We have trained deep convolutional neural networks (DCNs) to accelerate the computation of seismic attributes by an order of magnitude. These results are enabled by overcoming the prohibitive memory requirements typical of 3D DCNs for segmentation and regression by implementing a novel, memory-efficient 3D-to-2D convolutional architecture and by including tens of thousands of synthetically generated labeled examples to enhance DCN training. Including diverse synthetic labeled seismic in training helps the network generalize enabling it to accurately predict seismic attribute values on field-acquired seismic surveys. Once trained, our DCN tool generates attributes with no input parameters and no additional user guidance. The DCN attribute computations are virtually indistinguishable from conventionally computed attributes while computing up to 100 times faster.

Deep learning is increasingly being used as a component of geoscience workflows for processing and interpreting seismic data. Training a supervised deep learning network is a data-hungry task: Lots of data examples are needed and they must include labels. The data examples and their labels must have consistent patterns for the deep learning network to learn. Too few examples and/or poor-quality labels can lead to poor deep learning training results. One method to provide large quantities of training examples with high-quality labels is to create synthetic data. We discuss our techniques and experiences with our ongoing use of synthetic seismic data. We share our techniques as an open-source project concurrent with this paper at https://github.com/tpmerrifield/synthoseis. We hope that the geoscience community will share our enthusiasm for developing deep learning geoscience tools and for including synthetic seismic data in supervised deep learning training. We invite contributions from the geoscience community using the open-source model to collectively reduce the realism gap between synthetic data and field seismic data.

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SUMMARYWe describe a methodology for quantitatively characterizing the fractured nature of a hydrocarbon or geothermal reservoir from surface seismic data under a Bayesian inference framework. Fractures provide pathways for fluid flow in a reservoir, and hence, knowledge about a reservoir's fractured nature can be used to enhance production of the reservoir. The fracture properties of interest in this study (to be inferred) are fracture orientation and excess compliance, where each of these properties are assumed to vary spatially over a 2D lateral grid which is assumed to represent the top of a reservoir. The Bayesian framework in which the inference problem is cast has the key benefits of (1) utilization of a prior model that allows geological information to be incorporated, (2) providing a straightforward means of incorporating all measurements (across the 2D spatial grid) into the estimates at each grid point, (3) allowing different types of measurements to be combined under a single inference procedure, and (4) providing a measure of uncertainty in the estimates. The observed data are taken from a 2D array of surface seismic receivers responding to an array of surface sources. Well understood features from the seismic traces are extracted and treated as the observed data, namely the Pwave reflection amplitude variation with acquisition azimuth (amplitude versus azimuth, or AvAz, data) and fracture transfer function (FTF) data. AvAz data are known to be more sensitive to fracture properties when the fracture spacing is significantly smaller than the seismic wavelength, whereas fracture transfer function data are more sensitive to fracture properties when the fracture spacing is on the order of the seismic wavelength. Combining these two measurements has the benefit of allowing inferences to be made about fracture properties over a larger range of fracture spacing than otherwise attainable. Geophysical forward models for the measurements are used to arrive at likelihood models for the data. The prior distribution for the hidden fracture variables is obtained by defining a Markov random field (MRF) over the lateral 2D grid where we wish to obtain fracture properties. The fracture variables are then inferred by application of loopy belief propagation (LBP) to yield approximations for the posterior marginal distributions of the fracture properties, as well as the maximum a posteriori (MAP) and Bayes least squares (BLS) estimates of these properties. Verification of the inference procedure is performed on a synthetic dataset, where the estimates obtained are shown to be at or near ground truth for a large range of fracture spacings.

In many geophysical inverse problems, smoothness assumptions on the underlying geology are used to mitigate the effects of nonuniqueness, poor data coverage, and noise in the data and to improve the quality of the inferred model parameters. Within a Bayesian inference framework, a priori assumptions about the probabilistic structure of the model parameters can impose such a smoothness constraint, analogous to regularization in a deterministic inverse problem. We have considered an empirical Bayes generalization of the Kirchhoff-based least-squares migration (LSM) problem. We have developed a novel methodology for estimation of the reflectivity model and regularization parameters, using a Bayesian statistical framework that treats both of these as random variables to be inferred from the data. Hence, rather than fixing the regularization parameters prior to inverting for the image, we allow the data to dictate where to regularize. Estimating these regularization parameters gives us information about the degree of conditional correlation (or lack thereof) between neighboring image parameters, and, subsequently, incorporating this information in the final model produces more clearly visible discontinuities in the estimated image. The inference framework is verified on 2D synthetic data sets, in which the empirical Bayes imaging results significantly outperform standard LSM images. We note that although we evaluated this method within the context of seismic imaging, it is in fact a general methodology that can be applied to any linear inverse problem in which there are spatially varying correlations in the model parameter space.