Introduction

Western Shandong is located in the western part of Shandong Province, with its eastern and western boundaries respectively formed by the Yishu fault zone and the Liaokao fault zone1 (Fig. 1). Both of these fault zones are active deep large faults2, and historically, they have experienced destructive earthquakes, such as the MS8½ Tancheng earthquake in 1668, the MS7.0 Anqiu earthquake in 70BC, and the MS7.0 Heze earthquake in 19373,4. The seismic activity in Western Shandong is characterized by low frequency and high intensity5. In the event of a strong destructive earthquake, it would have a severe social impact and economic loss in the surrounding areas.

Earth’s gravity field observation is one of the key techniques for medium- and long-term earthquake forecasting, as its spatiotemporal dynamic changes are closely linked to the processes of strong earthquake preparation, occurrence, and post-seismic adjustment6,7,8,9,10. In the process of utilizing gravity changes for earthquake prediction, one of the primary prerequisites is to ensure that the observed gravity field variations are entirely the direct result of tectonic activities. However, in practical earthquake forecasting efforts, the gravity effects caused by non-tectonic factors such as land subsidence and groundwater level changes are often not adequately separated11. This may lead researchers to misinterpret these non-tectonic gravity anomalies as precursors to earthquakes12. Therefore, identifying and effectively eliminating these non-tectonic gravity effects is a crucial first step for accurately interpreting tectonic activities and enhancing the scientific reliability of earthquake prediction.

The northwestern Shandong Plain is located in the northwestern part of Shandong region. From 2017 to 2021, no earthquakes with MS≥5 occurred in this area. Based on this, this paper concludes that there was no abnormal tectonic activity in this region during this period. However, the gravity field in this area showed significant changes during this time.Since the 1980s, affected by large-scale groundwater extraction by human activities, large-area groundwater funnels and land subsidence have emerged in the northwestern Shandong Plain[13]. To deeply explore the non-tectonic gravity effects caused by these phenomena, this study integrated the observational data from dozens of Global Navigation Satellite System (GNSS) continuous observation stations in this area, thus accurately obtaining the detailed characteristics of the vertical deformation field of the Earth’s surface. Meanwhile, the research team also extensively collected the groundwater data of this area, aiming to quantitatively separate the non-tectonic gravity effects.

Previously, we conducted relevant research on the non-tectonic gravity effects along the Yishu Fault Zone12. Compared with this previous study, the area covered by this current research is more extensive, and the data used is also more comprehensive and richer. Moreover, through the method of constructing cross-sections, we carried out a comparative analysis of three different types of stratigraphic structures, namely the Quaternary strata, low-permeability bedrock, and karst areas. More importantly, this paper provides operational correction workflows for eliminating non-tectonic gravity effects in shallow groundwater depression zones, deep groundwater depression zones, and bedrock areas respectively. The main value of this work lies in the methodological aspect, that is, it can reliably detect tectonic signals when they appear. Through this series of operations, the residual gravity change information can be more accurately extracted, which can then be used to study tectonic activities and explore potential earthquake precursor information.

Data and methods

Mobile gravity data acquisition and processing methods

Mobile gravity data acquisition

In 2017, the Shandong Earthquake Agency completed the expansion project of the mobile gravity observation network, achieving full coverage of the gravity observation network in the western Shandong region (Fig. 1). From October 2017 to October 2021, we conducted 9 periods of mobile gravity observations using the CG-5 gravimeters, with 2 periods per year. Table 1 lists the observation situation of each period, with the average precision of the measurement points ranging from 8.5 to 16.0µGal, and the average precision of the 9 periods is 11.9µGal. The research shows that the absolute value of the non-linear term (including non-linear drift and the slight gravitational changes caused by material migration) in the multi-day continuous observation results of the CG-5 relative gravimeter is less than 15 µGal14. This result fully demonstrates that the overall accuracy of the above-mentioned nine periods of mobile gravity measurements is relatively high.

