Reservoir properties estimation from 3D seismic data in the Alose field using artificial intelligence

In an attempt to reduce the errors and uncertainties associated with predicting reservoir properties for static modeling, seismic inversion was integrated with artificial neural network for improved porosity and water saturation prediction in the undrilled prospective area of the study field, where hydrocarbon presence had been confirmed. Two supervised neural network techniques (MLFN and PNN) were adopted in the feasibility study performed to predict reservoir properties, using P-impedance volumes generated from model-based inversion process as the major secondary constraint parameter. Results of the feasibility study for predicted porosity with PNN gave a better result than MLFN, when correlated with well porosity, with a correlation coefficient of 0.96 and 0.69, respectively. Validation of the prediction revealed a cross-validation correlation of 0.88 and 0.26, respectively, for both techniques, when a random transfer function derived from a given well is applied on other well locations. Prediction of water saturation using PNN also gave a better result than MLFN with correlation coefficient of 0.97 and 0.57 and cross-validation correlation coefficient of 0.89 and 0.3, respectively. Hence, PNN technique was adopted to predict both reservoir properties in the field. The porosity and water saturation predicted from seismic in the prospective area were 24–30% and 20–30%, respectively. This indicates the presence of good quality hydrocarbon bearing sand within the prospective region of the studied reservoir. As such, the results from the integrated techniques can be relied upon to predict and populate static models with very good representative subsurface reservoir properties for reserves estimation before and after drilling wells in the prospective zone of reservoirs.

Stochastic modeling of subglacial topography exposes uncertainty in water routing at Jakobshavn Glacier

Subglacial topography is an important feature in numerous ice-sheet analyses and can drive the routing of water at the bed. Bed topography is primarily measured with ice-penetrating radar. Significant gaps, however, remain in data coverage that require interpolation. Topographic interpolations are typically made with kriging, as well as with mass conservation, where ice flow dynamics are used to constrain bed geometry. However, these techniques generate bed topography that is unrealistically smooth at small scales, which biases subglacial water flowpath models and makes it difficult to rigorously quantify uncertainty in subglacial drainage patterns. To address this challenge, we adapt a geostatistical simulation method with probabilistic modeling to stochastically simulate bed topography such that the interpolated topography retains the spatial statistics of the ice-penetrating radar data. We use this method to simulate subglacial topography using mass conservation topography as a secondary constraint. We apply a water routing model to each of these realizations. Our results show that many of the flowpaths significantly change with each topographic realization, demonstrating that geostatistical simulation can be useful for assessing confidence in subglacial flowpaths.

RIGID AND GAUGE NOETHER SYMMETRIES FOR CONSTRAINED SYSTEMS

We develop the general theory of Noether symmetries for constrained systems, that is, systems that are described by singular Lagrangians. In our derivation, the Dirac bracket structure with respect to the primary constraints appears naturally and plays an important role in the characterization of the conserved quantities associated to these Noether symmetries. The issue of projectability of these symmetries from tangent space to phase space is fully analyzed, and we give a geometrical interpretation of the projectability conditions in terms of a relation between the Noether conserved quantity in tangent space and the presymplectic form defined on it. We also examine the enlarged formalism that results from taking the Lagrange multipliers as new dynamical variables; we find the equation that characterizes the Noether symmetries in this formalism, and we also prove that the standard formulation is a particular case of the enlarged one. The algebra of generators for Noether symmetries is discussed in both the Hamiltonian and Lagrangian formalisms. We find that a frequent source for the appearance of open algebras is the fact that the transformations of momenta in phase space and tangent space only coincide on shell. Our results apply with no distinction to rigid and gauge symmetries; for the latter case we give a general proof of the existence of Noether gauge symmetries for theories with first and second class constraints that do not exhibit tertiary constraints in the stabilization algorithm. Among some examples that illustrate our results, we study the Noether gauge symmetries of the Abelian Chern–Simons theory in 2n+1 dimensions. An interesting feature of this example is that its primary first class constraints can only be identified after the determination of the secondary constraint. The example is worked out retaining all the original set of variables.

Constraint Coordination for the Single Motion State

The methods of constraint coordination are derived and applied to an industrial problem to synthesize a mechanism solution. The motion of an input constraint of unknown proportions is coordinated with the motion of a planar body to yield constraint dimensions. The motion of a secondary constraint is chosen to optimize the transmission angle over a cycle of motion.