Upper crustal azimuthal anisotropy and seismogenic tectonics of the Hefei segment of the Tan-Lu Fault Zone from ambient noise tomography

1.   Introduction

The Tan-Lu Fault Zone is a vast NNE-trending strike-slip and reverse fault with a length exceeding 2400 km and a width ranging from tens of kilometers to more than 200 km in eastern China (Xu JW et al., 1985, 1995; Xu JW and Zhu G, 1994). It is composed of several nearly parallel faults. This fault initiated its large-scale strike-slip movement during the Indosinian period, coinciding with the collision of the North China Block and the South China Block and the uplifting of the Dabie Orogen (Zheng YF et al., 2003; Wang YS et al., 2018). The Hefei Basin, which also originated with the uplifting of the Dabie Orogen, developed into a graben basin within the extensional Tan-Lu Fault Zone and gradually became extinct owing to the compressional movement of the Tan-Lu Fault Zone (Zhu G et al., 2001, 2002, 2004). The evolution of these tectonic units and their accessory products, such as rich metal minerals, geothermal resources, and earthquakes, strongly affect the security and development of eastern China. In particular, a series of earthquakes of limited magnitude occurred in the upper crust of the Tan-Lu Fault Zone near the city of Hefei, which sparked a wave of social panic. Therefore, it is crucial to comprehend the tectonic characteristics and seismogenic structures in this region.

Previous studies around the Tan-Lu Fault Zone and the Dabie Orogen have resulted in many achievements. The investigations have mainly focused on several topics, including the tectonic characteristics and evolution history of different segments of the Tan-Lu Fault Zone. The structure of the Moho discontinuity under the middle segment of the Tan-Lu Fault Zone was imaged by Chen L et al. (2006). The crustal structures of different segments of the fault zone were detected and the evolution processes were discussed based on the distribution and deformation patterns of the major tectonic units, for instance, by Gu QP et al. (2016), Meng YF et al. (2019), and Luo S et al. (2022). Zhang JD et al. (2010) and Zhao T et al. (2016) discussed the effect of plate subduction on the evolution of the fault zone. Studies on the geochronology (Wang YS et al., 2018), the deep structure of the Dabie Orogen (Luo YH et al., 2012), and the controlling effect on the multistage evolution mechanism of the Hefei Basin from the fault zone and orogen (Liu GS et al., 2002, 2006; Song CZ et al., 2003) have been carried out. Similarly, investigations of the upper crustal structure of these areas have also proceeded rapidly. Along the Tan-Lu Fault Zone, the upper crustal shear wave velocity structures have been imaged, such as those of the Feidong (Gu N et al., 2019), Lujiang (Li C et al., 2020), Chaohu (Luo S and Yao HJ, 2021), Suqian (Gu N et al., 2022), and Weifang (Jin JQ et al., 2023) segments, which revealed the fine structure of the Tan-Lu Fault Zone and its adjacent areas and have provided better constraints for studies on the fault zone. In addition, a few studies (Luo S and Yao, 2021; Jin JQ et al., 2023) paid attention to the anisotropic characteristics of the upper crust, especially the frequent seismic activities that have occurred in the upper crust of the Hefei segment of the fault. Fine isotropic and anisotropic models are needed to constrain the deformation patterns among the tectonic units and the seismogenic structure, to further explain the mechanism of the upper crustal earthquakes.

Seismic ambient noise tomography has already become a popular method because it can be used to image regional structures (e.g., Shapiro et al., 2005; Yao HJ et al., 2006; Fang HJ et al., 2015). In recent years, with the development of tomographic methods based on dense nodal arrays, surface wave signals with higher frequencies can be extracted from ambient noise data. The signals can be used to recover shallower crustal structures and have been applied widely in different scenarios, such as in cities (e.g., Li C et al., 2016), at oil and gas storage locations (Wang JJ et al., 2018), in areas of mineral deposits (e.g., Li C et al., 2023; Gao J et al., 2023), and in fault zones (Li C et al., 2020). Not only isotropic structures, but also anisotropic structures can be reliably obtained by using ambient noise tomography (e.g., Liu CM et al., 2019; Hu SQ et al., 2021; Luo S and Yao HJ, 2021; Luo S et al., 2022). An anisotropic model provides important constraints on depth-dependent deformation patterns of the underground media. It is related to the alignment of cracks and the distribution of faults and can be used to infer the geodynamic relationships among tectonic units.

