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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.