1. Introduction
The earthquake process involves two fundamental interrelated links: the tectonic background and the seismogenic environment. The tectonic background refers to the large-scale dynamic energy required for earthquake occurrence, while the seismogenic environment pertains to local conditions under which strong earthquakes occur. It depends on the physical properties of the medium, tectonic activity, and stress state of the location where the earthquake occurs [
1,
2].
Earthquakes are the result of sudden instability and rupture caused by the continuous accumulation of strain in discontinuous deformation areas, ultimately reaching the limit state under regional tectonic stress provided by the tectonic background [
3]. Non-continuous structural areas are often where strain is most easily accumulated and structural deformation is strongest, making them favorable locations for strong earthquake development.
Experiments in Structural Physics [
4,
5,
6,
7,
8] have indicated that main-aftershock type earthquakes predominantly occur in homogeneous medium environments. In contrast, fore-main-aftershock type earthquakes and swarm type earthquakes tend to occur in complex tectonic environments. Analysis of the modern tectonic stress field and intense seismic activity suggests a significant correlation between stress distribution and the occurrence as well as recurrence of earthquakes.
On the one hand, regions experiencing strong and complex tectonic stress, as well as changes in the direction and type of stress, are more susceptible to powerful earthquakes. It is common for large earthquakes to occur in areas where there is a relatively high accumulation of stress within active fault zones or in sections where fault zones are relatively locked; On the contrary, the local stress variation area in a uniform stress field background is an area where strong seismic activity is relatively concentrated. Under specific conditions, even a small stress variation of 0.1 bar magnitude can significantly impact seismic activity. Research conducted by Xu et al. [
9] has indicated that faults capable of generating high magnitude earthquakes often exhibit low b-values and high stress anomaly segments. Additionally, their pre-earthquake locking characteristics are essential prerequisites for stress or strain accumulation and the occurrence of high magnitude earthquakes.\
The type of earthquake sequence is also influenced by the overall level of stress. Isolation-type earthquakes typically occur under conditions of high prestress and/or low rupture strength, while front-main-residual type earthquake sequences tend to occur under conditions of medium prestress and/or medium rupture strength. Additionally, swarm-type earthquake sequences are associated with low prestress and/or high rupture strength conditions [
10].
When utilizing seismological methods to assess the risk of significant earthquakes within a research area, the M6.0 earthquake in Parkfield in 2004 serves as a typical illustration. Allmann and Shearer [
11] emphasized that enhanced stress is often observed in fault areas prior to a strong earthquake, and there is a substantial decrease in regional stress drop following the event. Hardebeck and Aron [
12] proposed that regions with higher strength or subjected to greater external shear stress are more likely to exhibit higher source stress drop, and areas with concentrated distribution of high stress drop may serve as potential nucleation sites for moderate to large magnitude earthquakes.
In addition, stress intensity provides crucial information regarding the potential energy release of earthquakes, while stress characteristics offer insights into the possible types of earthquakes. Tensile stress indicates regions under tension and suggests a potential occurrence of earthquakes on normal faults; compressive stress points to areas under compression, indicating a likelihood of earthquakes on reverse faults; neutral stress implies a strike-slip earthquake. Therefore, conducting quantitative research on the state of stress and its variations in the deep seismogenic layer is an essential method for investigating the issue of predicting strong earthquakes.
Due to challenges such as the difficulty in accessing the Earth’s interior and the infrequency of large earthquakes, direct measurement of stress and intensity in the deep crust remains elusive for humans. Numerous studies have indicated that earthquake source parameters and medium properties contain valuable information about changes in stress fields and medium properties at the focal depth. Monitoring the spatio-temporal evolution of these parameters can provide insights into changes in stress fields or medium properties within the seismogenic zone, offering an important means to overcome the Earth’s inaccessibility.
Scientists use various physical parameters to describe an earthquake, and these parameters that depict the mechanical characteristics of the source are known as the source mechanical parameters, abbreviated as the source parameters. Traditional “earthquake statistics” typically only focus on the “time, space, and intensity” sequence of earthquakes. In recent years, modern seismic parameters such as seismic moment, focal mechanism solution, source stress drop, corner frequency, radiated seismic energy, rupture radius, and apparent stress have been increasingly utilized to characterize source characteristics.
A plethora of earthquake examples indicate that the physical properties of large earthquakes differ from those of small and moderate earthquakes in actual earthquake processes. The source characteristics of the former largely reflect the seismic tectonic background, stress mode of the source, and result in a larger rupture area, while small and moderate earthquakes more so reflect non-uniform changes in stress state within a smaller area. The study of source parameters of small and moderate earthquakes not only serves as the basis for exploring the source process of large earthquakes but also provides new insights for studying regional stress states and evaluating potential earthquake magnitudes.
