Subsurface characterization is important for the detection and development of underground resources. Useful subsurface models can correctly make production forecast and optimize development plans, such as infill well location in an aquifer, geothermal, and hydrocarbon reservoir development. A useful subsurface model should honor geological concepts as well as all the available measurements, such as fluid production history, geophysical measurements. However, common subsurface modeling methods cannot efficiently honor the two concepts. To build subsurface models in a way that it is easy to condition them to both geological concepts and available measurements, we develop a new machine learning method, referred to as the stochastic pix2pix method. In this method, we use convolutional neural networks and adversarial neural networks to stochastically generate new subsurface models matching both geological concepts and static measurements, such as seismic and well data. This method first extracts the depositional patterns from analog training images, such as outcrops, high-resolution seismic images, and depositional process-based reservoir models, and then minimizes the Jensen-Shannon entropy between the training images and new subsurface models, as well as the mismatch of static measurements. The hydraulic inverse problem is solved with a machine learning-based proxy model on the model parameter space defined by stochastic pix2pix. The stochastic pix2pix method helps maintain the match of geological concepts and static measurements during the inversion. To verify and benchmark our procedure, we show the conditional subsurface models generated with stochastic pix2pix reproduce the geological concepts as good as synthetic unconditional process-based models. we successfully build reservoir models for channel and turbidite fan systems, where the depositional patterns of common geobodies are well reproduced. The synthetic well data, seismic interpretation, net-to-gross ratio, and time records of fluid production are well-matched with this new method. Additionally, we generate conditional subsurface models 90% faster than with conventional object-based modeling methods and with more accurate reproductions of the available measurements.

Recent advances in imaging techniques and related modeling have made it possible to study micron and sub-micron scales in unprecedented detail. Currently, performing direct simulations at a representative scale has proven computationally prohibitive, hence, the ability to simulate flow cannot keep up with the size of images available (e.g. x-ray micro-tomography or large area scanning electron microscopy). To overcome this issue, we propose to train a neural network architecture to understand relationships between pore-scale morphology and the simulation outputs. With this, we improve our portability and prediction time. Convolutional neural networks are attractive for this task because they support flexible input size, they are able to capture local interactions, and they can find places that present similar patterns. Generally, deeper networks have better prediction performance, but they are very difficult to train due to the vanishing gradient problem. Also, information from different scales is commonly lost along the network.

Saltwater disposal has been identified as the dominant causal factor that contribute to induced seismicity. Physical models rely on mechanistic understanding to infer causality where they evaluate various conditions for fault slips albeit with a high degree of uncertainty due to sparse data and subsurface heterogeneity. Given these uncertainties, statistical analysis is designed to measure statistical associations in the observed data with parametric regression models and interpret the significance of specific coefficient as evidence of causation. However, it is often difficult to interrogate the coefficients between different statistical models as the coefficients hold different implications. We propose a causal inference framework with the potential outcomes perspective to explicitly define what we meant by causal effect and declare necessary assumptions to ensure consistency between models for model comparison. The proposed workflow is applied to the Fort-Worth Basin of North Central Texas with the area of interest is discretized into non-overlapping grid blocks. Two statistical methods are employed to test the significance of the causal effect between the presence or absence of saltwater disposals and the number of the earthquakes and to estimate the magnitude of the average causal effect. In addition, our analysis is repeated for different grid configurations to directly assess the sensitivity of statistical results. We have identified a stable and statistically significant causal relationship between the presence of saltwater disposals and the number of earthquakes and have estimated there are, on average, 13 more earthquakes occurring in grids with saltwater disposals.