Deep learning for multidimensional seismic impedance inversion

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.