, 180, 190, 212, 216, 262

- approximation to ray velocity by a truncated Fourier cosine transform 266

- by linearization of phase velocity 266 - stereographic projection 591 reciprocity principle 482 record surface 426 reduction of noise 37-38 reflected signals and coherent noise 66 - in the frequency wave number

domain 66 reflected wave travel time, multi-layer

isotropic media 241 - time-distance relationship, parametric

forms 242 reflected wavefront 393 - radius of curvature 393 reflection amplitude 391 - factors affecting 391-407 reflection coefficient (R.C.) for normal

incidence 111 reflection coefficient for VTI media 389 - exact VTI solution 389 - approximation 389 - isotropic reflection coefficient 389 reflection coefficient variation 382 - condition of isotropy 382-388 - P-wave reflection coefficient for gas-brine

contact 387 - condition of anisotropy 388-391 reflection point dispersal 326 - stack smeared 327 reflection ray path 135 - elliptical anisotropy 135 - - zero-offset (normal incidence)

ray 135 - for isotropy 135 reflection record 521 - wiggle form 521 reflectivity of the earth 99 reflectivity 359 reflector surface 97, 426

- as the envelope of wavefronts 97 repetitive waveforms 53 - (line spectra, Fig. 3.6) 52, 53 representative wave types 34

631

- distance versus arrival time graph 34 research areas requiring special

emphasis 599 - 3-D synthetic seismograms 600 - AVO trends 600 - - key factors in interpretation:

anisotropy and viscoelasticity 600 - converted wave seismology 600 - influence on wave propagation,

viscoelastic medium 599 - reflection parameters, viscoelastic

medium 599 - true reflection amplitude recovery 600 - viscoelastic dissipation 600 - - energy and phase distribution

(distortion) 600 reservoir characterization 575 - field system examples 575-591 reservoir rocks 536 - porous fluid saturated 536-538 - elastic and physical properties, laws 536 - properties 538 - - effects on seismic velocities 538 residual time delays 258 reverberations in water layer 91 - effects of reverberations 90 - to reduce or eliminate the effects 90 - - by inverse filtering or

deconvolution 90 - reflection spectrum, modified due to

reverberations 91 reverberations 53, 90 - in the water layer 91 - within a geologic section of sedimentary

layers 53 Ricker wavelet 99, 526 RMS velocity (or VRMS' or VRMS) 78,80,

131, 243, 244, 245, 249, 252, 261, 287, 288 rock velocities 384 - effects of pore fluid 384 root mean square skew velocity 264 root mean square velocity 287 - for a multilayered elliptically anisotropic

medium 287-288 rotation of coordinate axes 152 - for first, second and fourth rank tensor

quantities 152 routine reflection processing 109 - attributes and pitfalls 109-142

632

S sampling interval 29, 518 - fundamental frequency 518 - harmonics 518 sampling theorem 56 - alias filters, cutoff frequency 57 - alias signals 57 - aliasing with spatial sampling 67 - aliasing with temporal frequencies 67 - aliasing 56 - Nyquist frequency 56 - Nyquist wave number 58 - sampling frequency 56 - use of 56 sand potential of the facies 11 0 sand reservoir 113 - bulk density 114 - Poisson ratio and constituent

compressibilities 113 - time-average equation 114 saturation of water, oil and gas 537 scalar wave equation 62 - in the space time domain 62 - (in the) the frequency domain 62 sedimentary facies 110 - sand prone 110 - shale prone 110 seismic amplitude 70 - factors that affect 70 seismic attributes of reflection data 111 seismic facies analysis concepts 5 - deltaic sequence 6 - - reflection configurations, expected 6 seismic facies and interpretation 4 - basic types of reflection

configurations 4 seismic filters 25, 26 - passband 25 - response 26 seismic lithology discrimination 535 seismic parameters 109 - geological interpretation 109 seismic processing 62, 326 - ultimate goal 62, 326 - - mapping true reflectivity of the

subsurface in their true positions 326 - as an inverse scattering problem 62 seismic properties of sedimentary

rocks 536 - factors influencing 536 seismic properties 536 - impedances 536 - P-wave velocity 536 - S-wave velocity 536 - VplVs ratio 536 seismic pulse 405

