A Go at Geoid (technical)

Consider for a moment the geoid, which is the difference in elevation between a reference spheroid and an equipotential.  The geoid has lots of neat properties, among them being directly related to the gravitational potential energy in the lithosphere. It is sensitive to density variations at great depths and so can give us insight into deep earth processes.  But there are some issues that casual readers of papers using geoid might want to be aware of.

Geoid has long been recognized as having a sensitivity to greater depths than gravity, but this is a mixed blessing as density variations far below the asthenosphere can affect the geoid, complicating a lithospheric interpretation. The most common approach is to filter the geoid to eliminate long wavelengths that are most sensitive to deep structure–but these same wavelengths are also sensitive to the difference between continents and oceans.  In the western U.S., the look you get from the geoid depends on how you filter it.  For instance, these are two images of the geoid, one as published in Jones et al., Nature, 1996, and the other with a different filter.

Geoid7-11-JonesEA96Geoid10-15-JonesEA96

The clearest difference is at the right, where the solid zero line has moved a lot, but also note that the scale of the color bar has changed.  It can be a bit hard to compare these, so another way of looking at it is to plot some points from each against each other:

WUS_GeoidByProv

Geoid by province in the southwestern U.S.; error bars reflect scatter in the subset of points within each province used to make this plot (points were where seismic structures were located in Jones et al., 1996)

The diagonal line would be where points would plot if both filters yielded the same values. Clearly the southern Rockies (SRM) pick up a lot of power in the degree and order 7-10 range compared with, say, the Sierra Nevada (SN). If interpreting this for potential energy, at D&O >7 taper to 11 the western Great Plains (GP) would have a positive GPE and would be expected to have normal faulting, but at D&O >10 taper to 15 it would be quite negative and you would expect to have compressional stresses and possible reverse faulting.

(Beyond the issues with the edge of the filter is the nature of the taper–a brute force cutoff can produce some artifacts you might not want to interpret.)

Anyways, what is the appropriate filter?  There is no simple answer for three reasons.  One is that the maximum depth you might care about probably varies across the region so a filter that cuts off in the asthenosphere in one place might also cut off the lower lithosphere in another. Another is that there is significant shallow power in the longer wavelengths/lower orders: continent/ocean boundaries have some real power in low degrees and orders. So when you filter out the long wavelengths, you can be removing shallow signal as well as deep signal. The third is that the sensitivity with depth is gradational, so a filter won’t fully cut off greater depths unless there is reduction in power from shallower ones.

(If you are wondering, in the paper we chose D&O 7-11 as the most appropriate filter for our purposes).

So be cautious when a filtered geoid is presented as a purely lithospheric signal, for it could be contaminated with deep sources or cutting off shallow ones.

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