Processing, Inversion and Reconstruction of Seismic Data

M.D. Sacchi

This course covers practical aspects of signal theory and inverse problems with application to seismic data processing. In particular, the course stresses regularization methods for inverse problems that arise in the inversion of seismic data, noise elimination and reconstruction of seismic surveys. The course is intended for geophysicists working in data processing, R&D, and for people with interest in understanding current and emerging technologies for seismic data processing. Please contact the instructor for more information.


Two days

Intended Audience


Prerequisites (Knowledge/Experience/Education Required)

Basic knowledge of Linear Algebra and Digital Signal Processing.

Course Outline

  1. Review of DSP and deconvolution
    1. Fourier transform, properties, symmetries, FT of simple signals
    2. Discrete signals, aliasing, DFT, IDFT
    3. Linear systems, invariance, convolution, z-transform
    4. Dipoles, min and max phase signals, inversion of dipoles
    5. Spectral response of simple signals and spectral decomposition
  2. Design of inverse filters
    1. Design of least squares inverse filters
    2. Wavelet inversion and wavelet shaping
    3. Pre-whitening and optimum lag
    4. Resolution/noise amplification trade-off
    5. White reflectivity assumption and wavelet estimation
    6. Blind deconvolution
    7. Minimum entropy
    8. Maximum kurtosis
  3. Reflectivity and impedance inversion
    1. Post-stack inversion
    2. Retrieval of full band-reflectivity sequences via sparsity constraints
    3. Impedance constraints
    4. Pre-stack inversion
    5. AVO as multi-channel deconvolution problem
    6. More advanced pre-stack inversion
      • Working with operators
      • Matrix-free methods and Conjugate Gradients
      • Least-squares migration
  4. SNR enhancement
    1. Signal model in the FX domain
    2. FX prediction filters and projection filters
    3. Radon Transforms
      • Linear, parabolic, hyperbolic Radon Transforms
      • Local Radon Transforms and connection to Curvelets
    4. High Resolution Radon Transforms
    5. Seismic signal enhancement via Rank-Reduction methods
      • TX and FX eigenimages
      • Cadzow filters and Multichannel Singular Spectrum Analysis
  5. Interpolation and Data reconstruction
    1. FX and FK interpolation
    2. Multidimensional Sampling
    3. Fourier Regularization Methods
      • Minimum Weighted Norm Fourier reconstruction
      • Sparseness constraints for Fourier reconstruction
      • Antileakage Fourier Transform
      • Reconstruction methods that use matching pursuit
      • Projection onto convex sets reconstruction
    4. Reduced rank reconstruction
      • Cadzow/MSSA reconstruction methods
      • Tensor Completions Methods (HO-SVD, Parallel Matrix Factorization)
    5. Compressive sensing and new paradigms

Learner Outcomes

  • Develop the signal analysis framework required to process seismic data and access current data processing technologies used for seismic exploration
  • Distinguish deconvolution techniques for minimum and non-minimum phase wavelets
  • Recognize the importance of seismic deconvolution and inversion methods in the construction of seismic volumes for interpretation of the subsurface
  • Identify algorithms that are required to attenuate seismic noise, improve resolution and estimate earth models
  • Identity the assumptions made by different algorithms and potential pitfalls associated to not honoring basic assumptions
  • Recognize the role of inverse theory at the time of designing methodologies for noise attenuation and seismic data reconstruction
  • Identify methodologies for seismic data reconstruction in the case of irregularly sampled surveys. Recognize that at the core of any interpolation/reconstruction method there is a simple signal model
  • Use linear inverse theory and tools from signal analysis to develop algorithms for data reconstruction, deconvolution, inversion, and noise attenuation
  • Recognize efficient methods for solving transform-based seismic de-noising and reconstruction problems
  • Analyze new paradigms in signal analysis including modern methods for data analysis based on compressive sampling

Instructor Biography

M.D. Sacchi