Elastic lithosphere thickness on the moon from mare tectonic features - A formal inversion

The thickness (T) of the lunar elastic lithosphere at the time (3.6 to 3.8 billion years ago) of the earliest preserved basalt flows in circular mare basins can be estimated by inverting the observed locations of extensional tectonic features in and surrounding the maria. In performing the inversion, the lithosphere is modeled as an elastic shell with a liquid interior, and the basalt load for each mare is approximated by a set of concentric cylinders. To permit solving the forward problem of placing radial limits on the positions of the rilles around a given mare, an additional parameter F, the ratio of the radial stress at the radial limits to the maximum radial stress, is introduced. T and F are chosen to give the best weighted-squares fit of the radial limits to the observations, and are used as the initial values in a linearized matrix inversion to check the resolution and estimate errors. The application of the procedure to three maria with prominent extensional features, Humorum, Orientale, and Serenitatis, gives values of T from about 40 + or - 10 to 50 + or - 10 km, and in each case the linearized matrix equation has an exact inverse.