Deep learning is a promising approach to velocity model building because it has the potential of processing large seismic surveys with minimal resources. By leveraging large quantities of model-gather pairs, neural networks (NNs) can automatically map data to the model space, directly providing a solution to the inverse problem. Such mapping requires big data, which proves prohibitive for 2D and 3D surveys of realistic size. We have developed a transfer learning (TL) strategy. A network is first trained on a smaller subproblem, which then becomes the starting solution to a larger, more difficult data set, akin to the hierarchical multiscale strategy for full-waveform inversion. We perform TL by having subobjectives that escalate in complexity and by first training an NN at estimating horizontally layered velocity models and then proceeding to train an augmented network at estimating 2D dipping layered models. TL improves convergence and allows using a lesser quantity of 2D models for training. For synthetic tests, the structural similarity index measure of 2D interval velocity models in the time domain is 0.893±0.052 and the root-mean-square (rms) error is (198±91) m/s. We benchmark our algorithm on the Marmousi2 model and observe that our method can apply to velocity models with continuous deformed layers with dips up to 35°. We benchmark our algorithm on 2D marine field data and produce an rms velocity model that leads to coherent stacking and a time interval velocity model that reproduces salient features of the stacked section. TL expedites and regularizes training and data-driven techniques may be applied to field data with minimal preprocessing even though we lack real target velocity models.

Seawater intrusion in coastal aquifers is a worldwide problem exacerbated by aquifer overexploitation and climate changes. To limit the deterioration of water quality caused by saline intrusion, research studies are needed to identify and assess the performance of possible countermeasures, e.g., underground barriers. Within this context, numerical models are fundamental to fully understand the process and for evaluating the effectiveness of the proposed solutions to contain the saltwater wedge; on the other hand, they are typically affected by uncertainty on hydrogeological parameters, as well as initial and boundary conditions. Data assimilation methods such as the ensemble Kalman filter (EnKF) represent promising tools that can reduce such uncertainties. Here, we present an application of the EnKF to the numerical modeling of a laboratory experiment where seawater intrusion was reproduced in a specifically designed sandbox and continuously monitored with electrical resistivity tomography (ERT). Combining EnKF and the SUTRA model for the simulation of density-dependent flow and transport in porous media, we assimilated the collected ERT data by means of joint and sequential assimilation approaches. In the joint approach, raw ERT data (electrical resistances) are assimilated to update both salt concentration and soil parameters, without the need for an electrical inversion. In the sequential approach, we assimilated electrical conductivities computed from a previously performed electrical inversion. Within both approaches, we suggest dual-step update strategies to minimize the effects of spurious correlations in parameter estimation. The results show that, in both cases, ERT data assimilation can reduce the uncertainty not only on the system state in terms of salt concentration, but also on the most relevant soil parameters, i.e., saturated hydraulic conductivity and longitudinal dispersivity. However, the sequential approach is more prone to filter inbreeding due to the large number of observations assimilated compared to the ensemble size.

Bayesian inversion using maximum a posteriori estimator is a quantitative approach that has been successfully applied to the electrical resistivity tomography inverse problem. In most approaches, model covariance parameters are generally chosen as stationary and isotropic, which assumes a statistical homogeneity of the studied field. However, the statistical properties of resistivity within the earth are, in reality, location dependent due to spatially varying processes that control the bulk resistivity of rocks, such as water content, porosity, clay content, etc. Taking into account the spatial variability of the resistivity field, we use the nonstationary Matérn covariance family, which is defined through linear stochastic partial differential equations. Two types of prior information are considered: structure orientation and spatially increasing the range with increasing depth. The latter is applied successfully on the first synthetic model, which aims at retrieving the depth of bedrock and the shape of the conductive lens. In the second synthetic example, a conductive dike model embedded into four layers is used to study the performance of structure orientation. Finally, the proposed approach is used to invert real data measured over an extensively characterized sandy-to-silty aquifer. First, the structure orientation of this aquifer was determined by applying a structure tensor calculated using gradients of the ground penetrating radar image. The introduction of this information gives a resistivity model that is more compatible with the aquifer structure.

Mineral prospectivity mapping (MPM), like other geoscience fields, is subject to a variety of uncertainties. When data about unfavorable sites to find deposits (i.e., drill intersections to barren rocks) is lacking in MPM using machine learning (ML) methods, the synthetic generation of negative datasets is required. As a result, techniques for selecting point locations to represent negative examples must be employed. Several approaches have been proposed in the past; however, one can never be certain that the points chosen are true negatives or, at the very least, optimal for training. As a consequence, methodologies that account for the uncertainty of the generation of negative datasets in MPM are needed. In this paper, we compare two criteria for selecting negative examples and quantify the uncertainty associated with this process by generating 400 potential maps for each of the three ML methods utilized (200 maps for each criterion), which include random forest (RF), support vector machine (SVM), and k-nearest neighbors (KNC). The results showed that applying a geological constraint to the creation of negative datasets reduced prediction uncertainty and improved overall model performance but produced larger areas of very high probability (i.e., >0.9) when compared to using only the spatial distribution of known deposits and occurrences as a constraint. SHAP values were used to find approximations for the importance of features in nonlinear methods, and kernel density estimations were used to examine how they varied depending on the negative dataset used to train the ML models. Prospectivity models for magmatic-hydrothermal gold deposits were generated using data from the shuttle radar terrain mission, gamma-ray, magnetic lineaments, and proximity to dykes. The Juruena Mineral Province, situated in Northern Mato Grosso, Brazil, represented the case study for this work.