# Dictionary:First time derivative of the trace envelope

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The first time derivative of the trace envelope is a seismic attribute. Calculated as the time rate of change of the envelope and shows the variation of the energy of the reflected events. The derivative computed at the onset of the events shows the absorption effects, a slower rise indicates larger absorption effects. A slower rise indicates larger absorption effects. The first time derivative of the envelope can be calculated by:[1]

${\displaystyle {\frac {dE(t)}{dt}}=E(t)*diff(t)}$

${\displaystyle E(t)}$ is the trace envelope while, ${\displaystyle *}$ denotes convolution and ${\displaystyle diff(t)}$ is the differential operator. Events with a sharp relative rise also imply a wider bandwidth, hence less absorption effects. This is a physical attribute and points to acknowledge when working with the rate of change of the envelope are:

• Sharpness of the rise time relates to absorption in an inversely proportional manner
• It is affected by the slope, rather than envelope magnitude
• Lateral variation shows discontinuities.

## References

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