Deep learning methods have shown promising performances in predicting acoustic impedance from seismic data which is typically considered as an ill-posed problem for traditional inver- sion schemes. Most of the deep learning methods, however, are based on a 1D neural network which is straightforward to implement but often yields unreasonable lateral discontinuities while predicting a multi-dimensional impedance model trace-by-trace. We introduce 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 a low-frequency trend control, which is helpful for both the 1D and 2D CNNs to yield stable impedance predictions. The proposed 2D CNN architecture is quite simple; however, due to lack of 2D impedance labels, training it is not straightforward. To prepare a 2D training dataset, 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 which 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 where the output 2D impedance model is adaptively evaluated at the well logs only in the partially labeled target. As the training datasets 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 inline or crossline directions. Synthetic and field examples show that the proposed 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.

Extracting horizons and detecting faults in a seismic image are basic steps for structural interpretation and important for many seismic processing schemes. A common ground of the two tasks is to analyze seismic structures and they are related to each other. However, previously proposed methods deal with the tasks independently, and challenge remains in each of them. We propose a volume‐to‐volume neural network to estimate a relative geologic time (RGT) volume from a seismic volume, and this RGT volume is further used to simultaneously interpret horizons and faults. The network uses U‐shaped framework with attention mechanism to systematically aggregate multi‐scale information and automatically highlight informative features, and achieves high prediction accuracy with affordable computational costs. To train the network, we build thousands of 3‐D noisy synthetic seismic volumes and corresponding RGT volumes with realistic and various structures. We introduce a loss function based on structure similarity to capture spatial dependencies among seismic samples for better optimizing the network, and use multiple reasonable assessments to evaluate the predicted results. Trained by using synthetic data, our network outperforms the conventional approaches in recognizing structural features in field data examples. Once obtaining an RGT volume, we can not only obtain seismic horizons by simply extracting RGT constant surfaces but also detect faults that are indicated by lateral RGT discontinuities. To be able to deal with large seismic volumes, we further propose a workflow to first estimate sub‐volumes of RGT and merge them to obtain a full RGT volume without boundary artifacts.

Abstract. Implicit structural modeling using sparse and unevenly distributed data is essential for various scientific and societal purposes, ranging from natural source exploration to geological hazard forecasts. Most advanced implicit approaches formulate structural modeling as least squares minimization or spatial interpolation, using various mathematical methods to solve for a scalar field that optimally fits all the inputs under an assumption of smooth regularization. However, these approaches may not reasonably represent complex geometries and relationships of structures and may fail to fit a global structural trend when the known data are too sparse or unevenly distributed. Additionally, solving a large system of mathematical equations with iterative optimization solvers could be computationally expensive in 3-D. To deal with these issues, we propose an efficient deep learning method using a convolution neural network to create a full structural model from the sparse interpretations of stratigraphic interfaces and faults. The network is beneficial for the flexible incorporation of geological empirical knowledge when trained by numerous synthetic models with realistic structures that are automatically generated from a data simulation workflow. It also presents an impressive characteristic of integrating various types of geological constraints by optimally minimizing a hybrid loss function in training, thus opening new opportunities for further improving the structural modeling performance. Moreover, the deep neural network, after training, is highly efficient for the generation of structural models in many geological applications. The capacity of our approach for modeling complexly deformed structures is demonstrated by using both synthetic and field datasets in which the produced models can be geologically reasonable and structurally consistent with the inputs.

One of the key objectives in geophysics is to characterize the subsurface through the process of analyzing and interpreting geophysical field data that are typically acquired at the surface. Data-driven deep learning methods have enormous potential for accelerating and simplifying the process but also face many challenges, including poor generalizability, weak interpretability, and physical inconsistency. We present three strategies for imposing domain knowledge constraints on deep neural networks (DNNs) to help address these challenges. The first strategy is to integrate constraints into data by generating synthetic training datasets through geological and geophysical forward modeling and properly encoding prior knowledge as part of the input fed into the DNNs. The second strategy is to design nontrainable custom layers of physical operators and preconditioners in the DNN architecture to modify or shape feature maps calculated within the network to make them consistent with the prior knowledge. The final strategy is to implement prior geological information and geophysical laws as regularization terms in loss functions for training the DNNs. We discuss the implementation of these strategies in detail and demonstrate their effectiveness by applying them to geophysical data processing, imaging, interpretation, and subsurface model building.

Integrating borehole data into a uniformly sampled grid were an essential but challenging task for seismic data processing and reservoir characterization. A major effort was to improve well-log interpolation when reservoir properties were only directly observed via well logs at sparsely sampled locations. The subsurface property models obtained from existing interpolation approaches often did not consistently follow geologic structures, but they were essential in determining the distribution of reservoir properties. To solve this problem, we developed an alternative way to increase the borehole data coverage from the well locations for achieving accurate quantitative reservoir characterization. Based on a seismic image, we first computed a relative geologic time (RGT) volume that provided an implicit map of all the geologic structures in the seismic image. We then constructed an interpolated field from borehole data by following the constant RGT value that corresponded to the same geologic layer, and thus obtained a realistic and high-resolution model honoring seismic structures and well logs. This model could provide a low-frequency control for a learning or seismic inversion method to further correct the interpolation errors, or could used as a reliable initial background model to improve the performance of full-waveform inversion. We used synthetic and field data examples to demonstrate the effectiveness of our method even when reservoir properties were only observed at sparsely scattered locations. In comparison to the existing approaches, our method could produce a more geologically consistent subsurface model and robustly compensate for the low-frequency gap between seismic data and borehole measurements.