Content of topics in seismic - and advanced seismic data processing
Stress-strain relationships and Elastic constants
1. Deformation and the strain tensor2. Traction and the stress tensor
3. Stress-strain relationships: Hooke’s law
4. The equation of motion
5. Symmetry properties of the strain tensor, stress tensor and stress-strain tensor
6. Definitions of elastic constants
7. Relationships between elastic constants
8. Equation of motion and constitutive relation in Cartesian and cylindrical coordinates
The wave equation
1. The acoustic wave equation
- The acoustic wave equation
- The reciprocity theorem
- The integral representation of the acoustic wavefield
- Monopoles, dipoles and multipole-source expansion
2. The elastic wave equation
- The general case
- The inhomogeneous isotropic case
- The homogeneous case
- From elastic to acoustic
- P-waves and S-waves
- Reciprocity theorems
- Green’s function and the Representation Theorems
3. The boundary conditions
4. Plane wave solutions
5. Lame’s Theorem
6. One-way elastic wave equations for P- and S-waves
7. Raytracing; the eiconal equation and transport equation
8. Phase-, group- and energy velocities
Wavefield extrapolation
1. Temporal and spatial Fourier transforms
2. The acoustic wave equation in the different domains
3. Wavefield extrapolation in the different domains
4. Wavefield extrapolation and migration in the spatial Fourier domain
5. Wavefield extrapolation in the tau,p-domain
6. Forward and backward wavefield extrapolation with the Kirchhoff integral
7. Design of wavefield extrapolators
Deconvolution
1. The convolutional seismic trace model
2. Deconvolution: definition of inverse-, spiking- or whitening filter
3. Examples:
- reverberation - dereverberation
- ghost - deghosting
- absorption - deabsorption
4. Resolution: signal dispersion as a function of amplitude and phase spectrum
5. The Z-transform, polynomials and factorization
6. Minimum-phase, mixed-phase and maximum-phase wavelets
7. The inverse filter of a two-point wavelet
8. The inverse filter of an arbitrary wavelet
9. Minimum-phase wavelets: properties in the different domains
10. Least-squares (ls) filters:
- the normal equations
- ls inverse filters
- ls prediction- and ls prediction error filters
11. Least-squares filters in the frequency domain: design and properties
12. Two-sided filters: design and properties
13. Filtering in the presence of noise
14. Special topics:
- tuning - detuning
- vibroseis deconvolution
- inverse array filtering = directional deconvolution
- surface consistent deconvolution
- maximum likelihood-, L1-norm-, and minimum entropy deconvolution
- deterministic deconvolution with measured or modeled wavelet
- homomorphic deconvolution
- over-under acquisition and deghosting
Velocity analysis
1. Definitions of various types of velocity
2. Traveltime expressions for paraxial rays
3. Expressions for azimuth dependent stacking velocities
4. Stacking velocity and normal incident wavefront curvature
5. Moveout expressions for special cases: 1D earth, long offsets, shifted hyperbola, near surface structure and anisotropy
6. Stacking velocity analysis: CVG, CVS. Semblance, differential semblance and the eigenvalue method
7. NMO stretch
8. Coherency inversion for stacking and velocity model building
9. Relationships between stacking, dmo and time migration
10. The common-reflection-surface (CRS) stack
11. Analytical time-depth relationships
Static corrections
1. Introduction
2. Methods for picking first arrivals
3. Modeling the near surface
4. Picking reflections
5. The residual statics equation and its solution
6. Stackpower optimization
7. Simulated annealing
8. Redatuming
Multiple elimination
1. Characterisation of multiples
2. Predictive deconvolution in (t,x)-domain and linear (tau,p)-domain:
- spiking deconvolution
- gapped deconvolution
3. Multiple elimination based on differences in moveout between primaries and multiples:
- straight stack
- weighted stackk
- (k,f)-transform domain filtering
- velocity stack
- parabolic Radon-transform domain filtering
- adaptive beamforming
4. Multiple elimination of OBC data by combining vertical geophone- and hydrophone data
5. Wave equation based multiple elimination
6. Multiple elimination based on redatuming of sources and receivers
7. SRME = (free-) surface related multiple elimination
Signal-to-Noise Enhancement
1. Noise characterisation
2. Random noise suppression based on stacking:
- straight stack
- weighted stackk
- diversity stack
- median stack
- smart stack
3. The parabolic Radon transform
4. Wiener smoothing filters
5. Matched filter and Output energy filter
