# Dictionary:Trace envelope

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The trace envelope is a seismic attribute, also known as instantaneous amplitude, is a representation of the amplitude ${\displaystyle E(t)}$ of an oscillatory function ${\displaystyle f(t)}$. The quantity ${\displaystyle E(t)}$ is of the same order as the absolute value of the amplitudes of the function. Instantaneous amplitude varies approximately between 0 and the absolute value of the maximum amplitude of the trace.

The envelope of seismic signals is independent of the phase and may be related directly to a variety of other trace attributes. The trace envelope of a seismic signal may represent the individual interface contrast or, the combined response of several interfaces, depending on the seismic bandwidth.[1]

The instantaneous amplitude of a seismic trace is related to a form of the trace called the analytic trace, which is the representation of the original seismic trace ${\displaystyle f(t)}$ as a complex-valued function ${\displaystyle s(t)}$. Thus the trace amplitude is given by the modulus at each time ${\displaystyle t}$

${\displaystyle E(t)={\sqrt {({\mbox{Re }}s(t))^{2}+({\mbox{Im }}s(t))^{2}}}}$

.

Here, the real part of the analytic trace ${\displaystyle {\mbox{Re }}s(t)}$, is just the original seismic trace ${\displaystyle f(t)}$. The imaginary part ${\displaystyle {\mbox{Im }}s(t)}$, also called the quadrature trace, is computed by taking the Hilbert transform of ${\displaystyle {\mbox{Re }}s(t)}$.

The trace envelope is a physical attribute and can be used as an effective discriminator for the following characteristics:

• Is proportional to the the acoustic impedance contrast, hence is related to reflectivity
• Bright Spots
• Possible gas accumulation
• Sequence boundaries
• Thin-bed tuning effects
• Unconformities
• Major changes in lithology
• Major changes in depositional environment
• Lateral changes indicating faulting
• Spatial correlation to porosity and other lithologic variations.

## References

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