Effects of the 2011 Mw 9.0 Tohoku-Oki Earthquake on the Locking Characteristics and Seismic Risk of the Yishu Fault Zone in China

Abstract

To ascertain the 2011 Tohoku-Oki Mw 9.0 earthquake’s impact on the stability of the Yishu fault zone, this study inverts the fault locking degree and slip rate defect distribution of the Yishu fault zone using GPS horizontal velocity field data covering the period from 1999 to 2009 and from April 2011 to 2019. This is based on the block negative dislocation model. Combined with the b value and strain field characteristics, the properties of deformation of the Yishu fault zone before and after the earthquake are comprehensively analyzed. The results show that before the 2011 Tohoku-Oki Mw 9.0 earthquake, the locking degree and depth of the northern segment of the Yishu fault zone were higher, while the locking depth of the southern segment of the fault was shallower. The 2011 Tohoku-Oki earthquake produced different coseismic effects on the southern and northern sections of the Yishu fault zone. The extension on the southern section and compression on the northern section caused the strain release in the southern sections of the Yishu fault zone following the earthquake. After it, the regional locking degree of the southern section of the Yishu fault zone was relieved. However, the locking degree of the northern segment of the fault zone was still high and the depth was deep, at about 26 km. In addition, the northern section of the Yishu fault zone was a section with an abnormally low b value and small earthquakes in the northern segment are sparse at present. The coseismic compression of the northern section caused by the 2011 Tohoku-Oki earthquake is conducive to its locking and easily accumulates stress, so it is necessary to pay attention to its seismic risk.

1. Introduction

The subduction of the Pacific plate affected the Tohoku-Oki Mw9.0 earthquake in Japan that occurred on 11 March 2011 [1,2,3]. Previous studies have shown that the 2011 Tohoku-Oki earthquake had an essential impact on the seismicity in the areas on both sides of the Yishu Fault Zone, which caused the coseismic horizontal displacement at a millimeter-to-centimeter level in North China and Northeast China [4,5,6]. The Yishu fault zone, the central segment of the Tanlu Fault Zone, is in the Shandong Peninsula, eastern China [7]. The Tanlu fault zone is characterized by linearly steep-dipping faults traversing the region in an SSW–NNE direction with a clear physiognomy and a synchronous dextral displacement of short gullies [8]. The Tanlu fault zone is the most important active fault zone and strong seismic tectonic zone in the eastern part of the Chinese mainland [9,10]. Historically, there was the Anqiu Ms 7.0 earthquake in 70 BC, the 1668 Tancheng Ms 8.5 earthquake, the 1888 Bohai Bay Ms 7.5 earthquake, the 1969 Bohai Bay Ms 7.4 earthquake, and the 1975 Haicheng Ms 7.3 earthquake.

The Shandong area is located at the southeastern margin of the Sino–Korean Block and the eastern end of the central orogenic area in the primary tectonic area of the Chinese continent. It has complex geological structures and a long evolutionary history. The modern tectonic movement is at the intersection of multiple active blocks and the dynamic environment is affected by the interaction of the Pacific, North American, and Eurasian Plates [9,11,12,13]. The strong earthquake activity in Tohoku-Oki, which is in the subduction zone of the Pacific Plate, has a significant effect on the earthquake activity in North China [4,14]. The Yishu fault zone and the Tohoku-Oki Trench belong to the same geological tectonic system and are also affected by the subduction of the Pacific Plate [15]. After the 2011 Tohoku-Oki earthquake, the seismicity of the Yishu fault zone and its surrounding areas increased significantly, which was related to the regional coseismic deformation and post-earthquake deformation characteristics [16]. Therefore, the impact of the 2011 Tohoku-Oki earthquake on the Yishu fault zone deserves attention.

