Liaohe Oilfield Reservoir Parameters Inversion Based on Composite Dislocation Model Utilizing Two-Dimensional Time-Series InSAR Observations

Abstract

To address the industry’s demand for sustainable oilfield development and safe production, it is crucial to enhance the scientific rigor and accuracy of monitoring ground stability and reservoir parameter inversion. For the above purposes, this paper proposes a technical solution that employs two-dimensional time-series ground deformation monitoring based on ascending and descending Interferometric Synthetic Aperture Radar (InSAR) technique first, and the composite dislocation model (CDM) is utilized to achieve high-precision reservoir parameter inversion. To validate the feasibility of this method, the Liaohe Oilfield is selected as a typical study area, and the Sentinel-1 ascending and descending Synthetic Aperture Radar (SAR) images obtained from January 2020 to December 2023 are utilized to acquire the ground deformation in various line of sight (LOS) directions based on Multitemporal Interferometric Synthetic Aperture Radar (MT-InSAR). Subsequently, by integrating the ascending and descending MT-InSAR observations, we solved for two-dimensional ground deformation, deriving a time series of vertical and east-west deformations. Furthermore, reservoir parameter inversion and modeling in the subsidence trough area were conducted using the CDM and nonlinear Bayesian inversion method. The experimental results indicate the presence of uneven subsidence troughs in the Shuguang and Huanxiling oilfields within the study area, with a continuous subsidence trend observed in recent years. Among them, the subsidence of the Shuguang oilfield is more significant and shows prominent characteristics of single-source center subsidence accompanied by centripetal horizontal displacement, the maximum vertical subsidence rate reaches 221 mm/yr, and the maximum eastward and westward deformation is more than 90 mm/yr. Supported by the two-dimensional deformation field, we conducted a comparative analysis between the Mogi, Ellipsoidal, and Okada models in terms of reservoir parameter inversion, model fitting efficacy, and residual distribution. The results confirmed that the CDM offers the best adaptability and highest accuracy in reservoir parameter inversion. The proposed technical methods and experimental results can provide valuable references for scientific planning and production safety assurance in related oilfields.

1. Introduction

Long-term underground oil and gas extraction activities primarily cause ground deformation in oil and gas fields. The internal pressure within the underground reservoirs gradually decreases throughout prolonged oil extraction, resulting in reservoir compaction and ground deformation [1]. Located in Liaoning Province in Northeast China, the Liaohe Oilfield was once the third-largest oilfield in China and remains one of the country’s principal heavy oil production bases. Long-term continuous oil extraction activities have affected the geological structure stability of the oilfield, leading to severe ground deformation. This not only impacts the oil recovery rate and the safety of oilfield operations but also poses threats to the local ecological environment [2,3,4]. Therefore, monitoring oilfield deformation and performing reservoir parameter inversion are crucial for understanding changes in the state of oilfield reservoirs, ensuring safe production, and promoting the sustainable development of the oilfield.

Interferometric Synthetic Aperture Radar (InSAR) technology, as a rapidly developing remote sensing technology for ground monitoring, offers advantages such as extensive area coverage, high precision, all-weather capability, and high efficiency [5,6,7]. The subsequent development of time-series InSAR techniques has further effectively mitigated the effects of temporal and spatial decorrelation as well as atmospheric delays [8], thereby enhancing the effectiveness of InSAR technology for long-term deformation monitoring. Currently, the commonly used time-series InSAR techniques include Permanent Scatterer InSAR (PS-InSAR) [9], Small Baseline Subset InSAR (SBAS-InSAR) [10], and the Stanford Method for Persistent Scatterers (StaMPS) [11]. These time-series InSAR techniques are now widely used in the monitoring of regional land subsidence [12,13], landslides [14], volcanoes [15], glacier movement [16], etc. Meanwhile, some scholars have also applied time-series InSAR techniques to monitor ground deformation in oil and gas fields and mining areas. For instance, Sun et al. [17] used multi-track PS-InSAR technology to monitor and quantitatively analyze ground deformation in the oilfield areas of the Liaohe Plain. Similarly, Yang et al. [18] employed InSAR technology combined with a Logistic model to monitor and predict dynamic subsidence in the Datong coal mining area. However, current time-series InSAR technology can only obtain one-dimensional deformation along the radar line-of-sight (LOS), which is merely a projection of the actual deformation in the SAR satellite’s line-of-sight direction and does not accurately reflect the accurate ground deformation [19]. Samsonov et al. [20] proposed the Multidimensional Small Baseline Subset (MSBAS) technique to address the LOS ambiguity, which extracts two-dimensional deformation in vertical and east-west directions. This method was successfully applied to extract two-dimensional time-series deformation in Mexico City. Scholars have gradually adopted it for monitoring two-dimensional deformation in oil and gas fields, proving its feasibility. Yang et al. [21] used the MSBAS technique to extract and analyze two-dimensional deformation in the Karamay oilfield, monitoring the deformation caused by subsurface fluid injection. Similarly, Liu et al. [19] employed the MSBAS method to analyze vertical and east-west directional deformation in the oilfield regions of the Qaidam Basin.

