Dictionary:Second time derivative of the trace envelope

{{#category_index:T|Second time derivative of the trace envelope}} 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.

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

$E(t)$ is the trace envelope while, $*$ denotes convolution and $diff(t)$ 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.