The Sichuan region (
Figure 1) is situated on the southeastern edge of the Qinghai-Tibet Plateau and is known for its strong eastward extrusion and structural deformation. The main fault zones in the area include the Xianshuihe Fault [
13], Anninghe Zemuhe Fault, and Longmenshan Fault. Over an extended period of geological evolution, this research region has undergone complex structural deformation, leading to a diverse seismic activity behavior within a dynamic environment.
The gray circle represents the background seismic event, while the orange circle signifies the seismic event that is involved in the calculation of source parameters. Additionally, the blue box indicates the six main tectonic areas in Sichuan.
Sichuan is an important area for strong earthquake monitoring in China, with at least 15 earthquakes of magnitude ≥ 7 occurring in just over 200 years. There are significant differences in the seismic activity characteristics of the regional main and secondary faults. Strong earthquakes of magnitude ≥7 mostly occur on the Xianshuihe fault. No earthquakes of magnitude ≥ 7 have occurred on the Anninghe fault since 1536, the Zemuhe fault since 1850, the Jinshajiang fault since 1870, or the Litang fault since 1948. Therefore, understanding the changes in stress state among different faults within this research area has become a focus of attention.
To understand the current stress distribution characteristics of the primary active faults in the region and identify sections where relatively high stress accumulation is occurring, this paper estimates the source parameters of small and medium-sized earthquakes (ML 1.5-5.2) in the main fault zones and adjacent areas in Sichuan. A total of 4,310 measurements of earthquake stress drops during the 5-year period from 2019 through 2023 are analyzed to draw a stress distribution image along the fault. The study discusses the stress distribution characteristics on major faults, variations of seismic stress drop with location, and correlations between stress-strain loading and regional deformation dynamic processes based on geometric structure, activity habits, and temporal spatial distribution of modern seismic activity in different sections of the region. This earthquake parameters training catalog provides an opportunity to understand how coseismic stresses change and how other geophysical factors relate to the distribution of stress drop as well as its evolution in space and time.
2. Main Fault Zones and Their Activity
2.1. Longmenshan Fault Zone (LMS)
The Longmenshan fault zone is located on the eastern edge of the Qinghai Tibet Plateau, at the junction of the Bayankala block and the Yangtze block. The Longmenshan fault zone has four main faults developing from northwest to southeast: the Maoxian Wenchuan Fault (Houshan Fault), the Beichuan Yingxiu Fault (Central Fault), the Jiangyou Guanxian Fault (Qianshan Fault), and the Guangyuan Dayi Fault (Hidden Fault in front of the Mountain). The dextral strike slip rate (<1mm/a) and vertical slip rate (<1mm/a) of the Longmenshan fault zone are both very small [
14,
15], and multiple periods of sliding have occurred. The secondary fault exhibits long-term creep deformation characteristics [
16,
17].
The 2008 Wenchuan 8.0 earthquake occurred on the Longmenshan Fault zone, causing both the Beichuan Yingxiu Fault (Central Fault) and the Jiangyou Guanxian Fault (Qianshan Fault) to rupture simultaneously. The surface rupture zone of the central fault is about 240km long, mainly characterized by reverse fault displacement, and also has a right lateral strike slip component. The surface rupture of the Qianshan Fault is about 72km long, which is a typical reverse fault displacement property. The 2013 Lushan 7.0 earthquake occurred in the southern section of the Longmenshan Fault zone, which was a blind reverse fault type earthquake. No structurally significant fractures were found on the surface.
2.2. Xianshuihe Fault (XSH)
The Xianshuihe fault of western Sichuan Province, China, is one of the world’s most active faults, can be divided into two segments of different structural styles, jointing at the pull-apart area of Huiyuan Monastery. The northwestern segment has a relatively simple geometric structure. While the southeastern segment exhibits a complex structure composed of several branches. In the southern part of Huiyuansi, the fault is divided into three secondary parts as Yalahe fault, Selaha fault, and Zheduotang fault. To the south of Kangding, it is manifested as a main fault with only local branching phenomenon, known as the Moxi fault.
The Xianshuihe fault is a highly active strike-slip fault system. Since earthquake records began in 1700, the Xianshuihe fault has experienced eight M>7.0 earthquakes, accounting for about half of the total earthquakes of the same magnitude in the entire western Sichuan region. The surface rupture zone of the earthquake almost covers various sections of the entire fault.
