Direct,partitioned and projected solution to finite element consolidation models

Direct, partitioned, and projected (conjugate gradient‐like) solution approaches are compared on unsymmetric indefinite systems arising from the finite element integration of coupled consolidation equations. The direct method is used in its most recent and computationally efficient implementations of the Harwell Software Library. The partitioned approach designed for coupled problems is especially attractive as it addresses two separate positive definite problems of a smaller size that can be solved by symmetric conjugate gradients. However, it may stagnate and when converging it does not prove competitive with a global projection method such as Bi‐CGSTAB, which may take full advantage of its flexibility in working on scaled and reordered equations, and thus may greatly improve its computational performance in terms of both robustness and convergence rate. The Bi‐CGSTAB superiority to the other approaches is discussed and demonstrated with a few representative examples in two‐dimensional (2‐D) and three‐dimensional (3‐D) coupled consolidation problems. Copyright © 2002 John Wiley & Sons, Ltd.     

Testing models of mid to late Holocene sea-level change,North Queensland,Australia

Understanding the nature of global ice-equivalent eustatic sea-level changes during the mid to late Holocene is important to our understanding of how ice sheets will respond to future climate change. This study re-analyses the indicative meaning and age control of existing relative sea-level (RSL) data from Cleveland Bay, North Queensland, Australia and presents new RSL data from a foraminifera-based transfer function as a preliminary test of global geophysical models in this region during the mid to late Holocene. The foraminifera-based transfer function produces reliable RSL estimates, consistent through the mid to late Holocene at different locations in Cleveland Bay. Analysis of the combined RSL database reveals that RSL rose above present between 8 and 6.2 ka cal. BP, with the peak of the sea-level highstand c. 2.8 m above present at c. 5 ka cal. BP, remaining relatively stable above +1.5 m from 6.2 until at least 2.3 ka cal. BP, falling to present in the last millennia. This long period of sea level above present in the mid to late Holocene suggests a gradual rather than abrupt end to global ice melt, which must have continued into the late Holocene. This new analysis also shows no evidence for episodic fluctuations within the highstand, although they cannot be entirely ruled out by this study. This study demonstrates that more sea-level data needs to be collected from locations uncontaminated by glacio-isostasy, hydro-isostasy and tectonic effects, in order to better constrain the late Holocene melt histories of the large polar ice sheets.     

Calibration of imperfect models to biased observations

The problem of assimilating biased and inaccurate observations into inadequate models of the physical systems from which the observations were taken is common in the petroleum and groundwater fields. When large amounts of data are assimilated without accounting for model error and observation bias, predictions tend to be both overconfident and incorrect. In this paper, we propose a workflow for calibration of imperfect models to biased observations that involves model construction, model calibration, model criticism and model improvement. Model criticism is based on computation of model diagnostics which provide an indication of the validity of assumptions. During the model improvement step, we advocate identification of additional physically motivated parameters based on examination of data mismatch after calibration and addition of bias correction terms. If model diagnostics indicates the presence of residual model error after parameters have been added, then we advocate estimation of a “total” observation error covariance matrix, whose purpose is to reduce weighting of observations that cannot be matched because of deficiency of the model. Although the target applications of this methodology are in the subsurface, we illustrate the approach with two simplified examples involving prediction of the future velocity of fall of a sphere from models calibrated to a short-time series of biased measurements with independent additive random noise. The models into which the data are assimilated contain model errors due to neglect of physical processes and neglect of uncertainty in parameters. In every case, the estimated total error covariance is larger than the true observation covariance implying that the observations need not be matched to the accuracy of the measuring instrument. Predictions are much improved when all model improvement steps were taken.     

Assessing landslide volume using two generic models: application to landslides in Whatcom County,Washington, USA

Landslides - Geomorphological analysis of landslide processes in mountainous terrains with difficult access has benefited from virtual representation of topography through the use of...     