To image the upper crust isotropic and azimuthally anisotropic structure in the Tan-Lu Fault Zone in the Hefei area, we collected the ambient noise surface wave phase velocity dispersion data from four subarrays in Lujiang, Chaohu, Feidong, and Hefei. These subarrays cover the major tectonic units in this area and include the northern boundary of the Dabie Orogen, the southeastern part of the Hefei Basin, Chao Lake, the Tan-Lu Fault Zone, and its conjugate fault system (Figure 1a). We used the phase velocity dispersion data within the period band of ~0.5–10 s to invert for a reliable isotropic shear velocity model in the first step and an azimuthally anisotropic model at depth in the second step. We also conducted a relocation of the Lujiang earthquake series. We further discuss the geological features, deformation patterns, and seismogenic structure in the upper crust of the southern Tan-Lu Fault Zone.

Figure  1.  (a) The main geological units and the location of the study area (red rectangle). (b) The distribution of stations (black triangles). The solid gray lines represent faults that have remained active from the early and middle Pleistocene, and the dashed gray lines represent faults shown to be active before the pre-Quaternary period as well as some other secondary fault systems. The white dots represent the distribution of local earthquakes that occurred between January 1990 and January 2023 with magnitudes larger than 0.5. The red star represents the location of the Feidong M4.7 earthquake in 2024. The main geological units include the North China Block (NCB), the South China Block (SCB), the Tan-Lu Fault Zone (TLF), the Dabie Orogenic Belt (DBO), the Hefei Basin (HFB), and Chao Lake (CH). Faults f1−f5 represent the Qingshan−Xiaotian Fault (QXF), the Meishan−Longhekou Fault (MLF), the Luan−Hefei Fault (LHF), the Chaohu Fault (CHF), and the Feizhong Fault (FZF), respectively. The red squares represent the positions of cities. HF represents Hefei city, and LJ and TC represent Lujiang County and Tongcheng County, respectively. Profiles A–A′, B–B′, C–C′, and D–D′ represent the locations of the four profiles shown in Figure 8. ZBL, Zhangbaling Uplift.

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2.   Data and Method

2.1   Data Acquisition

The dataset mainly contained data from ~400 temporal seismographs in four different subarrays, which cover the city of Hefei, the Lujiang area, the Chaohu area, and the Feidong area (Figure 1b). Phase velocity dispersion curves of Rayleigh waves from different subarrays had been extracted in earlier research (Gu N et al., 2019; Li C et al., 2020; Li LL et al., 2021; Luo S and Yao HJ, 2021) by using a time-frequency analysis method (Yao HJ et al., 2006, 2011). The period range of the dispersion curves is 0.5–10 s with an interval of 0.5 s. Even so, to ensure the quality of the noise correlation function (NCFs), we applied a path cluster error analysis method (Zhang YY et al., 2018) to eliminate outliers (Figure 2b). Finally, we obtained 33,776 high-quality interstation Rayleigh wave phase velocity dispersion data points. Figure 2b shows the number of paths at different periods. Notice that the data number reaches the highest point at the period of 3 s. In addition, to study the seismogenic relationship between the velocity structure and the distribution of earthquakes in this area, the locations of the 32 earthquakes in the Lujiang earthquake series from December 1 to 3, 2022, were relocated by using the double-difference earthquake relocation method (Waldhauser and Ellsworth, 2000; Zhang HJ and Thurber, 2006). Details of the relocation results are presented in the Supplementary Materials (Table S1).

Figure  2.  The phase velocity dispersion curves and data number before (a) and after (b) path cluster error analysis. The solid black lines indicate phase velocity dispersion curves and the dashed red lines indicate the data number.

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2.2   The Direct Inversion Method for the 3-D Isotropic and Azimuthally Anisotropic Model

A two-step direct inversion method was used to invert the 3-D isotropic and azimuthally anisotropic shear velocity model (Liu CM et al., 2019). Under the assumption that the phase velocity variations from azimuthal anisotropy are much smaller than those from isotropy, we inverted for a reliable isotropic ${V}_{\mathrm{s}}$ model as the first step based on a direct surface wave tomography method with fast-marching ray tracing at different periods (Fang HJ et al., 2015). This step will reduce a major part of the surface wave travel-time residual between the observed data and predicted data. As the second step, the prepared reliable isotropic ${V}_{\mathrm{s}}$ model from the first step was used as the initial model to invert both the isotropic and the azimuthally anisotropic structures. This process further decreased the travel-time residual. All the input data for the two steps were the same surface wave phase velocity dispersion data. More detailed descriptions of the algorithm for the isotropic and azimuthally anisotropic inversion can be found in Fang HJ et al. (2015) and Liu CM et al. (2019), respectively.

