Estimation of the Seismic Moment Rate from an Incomplete Seismicity Catalog, in the Context of the InSight Mission to Mars

We evaluate methods to estimate the global seismic moment rate of a planet from the k >= 1 largest events observed during a limited and possibly short-time span, as can be expected, for example, for lander missions to Mars. The feasibility of the approach is demonstrated with a temporary broadband seismometer that was recording in the Mojave desert, California, for 86 days in 2014, and by application to the Global Centroid Moment Tensor (CMT) catalog, subsets thereof, and a catalog of stable continental regions seismicity. From the largest event observed at Goldstone alone (M-w approximate to 7.9), we estimate the Earth's global moment rate to be 1.03 x 10(22) N . m/yr, whereas an estimation based on the 10 strongest events yields a rate of 5.79 x 10(21) N . m/yr. Summation of 42 yr of Global CMT solutions results in an average of 7.61 x 10(21) N . m/yr. In general, a 2 yr interval of Global CMT solutions is sufficient to estimate the Earth's annual moment rate to within a factor of 5 or better. A series of numerical experiments with more than 560 million synthetic catalogs based on the tapered Gutenberg-Richter distribution shows that the estimation is rather insensitive against an unknown slope of the distribution, and that bias and variance of the estimator depend on the ratio between moment rate and corner moment of the size frequency distribution. Moment rates of published Mars models differ by a factor of 1000 or more. Tests with simulated catalogs show that it will be possible to reject some of these models with data returned by NASA's InSight mission after two years of nominal mission life time.