Assuming lithospheric plates to be rigid, we systematically invert 68 spreading rates, 62 fracture zones trends and 106 earthquake slip vectors simultaneously to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set.The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable.We then invert the trends of 20 linear island chains and aseismic ridges under the assumptions that they represent the directions of plate motions over a set of hot spots fixed with respect to each other. We conclude that these hot spots have had no significant relative motions in the last 10 My.

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The distribution of Th over the Mare Imbrium and northern Oceanus Procellarum portions of the Apollo 15 lunar ground track has been modeled by deconvolving several fields of orbital gamma ray spectroscopy data. Including a prior study of the Apenninus region, a continuous swath from 10°E to 60°W in the northwest quadrant has now been analyzed. In the Aristarchus region, the crater dominates the Th distribution with a concentration of 20 ppm. Other enhancements are seen on the Aristarchus Plateau and south of the plateau. The concentration across the Aristarchus Plateau is not uniform. The average Th concentration in Oceanus Procellarum is less to the west than to the east of the Aristarchus Plateau. Substantial enhancements are found in mare regions around Brayley, and at the ejecta blankets of Timocharis and Lambert. Th in the Eratosthenian mare regions is generally low with one notable exception lying roughly between the craters Euler and Carlini. The existence of enhanced Th concentrations in mare basalt regions suggests that reservoirs of some late stage mare basalts incorporated KREEP‐rich material during formation or transit.