Quaternary sedimentology of the Rose Creek fan delta, Walker Lake, Nevada, USA, and implications to fan-delta facies models

The 3·2 km long Rose Creek fan delta of west‐central Nevada is prograding from an active rift margin into the 32 m deep Walker Lake. A case study of the forms, processes and facies of this fan delta reveals that the proximal and medial zones mainly are of sub‐aerial origin, and the distal zone is of lacustrine origin. Pebbly to bouldery rock‐avalanche mounds >100 m thick (Facies A) and muddy to bouldery debris flow levées 0·5 to 2·0 m thick (Facies B) dominate the proximal zone, whereas mostly matrix‐supported cobbly pebbly debris flow lobes 0·1 to 1·0 m thick (Facies C) typify the medial zone. Surficial pebble lags and gully fills (Facies D) are widespread in both zones but, in exposures, comprise only partings or lenticles between debris flow units. The distal fan delta mainly consists of lakeshore to lake‐bottom tracts formed by extensive wave reworking of debris flow facies. Nearshore deposits include erosional cobbly boulder lag beaches (Facies E), pebbly constructional beaches attached at headcuts or on barrier spits (Facies F), pebbly upper shoreface (Facies G) and sandy lower shoreface (Facies H) tracts positioned lakeward of the beach, and pebbly landward‐dipping foresets (Facies I) and backshore‐pond sand and mud (Facies J) present landward of the spits. Erosional lag beaches fringe the windward north side of the fan‐delta front, attached constructional beaches characterize the central zone, and southward‐elongating barrier spits typify the leeward south side, extending from the zone of greatest projection of the fan delta into the lake. Shoreline facies asymmetry results from largely unidirectional longshore drift caused by high fetch to the north and minimal fetch to the south, combined with the arcuate shape of the fan‐delta front. The spits overlie a platform deposited below common wave base consisting of south‐east‐trending cones of pebbly Gilbert foresets (Facies K) and sandy toesets (Facies L). Typically slumped silt and mud (Facies M) fringe both this platform and lower shoreface sand in deeper water. This case demonstrates facies types and patterns that are inconsistent with the widely promoted fan‐delta facies model having a front consisting of an apron of radially directed Gilbert foresets deposited where sub‐aerial flows enter the lake. The Rose Creek fan‐delta front instead features a sharp contact between sub‐aerial and lakeshore facies formed where waves erode, sort and redistribute heterogeneous debris flow sediment into the various shallow‐to‐deep lake facies. Gilbert foresets are present only in the lee of the fan delta where sediment moving by longshore drift reaches the brink of the spit front. This facies scenario results from the infrequency of fan‐building events versus nearly constant wind‐induced waves, a scenario that, in contrast to the popular Gilbert model, probably is the norm for fan deltas. The level of Walker Lake, and thus the position of wave reworking on the Rose Creek fan delta, fluctuated over a range of ～157 m during the last 18 kyr, producing complex interfingering between sub‐aerial and lakeshore facies across a 1700 m wide radial belt, typifying a wave‐modified, freestand lacustrine fan delta.     

Experiments and models of anhydrous,basaltic olivine-plagioclase-augite saturated melts from 0.001 to 10 kbar

 A new method for modeling fractional crystallization processes that involve olivine (ol), plagioclase (plag) and augite (aug) is presented. This crystallization assemblage is the major control on the chemical variations in mid-ocean ridge basalts. The compositional and temperature variations in ol-plag-aug saturated basalts over a range of pressures are described using empirical expressions. A data base of 190 experiments in natural and basalt-analog chemical systems is used to describe temperature, Al, Ca and Mg molar fractions as functions of Si, Fe, Na, Ti and K molar fractions and pressure. Increases in the abundances of Na and K cause Ca and Mg abundances to decrease and Al abundance to increase in ol-plag-aug saturated melts. The equations can be used to predict pressure and temperature and thus provide a useful thermobarometer. A model is described to calculate ol-plag-aug fractional crystallization as a function of pressure and melt composition, using melt and augite models developed here, combined with existing models for olivine-melt and plagioclase-melt equilibria. We compare the fractional crystallization sequence of ALV-2004-3-1 predicted from the models presented in this paper, Langmuir et al. (1992) modified by Reynolds (1995), Ghiorso and Sack (1995) and Ariskin et al. (1993) at 0.001 and 4 kbar. As an example the model is applied to estimate pressure of crystallization of glasses from the east flank of the East Pacific Rise at 11°45′N. Received: 24 July 1995 / Accepted: 12 January 1996     

Statistical thermodynamic models for ideal oxide and silicate solid solutions,with application to plagioclase

