A Convolutional Neural Network-Monte Carlo approach for petrophysical seismic inversion

We implement a machine-learning inversion approach to infer petrophysical rock properties from pre-stack data that combines a convolutional neural network and a discrete cosine transform of data and model spaces. This transformation is used for model and data compression. The network learns the inverse mapping between the compressed seismic and the compressed petrophysical domain. A theoretical rock-physics model relates elastic and petrophysical properties, while the exact Zoeppritz equations map the elastic properties onto the seismic domain. Training and validation examples are generated under the assumption of a Gaussian variogram model and a non-parametric prior. A Monte Carlo simulation strategy is employed for uncertainty assessment. We present synthetic inversions on a realistic subsurface model and the outcomes of the proposed approach are compared with those achieved by a standard linearized inversion. The network predictions are assessed in case of errors in the calibrated rock-physic model, in the estimated source wavelet, and in the assumed noise statistics. We also demonstrate that transfer learning avoids retraining the network from scratch when the target and training properties differ. Our experiments confirm that the implemented inversion successfully solves the petrophysical seismic inversion, opening the possibility to get instantaneous predictions of reservoir properties and related uncertainties.