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

Abstract

We evaluate methods to estimate the global seismic moment rate of a planet from the ≥ 1 largest events observed during a limited and possibly short time span, as can be expected e.g. 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 catalog, subsets thereof, and a catalog of stable continental regions seismicity. From the largest event observed at Goldstone alone (≈ 7.9) we estimate the Earth's global moment rate to be 1.03 × 10 22 ⁄ , while an estimation based on the 10 strongest events yields a rate of 5.79 × 10 21 ⁄. Summation of 42 years of GCMT solutions result in an average of 7.61 × 10 21 ⁄. In general, a two years interval of GCMT solutions is sufficient to estimate the Earth's annual moment rate to within a factor 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 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.

Initial results from the InSight mission on Mars

“…We note that the robust determination of b requires much larger datasets 43 and will only be possible later in the mission. To connect the seismicity to geodynamic modelling and the global heat budget 36 requires an estimate of the full planetary moment release, which is dominated by the largest events in the distribution 44 , at least for values of b near 1.…”

“…Seismic waveforms as well as data from all other InSight instruments and MOLA topographic data are available from NASA PDS (https://pds.nasa.gov/). The terrestrial stations CH.DAVOX and CH.FIESA are part of the Swiss Seismic Network 44 . The data from these stations are accessible from the Incorporated Research Institutes for Seismology (IRIS) at https://www.iris.edu/hq.…”

Magnitude Scales for Marsquakes Calibrated from InSight Data

“…Magnitude estimates of marsquakes are a key component in the characterization of the seismic activity rate of Mars (Knapmeyer et al, 2019). All pre-mission Martian seismicity models are based on estimated moment rates, which require magnitudes.…”

The Global Seismic Moment Rate of Mars after Event S1222a

“…With only one event left, we have to resort to the NLVR (Normalized Largest eVent eveR) estimator of Knapmeyer et al (2019), which assumes that the cumulative momentfrequency distribution follows a tapered Gutenberg-Richter (TGR) distribution with corner moment 𝑀 and magnitude of completeness 𝑀 , such that the relative number Φ of events exceeding magnitude 𝑀 is…”

“…2, to obtain a distribution of NLVR estimations. These estimations are compared with the above intervals to obtain the desired probabilities, called emission probabilities by Knapmeyer et al (2019). Figure 3 shows these probabilities in the moment-rate-corner-magnitude parameter space and in the form of the corresponding cumulative size-frequency distributions for both 𝑏 = 1.17 and 𝑏 = 1.0.…”