Table 1 Mobile gravity measurement in study area.
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Mobile gravity data processing methods

In terms of data processing, these observation data have been corrected for zero-drift, solid tides, instrument height, scale factor, and atmospheric pressure. Subsequently, using the absolute gravity points in Tai’an, Rizhao, Yantai, Rongcheng, Zibo, and Jiaxiang as the starting reference points, the classical adjustment method in the LGADJ software was used for processing and calculation to obtain the absolute gravity values of each measurement point. In addition, for a few measurement points with larger errors, gross error elimination and weighting reduction were implemented to improve the reliability of the data. Finally, we subtract the absolute gravity value in October 2017 from the calculated absolute gravity value in October 2021 to obtain the net change in gravity between 2017 and 2021. In the intermediate measurement data, we observed certain seasonal fluctuations. However, the amplitude of these fluctuations is basically within twice the measurement precision, so they will not have a substantial impact on the analysis and conclusions based on the net change.

Fig. 1
figure 1

Distribution of mobile gravity and GNSS measurement points. The graph was drawn using Generic Mapping Tools (GMT) software (https://www.generic-mapping-tools.org, Version 6.5.0).

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GNSS data acquisition and processing methods

GNSS data acquisition

The vertical time-varying data in the study area from 2010 to 2020 are derived from 85 continuous GNSS benchmark observation stations set up in the western Shandong and adjacent areas (Fig. 1).

In this study, the vertical movement rate of GNSS from 2010 to 2020 was relatively stable, so we extrapolated it for about one year to 2021. To evaluate the error caused by the extrapolation, we first established a trend model using the data from 2010 to 2019 and extrapolated it to 2020. By comparing the extrapolated values with the actual observed values, we obtained the approximate range of the extrapolation error. After evaluation, the error caused by the one - year extrapolation in the vertical direction was basically less than 15 mm, and this error would not have a substantial impact on the main conclusions of the study.

It should be noted that we failed to obtain Interferometric Synthetic Aperture Radar (InSAR) data in this study. We suggest that in subsequent work, InSAR data and GNSS data should be jointly analyzed. The high spatial resolution of InSAR data can provide more detailed surface deformation information, make up for the lack of spatial resolution of GNSS data, and help us understand the crustal deformation characteristics of the study area more comprehensively, thus improving the accuracy and reliability of the research results.

GNSS data processing methods

To improve the precision of the solutions, we corrected the data using tropospheric interference delay models and ocean tide correction models. Subsequently, using the GAMIT/GLBOK software under the ITRF2008 framework, we obtained daily solution time series data with millimeter-level accuracy. The preprocessing steps for the benchmark station time series data include: (1) normalizing the data with January 1, 2010, as the reference; (2) removing data with value jumps exceeding three times the median error to reduce the impact of gross errors on the results; (3) using cubic polynomial interpolation to smooth the time series data, thereby generating a complete and continuous vertical time-varying sequence; (4) constructing the vertical deformation rate field of the study area through spatial interpolation techniques.

Hydrogeological profile and groundwater data

Based on the differences in spatial location and geomorphological characteristics of the study area, this paper divides it into four main zones: the Northwest Shandong Plain, the Jiaolai Plain, the Yishu River Plain, and the Central Shandong Uplift (Fig. 2). A brief overview is provided below:

The Northwest Shandong Plain, as an important part of the North China Plain, has deposited hundreds of meters of thick Neogene, Quaternary, and loose sediments from the Cenozoic era15, which form high-quality groundwater reservoirs. However, the acceleration of urbanisation has led to a continuous increase in groundwater extraction. Figure 2 shows that the deep groundwater funnels are mainly distributed in Guangrao, Liaocheng, Heze, Dezhou, and other places, with an average decline rate of more than − 2.27 m/yr; the water level in the Leling observation well has changed by -15.2 m since 2014, with an average rate of -2.17 m/yr. The shallow groundwater funnels are mainly distributed in Zaozhuang, Zibo, and other places, with the fastest average water level change rate reaching − 1.0 m/yr16,17,18,19.

