Dr. Tom Smith presenting on Machine Learning at the 3D Seismic Symposium on March 6th in Denver
What is the "holy grail" of Machine Learning in seismic interpretation? by Dr. Tom Smith, GSH Luncheon 2018
Using Attributes to Interpret the Environment of Deposition - A Video Course. Taught by Kurt Marfurt, Rocky Roden, and ChingWen Chen
Dr. Kurt Marfurt and Dr. Tom Smith featured in the July edition of AOGR on Machine Learning and Multi-Attribute Analysis
Rocky Roden and Ching Wen Chen in May edition of First Break - Interpretation of DHI Characteristics using Machine Learning

Instantaneous Frequency

Instantaneous Frequency (Hz) is the rate of change of phase over time. While individual vectors may rotate in a clockwise motion, their resultant vector may at some instances form a cardioid pattern and appear to turn in the opposite direction. This is interpreted as the effect of interference of two closely arriving wavelets. This is also caused by noise interference in low amplitude zones. Because of these reversals, the instantaneous frequency will have unusual magnitudes and fluctuations.

Since instantaneous frequencies are influenced by the bed thickness, it is best to observe them without too much interference. This is accomplished by using several adjacent traces to form a consistent output. It has been shown that instantaneous frequency, computed as the time derivative of instantaneous phase, relates to the centroid of the power spectrum of the seismic wavelet.

Instantaneous frequencies relate the wave propagation and depositional environment; hence they are physical attributes and they can be used as effective discriminators.

Interpretation Use:

  • Corresponds to the average frequency (centroid) of the amplitude spectrum of the seismic wavelet
  • Seismic character correlator
  • Indicates the edges of low impedance thin beds.
  • Hydrocarbon indicator by low-frequency anomaly. The unconsolidated sands, due to the oil content of the pores, sometimes accentuate this effect.
  • Fracture zone indicator appears as low-frequency zones
  • Chaotic reflection zone indicator
  • Bed thickness indicator. Higher frequencies indicate sharp interfaces or thin shale bedding; lower frequencies indicate sand rich bedding
  • Sand/shale ratio indicator

Recommended Colorbar:

This attribute usually has a Gaussian distribution centering around a dominant frequency.  Using a lighter color for the dominant frequency will allow highlighting of lower and higher frequencies if desired.  Often bands of colors can be used to highlight specific ranges.

  Example colorbar and amplitude spectrum

Example colorbar and amplitude spectrum

Example: 

 Vertical display of Instantaneous Frequency

Vertical display of Instantaneous Frequency

 Time slice of Instantaneous Frequency

Time slice of Instantaneous Frequency

 Frequency Spectrum

Frequency Spectrum

Computation: 

Instantaneous Frequency (Hz) is the rate of change of phase over time:

Inst Frequency - 05.png

Since the phase function is multi-valued with 2π jumps, the instantaneous frequency is actually computed as the derivative of the arctangent function, which avoids the 2π discontinuities. 

References:

  • Chopra, S. and K. J. Marfurt, 2007, Seismic attributes for prospect identification and reservoir characterization:  Society of Exploration Geophysicists, Geophysical Developments #11.
  • Taner, M. T., 2001, Seismic attributes:  Canadian Society of Exploration Geophysicists Recorder, 26, no 7.