# Dictionary:Second time derivative of the trace envelope

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The second derivative of the envelope is a seismic attribute and gives a measure of sharpness of the envelope peak, which may be more useful as a principal attribute display. In black and white displays, it shows all peaks of the envelope, this corresponds to all of the reflecting interfaces visible within the seismic bandwidth. [1]

${\displaystyle {\frac {d^{2}E(t)}{dt^{2}}}=E(t)*diff(t)*diff(t)}$

${\displaystyle E(t)}$ is the trace envelope while, ${\displaystyle *}$ denotes convolution and ${\displaystyle diff(t)}$ is the differential operator. Characteristics of the second derivative of the envelope include:

• Shows all reflecting interfaces visible within seismic band-width.
• Shows sharpness of events.
• Indicates sharp changes of lithology.
• Large changes of the depositional environment, even when the corresponding envelope amplitude may be low.
• Very good presentation of the image of the subsurface within the seismic band-width.

## References

1. Taner, Turhan (1992), Attributes Revisited, Rock Solid Images Houston, Texas (published 2000)