The Global Positioning System (GPS) can provide comprehensive velocity field information and can be used to study large-scale tectonic deformation [17]. Fan et al. (2022) [18] investigated the adjustment of the in situ stress field of the Beijing Plain after the 2011 Tohoku-Oki earthquake based on in situ stress monitoring data. It shows that the stress accumulation level of faults in the Beijing Plain area increased in a short time after the earthquake and then gradually decreased. There have been many studies on the crustal deformation of the Yishu fault zone using GPS which have shown that the fault zone is characterized by right-lateral slip and compression [17,19,20,21,22,23,24,25]. Li et al. (2016) [26] used the GPS velocity field data from 2009 to 2014 as a constraint to invert the locking degree of the central and southern segment of the Tanlu fault zone and obtained the locking depth of the fault from north to south, first deep then shallow, along the strike. However, the existing studies have not investigated the degree of change of the deep locking in the Yishu fault zone before and after the 2011 Tohoku-Oki earthquake. An earthquake happens because of the continuous accumulation of strain on the active fault under the action of regional tectonic stress and the sudden instability and fractures after reaching the limit state [2,27,28]. How the strain characteristics change before and after the earthquake characterizes them. The slip inversions have successfully modelled the transient deformations [29,30], coseismic slips [31,32], and post-seismic slip [32] in different tectonic regions. Prioritizing earthquake risk is determined using the Turkish rapid assessment method, which shows that the study of micro-zoning is very important in minimizing earthquake damage [33]. In this paper, the horizontal strain field of the Yishu fault zone is analyzed based on GPS data and the locking depth and degree of the Yishu fault zone before and after the 2011 Tohoku-Oki earthquake are inverted using the TDEFNODE negative dislocation inversion model [30,34]. Based on seismic activity, the future seismic risk of the Yishu fault zone is discussed.

2. Overview of the Study Area

The Yishu fault zone is in the Shandong section of the Tanlu fault zone (Figure 1). It has the best exposure and strongest neotectonic activity in the Tanlu fault zone. The Yishu fault zone forms a compound graben structure of “two grabens sandwiched by a barrier” in the Yi River and Shu River Valleys of Luzhong. It starts from Laizhou Bay of Bohai Sea in the north and extends to the Xinyi Area of Jiangsu Province in the south. It consists of the Anqiu–Juxian fault (F5), the Changyi–Dadian fault (F1), the Baifenzi–Fulaishan fault (F2), the Yishui–Tangtou fault (F3), and the Tangwu–Gegou fault (F4), and includes five nearly parallel faults with a length of 330 km. The width of the northern section of the fault zone is about 55 km, which is reduced to about 25 km in the south, forming the structural boundary between the Luxi block and the Jiaoliao block. Among them, the Anqiu–Juxian fault is the most important Late Quaternary active fault in the Yishu fault zone, characterized by dextral strike-slip and thrust activity, and is a strong active zone of neotectonic movement, which controls the occurrence of earthquakes [35]. The north and south sections of the Anqiu–Juxian fault have different earthquake characteristics and can be divided into two permanent north–south earthquake rupture sections [36].

The Yishu fault zone is a deep fault zone. Since the Quaternary, the neotectonic movement in the fault zone has been strong, and the seismicity is characterized by large magnitude earthquakes and long active periods. The Anqiu earthquake with Ms 7.0 occurred in 70 BC and the Tancheng earthquake with Ms 8.5 occurred in 1668. The seismicity of the Yishu fault zone is segmented [37,38], which is mainly concentrated in the south section and less in the north section.

Figure 1. Tectonic setting and earthquake activity distribution in the study area. (a) Tectonics and historical earthquakes in the study area. Inset map on the upper right shows the study area. The blue box divides the Yishu fault zone into north and south segments. The size of the red circles is scaled to the magnitude of the earthquakes (from 2011 to 2019, ML > 2.0). The blue solid circle, triangle and diamond are the selected GPS sites (I1 is the Jidong–Bohai fault block, I2 is the Luxi fault block, II1 is the Ludong uplift, II2 is the Jiaolai basin, II3 is the Jiaonan fault block, II1, II2, and II3 jointly constitute the Ludong fault block). (b) Geological setting of Yishu fault zone and its vicinity [39] (F1 is the Changyi–Dadian fault, F2 is the Baifenzi–Fulaishan fault, F3 is the Yishui–Tangtou fault, F4 is the Tangwu–Gegou fault, and F5 is the Anqiu–Juxian fault).

