A new multiple-point statistics algorithm, SparseSim, is developed based on sparse approximation algorithm, which has wide applications for stochastic simulation in the field of geosciences and beyond. The current version is described in the context of reservoir characterization, which includes well and seismic data integration. In sparse approximation, a model image is represented as weighted linear combination of columns of the dictionary matrix. For this purpose, a parsimonious subset of the dictionary columns and their corresponding weights are selected using sparse coding methods. The dictionary is obtained by dictionary learning algorithms trained over and adapted for specific types of model images in the training set. Based on the sparse approximation algorithm, the approximated model image is generated by multiplication of the dictionary and the weight matrices. Intuitively, stochastic simulation of the coefficient (weight) matrix will lead to generation of new stochastic realizations. The SparseSim algorithm, as represented in this paper, works based on extracting the trend for nonzero elements in the significant rows of the weight matrix, and it is proposed under two general schemes: stochastically simulating the details of the training image or stochastically simulating both the details and the mean value of the training image. It is shown in this paper that under both schemes the generated realizations, while stochastically distinct, are similar to each other and to the training image. Different aspects of the SparseSim algorithm such as SparseSim in 3D, SparseSim in different scales, and data conditioning are also discussed.

基于稀疏逼近算法开发了一种新的多点统计算法SparseSim，该算法在地球科学及其他领域的随机模拟中具有广泛的应用。当前版本是在储层描述的背景下描述的，其中包括井和地震数据集成。在稀疏近似中，模型图像表示为字典矩阵列的加权线性组合。为此，使用稀疏编码方法选择字典列的简约子集及其相应的权重。字典是通过字典学习算法获得的，经过训练并适应训练集中特定类型的模型图像。基于稀疏逼近算法，近似模型图像是通过字典和权重矩阵相乘生成的。直观地说，系数（权重）矩阵的随机模拟将导致产生新的随机实现。SparseSim 算法，如本文所示，基于提取权重矩阵有效行中非零元素的趋势，并在两种通用方案下提出：随机模拟训练图像的细节或随机模拟两者细节和训练图像的平均值。本文表明，在这两种方案下，生成的实现虽然随机不同，但彼此相似并与训练图像相似。SparseSim 算法的不同方面，例如 3D 中的 SparseSim，不同尺度中的 SparseSim，