# Inline Dip, Crossline Dip, and Confidence

**Attributes Description:** The Inline dip and Crossline dip attributes are estimates of dip components along inline and crossline directions. Since the dip estimates are done using a multi-window search, the Confidence attribute is the semblance of the window with the maximum coherence.

**Interpretation Use:** The Inline and Crossline Dip attributes help to improve the estimation of seismic reflector dip and azimuth. These attributes can be used to delineate structural and stratigraphic features. Additionally, the Confidence attribute can be used similarly to a coherence attribute. It can highlight the presence of faults, lineaments, or subtle structural and stratigraphic features (Chopra and Marfurt, 2007). Attribute results are better analyzed in plan view or draped over a horizon display.

**Recommended color palette:** For the Inline Dip, Crossline Dip, and Confidence attributes a grayscale gradient color scheme is suggested. The color progression could begin with white (to highlight useful geological features) and finish with black (to denote shadow areas), or vice-versa. We suggest using the histogram of values to guide setting color value thresholds.

**Examples**

**Computation:** The Inline Dip, Crossline Dip, and Confidence attributes use seismic amplitude data (time or depth domain) as input. The Inline and Crossline Dip attributes are pre-requisites for almost all subsequent AASPI structural attribute computations as they offer an improved basis for edge detection, structural filtering, and volumetric estimates of curvatures (AASPI documentation).

To estimate the apparent angle dips θx and θy of a hypothetical planar 3-D reflection event, a Kuwahara multi-window dip-search algorithm is used (Figure 1). The algorithm avoids smearing dip estimates across faults and angular unconformities by scanning a suite of non-centered, overlapping analysis windows in addition to the centered one, all of which contain the analysis point of interest (Luo et al., 2002).

Then, the window with the maximum coherence is chosen. This, in turn, will provide the best estimates of the inline and crossline dip components, as well for the semblance attribute.

Therefore, the Confidence attribute is computed by fitting a quadratic surface through the semblance values at the neighboring apparent dip pairs θx and θy:

and solve for the coefficients αj in the least square sense (Marfurt, 2006). Then, the estimation of the apparent dips is done by solving,

and

Note that in the presence of noisy input data, the following structure-oriented filters can be also applied prior to computing the Inline Dip, Crossline Dip, and Confidence attributes: i) Lower-Upper-Middle (LUM), ii) Multistage Median-based Modified Trimmed-Mean (MSMTM), iii) Alpha-Trimmed Mean, and iv) Mean. Note that this filter option is turned off by default in Paradise. The structured-oriented filters are given by:

- Lum Filtered Data. The Lum filter calculates the median by the following steps (Al-Dossary and Marfurt, 2007):
- Sort the samples in the window of analysis as shown above for the case α = 0.5. Then, the user defines lower and upper order statistics
- Compare the value of the center sample of the window dc with these two order statistics. To smooth the output, the process takes the median of the lower order (d(k)), upper order ((d(N-k+1))), and the center sample:

- Multistage median-based Modified Trimmed-mean (MSMTM). It is a combination of the modified trimmed mean filter with a detail preserving filter (Al-Dossary and Marfurt, 2007). The MSMTM is computer as follows:
- Sample sare selected if they are in the range where q is a threshold value and dMSM is the multistage median filter consisting of four median filters (Chopra and Marfurt, 2007)
- The result of the filter is the average of the selected samples

- Alpha-Trimmed Mean. For all J samples falling within a window of analysis, the alpha-trimmed mean is given by (Al-Dossary and Marfurt, 2007):

where the Eq. 6 is replaced by the median filter . In this case, the samples are ordered using index *k* (e.g., ). If α = 0, the Eq. 6 is replaced by the mean filter

- Mean. The filter is a running sum window that outputs the average of all the samples that fall within an analysis window at its center (Al-Dossary and Marfurt, 2007):

**References**

- AASPI Documentation, http://mcee.ou.edu/aaspi/documentation/Volumetric_Attributes-filter_dip_components.pdf
- Al-Dossary, S., and K. J. Marfurt, 2007, Lineament-preserving filtering: Geophysics,
**72**, P1 – P8. - Chopra, S. and K. J. Marfurt, 2007, Seismic attributes for prospect identification and reservoir characterization: SEG Geophysical development series,
**11**, 187 – 218. - Luo, Y., W. G. Higgs, and W. S. Kowalik, 2002, Edge-preserving smoothing and applications: The Leading Edge,
**21**, 136 – 158. - Marfurt, K., 2006, Robust estimates of 3D reflector dip and azimuth: Geophysics,
**71**, P29 – P40.