Based on the seismic interpretation results and structural sequence interface, we compute the active throw and the stratum thickness of the hanging wall and footwall of fault F₄ in different periods and complete the “displacement-distance” curve, the “throw-depth” curve, and the expansion index curve. Finally, we determine the growth manner, faulting phase, and faulting intensity of fault F₄, providing reliable evidence for the reactivation of fault F₄ in the Cenozoic.

As the master fault of the No.4 structural zone in the Nanpu sag, the faulting activity of fault F₄ was distinctly different during different deposition periods in the Cenozoic. Fig. 3 shows that the fault can be divided into multiple fault segments, conforming to a “two segments and multiple sub-segments” growth mode. According to the displacement-distance curve of the interfaces from Es₃ to Es₁, there is an obvious segment point on the top interface of the pre-Cenozoic groups (the bottom interface of Es₃). Fault F₄ consists of two segments, namely F₄₁ and F₄₂. In particular, F₄₁ includes a branch fault F_41-2 in its northern part. The gray and red shallow zones representing the displacement differences in Fig. 3 are the active throws of F_41-2 on the bottom interface of Es₃ and Es₁. During the deposition of the Shahejie Formation, the southern part of F₄₁ had the largest active throw that gradually decreased from south to north, subsequently forming a branch fault at its end where the throw reaches 0. Namely, the fault grew from south to north. Unlike F₄₁, F₄₂ had its maximum throw in the central part, and the throw gradually decreased to both ends. In addition, based on the displacement-distance curve of the bottom interfaces of Ed and Nm, it is clearly that the extension of F₄ fault increased, forming six fault segments on the bottom interface of Ed₁ in the shallow structure. The southern 3 fault segments (F_41-1, F_41-2, and F_41-3) are characterized by large fault throws, while those 3 segments in the northern part (F_42-1, F_42-2, and F_42-3) have small throws.

The faulting intensity and phase of the different segments of F₄ fault are also different. In this study, we select typical cross sections from different positions from south to north for interpretation (Fig. 4c), and complete the corresponding throw-depth and expansion index curves. The results show that both the southern F₄₁ (Fig. 4b) and the central part of F₄₂ (Fig. 4c) in the north are long-term active faults. From bottom to top, the accumulated fault throw gradually increases, the throw gradient remains positive, and the expansion index is greater than 1. However, during the deposition of Es and Ed, the expansion index of F₄₂ was visibly smaller than that of F₄₁, indicating that the faulting intensity gradually decreased from south to north. In the northern end of F₄ fault (the northern segment of F₄₂), there is a maximum value in the throw-depth curve (Fig. 4d). The nucleation point is located in Ed, indicating that the starting time of faulting was in the depositional period of Ed, and the activity time of F₄ fault gradually became late northward.

The aforementioned analysis suggests that F₄ fault was reactivated in the Cenozoic. During the deposition of Es, two main faults were developed. The southern fault F₄₁ has an obvious strike-slip feature, with large throw and nearly vertical fault surface. The northern fault F₄₂ has only slight strike-slip feature, with small throw and dip angle. During the deposition of Ed, six fault segments were developed. Among them, the southern F₄₁ had the largest deformation intensity, with both strike-slip and extension characteristics. By comparison, the deformation intensity of the northern F₄₂ was smaller. Its end continued to propagate towards the north with a dominant extensional deformation. During the deposition of Ng-Nm, the displacement gradually decreased from south to north until the northern end, only manifested as extensional deformation.

At present, the No.4 fault zone is interlaced with the No.2 and No.3 fault zones in the Nanpu sag. The displacement-distance curve of cross-zone faults shows that the fault throws have an obvious low value, which is indicative of the segment point. According to the fault throw back-stripping, the cross-zone fault was generated by the segmental growth and connection of different segments during the deposition of Ng or Ed₁ (Fig. 5a-c). Furthermore, the segment point positions of the cross-zone fault are mainly in the “strike-diverting” parts. Namely, after passing the segment point, the strike changed from NWW to NEE, and the fault gradually terminated at the NE-trending fault zone (Fig. 5d). Therefore, there should be a structural transition zone between No.4 fault zone and No.2 and No.3 fault zones. The arc-shaped zone to the east of the transition zone was the No.4 fault zone, while No. 2 and No.3 fault zones were situated to the west of the transition zone (Fig. 5d). The along-strike cross section shows that all the newly developed secondary faults within the No.4 fault zone gradually terminated at the F₄ fault plane in Ed (Fig. 5e).

