Forgive me for jumping straight in with what is probably a rather difficult question, but I want to make sure I'm not "reinventing the wheel" here.
Does anyone know of any algorithms that allow one to incorporate trends from another variable without requiring a direct correlation? I'm trying to incorporate bathymetry data into the interpolation of magnetic anomalies at seafloor spreading centers. Normally this would relatively straightforward via kriging w/exd, cokriging, etc. However, there is no direct correlation between the values of the variables themselves; rather, they simply share the same trends. In other words, a high bathymetry value has no relation to a high magnetic anomaly, but pattern of highs and lows in the magnetics follows the pattern of highs and lows in the bathymetry. The obvious approach is to use the seafloor fabric to define transforms and pusedofaults and use these as breaklines, but I'd perfer a more generally applicable approach. I've played around with trying some sort of fuzzy logic correlation via indicator kriging using the gradient, curvature, etc. of the data sets rather than thier actual values. Unfortunately, this seems to be a dead end. My current idea is quantify the seafloor fabric for a region inside a moving window by extracting the eigenvectors of the cloud of unit normals to the seafloor surface within that window. This is basically the same approach mentioned in <a href="http://www.geovista.psu.edu/sites/geocomp99/Gc99/096/gc_096.htm";>this</a> conference document by Guth, 1999. A good example to visualize this is <a href="http://www.geovista.psu.edu/sites/geocomp99/Gc99/096/gc_96_07.htm";>this</a> figure in the document. This gives me a way to quantify the seafloor fabric, but the real problem is incorporating that into the interpolation of the magnetics. I had in mind an iterative process, by which one would krige the magnetics as normal, then adjust each 3x3 matrix of magnetic values such that that fabric of the magnetic grid comes into alignment with the fabric of the bathymetry. The error variance derived from the original kriging would be used to set a limit on how much the value of each cell is allowed to change. Obviously, this is a bit poorly thought out at this point, and I'm quite sure that the details will be hellish, so I'm hoping someone out there has a better idea! Has something like this already been done? I can't seem to find anything in the literature, but my searches are biased toward geoscience related journals, rather than statistical journals. I'm undoubtedly not looking for quite the right thing as well. At any rate, any input, suggestions, or warnings will be greatly appreciated. -Joe Kington
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