2.3. Jinshajinag Fault (JSJ)
The Jinshajiang fault is composed of multiple SN direction arc-shaped secondary reverse faults and the NNE trending Batang fault. There is almost no seismic activity on the arc-shaped secondary fault. Moderate historical earthquakes have occurred on the west segment of the Batang Fault, such as the earthquakes of 1989 M6.7, 2006 M 5.0, M 5.4 and M 5.6 in Balongda. From the perspective of active structure, the arc-shaped secondary reverse fault is a complex fracture zone composed of numerous small faults and fault combinations, which is not easy to concentrate stress. Seen from Google earth images, the Batang fault has a clear geomorphic expression, however, geometry and late Quaternary slip-rate are still unknown.
2.4. Muli-Yanyuan Fault (MLI)
The active fault system of this unit is mainly composed of the NE oriented Lijiang Xiaojinhe fault zone and secondary faults parallel to it, in addition to the Muli Arc Fault, Zhongdian-Daju Fault, and Ninglang Fault. These main and secondary active faults intersect and intersect locally, resulting in frequent seismic activity in this unit both historically and today. Among them, the Lijiang-Xiaojinhe Fault cuts through the Research diamond block and divides it into two parts: the northwest Sichuan secondary block and the central Yunnan secondary block. The Ninglang-Yanyuan and Muli areas are located at the junction of the south and north secondary blocks.
2.5. Anninghe-Zemuhe Fault Zone (ANH)
The Anninghe Fault zone is located on the axis of the Kangdian earth axis, starting from Shimian in the north and extending through Xichang to the Huili area. It generally runs in an NS direction and is mainly characterized by sinistral strike slip movement. In history, this area may have occurred 1470 AD earthquake.The Mianning-Xichang area in the southern section of the Anninghe fault was the main rupture part of the M 7½ in 1536.But since the M 63/4 earthquake in south of Mianning in 1952, there have been no larger earthquakes on the Anninghe Fault. A modern seismic gap gradually formed with the Liziping-Xichang section as the core, with the background of the first kind seismic gap.
The northern end of the Zemuhe fault is connected to the Anninghe fault, and the southern end is connected to the Xiaojiang fault. It extends from Xichang through Puge and Ningnan to Qiaojia, with an overall trend of 330°. There have been M 7 earthquakes in 814 AD and M 7½ earthquakes in 1850. The most recent moderate earthquake was the Xichang M5.1 earthquake on October 31, 2018. The Zemuhe fault is mainly characterized by sinistral strike slip movement, with a sinistral strike slip rate of about 6.4 ± 0.6 mm/a in the Holocene [
13], accompanied by a normal fault dip slip component between Xichang and Puge [
18]. In the southwest of Qiaojia, the southernmost fault of the Zemuhe fault zone deviates towards the south southwest direction.
2.6. Daliangshan Fault (DLS)
The Daliangshan fault is left-lateral strike-slip fault approximately 250 km long. The Daliangshan fault has a complex fault geometry characterized, and mainly composed of four secondary faults, including the Yuexi Fault, Puxiong Fault, Butuo Fault, and Jiaotong River Fault. The historic earthquake record is no M≥6.0 strong earthquakes on the Daliangshan fault. But seismic and geological studies have confirmed that the fault has experienced prehistoric strong earthquakes and has the structural conditions for the breeding and occurrence of strong earthquakes [
19,
20,
21]
.
3. Database
The estimation of source parameters is of great significance to reveal whether the rupture mechanism of large and small earthquakes has the same physical process, and to apply source parameters to the study of earthquake prediction and to understand the physical properties of earthquakes. The effective stress, stress drop, and source size can be estimated by comparing the measured seismic spectrum with the theoretical spectrum [
22]. Static stress drop is the simplest method to measure the overall reduction in shear stress caused by sliding of fracture zones [
23]. It is the difference between the average shear stress on the fault zone before and after the earthquake, and represents the stress released on the fault plane during the earthquake. Assuming that the static initial shear stress on the fault plane before the earthquake is
and the final shear stress on the fault plane after the earthquake is
, the static stress is reduced by
Since the stress drop of a real earthquake varies throughout the fault zone, the overall static stress drop is the sliding weighted average of the spatially variable stress drop [
23].
The corresponding dynamic stress drop is more complex because the space-time history of stress drop can be quite variable. Any individual part of the fault plane may have a variable stress drop during sliding. Due to the impossibility of reliably inverting seismic waves to determine the complete spatiotemporal process of dynamic stress drop, the simplest viewpoint is that the dynamic stress drop is constant on the spatiotemporal window of fault sliding.