Figure 1. Tectonic setting and earthquake activity distribution in the study area. (a) Tectonics and historical earthquakes in the study area. Inset map on the upper right shows the study area. The blue box divides the Yishu fault zone into north and south segments. The size of the red circles is scaled to the magnitude of the earthquakes (from 2011 to 2019, ML > 2.0). The blue solid circle, triangle and diamond are the selected GPS sites (I1 is the Jidong–Bohai fault block, I2 is the Luxi fault block, II1 is the Ludong uplift, II2 is the Jiaolai basin, II3 is the Jiaonan fault block, II1, II2, and II3 jointly constitute the Ludong fault block). (b) Geological setting of Yishu fault zone and its vicinity [39] (F1 is the Changyi–Dadian fault, F2 is the Baifenzi–Fulaishan fault, F3 is the Yishui–Tangtou fault, F4 is the Tangwu–Gegou fault, and F5 is the Anqiu–Juxian fault).

3. Data and Research Method

3.1. Data Processing

In this paper, the GPS observation site data of the Crustal Movement Observation Network of China (CMONOC), the Crustal Movement Observation Network of Shandong (CMONOSD), and the Shandong Continuously Operating Reference Station System (SDCORS) (Figure 1) were used. Additionally, GAMIT/GLOBK software was used to solve the data and obtain GPS site coordinates and time series data (Figure 2).

When solving the GPS data, the elevation mask angle of the satellite was set to 15° and the data sampling rate is 30 s. The global atmospheric pressure model and temperature models GPT (Global Pressure Temperature) and GMF (Global Mapping Function) were used as the prior tropospheric dry delay model and convection projection function. The FES2004 ocean tide loading model was used to correct the ocean tide to weaken the influence of ocean tide loading on the station. The IGS (International Global Navigation Satellite System Service) tracking stations around the Shandong area were selected and the one-day relaxation constraint solutions of all the stations were obtained by combining the one-day solutions of the stations in the study area with the existing relaxation solutions of the IGS stations by using the GLOBK software. The data were processed using GLOBK software with the continuous Kalman filter to obtain the coordinate time series and velocity field results for each station under the ITRF2014 (International Terrestrial Reference Frame 2014) framework. The GPS velocity field to the velocity field under the Eurasian framework was converted and the GPS stations whose direction and size deviated were removed from the regional motion background (Figure 3 and Figure 4).

Since the study area is far from the epicenter of the 2011 Tohoku-Oki earthquake (more than 2200 km), nonlinear effects such as creep-slip during the short period can be neglected. Considering the accuracy of GPS observation, a continuous GPS observation sequence of 10 days each before and after the 2011 Tohoku-Oki earthquake was used to estimate the coseismic displacement and its error using the least squares method [6]. The coseismic displacements calculated are shown in Figure 5.

The crustal strain fields from 1999 to 2010 and from April 2011 to 2019 were calculated using the GPS horizontal velocity field and the deformation characteristics of the Yishu fault zone before and after the 2011 Tohoku-Oki earthquake were analyzed. The 3D b value distribution was calculated using the seismic activity catalogue from 1970 to 2019. Finally, the seismic hazard of the Yishu fault zone was studied by determining the degree and extent of the Yishu fault zone’s locking using inversion. The research technical route is shown in Figure 2.

3.2. Calculation of Crustal Strain Field

The crustal strain field analysis is independent of the spatial datum analyzing the variation of deformation within the region and can more comprehensively express the intensity of crustal deformation. To overcome the influence of earth curvature or projection deformation, a more accurate calculation method in a spherical coordinate system is used to calculate the strain (rate) field [40]. In practical applications, only the horizontal strain field is considered due to the poor reliability of the GPS vertical velocity component, and the formula is as follows [40]:

$$\begin{array}{l}{u}_{\phi }=-{\overline{\omega }}_{\theta }{r}_0-{\overline{\omega }}_{\phi }\cos {\theta }_0\Delta \phi +{\overline{e}}_{\phi \phi }{r}_0\Delta \phi +{\overline{e}}_{\theta \phi }{r}_0\Delta \theta +{\overline{\omega }}_r{r}_0\Delta \theta \\ u_{\theta }=-{\overline{\omega }}_{\theta }{r}_0\cos {\theta }_0\Delta \phi +{\overline{\omega }}_{\phi }{r}_0+{\overline{e}}_{\theta }{}_{\phi }{r}_0\sin {\theta }_0\Delta \phi +{\overline{e}}_{\theta \theta }{r}_0\Delta \theta -{\overline{\omega }}_r{r}_0\sin {\theta }_0\Delta \phi \end{array}$$