The velocity of Rayleigh waves of a specific period is most sensitive to the shear velocity structure at a depth that is approximately one-third to one-half of the wavelength. Therefore, the average phase velocity of surface waves with different periods and the corresponding most sensitive depth were calculated based on the extracted phase velocity dispersion curves. The most sensitive depth and average velocity were interpolated into regularly spaced depth grid points to form a one-dimensional (1-D) initial model (Li C et al., 2020; Figure 3), and then extended horizontally to form a 3-D initial model. This process resulted in 66 and 76 grid nodes with a grid spacing of 0.02° in the E-W and N-S directions, respectively. In the depth direction, there were 28 grid nodes, with an interval of 0.2 km from 0.5−1.1 km depth, 0.3 km from 1.1−2 km depth, and 0.5 km from 2−12 km depth. Because the average water depth of Chao Lake is only approximately 2.8 m, which is much smaller than the wavelength of surface waves at the period of 0.5 s, the effect of the water in Chao Lake on the inversion was ignored.

Figure  3.  (a) The black dots indicate the dispersion data at each period, and the dashed black line indicates the average dispersion curve. (b) The initial 1-D shear wave velocity model used for 3-D isotropic shear velocity inversion.

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3.   Results

3.1   Data Residuals and Ray Path Distribution

The standard deviation of the surface wave travel-time residuals was calculated at every iteration, which decreased from 2.07 to 1.81 s in the isotropic inversion step (Step 1), and from 1.81 to 1.79 s in the azimuthally anisotropic inversion step (Step 2). Each inversion step contained 10 iterations with the root mean square (RMS) residual decreasing gradually (Figure 4a), which indicated the convergence of the inversion. The mean of the residuals approached zero, and the standard deviation decreased (Figure 4b). Figure 5 shows the ray path distribution of Rayleigh wave phase velocity measurements at the periods of 1, 3, 5, and 8 s.

Figure  4.  (a) Decrease in the standard deviation of surface wave travel-time residuals with the iteration number in two steps: the black line indicates the first isotropic inversion step, and the red line indicates the second azimuthally anisotropic inversion step. (b) Distribution and mean value of travel-time residuals before inversion (red histogram), after isotropic inversion (black histogram), and after anisotropic inversion (green histogram).

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Figure  5.  Ray path distribution for phase velocities at four different periods: (a) 1 s, (b) 3 s, (c) 5 s, and (d) 8 s. The black lines represent ray paths after ray tracing. The number in the lower right corner shows the total ray path number at the corresponding period.

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3.2   Shear-Wave Velocity Model and Earthquake Distribution in the Upper Crust

We used the phase velocity dispersion data from four subarrays to obtain the 3-D isotropic shear velocity model of the upper crust from the surface to 10 km depth. Figure 6 shows the final isotropic shear velocity structure at six depths: 1, 2, 4, 6, 8, and 10 km. The second panels in a later figure also show the isotropic shear velocity model for four profiles A–A′, B–B′, C–C′, and D–D′, respectively. The tomographic results from the joint data from the four subarrays correlate well with the geological and geomorphological background, as well as the results of previous works (e.g., Gu N et al., 2019; Li C et al., 2020; Luo S and Yao HJ, 2021). The results show the low-shear velocity zones, indicating a sedimentary area, including the Hefei Basin (area A) and Chao Lake (area E) in Figure 6a. Moreover, the areas marked as B, C, D, and F in Figure 6a represent the regions covered by intrusive rocks in the Tan-Lu Fault Zone, the Dabie Orogenic Belt, the Zhangbaling Uplift, and Yinping Mountain, respectively, which show relatively high shear velocity characteristics. In addition, the profiles show the morphology and the margins of some special tectonic structures much more clearly. For example, if we regard the velocity of 2.7 km/s as the empirical maximum shear velocity for sedimentary material, the profiles show the bottom depth of the Hefei Basin is approximately 7 km deep and the maximum sedimentary depth is not in Chao Lake but in the northeast of the Dabie Orogen (Figure 6e). This result fits quite well with other geological results (Lu GM et al., 2002; Liu GS et al., 2006).

