Extrema classification

Fig. 5. Extrema class indexes are extracted along a horizon interpretation, where the extrema classification was run with two (left), four (center) and seven (right) attributes. Each color represents one class, and the white regions are fault zones void of horizon interpretation.

Fig. 6. A set of horizon patches is extracted from a seismic cube using extrema classification. The patches belong to three different classes, assigned three different gray scale colors, and are drawn as 3D surfaces expanding out from a vertical seismic cross section.

Fig. 7. The figure compares an existing seismic horizon interpretation (left) with the corresponding interpretation obtained using extrema classification (center). White regions are fault zones void of horizon interpretation. The absolute value of the difference between the two interpretations (right) is mainly within 0.5 sample.

The unsupervised extrema classification method (Subsection 4.3) has been applied to automatically extract an overburden horizon from a North Sea field, offshore Norway. The extrema classification was applied within a sub-... 

Fig. 8. A seismic horizon extracted using extrema classification is marked (dashed line) on a vertical cross section through the seismic cube.

In the following example unsupervised extrema classification (Subsection 4.3) is applied to map the extent of high amplitude anomalies observed within an overburden formation in a North Sea field, offshore Norway. The anomalies are interpreted to represent volumes of ancient gas stored within a chaimel and moraine system in the formation. The top and base of the formation is interpreted manually in advance, and the extrema classification is rim in a seismic sub-volume confined by these two interpretations. The sub-volume covers a horizontal region of 711 x 446 samples, with a sample rate of 12.5m in both directions. The vertical extent of the classification volume is up to 50 samples, with an average of 29 samples, and the vertical two-way travel-time sample rate is 4ms. The extrema points within the formation was classified into six classes, using eight attributes. 

Classification of seismic horizons, denoted extrema classification, has been described, and has proved valuable for mapping automatically seismic horizons in structurally complex regions. Furthermore, a new procedure for automatic fault displacement estimation across pre-interpreted fault surfaces is designed with the extrema classification as the core methodology. The performance of the extrema classification method has been illustrated through a set of real data examples. 

The extrema classification helps detect the most possible lateral continuation of a horizon or structure in complex regions, in particular across faults. Structural interpretations can be obtained by focusing on a single class, and extracting automatically class consistent surfaces from the sparse extrema classification cube. The automatic extraction provides a set of horizon patches, where the structural interpreter is afterwards able to manually combine the segments into a full coverage horizon interpretation. Horizon patches obtained through extrema classification also form the basis for automated fault displacement assessment. 

Figure 6.12 Classification of all types of extremum or critical point that can occur in one-, two-, and three-dimensional functions a one-dimensional function can possess only a maximum or a minimum a two-dimensional function has maxima, minima, and one type of saddle point a three-dimensional function may have maxima, minima, and two types of saddle point. The arrows schematically represent gradient paths and their direction. At a maximum all gradient paths are directed toward the maximum, whereas at a minimum all gradient paths are directed away from the minimum. At a saddle point a subset of the gradient paths are directed toward the saddle point, whereas another subset are directed away from the saddle point (see Box 6.2 for more details).

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