(1)

where $\phi$, $\theta$, and $r$ are the longitude angle, the colatitude angle, and the earth radius in the earth coordinate system, respectively. ${\phi }_0$, ${\theta }_0$ represents the plane coordinates of the regional geometric center point and $r_0$ represents the earth radius of the regional geometric center point. When $\phi$, $\theta$, and $r$ are used as subscripts, they represent the longitude direction (east direction), the latitude direction (north direction), and the radial direction (vertical direction), respectively. $u$ represents the displacement of each observation point. $\Delta \phi$, $\Delta \theta$, and $\Delta r$ represent the three-direction distance from the observation point to the center point of the observation network, respectively, ${\overline{e}}_{\phi \phi }$, ${\overline{e}}_{\theta \theta }$, and ${\overline{e}}_{\theta \phi }$ represent the strain components, and ${\overline{\omega }}_{\phi }$, ${\overline{\omega }}_{\theta }$, and ${\overline{\omega }}_r$ represent the Euler rotation vectors, respectively. Therefore, as long as the horizontal displacements of more than three GPS observation points are known, the above six unknown parameters (${\overline{e}}_{\phi \phi }$, ${\overline{e}}_{\theta \theta }$, ${\overline{e}}_{\theta \phi }$, ${\overline{\omega }}_{\phi }$, ${\overline{\omega }}_{\theta }$, and ${\overline{\omega }}_r$) can be solved using Equation (1) and the least square method.

3.3. Calculation of Seismic b Value

The earthquake b value is derived from the Gutenberg–Richter magnitude–frequency relationship ($\lg \mathrm{N}=a-bM$) [41]. Starting from the laboratory discovery of the relationship between rock fracture stress and the b value, many observations have shown that there is a negative correlation between b value and differential stress [27,28]. Because the seismic b value is closely related to seismic activity and the crustal stress state, it is often used as a crustal “stress gauge” [42].

The earthquake catalogue’s completeness is particularly significant for the calculation of the b value. The b value will be low due to the lack of small earthquake data caused by the weak monitoring ability of the network. The Mc (Magnitude of completeness) can be used to evaluate the seismic measuring ability of the station. The Mc is regarded as a critical magnitude, which represents the minimum complete magnitude that can be monitored by the network. When calculating the b value, only events greater than or equal to the Mc value are selected. In this paper, the Mc values were calculated for earthquakes with ML > 2.0 from 1970 to 2019 using the ZMAP program [43]. The maximum curvature method was used to calculate the Mc in the study area and the magnitude corresponding to the maximum of the first derivative of the magnitude frequency curve function was regarded as the Mc.

The maximum likelihood estimation method is a method of estimating model parameters using observation data generated with high probabilities. Based on the maximum likelihood method and according to the exponential distribution relationship between earthquake frequency and magnitude [41],

$$n\left(M\right)=e^{\left(a-bM\right)}$$

(2)

$$b=\frac{\lg \mathrm{e}}{M-M_0}.$$

(3)

In Equations (2) and (3), $M$ is the starting magnitude, $M_0$ is the average magnitude, $\lg \mathrm{e}=0.4343$, and when $n$ is the total number of earthquakes, the standard deviation of the 95% confidence level [41] is

$$\sigma =1.96\frac{b}{\sqrt{n-1}}.$$

(4)

3.4. Fault Slip Inversion Model

The occurrence of a large earthquake is closely related to the seismogenic fault’s locking degree. As per the classical dislocation theory, the fault’s earthquake preparation is directly related to the fault’s locking depth and the urgency and risk of seismicity are higher when the fault’s earthquake preparation is close to the late stage [44,45]. The TDEFNODE negative dislocation inversion model can use the simulated annealing method and grid search method to estimate the block rotation, internal strain, and fault locking degree under the constraints of GPS velocity field and seismic data. The depth along the longitudinal strike of the fault is specified by the node [30,34]. The program assumes that the movement of points inside the plate is the sum of surface elastic deformation caused by block rotation and the sliding deficit at the block boundary due to fault locking. The inversion result has a certain reliability and good stability [30,34].