Long-term intensive over-extraction in oilfields leads to a decrease in reservoir pressure, causing compression in the oil and gas layers as well as clay layers. This results in large-area, slow ground deformation, indicating that ground deformation in oilfield regions directly manifests changes in reservoir pore pressure, geometric shape, location, and other reservoir parameters [22,23]. By inverting underground reservoir parameters in oilfields, one can comprehensively understand the changes in related parameters and analyze the deformation monitoring information of the oilfield. Existing research has utilized relevant geophysical models for reservoir parameter inversion and mechanism interpretation in oilfields. For instance, Yang et al. [21] employed the Mogi and Sill models for parameter inversion in the uplift area of the Karamay oilfield. At the same time, Sun et al. [17] used the Okada model to interpret the deformation caused by oil exploration in the Liaohe Oilfield. Currently, the commonly used models for estimating underground oilfield reservoir parameters and inversion include the Mogi, Ellipsoidal, and Okada models [17,19,21,24,25]. Nikkhoo [26] first proposed a composite dislocation model (CDM) with a higher degree of freedom and applied the model to the inversion of surface 3D deformation and subsurface fluid volume change of volcanoes. Wang et al. [27] introduced the CDM to realize the inversion of the volume change of subsurface gas reservoirs and estimation of surface 3D deformation. This demonstrates the feasibility of the CDM for such subsurface fluid volume inversion and deformation modeling in oil fields. However, these models have limitations, such as a lack of complete rotational freedom, making it challenging to fully simulate reservoirs at any angle in space [26]. Moreover, current physical model inversions typically use one-dimensional LOS deformation results as observational data for inversion and simulation. Some scholars have explored the feasibility of incorporating two-dimensional deformation from combined ascending and descending into model inversions, achieving significant results. Liu et al. [19] integrated vertical and east-west two-dimensional deformation results into the Ellipsoidal and Okada models for reservoir parameter inversion, introducing nonlinear inversion constraints, further improving inversion efficiency and accuracy. This demonstrates that incorporating a two-dimensional deformation field in reservoir parameter inversion can mitigate the non-uniqueness of inversion results, leading to more reliable reservoir parameters.

This study focuses on the Liaohe Oilfield as a typical research area, utilizing Sentinel-1 ascending and descending SAR images from January 2020 to December 2023. Based on MT-InSAR, we obtained time-series ground deformation information in the LOS direction from different perspectives. Subsequently, we derived a time series of vertical and east-west ground deformations by integrating ascending and descending data and solving for two-dimensional ground deformation. On this basis, reservoir parameter inversion and modeling were conducted in the subsidence trough area using the CDM and nonlinear Bayesian inversion method. The research results can provide valuable references for two-dimensional ground deformation monitoring and model selection for reservoir parameter inversion in related oilfields.

2. Methodology

In this paper, based on the MT-InSAR techniques, the new small baseline subset (NSBAS) method with temporal constraints is employed to extract LOS direction ground deformation. This extraction process involves SBAS inversion of interferograms, introducing temporal constraints, and spatio-temporal filtering of the time series. Meanwhile, this paper extracts the vertical and east-west time-series ground deformation based on the MSBAS method after the temporal and spatial datum unification and singular value decomposition of the ascending and descending data of the same acquisition period. Subsequently, the two-dimensional deformation field was introduced into the reservoir parameter inversion process. Quadtree subsampling technology was employed to enhance inversion efficiency. The CDM was selected as the primary inversion model, while the Mogi, Ellipsoidal, and Okada models were chosen for comparison. The optimal inversion parameters for each model were obtained using the nonlinear Bayesian inversion method. Finally, these parameters were used for forward modeling to simulate the two-dimensional deformation field in vertical and east-west directions. The specific methodological and technical workflow is illustrated in Figure 1.

2.1. Multitemporal InSAR LOS Ground Deformation Analysis

This paper employs the NSBAS method [28,29] within the MT-InSAR technique to extract LOS time series ground deformation. By incorporating temporal constraints, this method enhances the traditional SBAS approach, optimizing spatio-temporal baselines and resolving long-term interferometric phase sequences. This approach effectively mitigates observation discontinuities and phase unwrapping errors that can arise due to extensive temporal baselines.

