Permeability Estimation with the Augmented Lagrangian Method for a Nonlinear Diffusion Equation

We consider numerical identification of the piecewise constant permeability function in a nonlinear parabolic equation, with the augmented Lagrangian method. By studying this problem, we aim at also gaining some insight into the potential ability of the augmented Lagrangian method to handle permeability estimation within the full two-phase porous-media flow setting. The identification is formulated as a constrained minimization problem. The parameter estimation problem is reduced to a coupled nonlinear algebraic system, which can be solved efficiently with the conjugate gradient method. The methodology is developed and numerical experiments with the proposed method are presented.     

Adaptive Multiscale Permeability Estimation

With multiscale permeability estimation one does not select parameterization prior to the estimation. Instead, one performs a hierarchical search for the right parameterization while solving a sequence of estimation problems with an increasing parameterization dimension. In some previous works on the subject, the same refinement is applied all over the porous medium. This may lead to over-parameterization, and subsequently, to unrealistic permeability estimates and excessive computational work. With adaptive multiscale permeability estimation, the new parameterization at an arbitrary stage in the estimation sequence is such that new degrees of freedom are not necessarily introduced all over the porous medium. The aim is to introduce new degrees of freedom only where it is warranted by the data. In this paper, we introduce a novel adaptive multiscale estimation. The approach is used to estimate absolute permeability from two-phase pressure data in several numerical examples.     

Overview,roles, and performance of the North East Atlantic fisheries commission (NEAFC)

According to the 1995 United Nations Fish Stocks Agreement (UNFSA), straddling fish stocks and highly migratory fish stocks are to be managed by Regional Fisheries Management Organisations (RFMOs), consisting of coastal states and relevant Distant Water Fishing Nations (DWFNs). In the North East Atlantic there are several straddling stocks, including herring, mackerel, blue whiting, redfish and numerous deep sea stocks that are exploited both within coastal states’ 200 mile Exclusive Economic Zones and on the high seas. Management of such stocks poses special management problems. In this area, the North East Atlantic Fisheries Commission (NEAFC) represents the relevant RFMO. So far the literature has devoted little attention to RFMOs in general and to NEAFC in particular. The purpose of this report is, first, to provide an overview of the organisation, structure, and objectives of NEAFC and, second, to consider its performance with regard to resource management.     

A level-set corrector to an adaptive multiscale permeability prediction

We consider the inverse problem of permeability estimation for two-phase porous-media flow. The novel approach is based on regularization by zonation, where the geometry and size of the regions are chosen adaptively during the optimization procedure. To achieve this, we have utilized level-set functions to represent the permeability. The available data are sparsely distributed in space; hence, it is reasonable to confine the estimation to coarse-scale structures. The level-set approach is able to alter the boundaries between regions of different permeability without strict restrictions on their shape; however, when the data are sparse, a reasonable initial guess for the permeability is required. For this task, we use adaptive multiscale permeability estimation, which has the potential of identifying main permeability variations. These are described by a piecewise constant function, where the constant values are attained on rectangular zones. In the current work, we develop a level-set corrector strategy, assuming adaptive multiscale permeability estimation as a predictor.     

Reassembling the Paleogene–Eocene North Atlantic igneous province: New paleomagnetic constraints from the Isle of Mull, Scotland

The paleomagnetic data sets from the British Tertiary Igneous Province (BTIP) have recently been criticized as being unreliable and discordant with data from elsewhere in the North Atlantic Igneous Province (NAIP) [Riisager et al. Earth Planet. Sci. Lett. 201 (2002) 261–276; Riisager et al. Earth Planet. Sci. Lett. 214 (2003) 409–425]. We offer new paleomagnetic data for the extensive lava flow sequence on the Isle of Mull, Scotland, and can confirm the paleomagnetic pole positions emanating from important earlier studies. Our new north paleomagnetic pole position for Eurasia at 59 ± 0.2 Ma has latitude 73.3°N, longitude 166.2°E (dp/dm = 5.2/7.0).A re-evaluation and an inter-comparison of the paleomagnetic database emanating from the NAIP were carried out to test for sub-province consistency. We find a general agreement between the Eurasian part of NAIP (BTIP and Faeroes) and East Greenland data. However a compilation of West Greenland data displays a large and unexplained dispersion. We speculate on if this is related to different sense of block rotation of the Tertiary West Greenland constituents. Combining all data from the NAIP constituents, give a pole position at 75.0°N, 169.9°E (N = 25, K = 84.3, A₉₅ = 3.2) in Eurasian reference frame.     

Multi-level parameter structure identification for two-phase porous-media flow problems using flexible representations

We consider identification of absolute permeability (hydraulic conductivity) based on time series of pressure data in sparsely distributed wells for two-phase porous-media flow. For this problem, it is impossible to recover all details of the parameter function. On the other hand, a coarser, approximate recovery may be sufficient for many applications. We propose a novel solution approach, based on reparametrization, for such approximate identification of the parameter function. We use a nonlinear, composite representation, which is detached from the computational grid, allowing for a flexible representation of the parameter function at many resolution levels. This is utilized in a sequential multi-level estimation of the parameter function, starting at a coarse resolution, which is then gradually refined. The composite representation is designed to allow for smooth as well as sharp transitions between regions of nearly constant parameter value. Moreover, it facilitates the estimation also of the structure and smoothness of the parameter function itself. As a limiting case, the chosen representation is reduced to a zonation with implicit representation of the interior boundaries that is equivalent to a level-set representation. A motivation for the selected representation and the multi-level estimation is presented in terms of an analysis of sensitivity and nonlinearity. Numerical examples demonstrate identification of coarse-scale features of reference permeability distributions with varying degree of smoothness. Comparisons show how the multi-level strategy stabilize the identification and avoid local minima of the objective function compared to a single-level strategy.