$${\overline{V}}_{sf}={\overline{V}}_{br}+{\overline{V}}_{is}+{\overline{V}}_{fs}$$

(5)

where ${\overline{V}}_{sf}$ is the measured surface velocity, ${\overline{V}}_{br}$ is the velocity caused by block rotation, ${\overline{V}}_{is}$ is the velocity caused by the internal strain of the block, and ${\overline{V}}_{fs}$ is the velocity caused by fault-locked negative dislocations. The fault locking coefficient value is represented by Phi [30,34].

$$\mathrm{Phi}(\Sigma )={\Sigma }^{-1}{\displaystyle {\int }_{\Sigma }\left[\frac{1-V_C\left(s\right)}{V\left(s\right)}\right]}$$

(6)

where $V$ is the long-term fault slip rate and $V_C$ is the short-term slip rate; $\Sigma$ is the defined grid area on the fault, and, using $\Sigma$ to be larger than the characteristic wavelength of the $V_C$ variation, we obtain a continuous approximation of the distribution. When Phi = 0, it indicates that the fault is in a complete creep state and there is no locking. When Phi = 1, it indicates that the fault is completely locked. Generally, the range of values 0–1 is used on the fault to represent the locking state of the fault. When Phi is between 0 and 1, it indicates that the fault is not completely locked and there is a certain creep.

4. Experimental Results

4.1. Strain Field near the Yishu Fault Zone

Considering the impact of the 2011 Tohoku-Oki earthquake, the strain field and the maximum shear strain field in the study area were obtained based on the GPS horizontal velocity field from 1999 to 2009 and from April 2011 to 2019, as shown in Figure 6 and Figure 7. The regional strain of the Yishu fault zone is relatively weak, the overall upper north section is compressive, the southern section is tensile, the differential movement of the crust is weak, and the magnitude of the strain rate is small. The northeastward pushing of the western Indian Ocean Plate and the westward pushing of the eastern North American Plate and the Pacific Plate control the distribution characteristics of the national strain field [16]. These cause the strain rate field in the Chinese mainland to show an obvious feature of strength in the west and weakness in the east. Comparing Figure 6a with Figure 7a, the northern segment of the Yishu fault zone is evidently still in a compressive state, while the southern segment is in an extensional state, but it is slightly smaller than it was before the 2011 Tohoku-Oki earthquake.

In rock experiments, the differential stress is expressed by the difference between the maximum principal stress and the minimum principal stress. Correspondingly, when the vertical crustal deformation is not considered, the plane maximum shear strain can be used to approximately reflect the regional differential stress state. According to the comparison between Figure 6b and Figure 7b, the maximum shear strain in the Yishu fault zone did not significantly change before and after the 2011 Tohoku-Oki earthquake but decreased on both sides of the fault zone.

Considering the GPS observation accuracy, the continuous GPS observation sequences 10 days before and 10 days after the 2011 Tohoku-Oki earthquake were selected; the coseismic displacement was estimated by linear fitting the time series before and after the earthquake and the coseismic strain field and maximum shear strain field of the earthquake are obtained, as shown in Figure 8. The coseismic strain field (Figure 8a) shows that the eastward tension caused by the 2011 Tohoku-Oki earthquake causes the entire study area to be in a tensile strain state. The maximum shear strain field (Figure 8b) shows that the coseismic deformation field of the 2011 Tohoku-Oki earthquake produced obvious shear strain in the Ludong uplift (II1) area and Luxi fault block (I2, Luxi uplift), a certain shear strain in the southern section of Yishu fault zone, and gentle shear strain in the northern section.