Assuming N + 1 SAR images covering the study area are acquired, these selected images are registered to a common master image. An appropriate vertical baseline threshold is set, and images that meet this baseline threshold are grouped. This results in the formation of M differential interferometric pairs. The range of M can be expressed as:

$${\displaystyle \frac{N+1}{2}}\le M\le N({\displaystyle \frac{N+1}{2}})$$

(1)

For the j-th differential interferogram obtained from the SAR images at imaging times t_B (master image) and t_A (slave image), the interferometric phase at azimuth coordinate x and range coordinate r can be expressed as [30]:

$$\begin{array}{ll}\delta {\varphi }_j\left(x,r\right)& ={\varphi }_B\left(x,r\right)-{\varphi }_A\left(x,r\right)\\ & \approx {\displaystyle \frac{4\pi }{\lambda }}[d(t_B,x,r)-d(t_A,x,r)]+\mathsf{\Delta }{\varphi }_{\mathrm{topo}}^j\left(x,r\right)\\ & +\mathsf{\Delta }{\varphi }_{atm}^j\left(t_B,t_A,x,r\right)+\mathsf{\Delta }{\varphi }_{\mathrm{noise}}^j\left(x,r\right)\end{array}$$

(2)

where λ represents the radar wavelength, $d(t_B,x,r)$ and $d(t_{\mathrm{A}},x,r)$ describes the cumulative deformation along the LOS direction at the imaging times of the master and slave images relative to the initial time $t_0$, $\mathsf{\Delta }{\varphi }_{\mathrm{topo}}^j\left(x,r\right)$ represents the phase difference caused by topographic errors, $\mathsf{\Delta }{\varphi }_{atm}^j\left(t_B,t_A,x,r\right)$ represents the phase difference caused by atmospheric delay, and $\mathsf{\Delta }{\varphi }_{\mathrm{noise}}^j\left(x,r\right)$ represents the phase difference caused by other noise sources.

The topographic error $\mathsf{\Delta }{\varphi }_{\mathrm{topo}}^j\left(x,r\right)$ can be expressed as:

$$\Delta {\varphi }_{\mathrm{topo}}^j\left(x,r\right)={\displaystyle \frac{4\pi }{\lambda }}{\displaystyle \frac{B_{\perp j}\Delta h}{r\sin \theta }}$$

(3)

where $B_{\perp j}$ represents the length of the vertical baseline, and θ represents the radar incidence angle.

To obtain physically meaningful time-series deformation, the phase in Equation (2) is expressed as the product of the average phase velocity between two acquisition times and the time interval:

$${\nu }_j={\displaystyle \frac{{\varphi }_j-{\varphi }_{j-1}}{t_j-t_{j-1}}}$$

(4)

The phase value of the j-th interferogram can be expressed as:

$$\delta {\varphi }_j={\displaystyle \sum _{k=t_{A,j}+1}^{t_{B,j}}\left(t_k-t_{k-1}\right)}{\nu }_k$$

(5)

In addition, we introduce a temporal constraint factor to constrain based on the spatio-temporal baseline combination of the classic SBAS method. Suppose we have a stack of M-unwrapped interferograms $d={[d_1{d}_2\cdot \cdot \cdot d_{\mathrm{M}}]}^{\mathrm{T}}$ produced from N images acquired at $(t_0{t}_1\cdot \cdot \cdot t_{N-1})$, m represents the vector of phase delay increments contained between the two view approximation images, $m={[m_1{m}_2\cdot \cdot \cdot m_{N-1}]}^{\mathrm{T}}$, and the vector $d_L$ of interfering phases can be expressed as:

$$d_L=Gm$$

(6)

where G is a M × (N − 1) design matrix of zeros. The cumulative deformation (i.e., time-series deformation) for each monitoring period can be calculated by summing the displacement increments. The average deformation rate is then derived from the cumulative deformation by least squares based on the singular value decomposition (SVD) algorithm of Equation (6). To overcome the SVD bias when the independent images do not overlap, Equation (7). is used to provide an additional constraint.

$${\displaystyle \sum _{n=1}^{k-1}\delta }{\phi }_n-f(\Delta t_k)+e{B}_{\perp }^k=0$$

(7)

where n is the acquisition date; $e{B}_{\perp }^k$ is the vertical baseline of the acquired image at time k; e represents the unit vector in the direction of the baseline; $f(\cdot \cdot \cdot )$ is the regularization function, which means the parameterization of the temporal form of the deformation, and can be expressed as $f(t)=vt+c$. Moreover, we add a temporal constraint factor to solve the problem to obtain a more realistic deformation when there are vacancies in the temporal baseline.

