## 3 Materials and Methods  
### Materials  
A weathering profile was collected, with 16 samples (including 3 rock samples, 5 weathered debris samples, and 8 soil samples), which included 2 sub-profiles labelled as PM-1 and PM-2 (Figure 2c-e). The specific descriptive information and analytical data of the 16 samples are shown in Table 3 and Table S1 in Supplementary Materials. The sampling length or regolith depth of PM-1 is ca. 7.5 m and that of PM-2 is ca. 7.6 m. There is a boundary or platform between the two parts and the total depth of the weathering profile is ca. 15.1 m (Figure 2c-e). The profile samples are divided into three parts from the top to the bottom sequentially as soil, debris, and rock. When collecting soil or debris samples from the weathering profile, the lateral exposed surface soil should be removed at a depth of about 10-20 cm, while rock samples should be collected by removing the external weathering surface and taking the fresh part. The location of this weathering profile is just located near the boundary between the first section of the Lower Cretaceous Tujingzi Formation (K\({}_{1}\)_1_) and the upper Neogene Hannuoba Formation (N\({}_{3}\)) (Figure 2b).  
In order to trace soil migration scientifically according to the topography of the terrain, which can be initially recognized as two pathways, it is necessary to determine the main direction of migration firstly. In total, 10 vertical sediment profiles were laid out along these two migration directions. The first pathway profile CJPM-1 along the primary channel from N-S, with a vertical elevation difference of about 260 m and a transverse migration distance of about 5 km, includes 7 profiles of TP1, TP2, TP3, TP4, TP5, TP7, and TP8, which were spaced almost equally except the distance between TP5 and TP7. The second pathway profile CJPM-2 includes 4 profiles, TP14, TP15, TP16, and TP4 (used repeatedly), along the E-W tertiary channel, which were spaced almost equally with an interval of ca. 2 km and with a height difference of ca. 150 m. With respect to these 10 profiles, 5 samples in each profile were collected sequentially from the surface soil to the bottom soil. Each sample is collected continuously within a depth of 0.2 m and, therefore, the depth of each soil profile is 1 m. Thus, 50 soils samples in these 10 profiles were collected (Table S2 in Supplementary Materials).  
Figure 2: Location of the study area in the Chinese mainland (**a**) and its geological map (**b**) after the K5025 geological map with a scale of 1:200,000 in which a weathering profile (**c**) is located and composed of sub-profiles of PM-1 (**d**) and PM-2 (**e**). Notes in (**b**): 1—Holocene sub-clay, sub-sand, silt with gravel; 2—Upper Pleistocene sub-clay, sub-sandstone, gravelly layer; 3—Middle Pleistocene gravelly sandstone, sub-clay; 4—Upper Neogene basalt with clay and shale in the middle and upper part; 5—The second section of lower Cretaceous Tujingzi Formation siltstone, mudstone, conglomerate sandstone; 6—The first section of lower Cretaceous Tujingzi Formation conglomerate; 7—The second section of middle Jurassic Yanjiayao Formation sandstone, sandy shale; 8—The first section of middle Jurassic Yanjiayao Formation gravelly coarse sandstone, sandstone, shale; 9—Lower Jurassic sandy shale, siltstone, conglomerate sandstone; 10—Lower Sinai quartzite, dolomitic sandstone, shale, dolomite; 11—Archean hematite, striped mixed rock; 12—Diabase; 13—Petrological boundary; 14—Fault; 15—Locations of vertical profiles; 16—Location of the weathering profile illustrated in (**c**–**e**); 17—Range of the pathway profiles.  
In the study area of Wanquan with an area of about 1080 km\({}^{2}\), 278 geochemical records (or samples) of stream sediments were retrieved from the database of the RGNR (Regional Geochemistry-National Reconnaissance) project [20]. In this project, stream sediment is the sampling media with a scale of 1:200 000 and was analyzed with 10 major components and 29 trace elements [21].