The Effect of Free-surface Topography on Seismic Waves in the Moon

Introduction: During the Apollo era, a four station seismic network was deployed upon the nearside of the Moon, and returned the first-ever seismic dataset for another body in the Solar System (Fig. 1). The Apollo passive seismic network consisted of four separate stations, deployed on the Moon by the Apollo 12, 14, 15, and 16 astronauts from 1969 to 1972, and remained in continuous operation until 1977. Each seismic package consisted of a three-axis long period (LP) and a short period (SP) vertical axis seismometer, with peak sensitivities in 0.45 Hz range (LP) and 8 Hz range (SP), and sample rates of ~0.15 s (LP) and ~0.02 s (SP) [1]. The seismic array was arranged on the nearside of the Moon in the form of an equilateral triangle, with each station approximately 1200 km apart, and the Apollo 12 and 14 sites located at one vertex of the triangular array (Fig. 1). The seismometers recorded ~13,000 seismic events on and within the Moon [2, 3]. These are categorized into several type of moonquakes, the most numerous being deep quake “swarms” of multiple closely located events at 700-1000 km depth [4]. Also detected were 8 artificial impacts, 32 shallower quakes, and 26 meteoroid impacts [5]. Thus, the Moon is a seismically active body, with seismic events up to a moment magnitudes of near 5.0 [6], allowing the application of terrestrial seismic techniques to study the dataset. The entire lunar dataset is freely available for download on the Incorporated Research Institutions for Seismology Data Management Center (IRIS-DMC) website. This dataset has been incredibly fruitful in constraining a number of important parameters relevant to the thermal and compositional evolution of the Moon, as it provided estimates for lunar crustal thickness and structure [7], seismic wave velocity and the bulk structure of the lunar mantle [8], and provided constraints on the attenuation and scattering structure of the lunar interior [9, 10]. However, many primary questions remain about the Moon’s internal structure, including the size, composition, and state of the core, the detailed vertical structure of the lunar mantle, the global thickness of the crust, the nature of seismic scattering in the crust and mantle, and the extent of lateral heterogeneity in all these regions. Constraining these properties has important implications for the formation and dynamical evolution of the Moon. Here we investigate the effects of the lunar surface topography on the propagation of seismic waves to improve estimates of lunar crustal structure and scattering properties. Topographic roughness can strongly amplify seismic waves traveling along the surface near the source and produce scattering of the seismic wavefield [11]. There are numerous approaches to modeling the effect of free surface topography on seismic waves in elastic bodies; a primary conclusion is that topographic effects are most pronounced in regions possessing steep slopes and where topography is on the order of the wavelength of the seismic waves [12]. These models suggest that topography on the Moon strongly affects the character of the lunar seismic wavefield. Quantifying the contribution of topography will greatly improve inversions and forward models attempting to determine lunar crustal and mantle structure from the Apollo and future seismic datasets.