Figure  6.  (a−f) Horizontal slices of the isotropic shear velocity model at depths of 1, 2, 4, 6, 8, and 10 km, respectively. The solid gray lines represent faults that have remained active from the early and middle Pleistocene, and the dashed gray lines represent faults shown to be active before the pre-Quaternary period, along with some other secondary fault systems. The solid white lines represent the locations of lakes and rivers. A, B, C, D, E, and F in black boxes represent the Hefei Basin, the regions with intrusive rocks in the Tan-Lu Fault Zone, the Dabie Orogenic Belt, the Zhangbaling Uplift, the sedimentary area in Chao Lake, and Yinping Mountain, respectively. The black dots in (b) represent the distribution of earthquakes in this region with magnitudes greater than 0.5 that occurred between January 1990 and January 2023. The red star represents the location of the Feidong M4.7 earthquake. The red boxes represent the areas with densely distributed earthquakes. The red dots in (c) to (f) represent the distribution of the relocated Lujiang earthquake series at depths.

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The locations of the Feidong M4.7 earthquake in 2024 and the Lujiang earthquake series in the upper crust that occurred between January 1990 and January 2023 are plotted in Figure 6b as an example because of the lack of reliable depth information for most of the earthquakes. The earthquakes in the upper crust occurred mostly at the transition zone between high- and low-velocity areas.

3.3   3-D Azimuthal Anisotropy of the Upper Crust

The azimuthally anisotropic model was further inverted based on the 3-D isotropic shear velocity structure as the initial model. Figure 7 shows the horizontal slices at six depths: 1, 2, 4, 5, 7, and 8 km, respectively. Figure 8 shows the upper crustal anisotropic structure of the four profiles A–A′, B–B′, C–C′, and D–D′, as shown in Figure 1b. The maximum amplitude of azimuthal anisotropy is approximately 4%. The amplitude of anisotropy in the low-velocity area (sedimentary basins) is obviously larger than that in the high-velocity area. Moreover, features of the anisotropic structure fit well with the major geological units in the upper crust (Figure 7). The north part of the Dabie Orogenic Belt near the Qingshan-Xiaotian Fault and the area near the Meishan−Longhekou Fault (marked as A in Figure 7c) reveal a fast NW-SE direction that is approximately parallel to the direction of the faults. Similarly, the results reveal fast directions parallel to the strike of the Tan-Lu Fault Zone (a fast NE-SW direction in area B) and the Chaohu Fault (a fast NWW-SEE direction in areas C and D). Meanwhile, across the transition zone of the fast direction (e.g., areas between A and B, B and C, and B and D), the fast direction of azimuthal anisotropy changes gradually. In the Hefei Basin and in areas far away from the main tectonic units, the fast direction of azimuthal anisotropy basically reveals a NW-SE direction, which is also similar to the result from Luo S and Yao HJ (2021).

Figure  7.  (a−f) Horizontal slices of the final shear velocity model (color bar) and azimuthally anisotropic model (black bars) at depths of 1, 2, 4, 5, 7, and 8 km, respectively. TLF represents the Tan-Lu Fault Zone. The labels f1, f2, and f4 represent the Qingshan−Xiaotian Fault (QXF), the Meishan−Longhekou Fault (MLF), and the Chaohu Fault (CHF), respectively. The red boxes represent areas with typical azimuthal anisotropy patterns: areas adjacent to the Meishan−Longhekou Fault (A), the Tan-Lu Fault Zone (B), the Chaohu Fault (C, D), and Hefei Basin (E), and an area far away from the major tectonic unit (F).

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Figure  8.  The azimuthally anisotropic shear wave velocity structures along four vertical profiles shown as the red lines in Figure 1: (a) A–A′, (b) B–B′, (c) C–C′, and (d) D–D′. In each profile, the upper panel shows the topography, the middle panel shows the isotropic shear wave velocity structure, and the bottom panel shows the azimuthally anisotropic shear velocity structure. The upward direction in each bottom panel represents the fast S-N direction. DBO represents the Dabie Orogenic Belt, HFB represents the Hefei Basin, TLF represents the Tan-Lu Fault Zone, and ZBL represents the Zhangbaling Uplift. The labels f1 and f2 represent the Qingshan−Xiaotian Fault (QXF) and the Meishan−Longhekou Fault (MLF), respectively. The solid gray lines represent the positions of the main faults.

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3.4   Model Recovery Test and Data Fitness Test

To test the capability of the data to recover the model, we used the final isotropic and azimuthally anisotropic model as the true model to generate theoretical travel-time data. Because approximately 1% error will be brought into the phase velocity dispersion data owing to an uneven distribution of noise sources (e.g., Yao HJ and van der Hilst, 2009), we added 1% random error to the theoretical travel-time data. The initial model was still the same 1-D model as mentioned in Step 1. After the two-step inversion, we obtained the recovered model (Figure 9). Compared with the true model (Figures 8 and 9), the major tectonic units and the anisotropy patterns were basically recovered, which indicates that the 3-D isotropic and azimuthally anisotropic shear velocity model was reliable.