$$\left.\left[\begin{array}{c}{d}_L\\ 0\end{array}\right.\right]=\left[\begin{array}{c}\left[\begin{array}{ccccccccccccc}& & & & & & G& & & & & & \end{array}\right]\left[\begin{array}{cccccccc}0& & & & & & & 0\end{array}\right]\\ \gamma \left[\begin{array}{ccccccc}1& 0& \cdots & \cdots & 0& 0& B_{\perp }^1\\ ⋮& 0& \cdots & & ⋮& -f(\Delta t_1)& B_{\perp }^2\\ 1& \cdots & 1& \ddots & ⋮& ⋮& ⋮\\ ⋮& & ⋮& \ddots & 0& ⋮& ⋮\\ 1& \cdots & 1& \cdots & 1& -f(\Delta t_N)& B_{\perp }^M\end{array}\right]\end{array}\right]\left[\begin{array}{c}m\\ v\\ c\end{array}\right]$$

(8)

where γ represents a weighting factor of the temporal constraint; when γ is small, the solutions within the connected part of the network are also less affected by the time constraint. Therefore, the time-constrained part only affects the network’s connectivity of the time-baseline vacancies. Good inversion results can be obtained by using this method regardless of whether the SBAS constitutive network is complete [31].

2.2. Two-Dimensional Deformation Modeling and Analysis

Due to the side-looking imaging characteristics of SAR satellites, the extracted ground deformation represents the one-dimensional deformation projected onto the LOS direction [3,32]. In monitoring deformation within large-scale subsidence areas, such as the Liaohe Oilfield in this study, the region experiences significant vertical subsidence and notable horizontal deformation. Therefore, in the presence of multi-directional deformation components, LOS-based deformation monitoring may lead to incomplete deformation information, making it challenging to interpret the deformation mechanism and characteristics comprehensively [33]. As illustrated in Figure 2, bowl-shaped oilfield deformation features centripetal horizontal displacement around the subsidence center. The horizontal deformation tends to zero at the subsidence center and the edges but reaches a maximum value between the center and the edges [3]. Therefore, when analyzing such bowl-shaped oilfield deformations, it is crucial to consider and analyze the impact of horizontal deformation instead of directly interpreting LOS deformation as vertical deformation. Additionally, due to the near-polar orbit characteristics of SAR satellites, InSAR technology exhibits lower sensitivity to north-south deformation components. Thus, the deformation is primarily decomposed into east-west and vertical components to ensure the accuracy of the derived deformation measurements.

The two-dimensional deformation decomposition modeling adopts the MSBAS method. For the overlapping ascending and descending interferograms in time and space, the geographic encoding and resampling to the same grid size are performed to achieve spatial baseline unification. Then, a time matrix interpolation is created to realize temporal baseline unification. Singular value decomposition is used to solve for the vertical and east-west deformation rates, and numerical integration of the deformation rates is performed to reconstruct the deformation time series.

We use four ascending and four descending SAR images as examples (Figure 3) to illustrate the unification of the time reference for two-dimensional time series. Assume that the acquisition time of the first ascending image is earlier than that of the first descending image. Therefore, we use factor (t₂ − t₀)/(t₂ − t₋₁) to compensate for the first ascending interferogram and factor (t₅ − t₃)/(t₆ − t₃) for the last descending interferogram. After boundary correction, we can consider that the ascending and descending data are simultaneously acquired at times t₀ and t₅, respectively, thus achieving the unification of the time reference [20].

In the observation equation of MSBAS, Tikhonov regularization is introduced to address the rank deficiency issue. This can be expressed as [34]:

$$\left(\begin{array}{cc}-cos\theta sin\phi \Delta t& cos\phi \Delta t\\ \lambda L& \end{array}\right)\left(\begin{array}{c}{V}_E\\ V_U\end{array}\right)=\left(\begin{array}{c}\widehat{\varphi }\\ 0\end{array}\right)$$

(9)

where θ and φ represent the azimuth and sensor incidence angles, respectively; Δt denotes the time interval between two SAR images; λ is the regularization parameter, where a larger λ value indicates a smoother solution; L is the regularization matrix; V_E and V_U are the unknown eastward and vertical velocity rates to be determined; and $\widehat{\varphi }$ represents the differential interferogram phase matrix for ascending and descending. Finally, Singular Value Decomposition (SVD) is used to solve the values of V_E and V_U for each pixel. The computed deformation rates are then integrated numerically to obtain the time series of eastward and vertical deformations [35].

$$d_i^E={\displaystyle \sum _{i=1}^n{V}_i^E}\Delta t_i,d_i^U={\displaystyle \sum _{i=1}^n{V}_i^U}\Delta t_i$$

(10)

where, d represents the cumulative deformation phase time series, and n is the total number of multi-orbit SAR images.

