**1. Introduction**

The Chinese Chang'E-4 mission for moon exploration has been successfully completed. The Chang'E-4 probe achieved the first-ever soft landing on the floor of Von Kármán crater (177.59◦E, 45.46◦S) of the South Pole-Aitken (SPA) basin on January 3, 2019 [1–3]. SPA basin is the broadest basin on the Moon. This ancient basin was born from asteroid impacts 4 billion years ago, recording the evolutionary history of the far side of the Moon, and is of grea<sup>t</sup> significance for researching the internal materials and structures of the Moon [4–6]. Von Kármán crater is one of the primary craters in the SPA basin, with a diameter of 186 km. Recent studies have revealed that the ejecta from adjacent craters have various contributions to the subsurface material of Von Kármán crater, which results in the complex subsurface structure at the Chang'E-4 landing site [1,3,4].

In order to patrol and investigate the lunar surface, a Yutu-2 rover is carried by Chang'E-4 probe. Yutu-2 rover is mounted with several scientific instruments containing a lunar penetrating radar (LPR)

which has been verified to be an effective device for detecting the lunar subsurface structure [7,8]. The LPR is equipped with two types of channels (CH-1 and CH-2), the center frequencies of which are 60 MHz and 500 MHz [9,10]. In addition, the CH-2 possesses one transmitting antenna and two receiving antennas of different offsets which are also known as CH-2A and CH-2B [10–12]. With different frequencies, CH-1 and CH-2 have different detecting missions. The objective of CH-1 is to detect the deep structure of Von Kármán crater [13]; CH-2 is to map the detail of near surface layers, leading to the property analysis of lunar regolith [14,15].

During the interpretation of LPR data, subsurface velocity of electromagnetic waves is a vital parameter necessary for stratigraphic division and computing other properties. However, the velocity analysis of field LPR data faces many difficulties. Complex subsurface structure and interference of noise always result in the incomplete, interlaced, and amplitude-varying hyperbolas. In previous studies of Chang'E-3, Feng et al. proposed hyperbolic fitting method for velocity analysis of LPR data [10]; Lai et al. used two-way delay method to acquire the velocity [16]; Zhang et al. applied CH-2A and CH-2B data of different offsets to estimate the velocity [17]. However, these methods need humans to select the hyperbolas, which is highly subjective. Thus, in this article, we applied 3D normalized velocity spectrum to estimate the velocity [18]. This method can automatically and objectively select hyperbolas and analyze the velocities; the normalization processing can solve the error brought by different amplitudes of different positions on hyperbolas; subsequently, during the computation, we applied a variable horizontal computation window along longitudinal direction to satisfy the field situation that rock sizes increase vertically.

This paper is organized as follows. Section 2 introduces basic theory of 3D velocity spectrum and properties analysis. In Section 3, firstly a model test is performed to verify the feasibility of 3D velocity spectrum; subsequently the method is applied to the CH-2B data analysis. Subsequently, based on the 3D velocity spectrum, we obtain the positions and velocities of the points where hyperbolas exist; then the property structures of lunar regolith are computed including velocity, relative permittivity, density, and content of FeO and TiO2. In Section 4, we discuss the computation error of each hyperbola. Section 5 is the conclusion.