Activity-composition relations are derived for ideal substitutional solid solutions through the Helmholtz free energy expressed in terms of the partition function. For solutions of the type (A, B)_uZ_w involving mixing on one type of atom site, ideal activities of end-member components are expressed by: a_AuZw = (X_AuZw)^u, and a_BuZw = (X_BuZw)^u. With multi-site mixing excluding charge balance restrictions, as in (A, B)^α_u (C, D)^β_vZ_w, the ideal activity of an end-member component such as A_uC_vZ_w is calculated as: a_AuCvZw = (X^α_A)^u (X^β_c)^v. These expressions support the ‘ionic solid solution model for the activities of components in ideal solid solutions. Ideal solution models for coupled substitutions involving charge balance are considered using plagioclase as an example. Ideal activity expressions for solid solution of albite and anorthite are derived with and without adherence to the Al avoidance principle. Mixing models involving local electrostatic balance are contrasted with those involving independent, random mixing of Na-Ca and Al-Si. Of several possible ideal solution models for plagioclase, only that specifying complete Al-Si ordering and local electrostatic neutrality yields activities conforming to Raoult's Law.     

A comparison of logistic regression-based models of susceptibility to landslides in western Colorado,USA

The Paonia-McClure Pass area of Colorado has been recognized as a region highly susceptible to mass movement. Because of the dynamic nature of this landscape, accurate methods are needed to predict susceptibility to movement of these slopes. The area was evaluated by coupling a geographic information system (GIS) with logistic regression methods to assess susceptibility to landslides. We mapped 735 shallow landslides in the area. Seventeen factors, as predictor variables of landslides, were mapped from aerial photographs, available public data archives, ETM + satellite data, published literature, and frequent field surveys. A logistic regression model was run using landslides as the dependent factor and landslide-causing factors as independent factors (covariates). Landslide data were sampled from the landslide masses, landslide scarps, center of mass of the landslides, and center of scarp of the landslides, and an equal amount of data were collected from areas void of discernible mass movement. Models of susceptibility to landslides for each sampling technique were developed first. Second, landslides were classified as debris flows, debris slides, rock slides, and soil slides and then models of susceptibility to landslides were created for each type of landslide. The prediction accuracies of each model were compared using the Receiver Operating Characteristic (ROC) curve technique. The model, using samples from landslide scarps, has the highest prediction accuracy (85 %), and the model, using samples from landslide mass centers, has the lowest prediction accuracy (83 %) among the models developed from the four techniques of data sampling. Likewise, the model developed for debris slides has the highest prediction accuracy (92 %), and the model developed for soil slides has the lowest prediction accuracy (83 %) among the four types of landslides. Furthermore, prediction from a model developed by combining the four models of the four types of landslides (86 %) is better than the prediction from a model developed by using all landslides together (85 %).     

Re-specifying disaster risk: concepts,methods, and models

The discussion on the social-ecological dimensions of hazards is constantly evolving. This paper explores the trajectory of research relating to hazards and their impact on vulnerable human populations. Interpretations of disaster risk have included estimating losses in terms of human life and property, and analyzing the social mechanisms in place that exacerbate or mitigate a population’s sensitivity to hazard events. In keeping with recent trends in research relating to disaster risk, the paper focuses on the social dimension of vulnerability and the contribution of social structures and relationships in building community resilience. Institutional frameworks and policies in particular determine the quantity and quality of resources and services available to people that contribute to resilience over time. The hazard-risk-location-model (HRLM) is proposed that is based on re-specifying disaster risk in terms of exposure and coping ability to capture the focus on social vulnerability and resilience. The framework of the HRLM incorporates the following components: (1) linkages within existing social capital; (2) spatial variation in social and institutional frameworks; (3) positive and negative feedbacks; and (4) characteristics of the hazard event. The model contributes to the range of place-based assessments designed to address the human-environmental impacts of hazards and disasters.     