Figure  9.  (a, b) Results of the model recovery test for profiles B–B′ and D–D′, respectively. HFB represents the Hefei Basin, TLF represents the Tan-Lu Fault Zone, and DBO represents the Dabie Orogenic Belt. (c−e) Results of the model recovery test for horizontal slices at depths of 1, 4, and 8 km, respectively.

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To quantify the balance of model complexity with its goodness of data fit statistically, we used the F-test and Akaike information criterion (AIC; Bem et al., 2022). These methods help determine how much lower or higher the misfit of the anisotropic model is than that of the isotropic model. A detailed description is given in text S1 of the Supplementary Materials. The results of the F-test and the AIC were consistent, revealing that the anisotropic model offered a statistically better fit to the data than did the isotropic model. The results indicate the robustness of the isotropic and anisotropic models from the inversion.

4.   Discussion

4.1   Deformation Characteristics

Multiple-stage tectonic activities have led to relatively complex deformation characteristics of the Tan-Lu Fault Zone. By analyzing the 3-D anisotropy results and those from Luo S and Yao HJ (2021), several typical areas were identified (Figure 10a). The azimuthal anisotropy at three depths (1, 7, and 25 km) represents deformation in different crustal layers: the shallow crust, upper crust, and middle to lower crust. In general, the direction of the fast axes at depths of 1 and 7 km correlates well in areas O, P, Q, and S. This result suggests that the shallow crust and the upper crust in each of these areas share a vertically coherent deformation mechanism, except in area R in Feidong, with a clear depth variation. The fast direction of anisotropy primarily aligns with the distribution of the main fault systems. In area O, the fast NW-SE direction aligns with the Qingshan−Xiaotian Fault and the Meishan−Longhekou Fault (marked as faults f1 and f2, respectively, in Figures 1b and 7). In area P, the fast NE-SW direction concurs with the Tan-Lu Fault Zone, as also confirmed by Luo S and Yao HJ (2021). In area Q, the fast NW-SE direction aligns with the Chaohu Fault (marked as fault f4 in Figures 1b and 7).

Figure  10.  (a) Comparisons of azimuthal anisotropy at different depths: 1 km (black lines), 7 km (dark green lines), and 25 km (red lines), respectively. The anisotropic structure at the depth of 25 km is from Luo S et al. (2022). The red boxes represent five typical areas, which stand for the Hefei Basin (O), the Tan-Lu Fault Zone (P), the conjugated faults of the Tan-Lu Fault (Q and R), and an area far away from the major tectonic units (S), respectively. (b) Comparisons of some other datasets: the absolute plate motion (APM, green arrows), the maximum horizontal stress (black lines), azimuthal anisotropy of ${\mathrm{P}}_{\mathrm{n}}$ wave tomography (red lines), and XKS splitting (purple lines) from previous studies. The APM data are from the Global Strain Rate Model (GSRM) v2.1 (Kreemer et al., 2014). The maximum horizontal stress data were extracted from the World Stress Map database (Ziegler and Heidbach, 2017; Heidbach et al., 2018). The ${\mathrm{P}}_{\mathrm{n}}$ wave anisotropic results were obtained from Lü Y et al. (2020). The XKS splitting results are from Yang XY et al. (2019).

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In the middle to lower crust, a relatively different pattern of azimuthal anisotropy is observed from a previous study (Luo S et al., 2022) compared with that in the upper crust (Figure 10a). In area O, the fast direction shifts from NW-SE in the shallow crust to NNW-SSE in the deep crust. In area Q, the fast NE-SW direction in the lower crust is almost perpendicular to the fast NW-SE direction in the upper crust, suggesting a distinctly different tectonic deformation condition (Figure 10a). In contrast, in the Tan-Lu Fault Zone and its adjacent areas, the fast direction of anisotropy in the lower crust remains consistent with that of the upper crust. Because P_n waves have better sensitivity to the lower crust or uppermost mantle (Gu QP et al., 2016), the anisotropic structure derived from P_n travel-time tomography (Lü Y et al., 2020; Figure 10b) correlates well with the azimuthal anisotropy in the middle to lower crust of the Tan-Lu Fault Zone, particularly in areas P and Q (Figure 10a). However, some differences still exist in areas with more complex structures, such as area O, which is influenced by the Dabie Orogen. In contrast, the results from XKS splitting (Yang XY et al., 2019) show the directional consistency between the anisotropy mainly in the upper mantle and the direction of absolute plate motion.