6. Singular value decomposition (SVD) and the Karhunen-Loeve (KL) transform
7. Suppression of acquisition footprint
8. Despiking
9. (f,x)-prediction filtering for noise suppression
10. Methods for ground roll filtering
11. Arrays: field arrays and digital group forming (DGF)
12. Data regularization and trace interpolation
Migration
1. Migration, modeling and inversion
2. Geometric approach to summation migration = diffraction stack migration
3. Resolution before and after migration
4. Migration stretch (pulse distortion)
5. Aliasing of the migration operator and its cures
6. Normal incidence rays, image rays and vertical traveltime
7. Definitions of depth migration and time migration
8. The wave equation and its factorization; Green's functions
9. Wavefield extrapolation in the various domains
10. Imaging conditions for shot records, survey sinking and zero-offset data
11. The Kirchhoff integral and the Rayleigh integral for migration
12. Characteristics of summation migration
13. Migration in terms of double focused array synthesis
14. Migration algorithms:
- k,f-migration
- phase-shift migration, phase-shift plus interpolation, and (extended-) split step Fourier
- phase screen migration
- finite difference migration
- summation migration
15. Reverse time migration (RTM)
16. Different implementations of summation migration:
- Beam migration
- Gaussian beam migration
- Parsimonious migration and Fresnel zone migration
- Wavepath migration
- Map migration
17. Migration and demigration
18. Diffraction tomography, point-spread function and resolution
19. True-amplitude migration
20. Migration and inversion
True-amplitude migration
1. Factors describing amplitude effetcs
2. Minimal datasets
3. Common-angle image gathers
4. True-amplitude imaging conditions
5. True-amplitude migration as a weighted diffraction stack
6. The Beylkin determinant
7. Migration and illumination
DMO (dip moveout) and PSI (pre-stack imaging)
1. Effects of structure on stacking velocities
2. The DMO concept
3. The DMO equation and DMO impulse response
4. 3D DMO
5. PSI (pre-stack imaging): principle and equations
6. DMO and velocity analysis
7. DMO algorithms
8. DMO and vertically varying velocity functions
9. DMO and related processes: MZO, DZO and AMO
10. DMO and generalized data mapping, inverse DMO and trace interpolation
11. DMO and velocity model building
12. Common-reflection-surface (=CRS) stack
Velocity model building and updating
1. Minimal datasets and common image gathers (CIG’s)
2. Iterative velocity model building with CIG’s (common-offset, common-shot, common-angle)
3. The migration conditions
4. Migration and traveltime inversion
5. Migration and demigration
6. Normal incidence wavefront curvature and stacking velocity
7. Velocity model parameterisation
8. Velocity model building methods:
- Coherency inversion or model based stack
- Map migration
- Dynamic map migration (DMM) or curvature inversion
- Stereotomography
- Traveltime inversion (TTI)
- Tomographic velocity model building
- Traveltime inversion in the migrated domain (TTIMD)
- Depth focusing analysis (DFA)
- Common focus panel (CFP) analysis
- Differential semblance optimisation (DSO)
- Full waveform inversion (FWI)
Anisotropy
1. Introduction and definition of anisotropy
2. The stress tensor, the Voigt form and symmetries
3. Plane wave solutions of the wave equation and the Christoffel equations
4. Phase velocity and Group velocity
5. Relationships between Wave surface and Slowness surface
6. Measurement of group velocity and phase velocity
7. Raytracing, the eiconal equation and the transport equation
8. Shear-wave splitting
9. Definitions pertaining to anisotropy
10. Transverse isotropy (TI):
- Angle dependency of velocities in VTI media
- The Thomsen constants for weakly anisotropic media
- Effective elastic constants for finely layered media
- Crack and fracture properties
- Angle dependency of reflection and transmission coefficients
- HTI media and azimuthal anisotropy
11. Anisotropy from seismic survey design and processing
Multi-component seismic, shear seismic and anisotropy
1. The data matrix
2. Polarization analysis of multi-component seismic
3. Polarization filtering
4. Rotation of sources and receivers
5. Characteristics of P-, SV- and SH waves
6. P-SV converted waves: generation and processing
7. Displacement components of geophones at the free surface
8. The wavefield generated by a vertical and horizontal vibrator
9. P- and S-wavefield separation:
- VSP data
- Surface seismic data
10. Elastic wavefield decomposition at the source and at the receiver
11. Elastic wavefield redatuming and migration
OBC (ocean bottom cable)seismic and OBS (ocean bottom system) seismic
