Seismic tomography of the Moon

Dapeng  Zhao

Seismic tomography of the Moon

Dapeng Zhao

2008, Chinese Science Bulletin

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Abstract

We attempted to determine the first three-dimensional P and S wave velocity and Poisson's ratio structures of the lunar crust and mantle down to 1000 km depth under the near-side of the Moon by applying seismic tomography to the moonquake arrival-time data recorded by the Apollo seismic network operated during 1969 to 1977. Our results show that significant lateral heterogeneities may exist in the lunar interior. Because there is no plate tectonics in the Moon, the lateral heterogeneities may be produced at the early stage of the Moon formation and evolution, and they have been preserved till today. There seems to be a correlation between the distribution of deep moonquakes and lateral velocity variations in the lunar lower mantle, suggesting that the occurrence of deep moonquakes may be affected by the lunar structural heterogeneity in addition to the tidal stresses. Although this is an experimental work and the result is still preliminary, it indicates that tomographic imaging of the lunar interior is feasible.

Figures (17)

Figure 1 Distribution of moonquakes (open circles) that had P-wave arrival-time data used in this study in (a) plan view, and (b) north-south and (c) east-west vertical cross sections. The open triangles in (a) denote the four seismic stations installed during the Apollo missions. The two cross sections (b, c) are along the lunar central meridian and the equator, respectively. The dotted lines in (b) and (c) denote depths of 400, 650, and 1000 km for better visualizing the hypocenter distribution of moonquakes. quake data. This is due to the differences in waveforms between earthquakes and moonquakes. Moonquake waveforms exhibit low attenuation, strong scattering and long duration! *), Figures | and 2 show the hypocentral distribution of the moonquakes that have the selected P and S wave data, respectively. Some shallow moon- quakes have very close hypocenter locations. The deep moonquakes occurred in a depth range of 747—1419 (1) km, which were located by Nakamura’ ” using the 1-D P and S wave velocity model of Nakamura“! (Figure 3). Velocities are shown down to 1000 km depth in Figure 3) In our analyses we assumed that P and S wave ve- locities in deeper areas are the same as those at 1000 km depth. One moonquake has a focal depth of 559 km (Figure 2(b), (c)), which is not a typo but a result of moonquake location procedure (Y. Nakamura, personal

Figure 2 The same as Figure | but for the moonquakes with S-wave data used in this study. 3-D structure of the lunar deep mantle. Nakamura’™ d communication in November 2007). These invaluable data from the deep moonquakes enable us to determine a 3-D structure of the lunar deep mantle. Nakamura'! di-

Figure 3 One-dimensional P and S wave velocity model of the Moor determined by Nakamura!”).

We applied a seismic tomography method!''! to the selected lunar data set to determine 3-D P and S wave velocity structures of the Moon. A 3-D grid is set up in the lunar crust and mantle down to 1000 km depth (Fig- ure 4). The grid spacing is 10 degrees in the horizonta! direction (about 303 km at the lunar equator), which is comparable to the grid interval adopted in the global omography of the Earth!!! 3), Six layers of grid mesh are set up at 20, 150, 300, 500, 700, and 900 km depths Figure 4(b)). The velocity perturbations at the gric nodes are taken as unknown parameters. The velocity perturbation at any point in the model is calculated by inearly interpolating the velocity perturbations at the eight grid nodes surrounding that point. A 3-D ray-trac- '415] ig used to compute travel times anc ing technique! ray paths of the P and S wave data. Station elevations are taken into account in the 3-D ray tracing. The LSQR algorithm!’®! with damping and smoothing regulations 1s used to solve the large but sparse system of observa- tional equations that relate the arrival-time data to the unknown velocity parameters!'"!, Figure 4 Distribution of the grid nodes adopted for the tomographic inversion in plan view (a) and vertical cross section (b). The open trian- gles in (a) denote the four Apollo seismic stations.

Figure 5 Distribution of ray paths for P-wave arrival-time data used in this study in (a) plan view, and (b) north-south and (c) east-west vertical cross sections. The open circles and triangles in (a) denote the moon- quakes and the four Apollo seismic stations, respectively. In the tomographic inversions, we used the absolute travel-time residuals from the shallow moonquakes be-

Figure 6 Same as Figure 5 but for the S-wave rays used in this study. cause the origin time and hypocenter location of each shallow moonquake are determined'*!, In contrast, rela- tive travel-time residuals from the deep moonquakes are used in the tomographic inversions, because the indi- vidual deep moonquakes have a small magnitude and so (used a their seismic signals are weak, hence Nakamura waveform-stacking method to measure the P and S travel times from a group of deep moonquakes located in the same nest. Thus the origin times of the deep moonquakes are not available in the data set complied by Nakamura!'!, Our procedure for the calculation of relative travel-time residuals for the deep moonquakes is the same as that for the teleseismic events in the terres- trial tomography!'”!*!

