1968, Phys. Earth Planet. Interiors 1, 151—154. North-Holland Publishing Company, Amsterdam
A NEW ESTIMATE OF LUNAR SEISMICITY DUE TO METEORITE IMPACT
STANLEY J. LASTER and FRANK PRESS Department of Geology and Geophysics Massachusetts Institute of Technology Cambridge, Massachusetts 02139, U.S.A. Received December 1967
Using Shoemaker’s new meteorite statistics, meteorite impacts on the moon should produce more seismic events than previously estimated. Whether the meteoritic seismic sources can provide useful information concerning the structure of the moon or
contribute to the ambient noise depends on the inelastic attenuation. If Q 300, meteorites might generate a useful number of seismic events. If Q ~ 100, no useful events would occur.
1. A new estimate of Lunar Seismicity due to Meteorite Impact
The purpose of the present study was to update these estimates in light of newer meteorite statistics, more complete yield-ground motion data for nuclear explosions, and recent thinking on the moon’s internal structure. Recently SHOEMAKER (1966) proposed new meteorite impact statistics based on observation of atmospheric internal gravity waves excited by meteorites. This method has the advantage that small meteorites may be detected even if they cannot be visually observed or do not survive to reach the earth’s surface. Shoemaker gave his results directly in terms of yield of an equivalent nuclear blast by comparing the meteoric gravity waves with gravity waves due to nuclear explosions of known energy. His formula for the number of meteorites of energy E (in kilotons) or greater impacting on the moon in one year is F(E) 12 5 ‘E
A passive lunar seismic experiment using a single recorder is of considerable interest to the geophysical community, since the length of time of observation can be very much greater than in similar active experiments. One suggested source of seismic energy for such an experiment is meteoritic impacts. It is useful to estimate how often one would record events of this type. Initial estimates of lunar seismicity due to meteorite impacts were given by PREsS, BUWALDA and NEUGEBAUIER (1960) using the meteorite statistics of BROWN (1960). Brown’s results were given in terms of the expected flux of meteorites of given mass. A value of 25 km/sec was assumed for the meteorite velocity (relative to the moon). The seismic ground motion amplitude to be expected was obtained by normalizing to a nuclear explosion of known energy (CARDER and CLOUD, 1959). Press et a!. assumed simple models of lunar structure in which either the seismic velocities were constant, or increased with depth due to gravitational self-compression. The results differed only slightly in the two cases. However, significant changes resulted when inelastic attenuation was introduced. Press et a!. concluded that between 2 and 8 events per year would be recorded by a seismometer with one millimicron threshold sensitivity if inelastic attentuation were absent. If attenuation as large as 0.002 per kilometer were present this would be reduced to one event every three to ten years.
Using this expression we can estimate the total number of events which would be recorded by rE2 25 P(E S) 12 5 dE + N/yR = E2
Here F(E, S) is the probability of recording an event of energy E with a seismometer of threshold sensitivity S. This depends on the efficiency of excitation of seismic energy by the impacting meteorites and on the seismic amplitude decay with distance for the moon, since every recorded event (regardless of the point of impact) must produce a signal that arrives at the receiver with a minimum amplitude S. The energy E 1 is
STANLEY J. LASTER AND FRANK PRESS
the minimum energy meteorite that will just produce the amplitude S if it lands directly on top of the receiver. On the other hand, E2 is the energy of the smallest meteorite which would produce a seismic signal of amplitude S or greater everywhere on the moon’s surface. Thus the integral represents events recorded over only a portion of the moon’s surface, while the second term represents moonwide events. In the present study we have taken the threshold sensitivity to be 1 millimicron of ground motion. SPRINGER (1966) has given improved seismic amplitude-yield data for nuclear explosions. He has considered three coupling materials—granite, tuff, and alluvium. The latter would not be expected on the moon, but those values may be used as an estimate of excitation in soft near surface materials of the moon. In order to use these data in the present study it was necessary to make the assumption that amplitude ratios between nuclear explosions and meteorite impacts are the same for seismic waves as for acoustic gravity waves. It is difficult at the present time to assess the validity of this assumption, but due to the large uncertainty in other variables, such as the moon’s structure, we accept it without further discussion. The third consideration in the present study is the moon’s internal structure, which controls the seismic amplitude decay with distance. Current thinking is that the lunar interior is relatively