Subject Index

- input spike pulse 405, 406 - frequency selective absorption

effect 405-406 - pulse spectrum measured at different

times 405, 406 seismic range equation 408 - AVO correction with offset 408 seismic recording 26 - analog magnetic tape recording 26 - digital magnetic tape recording 26 - photographic paper (recording) 26 - recording heads 26 seismic response of the reservoir 539 - (role of) degree of saturation 539 - (role of) environmental factors 540 - - pressure and temperature 540 - (role of) pore fluids properties 539 - (role of) anisotropy 540 seismic rock physics 535-543 seismic sections, displays 99-102 - information content of seismic

sections 100 - displays of three-dimensional data 99

time slice (seiscrop) map 101 - - time contour maps 100 - - sectional displays 10 1 - variable area (mode) 99 - variable density mode 99 - wiggly trace mode 99 seismic stratigraphy 103 - depositional time surfaces 103 - stratigraphic correlation 103 - unconformities, seismic sequences 103 seismic tomography 529 - ART 529 - - for a weakly anisotropic

medium 530-532 - BPT 529 - constrained dual tomography 532-533 - - Lagrange multipliers 532 - cross borehole tomography 529 - SIRT 529 - use of tomographic reconstruc-

tion 529-535 seismic-swath arrangement 32 seismogram (or synthetic seismogram) 1,

197, 549, 551 - recorded seismogram 198 - rotation 198 - transformation 197-198 semblance analysis 272, 303 - over (Vh) and (V,,) 272 - - results 272 " - along skewed hyperbolic travel time

curves 303 semblance scan 268

Subject Index

- over three velocity parameters 268 semblance 78, 253 - semblance analysis for non-hyperbolic

reflection moveout 257 - vertical and skew moveout velocities,

estimation 257 - semblance coefficient 254 separable signal model 410 - AVO 410 - - in offset domain 410 - - effect of NMO stretch 410 - block NMO for each time window 410 - residual NMO 410 - - using cross-correlation technique

410 - zero offset reflection amplitude

section 411 - offset-independent pulse p (t) 411 shear modulus 537 shear wave double refraction 195

see shear wave splitting shear wave seismic surveys 41 shear waves 183 - pure mode and degenerate 183 - - circular or elliptical polarization 183 shear-wave birefringence (or S-wave

birefringence) 195, 198, 205, 554 see shear wave splitting

shear-wave splitting (or split share waves) 167, 195, 196, 198, 557, 572, 575, 576,577

short-path multiples 2 - ghost 2 - near surface multiples or peg leg

multiples 2 side-slip of zero offset reflection

events 220 side-slip effect 140 signal and noise 35 - signal to noise ratio 37 simultaneous downward movement of both

sources and receivers 483 - before-stack migrated picture 483 simultaneous inversion 310 - velocities and model parameters 310 sine function 59 singular value decomposition method 310 skew moveout interval velocities 304 skew moveout velocity 300 skewed hyperbolic analysis 261, 274 - normal moveout correction for stacking

(improvement) 274 skewed hyperbolic fit 271 slant path correction (NMO

correction) 33 slant stack migration 457-464

- partial coherency stack (from one direction) 457

- p-gather 460 - potential technique for multiple

removal 464 slant plane wave section or p-section 463

slowness vector 289

633

Snell's law 8,208, 209, 210, 212, 213, 214, 216, 217, 458

- (for) converted wave 8 - for an anisotropic medium 210-217 - for anelastic media 402 - for an isotropic medium 209 - for a vertically stratified earth 458 - in terms of wave characteristics

(frequency '0)' and wave vector 'k') 216 - - for a completely general case including

converted waves 216, 217 - conventional and generalized

forms 208-217 source wavelet 98 - for deterministic wavelet processing 98 spatial location of cracks and cracks

density variation, coal bed methane reservoir, Cedar Hill Field, New Mexico 584-590

- data processing sequence 584, 585 integration of 3-D, three-component seismic data and AVO analysis 584 swath, CMP bins, for pre-stack amplitude analysis 585 AVO analysis 588-590

bin-azimuth trace 589 fracture orientation 590 Poisson ratio variation 588 Poisson reflectivity anomalies 589 Poisson reflectivity 588

- AVO modeling 585-588 AVO gradient 587 AVO product 587 tuning effect on AVO estimates 587

specialized processing 8 - converted waves 8

effective velocity ratio 10 - - moveout 8 - - converted wave processing 9 spherical divergence (or divergence effect

on amplitude) 380, 391 see geometrical spreading

spherical harmonics 590 - expansion of the inverse squared ray

velocity 590 split shear waves 557 - fast shear wave 558

634

- slow shear wave 557 spread 29 - cross spread 30 - end-on-spread 29, 34 - in-line offset spread 29 - L spread 30 - split or straddle spread 29 - spread length 33 subsurface cross section in reflection time