The Quaternary loose sediments deposited on the Jiaolai Plain are high-quality groundwater storage spaces and transport channels, forming a shallow water-rich area. However, in recent years, due to the extensive extraction of groundwater in places like Changyi and Pingdu, the maximum water level decline rate can reach − 2.2 m/yr, forming shallow groundwater funnels.

The Yishu River Plain, centred around the Yishu River basin, is surrounded by mountains on the north, west, and east sides, and extends southward to form a fan-shaped alluvial plain. The surface of this plain is covered with approximately 30 m of loose Quaternary deposits. Underlying these deposits are aquifers primarily composed of Ordovician and Upper Cambrian limestone, dolomitic limestone, and marl of the Fengshan Formation. These rock layers are thick and extensively distributed, with developed fissures and karstification providing excellent pathways for groundwater migration and ample storage space, forming a strongly water-rich karstic area. In recent years, due to industrial water extraction, the average rate of change of shallow groundwater levels in Linyi and other places has reached − 3.0 m/yr, leading to the formation of groundwater funnels.

The Central Shandong Uplift mainly exhibited uplift characteristics during the neotectonic movement period. The surface is extensively exposed to Archean metamorphic rocks and polyphase intrusive rocks. These rocks have undergone high-temperature and high-pressure metamorphism and intrusive actions, resulting in a hard texture, strong resistance to weathering, and low porosity. Their water storage capacity is far inferior to that of Quaternary loose sediments. Therefore, the groundwater resources in the Central Shandong Uplift area are relatively scarce, and unable to support large-scale groundwater development. The distribution of groundwater funnels in the area is limited, and the groundwater level changes are relatively stable (Fig. 2).

Fig. 2
figure 2

Distribution of groundwater funnels and changes in groundwater levels. The graph was drawn using Generic Mapping Tools (GMT) software (https://www.generic-mapping-tools.org, Version 6.5.0).

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Infinite plane layer model corrected method

The basic principle of the infinite plane layer model is based on the gravitational field theory in geophysics. It assumes that a certain area of the Earth can be approximately regarded as an infinitely extended plane layer, within which the distribution and properties of matter are relatively uniform. When considering land subsidence or changes in the groundwater level, in fact, the mass distribution of matter within this plane layer has changed. According to Newton’s law of universal gravitation, a change in mass will lead to a change in the gravitational field.Specifically, land subsidence means the vertical displacement of matter within a certain range of this plane layer, which is equivalent to the redistribution of mass in the vertical direction. Changes in the groundwater level directly affect the mass distribution of water within this plane layer.

Results

Vertical deformation rate

Taking the data from January 1, 2010, as the baseline, we plotted the vertical displacement time series of some GNSS stations (Fig. 3). Multiple stations in the northwest Shandong Plain show a clear fluctuating downward trend. In this paper, we used a linear fit to eliminate the seasonal effects contained in these fluctuations, and the resulting fitted line more clearly reflects the long-term trend of decline. The slope of the line represents the annual vertical change rate. Among the stations with more significant changes, the annual vertical change rate in Guangrao is -85.2 ± 0.1 mm/yr (Fig. 3a), Shouguang is -63.6 ± 0.2 mm/yr (Fig. 3b), Dezhou is -34.8 ± 0.1 mm/yr (Fig. 3c), Shanxian is -35.4 ± 0.1 mm/yr (Fig. 3d), and Dongming is -35.1 ± 0.1 mm/yr (Fig. 3e). These data clearly reveal the significant degree of continuous surface subsidence in the northwest Shandong Plain area. On the other hand, stations in areas such as the Central Shandong Uplift, Jiaolai Plain, and Yishu River Plain have vertical change rates within ± 10.0 mm/yr, indicating no significant surface subsidence in these regions.