hot. Petrological models have been proposed by numerous investigators, in particular PHINNEY and ANDERSON (1965). Using hypothesized lunar ages of 0.9 billion years and 4.5 billion years they have computed internal temperature distributions for the moon. For the greater age a substantial portion of the lunar interior would be molten. Little is known about the equation of state for such molten material. However, using the younger age ENGLAND Phinney-Anderson moon. The compressional wave velocities (fig. 1) show a sharp decrease with depth near (1966) computed a seismic velocity distribution for the the surface, a velocity minimum, and finally a monotonic increase to the moon’s center. The shear wave velocity distributionhas a similar behaviour, but due to the greater uncertainty of shear wave excitation by impact these will not be considered in this paper. However, in addition to the compressional waves we will consider surface waves because of their inherently high amplitudes,
Phinney-Anderson 0.9 by Moon
800 Depth (km)
Fig. velocity as a lunar function of depth1.forSeismic the 0.9 compressional billion year old wave Phinney-Anderson model. (After ENGLAND, 1966).
Consider first the short period (1 cps) compressional (body) waves which are first arrivals. Using standard ray theory techniques (BULLEN, 1963) the amplitude decay-distance relation for this lunar model was cornputed using a computer program kindly lent us by Dr. Ralph Wiggins. In order to estimate the effects of inelastic attenuation the lunar material was assumed 10
\ Moon phinneY - Anderson
Fig. 2. Seismic amplitude decay with distance for compressional waves. Peaks in the curves for the Phinney-Anderson model are artifacts due to the method of computation.
LUNAR SEISMICITY DUE TO METEORITE IMPACT
to have a uniform, frequency independent quality factor (Q). Three values were considered: Q = 100, 300, 1000. The first of these might be characteristic of near surface earth materials, while the second and third probably bracket the Q of the earth’s mantle. The amplitude distance relations are shown in fig. 2. Wiggin’s program divides the lunar model into spherical shells, each having a power law velocity function. The exponent of the power law in each layer is chosen to give a good fit to the Phinney-Anderson model. The change in slope of the velocity function at the layer boundaries leads to the discrete peaks in the amplitude distance curves, These artifacts introduce only a minor error because of the integration which is performed. For reference the amplitude distance curve for a constant velocity moon with no inelastic attenuation is included. The chief difference between this curve and the Q = 1000 curve is due to the near surface velocity decrease in the Phinney-Anderson model. In models with a more severe velocity decrease there may even be a shadow zone near the source. Despite this fact, it is obvious that the quality factor is the most important factor controlling the amplitude distance relation. The integral given earlier was computed numerically for the curves in fig. 1. The results for the constant velocity model are given in table 1. It is seen that the TABLE 1
Number of events recorded per year Phinney-Anderson moon
the recorded events have impact points very near the receiver, so that they have little value for interpretation of lunar structure. They have more value if a passive seismic experiment is viewed as a test of the various hypothesized meteorite statistics. It should also be observed that if the quality factor is 100 or lower the passive experiment will yield little useful data. Next consider long period (10 second) surface wave arrivals. It will be assumed that these events travel directly along the surface with a constant velocity, since the dispersion relations are very uncertain. The amplitude-distance curves for these events are shown in fig. 3. The amplitude decay is so great that these are presented on a log-log scale. On a perfect sphere there would be an increase of amplitude at an epicentral distance of 180°,however because of the rough surface of the moon we have assumed that the waves would not arrive in phase at the antip ode, so that this amplitude increase would not be observed. 0.01
Number of events recorded per year
Surface wave amplitude
Constant velocity moon Granite Tuff Alluv
12600 3800 1600 0.001
number of expected events is greater than that given by PRESS, BUWALDA and NEUGEBAUER (1960) by about two orders of magnitude. This is a direct measure of the differences between the meteorite statistics of Shoemaker and those of Brown. However, these results should not be taken too seriously because of the more realistic lunar structures that must be considered. The results for the Phinney-Anderson moon are given in table 2. The values for Q = 1000 represent about 4 events per day, 1 per day, and 1 every 2 days for the three coupling materials. These numbers are encouraging, but it must be remembered that many of
1 1 A (degrees)
Fig. 3. Seismic amplitude decay with epicentral distance for surface waves on a 0.9 billion year old Phinney-Anderson moon.
