# Dictionary:Trace envelope

The trace envelope is a seismic attribute, also known as *instantaneous amplitude,* is a representation of the
amplitude **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle E(t) }**
of an oscillatory function **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f(t) }**
. The quantity **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\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 **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f(t) }**
as a complex-valued function **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle s(t) }**
. Thus the trace amplitude is given by
the modulus at each time **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle t }**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle E(t) = \sqrt{ (\mbox{Re } s(t))^2 + (\mbox{Im } s(t))^2 }}**

.

Here, the real part of the analytic trace **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \mbox{Re } s(t) }**
, is just the original seismic trace **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f(t) }**
.
The imaginary part **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \mbox{Im } s(t) }**
, also called the *quadrature trace,* is computed by taking the *Hilbert transform* of **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\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

- ↑ Taner, Turhan (1992), Attributes Revisited, Rock Solid Images Houston, Texas (published 2000)