Towards Reliable Sub-Division of Geological Areas: Interval Approach

An appropriate subdivision of a geophysical area into segments enables us to extrapolate the results obtained in some locations within the segment (where extensive research was done) to other locations within the same segment, and thus, get a good understanding of the locations which weren’t thoroughly analyzed. Often, different evidence and different experts’ intuition support different subdivisions schemes. For example, in our area – Rio Grande rift zone – there is some geochemical evidence that this zone is divided into three segments, but, in the viewpoint of many researchers, this evidence is not yet sufficiently convincing. We show that if we use topographical information (this information, e.g., comes from satellite photos), then interval methods lead to a reliable justification for the tripartite subdivision of the Rio Grande rift zone. Appropriate subdivision is important in geophysics. In geophysics, appropriate subdivision of an area into segments is extremely important, because it enables us to extrapolate the results obtained in some locations within the segment (where extensive research was done) to other locations within the same segment, and thus, get a good understanding of the locations which weren’t that thoroughly analyzed. A problem: it is often difficult to produce a reliable subdivision. The subdivision of a geological zone into segments is often a controversial issue, with different evidence and different experts’ intuition supporting different subdivisions. For example, in our area – Rio Grande rift zone – there is some geochemical evidence that this zone is divided into three segments [5]: the southern segment which is located, approximately, between the latitudes y and y ; the central segment – from y to y ; and the northern segment – from y to y . However, in the viewpoint of many researchers, this evidence is not yet sufficiently convincing. It is therefore desirable to develop new techniques for zone sub-division, techniques which would be in the least possible way dependent on the (subjective) expert opinion and would, thus, be maximally reliable. Main idea: using topographic information. One reason for subjectivity is the fact that the existing subdivision is often based on the chemical and physical analysis of several samples collected throughout the area, and often, we do not have a statistically sufficient amount of thoroughly analyzed geological samples to make the conclusion about the subdivision statistically convincing. To make this conclusion more reliable, we can use, instead of the more rare geological samples, a more abundant topographical information (this information, e.g., comes from satellite photos). We can characterize each part of the divided zone by its topography. Preserving only geophysically meaningful topographic information: the use of spectral values corresponding to long wavelengths. In topographical analysis, we face a new problem: of too much data, most of which is geophysically irrelevant. To eliminate some of this irrelevant data, we can use the Fourier transform; indeed, it is known that while (at least some) absolute values of the map (forming a so-called spectrum) are geophysically meaningful, the phases usually are random and can be therefore ignored. So, we should only use the spectrum. Since we are interested only in the large-scale classification, it makes sense to only use the spectrum values corresponding to relatively large spatial wavelengths, i.e., wavelengths L for which L L for some appropriate value L . In particular, for the sub-division of the Rio Grande rift, it makes sense to use only wavelengths of L km or larger. Also, for the Rio Grande Rift, we are interested in the classification of horizontal zones, so it makes sense to do the following: divide the Rio Grande Rift into 1 zones y y (with y from y to y , from y to y , . . . , from y to y ); for each of these zones, take the topographic data, i.e., the height h x y described as a function of longitude x and latitude y; for each zone and for each y, compute the Fourier transform H y with respect to x; for each zone, combine all the spectral values which correspond to large wavelength (i.e., for which L ), and compute the resulting spectral value