Sea-level changes, geoid and gravity anomalies due to Pleistocene deglaciation by means of multilayered, analytical Earth models

A new class of analytical, multilayered, viscoelastic Earth models based on PREM, with an incompressible, linear, viscoelastic Maxwell rheology, is applied to the modeling of global sea-level changes due to Pleistocene deglaciation. Until now, analytical schemes based on normal mode theory, have dealt with at most five layers, an elastic lithosphere, a three layered mantle including a transition zone, and a core (Spada et al., 1992. Geophys. J. Int. 109, 683–700). The novelty of our approach, used for the first time in sea-level studies, stands on an analytical scheme that can reproduce continuous elastic and rheological stratification when a sufficient number of layers is taken into account. We specifically assess the importance of our results for the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission. GOCE will resolve the gravity field with a spatial resolution (half-wavelength) of 75 km and amplitude of 1.5 mgal, with a uniform coverage over the Earth, including presently unsurveyed, remote areas. Our models lead to post-glacial rebound induced free air gravity anomalies of a few mgals peak-to-peak in the harmonic degree range l=80–200, which will be discernible by GOCE. This finding demonstrates that post-glacial rebound has a high frequency component in the gravity field that can in principle be resolved by high resolution gravity satellite missions. We show that post-glacial rebound can contribute a substantial fraction to present-day sea-level variations and point out that for the Mediterranean Sea they are of the same order of magnitude as those induced by tectonic processes.     

Ensemble-based conditioning of reservoir models to seismic data

While 3D seismic has been the basis for geological model building for a long time, time-lapse seismic has primarily been used in a qualitative manner to assist in monitoring reservoir behavior. With the growing acceptance of assisted history matching methods has come an equally rising interest in incorporating 3D or time-lapse seismic data into the history matching process in a more quantitative manner. The common approach in recent studies has been to invert the seismic data to elastic or to dynamic reservoir properties, typically acoustic impedance or saturation changes. Here we consider the use of both 3D and time-lapse seismic amplitude data based on a forward modeling approach that does not require any inversion in the traditional sense. Advantages of such an approach may be better estimation and treatment of model and measurement errors, the combination of two inversion steps into one by removing the explicit inversion to state space variables, and more consistent dependence on the validity of assumptions underlying the inversion process. In this paper, we introduce this approach with the use of an assisted history matching method in mind. Two ensemble-based methods, the ensemble Kalman filter and the ensemble randomized maximum likelihood method, are used to investigate issues arising from the use of seismic amplitude data, and possible solutions are presented. Experiments with a 3D synthetic reservoir model show that additional information on the distribution of reservoir fluids, and on rock properties such as porosity and permeability, can be extracted from the seismic data. The role for localization and iterative methods are discussed in detail.     

Rural community well-being: models and application to changes in the tobacco-belt in Ontario, Canada

In this paper we develop a model of changes in rural community well-being. The model conceptualizes four interrelated dimensions of rural community well-being: physical, psychological, social, and economic. The model recognizes that a range of external forces (political, economic, etc.) exert pressures on rural communities, of which changes in well-being are one outcome. The paper then applies the model to changes which occurred in the tobacco growing region of southern Ontario, Canada. It is argued that this region was impacted by a variety of forces, some general to farming, others specific to tobacco farming, particularly between 1979 and the early 1990s. The empirical application is based on a personally administered farm survey (n=63) conducted between July 1996 and January 1997 and agricultural census data for the years 1981, 1986, 1991, and 1996. The paper concludes by suggesting that the model provides a useful framework for analysing the forces and changing conditions of other rural communities, not only in Canada, but beyond.     

A multi-resolution workflow to generate high-resolution models constrained to dynamic data

Distance-based stochastic techniques have recently emerged in the context of ensemble modeling, in particular for history matching, model selection and uncertainty quantification. Starting with an initial ensemble of realizations, a distance between any two models is defined. This distance is defined such that the objective of the study is incorporated into the geological modeling process, thereby potentially enhancing the efficacy of the overall workflow. If the intent is to create new models that are constrained to dynamic data (history matching), the calculation of the distance requires flow simulation for each model in the initial ensemble. This can be very time consuming, especially for high-resolution models. In this paper, we present a multi-resolution framework for ensemble modeling. A distance-based procedure is employed, with emphasis on the rapid construction of multiple models that have improved dynamic data conditioning. Our intent is to construct new high-resolution models constrained to dynamic data, while performing most of the flow simulations only on upscaled models. An error modeling procedure is introduced into the distance calculations to account for potential errors in the upscaling. Based on a few fine-scale flow simulations, the upscaling error is estimated for each model using a clustering technique. We demonstrate the efficiency of the method on two examples, one where the upscaling error is small, and another where the upscaling error is significant. Results show that the error modeling procedure can accurately capture the error in upscaling, and can thus reproduce the fine-scale flow behavior from coarse-scale simulations with sufficient accuracy (in terms of uncertainty predictions). As a consequence, an ensemble of high-resolution models, which are constrained to dynamic data, can be obtained, but with a minimum of flow simulations at the fine scale.     

