Adaptive Sobel Based Edge Detection for Enhaced Fault Segmentation
Authors: Aqrawi Ahmed Adnan 
Published: March 2015

Abstract
In this work, we suggest an improved method of traversing post-stack seismic data with an adaptive operator size for detecting edges. Attributes, in the coherence family, used for edge detection usually have a static operator size (Marfurt and Chopra, Seismic attributes for prospect identification and reservoir characterization, 2007). This can prove to be limiting in that one would under or over sample in regions of higher or lower frequencies respectively. By looking at the nature of seismic data, which commonly changes from short wavelength to longer wavelength signals in depth/time, an adaptive approach is more suitable for detection of features. By adjusting the operator size in relation to the depth/time, we are better following the frequencies of the data as we filter them. To increase the accuracy and resolution of our filtering we have chosen to interpolate between adjacent seismic traces. However, seismic data is not that simple in structure such that one can only vary in depth/time. Geological features such as dipping, salt and gas result in chaotic and varying frequencies regardless of when they occur. This is why we have introduced a textural analysis to account for this change and adapt our filtering to it. We have chosen to use chaos (Iske and Randen, 2005) as our seismic texture change indicator, as we are looking for changes to higher frequencies that usually results in chaotic textures.
The attribute we have chosen to implement is a 3D Sobel based edge detector, namely amplitude contrast (Aqrawi & Boe, 2011). In essence, the textural analysis in this case will decide the outcome of two things. One, the choice of preconditioning prior to filtering, and the second is the normalization method used. While, when implementing the operator size of our edge filter, relative depth/time is used to adjust it adaptively. As such, the algorithm operator size is time variant and accounts for seismic texture by varying the selected algorithm to filter with and the appropriate operator size to do so. To test our algorithm, a heavily faulted seismic dataset from the Norwegian North Sea has been used to test the methodology of the adaptive calculations. Our results indicate that the adaptive edge method ensures a higher level of detail, and highlights the smaller amplitude discontinuities better than a static operator size approach. It also proves to increase continuity and reduces the detection of noise, which overall gives a more accurate edge detection of the seismic data.

Adapting Attribute Calculations to the Nature of Seismic Data
Seismic data is highly varying in nature given the way it is acquired. There is more detail in the seismic image in the overburden where one has higher frequency information. As we propagate along time, we see that the loss of higher frequency signal gives longer wavelength information and hence is not as rich in detail. As such, similar geological features will look and respond differently depending on when they are captured. As an example, a fault is often seen as an amplitude discontinuity in higher frequency information, but a change in phase in lower frequency signals. In this example, we are looking at the same fault feature, but its representation in the seismc data has changed (see Figure 1).
Not only do we see a variation in the seismic signal in time, but also in seismic texture given changes in geological features captured (see Figure 1). For example, a chaotic texture for a geological feature such as salt will result in a nosier signal and hence capture higher frequency information than the surrounding signal data. This means that seismic data varies in time, but also along the lateral directions at the same time as we have variations in seismic texture. This is why it is more accurate to have a changing operator size that accounts for both variations along the vertical axis of the seismic data, as well as seismic texture. This basically means if one has high frequency information, using a smaller operator size will account for all the detailed features. While in low frequency regions, one uses a larger operator to avoid the detection of noise together with features.