It should be noted that the GNSS vertical deformation rate error of approximately ± 0.1 mm/year given may be overly optimistic (Fig. 3). In fact, GNSS measurement results are susceptible to interference from various factors. Among them, the impact of seasonal factors and reference frame uncertainties on the four-year cumulative total of GNSS vertical deformation may range from a few millimeters to a few centimeters. The gravity effect error caused by the above-mentioned impacts is estimated to be within 10 µGal after analysis. This value is smaller than the observation error of mobile gravity. In view of this, from the perspective of actual measurement error comparison, the impact of seasonal factors and reference frame uncertainties on the four-year cumulative total can be neglected.

Fig. 3
figure 3

Time series of GNSS reference stations.

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The vertical deformation rate field in the western Shandong from 2010 to 2020 is shown in Fig. 4. Overall, the region primarily exhibits a subsidence trend, although there is still a minor tectonic uplift in the central part of the study area. Specifically, the Central Shandong Uplift displays a characteristic of differential movement between the north and south: the northern part shows a slow uplift, with the Tai’an station having the highest uplift rate of 1.4 mm/yr (Fig. 3f), while the southern part generally exhibits a slight subsidence trend, with subsidence rates within − 5.0 mm/yr.

In the northwest Shandong Plain, two significant subsidence areas were observed (Fig. 4). The first is a large elliptical subsidence zone centered around Guangrao, with a planar extent exceeding 100.0 km. At the center of this subsidence zone, Guangrao has a subsidence rate of -85.2 mm/yr, while Shouguin reaches − 63.6 mm/yr. Additionally, the contour lines in this area are densely distributed in concentric ellipses, with a large horizontal gradient, indicating that this subsidence zone not only has a high subsidence rate but also a relatively concentrated distribution area. The second subsidence area is located at the western edge of the northwest Shandong Plain, manifesting as a nearly north-south-oriented subsidence belt. Within this zone, most stations have vertical rates of less than − 20 mm/yr, with four subsidence centers—Dezhou, Guanxian, Dongming, and Shanxian—even experiencing subsidence rates of less than − 30 mm/yr.

Through comparative analysis, it has been found that there is a strong correlation between these subsidence areas and the distribution of deep groundwater funnel areas, while the correlation with shallow groundwater funnels is relatively small (Fig. 4). In addition, the subsidence belt on the western edge shows a certain correlation with the Liaokao fault zone in terms of spatial distribution and orientation. This may be due to the fact that the Liaokao fault zone has experienced intense tectonic movements, resulting in a higher degree of rock fragmentation compared to areas without fault development on either side. Therefore, when excessive groundwater extraction occur, the force balance of the strata is more easily disrupted, leading to a faster rate of ground subsidence.

Fig. 4
figure 4

Vertical deformation rate field in western Shandong. The graph was drawn using Generic Mapping Tools (GMT) software (https://www.generic-mapping-tools.org, Version 6.5.0).

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Gravity field changes

Based on the data from October 2017, the original gravity changes in western Shandong from October 2017 to October 2021 were calculated. As shown in Fig. 5, multiple positive gravity change anomaly areas were formed in places such as Dezhou and Guangrao. In particular, the gravity change in the Guangrao area exceeded + 60µGal, and the diameter of the area was greater than 100.0 km. On the contrary, the gravity changes in Linyi and Changyi showed negative values, with the central change amount reaching − 40µGal in both areas, and the diameter of the areas was about 70.0 km. It is worth noting that there were obvious positive-negative difference characteristics in the gravity changes on the east and west sides of the northern section of the Yishu Fault Zone.

Through comparative analysis, it was found that there was a strong correlation between the positive gravity change anomaly areas and the distribution of deep groundwater funnels, such as in Guangrao and Dezhou; while the negative gravity change anomaly areas were relatively consistent with the distribution of shallow groundwater funnels, such as in Changyi and Linyi (Fig. 5).

Fig. 5
figure 5

Measured gravity changes in western Shandong from October 2017 to October 2021. The graph was drawn using Generic Mapping Tools (GMT) software (https://www.generic-mapping-tools.org, Version 6.5.0).