4.2   Mechanism of Azimuthal Anisotropy in the Crust

Multiple factors can influence the anisotropic structure. In the crust, two primary mechanisms exist. The first is shape-preferred orientation (SPO), resulting from thin layers or small aligned cracks. The second is lattice-preferred orientation (LPO), arising from the alignment of anisotropic minerals in the medium (Shearer, 2009; Maupin and Park, 2015). Consistent with the results of Luo S and Yao HJ (2021), the shape-preferred orientation is the dominant mechanism driving azimuthal anisotropy in the upper crust of this area. The fast direction of azimuthal anisotropy aligns closely with the distribution of specific fault systems discussed in Section 4.1. A notable characteristic shared by these faults is that they have retained continuous large-scale activities from the early and middle Pleistocene, including the Tan-Lu Fault Zone, the Meishan-Longhekou Fault, the Qingshan-Xiaotian Fault, and the Chaohu Fault (Wu ZH et al., 2016). The NE-SW Tan-Lu Fault is a major reverse fault characterized by right-lateral strike-slip motion (Zhu G et al., 2016). Under the specific maximum horizontal stress and NW-SE-directed absolute plate motion (Figure 10b), the associated conjugated faults, such as the Tan-Lu Fault Zone, the Meishan−Longhekou Fault, the Qingshan−Xiaotian Fault, and the Chaohu Fault, act as reverse faults with left-lateral strike-slip characteristics (Wang HN et al., 2016). Recent activities of the faults have generated a wide range of aligned fractures, leading to seismic anisotropy with considerable amplitude. Additionally, there exist numerous large-scale faults and various secondary fault systems with diverse directional distributions in this region, such as the Luan-Hefei Fault and the Feizhong Fault, marked as f3 and f5 in Figure 1b. However, they do not contribute substantially to azimuthal anisotropy because they were active before the pre-Quaternary period and have remained stable for a long period of time. Secondary faults may cause slight anisotropy in the shallow crust, but the amplitude of this anisotropy may be difficult to observe in our tomography model.

Variations in anisotropic structures indicate that they are controlled by multiple modes of geodynamic forces. The formation of the Hefei Basin and its associated fault systems is closely linked to the uplift of the Dabie Orogen and the three-stage evolution of the Tan-Lu Fault Zone (Zhu G et al., 2004). Plate collisions and orogenic movements provide the primary driving force for the complex anisotropic structures in the upper crust. Although the crustal layers generally maintain a coupled deformation pattern, some differences still exist among them. This anisotropic variation stems from a structural distinction between the upper crust and the middle to lower crust. The Tan-Lu Fault Zone extends directly into the upper mantle, whereas its conjugate fault system is primarily distributed and acts in the upper crust (Wu ZH et al., 2016). As the medium in the middle to lower crust moves along with the absolute plate motion (Luo S et al., 2022), the upper crust material undergoes relative motion with respect to the medium of the middle to lower crust owing to the left-lateral strike-slip movement along the conjugate faults. This action results in substantial anisotropic structural differences between the crustal layers.

4.3   Seismogenic Structure in the Upper Crust

As shown from previous studies, the lateral inhomogeneity of the crustal structure exhibits good correlation with the earthquake distribution (Tian Y et al., 2007; Qu ZD et al., 2018; Ruan QF et al., 2022), particularly with a high seismic velocity medium (Huang JL and Zhao DP, 2005). Earthquakes within the crust predominantly occur in regions of high seismic velocity, along the boundaries between high and low seismic velocity anomalies, or in areas characterized by a lower Poisson ratio with high P and S wave velocities (Zhao DP et al., 1996; Kato et al., 2010). Crustal regions with uniformly high seismic wave velocities are classified as brittle media, which are prone to stress accumulation and subsequent earthquake occurrence. Conversely, regions of low seismic velocity may indicate extensive fault rupture zones, rich fluid contents, or high-temperature ductile zones, which are often associated with aseismic deformation and swarms of small earthquakes (Tian Y et al., 2007; Ruan QF et al., 2022).

