A Monte-Carlo game theoretic approach for Multi-Criteria Decision Making under uncertainty

Game theory provides a useful framework for studying Multi-Criteria Decision Making problems. This paper suggests modeling Multi-Criteria Decision Making problems as strategic games and solving them using non-cooperative game theory concepts. The suggested method can be used to prescribe non-dominated solutions and also can be used as a method to predict the outcome of a decision making problem. Non-cooperative stability definitions for solving the games allow consideration of non-cooperative behaviors, often neglected by other methods which assume perfect cooperation among decision makers. To deal with the uncertainty in input variables a Monte-Carlo Game Theory (MCGT) approach is suggested which maps the stochastic problem into many deterministic strategic games. The games are solved using non-cooperative stability definitions and the results include possible effects of uncertainty in input variables on outcomes. The method can handle multi-criteria multi-decision-maker problems with uncertainty. The suggested method does not require criteria weighting, developing a compound decision objective, and accurate quantitative (cardinal) information as it simplifies the decision analysis by solving problems based on qualitative (ordinal) information, reducing the computational burden substantially. The MCGT method is applied to analyze California’s Sacramento-San Joaquin Delta problem. The suggested method provides insights, identifies non-dominated alternatives, and predicts likely decision outcomes.     

Determining the best search neighbourhood in reserve estimation, using geostatistical method: A case study anomaly No 12A iron deposit in central Iran

Ordinary kriging and non-linear geostatistical estimators are now well accepted methods in mining grade control and mine reserve estimation. In kriging, the search volume or ‘kriging neighbourhood’ is defined by the user. The definition of the search space can have a significant impact on the outcome of the kriging estimate. In particular, too restrictive neighbourhood, can result in serious conditional bias. Kriging is commonly described as a ‘minimum variance estimator’ but this is only true when the neighbourhood is properly selected. Arbitrary decisions about search space are highly risky. The criteria to consider when evaluating a particular kriging neighbourhood are the slope of the regression of the ‘true’ and ‘estimated’ block grades, the number of kriging negative weights and the kriging variance. Search radius is one of the most important parameters of search volume which often is determined on the basis of influence of the variogram. In this paper the above-mentioned parameters are used to determine optimal search radius.     

A new approach for the geological risk evaluation of coal resources through a geostatistical simulation

Estimations of mineral resources and ore reserves have been recently widely used by mining engineers and investors. The classification framework based on the prepared code by the Joint Ore Reserves Committee of The Australasian Institute of Mining and Metallurgy, Australian Institute of Geoscientists and Minerals Council of Australia (JORC code), which is one of the international standards for mineral resource and ore reserve reporting, provides a template system that conforms to international society requirements. Recent research has shown that an existing fault risk can affect the mineral resource and ore reserve estimation. According to this research, the faulted area that is involved in the effect on the estimated region is so extensive that it is not distinguishable. In this research, a new method called FGT (F for fault, G for grade and T for thickness) is introduced and presented for the estimation of mineral resources. The proposed method can provide an error map of a particular aspect of the combination of coal accumulation (G), fault risk (F) and thickness (T), and its output would categorise the mineral resources. This method was implemented in the Parvadeh Ш coal deposit, which is located in the eastern portion of Central Iran. The deposit contains five seams named B1, B2, C1, C2 and D; of these, C1 was selected as the most important seam in the exploratory grid analysis. Thus, C1 alone can reflect the properties of the Parvadeh Ш deposit. In this study, we compared the conventional method and the FGT method. This comparison indicated that the areas that should be rejected from the region in the FGT method are less and more distinguishable than those determined with the conventional method. Therefore, the inferred resources can be completely differentiated from the indicated and measured resources with a high resolution. The conventional method cannot distinguish between these three categories at this level of resolution. Therefore, the FGT approach has high precision in classifying the coal resource compared to the conventional method.     

Fault detection in 3D by sequential Gaussian simulation of Rock Quality Designation (RQD)

Gazestan phosphate ore deposit (Central Iran) is an apatite deposit which is instrumental in selecting the method of excavation. The position of fault systems and the condition of rock quality also play a role in the method used for mineral resources and ore reserves estimation. Conversely, the Rock Quality Designation (RQD) is a parameter that provides a quantitative judgment of rock mass quality obtained from drill cores. This factor can be applied to detect the fractured zones which occur due to fault systems. Additionally, the faulted areas can be determined by surface geological map and a few by core drilling. Some of the faulted areas are not distinguishable in the surface and are covered by soils, especially within 3D modeling and visualization. In this study, an attempt has been made to establish a relationship between the RQD percentages which were geostatistically simulated and faulted areas through the region. In comparison, the results showed that low RQD domains (RQD <20 %) can be interpreted as fault zones; high RQD domains (RQD >50 %) correspond to less fractured areas, and the contact between high and low RQD domain is gradual. Therefore, this categorization of RQD domains can be incorporated to detect the faulted zones in 3D models for mine design. Based on the categorization, the uncertainty within the area was calculated to introduce two new core drilling points for the completion of this phase of exploratory grid from the fault structural viewpoint, in order to have a proper model of ore reserve to estimate. It was concluded that this procedure can be utilized for conceptual comprehension of fault trends in 3D modeling for the method selection of excavation and complete the estimation procedure phase.     

