3D seismic fault detection using the Gaussian process regression, a study on synthetic and real 3D seismic data

Abstract

Faults are natural tectonic events as planar features along which rock units are moved. The patterns of these planes on seismic sections include linear or curvilinear features that are called edge in image processing, where amplitudes sharply change. In seismic data, these edge features made by fault traces are usually detected by seismic attributes, which need complex mathematical calculation such as a dip-steered cube. In this study, we introduce faults as global anomalies which disturb the normal interaction of seismic reflectors. Here, the normal interaction means the absence of intensive changes in reflectors trend in seismic sections. Fault detection as a global anomaly is done by the Gaussian process regression model (GPR), which is a nonparametric probabilistic model based on Bayesian statistics supporting noisy (Gaussian noise) and sparse features in data. In data mining, anomaly detection identifies items or events that do not match an expected pattern in a dataset. Global anomalies are sparse and affect a wide range of normal trends of data which are also held by fault features in seismic data. In this study, the GPR-based anomaly detection algorithm was implemented on the 3D seismic data of the Gulf of Mexico containing normal growth faults and a salt dome to detect salt boundary and fault traces in seismic data. In this respect, the reflections from rock units and fault features were taken into account as normal interactions and global anomalies, respectively, because faults disrupted the normal trend of reflectors in seismic sections. To detect fault locations, the location of a voxel in voxel grid where it is a part of fault in seismic data, after smoothing the seismic data, a Gaussian process (GP) model was trained on seismic data, attempting to describe the seismic amplitude data as a multivariate Gaussian model. However, GP regression fails to describe the seismic data at fault locations. Thus, the failure of the GP in the regression step was analyzed to separate the probable fault points, highlighted by calculating the variance of the GPR results. Finally, the detected probable fault points were improved and separated from background results by implementing a consistent reconstruction morphological algorithm. The results were validated using a similar structural index method, mean square error, and power signal to noise ratio indices in comparison with interpreted faults, implying the superiority of the proposed method in comparison with seismic attributes. The faults detected by the proposed method have the most structural similarity to faults interpreted. This similarity has improved by 22% compared to used attributes.