Content of topics in seismic - and advanced seismic data processing

Stress-strain relationships and Elastic constants

1. Deformation and the strain tensor

2. 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

Rock physics

1. Vp-Vs relationships for different lithologies

2. Vp-density relationships for different lithologies

3. Effective media expressions for different elastic constants

4. The Gassmann equation for the calculation of the effect of fluid substitution

5. Rock physics models and workflows

The wave equation

1. The acoustic wave equation

      - The acoustic wave equation

      - The reciprocity theorem

      - The integral representation of the acoustic wavefield - the Kirchhoff integral

      - 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, reflection and transmission and the Zoeppritz equations

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


1. The convolutional seismic trace model

2. Digital convolution in matrix notation

3. Deconvolution: definition of inverse-, spiking- or whitening filter

4. Examples:

      - reverberation - dereverberation

      - ghost - deghosting

      - absorption - deabsorption

5. Resolution: signal dispersion as a function of amplitude and phase spectrum

6. The Z-transform, polynomials and factorization

7. Minimum-phase, mixed-phase and maximum-phase wavelets

8. The inverse filter of a two-point wavelet

9. The inverse filter of an arbitrary wavelet

10. Minimum-phase wavelets: properties in the different domains

11. Least-squares (ls) filters:

      - the normal equations

      - ls inverse filters

      - ls prediction- and ls prediction error filters

12. Least-squares filters in the frequency domain: design and properties

13. Two-sided filters: design and properties

14. Filtering in the presence of noise

15. 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

      - deghosting of data of over-under acquisition, dual-sensor streamer data and variable-depth streamer data

Velocity analysis

1. Definitions of various types of velocity

2. Traveltime expressions for paraxial rays

3. Expressions for stacking velocities for 3D seismic (= azimuth dependent)

4. Stacking velocity and the curvature of the wavefront associated with the normal-incidence ray

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 (FAs)

3. Modeling the near surface from FAs - refraction/turning ray tomography

4. Methods for picking reflections

5. The residual statics equation and its solution

6. Statics coupling

7. Stackpower optimization with static corrections via Simulated annealing

8. Redatuming

Multiple elimination

1. Characterisation of multiples

2. Spiking deconvolution or Predictive gapped deconvolution:

      - in the (t,x)-domain

      - in the slant stack or linear Radon-transform domain

3. Multiple elimination based on differences in moveout between primaries and multiples:

      - straight stack

      - weighted stack

      - (k,f)-transform domain filtering

      - velocity stack

      - parabolic Radon-transform domain filtering

      - adaptive beamforming

4. Multiple elimination of OBC data by combining 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

      - the convolution method

      - the recursive method

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. Structure enhancing filtering

11. Velocity filters (pie-slice filter or fan filter)

12. Methods for ground roll filtering

13. Arrays: field arrays and digital group forming (DGF)

14. Data regularization and trace interpolation


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, the point-spread function (PSF) 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. Wavefront curvature associated with normal-incidence rays 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)

      - Traveltime inversion in the migrated domain (TTIMD)

      - Common focus panel (CFP) analysis

      - Tomographic velocity model building

      - Depth focusing analysis (DFA)

      - Extended imaging conditions and Wave equation migration velocity analysis (WEMVA)

      - Differential semblance optimisation (DSO)

      - Full-waveform inversion (FWI)


1. Introduction and definition of anisotropy

2. The stress tensor, symmetries and the Voigt notation

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 (vertical axis of symmetry)

      - The Thomsen constants for weakly anisotropic media

      - Effective elastic constants for finely layered media - Backus averaging

      - Crack and fracture properties

      - Angle dependency of reflection and transmission coefficients

      - HTI media and azimuthal anisotropy (horizontal axis of symmetry)

      - TTI media (tilted axis of symmetry)

11. Anisotropy from seismic survey design and processing

Multi-component seismic, shear seismic and anisotropy

1. The data matrix

2. Sources and receivers for multi-component seismic data acquisition

3. Polarization analysis of multi-component seismic - hodograms

4. Polarization filtering

5. Rotation of sources and receivers

6. Characteristics of P-, SV- and SH waves

7. P-SV converted waves: generation and processing

8. Displacement components of geophones at the free surface

9. The wavefield generated by a vertical and a horizontal vibrator

10. P- and S-wavefield separation:

      - VSP data

      - Surface seismic data

11. Elastic wavefield decomposition at the source and at the receiver

12. 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. Geophysical advantages of wide-azimuth OBC/OBS data

3. Acquisition:

      - Acquisition geometries

      - Receiver location determination

      - Calibration of the various receivers

4. Processing:

      - P-SV data processing

      - Deghosting and dereverberation processing

      - Wavefield decomposition with various combinations of multi-component receivers

5. Case studies

6. Dual-sensor streamer data and SWIM (= separated wavefield imaging)

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 the 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) with its applications

Inversion : overview of different methods

1. Linear least-squares estimation

2. Singular Value Decomposition (SVD)

3. Resolution and reliability: resolution matrix and covariance matrix

4. Baysian estimation, use of a priori knowledge

5. Linear least-squares estimation and methods for regularization

6. Iterative linearized least-squares estimation:

      - Gradient search or Steepest descent (SD)

      - Newton's method

      - Gauss-Newton method

      - Conjugate Gradient method (CG)

7. The Monte Carlo sampling search method

8. The flexible polyhedron search method

9. Simulated annealing (SA)

10. Genetic algorithms (GA)

11. Neural nets (NN)

12. Entropy methods

13. Neighborhood algorithm (NA)

14. Particle swarm optimization (PSO)

4D seismic or time-lapse seismic

1. Introduction and examples

2. Rock physics and fluid substitution with the Gassmann equation

3. Modeling of 4D effects and feasibility analysis

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

11. Case studies

Seismic-to-Well Matching

1. Acoustic impedance (AI), reflectivity and the convolutional trace model

2. Resolution and bandwidth

3. Reflectivity estimation from well data and seismic modeling

4. Model based wavelet estimation

5. Filter design to match different datasets

6. Using well data to calibrate seismic data

7. Methods for seismic-to-well matching with:

      - matched filter

      - time-shift and scaling

      - time-shift, scaling and phase rotation

      - least-squares (Wiener) filter

8. Least-squares seismic wavelet estimation with well data

9. Industry packages for seismic-to-well matching

Seismic Inversion

1. From reflectivity to acoustic impedance (AI) and vice versa

2. Consequences of the bandlimitation of the seismic data and the importance of low frequencies

3. Least-squares estimation

4. Singular value decomposition (SVD)

5. The Resolution matrix and the Covariance matrix

6. Probability theory and the Bayesian approach to inversion

7. Deterministic inversion and Stochastic inversion

8. Markov chain Monte Carlo (MCMC) sampling of model space

9. Elastic inversion and lithologic inversion

10. FWI: full waveform inversion of seismic reflection data

11. Kriging, cokriging and sequential Gaussian simulation (SGS)

12. Classification and discrimination methods:

      - Cluster analysis

      - k-means clustering

      - Factor analysis (FA)

      - Principal component analysis (PCA)

      - Gaussian classification

      - Discriminant analysis

      - The self organizing map (SOM)

      - Multi-variate statistical analysis

      - Neural net reservoir characterization

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