4.2. Three-Dimensional Seismic b Value

In this paper, the maximum likelihood method was used for scanning the three-dimensional b value along the Yishu fault zone to analyze the current stress level of the fault zone. Since the maximum likelihood method has high requirements for the earthquake catalogue’s integrity and there is a lack of small earthquake data, the b value will be low; hence, the Mc is usually used to evaluate the seismic measurement capacity of the station [43]. As shown in Figure 9, the magnitude of completeness, Mc = 2.0, can be obtained. Therefore, it is more reliable to select the seismic data with M_L > 2.0 to calculate the b value in this paper.

The study area is divided into a grid with a spacing of 0.1° × 0.1°, taking the grid node as the center, the earthquakes larger than Mc in the circular area with a radius of 20 km are selected, and calculate the b value of each grid point by the least square method. The minimum number of earthquakes is set to be no less than 15. Since there are fewer earthquakes in some areas, the radius is then increased to a maximum of no more than 40 km, and the b value is null when the number of earthquakes is still less than 15. When calculating the b value of depth, the maximum radius of grid nodes is 5 km, and calculate the distribution of b values at different depths.

Using the catalogue data of M_L > 2.0 earthquakes from 1970 to 2019 derived from the Shandong Earthquake Agency, we calculated the b value of the Yishu fault zone and obtained the b value at depths of 0 km (Figure 10b) and 20 km (Figure 10c). The b value of the cross section of the fault zone is calculated, as shown in Figure 10. It can be seen from Figure 10 that there is an area with a low b value in the northern segment of the Yishu fault zone, at about 0.6–0.8, reflecting that the stress level of this segment is relatively high today, that this segment is the unruptured segment of the 1668 Tancheng Ms 8.5 earthquake, and that similar seismic gap characteristics are observable. Some studies or articles [35,46] speculate that the region is currently locked, as it has accumulated more strain energy, so its seismic risk is worthy of attention.

4.3. Locking Characteristics of Deep Fault

The occurrence of major earthquakes is closely related to seismogenic faults’ locking degrees. Based on the GPS velocity field results, the distribution of locking depths or locking degrees on the fault planes can be obtained using inversion or other means.

Considering that the Anqiu–Juxian fault is the most active in the Yishu fault zone, the setting of the fault model mainly refers to the section parameters of this fault. Wang et al. [47] completed the zonal mapping of the 1:50,000 active faults of the Anqiu–Juxian fault and determined the geometric structure, spatial distribution characteristics, and active nature of the fault. The overall strike of the Anqiu–Juxian fault is NNE 10°–20°, the inclination is NW, and the inclination angle is 70°–80°. Many studies or articles have used geophysical methods such as magnetotelluric sounding and artificial seismic sounding to detect that the crustal thickness of the Yishu fault zone is about 31–36 km [48,49]; the three-dimensional b value also indicates that there are low-value areas within 40 km of the deep fault depth. Therefore, we established the fracture zone model based on the above research results, as shown in Figure 11. The Luxi fault block is set as the hanging wall, the Ludong block is the footwall, the dip angle is set to 70°, and a total of nine nodes are arranged along the fault strike, which is distributed between the sections of the Anqiu–Juxian fault. The model depth is set to 40 km and a total of nine isobaths are set at 0.1 km, 5 km, 10 km, 15 km, 20 km, 25 km, 30 km, 35 km, and 40 km, respectively, along with the fault inclination.

4.3.1. Locking Degree of Deep Fault

According to the above fault model, the spatial variation distribution of the locking degree of the Yishu fault zone before and after the 2011 Tohoku-Oki earthquake was obtained. Figure 12 demonstrates that, before the 2011 Tohoku-Oki earthquake, the north of Juxian in the Yishu fault zone’s locking was high degree, deep, and had a maximum locking depth of about 26 km. Additionally, Figure 12 indicates that there was a locking area in the south of Juxian, but the locking depth was shallow, about 6 km, and the deep area was in creep state. The results in Figure 13 show that the locking area changed after the 2011 Tohoku-Oki earthquake. The northern section of the Yishu fault zone still has a high locking degree and a deep locking depth, with a maximum locking depth of about 26 km. The south section’s conditions may be due to the tensile effect of the 2011 Tohoku-Oki earthquake on the area (Figure 8) or because the accumulated strain energy is released frequently by small earthquakes that alleviate the locking degree in the area.

