Deep-learning (DL) methods have shown promising performance in predicting acoustic impedance from seismic data that is typically considered as an ill-posed problem for traditional inversion schemes. Most of DL methods are based on a 1D neural network that is straightforward to implement, but they often yield unreasonable lateral discontinuities while predicting a multidimensional impedance model trace by trace. We have developed an improvement over the 1D network by replacing it with a 2D convolutional neural network (CNN) and incorporating the constraints of an initial impedance model. The initial model is fed to the network to provide low-frequency trend control, which is helpful for 1D and 2D CNNs to yield stable impedance predictions. Our 2D CNN architecture is quite simple; however, due to the lack of 2D impedance labels, training it is not straightforward. To prepare a 2D training data set, we first define a random path that passes through multiple well logs. We then follow the path to extract a 2D seismic profile and an initial impedance profile that together form an input to the 2D CNN. The set of well logs (traversed by the path) serves as a partially labeled target. We train the 2D CNN with weak supervision by using an adaptive loss in which the output 2D impedance model is adaptively evaluated at the well logs only in the partially labeled target. Because the training data sets are randomly extracted in all directions in a 3D survey, the trained 2D CNN can predict a consistent 3D impedance model section by section in either the inline or crossline directions. Synthetic and field examples indicate that our 2D CNN is more robust to noise, recovers thin layers better, and yields a laterally more consistent impedance model than a 1D CNN with the same network architecture and the same training logs.

中文翻译：

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多维地震阻抗反演的深度学习

深度学习 (DL) 方法在从地震数据中预测声阻抗方面表现出良好的性能，这通常被认为是传统反演方案的不适定问题。大多数 DL 方法基于易于实现的一维神经网络，但它们通常会在逐条预测多维阻抗模型时产生不合理的横向不连续性。我们通过用二维卷积神经网络 (CNN) 替换一维网络并结合初始阻抗模型的约束，对一维网络进行了改进。初始模型被馈送到网络以提供低频趋势控制，这有助于一维和二维 CNN 产生稳定的阻抗预测。我们的 2D CNN 架构非常简单；然而，由于缺乏 2D 阻抗标签，训练它并不简单。为了准备一个 2D 训练数据集，我们首先定义一个通过多个测井的随机路径。然后，我们沿着路径提取二维地震剖面和初始阻抗剖面，它们共同构成了 2D CNN 的输入。测井集（由路径遍历）用作部分标记的目标。我们通过使用自适应损失训练具有弱监督的 2D CNN，其中输出 2D 阻抗模型仅在部分标记的目标中的测井处进行自适应评估。因为训练数据集是在 3D 调查中在所有方向随机提取的，所以训练过的 2D CNN 可以在内联或横线方向逐节预测一致的 3D 阻抗模型。合成和现场示​​例表明我们的 2D CNN 对噪声更鲁棒，