Zoophycos and related trace fossils from the Chefar El Ahmar Formation,Upper Emsian-Frasnian Ia-Ib (Ougarta,SW Algeria)

The Upper Emsian to Frasnian Ia-Ib strata of the Marhouma area (or “km 30” outcrop), exposed in the Ougarta Range (SW Algeria) belong to the Chefar El Ahmar Formation. On the basis of distinct lithological and palaeontological features, this formation is subdivided into three members (Lower Marly Limestones Member, Middle Marly Limestones Member, and Upper Marly Limestones Member). The studied beds show low to moderate diversity of trace fossil assemblage which contains thirteen ichnotaxa: Chondrites intricatus, Chondrites isp., Chondrites cf. targionii, Circulichnis cf. montanus, Cochlichnus isp., Neonereites biserialis, Neonereites multiserialis, Nereites isp., Palaeophycus isp., Planolites isp., Thalassinoides isp., Zoophycos aff. cauda-galli, and Zoophycos isp. A. The two latter ichnotaxa are the most common trace fossils in the assemblage and occur at three different levels showing different bioturbation intensities. The first Zoophycos-bearing level (Zl 1) is characterised by an overall high bioturbation intensity reflecting a very high oxygenation rate and nutrient supply, allowing the development of large and dense Zoophycos specimens. The second Zoophycos-bearing level (Zl 2) has a considerable reduction of bioturbation intensity as compared to the previous level, with an abundance of Chondrites, which is probably due to radical palaeoecological changes that suggests dysoxic and stressful conditions. The third Zoophycos-bearing level (Zl 3) is characterised by an overall moderate bioturbation intensity. The distribution of trace fossils was influenced by lithology, sedimentation rate, energy level (storm events), bottom oxygenation, and nutrient supply. The lithofacies and trace fossils of the Chefar El Ahmar Formation both indicate a depositional environment fluctuating from the lower shoreface to lower offshore zone.     

Nonparametric Geostatistical Simulation of Subsurface Facies: Tools for Validating the Reproduction of,and Uncertainty in,Facies Geometry

Delineation of facies in the subsurface and quantification of uncertainty in their boundaries are significant steps in mineral resource evaluation and reservoir modeling, which impact downstream analyses of a mining or petroleum project. This paper investigates the ability of nonparametric geostatistical simulation algorithms (sequential indicator, single normal equation and filter-based simulation) to construct realizations that reproduce some expected statistical and spatial features, namely facies proportions, boundary regularity, contact relationships and spatial correlation structure, as well as the expected fluctuations of these features across the realizations. The investigation is held through a synthetic case study and a real case study, in which a pluri-Gaussian model is considered as the reference for comparing the simulation results. Sequential indicator simulation and single normal equation simulation based on over-restricted neighborhood implementations yield the poorest results, followed by filter-based simulation, whereas single normal equation simulation with a large neighborhood implementation provides results that are closest to the reference pluri-Gaussian model. However, some biases and inaccurate fluctuations in the realization statistics (facies proportions, indicator direct and cross-variograms) still arise, which can be explained by the use of a single finite-size training image to construct the realizations.

     

Capturing Hidden Geochemical Anomalies in Scarce Data by Fractal Analysis and Stochastic Modeling

Natural Resources Research - Fractal/multifractal modeling is a widely used geomathematical approach to capturing different populations in geochemical mapping. The rationale of this methodology is...     

Investigation of rock quality of Shirinrud dam site by engineering seismology

At this paper, we studied about the rock quality of Shirinrud dam site by engineering seismology. Shirinrud dam site is located 80 km far from Kerman and 18 km far from Hojadk village. The dam and its constructions are established in the Bidu Formation which consists of seven rock units, and the refraction profiles were surveyed on Jb_3/2, Jb₄, and Jb₅ rock units. To evaluate the rock mass quality and basement topography at this site, nine refraction seismic profiles by primary waves and two refraction seismic profiles by secondary waves were surveyed. We used some methods such as Palmer method, the reciprocal method, plus–minus method, etc. to process and interpret data. Based on investigations, primary wave velocity in unit Jb_3/2 varies between 2,100 and 2,200 m/s, in unit Jb₄ is between 2,100 and 4,200 m/s, and in unit Jb₅ is between 2,500 and 3,000 m/s. The Q values on these three units are 0.05, 1.2, and 1.9, and the rock mass rating (RMR) values are 27.1, 40.5, and 33.5, respectively. With respect to wave velocity, Q, and RMR values, the units Jb_3/2, Jb₄, and Jb₅ are evaluated as very weak, intermediate, and weak, respectively.     

Modeling the effects of controlled drainage at a watershed scale using SWATDRAIN

The recently developed SWATDRAIN model was employed to assess the impact of controlled drainage on the water table dynamics, subsurface drainage, and surface runoff in an agricultural watershed in Ontario, Canada. Controlled drainage was defined with a depth of 1.0 m to restrict flow at the drain outlet to maintain the water table at 0.5 m below the surface level during the winter (November–April) and at 0.6 m during the summer (June–August) months. The effects of the absence, or implementation, of drainage water management were predicted for the 3-year period of 1991–1993. Implementing controlled drainage resulted in a 16 % reduction in the mean annual drain flow, while increasing surface runoff by as much as 71 %. This indicates that overall watershed hydrology could be significantly impacted by the implementation of controlled drainage. This research demonstrates the SWATDRAIN model’s ability to predict the controlled drainage in small agricultural watersheds.