(CONOCO Inc.) 102 superposition and convolution 504 stack section 358 - after application of true-amplitude

integral DMO steps (example) 358 stacked records 548 stacked section 440 stacking velocity 251 - best-fit criterion 252 - best-fit hyperbola 251 - stacked traces 252 - Vs, VRMS, VAVG (relationship) 252 stacks 258 - along curved trajectories, beam

stack 258 - on straight line trajectories, slant

stack 258, 457-464 stages in the deformation 150 - elastic deformation 150 - linear deformation 150 - non-linear deformation 150 - plastic deformation 150 static correction 73 - field statics 74 - residual statics 74 - low velocity layer (LVL) 73, 74 - - characterized by 74 stiffness matrix 154 - original stiffness matrix 154 - transformed stiffness matrix 154 stiffness or compliance constants 154 - in abbreviated subscript notations 154 strain transformation matrix 155 stress anisotropy and fracturing 561-566 - cracks (opening) 561 - - crack induced anisotropy 575 - dilatancy 561 - Mohr stress circle 563, 564 stress history of the rock 541 stretch factors 356, 357 - wavelet stretch relationship 356 strong reflectors 111 superposition and convolution 504 surface conversion coefficients 362, 363 SV-wave anisotropy 364 SV-wave phase velocity surface 365 S-wave birefringence 205

- horizontal refringence 205 - vertical refringence 205 symmetry classes 146 symmetry systems 146 synthetic seismogram 1

Subject Index

- Kirchoff summation procedure synthetic split spread (record) using

reciprocity 500

T T. I. media (or transversely isotropic media,

transverse isotropy, transversely isotropic solid, transversely isotropic medium, T. I. model, azimuthally isotropic, trans­versely isotropic stuctures, VTI media) 126, 128, 146, 149, 160, 166, 173, 175, 186, 2l3, 232, 239, 261, 276, 278, 285, 293, 348, 366, 371, 395, 469, 534, 554

- three measures of anisotropy 175 two elastic moduli 175

- weak anisotropy 173-181 t2_x2 graph 292 - see also t2 - x2 curves - deviation from straight line 292 - inhomogeneity and transverse isotropy,

e_x2 graph curved 292 t2_x2 curves for anisotropic models 275 - interpreting e_x2 curves for

anisotropy 281-286 - for multi-layered media 286 - interpretation for isotropy, anisotropy

and inhomogeneity 289-293 Taylor series approximation 8, 288, 290,

292 Taylor series expansion 318 thermal EOR 541 - seismic monitoring 541 Thomsen parameters for HTI media 170 - equivalent VTI media 170 "Thomsen style" anisotropy parameters for

HTI media 389 three-dimensional CDP gather 32 three-dimensional reflection surveying at

sea (PRAKLA SEISMOS AG) 44 time-offset relationship 263 - for multilayered azimuthally anisotropic

media 263 - for multilayered azimuthally isotropic

media 263 time break pulse 15 time-dip 225, 237 - from stacked data 225 - on a stacked seismic section 237 timing errors in stacking 104 tomographic determination 310 - 3-D model 312

Subject Index

- of velocity and interfaces 310 transformed compliance matrix 156 transformed elastic stiffness constant

matrix 156 transient seismic pulse 52 - simple transients, their Fourier

spectra 51 transmission loss 380 transverse isotropy 278, 289 - due to periodic layering 278, 289 - - k-medium 289 transversely isotropic medium (or

media) 10, 269, 278, 366 - equations for weak anisotropy 173 - linearized reflection coefficient 366 - linearized transmission

coefficients 366 - phase and group velocities 173 - their linearized forms 173-179 - tilted symmetry axis, steeply dipping

reflector 10 - - eMP gather 11 - - no specular reflection 11 - multilayered 269 - - Dix hyperbolic formula, a

generalization 269 - horizontal moveout velocity 270 - a measure of skewness of the ray velocity

surface 270 - wave surfaces of P and S waves 278 transversely isotropic, VTI medium with a

vertical axis of symmetry 146 travel time inversion 309,319,321 - both for velocity and structure 319 - for inverting the seismic velocities 319 - for the structure of interfaces 319 - non-uniqueness 321 travel time tomography 259 travel-time inversion algorithm 300 - simultaneous determination of all layer

parameters 312-315 - travel time inversion (example) 315-317 true amplitude imaging 55 true amplitude formulation algorithm 357 - useful in DMO-processed amplitudes for

amplitude vs. offset (AVO) studies 357 true-amplitude information 380 - geologic in origin 380 tuning effect 558 two anisotropy parameters 375 - of P-SV group 375 two-way transmission coefficient 112 typical reservoir model 380 - offset-amplitude patterns 380

