Magnitude Scales for Marsquakes

In anticipation of the upcoming 2018 InSight (Interior exploration using Seismic Investigations, Geodesy and Heat Transport) Discovery mission to Mars, we calibrate magnitude scales for marsquakes that incorporate state-of-the-art knowledge on Mars interior structure and the expected ambient and instrumental noise. We regress magnitude determinations of 2600 randomly distributed marsquakes, simulated with a spectral element method for 13 published 1D structural models of Mars' interior. The continuous seismic data from InSight will be returned at 2 samples per second. To account for this limited bandwidth as well as for the expected noise conditions on Mars, we define and calibrate six magnitude scales: (1) local Mars magnitude M-L(Ma) at a period of 3 s for marsquakes at distances of up to 10 degrees; (2) P-wave magnitude m(b)(Ma); (3) S-wave magnitude m(bS)(Ma) each defined at a period of 3 s and calibrated for distances from 5 degrees to 100 degrees; (4) surface-wave magnitude M-s(Ma) defined at a period of 20 s, as well as (5) moment magnitudes M-FB(Ma); and (6) M-F(Ma) computed from the low-frequency (10-100 s) plateau of the displacement spectrum for either body waves or body and surface waves, respectively; we calibrate scales (4)-(6) for distances from 5 degrees to 180 degrees. We regress stable calibrations of the six scales with respect to the seismic moment magnitude at M-w 5.5 by correcting filtered phase amplitudes for attenuation with distance and source depth. Expected errors in epicentral distance and in source depth (25% and 20 km, respectively) translate into magnitude errors of 0.1-0.3 units. We validate our magnitude relations with an independent test dataset of 2600 synthetic marsquakes (1.0 15 degrees are expected to be hidden in the Mars background noise and will likely not be detectable.