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Discussion

Analysis of land subsidence gravity effect

During the period from 2017 to 2021, the highly positive value areas in the gravity field changes highly overlap with the rapid subsidence areas in the vertical deformation rate field (Fig. 6), such as Dezhou, Heze, Guangrao, and other places. These areas are located in the northwest Shandong Plain, where thick Quaternary loose sediments are deposited, and there is a huge volume of underground confined water extraction.

Fig. 6
figure 6

Comparison diagram of gravity changes and vertical deformation rate fields from October 2017 to October 2021. The graph was drawn using Generic Mapping Tools (GMT) software (https://www.generic-mapping-tools.org, Version 6.5.0).

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Confined water does not have a free water surface, and the water body is under the action of hydrostatic pressure. The change in its water level reflects the change in the pressure of the deep-seated water body, but it does not represent the actual change in the water volume. Therefore, it cannot be directly used to calculate the gravity effect of the reduction of confined water. As the hydrostatic pressure decreases, the solid skeleton has to bear more of the upper load pressure. When the pressure on the Quaternary loose sediments acting as the water reservoir exceeds their bearing capacity limit, irreversible plastic deformation occurs, the pores are compacted, and the reservoir space decreases20 (Fig. 7). Macroscopically, it is manifested as land subsidence and causes a positive gravity change, which has a huge interference with gravity observations aimed at medium and long-term earthquake prediction12.

Fig. 7
figure 7

Schematic diagram of groundwater exploitation and land subsidence process.

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When calculating the gravity effects caused by vertical deformation, the appropriate calculation method should be selected based on the specific geometric shape of the subsiding area. If the magnitude of vertical deformation is much smaller than the horizontal radius of the subsiding area, the area can be approximated as an infinitely large planar layer, and the Bouguer correction principle in static gravity fields can be referenced to obtain an approximate ratio relationship between gravity changes and vertical deformation21. Under this premise, the calculation error is usually no more than 1%22,23,24. For example, when the maximum gravity effect due to vertical deformation is 74.98 µGal, the corresponding model error is less than 0.75 µGal. However, when the vertical deformation is large, the results obtained using the approximate ratio relationship may have an error exceeding 10%, and mathematical models should be constructed and integrated for solutions25.

In this study, the maximum vertical deformation h1 in the subsidence area is less than 0.4 m, but the regional radius exceeds 20 km. Therefore, it is reasonable to treat the area as an infinite planar layer and adopt the approximate ratio relationship method for calculations. However, gravity changes are influenced not only by the gravity effects of subsidence but also by variations in shallow groundwater levels, making it difficult to directly obtain the ratio between gravity changes (△g1) and elevation changes (△h1) through fitting. Researches23,24 indicate that when ground subsidence occurs in Quaternary loose sediments, the ratio of gravity changes to elevation changes generally ranges between 0.214 × 10− 5 s− 2 and 0.23 × 10− 5 s− 2. Based on this, this study selects 0.22 × 10− 5 s− 2 as the ratio value, yielding:

$$\Delta\:g_{1}=-0.22\times\:\Delta\:h_{1}$$
(1)

where △h1 is the vertical elevation change at the measurement point (unit: mm).It should be noted that the gravity effect of land subsidence consists of three parts: the proximity effect (Δh1 in Fig. 7), the mass loss effect of the subsided part (the blank area corresponding to Δh1 in Fig. 7), and the weak positive gravity effect caused by the increase in formation density (the confined-water depression cone area in Fig. 7). Overall, the negative mass loss effect weakens the positive proximity effect to a certain extent. Therefore, it is reasonable that the fixed ratio of 0.22 × 10− 5 s− 2 (i.e., 0.22 µGal/mm) is lower than the free-air gradient (approximately 0.3086 µGal/mm).

Using Fig. 4, the vertical deformation rates at each gravity point were extracted, and Eq. (1) was applied to calculate the gravity effects of cumulative vertical changes from October 2017 to October 2021. Table 2 lists some measurement points with significant subsidence rates, including Guangrao, Liuqiao, Shouguang, Daotian, Dezhou, Shanxian, and Juancheng, where the gravity effects of vertical deformation exceed 30µGal.