U unit cell 144 unit vector 169 - in the slowness direction 169

V variation of phase velocity 282 - reduced equations 282 - - linear in elastic constants 282 variation of reflection coefficient 379

635

- velocity contrast and the Poisson ratio, interplay 379

variations in amplitude response 116 - bright spot 43, 116 - dim spot 116 - polarity reversal 116 various kinds of processing 67-99 velocities of the reflected signals 66 - on the k-w plot 66 velocity analysis 77-79, 255, 487 - for determining interval velocities 79 - hyperbolic moveout trajectories 255 - main objective 79 - new anisotropy velocity analysis

scheme 487 - results display 78 - stacking velocity 78 - - contours of semblance 78 velocity anisotropy in shale 147 velocity- dispersion logging 407 - for estimating reservoir properties 407 velocity estimation 13, 255 - by beam stack 13, 255

applicable to geologically complex areas 255 local stacking operator 258

beam stack semblance 259 - information on non-hyperbolic

moveout 255 - high resolution wave front method or

spectral eigenstructure method 255 - stacking trajectory 257 velocity filtering 35 velocity ratio and lithology 273 velocity 244 - average velocity 244 - velocity heterogeneity 245 - - heterogeneity factor 245 - instantaneous velocity 244

interval velocity 244 - normal moveout velocity 244 - stacking velocity 244 - - for a layered structure 251-252 - - bias, (V s -V RMS) 252 - velocity spectra 254-257

636

- weighted average velocity (RMS velocity) 244

velocity-independent DMO 335, 337 vertical interval velocities 304 vertical seismic profiling (VSP) 38, 299 - application of VSP data 39 - ascending waves 40, 41 - descending waves 40, 41

direct waves 40 - fluid waves 39 vertical stacking 548 VHR small-scale 3-D work 595 vibrosies 17, 510 - downsweep 17 - linear sweep 17 - sweep time 17 - sweep 17 - upsweep 17 - upsweep signal 510 visco-elastic homogeneous wave 403 V p/V s ratio 538, 542 VTI and HTI media 168 - limited equivalence 168 VTI equivalent model 170 VTI media 173

see transversely isotropic media 366

W water saturation 112 - (effect on) reflection coefficient and

velocity 112 wave equation calibration procedure 354 - standard imaging sequence 354 wave equations in elastic media, Christoffel

equation 181-193 wave equations 13 - integral solutions 13 wave number 187 - scalar quantity, isotropic

propagation 187 - vector, in an anisotropic medium 187 wave surface and phase velocity surface,

relationship 265 wave surface 161,217 - the envelope of all plane wave

fronts 161 wavefield extrapolation and imaging 474 - basic equation 474

Subject Index

- stacked seismic data, imaging 479-481 wavefield extrapolation 453-454, 501 - extrapolation equations 454 - phase-shift methods 454 - use of a high-frequency approximation of

Green's function 501 waveform manipulation 48 - convolution 48 - superposition 48 waveform 59, 518 - combined waveform 522 - - phase relationship of the individual

waveforms 522 - frequency domain description 518 - sampling and reconstruction 59

sinusoidal waveform 522 - transient waveform 520 wavelet processing 97-99 - benefits 98

wavelet compression 98 sharpening of events 98 better resolution of stratigraphic features 98

- effective wavelet shape 97 - embedded wavelet 97 wavelets 524 - linear phase wavelets 528 - maximum phase wavelets 525

minimum phase wavelet 524, 525 - complex plane representation 526 - mixed phase (wavelets) 527 - zero phase wavelets 528 weak anisotropy 173, 177 - equations for phase velocities 177 weathered zone 547 wide cycle breadth reflections 116 Wiener filtering 99 - changing effective wave shape 99 - desired wave shape, zero phase 99

Z zero offset ray 234, 235 - layered T.!. subsurface model 235 - stratified anisotropic model 234 zero-phase source wavelet 356 Zoeppritz equations 379 Z-transform 514 - unit delay operator 514