## 3 Methods and Model Setup
### Model Setup
The initial model size was 400 km \(\times\) 250 km (Figure 4) and was divided into six layers. The top of the model is a sticky layer, it is a weak fluid layer with a low density and low viscosity (viscosity \(\eta\) = 1 \(\times\) 10\({}^{18}\) Pa-s) [75]. Under the above conditions and with sufficient thickness, the layer interface operates as an internal free surface [76]. Usually, the density of the layer corresponds to either water (1000 kg/m\({}^{3}\)) or air (1 kg/m\({}^{3}\)). Considering that in the Paleocene-Early Eocene, the continental margin of the South China Sea was mostly fluvial-lacustrine facies and Marine facies, the density of the sticky layer was set at 1000 kg/m\({}^{3}\)The initial thickness of the sticky water layer was 10 km. Below the sticky layer, from top to bottom, are the sediment, upper crust, lower crust, lithospheric mantle, and asthenosphere mantle. [PERSON] et al. (2022) [71] calculated the thickness of the crustal lithosphere, and the normal crust of South China is 30-32 km, the uniform thinning zone of the shelf is about 24-28 km, and the crustal stretching coefficient is less than 1.2 [71], and referring to the cross section of Figure 2, it is assumed that the thickness of the crust before the stretching is about 38 km. Therefore, the thickness of the sediment layer was 2 km, the upper crust was 18 km, the lower crust was 20 km, and the lithospheric mantle was 65 km. The rheological flow law of sedimentary layer was set according to wet quartz [64], the parameters of the rheological flow law of the upper crust were referred to the reference [77,78], the rheological flow law parameters of lower crust were set according to plagioclase An75, and the lithospheric mantle and asthenosphere mantle are dry peridotite [63]. Other parameters of the model were set according to reference [44,59,75,79] and actual geological conditions (Table 1). The top boundary of the model had a free-slip condition. Symmetric, horizontally outward, constant velocity boundary conditions were imposed on both sides of the model. The lower lithosphere boundary was not specified. It was a spontaneously formed rheological boundary between the stronger, colder parts of the mantle and the weaker, hotter region below. We used an evolving non-uniformly spaced numerical grid combined with a  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Sticky Layer** & **Sediment** & **Upper Crust** & **Lower Crust** & \ \begin{tabular}{c} **Lithospheric** \\ **Mantle** \\ \end{tabular}  & \begin{tabular}{c} **Asthenosphere** \\ **Mantle** \\ \end{tabular}  \\ \hline \(\rho\) (kg/m\({}^{3}\)) & 1000 & 2650 & 2700 & 2800 & 3300 & 3300 \\ \(n\) & / & 2.3 & 4 & 3.2 & 3.5 & 3.5 \\ \(Ea\) (kJ/mol) & / &  
time-varying model size in response to imposed bulk extension. The model grid resolution was 161 \(\times\) 61 nodes with 120,000 randomly distributed markers. In the simulation, the temperature at the top of the model was 273 K, and the temperature at the bottom was 1663 K. The adiabatic temperature gradient in the asthenosphere = 0.5 K/km, with an acceleration of gravity \(g_{y}\) = 9.78 m/s\({}^{2}\). Thermal perturbation in the base of the lithosphere is 10 K.  
The full spreading rates of the ESB and the SWSB were 20-80 mm/a and 35-50 mm/a, respectively. The spreading velocity of the ESB was about 70 mm/a during 32-29 Ma. At 29-26 Ma, the spreading rate was about 25 mm/a. The spreading rate remained at about 70 mm/a before the southward transition of 23.6 Ma, and then the spreading rate varied from 50 mm/a to 35 mm/a from 15.5 Ma, which was similar between the ESB and the NWSB [31; 80]. The SWSB began spreading around 23.6 Ma and stopped spreading around 16 Ma. [PERSON] et al. (1993) [19] suggested an average expansion rate of 40 mm/a [19], while [PERSON] et al. (2014) [81] proposed a high spreading rate (76-80 mm/a) for the SCS during the final spreading phase [81]. The anomalously thin crust of the SWSB supported a slower spreading rate (half-spreading rate 12.6 mm/a) [82].