From: Peter Bird Date: April 15, 2009 10:33:27 AM PDT To: "Sandwell, David" , "freed@purdue.edu" , "tparsons@usgs.gov" , Corne Kreemer Subject: Bird's files for strain-rate comparison are ready Dear Dave, Corne, Tom, & Andy: To contribute to the comparison of strain-rates from different models of California, I have prepared files in your requested format: http://peterbird.name/oldFTP/temporary/strain-rates/Bird_GCN2008088_exx.dat.txt http://peterbird.name/oldFTP/temporary/strain-rates/Bird_GCN2008088_exy.dat.txt http://peterbird.name/oldFTP/temporary/strain-rates/Bird_GCN2008088_eyy.dat.txt and I have also included a file with the outline contour of my model area: http://peterbird.name/oldFTP/temporary/strain-rates/outline_of_GCN8p9.feg.dig.tx t Note that the final file-name-extensions of ".txt" were needed to get these files served properly by the host (IIS); you should feel free to remove them after download. The modeling project is described in a manuscript that some of you may have read: http://peterbird.name/oldFTP/temporary/Bird_GCN_manuscript_2008_12.pdf which is currently under revision--hopefully to be accepted in May/June by JGR. The model I am sending is the "preferred model" of that manuscript: GCN2008088. The F-E grid for this model is GCN8p9.feg, which is composed of 12627 contiguous spherical triangles (defined by 6452 shared nodes where velocities were computed); its outer bounding box is -128.2 to -103.9 East by 30.1 to 49.3 North (but it does not fill that area). The finite elements are mostly of 3 discrete sizes: * ~equilateral with sides of 30 km (in low strain-rate areas) * ~equilateral with sides of 15 km (in high strain-rate areas) * elongated, approximately 4 km x 15 km (along fast faults) Because these triangles are so small (compared to Earth radius) the distinction between spherical triangle elements and ordinary planar "constant-strain triangles" is academic, and I ignore it here. The strain-rates given are my best estimates of the long-term-average (e.g., over 10^4 to 10^6 years) so they are ANelastic by definition. I computed the (constant) horizontal-plane strain-rate tensor in each of these finite elements, expressed it as exx, exy, and eyy (in /s) and reported the same identical value at 4 points in each of my elements: Internal coordinates: S1 S2 S3 point #1: 1/3 1/3 1/3 point #2: 0.8 0.1 0.1 point #3: 0.1 0.8 0.1 point #4: 0.1 0.1 0.8 (S1+S2+S3==1 by definition of ternary coordinates.) That is, I report the same value at the element centroid, and also at 3 points that are near (but not at) the 3 corner nodes. I think the best way to interpolate these values would be by Delaunay triangulation (leading to a new grid of ~75000 triangles) followed by linear interpolation within each little new triangle. This would give flat values in the centers of my elements, and steep linear transitions around the sides of my elements. I suspect most integral measures would be ~conserved. (Result would be C0-continuous but not C1-continuous.) I also tried interpolating values by kriging (to make a test plot), but this was not very satisfactory. The variogram actually declines with distance (due to screwy statistics of a biased sampling of a quasi-fractal field), and the results had negative side-lobes around all major faults. I don't know what splines would do, but I suspect they would have problems due to the ~fractal nature of the data. If Delaunay triangulation is too slow to be practical (e.g., in my version of MATLAB it crashes), then nearest-neighbor would probably be the next-best interpolation method. Plotting these values in color will also be a challenge, due to the extreme dynamic range (concentrated along major faults, where slip-rate is typically averaged over ~4000 m to get the strain-rate). We cannot use the trick of taking logarithms because ~1/2 of strain-rate component values are negative. Perhaps a good plot could result from setting color temperature proportional to: arctan(exx/(1E-15 /s)) ? (I am just guessing when I suggest 1E-15 /s as the scale; obviously this would have to be chosen so as to produce ~satisfactory plots of ALL the models in this comparison.) Best wishes, Peter Bird ------------------------------------------------------------ Prof. Peter Bird Department of Earth and Space Sciences University of California Los Angeles, CA 90095-1567 (310) 825-1126 pbird@ess.ucla.edu http://PeterBird.name