The above analysis indicates that the evolution of No.4 fault zone was controlled by the reactivation of F₄ fault, which was not an isolated activity. Instead, it was an intense interaction under a unified stress field between No.4 fault zone and the adjacent No.2 and No.3 fault zones. The three fault zones were developed independently during the deposition of Es and Ed, controlled by different fault systems. During the later deposition of Ng or Ed₁, the three zones were hard-linked, forming the current structural styles.

The regional stress regime for the reactivation of the Pre-Cenozoic basement fault in the Nanpu sag and the late fault development in Paleogene has always been controversial ^[29,32]. Based on the study results about transformation mechanism of regional stress through analysis of balanced cross section, numerical simulation, and physical simulation experiments, it is found that under the background of tectonic evolution pattern transformation of Bohai Bay Basin, the Paleogene tectonic evolution of Nanpu sag is characterized by multi-episode development, which is the result of the superimposed deformation of two phases of oblique extension. The extensional direction changed from NW-SE during the deposition of Es to N-S during the deposition of Ed ^[34⇓-36]. The initial deposition stage of Ed was the critical period of tectonic regime transformation, which may be caused by the subduction direction change of the Pacific Plate to the Eurasian Plate at 36 Ma ago^[1,37]. During the deposition of Es, the NW-SE extension controlled the formation of the NE-trending master faults. The NNE- and NE-trending segments of the Xinanzhuang fault, the Baigezhuang fault, and the NNE-trending basement faults were all reactivated. Due to the influence of boundary faults and pre-existing faults, different structural zones had different stress field characteristics. In detail, the NW-SE extension produced regional extension stress field in the NNE-trending No.1 structural zone and generated regional sinistral strike-slip stress field in the NW-trending No.4 structural zone, leading to sinistral strike-slip deformation on F₄ fault. Due to the fact that the displacement was mainly concentrated on F₄ fault, a vertical structure and a linear faulting pattern are observed in the cross section and plane, respectively. During the deposition of Ed, affected by the N-S extension, a handful of E-W and NEE-trending faults were generated inside the Nanpu sag. The faulting intensity of the E-W segment of the Xinanzhuang fault increased. Furthermore, the NNE-trending No.1 fault zone oblique intersected with the N-S extension through a counterclockwise 35°-40° angle, producing a dextral transtension stress field. By contrast, the NW-trending F₄ oblique intersected it with a clockwise 45° angle, thus forming a sinistral transtension stress field, with sinistral strike-slip and extension deformations at the same time. As a result, many secondary en echelon faults were generated in the overburden rock, forming a flower structure in the cross section. During the deposition of Ng-Nm, substantial E-W secondary faults were generated, and the faulting intensity of F₄ fault increased due to the oblique extension.

The reactivation of F₄ fault in the Nanpu sag was closely related to the regional stress state. During the deposition of Es, the stress direction was parallel to F₄ fault. However, during the deposition of Ed, the stress field rotated, and the NW-trending F₄ fault was in a non-dominant direction of strike. As the pre-existing structure in the basin, it was easy to be reactivated ^[38-39].

During the deposition of Ed, the NW-trending F₄ fault oblique intersected with the nearly N-S extension, with both strike-slip component and dip-slip component. Whether the deformation of F₄ fault is caused by the extension stress field or by the strike-slip stress field has become the most concerned question. It is well accepted that under oblique extension, structural styles similar to strike-slip (especially transtension) deformations can also be generated, but the corresponding stress state of the two types of deformation is different. This depends on the direction of the primary stress σ₂. Oblique extension refers to the situation that the pre-existing basement fault is reactivated under the Anderson stress state of normal faults (σ₁ vertical, σ₂>σ₃, σ₃ horizontal). By contrast, transtension refers to the situation that the deformation zone is partitioned and simultaneously possesses both strike-slip and dip-slip components, under the Anderson stress state of strike-slip faults (σ₂ vertical, σ₁ and σ₃ horizontal). In this study, we establish the oblique-extension-direction kinematic model of the pre-existing basement fault (Fig. 6a) and introduce kinematic vorticity (W_k) to represent the weighting factor of pure shear and simple shear ^[40] (Fig. 6b):

When 55°≥θ>45°, 1≥W_k>0.81, the ε₂ direction is vertical, and the deformation belongs to simple-shear-dominated strike-slip/transtension; when θ=55°, W_k=0.81, the ε₂ direction alters; when 90°≥θ>55°, 0.81>W_k≥0, the ε₂ direction remains horizontal, and the deformation belongs to pure-shear-dominated orthogonal extension/oblique extension (Fig. 6b).

