SOURCE CUTOFF FREQUENCY ESTIMATIONS FOR A NUMBER OF IMPACTS DETECTED BY THE APOLLO SEISMOMETERS T.V.Gudkova a, Ph. Lognonné b, J. Gagnepain-Beyneix b, V. Soloviev a a- Schmidt Institute of Physics of the Earth RAS, B.Gruzinskaya, Moscow - RUSSIA ( b- Institut de Physique du Globe de Paris, Planetary and Space Geophysics, 4 av. De Neptune SAINT-MAUR des Fossés – FRANCE

Each seismic station contained four seismometers: three long-period (LP) instruments (two horizontal and one vertical; and one short-period (SP) vertical instrument. The Moon is the only planetary body besides the Earth for which seismic data were obtained. Between 1969 and 1977 a network of four stations was operating on the nearside of the Moon.

More than seismic events were recorded. The seismic events were generated by both impacts (meteoroids and artificial impacts) and quakes (deep, shallow and thermal events). In all cases a long reverberation is observed, as a consequence of the high scattering and low absorption of the upper part of the Moon’s lithosphere. Seismograms corresponding to the Moonquakes recorded on the Apollo seismometers from ( Nakamura et al ) Meteoroid impacts are important seismic sources for constraining the crustal and upper mantle structure: 1)As they are impacting the Moon continuously, they are a source of microseismic noise, in addition to such other sources as deep moonquakes or thermal quakes. 2)The surface location of the source: only time and selenographic position are necessary to characterize their location. Moreover, these events are associated with a light flash generated during the impact, which can be detected from the Earth.

Artificial impacts used for the calibration Lunar Module (LM) Ascent stage, S-IVB rocket stage (Data are taken from Toksoz et al., 1974) ImpactDataLatLong Impact velocity (km/s) Mass (kg) Distance from stations Kinetic energy (erg) mv (kg m/s) S12S14S15S16 12LM 13S4 14S4 14LM 15S4 15LM 16S4 17S4 17LM S 2.75S 8.09S 3.42S 1.51S 26.36N 1.30N 4.21S 19.96N 21.20W 27.86W 26.02W 19.67W 11.81W 0.25E 23.80W 12.31W 30.50E ? ?       ? 4.71         10 7 ? 3.69   10 7 Seismic records from the Apollo Seismic network of the impact of the Apollo 17 Saturn V upper stage (Saturn IVB) on December 10, 1972 distances of 338, 157, 1032, and 850 km from the Apollo 12,14, 15 and 16 stations X,Y,Z are the long-period seismometers, z is the short-period seismometer. Numbers at the right are peak amplitudes in digital units

The abscissa is the duration (s), the ordinate is the amplitude (in DUs). The date of the event and the name of the station recorded the event are given. The data set and synthetics are band-pass filtered, with a cosine taper with frequencies between 0.2 and 0.4 Hz. Synthetic lunar seismograms compared with data set recorded at the stations (left) for the events: 25 January 1976 and 14 November By using the artificial impact, we first develop a calibrated analysis for extracting the impulse (i.e. mass times impact velocity) from the amplitude of seismic waves. For artificial impacts of the LM and SIVB Apollo upper stages the method allows us to retrieve the mass within 20% of relative error. Synthetic seismograms are computed for a spherical model of the Moon. They are unable to match the waveforms of the observations, but nevertheless provide an approximate measure of the energy of seismic waves in the coda. It allows us to compute a rough estimation of the seismic energy in a given time window. Its square root, equivalent to the mean rms in the window, is proportional to the seismic impulse, i.e. the time integrated seismic force. Synthetic lunar seismograms (right) and data set recorded at the stations (left) for man-made signals.

Meteoroid impacts DataLatLong Origin time Distance from stations (km) S12S15S16 13 Jan Jan Nov Estimated masses and diameters of meteoroids The velocity of meteorites have been taken in the range of 10 and 30 km/s. The density can be varied from 1 to 3 g/cm 3. Taking value of the density equal to 3 g/cm 3, we have diameter of meteoroids of 2-3 meters. Date mv I (kg m/s) Mass (tones) Diameter (m) 13 Jan Jan Nov   

The comparison of typical spectra of impact signals (14 Nov 1976, lat , long ) with those of quakes (3 Jan 1975, lat , long ). The events are at comparable distances Z is long period and z is short period components, respectively. Solid and dashed lines indicate  2 and  3 slopes. Below 0.5 Hz, we recognize the ω 3 and ω 2 slopes, but see a clear weakening of the impact spectrum above about 1 Hz. As we will see, the differences in the spectrum are mainly due to source processes. By combining both the Apollo long period and short period data, further analysis can be made on the dynamic of the seismic source.

