ESE 502 Tony E. Smith ASSIGNMENT 3 (1) In this study you will use some of the Cobalt data from “Vancouver Island Geochemistry” data set in B&G (pp.150, 202) to carry out essentially the same type of analysis done in class for the Nickel data. This is basically a two-part study. In the first part [sections (a) and (b) below] you will analyze the pattern of spatial dependencies among these cobalt values in terms of variograms and their derived covariograms. In the second part [sections (c) and (d) below] you will use the covariances estimated in the first part to carry out stochastic interpolation of cobalt values in terms of a simple kriging model. To gain further perspective on these statistical methods of geochemical prospecting: - I have included two short references, Geochemical_Prospecting.pdf and Geochemistry_in_BC.pdf in T:\sys502\arcview\projects\Cobalt_2. Both were obtained by a Google search. You can find further useful information on Google (including good maps of Vancouver Island). - In the Reference Materials, I have also included a standard reference on Geochemical Mapping, namely Chapter 5 in Howarth, R.J. (ed.) Statistics and Data Analysis in Geochemical Prospecting, 1984, Elsevier: Amsterdam. This is intended simply to give you some idea of the many mapping techniques used in geochemical prospecting. (This is a long chapter, so you may want to look at it before downloading.) To view this data, open ARCMAP and then open the class file T:\sys502\arcview\ projects\Cobalt_2\Cobalt_2.mxd. [Note that the interpolation grids saved in this assignment (and later assignments) can be large. Since space is limited on personal ENIAC accounts, you may need to store these on some form of diskette, depending on your available space.] (a) Your first task is to recreate this map document in your home directory so that you can edit it. 1. In “My Computer” navigate to T:\sys502\arcview\projects\Cobalt_2 and copy the entire directory it to your home directory, say S:\home\Cobalt_2. [Note: At this point you could simply take my version of Cobalt_2.mxd and change all the “source” paths to your home directory. Hence the purpose of this exercise is partly to give you experience in constructing such a map document (.mxd) file from scratch.] 2. Now return to ARCMAP and clear Cobalt_2.mxd by clicking File  New, and in the “New” window, clicking My Templates  Blank Document  OK. In this new document click “Add Data” on the toolbar. Then, in the “Add Data” window, click on the “Connect to Folder” icon on the Toolbar, and2open your home directory, S:\home\Cobalt_2. (Ignore any error messages about “spatial references”.) 3. Next add the three shape files (geo_bnd.shp, mask.shp, geo_dat.shp) to the open data frame “Layers”. [Be sure to add them exactly in this order.] They will now appear as Layers (subheadings) in the Table of Contents). 4. Change the name of the data frame to “Cobalt Region” by right clicking on “Layers”, and clicking Properties  General. Similarly, rename the layers “geo_bnd” and “geo_dat” as “Vancouver Island” and “Cobalt Data”, respectively, by right clicking on each of their labels. Now save this document in your home directory as Cobalt_2. (You might first rename the existing copy of this file in your directory as Cobalt_2_old – if you do not wish to overwrite it.) 5. You should now see “Vancouver Island” together with the locations of the “Cobalt Data”. a. To display the “mask” properly, double click on its colored square in the Table of contents, and set Fill Color = “White”, Outline Color = “Black”, and Outline Width = “2”. b. You can change the color of the Vancouver map as you like. c. Be sure to re-save the file every time you make additions or changes. 6. To display the Cobalt data values:1 a. Right click on “Cobalt Data” in the Table of Contents, and click: Properties  Symbology  Quantities (on the left side) b. In the “Quantities” window [which should be set to “Graduated colors”] set Value = “CO”. (You can then edit the number of classes or values symbols for Cobalt as you like.) c. Click Apply and then OK. 7. To set the proper distance units to meters, right click on the “Cobalt Region” data frame, click Properties (which should open to the “General” tab) and in 1 The values shown are obtained from stream measurements. Stream sediment is filtered through a mesh [typically around 100 microns (millionths of an inch)] and the measurements of cobalt concentration are then in terms of parts per million (ppm). So a cobalt value of say 20 means “20 ppm in filtered stream sediment”.3the Units box, change Map units to “Meters” and then change Display units to “Meters”. Click Apply and OK. 8. Save one more time, and leave this file open for later use in the Assignment. (b) Next you will construct a variogram (and its derived covariogram) for this Cobalt data in MATLAB. The data for this construction is contained in the workspace cobalt_2.mat. 1. The matrix, cobalt_2, in this workspace contains the coordinates and cobalt values ( , , )iiixyz for the 286 locations in this region. 2. To examine possible maximum distances for the desired variogram, observe first (by an application of the measurement tool in ARCMAP) that a neighborhood of 20000 meters around typical sites (about Dmax/4) appears to be large enough to contain most positive dependencies with other sites. So try a variogram with this maximum distance (using the options structure, opts): » opts.maxdist = 20000; var_spher_plot(cobalt_2,opts); What does the derived covariogram suggest about local dependencies among neighboring cobalt sites? 3. Next, observe (again by using the measurement tool) that the usual “max/2h ” value of maximum distance in this case is about 40,000 meters. So try this variogram: » opts.maxdist = 40000; var_spher_plot(cobalt_2,opts); 4. What are the differences between these two derived covariograms ? Try to explain these differences in terms of the pattern of Cobalt values displayed in ARCMAP. (c) Next you will Krige this data in MATLAB using the program krige_simple.m. Here we will use the variogram estimate obtained for the 20,000 meter max distance. (i) To do so, rerun var_spher_plot and define the parameter vector, p, as follows: » opts.maxdist = 20000; OUT