Through the validation from theoretical analyses and physical simulation experiments, it is found that when the extension direction and the pre-existing structure boundary formed a cross-cutting pattern, the maximum instantaneous horizontal tensile axis (ε₁) of the regional stress field was induced to be the included angle (i.e. α) of the relative motion direction of the block and the pre-existing boundary ^[41] (Fig. 6a):

According to Eq. (1) and Eq. (3), when α=90°, only strike-slip deformation occurred; when 70°<α<90°, simple-shear-dominated transtension associated with regional stress field occurred on the pre-existing structure; when α=70° (critical value), the direction of ε₂ changed from vertical to horizontal; when 0°<α<70°, pure-shear- dominated oblique extension associated with regional stress field occurred on the pre-existing structure; when α=0°, orthogonal extension occurred.

Based on the relationship between θ (the included angle between the maximum instantaneous horizontal tensile axis and the shear zone), α (obliquity), and W_k (kinematic vorticity), we establish a reactivation identification chart (Fig. 6b) under the extension of the direction of oblique intersecting pre-existing structure. During the deposition of Es in which the NW-trending Cenozoic pre-existing F₄ fault extended in the NW-SE direction, the relative motion direction of the two walls was parallel to the extension direction, producing strike-slip stress and strike-slip deformation. During the deposition of Ed-Ng-Nm, under the N-S extension, the angle between the relative motion direction and the pre-existing structure was 45°. In this situation, F₄ fault was reactivated and pure-shear-dominated oblique extension occurred.

Numerous studies have been conducted through physical simulation experiments about the reactivation of pre-existing faults. In this study, on the basis of the actual fault development, we design the experiment whereby the reactivation of F₄ fault and its interaction with adjacent faults are simulated. The experiment model is a simplified pre-existing basement fault model. In the experiment, we attached a rigid foam to a soft rubber. The boundary between the foam that had a dip angle of 80° and the rubber was used to simulate the reactivated NW-trending fault in the Shahejie Formation. The fault extended obliquely under the N-S extension. It should be noted that there is no other pre-existing structures in the remaining parts of the rubber; thus, we could simulate both the orthogonal extension deformation in the area unaffected by pre-existing structures and the interaction deformation with F₄ fault. Regarding the experiment material, we chose dry sand whose deformation conformed to the Mohr Coulomb failure criterion. In addition, the internal friction angle is set to 31°, similar to that in the strata^[42]. The experimental facility and basement configuration are shown in Fig. 7a-7b, and the experimental process is shown from Fig. 7c to 7h.

The results obtained from the experiment are reflected in two aspects. (1) Under the effect of the N-S extension, two types of fault zones are generated in the areas with and without the pre-existing NW-trending fault, namely, the reactivation fault zone and the extensional fault zone (Fig. 7c-7h). The former is deformed and extended obliquely; the entire fault shows an en echelon pattern along the pre-existing structure (Fig. 7c-7f). This fault zone is simultaneously characterized by strike-slip and extensional displacements, with a partition feature. Specifically, the strike-slip displacement is mainly concentrated in the relatively narrow fault zone. As the displacement increases, the en echelon faults gradually terminate at the southern end and splays at the northern end. Meanwhile, the strike gradually turns to be parallel to the vertically extensional direction and the fault displacement mechanism changes from strike-slip to extension (Fig. 7d-7h). By comparison, the latter is deformed and extended orthogonally throughout the entire region. The strike is normal to the extension direction (Fig. 7d, 7f). As the displacement increases, the fault number increases as well. The displacement and fault length also increase (Fig. 7e, 7h). (2) Under the effect of the uniform stress field, the two fault zones are developed independently in the initial deformation period (Fig. 7c, 7f). As the displacement increases, the extension length of the newly developed faults in the extensional fault zone increases (Fig. 7d, 7g), with its end interacting with the bending fault in the reactivation fault zone (i.e. yellow rectangle in Fig. 7d). As the displacement further increases, the width of the reactivation zone increases, and the displacement and length of the fault increase as well (Fig. 7e, 7h). The ends of the faults interact and connect with each other (i.e. yellow rectangle in Fig. 7e). Such phenomena are consistent with the “grew separately, contacted and connected,” process (Fig. 7i-7k) according to the aforementioned analyses.

