The deep-reflection multichannel seismic Line 1, provided by China National Offshore Oil Corporation, was chosen for this study (see location in Figure 1B). The profile is perpendicular to the structural strike and well-developed faults in the central part of Qiongdongnan Basin. Eighteen planar normal faults (F1 to F18; Figure 2) developed during the rifting were identified, which show variability in dips and sizes. F18 at the southeast end is the largest fault with greatest offset and low-angle dip. F3, F13, and F15 have steeper dip angles with θ > 50°. These faults, tilting SE and NW, compose a graben and half-grabens which exhibit features of both symmetric and asymmetric geometry. The profile recorded reflectors of the stratigraphic unconformities and Moho depth with discontinuity. The unconformities at S100 (∼45 Ma) and S60 (∼23 Ma) correspond to the start and end of the syn-rifting, respectively.

The stretching factors of the upper crust (β_uc) along Line 1 are estimated using three methods: the aforementioned method (β_w), as well as methods based on fault geometry (β_f) (Davis and Kusznir, 2004) and zone division (β_z) (Zhao et al., 2018). Parameters for each fault and zone (Figure 2B) are given in Table 2.

In Eqs 5–9, the initial thickness of the brittle layer (H₀) is unknown. It is usually infeasible to estimate, because the transition of brittle and ductile crust is difficult to identify on the seismic profile. To assess the range of reasonable values, we propose 10 km as the H₀ minimum, which corresponds to ∼33% of the initial whole crust thickness in the west of Qiongdongnan Basin (∼22–40 km; Zhao et al., 2018) as the case of the northern SCS at the Early Cenozoic suggested by Dong (2020). It also conforms to the 10–15 km range suggested for the transition depth of brittle and ductile crust in the present South China Block (Zuber et al., 1986; Clift et al., 2001). Furthermore, since faults do not cut through the Moho as shown in Figure 2A, thus we propose the present crust thickness (CT) at the breaking point (x₂ in Figures 4B,C) on the footwall as the H₀-maxima (Table 1; for H₀ = CT in Figure 7A). In Eqs 1, 2, since W has been assumed ranging of 75–150 km, we also evaluate W at 150 km and 75 km. To account for the unrecognized or small-scale faults below the seismic resolution, the amount of fault heaves (β_f) is increased by 40% (Walsh et al., 1991).

The whole crust stretching factor (β_c) is defined as the ratio of the initial crust thickness to the final crust thickness. The pre-rifted crustal thickness of the northern SCS margin is assumed to be 32 km in this study (Zhao et al., 2018). The thicknesses of syn-rift (45–23 Ma), and post-rift (23–0 Ma) sediments are estimated using two-way travel time (TWT) of the seismic data (Figure 2A). The time-depth conversion of the stratigraphic sequences is based on VSP data (Zhao et al., 2015). The crustal thickness is derived by assuming an average crustal P-wave velocity of ∼6.5 km/s as previous studies (Zhao et al., 2015).

In the upper crust, β_w is 1–2.4 by assuming H₀ = CT, while β_w varies from 1 to 3.3 by applying H₀ = 10 km to all faults (Figure 7A). The curve of β_w (H₀ = 10) exhibits β-maxima at a distance of ∼95 km with the highest frequency variation among all the three methods on upper crust.

β_f shows a smooth function curve between 1.6 and 2.0 with W = 150 km for each fault set and between 1.7 and 2.3 with W = 75 km, while it expands to 1.4–2.9 with W = 20 km (Figure 7A). When applying lower values of W from 150 km to 20 km, the variation of β_f is gradually amplifying; e.g., when W = 20 km, a peak of β_f = ∼2.9 is indicated at the distance of ∼100 km. The curve of β_f (W = 150 km) exhibits near-symmetry, while that of β_f (W = 20 km) is characterized by asymmetry. All three β_f -minima exceed those of β_w and β_z as the result of correction.

β_z values of six zones (1.2–3.1; Table 1) are presented in Figure 7A. Compared to the other curves, β_z is shown as a stepwise line with large Δβ_z, since values are estimated on the basis of averaging the exaggerated geometry of trough and crest in each zone.

Along Line 1, the crust thickness shows a large variation ranging from maxima of >20 km at the basin margins to a minimum of <10 km at a distance of ∼20 km (Figure 7B). The thinner crusts of ∼10 km at the two flanks of Songnan Sag and Songnan Uplift correspond to the maxima of β_c. Between the distance of 20 and 110 km, the thickness varies around ∼12.5 km with a slight increase from ∼10 km to ∼15 km.