4.3.2. Fault Slip Rate Deficit Distribution

The relative motion between the faults is determined by the Euler poles of the blocks on both sides of the fault and the fault sliding loss rate is the product of the locking degree and the relative motion on the fault between the two blocks [29,30,31,34]. The sliding loss caused by fault locking accumulates as strain energy at and near the fault plane [31]. Figure 14 shows the slip rate deficit distribution in the Yishu fault zone from 1999 to 2009. The north of Juxian has a dextral compression slip rate deficit from the surface to the depth of 26 km, which is about 0.4~0.8 mm/a, and 26–40 km is basically a creep state without the slip rate deficit. The locking depth of the southern section of the fault zone is small, the deficit of sliding rate is large, about 1.1 mm/a, and the fault depth is 5–40 km, which is basically a creep state. The results in Figure 15 show that the locking range of the Yishu fault zone decreased after the 2011 Tohoku-Oki earthquake and the south section basically entered a creep state. The sliding rate deficit is mainly concentrated in the north section of the fault and the rate deficit reduced to about 0.4–0.6 mm/a.

4.3.3. Uncertainty Analysis of Inversion Results

By comparing the residuals of the model fitting (comparing the total GPS rate values at each point obtained from the model inversion with the rate values obtained from the direct fitting of the time series), the quality of the fitting of the inversion results can be checked to some extent [50]. Figure 16 compares the residual fitting velocity of the model. The residuals before and after the 2011 Tohoku-Oki earthquake are small, both less than 0.5 mm/year, and the direction of the residuals is random, indicating that the inversion results are good.

Since the model assumes that the internal deformation of the block is uniform, the inhomogeneity of the spatial distribution of deformation, crustal medium, wave velocity structure, and so on are not considered, which is a source of uncertainty in the inversion results [2]. The distribution and number of near-field GPS observation stations of faults have a certain influence on the inversion results [50]. Whether the block is rigid or not has a larger influence on the inversion results. Different reference frames have relatively little influence on the inversion results and different stable blocks as reference frames have almost no influence on the inversion results [26]. In conclusion, we have obtained good results for the inversion of the locking degree in the Yishu Fault Zone, but this is still affected by uncertainties.

5. Discussion

The 2011 Tohoku-Oki earthquake caused significant coseismic and post-earthquake effects on eastern mainland China [21,51], which influenced the crustal deformation and seismic risk of the Yishu fault zone [5,52]. The results for the fault locking degrees obtained from two phases of GPS horizontal velocity field inversion show that the Anqiu–Juxian section of the Yishu fault zone has a high locking degree and deep locking depth, which is due to the compression sliding deficit. After being affected by the 2011 Tohoku-Oki earthquake, the locking state of the southern section of the Yishu fault zone has eased, the compression activity has weakened, and the sliding rate deficit has decreased. However, the coseismic compression of the northern section caused by the 2011 Tohoku-Oki earthquake is conducive to its locking, so the northern section of the Yishu Fault Zone is still in a strong locking state. Due to the complexity of the crustal structure, the block negative dislocation model cannot fully simulate the crustal deformation in this area. At the same time, the number and distribution of GPS observation stations near the fault will also have a certain impact on the results. Therefore, there is some uncertainty in the inversion of the fault locking degree. Compared with the results of Li et al. (2016) [26] and Tao et al. (2022) [25], the main difference is observable in southern Tancheng. The former uses GPS data from 2009 to 2014, without considering the impact of the 2011 Tohoku-Oki earthquake on the Yishu fault zone. The difference from the latter is small; we believe that this is due to the near-field GPS data integration we use and that this is caused by the integration of near-field data. The results of each study are different from the fracture zone segmentation nodes used in this paper, so there will be some differences in the results.