Within the upper crust of the study area, earthquakes with magnitudes exceeding 0.5 have predominantly occurred along the boundaries of high and low seismic velocity anomalies (Figure 6b). The Feidong M4.7 earthquake in 2024 and the Lujiang earthquake series serve as noteworthy examples for further discussion on seismogenic structures within the upper crust (Figures 6c−6d and 8b). After relocation, these earthquakes were still positioned along the boundaries of high- and low-velocity anomalies at various depths within the upper crust. Furthermore, several NE-SW-trending tectonic units were distributed along the fault, including the Hefei Basin, an intrusive rock belt, sedimentary areas within the fault zone, and Yinping Mountain (areas A, B, E, and F in Figure 6a). These tectonic units exhibit distinct shear velocity characteristics: low-high-low-high from west to east. Within the sedimentary region of the Tan-Lu Fault Zone, secondary faults and fractures are well developed (Figures 1b and 6), with much weaker rigidity. With the absolute plate motion and the accumulation of principal compressive stress in the NW-SE direction, the Tan-Lu Fault Zone is in a compressional environment (Zhu G et al., 2004). The areas with high shear velocity, comprising the area with intrusive rocks and Yinping Mountain, facilitate stress transmission because of the increased stiffness and brittleness of media. Conversely, the zones with low shear velocity, consisting of sedimentary materials with softness and plasticity, are sandwiched between these intrusive rocks and mountains. This regional stress results in the development of cracks, small-scale faults, and ruptures in the upper crust, through which the accumulated stress is released. This may explain why destructive events with magnitudes exceeding 5 are relatively infrequent even though numerous earthquakes occur in the upper crust of this region.

5.   Conclusions

We collected surface wave phase velocity dispersion curves from four subarrays located in the cities of Lujiang, Chaohu, Feidong, and Hefei in Anhui Province, which are distributed along the Tan-Lu Fault Zone. We then inverted for the 3-D isotropic and azimuthally anisotropic models in the array area by using a direct inversion method from surface wave travel times. The isotropic model in the upper crust revealed the distribution of several major tectonic units, including the Dabie Orogen, the Hefei Basin, and the details of the Tan-Lu Fault Zone. Furthermore, the 3-D azimuthally anisotropic model illuminated the distribution of fast axes at different depths in the upper crust. Within the Tan-Lu Fault Zone, the fast axis of azimuthal anisotropy aligns with the NE-SW orientation, parallel to the strike of the Tan-Lu Fault Zone. In contrast, the fast axis to the north of the Dabie Orogen and Chao Lake aligns with the NW-SE orientation, parallel to the Meishan−Longhekou Fault and the Chaohu Fault. A notable characteristic of these conjugate faults and the Tan-Lu Fault is their persistent tectonic activity since the early and middle Pleistocene. The azimuthally anisotropic structure of the upper crust in this area is mainly governed by such active fault systems. By integrating insights from the anisotropic structures of both the upper crust and middle to lower crust, we postulated a model that accounts for variations in azimuthal anisotropy and relative movements between the upper crust and middle to lower crust. Ultimately, our findings highlighted a prominent feature in earthquake distribution within the upper crust: a large number of earthquakes have occurred along the boundaries between high and low seismic velocities. We suggest, based on the relocation results of the Lujiang earthquake series, that the relatively fractured medium with a high-level development of cracks and small-scale faults is jammed between more rigid areas, which leads to earthquakes and ruptures occurring around the structural boundaries.

Supplementary Material

  S1.  The relocation result of the Lujiang earthquake series.

Longidute (°)	Latitude (°)	Depth (km)	Magnitude
117.427208	31.369854	7.550	1.3
117.433846	31.353973	9.148	1.8
117.418877	31.357990	7.070	1.5
117.448898	31.350677	10.330	1.8
117.433395	31.351601	9.834	2.8
117.455528	31.346317	4.192	1.2
117.447479	31.352625	4.310	1.0
117.460869	31.351200	6.072	0.8
117.452988	31.353226	6.046	0.9
117.441849	31.348650	4.170	0.9
117.457550	31.352037	6.883	1.1
117.437729	31.353823	9.709	3.7
117.454323	31.348356	6.381	0.6
117.466301	31.352669	7.741	1.4
117.422157	31.365988	6.899	1.3
117.449608	31.365944	8.671	0.6
117.455841	31.356310	6.733	0.7
117.455154	31.356388	7.231	0.8
117.469650	31.359606	8.545	1.3
117.445488	31.344511	6.396	0.7
117.432251	31.352448	9.596	1.7
117.432083	31.355740	9.401	1.5
117.434586	31.351791	10.075	2.1
117.472504	31.360052	9.427	1.0
117.463463	31.351952	9.903	1.6
117.414642	31.345131	9.533	1.7
117.452019	31.347675	7.225	0.6
117.463242	31.355698	5.719	0.3
117.431305	31.355844	7.540	1.5
117.454872	31.352007	7.816	1.4
117.423698	31.352146	9.564	2.5
117.455444	31.350845	8.698	0.6