In Figure 7A, the extension discrepancy is indicated at a distance of c. 20–70 km, which is significant in the center of Songnan Sag and Songnan Uplift. However, it appears to be ambiguous in the Beijiao Sag and Southern Uplift where the water depth stabilizes at ∼1.6 km.

Fault deformation width (W) has been an unknown parameter and cannot be calculated (Roberts, 1993; Davis, 2004; Zhao, 2018), which is fundamentally important in determining the stretching factor of brittle crustal extension. Roberts (1993) set up W as constant of 75–150 km for contrastive analysis of backstripping and forward modelling in the North Sea, and it has since been adopted as default by subsequent works. However, the assumption contains potential uncertainties, because it is disregarding differences in faults heaves, dips and initial brittle crustal thicknesses. To capture the uncertainty derived from using the constant W range, we revisit the conventional method (Davis and Kusznir, 2004) and evaluate the role of W (Figure 8). Theoretically, applying the most favorable W value in the suggested range (75–150 km) to one single fault leads to Δβ_f = 0.14 at most. W, therefore, seems to have negligible impact on β_f. However, its importance becomes more apparent as it decreases, e.g., Δβ_f = 0.8 if a maximum of 150 km and a minimum of 20 km are assigned to W. Even a proposed value of W (W = 75 km) results in a substantial underestimation (i.e., Δβ_f = 0.7).

Our results indicate that W is generally less than 80 km and narrow it down to the range of 10–60 km even in the marginal case of H₀ = 50 km with dip in the range of 30°–75° (Figure 4). Since the ductile-brittle transition is suggested between 10 and 15 km in the modern South China Block (Zuber et al., 1986; Clift et al., 2001), the W value in the northern SCS is proposed as less than 50 km (extreme case is H₀ = 15 km in Figure 4). As we decrease W = 150 km to W = 20 km, the trend of β_f curves changes to multi-wave converging towards the functions of β_z and β_w as shown in Figure 7A. Our findings demonstrate that W is an important control on the brittle extensional estimation, but has been overestimated in previous studies. A lower W value than the conventionally used range may lead to more accurate model outcomes. The discord is likely a critical cause for underestimation of the upper crustal stretching factor.

Stretching estimation based on current fault geometry shown in seismic image is insufficient to evaluate the brittle upper crust thinning due to undetected faulting. According to Reston (2005; 2007), polyphase faulting incurs geometric changes such as shallower-dipping, which could be crosscut by steeper normal faults developed in later stages. The extension by unrecognized faulting is generally corrected by increasing its value by a factor of 40% (Walsh et al., 1991). However, since more complex fault geometries have experienced larger heaves and stronger deformation, a different degree of correction is required in consideration of geometric complexity (Clift et al., 2001), and vice versa. Our method improves this accuracy by numerical analyses of W (Figure 7A). Our results show that β_f at W = 150 stays mostly uniform over the entire profile with a slight maximum in the Songnan Sag, but peaks of β_f curves at lower W values were recorded in the Beijiao Sag, with 2.3 for W = 75 and 2.9 for W = 20, respectively (Figure 7A). The peaks correspond to the β_z trend, which shows the highest value in the Beijiao Sag and the second highest value in the Songnan Sag (Figure 7A). Although β_z is less accurate by exaggerating both maxima and minima, it is advantageous to see the overall variation trend with limits.