Physical models of rifting and transform faulting, due to ridge push in a wedge-shaped oceanic lithosphere

By scaled physical modelling, we have investigated the mechanical response to gravitational forces in an oceanic lithosphere, overlying a less dense asthenosphere. In the models, an upper wedge-shaped layer of sand represented an oceanic lithosphere (0–35 Ma old, with a half-spreading velocity of 3 cm/yr), and a lower layer of polydimethylsiloxane (PDMS), mixed with dense wolframite powder, represented the asthenosphere. In the models, as in nature, isostatic compensation resulted in uplift of ridges and subsidence on their flanks. The resulting relief was responsible for ridge push. We tested two main configurations: straight ridges and offset ridges. In all the models, ridge push was sufficient to cause plate motion, underlying advection, and symmetrical rifting at the ridge axis. There was no need to impose plate motions through external pistons and motors. In models of straight ridges, the style of normal faults in the axial rift zone depended on the local thickness of the brittle sand layer. For thick layers, normal faults rafted out from the active zone of rifting, creating a fossil topography of tilted blocks, between faults dipping toward the ridge. In a model of an offset ridge, with thin lithosphere at the ridge crest and no embedded weakness, ridge push was responsible for a short transform fault, linking en-échelon rifts. In a similar model, but with thick lithosphere, an oblique rift formed at about 20° to the offset trace. We conclude that ridge push was not adequate to create an ideal transform fault. In a model of an offset ridge, with an embedded thin vertical layer of pure PDMS at 90° to the ridge, transform motion concentrated along this weak layer, and the resulting structural style was very similar to that in nature. On the basis of these results, we infer that, in nature, (1) ridge push can indeed drive plate motion, and (2) ridge push can drive strike-slip motion on transform faults, provided that these are weaker than the adjacent oceanic lithosphere and that they form early in the history of spreading.     

Melts of garnet lherzolite: experiments, models and comparison to melts of pyroxenite and carbonated lherzolite

Phase equilibrium experiments on a compositionally modified olivine leucitite from the Tibetan plateau have been carried out from 2.2 to 2.8 GPa and 1,380–1,480 °C. The experiments-produced liquids multiply saturated with spinel and garnet lherzolite phase assemblages (olivine, orthopyroxene, clinopyroxene and spinel ± garnet) under nominally anhydrous conditions. These SiO₂-undersaturated liquids and published experimental data are utilized to develop a predictive model for garnet lherzolite melting of compositionally variable mantle under anhydrous conditions over the pressure range of 1.9–6 GPa. The model estimates the major element compositions of garnet-saturated melts for a range of mantle lherzolite compositions and predicts the conditions of the spinel to garnet lherzolite phase transition for natural peridotite compositions at above-solidus temperatures and pressures. We compare our predicted garnet lherzolite melts to those of pyroxenite and carbonated lherzolite and develop criteria for distinguishing among melts of these different source types. We also use the model in conjunction with a published predictive model for plagioclase and spinel lherzolite to characterize the differences in major element composition for melts in the plagioclase, spinel and garnet facies and develop tests to distinguish between melts of these three lherzolite facies based on major elements. The model is applied to understand the source materials and conditions of melting for high-K lavas erupted in the Tibetan plateau, basanite–nephelinite lavas erupted early in the evolution of Kilauea volcano, Hawaii, as well as younger tholeiitic to alkali lavas from Kilauea.     

Arcuate and growth faults in basin models, with an application to a south Louisiana roll-over structure

Using a two-dimensional fluid-flow/compaction code an investigation is given of the influence of dynamically evolving curved faults in impacting the overpressure development of a sedimentary basin. Four synthetic cases are examined: an homogeneous sandy-shale section, and a mixed layered section of sand and shale, with fault conditions investigated being open to fluid flow, and closed to fluid-flow, respectively. Fault throws can be instantaneous either in time (such as a gravity slump) or can be progressive in time (such as a growth fault). A case history from south Louisiana also is examined to illustrate typical response patterns.     

Problems related to single gully debris flow assessment models

Natural Hazards - In recent years, various models for single gully debris flow assessment have been proposed. Due to various factors affecting the mechanisms of debris flows, these models face many...