Figure 7 Plan views of P-wave tomography at different depth slices. The depth is shown above each map. Red and blue colors denote low and high velocities, respectively. The scale of velocity perturbations relative to the 1-D velocity model (Figure 3) is shown at the bottom. White triangles denote the four Apollo seismic stations. Figure 8 Same as Figure 7 but for S-wave tomography. ZHAO DaPeng et al. Chinese Science Bulletin | December 2008 | vol. 53 | no. 24 | 3897-3907

the numbers and locations of seismic stations, moon- quakes, and P and S wave rays are the same as those in the real data set (Figures 5 and 6). For the synthetic tests, we first construct an input model that contains the main features of velocity anomalies appeared in the obtained Before describing the obtained tomographic results, the numbers and locations of seismic stations, moon- the real data set (Figures 5 and 6). For the synthetic tests, ages. In this study we made a number of synthetic tests

Figure 9 Vertical cross sections of P-wave tomography along the four profiles shown on the map. Red and blue colors denote low and high velocities, respectively. The scale of velocity perturbations relative to the 1-D velocity model (Figure 3) is shown below (c). White dots denote moonquakes occurring within 150 km width of each profile. Open triangles on the map denote the four Apollo seis- mic stations.

depth range of 200—800 km under the Apollo seismic network, and several high-velocity (high-V) zones exist in the upper and middle mantle around the low-V anom- aly. A few smaller low-V zones are visible in the lower mantle at depths of 700—1000 km, while average to higher velocities prevail in the shallow mantle (Figure 9). levels of 0.5 and 2.0 s, respectively. Similar synthetic test results for S-wave tomography are shown in Figures 13 and 14. These tests indicate that velocity anomalies with a size larger than 300 km in the lunar mantle under the Apollo seismic network can generally be recon- structed, though smearing occurs around the edges of the velocity anomalies (Figures 11—14).

Figure 13 Same as Figure 11 but for S-wave tomography. under the Apollo seismic network, and a few low-V anomalies exist around the high-V zones (Figure 10). under the Apollo seismic network, and a few low-V

Figure 14 Same as Figure 12 but for S-wave tomography.

Figure 15 Plan views of Poisson’s ratio image at different depth slices. The layer depth is shown above each map. Red and blue colors denote high and low values of Poisson’s ratio, respectively. The scale of perturba- tions relative to the average value (0.25) is shown at the bottom. The open triangles denote the four Apollo seismic stations.

hypocenter locations ranges from a few to tens of kilo meters, which certainly prevents us from determining « precise tomographic image of the lunar interior. As | matter of fact, even the 1-D velocity models determine: by different researchers show large discrepancies'**”® The lunar tomography, however, has some advantage over the terrestrial tomography. The first is that moon quakes occur down to as deep as 1400 km depth (not that the lunar radius is 1738 km), thus seismic wave from the deep moonquakes can sample a large fractior of depth range in the lunar interior even with a loca seismic array, which is very favorable from a viewpoin of seismic tomography. In contrast, earthquakes occu only down to 670 km depth (1/9 of the Earth’s radius) and so deep Earth tomography cannot be determine: without a global seismic network. The second advantagi is related to the fact that the Moon is much smaller thai he Earth. A distance of 10 degrees at the lunar equato is 303 km, while it is 1112 km on the Earth. As shown 11 his work, we can determine a lunar tomography with | ateral resolution scale of 300 km or shorter with a loca or regional seismic array consisting of a few stations, i he moonquake hypocenters can be located reasonabh well with the seismic array (uncertainty < 10 km). Thi resolution scale is comparable or even better than that o he current global tomography of the Earth. Therefore resolution scale is comparable or even better than that of ZHAO DaPeng et al. Chinese Science Bulletin | December 2008 | vol. 53 | no. 24 | 3897-3907

Gary Latham

Reviews of Geophysics, 1974

Natural seismic events have been detected by the long-period seismometers at Apollo stations 16, 14, 15, and 12 at annual rates of 3300, 1700, 800, and 700, respectively, with peak activity at 13-to 14-day intervals. Repetitive moonquakes from 41 hypocenters produce seismograms characteristic of each. About 90% of the long-period signaJs are from these and other numerous, less active hypocenters, and meteoroid impact signals account for the remainder. At each hypocenter, moonquakes occur only within an active period of a few days during a characteristic phase of the monthly lunar tidal cycle. An episode of activity may contain up to four quakes from one hypocenter. Nearly equal numbers of hypocenters are active at opposite phases of the monthly cycle, accounting for the 14-day peaks in total lunar seismic activity. A period of about 206 days in the seismic activity of several of the hypocenters is superimposed on a strong one-to two-year trend where the signal amplitudes decrease to the instrumental detection threshold. A 206-day period with no secular decrease in amplitude is also observed in the total lunar seismic activity, sugge.sting that the total number of active hypocenters does not vary appreciably with time. Moonquake magnitudes range between 0.5 and 1.3 on the Richter scale with a total energy release estimated to be about 10 n ergs annually. With several possible exceptions, the moonquake loci located to date occur in two narrow belts on the near side of the moon. Both belts are 100-300 km wide, about 2000 km long, and 800-1000 km deep, and they lie along great-circle arcs. Seismic data from a far-side focus and a large far-side meteorold impact define the base of the lunar lithosphere at a depth of about 1000 km. In our present model the rigid lithosphere overlies an asthenosphere of reduced rigidity in which present-day partial melting is probable. Tidal deformation presumably leads to critical stress concentrations at the base of the lithosphere, where moonquakes are found to occur. The striking tidal periodicities in the pattern of moonquake occurrence and energy release suggest that tidal energy is the dominant source of energy released as moonquakes. Thus, tidal energy is dissipated by moonquakes in the lithosphere and probably by inelastic processes in the asthenosphere. The low level of seismicity and the absence of shallow seismicity implies that the moon is neither expanding nor contracting at an appreciable rate. The secular accumulation of strain implied by the uniform polarities of moonquake signals may result from weak convection in the asthenosphere or from secular recession of the moon from the earth.

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