Our methodology underlines the importance of W, which is beneficial to estimate the upper crustal extension and can be applied to other studies on brittle extension. However, if the estimation requires sophisticated controls for the extension over time and depth, some improvements are required. Above all, the rotation of faults or beds has to be considered as the stretching factor β_d is based on a domino-style fault block model, which can contribute critically to avoid underestimation of β_f as well as the uncertainty of extension discrepancy. Several studies have indicated that initial dips of normal faults may subsequently rotate to shallower ones due to isostatic response (Spencer, 1984; Wernicke and Axen, 1988), particularly faults with large offsets (Buck, 1988), i.e., their initial dips are larger than the current dips identified from profiles. A numerical simulation model by Lavier and Manatschal (2006) confirmed that steep normal faults rotate to conjugate concave downward faults, which lead to crust thinning at magma-poor margins. A balanced kinematic model proved that sequential faulting turns high-angle normal faults into low-angle ones as accommodation of thinning, which is limited by lower crust, deforming in response to upper crust in the cold basin or lithosphere (Ranero and Perez-Gussinye, 2010). For instance, we infer that the original dip of F18 with offset up to ∼14.7 km could be much higher than 15.9°. It is supported by the cases that normal faults in the brittle upper crust develop at dips θ>45° and stay active at dips θ ≥ 30° with offset <10 km (Anderson, 1951; Byerlee, 1978; Sibson, 1985; Buck, 2007; Reston, 2007). This is one potential cause for the drastic drop of β_w in the Beijiao Sag and Beijiao Uplift. Another aspect to consider is the inapplicability of heat flow on older basins and underestimation of crustal thinning affected by asthenospheric melting. During the rifting, heat flow increases due to lithosphere thinning and rising of the asthenospheric mantle, which is closely associated with the crustal stretching, flexural uplift, and subsidence. The thermal effect of depositing cold sediments on top of the lithosphere leads to a depression in the thermal gradient, extending down into the lithosphere (the thermal blanketing effect) (Karner, 1991; Kim et al., 2020). Such lithospheric and asthenospheric-scale mechanisms during rifting require comprehensive considerations of the thermal evolution in our numerical methods.

The extension discrepancy has been widely reported in the northern SCS (Clift et al., 2002; Tsai et al., 2004; Bai et al., 2019). In this study, significant extension discrepancy was also indicated at the distance of c. 20–70 km of Line 1 (Figure 7A), which corresponds to the Songnan Sag and Uplift characterized by asymmetrical half-grabens. In the Beijiao Sag which is dominated by grabens, positive extension discrepancy is indicated by β_f when applying W = 150, while inverse discrepancy is widely discovered when evaluating β_f with W = 20. We infer that the extension discrepancy in previous studies is over-predicted by an overestimated W. The inverse discrepancy has so far been overlooked in the northern SCS. A balancing of positive discrepancy and inverse discrepancy along the extension direction supports the presence of crustal extension discrepancy, as the same amount of thinning is expected across the entire profile at crustal scale (Reston, 2007), i.e. cross sectional area of crust along the extension direction maintains the uniform β during syn-rifting and post-rifting (Figure 9A).

Depth Dependent Stretching (DDS) or Depth Dependent Thinning (DDT) (Royden and Keen, 1980; Rowley and Sahagian, 1986; Roberts et al., 1993; Kusznir and Karner, 2007) seems to be the convincing model to explain the mechanism of extension discrepancy. However, the depth dependence at lithospheric level is unsuitable to explain the estimation in the central part of Qiongdongnan Basin where a local positive discrepancy is located next to a local inverse discrepancy. The potential explanations for inverse discrepancy include: 1) upper plate (hanging wall) of detachment fault of simple shear (Wernicke, 1985) which is in conflict with the observation showing symmetric grabens and asymmetric half-grabens, being firstly excluded. 2) top-down break up (Anderson, 2001). i.e., the first degree break-up of upper crust precedes that of lower crust as tensile stress instead of magmatism upwelling from asthenosphere takes charge. This is an attractive interpretation since the magmatism upwelling did not occur in the central part of Qiongdongnan Basin during rifting. However, this model suggests that the upper crust thinning is greater than that of lower crust, which results in an inverse discrepancy at the thinnest whole crust location (Reston and McDermott, 2014). It does not fit in the study area that a positive discrepancy is described at the thinnest crust. Moreover, previous studies (Davis and Kusznir, 2004) suggested that the breakup of lithosphere inclines to bottom up in the deep-water area, like the Beijiao Sag. 3) lower crust flow in hot lithosphere like northern SCS (Figure 9B). During rifting, the syn-rift sediments were deposited up to ∼8 km in the northwest (Figure 7B), which is closer to Hainan Island and exhibits positive discrepancy. The inverse discrepancy is predominant in the southeast where it shows relatively thin thickness of syn-rift sediments (up to 4 km; Figure 7B). Compared to the northwest, the southeast area was far away from provenance. Such variation in sediment thickness could contribute to a laterally differential pressure, which might drive the lower crust flow causing transitions between inverse and positive discrepancies. The ductile lower crust is generally inclined to flow along the rifting direction (McKenzie and Jackson, 2002). This is an elementary impact since sediment thickness is also dependent on subsidence associated with tectonic processes and thermal effects, which we will investigate further to understand the mechanism in the future studies.