Let us consider the source excitation process for an impact where an impactor is instantaneously absorbed by the surface without ejecta generation. The associated seismic force can then be modeled as a point force, with a seismic force given by F 0 (t, x )=m v  (t)  ( x - x s ), (1) where m is the mass, v is the velocity vector (v being the velocity amplitude),  is the Dirac’s delta function, t and x are time and position variables. Below 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, which takes into account the fact that part of the seismic force could be associated with ejecta material. Let the time dependant seismic source function be in the form: f(t, x ) = m v δ(x-x s ) g(t) = f(t) δ (x-x s ) = F 0 (t, x )*g(t), g(t)=1+cos ω 1 t for -  /ω 1 <t<  /ω 1, g(t)=0 otherwise, (2) where g(t) is the time dependence of the source, * is a convolution product. We introduce the time constant, , equal to 2  /ω 1 to denote the time-duration of the excitation process, as well as the seismic impulse, defined as an intergral of the equivalent force f(t). We define the seismic amplification parameter as S=I/mv. The Fourier transform of g(t) is proportional to ω -3 for angular frequencies higher than the cutoff angular frequency ω 1. That is why we expect the seismic acceleration spectrum, which varies as ω 3 at low frequency for an impact, to be flat after the cutoff frequency and even to decrease due to additional effects such as attenuation.

Log-log plot of the scaled acceleration spectral density for three SIVB impacts as recorded on the four Apollo stations. In addition to the seismic impulse scaling, the attenuation effect has been corrected by multiplying the spectrum by exp ( w t prop /2Q), where Q is the quality factor found by the least squares inversion. Solid lines show the theoretical scaled acceleration spectral density for the source functions given by a) Eq. (2) and b) Eq. (1).  =0.65s Q  The amplitude of the spectrum recorded at a given epicentral distance D can be approximated as where B is a constant depending on the seismic impulse and epicentral distance, Q the quality factor related to attenuation, exp(- wt prop/ 2Q) –attenuation effect. We determined by a least squares fit to the logarithmic amplitudes, the best values for Q,  (the time duration of the excitation process) and B by a grid search. We get a very good fit to the data for seismic source function in the form (2) (with account of ejecta material), and an unrealistically low Q values for (1). Q=650 Much lower then any of the Q value reported for the crust and upper mantle

Log-log plot of the scaled acceleration spectral density for three large meteoroids impacts, recorded on LP and SP vertical components at stations 15 and 16. The blue, red and green lines are the theoretical scaled acceleration spectral densities calculated for simulated events (13 January, 25 January and 14 November 1976,  =0.7, 0.8, 1.05 s, respectively) with the assumed source function in the form of (2). The dashed lines are least square fit of logarithmic amplitudes. In addition to the seismic impulse scaling, the attenuation effect has been corrected by multiplying the spectrum by exp(  t prop /2Q), where Q is the quality factor found by the least squares inversion. The larger an impact is, the lower is its cutoff frequency. Q>20000  -0.7; 0.8 and 1.05 s for the impacts on 13 th, 25 th and the 14 th of November, respectively. (5x10 8 ; 8x10 8 and 9x10 8 kg m/s) The results without considering ejecta material are not satisfactory.

For our analysis we have selected 40 impacts well enough recorded on vertical component by the most of the stations. Note that many of the impacts under consideration occur on the nearside of the Moon, and limited seismic recordings of impacts (impacts on farside) were made at large epicentral distances from the nearside Apollo network bb Location of the impacts under consideration.

Time duration of the impact process as function of the momentum transfer of the meteoroids. Dashed line is approximation for the impacts on the rock material, and the dot-dashed line is for the soil. We propose that the difference between the source cutoff frequency for the impacts with the same momentum transfer are caused by the excitation processes due to the location (subsurface composition) and incident angle, as the seismic radiation of the shock wave depends on the most-upper regolith layers. Some uncertainties exist due to factors that include instabilities of the amplitudes of seismic signals and shape of the spectrum associated with propagation effects, variations in the upper mantle attenuation beneath different sites. The response is calculated for idealized structure, as the local geophysical conditions were not taken into account. But the tendency is seen the larger an impact is, the lower is its cutoff frequency for the impacts falling in the same area. The cutoff frequency is lower for the impacts falling on rock in comparison with the cutoff frequency for the impacts falling on soil. mv, momentum transfer of the meteoroid 

We have estimated the impulse response and frequency properties of some largest meteoroid impacts. Their masses can be estimated with rather simple modeling technique and that high frequency seismic signals have reduced amplitudes due to a relatively low ( about 1sec) corner frequency resulting from the duration of the impact process and the crater formation. Current estimates of the size of the meteoroids (diameter of 2-3 meters) indicate that they could create craters of about meters in diameter: The estimate of source cutoff frequency for a number of impacts detected by the Apollo seismometers was done in order to find the dispersion of parameters depending on the location (subsurface composition) and the amplitudes of the seismic signals. The recordings of the meteoroid impacts are well explained by the model of the seismic impulse due to the impactor, resulting ejecta and the effects of attenuation. The target material which vary a great deal between nearside and farside of the Moon acts the efficiency of the impact. Conclusion