Due to the reactivation of the basement pre-existing strike-slip faults, the fault propagated upward and grew, playing a significant role in connecting hydrocarbon sources. In the study area, due to the reactivation of the F₄ fault, the basement fault propagated upward and penetrated the overlying caprock. In addition, it induced the formation of new en echelon faults in the cap rock, and caused vertical lap joint with the pre-existing faults in the basement. Both of them communicated well with the primary source rocks in the lower Es₁ and Es₃, providing the hydrocarbon migration channels to shallow layers (Fig. 8). The oil reservoirs in the southern part of the No. 4 structural zone are primarily distributed in multiple layers around the strike-slip reactivation zone. Hydrocarbon is enriched in Es₁ to Nm, indicating that the reactivation of the F₄ fault controlled the vertical cross-layer hydrocarbon migration and adjusted the hydrocarbon accumulation location. For the Well np4-12, hydrocarbon shows have been observed in Ed₂ and Ng. In order to verify whether there is a paleo-reservoir in Ed₁, which was adjusted to the shallow layer at the later stage, the debris samples from Well np4-12 at Ng, Ed₁ and Ed₂ of the were collected, and the quantitative grain fluorescence analysis (Q) ^[43] and quantitative fluorescence analysis on extract (Q_e) ^[43] were conducted. Both analytical techniques belong to the reservoir quantitative fluorescence technology, which can quantitatively detect the fluorescence intensity and spectral characteristics of the adsorbed hydrocarbons on the surface of the reservoir particles and the oil inclusions inside the particles. The techniques are used to identify the reservoir's hydrocarbon-bearing properties, distinguish between the present and ancient oil layers, etc. The results indicate that the Q index of the tested samples is greater than 4, and the Q_e index is less than 20 (Fig. 8), indicating that a paleo-reservoir has existed in Ed₁. The vertical hydrocarbon migration occurred during the later period.

Due to the reactivation of strike-slip faults in the basement, the en echelon faults were developed in shallow layers. The transition zone formed by the superimposed faults was an important channel for the water system into the basin, which controlled the distribution of sand bodies. Several right-step en echelon fault segments were developed due to F₄ fault reactivation and fault growth. Due to the strong oblique extension, a sinistral right-step extensional transition zone was formed at the superimposed part. Considering the relationship between the fault distribution and the sand configuration in Ed₂, the structural transition zone formed in the fault superimposed zone is apparently located in the channel development zone, forming fan delta sand (Fig. 9). Therefore, the transition zone formed due to the reactivation of the F₄ fault controlled the position of the sand into the basin. The sand extended to the deep part of the lake basin along the vertical fault strike after entering the basin from the transition zone.

The reactivation of the basement pre-existing strike- slip faults in the Cenozoic controlled the formation of two types of fault traps, namely the strike-slip fault trap and the extensional fault trap. The strike-slip fault trap is mainly developed in Ed-Nm, distributed in the northern part of the No. 4 fault zone. The trap formation is controlled by two factors: (1) Due to the large dip angle of the F₄ fault basement, the upward propagation of the fault caused the uplift and deformation of the formation (Fig. 8). (2) Due to the F₄ fault reactivation during the deposition of Ed to Nm, oblique extension deformation occurred, forming en echelon fault. Together with the basement fault, a "chair-shape" fault type was formed. They jointly controlled the "anticlinal negative flower structure" in the hanging wall, providing space for hydrocarbon accumulation. The extensional fault trap is primarily distributed in Ed₂ to Nm. It is distributed on the plane at the tectonic transition zone where the No. 4 fault zone interacted with the adjacent No. 2 and No. 3 fault zones. In Fig. 10a, the JJ° profile along the fault strike indicates that the footwall strata were uplifted at the "bend" of the connected fault strike (Fig. 10b). A series of fault-block traps have been developed (Fig. 10a), which are favorable locations for hydrocarbon accumulation.

In conclusion, the control effects of the basement pre-existing strike-slip faults reactivation on the hydrocarbon accumulation of the Neogene include three aspects: (1) As the hydrocarbon migration channel, it is favorable for the hydrocarbon accumulation in shallow layers. (2) Control the distribution of sand bodies. (3) Control the formation of shallow traps, favorable for hydrocarbon accumulation in shallow layers.