Outline1

Seismic Exploration Methods - EAS 8803 - FH

General introduction

Basic seismic data processing

  • Explanation of the seismic method
  • Seismic acquisition, different gathers, basics land and marine acquisition
  • Post-stack seismic-data processing flow to create a seismic image:
    • Common-midpoint sorting
    • Normal-moveout correction
    • Stack
    • Zero-offset migration
  • Time-to-depth conversion
  • Time or depth migration
  • Drawbacks of post-stack processing
  • Intro pre-stack migration and velocity analysis

Wavefield extrapolation, pre-stack migration, and velocity analysis

  • Wavefield extrapolation via Rayleigh II
  • Wavefield extrapolation via the f-k domain
  • (V(z)) migration
  • Shot record migration
  • Recursive extrapolation in varying media
  • Pre-stack shot migration
  • One-way wave-equation migration
  • Reverse-time migration
  • Velocity-model estimation
    • Traveltime tomography
    • migration-velocity analysis

Filtering

  • f-k filtering
  • Radon filtering
    • Linear Radon
    • Multiple-removal via parabolic Radon transform
    • Parabolic versus hyperbolic Radon
  • Deconvolution

Seismic data acquisition

  • Marine acquisition
  • Challenges of 3D acquisition
  • Wide-azimuth marine acquisition
  • Coil sampling

From processing to inversion

  • General Forward problem
  • Linear Forward problem
  • Forward and inverse problems nonlinear and linear
  • Strict inverse for invertible matrices
  • When inverse does not exist
  • Least-squares solution by setting gradient least-squares solution to zero
  • Inverse for non-unique problems including definition of non-uniqueness
  • Minimum-norm solution
  • Definition of transpose and adjoint of a matrix, unitary matrices
  • SVD
  • Nullspaces
  • Non-null and null spaces in terms of SVD
  • Pseudo/generalized inverses
  • Four cases of pseudo inverse
  • Over and underdermined problems noise free and noisy
  • Inverse and pseudo inverses from http://en.wikipedia.org/wiki/Fundamental_theorem_of_linear_algebra
  • Condition number ill and well conditioned
  • truncated SVD
  • Regularization
  • Conditions for well-posed problems
  • Least-squares and damped least-squares inversion
  • Tikhonov regularization + LS solution
  • Pseudo inverse and regularization
  • Deconvolution as an inversion problem (‘matrix inverse’)
  • Forward operator for NMO and least-squares NMO
  • Removing multiples by high-resolution Radon transform

Compressive sensing

  • Nyquist sampling and aliasing
  • Exploiting structure is seismic data by transform-domain sparsity promotion
  • Basics of Compressive Sensing
  • Design principles of Compressive Sensing
  • Application of Compressive Sensing to Exploration Seismology
  • Jittered sampling of shots
  • Simultaneous ‘land’ acquisition by summing randomly weighted shots
  • Simultaneous ‘marine’ acquisition with time-dithered sources

Linearized inversion

  • Introduction linearized amplitude versus offset/angle inversion
  • Linearization of the reflection and transmission coefficients w.r.t. contrasts in density, compressional, and shear wavespeeds.
  • Convolutional model for seismic reflectivity
  • Relation between amplitudes of seismic data in the Radon domain and the linearized reflection coefficient.
  • Practical workflow for linearized inversion of amplitude-versus-offset data.

RTM & FWI

  • Basics of reverse-time migration (RTM) and full-waveform inversion (FWI) via the adjoint state method from physical and mathematical perspectives
  • Derivation of expressions for the Jabobian and its adjoint
  • Migration as the gradient of FWI
  • Least-squares migration as the Gauss-Newton Hessian of FWI
  • FWI with gradient descents
  • FWI with Gauss-Newton
  • Latest developments

Footnotes

  1. This outline is subject to change throughout the semester. We will try to keep these updates to a minimum. ↩︎

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