STANLEY J. LASTER AND FRANK PRESS
Springer’s results do not hold for surface waves, so seismic amplitude-yield results were compiled from the literature for a number of nuclear explosions. The surface wave amplitudes were considerably higher than the corresponding compressional amplitudes, The results for surface waves are shown in table 3. In this case for Q = 1000 the numbers correspond to 1 per hour, 4 per day, and 1 per day for the three TABLE
Number of surface wave events recorded per year on a Phinney-Anderson moon —
Q Granite Tuff Alluv.
1000 9200 1870
300 6400 1300
coupling materials. Also, a significant number of events would be recorded even if the quality factor is as low as 100. However, these will be primarily those events which are generated very near the receiver, Even if passive recording of seismic events can be achieved, it is not clear how the results can be interpreted in terms of lunar structure if only a single recorder is used. There is however one experiment that has a relatively simple interpretation. Seismic surface waves will travel round and round the moon until their energy is converted to heat by the processes of inelastic attenuation. If a given wave train can be recorded on two or more passes around the moon it is a straightforward process to measure the dispersion and phase velocity as a function of frequency for the wave. A measure of inelastic attenuation can also be obtained. While neither of these quantities can give a unique structure we note that much of the earth’s crustal and
Number of surface waves per year recorded on their second passage around the moon 10 Q 1000 300 0 Granite 1200 75 0 Tuff 245 15 0 Alluv. 40 3 0
mantle structure has been determined in this manner. Table 4 gives the number of events which will produce an amplitude of at least 1 millimicron ground motion on their second pass around the moon. Unless the inelastic attenuation is severe (Q less than 100), a passive experiment interpreted in this manner should give significant information of the moon’s structure. In summary, despite the uncertainties involved the present study indicates that meteorite impacts should produce many more seismic events than previously estimated. These events may even contribute significantly to the ambient seismic noise if the inelastic attenuation is not too large. The cause of this increase in number events is mainly due to Shoemaker’s new meteorite statistics. The most critical assumption made concerns the relation between seismic and acoustic gravity wave amplitudes. The lunar structure is also only poorly known, although this affects the results less. Unfortunately the inelastic properties of lunar materials are very important to our conclusions, although these parameters are among the most difficult to estimate at the present time. Acknowledgement The research reported in this paper was supported by a grant from the National Aeronautics and Space Administration, grant number NGR22-009-l87. References BULLEN,
K. E. (1963), Introduction to the Theory of Seismology,
Cambridge University Press, England. BROWN H. (1960) The density and mass distribution of meteoritic .
bodies in the neighborhood of the earth s orbit. In First National Space Science Symposium, Nice, France. CARDER,
D. S. and
W. K. (1959), J. Geophys. Res. 64, .
A. W. (1966), Lunar seismic velocities based on existing estimates of lunar temperature-depth profiles. In: Interim Technical Report, M.I.T. Department of Geology and Geophysics. PHINNEY, R. A. and D. L. ANDERSON, (1965) Internal temperatures of the moon. In: Report of the Tycho Study Group, University of Minnesota. PRESS, F., P. BUWALDA and M. NEUGEBAUER (1960), J. Geophys. Res. 65, 3097. SHOEMAKER, E. (1966), New statistics for meteoritic materials in the neighborhood of the earth. Personal communication. SPRINGER, D. L. (1966), Bull. Seismol. Soc. Am. 56, 861. ENGLAND,