Table 2 Surface vertical deformation and its gravity effects.
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From the distribution map of gravity effects of vertical deformation, it can be observed that gravity observations in the northwestern Shandong Plain are generally subject to significant positive interference. The maximum value appears in a circular area centered on Guangrao, with a diameter of approximately 100 km. Additionally, in the Dezhou–Liaocheng–Heze region, there is a nearly north-south-oriented band of positive gravity changes, with Dezhou, Heze, and Shanxian forming three centers of positive gravity changes. Apart from the aforementioned areas, the gravity effects of vertical deformation in other regions of western Shandong range between − 10µGal and 10µGal (Fig. 8).

Fig. 8
figure 8

Distribution map of gravity effects of vertical deformation. The graph was drawn using Generic Mapping Tools (GMT) software (https://www.generic-mapping-tools.org, Version 6.5.0).

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Analysis of phreatic water gravity effect

During the period from 2017 to 2021, the regions with negative values having relatively large absolute values in the gravity field changes exhibited spatial consistency with the phreatic water funnels (Fig. 5), such as in Changyi and Linyi. These areas primarily extract shallow phreatic water, which has a free surface and is influenced solely by gravity, without bearing the pressure of overlying strata (Fig. 7). Consequently, during the extraction process, the original stress structure of the strata does not undergo significant changes, nor does it lead to notable ground subsidence. However, the depletion of groundwater causes a reduction in the density of the strata, thereby decreasing the direct gravitational attraction to the measurement points, ultimately resulting in negative gravity changes. This study employs the infinite plane layer model to calculate the direct gravitational attraction of the depleted water body26,27. The calculation formula is as follows:

$$\Delta\:g_{2}=2\times\:\pi\times\:G\times\mu\times\Delta\:{h_{2}}\approx42\times\:\mu\times\Delta\:h_{2}$$
(2)

In the formula:

G represents the gravitational constant,

µ denotes the specific yield,

△h2 represents the phreatic water cumulative change over a certain period (unit: m).

When calculating the gravity effects of phreatic water change, selecting an appropriate value for the specific yield µ is crucial. This study focuses on the data collected from the observation points in Changyi and Hanting between 2010 and 2021, where only the decline in the phreatic water level is observed, and no ground subsidence has occurred. By analyzing the relationship between gravity changes and phreatic water changes, and fitting the data using formula (2), the specific yield of the phreatic aquifer in the study area is determined to be 0.103 ± 0.010, with a correlation coefficient R of 0.801 (Fig. 9). The discrete sources may be factors such as heterogeneous aquifer properties, timing differences, and observation errors.

Fig. 9
figure 9

Correlation fitting between gravity changes and phreatic water changes.

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(µ represents the specific yield of the phreatic aquifer, and the slope of the fitted line is 42µ)

According to formula (2), we calculated the gravity effects caused by phreatic water changes from October 2017 to October 2021. Table 3 presents the calculation results for selected areas, among which Linyi exhibits the maximum gravity effect of -51.91µGal, Pingdu shows − 38.07µGal, Changyi displays − 29.20µGal, and Shouguang records − 29.85µGal. In contrast, regions such as Laiwu and Guangrao demonstrate slight positive gravity effects.

Table 3 Phreatic water changes and their gravity effects.
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This paper applies the Kriging interpolation method to obtain the spatial distribution of the gravity effects of phreatic water changes (Fig. 10). Several negative change areas exist, centered around Shouguang, Changyi, Zibo, Linyi, Zaozhuang, and other places, mainly distributed around the periphery of the Central Shandong Uplift, with the largest diameter of these areas exceeding 50 km.

Fig. 10
figure 10

Gravity effect of phreatic water change. The graph was drawn using Generic Mapping Tools (GMT) software (https://www.generic-mapping-tools.org, Version 6.5.0).

