Intelligent interpolation by Monte Carlo machine learning

Acquisition technology advances, as well as the exploration of geologically complex areas, are pushing the quantity of data to be analyzed into the "big-data" era. In our related work, we found that a machine-learning method based on support vector regression (SVR) for seismic data intelligent interpolation can fully use large data as training data and can eliminate certain prior assumptions in the existing methods, such as linear events, sparsity, or low rank. However, immense training sets not only encompass high redundancy but also result in considerable computational costs, especially for high-dimensional seismic data. We have developed a criterion based on the Monte Carlo method for the intelligent reduction of training sets. For seismic data, pixel values in each local patch can be regarded as a set of statistical data and a variance value for the patch can be calculated. A high variance means that there are events centered around its corresponding patch or the pixel values in the patch range obviously. The patches with high variances are regarded as more representative patches. The Monte Carlo method assigns the variance as constraint and selects only the representative patches with a higher probability through a series of random positive numbers. After the training set is intelligently reduced through the Monte Carlo method, only these representative patches, constituting the new training set, are input to the SVR-based machine learning frame to construct a continuous regression model. Meanwhile, the patches with lower variances can be readily interpolated using a simple method and only present a minor influence in the construction of the regression model. Thus, the representative patches are called effective patches. Finally, the missing traces can be generated from the learned regression model. Numerical illustrations on 2D seismic data and results on 3D or 5D data show that the Monte Carlo method can intelligently select the effective patches as the new training set, which greatly decreases redundancy and also keeps the reconstruction quality.