A Meshless Surface-Fitting Method for Fault Detection

Seismic data adequately reveal subsurface geological structures but require special analysis techniques to detect subtle geological features such as faults. Detection of faults in seismic data is, for the most part, a qualitative procedure requiring proper data interpretation, sometimes leading to a source of ambiguity for the real fault location. Quantitative techniques based on seismic attribute analysis are employed to reduce this ambiguity and are the focus of this study. A new numeric method based on the meshless Moving Least Squares (MLS) is used to enhance the fault detection technique introduced by Gibson et al. (IEEE 43:2094–2102, 2005). This method generates a set of points called seed points, which lie on the fault surface, by examining the eigenvalues (i.e. the local covariance matrices of the structural tensor) of cubes from the data. Next, the seed points are grouped together using the neighborhood relationship (compatibility) between every two individual points. Finally, the seed points are used to create the final surface. A meshless technique is then used to fit a surface through these points. Fitting the meshless surface is found to be more efficient than traditional mesh-based techniques. This study also compares various mesh-based and meshless techniques. It is found that meshless methods have better accuracy, are more efficient in determining point connectivity on-the-fly at run-time, and avoid mesh-alignment issues. Also, traditional surface fitting techniques divide the fault surfaces into smaller surfaces (a common problem called over-segmentation), which is less of a problem using meshless methods. The MLS-based meshless surface fitting approach has shown promising results with potential benefits to seismic data interpretation and geological structure delineation. This method has not yet been adopted in the oil industry. However, the results have shown great potential for improving the quality of seismic interpretation in general and fault detection in particular.