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Corrected gravity change

Based on the measured gravity changes from October 2017 to October 2021 (Fig. 5), the gravity effects of vertical deformation and phreatic water change were deducted (Figs. 8 and 10), respectively, to obtain the corrected gravity changes for the period from October 2017 to October 2021. The results show that the gravity changes in western Shandong are generally stable, with relatively sparse gravity change isolines (Fig. 11). The corrected gravity changes at each gravity point range from − 12.30 µGal to 12.96 µGal (Table 4). Referring to the accuracy of mobile gravity measurements (Table 1) and the results of the non-linear term of static observations, the corrected gravity changes are within the normal range.

Table 4 Correction results of phreatic water change and land subsidence in typical areas (“-” indicates no change in phreatic water level; Corrected = Measured − (△g1 + △g2)).
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By comparing Fig. 5 with Fig. 11, it can be observed that the gravity changes in Dezhou, Heze, and Guangrao in Fig. 5 have shifted from positive to negative values, or the magnitude and spatial distribution of the positive values have decreased. This indicates that the positive gravity changes in these areas are primarily caused by the non-tectonic gravity effect induced by land subsidence. Meanwhile, the gravity changes in Changyi and Linyi have transitioned from negative to positive values, or the magnitude and spatial distribution of the negative values have diminished. This suggests that the negative gravity changes in these regions are due to the non-tectonic gravity effect resulting from a decrease in phreatic water, which leads to a reduction in formation density.

Fig. 11
figure 11

Corrected gravity changes from October 2017 to October 2021. The graph was drawn using Generic Mapping Tools (GMT) software (https://www.generic-mapping-tools.org, Version 6.5.0).

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Section characteristic analysis

To investigate the spatial distribution characteristics of gravity changes, phreatic water, land subsidence, and strata in western Shandong, two sections (AA’ and BB’) were selected in areas with significant gravity changes, as shown in Fig. 5. These sections start at points A and B, respectively, and sample the measured gravity changes, corrected gravity changes, phreatic water gravity effects, and subsidence gravity effects at intervals of 2 km along the sections. Finally, corresponding stratigraphic section diagrams were drawn.

Section AA’ (Fig. 12) traverses the northern part of the northwestern Shandong Plain, starting from Dezhou in the west and crossing the Yishu Fault Zone to the Jiaolai Plain in the east. The geological section reveals that the area west of the Yishu Fault Zone is covered by thick Quaternary loose sediments, with extensive groundwater extraction and land subsidence phenomena. The numerical curve of the section shows that the measured gravity (red line) in Dezhou, Guangrao, and Shouguang exhibits positive changes, and it intersects multiple times with the land subsidence gravity effect curve (yellow line), displaying similar morphological characteristics. Additionally, the phreatic water gravity effect shows a slight negative change. These phenomena collectively indicate that land subsidence caused by excessive extraction of deep groundwater is the primary factor driving the gravity changes, while the decline in phreatic water has somewhat reduced the magnitude of the positive gravity changes.

To the east of the Yishu Fault Zone in the Jiaolai Plain, the lower part is primarily composed of pre-Tertiary bedrock strata, overlain by Quaternary loose deposits with a thickness of only a few tens of meters. As a result, there is no extraction of deep groundwater or associated land subsidence issues in this area. The numerical curve of the section shows that the measured gravity (red line) is below − 40µGal, intersecting multiple times with the phreatic water gravity effect curve (blue line), with both exhibiting similar morphological characteristics. Meanwhile, the subsidence gravity effect is relatively minor, indicating that the significant negative gravity changes in this region are primarily caused by the extraction of shallow phreatic water.

The corrected gravity change curve (represented by the green line) fluctuates near the zero-value line, with an amplitude ranging from − 10.5 to + 13.0µGal. Applying the dominant correction method will makes the residual curve tend to be smooth, which suggests that the gravity anomaly changes in the northern part of the northwestern Shandong Plain are mainly influenced by land subsidence and groundwater decline, while tectonic gravity changes remain relatively stable.

Fig. 12
figure 12

Gravity changes along Section AA’.

