Impactor mass and source cutoff frequency estimations for three large impacts detected by the Apollo seismometers

Let us consider the source excitation process for an impact. Following [1], we assume a simple model for the seismic source function, namely, a time-dependent force acting downward on the surface of the planet during the impact: f(t)=G g(t)=G g(t)*δ(t),g(t)=1+cosω1t for t in the interval (-π/ω1,π/ω1), g(t)=0 otherwise, where g(t) is the time dependence of the source, G is used to denote the amplitude of the applied force. This takes into account the fact that part of the seismic force could be associated with ejecta material [2]. We introduce the time constant,τ, equal to 2τ/ω1 to denote the time-duration of the excitation process. For SIVB’s and LM impacts we have τ=0.6 sec and 0.45 sec, respectively and a very good fit explaining practically for all the data and a very high quality factor. In contrast, for the seismic force as a point force (without ejecta generation) we find not only an unrealistically low Q values, but, moreover, a much lower variance reduction. The same fit was done for large meteoroids impacts (impacts on day the 13th and the 25th of January and the 14th of November 1976) (τ = 0.7, 0.8 and 1.05 sec, respectively). We get a very good fit explaining practically for all the data with 98% variance reduction and a very high quality factor. In contrast, the results with the seismic force as a point source are not satisfactory. For all these impacts, we have determined the values of the seismic impulse by matching the energy in the observed and modeled waveforms. To get the mass of a meteoroid we should correct for the ejecta effects, which lead to a mv product smaller by a ratio 1.5 to 1.7 as compared to the seismic impulse. This gave estimates on the mass and size of the meteoroids. Current estimates of the size of the meteoroids (diameter of 2-3 meters) indicate that they could create craters of about 50-70 meters in diameter: it might therefore be possible for the NASA Lunar Reconnaissance Orbiter mission to detect these craters. These impacts were insufficient to generate surface waves above the detection threshold of the Apollo seismometer. Future seismometers must have performances at least 10 times better than Apollo in order to get these surface waves from comparable impacts. Such a resolution will also allow the detection of several impacts of low mass (1-10 kg) at a few 10s to hundred km of each station, which might be used to perform local studies of the crust. Acknowledgements. This work was supported by Programme National de Planetologie from INSU, the French Space Agency (R&T program).and Grant No. 09-02-00128 and 09-05-91056 from the Russian Fund for Fundamental Research. References [1] McGarr, A., Latham, G.V., and Gault, D.E. 1969. JGR, Vol.74 (25), pp.5981-5994. [2] Lognonné, Ph., Le Feuvre, M., Johnson, C.L., and Weber, R.C. 2009. JGR, Vol. 114, E12003. [3] Gagnepain-Beyneix, J., Lognonné, P., Chenet, H., Lombardi, D., and Spohn, T. 2006. PEPI, Vol.159, pp.140-166. [4] T.V.Gudkova, Ph. Lognonné, and J. Gagnepain-Beyneix 2010. submitted to Icarus, 2010.