Geophysical Applications of Time-Frequency Analysis

by Marcílio Matos

Duration:
Two days

Intended Audience: All levels

Prerequisites (Knowledge/Experience/Education Required): The course is designed to be followed by anyone with a broad geoscience background. Although mathematics is kept to a minimum, some understanding of signal analysis will be useful.

Summary:
This course shows how basic knowledge of joint time-frequency (JTF) analysis theory associated with pseudo computer programming can help geoscientists to take full advantage of their real world applications. Several JTF exploration geophysics applications are detailed, like spectral decomposition, data compression, filtering, etc. Starting from Fourier theory review, advanced time-frequency techniques are introduced by showing practical applications and by hands on introductory computer programming.

Course Outline:

  • Introduction.
  • Reading exploration geophysics data as computer matrices. SEGY and LAS file examples.
  • Signal processing and Discrete Fourier Transform review. Applications: Computing spectra, the effect of data windowing, conventional bandpass vs. wavelet-based filtering, footprint suppression on time slices, spectral balancing and spectral decomposition. Hands-on FFT computation using MS Excel spreadsheets and scripting languages.
  • Complex seismic trace analysis. Hilbert transform review. Instantaneous seismic attribute applications. Phase unwrapping and relative geologic time. Hands-on coding: instantaneous frequency, unwrapped phase and phase discontinuities.
  • Sliding window Fourier transform and Gabor Transform. Applications and hands-on coding: extending spectral decomposition to the whole 3D volume.
  • Improving interpretation using advanced JTF techniques like Wavelet Transform, S-transform, Curvelets, Wigner-Ville, Empirical mode decomposition, Hilbert-Huang transform, Least square spectral analysis, Local attributes, Matching Pursuit, etc. Hands-on coding examples.
  • JTF exploration geophysics applications: Data compression, Q compensation, data conditioning, texture analysis, facies classification, pre-stack attributes, etc.
  • Conclusions, discussions and suggestions.
  • Course attendees will receive a DVD or a USB flash drive that includes the class handouts, the code examples and data. Participants are encouraged to bring their laptops. The practical hands-on examples and exercises are in GNU Octave/Matlab (octave.org) and Python (python.org) scripting languages.

Learner Outcomes:

  • Demonstrate the use of joint time-frequency spectrum to identify thin bed tuning due to changes in stratigraphic thickness, anomalous attenuation due to rugosity or absorption, and anomalous phase changes associated with structural styles.
  • Optimize your parameter selection when using commercial spectral decomposition software packages.
  • Recognize artifacts in spectral interpretation, including the effects of window size, structural dip.
  • Use joint time-frequency techniques to attenuate random and coherent noise.
  • Quantify the assumptions and potential value of emerging JTF geophysical applications including Q compensation, uniformity delineation, and phase unwrapping for stratigraphic interpretation.
  • Employ a new interpretation mindset when interpreting depth-migrated rather than time migrated data for changes in dip and wavelength.

Instructor Biography:
Marcílio Matos