The 2011 Tohoku-Oki earthquake caused by the subduction of the Pacific Plate has a direct impact on the dynamic environment of the region [53,54]. The state of the horizontal strain field after the 2011 Tohoku-Oki earthquake has weakened. Combined with the seismic strain field (Figure 8), the eastward tension generated by the 2011 Tohoku-Oki earthquake causes the entire study area to be in a tensile strain state. Since the Yishu fault zone is characterized by strike-slip movement, the 2011 Tohoku-Oki earthquake has a strain energy release and delayed seismic latent effect on it. However, due to the complex structural characteristics in the study area, especially the structural differences between the neotectonic units [24], the drag from below the crust may produce uneven tension on the upper crust and compressive strain in local areas. Such drag and strain have different coseismic effects on the south and north segments of the fault zone, including tensile effects on the south segment and a compressive effect on the north segment. The tensioning effect on the southern section is more significant, given the activity magnitude of the southern section is larger than for the northern section [16]. The Coulomb stress changes induced by the 2011 Tohoku-Oki earthquake on the northern segment of the Yishu fault zone are positive with a value of 0.23 KPa while the changes are smaller on the southern segment with a value of 0.08 KPa. The 2011 Tohoku-Oki earthquake helped to accumulate stress on the northern segment of the Yishu fault zone [55].

According to the earthquake distribution statistics in the study area, 285 earthquakes with M_L > 2.0 occurred in the southern section of the Yishu fault zone and 75 earthquakes occurred in the northern section of the Yishu fault zone from 1970 to 2019, accounting for only one-quarter of the southern section of the Yishu fault zone. The small earthquake activity in the northern section presents an abnormally sparse state; a seismic gap [56] formed in the northern segment of the fault zone that easily accumulates stress. Additionally, there is a low b value area in the north section, indicating that the stress level is relatively high. To study the current seismicity of the Yishu fault zone, the earthquakes from 2011 to 2019 were selected from the earthquake catalogue and the seismic distribution profile was drawn (Figure 17). Small earthquakes occurred within the depth of 30 km. At present, there are still fewer small earthquakes in the north section of the Yishu fault zone and the strain energy continues to accumulate, which is in good agreement with the fault locking range. The accumulated strain energy in the south section of the fault zone can be released in time through medium and small earthquakes, which is conducive to delaying the risk of strong earthquakes in the surrounding areas.

The northern and southern sections of the Yishu fault zone have different seismic risks and the seismic risk of the northern section is still relatively high. An earthquake of Ms 7.0 occurred in Anqiu in 70 BC, but no ruptured segment corresponding to the earthquake has been found [35]. In 1668, an earthquake of Ms 8.5 occurred in Tancheng in the southern segment and the northern segment was the unruptured segment of the earthquake. Several studies have obtained the segmental characteristics of the upper- and middle-crustal mediums in the southcentral section of the Tanlu fault zone using the double-difference seismic tomography method and found that the velocity and Poisson’s ratio of the crustal medium in the section north of Tancheng in the Yishu fault zone show relatively high values [57,58,59]. According to the recurrence period of 3500a [60], the last occurrence time accounted for 60% [6], meaning the earthquake risk is relatively high.

6. Conclusions

By using the GPS-derived horizontal velocity field and historical earthquake distribution in the Shandong Province in the period from 1999 to 2009 and April 2011 to 2019, the crustal strain field was calculated and the deformation difference characteristics in the Yishu fault zone were analyzed. The 3D b values were also calculated using the historical seismic distribution to present a preliminary determination of the fault locking depth. Finally, based on the block negative dislocation model, the locking degree and sliding rate deficit of the Yishu fault zone before and after the 2011 Tohoku-Oki earthquake were inverted. The results show the following.

Before the 2011 Tohoku-Oki earthquake, there was a high locking degree area in the south section of the Yishu fault zone, with a shallow depth of about 6 km, while the locking depth in the north section of the Yishu fault zone was about 26 km. The 2011 Tohoku-Oki earthquake alleviated the westward subduction and compression of the Pacific Plate. The eastward tension caused the entire study area to be a tensile strain state. Combined with the negative dislocation inversion results, the southern section’s locking in the Yishu fault zone changed to a creep state after the 2011 Tohoku-Oki earthquake and the locking range was relatively reduced. However, the locking degree in the northern section of the Yishu fault zone is still high and deep. Moreover, the b value in the north section of the Yishu fault zone is low and the small earthquake activity is sparse. This is the unbroken section of the Tancheng Ms 8.5 earthquake from 1668, which easily accumulates stress, so its seismic risk is worthy of attention.