Space-Time Forecasting Using Soft Geostatistics: A Case Study in Forecasting Municipal Water Demand for Phoenix, AZ

Managing environmental and social systems in the face of uncertainty requires the best possible forecasts of future conditions. We use space-time variability in historical data and projections of future population density to improve forecasting of residential water demand in the City of Phoenix, Arizona. Our future water estimates are derived using the first and second order statistical moments between a dependent variable, water use, and an independent variable, population density. The independent variable is projected at future points, and remains uncertain. We use adjusted statistical moments that cover projection errors in the independent variable, and propose a methodology to generate information-rich future estimates. These updated estimates are processed in Bayesian Maximum Entropy (BME), which produces maps of estimated water use to the year 2030. Integrating the uncertain estimates into the space-time forecasting process improves forecasting accuracy up to 43.9% over other space-time mapping methods that do not assimilate the uncertain estimates. Further validation studies reveal that BME is more accurate than co-kriging that integrates the error-free independent variable, but shows similar accuracy to kriging with measurement error that processes the uncertain estimates. Our proposed forecasting method benefits from the uncertain estimates of the future, provides up-to-date forecasts of water use, and can be adapted to other socioeconomic and environmental applications.

Fracture Characterization from Scattered Energy: A Case Study

We use 3D surface seismic data to determine the presence and the preferred orientation of fracture corridors in a field. The Scattering Index method is proving to be a robust tool for detecting and mapping fracture corridors. Fracture corridors largely control permeability and fluid flow in some fractured reservoirs. To apply the Scattering Index method, we compute the scattering transfer functions from the reservoir interval using prestack migrated data collected in four azimuth sectors. By measuring the azimuthal differences in the amount of scattering, we obtain maps of density of fracture corridors and their orientation across the survey area. We use geostatistical filtering to improve the spatial correlation of scattering index maps. The distribution and orientation of the final fracture corridors are interpreted considering the structure, fault network, and stress information. In the field, we observe several regions of high fracturing near the anticline’s crest and on its steepest slopes, on the southwest flank. Around well locations, fractures are oriented to the NW and NNW, which agrees with estimates of maximum stress direction from well data.Massachusetts Institute of Technology. Earth Resources Laborator