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Text S1. Test Goodness of Fit

To estimate the balance of isotropic and anisotropic model complexities with their goodness of fit to data, we applied the F-test or Akaike information criterion (AIC). The basic assumption in the F-test is that the anisotropic model is more complex and with more parameters while the isotropic model is simple and 'nested' within the anisotropic model.

For N data points from which parameters of both isotropic and anisotropic models are estimated, the chi-squares and F-test statistic can be estimated as in Equations (A1) and (A2).

where ${\chi }^{2}={\chi }^{2}_{\mathrm{i}\mathrm{s}\mathrm{o}}\;\mathrm{o}\mathrm{r}\;{\chi }^{2}_{\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{o}}$; ${\chi }^{2}_{\mathrm{i}\mathrm{s}\mathrm{o}}$is the chi-square misfit of the isotropic model; ${\chi }^{2}_{\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{o}}$ is the chi-square misfit of the anisotropic model; ${\sigma }_{M}$ is the standard deviations of the model predicted data (${DM}_{i}$) from the observed data (${D}_{i}$); N is the data size; ${p}_{\mathrm{i}\mathrm{s}\mathrm{o}}= \left(nx-2\right)\left(ny-2\right)\left(nz-1\right)$ and ${p}_{\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{o}}=3\left[\left(nx-2\right)\left(ny-2\right)\left(nz-1\right)\right]$ are the number of parameters in the isotropic and anisotropic models; $nx,ny,nz$ are the number of $x,y,z$ parameters in the models and have values of 66, 76, 22 respectively.

Four steps are taken to obtain the F-test as follows:

(1) Calculate the F-statistic (using Equation (A1)).

(2) The F-statistic is itself a random variable. For this, we identify the Probability Density Function (pdf) that the F-value represents. This can be done by extracting the p-value from F-table in MATLAB.

(3) If the p-value is greater than the error threshold such as $\alpha =0.05$, then the null hypothesis is true with a probability of error equal to the threshold error.

(4) If the p-value is less than the error threshold such as $\alpha =0.05$, then the second model is statistically better than the first at a confidence level of $1-\alpha$ (i.e. 95% confidence level).

Using 33776 travel time data sizes, we followed Equation (A1) and calculate the F-test value to be 0.6485. Under the null hypothesis that the anisotropic model provide a better fit than the isotropic model.

In addition, we also calculated AIC for isotropic (${\mathrm{A}\mathrm{I}\mathrm{C}}_{\left(\mathrm{i}\mathrm{s}\mathrm{o}\right)}$) and joint inversion (${\mathrm{A}\mathrm{I}\mathrm{C}}_{\left(\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{o}\right)}$) using Equation (A3), then computed the difference as ${\Delta \mathrm{A}\mathrm{I}\mathrm{C}=\mathrm{A}\mathrm{I}\mathrm{C}}_{\left(\mathrm{i}\mathrm{s}\mathrm{o}\right)}-{\mathrm{A}\mathrm{I}\mathrm{C}}_{\left(\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{o}\right)}$. The AIC score also gives a way to measure the goodness-of-fit of a model, while at the same time penalizing the model for over-fitting the data. An AIC score of a model is not useful unless one compares it with the score of a competing model. A lower AIC score indicates superior goodness-of-fit and a lesser tendency to over-fit.

where N is the data size (40279), $\mathrm{S}\mathrm{S}\mathrm{R}$ is the sum of squares residuals, ${p}_{i}$ is the number of parameters of the $i\mathrm{t}\mathrm{h}$ model, $i$ is the isotropic or anisotropic model. The results give ${\mathrm{A}\mathrm{I}\mathrm{C}}_{\left(\mathrm{i}\mathrm{s}\mathrm{o}\right)}$is 131794 and ${\mathrm{A}\mathrm{I}\mathrm{C}}_{\left(\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{s}\mathrm{o}\right)}$ is 131565. The difference $\Delta \mathrm{A}\mathrm{I}\mathrm{C}$ is 229, indicating that the anisotropic model has a smaller AIC value than the isotropic model. Both the F-test and the AIC results are consistent that the anisotropic model fit the data better.