We have developed a prestack inversion algorithm that combines a discrete cosine transform (DCT) reparameterization of data and model spaces with a convolutional neural network (CNN). The CNN is trained to predict the mapping between the discrete cosine-transformed seismic data and the discrete cosine-transformed 2D elastic model. A convolutional forward modeling based on the full Zoeppritz equations constitutes the link between the elastic properties and the seismic data. The direct sequential cosimulation algorithm with joint probability distribution is used to generate the training and validation data sets under the assumption of a stationary nonparametric prior and a Gaussian variogram model for the elastic properties. The DCT is an orthogonal transformation that we used as an additional feature extraction technique that reduces the number of unknown parameters in the inversion and the dimensionality of the input and output of the network. The DCT reparameterization also acts as a regularization operator in the model space and allows for the preservation of the lateral and vertical continuity of the elastic properties in the recovered solution. We also implement a Monte Carlo simulation strategy that propagates onto the estimated elastic model the uncertainties related to noise contamination and network approximation. We focus on synthetic inversions on a realistic subsurface model that mimics a real gas-saturated reservoir hosted in a turbiditic sequence. We compare the outcomes of the implemented algorithm with those provided by a popular linear inversion approach, and we also evaluate the robustness of the CNN inversion to errors in the estimated source wavelet and to erroneous assumptions about the noise statistic. Our tests confirm the applicability of our proposed approach, opening the possibility of estimating the subsurface elastic parameters and the associated uncertainties in near real time while satisfactorily preserving the assumed spatial variability and the statistical properties of the elastic parameters.

中文翻译：

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通过离散余弦变换重新参数化和卷积神经网络进行弹性叠前地震反演

我们已经开发了一种叠前反演算法，该算法将卷积神经网络（CNN）与数据和模型空间的离散余弦变换（DCT）重新参数化结合在一起。训练CNN来预测离散余弦变换的地震数据和离散余弦变换的2D弹性模型之间的映射。基于完整的Zoeppritz方程的卷积正演模型构成了弹性属性与地震数据之间的联系。在具有固定非参数先验和弹性特性的高斯变异函数模型的假设下，采用具有联合概率分布的直接顺序协同仿真算法来生成训练和验证数据集。DCT是一种正交变换，我们用作附加的特征提取技术，可减少反演中未知参数的数量以及网络输入和输出的维数。DCT重参数化还充当模型空间中的正则化算子，并允许保留回收溶液中弹性特性的横向和垂直连续性。我们还实施了蒙特卡洛模拟策略，该策略将与噪声污染和网络近似有关的不确定性传播到估计的弹性模型上。我们将重点放在模拟真实地下模型的合成反演上，该模型模仿以湍流序列托管的实际含气饱和储层。我们将实现的算法的结果与流行的线性反演方法提供的结果进行比较，我们还评估了CNN反演对估计的源小波中的误差以及关于噪声统计量的错误假设的鲁棒性。我们的测试证实了我们提出的方法的适用性，打开了近乎实时估计地下弹性参数和相关不确定性的可能性，同时令人满意地保留了假定的空间变异性和弹性参数的统计性质。