On the value of information for spatial problems in the earth sciences [electronic resource]
Keywords: Earth, Energy and Environmental Sciences.

Two value of information (VOI) methodologies for spatial Earth problems are proposed. VOI is a tool to determine whether purchasing a new information source would improve a decision-maker's chances of taking the optimal action. These actions represent alternatives to spatial decisions regarding the sustainability of aquifers or enhanced recovery of oil or minerals. These decisions are difficult due to uncertainty in the Earth properties and the predictions made from Earth models. The risk of making poor decisions due to this uncertainty may justify the collection of more information. Both the prior geologic uncertainty and the information reliability must be quantified before the data are collected to estimate the VOI, making it challenging to obtain. A flexible prior geologic uncertainty modeling scheme is presented that allows for the inclusion of many types of spatial parameters and used for both VOI methodologies. In the first methodology, we describe how to obtain a physics-based reliability measure by simulating the geophysical measurement on the generated prior models and interpreting the simulated data. Repeating this simulation and interpretation for all datasets, a table can be obtained that describes how many times a correct or false interpretation was made by comparing them to their respective original model. This table is the reliability measure, which is required for the VOI calculation. An example VOI calculation is demonstrated for a spatial decision related to aquifer recharge where two geophysical techniques are considered for their ability to resolve channel orientations. As necessitated by spatial problems, this methodology preserves the structure, influence and dependence of spatial variables through the prior geological modeling and the explicit geophysical simulations and interpretations. The focus of the second methodology is to 1) represent the uncertainty of a dynamic response of the unknown subsurface, 2) provide a quantitative data reliability and 3) use both of these to propose a VOI workflow for spatial decisions and data. The dynamic response of the subsurface is the result of some stress or perturbation (which is either important for or representing the decision action) and the geologic spatial heterogeneity. Prior models are used to capture the prior uncertainty of the dynamic response. Geostatistical simulation and a dynamic simulation function are both used to actualize the data reliability. The geostatistical simulation requires a likelihood function. Likelihood functions describe a particular data attribute's discrimination ability of the key geologic indicators (deemed to influence the decision outcome). The geostatistical simulation creates Earth models conditioned to the synthetic geophysical data, thereby representing possible interpretations that could be made if the information was purchased. Using these prior and conditioned models' dynamic responses, a VOI workflow is proposed for dynamic spatial problems. Specifically, two VOI calculations were determined using two different likelihoods. This thesis contributes VOI methodologies that incorporate the spatial element into Earth science decisions. Previous VOI studies ignored the spatial dimension. Spatial modeling is included in the prior model uncertainty and in both proposed information reliability methodologies. In the first method, the spatial aspect is included by simulating the interpretation of a geophysical image. The second method proposes geostatistical simulation to represent the variability in the geophysical message and how geophysics could resolve the static properties which influence a dynamic response. These methods for obtaining spatial data reliability and consequently a VOI estimate will become increasingly important with changing uncertainties and risks regarding decisions related to the management of our natural resources.