Chapter 2
Seismic Modeling

This chapter presents information about seismic modeling. Topics range from why we perform modeling in the first place through a brief overview of the mathematics involved in several different types of modeling.

  Primary Concerns
  Three Earth Models
   Acoustic or Fluid
   Isotropic Elastic
   Anisotropic
   Summary
  Seismic Acquisition: The Basic Idea
  Why Model?
   Determining Reflector Location
   Geologic Complexity
   Hypothesis Testing
   Acquisition
  Waves and Wavefields
  The Scalar Wave Equations
   The 1-D Scalar Wave Equation
   Scalar Wave Equation in Higher Dimensions
   Pressure Formulation
  Stress-Strain Equations
   Symmetry
   Acoustic
   Isotropic Elastic
   Vertical Transverse Isotropy (VTI)
   Polar Isotropy
   Orthorhombic Isotropy
   Thomsen Parameters
  Algorithms
  Variational Formulation and Finite Elements
   An Old Movie
  Finite Differences
   Polynomial Differences
   Taylor Series Differences
   Second Order Differences
   High Order Differences
   Finite Differences for the Pressure Formulation
   Graphical Descriptions
   Lax-Wendroff Method
   Elastic Finite Differences
   Staggered Grids
   Predictor-Corrector Schemes
   Splitting
   Propagation Stability
  Model Boundaries
   Free Surface
   Non Free Surface
   FEM versus FDM Differences
   Two-Way Implicit Modeling
   One-Way Modeling
   One Way Implicit Finite Difference
  Fourier Based Methods
   FX Finite Difference
   Pseudo-Spectral Methods
   Constant Velocity FK Modeling
   Phase-Shift Modeling
   Phase Shift Plus Interpolation (PSPI) Modeling
   Dual Domain or FKX One-Way Methods
   Split-Step
   Extended Split Step
   Higher Order FKX Methods
  A Word About Sources
   Compressional and Shear Point Sources
   Plane Wave Sources
  Huygens Principle and Integral Methods
   Scattering
  Raytracing
  Raytrace Modeling
  Zero Offset Modeling
 
Introduction
Seismic Modeling
History
Zero Offset Migration Algorithms
Exploding Reflector Examples
Prestack Migration
Prestack Migration Examples
Data Acquisition
Migration Summary
Isotropic Velocity Analysis
Anisotropic Velocity Analysis
Case Studies
Course Summary