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Section BB’ (Fig. 13) traverses the southern part of the study area, starting from Heze in the west and reaching Linyi in the east. The geological section reveals that the Quaternary loose sedimentary layers is significantly developed in the northwestern Shandong Plain. Long-term over-extraction of groundwater has triggered regional land subsidence, with the subsidence magnitude decreasing from west to east, gradually approaching zero at the western edge of the Central Shandong Uplift. The numerical curve of the section shows that the measured gravity changes are relatively small, but the gravity effect of land subsidence is significant, exceeding + 30µGal in the Heze area and gradually weakening as it extends westward.

The eastern part of the section spans the southern part of the Central Shandong Uplift, where pre-Tertiary rigid bedrock is widely exposed. In the Yishu River Plain, thick carbonate rocks are developed in the lower part, forming a karst aquifer system. In recent years, the regional phreatic water has been continuously and rapidly declining (Fig. 2). The profile’s numerical curve shows that the measured gravity exhibits a negative change, with the magnitude gradually increasing eastward, approaching − 40µGal in the Yishu River Plain. Additionally, the intersection of the phreatic water gravity effect curve with the measured gravity change curve indicates that the phreatic water gravity effect is the primary cause of the gravity changes.

After correction, the gravity changes (green line) exhibit negative fluctuations, with a reduced magnitude and significantly diminished east-west differences. Applying the dominant correction method makes the residual curve tend to be smooth, which suggests that the east-west gravity change in the southern part is primarily driven by non-tectonic factors, namely land subsidence and phreatic water decline.

Fig. 13
figure 13

Gravity changes along Section BB’.

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There are significant differences between Guangrao and Linyi in terms of geological structure, groundwater activities, and gravity change characteristics. Guangrao is located in the northern part of the northwestern Shandong Plain west of the Yishu Fault Zone along Profile AA’. The thick Quaternary loose sediments in this area result in abundant confined water. Long-term and large-scale extraction of deep-seated confined water has led to land subsidence. In Guangrao, the measured gravity shows a positive change and is close to the gravity effect of land subsidence. Although there is a slight negative change in the phreatic water gravity effect, land subsidence caused by excessive extraction of deep groundwater remains the dominant factor driving the positive gravity change. That is, it presents the characteristic of “confined water pumping → land subsidence → positive gravity change”.

On the other hand, Linyi is situated in the southern part of the Central Shandong Uplift along the eastern part of Profile BB’. The thick carbonate rocks in the lower part form a karst aquifer system. In recent years, the phreatic water level in Linyi has been continuously and rapidly declining. The measured gravity change is close to -40 µGal and is close to the phreatic water gravity effect, indicating that “karst bedrock, phreatic water loss → negative gravity change with relatively small subsidence” is the typical characteristic of the Linyi area. This comparison helps to gain a deeper understanding of the influence mechanism of groundwater activities on gravity changes under different geological backgrounds.

Conclusion

From October 2017 to October 2021, the abnormal gravity changes in western Shandong showed strong correlations with groundwater level decline and land subsidence. The maximum cumulative non-tectonic gravity effect reached + 78.22µGal. After correction using an infinite plane layer model, the residual gravity changes fell within normal ranges.

The non-tectonic gravity effect in Quaternary sedimentary basins (such as the northwest Shandong Plain) is significantly higher than that in exposed bedrock areas. In areas with developed loose sedimentary layers, the compaction of strata caused by deep confined water extraction can produce a significant positive gravity effect. While in the bedrock area, the exploitation of confined water or the loss of shallow phreatic water mainly leads to a decrease in density due to rock dehydration, producing a negative gravity effect. However, due to the rigid support of rock masses, the magnitude of surface subsidence remains relatively small.

We have developed a method capable of reliably detecting tectonic signals when they occur. This method proposes establishing a multi-source data fusion correction process in plain areas, providing a reference model for future related research in similar regions. The specific process is as follows: jointly calculate the vertical deformation field using Interferometric Synthetic Aperture Radar (InSAR) and Global Navigation Satellite System (GNSS), calculate the aquifer mass migration based on hydrological data, calculate the non-tectonic gravity effect through forward modeling, and finally extract the residual signal of gravity changes related to tectonics.