Google Earth: Restoration Parameters and Restoring Data Points

McQuarrie and Wernicke (2005) produced a series of reconstructions of the southwestern United States from 36 Ma to present, as discrete blocks displaced from one another and from the stable midcontinent. These reconstructions were defined by shapefiles incorporating polygons outlining each block. Using GeoGraphix Discovery, the polygons in the shapefiles were converted to latitude and longitude. For each block and reconstruction, finite rotations from the reconstructed age to present were calculated. For the northwestern United States, discrete reconstruction sets for two different ages are derived from maps produced by Atwater.
Method for calculating restorations
For a particular reconstruction age, the finite rotation of each block from that age to the present was derived using a four point method. Given points a1 and a2 on Block A, and corresponding points a1' and a2' on rotated Block A': determine that one of the two poles that is 90 degrees away from both points and then the angle that rotates a1' to a1 around the pole. Rotate a2' using the same pole and angle to produce a2''. Then determine the angle (positive or negative) that rotates a2'' to a2 around a1 (serving as the pole). From the two resulting sets of rotation parameters, compute the total, equivalent rotation.

Then, to allow restoration of discrete data points within the reconstruction region, form a grid comparable to or at a higher resolution than the reconstructed block spacing. Convert the reconstruction parameters to pseudovectors with magnitude equal to the rotation angle and assign them to each node of the corresponding block in present-day coordinates. Interpolate the pseudovectors onto the grid using a Gaussian distance filter and the twelve nearest block nodes to the grid node. Because the filter is exponential with distance, grid points falling within a block should produce interpolated pseudovectors equivalent to that assigned to the entire block. The result is three grids for each age corresponding with each pseudovector component and reconstruction age.

Given a discrete data point of a specific age, interpolate the pseudovectors for the two reconstruction ages that bracket the data point age using the same Gaussian distance filter method used to calculate the grid. Then linearly interpolate the pseudovector components using the ages. Convert the pseudovector to rotation parameters and apply to the data point.

Subsequent posts will provide examples of this approach.

Basalts of the Western US in Google Earth

Isotopic age dates in Ma (millions of years before present) of basaltic igneous rocks from western United States, 0-40 Ma. Source: US Geological Survey. Posted on Google Earth Community website: Link.

This is a reduction of the larger data set posted previously (US Cordilleran Igneous Isotopic Dates LT 40 Ma).

SW US Reconstructions in Google Earth

McQuarrie and Wernicke (2005) produced a highly detailed series of reconstructions of the principal tectonic blocks of the southwestern United States from 36 Ma to Present. I have converted the shapefiles they produced to single KMZ file for viewing in Google Earth, including a set of polygons for each reconstruction age.

From their reconstructions, I have derived equivalent finite rotation parameters for each tectonic block from the reconstruction age to present. Watch for subsequent posts that utilize these parameters...

Source: McQuarrie, N., and Wernicke, B.P., An animated tectonic reconstruction of Southwestern North America since 36 Ma, Geosphere; December 2005; v. 1; no. 3; p. 147-172; DOI: 10.1130/GES00016.1. http://geosphere.geoscienceworld.org/cgi/content/abstract/1/3/147

Plate-Hotspot Loci in Google Earth

A new model data set is available for Google Earth: Pacific and Nazca plate loci in four frames .

These calculated loci, representing motion of the Pacific and Nazca plates in four different reference frames, demonstrate the remarkable correspondence of motion among the Hawaiian hotspot frame and the North and South American plates. Pilger (2007) has discussed the implications of this correspondence for the existence of at least two different hotspot reference frames: Hawaiian (beneath the plates of the Pacific) and Tristan (beneath the Atlantic and Indian Oceans and adjacent continents). This contrasts with the persistent assumption that the global hotspot set represents a single hotspot reference frame. By viewing in Google Earth, the correspondence is apparent over the extent of the Pacific plate where long-lived hotspot traces exist.

Data sharing via Google Earth

I've prepared an introduction to Google Earth, together with a proposal for other Earth Scientists to add tectonically-oriented data sets to the Google Earth Community website. This proposal is posted at: http://www.mantleplumes.org/WebDocuments/GoogleEarthProposal.pdf.