Raines, G.L. 1 , Zientek, M.L. 2 , Causey, J.D. 2 , and Boleneus, D.E 2 .

1. Spatial-Temporal AnalysisA Cellular Automata Model of Mineral-Related Activity from 1998 to 2010 for Idaho and Western Montana Raines, G.L.1, Zientek, M.L.2, Causey, J.D.2, and Boleneus, D.E2. 1) U.S. Geological Survey, MS 176 c/o Mackay School of Mines, UNR, Reno, Nevada 89557; Email:graines@usgs.gov 2) U.S. Geological Survey, 904 W. Riverside Ave. Room 202, Spokane, WA 99201

2. Spatial Modeling Extension • Kemp, L.D., Bonham-Carter, G.F. and Raines, G.L., 1999, Arc-WofE: Arcview extension for weights of evidence mapping. • http://gis.nrcan.gc.ca/software/arcview/wofe • Kemp, L.D., Bonham-Carter, G.F. and Raines, G.L., 2001, Arc-SDM: Arcview extension for spatial data modelling using weights of evidence, logistic regression, fuzzy logic and neural network analysis. • http://gis.nrcan.gc.ca/software/arcview/sdm

3. What is a cellular automata? • Cellular automata (CA) are defined by an array of cells. • The state of each cell evolves by a simple transition rule, the automaton. • Implementation of a CA in a GIS involves a summation filter with an if-then or logic rule.

4. Conway’s Game of LifeProbability of Life in Next Generation Assumes using a 3x3 neighborhood or kernel, that is 8 neighbors plus the center cell.

28. How have CAs been used? • Modeling evolution of cities • Project Gigalopolis http://www.ncgia.ucsb.edu/projects/gis/project_gig.htm • Flow of lava • Evolution of forest fires • Physics – diffusion, Brownian motion, defraction • Biology – life processes

29. Statement of Problem • Project mineral-related activity on public land to 2010 • Objective is to make a probabilistic prediction of total activity • Not necessary to know annual activity • Data on mineral activity from 1989 to 1998 are available to calibrate the CA • Permitting rules changed in 1992.

30. Public Lands USFS BLM Private Land

31. Neighbors Adjustment at Edges Butte Montana Neighbors 9 4 8 3 7 2 6 1 5 0 SE Idaho

32. Fuzzification of Resource Themes

33. Small Fuzzification Algorithm Where f1 is the steepness of the transition from a membership value of 1 to 0 and f2 is the mid point where the membership value is 0.5 (Tsoukalas and Uhrig, 1997).

34. > .90 .75-.90 <.75 0 Resource Thresholds Butte Montana Membership SE Idaho

35. States - Echo and Trace • Echo Status (State of a cell, 1.6 x 1.6 km) • Stayed alive • Stayed died • Just born • Just died • Trace (Sum of times a cell is alive)

36. State Stayed Alive Stayed Dead Just Born Just Died Permit Activity 1988-1998 Expansive Period

37. State Stayed Alive Stayed Dead Just Born Just Died Expansive Period

38. State Stayed Alive Stayed Dead Just Born Just Died Expansive Period

39. State Stayed Alive Stayed Dead Just Born Just Died Expansive Period

40. State Stayed Alive Stayed Dead Just Born Just Died Expansive Period

41. State Stayed Alive Stayed Dead Just Born Just Died Rule Change

42. State Stayed Alive Stayed Dead Just Born Just Died Contractive Period

43. State Stayed Alive Stayed Dead Just Born Just Died Contractive Period

44. State Stayed Alive Stayed Dead Just Born Just Died Contractive Period

45. State Stayed Alive Stayed Dead Just Born Just Died Contractive Period

46. State Stayed Alive Stayed Dead Just Born Just Died Contractive Period

47. Years Active 11 10 9 8 7 6 5 4 3 2 1 0 Trace 1988-1998 Butte Montana SE Idaho

48. Expansive Contractive Calibration – Echo States Actual CA Calculated

49. Voting RuleProbability of Life in Next Generation Does not differentiate between live and dead center cells! For mineral-related activity results in rapid death of all activity.

50. Annealed Voting RuleProbability of Life in Next Generation Softened (annealed) the boundary between 4 or 5 neighbors so mineral-related activity lasts a little longer. Still does not differentiate the status of center cell!