When the earthquake rupture begins to expand, the stress at this point gradually increases to the horizontal stress that the rock can withstand, the rupture occurs at this point. For the region without rupture, is the shear fracture strength of the material or rock. To have broken down, for the two discs of the fault and squeezed together by static friction stress, is the maximum static friction stress. When sliding occurs, the stress decreases from to the dynamic friction stress , and the dynamic friction stress remains unchanged during sliding. As the rupture process on the whole fault surface stops, the stress transitions from the dynamic friction stress to the final stress .
The shear rupture strength, or the difference between the maximum static friction stress
and the dynamic friction stress
, is called the effective stress
In the Brune [
22] disk model, assuming that shear failure occurs simultaneously and
, the effective stress
is the dynamic stress drop
Seismologists generally use simple constant stress drop model to estimate the seismic stress drop. In the method of estimating stress drop using the scaling relation [
24,
25], regardless of the details of fault geometry and slip distribution, assuming that the earthquake rupture process is a linear elastic process in semi-infinite space. The basic formula for stress drop is as follows
where
is the average displacement that occurs on a fault of length
L at the time of the earthquake,
is the elastic shear modulus. Since seismic moment (
M0) for most large earthquakes can be reliably determined from seismic waves, rewrite the above equation as:
where
is the fault shape parameter,
,
refers to the length of the fault, and
refers to the width of the fault. Then
or
is the fault area.From formula (7) and (8), we need three quantities to calculate stress drop: a measurement of the seismic moment (), some estimate of the fault area (A), and then some appropriate choice for the characteristic fault dimension ().
In practice, it is very difficult to determine the characteristics of seismic source rupture. It is common to assume a theoretical rupture model to calculate the stress drop, then different geometric coefficients
and fault feature length
are taken according to the calculation model [
25]. For large earthquakes, the rupture scale in the direction of the fault can be tens to hundreds of kilometers, the depth direction is limited by the focal depth, and generally adopt
×
rectangular model, taking
, then the stress drop
is expressed as
For the infinite dip-slip fault model,
is the Lame coefficient.
For small magnitude earthquakes, Brune’s [
22] disk rupture model is often used, which assumes that earthquake rupture occurs on a circular fault plane with uniform stress drop and constant rupture velocity. Usually c=7π/16, take the disc radius
, stress drop is expressed as
For the acquisition of the rupture radius
, the source rupture process can be retrieved from the far-field seismic records in seismology, by the frequency domain of corner frequency
indirect access to the source physical dimension information [
26,
27], expressed as
is the shear velocity near the source.
Then formula (11) is rewritten as
is a constant, depending on the type of model used to correlate the relationship between the corner frequency
and the focal rupture radius
. In Brune [
22] model,
; In the Madariaga [
28] model,
[
29,
30]; In Sato and Hirasawa [
31],
depends on the source rupture velocity [
32].
The obtained by equation (13) is proportional to the cube of , so the stress drop is very sensitive to the error of . Even if the fault model is close to the actual fault, the small observation error of will reduce the reliability of , which is also the limitation of the traditional seismological method to give the seismic stress value.
6. Conclusion
The spectral analysis of body waves from 100 Broadband Seismograph (BBS) stations within the Sichuan Seismic Network has been conducted to investigate the scaling relation and self-similarity of small to moderate size earthquakes in Sichuan. These scale relations encapsulate the unique characteristics of the study area and lay a foundation for future predictions of local seismic calibration coefficients in Sichuan. The primary objective behind establishing these scaling relationships is essentially to provide a benchmark against which data can be juxtaposed, thereby serving as a valuable reference point for analysis.
The presence of stress drop scaling and coherent regional variations in source spectral parameters holds profound implications for earthquake physics and seismic hazard assessment. High frequency peak ground motions are, to some extent, contingent upon stress drop, thereby prompting the development of non-ergodic, region-specific ground motion prediction equations to accommodate systematic fluctuations in source parameters. Departures from self-similarity may carry significant ramifications for extrapolating observations of minor earthquakes to constrain the hazards posed by larger ones.
The use of spatial and temporal variation in stress drops as a proxy for the seismic response of fault systems provides an optimal data setting to explore the relationship between fault mechanics, geological setting, and stress drop variation. The spatio-temporal distribution of stress drop values within a complex seismic sequence could potentially provide valuable support for a more comprehensive comprehension of the earthquake rupture process and the development of seismic sequences. Furthermore, it has the potential to identify specific regions where stress loading is concentrated, thus carrying significant implications for short and intermediate-term estimations of seismic hazard.