Prestack or angle stack gathers are inverted to estimate pseudologs at every surface location for building reservoir models. Recently, several methods have been proposed to increase the resolution of the inverted models. All of these methods, however, require that the total number of model parameters be fixed a priori. We have investigated an alternate approach in which we allow the data themselves to choose model parameterization. In other words, in addition to the layer properties, the number of layers is also treated as a variable in our formulation. Such transdimensional inverse problems are generally solved by using the reversible jump Markov chain Monte Carlo (RJMCMC) approach, which is a tool for model exploration and uncertainty quantification. This method, however, has very low acceptance. We have developed a two-step method by combining RJMCMC with a fixed-dimensional MCMC called Hamiltonian Monte Carlo, which makes use of gradient information to take large steps. Acceptance probability for such a transition is also derived. We call this new method “reversible jump Hamiltonian Monte Carlo (RJHMC).” We have applied this technique to poststack acoustic impedance inversion and to prestack (angle stack) AVA inversion for estimating acoustic and shear impedance profiles. We have determined that the marginal posteriors estimated by RJMCMC and RJHMC are in good agreement. Our results demonstrate that RJHMC converges faster than RJMCMC, and it therefore can be a practical tool for inverting seismic data when the gradient can be computed efficiently.

An inversion algorithm is commonly used to estimate the elastic properties, such as P-wave velocity ([Formula: see text]), S-wave velocity ([Formula: see text]), and density ([Formula: see text]) of the earth’s subsurface. Generally, the seismic inversion problem is solved using one of the traditional optimization algorithms. These algorithms start with a given model and update the model at each iteration, following a physics-based rule. The algorithm is applied at each common depth point (CDP) independently to estimate the elastic parameters. Here, we have developed a technique using the convolutional neural network (CNN) to solve the same problem. We perform two critical steps to take advantage of the generalization capability of CNN and the physics to generate synthetic data for a meaningful representation of the subsurface. First, rather than using CNN as in a classification type of problem, which is the standard approach, we modified the CNN to solve a regression problem to estimate the elastic properties. Second, again unlike the conventional CNN, which is trained by supervised learning with predetermined label (elastic parameter) values, we use the physics of our forward problem to train the weights. There are two parts of the network: The first is the convolution network, which takes the input as seismic data to predict the elastic parameters, which is the desired intermediate result. In the second part of the network, we use wave-propagation physics and we use the output of the CNN to generate the predicted seismic data for comparison with the actual data and calculation of the error. This error between the true and predicted seismograms is then used to calculate gradients, and update the weights in the CNN. After the network is trained, only the first part of the network can be used to estimate elastic properties at remaining CDPs directly. We determine the application of physics-guided CNN on prestack and poststack inversion problems. To explain how the algorithm works, we examine it using a conventional CNN workflow without any physics guidance. We first implement the algorithm on a synthetic data set for prestack and poststack data and then apply it to a real data set from the Cana field. In all the training examples, we use a maximum of 20% of data. Our approach offers a distinct advantage over a conventional machine-learning approach in that we circumvent the need for labeled data sets for training.

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During major power system disturbances, when multiple component outages occur in rapid succession, it becomes crucial to quickly identify the transmission interconnections that have limited power transfer capability. Understanding the impact of an outage on these critical interconnections (called saturated cut-sets) is important for enhancing situational awareness and taking correct actions. This paper proposes a new graph theoretic approach for analyzing whether a contingency will create a saturated cut-set in a meshed power network. A novel feature of the proposed algorithm is that it lowers the solution time significantly making the approach viable for real-time operations. It also indicates the minimum amount by which the power transfer through the critical interconnections should be reduced so that post-contingency saturation does not occur. Robustness of the proposed algorithm for enhanced situational awareness is demonstrated using the IEEE-118 bus system as well as a 17,000+ bus model of the Western Interconnection (WI). Comparisons made with different approaches for power system vulnerability assessment prove the utility of the proposed scheme for aiding power system operations during extreme exigencies.

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