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

Envelope Second Derivative

Attribute Description: Envelope Second Derivative gives a measure of sharpness of the envelope peak, which may be more useful as a principal attribute display. In black and white, it shows all peaks of the envelope, which corresponds to all the reflecting interfaces detectable within the seismic bandwidth.

Interpretation Use:  This attribute may provide value because it:

  • Shows the reflecting interfaces visible within the seismic bandwidth.
  • Shows the sharpness of each event.
  • Indicates changes in the lithology.
  • Shows the large changes of the depositional environment, even though the corresponding envelope amplitude may be small.
  • Is a good representative image of the subsurface within the seismic bandwidth

Recommended Colorbar: 

Since the distribution of this data is Gaussian in nature, a standard seismic colorbar can work.

In this example, we are using a Standard White - Black colorbar giving a standard seismic look and feel. The higher amplitudes show the sharper events in the positive realm while the negative values show those events in the envelope minima. 

 Example Colorbar

Example Colorbar

Example:

 Vertical display of Envelope Second Derivative

Vertical display of Envelope Second Derivative

 Time slice of Envelope Second Derivative

Time slice of Envelope Second Derivative

 Frequency Spectrum

Frequency Spectrum

Computation: 

This is the second derivative of the envelope, the envelope being the modulus of the complex function, with the analytic trace defined as the real part of the trace f(t) and the imaginary part of the complex trace g(t):

Envelope Second Derivative - 5.png

The envelope is the modulus of the complex trace function:

Envelope Second Derivative - 6.png

This is the second derivative of the Envelope:

Envelope Second Derivative - 7.png

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.