1. OBS and OBC features: 4C data and P-SV characteristics
2. Acquisition:
- Acquisition geometries
- Receiver location determination
- Calibration of the various receivers
3. Processing:
- P-SV data processing
- Wavefield decomposition with various combinations of multi-component receivers
- Demultiple and designature processing
4. Case studies
AVO : Amplitude Versus Offset and AVA : Amplitude Versus Angle
1. Factors affecting seismic amplitudes
2. The boundary conditions
3. Example of normal incidence reflection and transmission
4. Reflection and transmission coefficients - the Zoeppritz equations
5. Approximate expressions for reflection coefficients
6. Reflectivity from logs and AVO modeling
7. Modeling of tuning effects and wavelet stretch
8. Processing for AVO analysis
9. Estimation of AVO parameters
10. Calculation and interpretation of AVO attributes
11. Crossplotting of AVO attributes and AVO classification
12. Elastic inversion based on AVO behaviour
13. Angle stacks and elastic impedance (EI)
Inversion : overview of different methods
1. Linear least-squares estimation
2. Linear least-squares estimation and methods for regularization
3. Damped least-squares estimation with the Marquardt and Levenberg method
4. Singular Value Decomposition (SVD)
5. Resolution matrix and covariance matrix
6. Resolution and reliability
7. Baysian estimation, use of a priori knowledge
8. Iterative linearized least-squares estimation; the Gauss-Newton method
9. Gradient search methods: steepest descent (SD) and conjugate gradient (CG)
10. The Conjugate Gradient (CG) method
11. The Monte Carlo sampling search method
12. The flexible polyhedron search method
13. Simulated annealing (SA)
14. Genetic algorithms (GA)
15. Neural nets (NN)
16. Entropy methods
17. Classification and discrimination methods:
- The self organizing map (SOM)
- Cluster analysis
- Principal component analysis (PCA)
- Gaussian classification
- Discriminant analysis
- Factor analysis (FA)
4D seismic or time-lapse seismic
1. Objectives and feasibility analysis
2. Rock physics
3. Fluid substitution with the Gassmann equation
4. Measurement of traveltime differences and amplitude differences
5. Quantification of repeatibility of acquisition and processing
6. Time lapse data acquisition and time lapse processing
7. Methods to assess the comparison of two datasets
8. Methods for cross-equalization of two datasets
9. 4D modeling of different scenarios
10. The 4D workflow
Seismic-to-Well Matching
1. Model based wavelet estimation
2. Filter design to match different datasets
3. Seismic-to-well matching by relative time shifts and amplitude calibration
4. Reflectivity estimation from well data; the O'Doherty Anstey model
5. Quantitative measures to assess the likeness of two datasets
6. Least-squares seismic wavelet estimation with well data
Seismic Inversion
1. From reflectivity to acoustic impedance (AI)
2. Least-squares estimation
3. Singular value decomposition (SVD)
4. The Resolution matrix and the Covariance matrix
5. Probability theory and the Bayesian approach to inversion
6. Deterministic inversion and Stochastic inversion
7. Elastic inversion and lithologic inversion
8. FWI: full waveform inversion of seismic reflection data
9. Kriging, cokriging and sequential Gaussian simulation (SGS)
10. Classification and discrimination methods
Seismic attributes
1. Introduction to seismic attributes
2. Analytic traces: instantaneous amplitude, - phase, and - frequency
3. Overview of attributes and attribute classification
4. The geometric attributes of dip and azimuth
5. The coherence attribute and the Coherency Cube
6. Curvature and reflector shape
7. Spectral decomposition and the Wavelet transform
8. Structure-oriented filtering and image enhancement
Survey design and assesment of different acquisition geometries
1. Minimal data sets
2. Diffraction tomography
The Lippmann-Schwinger equation and the Born and Rytov approximations
3. The point-spread function (PSF)
4. Survey design, k-spectrum coverage and resolution
5. Generation of subsurface illumination attributes
Borehole geophysics: VSP and hole-to-hole seismic
1. VSP seismic:
- Acquisition geometries; multi-component datasets
- Wavefield separation: P-waves and S-waves; Upgoing- and Downgoing waves
- Deconvolution
- Migration
- VSP data matching to surface seismic and to well data
2. Hole-to-hole seismic:
- Data acquisition
- Cross-well wavefield separation
- The projection slice theorem and image reconstruction
- Traveltime tomography: ART-, SIRT alhgorithms and the Radon transform
- Diffraction tomography, k-space coverage and imaging
- Migration
- Borehole waves
