# Amplitude -> E_gauss, E_mean, E_max_azimuth, and E_min_azimuth

**Attribute Description:** The E_pos and E_neg attributes are measures of the most-positive and most-negative curvature anomalies, whereas the E_max and E_min attributes correspond to the maximum and minimum curvature anomalies.

**Interpretation Use:** The E_pos, E_neg, E_max, and E_min attributes correspond to the maximum and minimum curvature anomalies. These attributes capture geologic information in the form of the second derivative of the amplitude behavior of seismic data. They can be used to identify stratigraphic features, faults, and fractures (Chopra and Marfurt, 2007; Chopra and Marfurt, 2013). Attribute results are better analyzed in plan view or draped over a horizon displays.

**Recommended color palette:** For the E_pos and E_neg attributes a divergent color scheme is suggested. The midpoint color is white to emphasize the progression outward two different dark hues. In the examples below, the dark hues were set to blue and red to better highlight geologic features. We suggest using the histogram of values to guide setting color value thresholds.

**Examples:**

**Recommended color palette:** For the E_max and E_min attributes, a divergent color scheme is suggested. The midpoint color is white to emphasize the progression outward two different dark hues. In the examples below, the dark hues were set to blue and red to better highlight geologic features. We suggest using the histogram of values to guide setting color value thresholds.** **

**Examples:**

**Computation:** The E_max, E_min, E_pos, and E_neg attributes use seismic amplitude data (time or depth domain). Unlike to structural curvature attributes that measure the changes in the dip in *m/m* or *ft/ft*, the amplitude curvature attributes to measure the dip in *mV2/m* or *mV2/ft* (assuming the amplitude is measured in *mV* [milli-volts]). Figure 1 shows the definition of 3D shapes expressed as a function of the most-positive curvature (E_pos) and the most-negative curvature (E_neg):

Then, the computation process uses this workflow:

Input data → Estimates of reflector dip → Estimates of coherent energy gradients through measurements of similarity → Curvature amplitude data

It can be summarized as follows (AASPI documentation):

- Take the Inline Dip, Crossline Dip, and seismic amplitude volumes as input data (refer to Filter Dip Components → Inline Dip, Crossline Dip, and Confidence attribute description section)
- Run a similarity computation (refer to Similarity attributes description section).
- Computing the covariance matrix from the complex trace signal
- Decomposing the covariance matrix into its corresponding
*kth*eigenvalue and*vth*eigenvectors. Then normalize the eigenvectors to be unit length - Estimating a scaled principal component, where the scale is the inner product or correlation of the eigenvector
- Generate estimates of inline and crossline coherent energy gradient
- Use the inline and crossline energy gradients to solve the coefficients of the quadratic surface:

and,

- Then, the E_max and E_min attributes are generated using the following relationships (AASPI documentation):

**References**

- AASPI documentation, http://mcee.ou.edu/aaspi/documentation/Volumetric_Attributes-curvature3d.pdf
- Chopra, S. and K. J. Marfurt, 2007, Seismic attributes for prospect identification and reservoir characterization: SEG Geophysical development series,
**11**, 110 – 111. - Chopra, S. and K. J. Marfurt, 2013, Structural curvature versus amplitude curvature: The Leading Edge,
**32**, 178 – 184.