2.3. Reservoir Parameter Inversion Models and Methods

Geodetic inversion primarily consists of geodetic data, geophysical inversion models, and inversion algorithms. In this paper, the vertical and east-west two-dimensional InSAR deformation data from the Shuguang Oilfield area are used as geodetic data. By combining the composite dislocation model with the nonlinear Bayesian inversion algorithm, the internal structure and physical parameters of the reservoir are obtained. The following sections will introduce the composite dislocation model and the nonlinear Bayesian inversion algorithm used in this study.

2.3.1. The Compound Dislocation Model

The CDM, initially proposed by Nikkhoo [26], comprises three mutually perpendicular rectangular dislocations (RDs). This geometric model can represent various planar and volumetric sources with different aspect ratios, allowing for arbitrary sizes and spatial orientations. As illustrated in Figure 4, the CDM employs two coordinate systems: the local Earth-fixed Cartesian coordinate system (XYZ) and the Cartesian coordinate system (xyz). In the Earth-fixed Cartesian coordinate system (XYZ), the origin is located on the Earth’s surface, with the positive directions of the X, Y, and Z axes pointing east, north, and upward, respectively. The angles ωX, ωY, and ωZ represent the clockwise rotation of the CDM around the X, Y, and Z axes. The origin of the xyz coordinate system is at the centroid of the model, with the semi-axis lengths of the model along the x, y, and z directions denoted as a, b, and c, respectively. The CDM is described by the rotation angles (ωX, ωY, ωZ) around the X, Y, and Z axes and the centroid position of the CDM (X₀, Y₀, −d), where d represents the depth. Together, the rotation and displacement parameters define the final position and orientation of the CDM in space. Furthermore, each reference system of the CDM has the same number of uniform openings, resulting in a total of 10 parameters for the CDM: the centroid position (X₀, Y₀, −d), the rotation angles (ωX, ωY, ωZ), the semi-axes (a, b, c), and the opening.

In geophysical inversion models, such as the Mogi [36], Okada [37], and Ellipsoidal models [38], although they are widely used, they are typically constrained by fixed geometric shapes and limited rotational degrees of freedom. For instance, the Mogi model describes only the volumetric changes of spherical sources, while the Okada model mainly addresses ground deformations caused by fault slip. These models offer limited support for rotational parameters and are insufficient for handling complex three-dimensional spatial deformations. In contrast, the CDM significantly extends the applicability of the model due to its complete rotational freedom. The CDM can represent any tri-axial Ellipsoidal and simulate deformations at any angle in space, providing a theoretical foundation for precise inversion of complex deformations. More importantly, the flexibility of the CDM allows for detailed adjustment of inversion strategies through additional model parameters, enhancing the model’s constraints. This capability is crucial for accurately inferring parameters of subsurface structures such as oil reservoir layers.

2.3.2. Nonlinear Bayesian Inversion Method

In oil reservoir parameter inversion, the relationship between observation data and model parameters is often complex and nonlinear. Traditional linear inversion methods need help to capture this complexity. Therefore, this study employs a nonlinear Bayesian inversion algorithm for reservoir parameter inversion. The core of Bayesian inversion lies in incorporating prior information to establish the prior probability density function and using forward modeling to calculate theoretical deformation values based on initial model parameters. These deformation values are then used to compute the likelihood function. Additionally, the Monte Carlo sampling method (MCMC) and the Metropolis–Hastings algorithm are utilized to accurately estimate the posterior probability density function of the model parameters [39].

The relationship between the deformation observation data d obtained using InSAR technology and the inversion parameters m can be expressed by the following equation: G is the nonlinear function relating the deformation results to the inversion parameters, and ε represents the error in the deformation observation results.

$$d=G(m)+\epsilon$$

(11)

In the Bayesian framework, p(m) describes the prior probability of the parameter value m, while $p(m|d)$ represents the posterior probability of the model parameters. The posterior probability $p(m|d)$ describes the likelihood that the model parameters m can explain the data d, considering the prior information. In other words, it is the conditional probability of the observation data d given the model parameters m.

$$p(m|d)={\displaystyle \frac{p(d|m)p(m)}{p(d)}}$$

(12)

The likelihood function plays a crucial role in parameter estimation, as it describes the possible values of the unknown model parameters m given the known data d, reflecting the uncertainty of the parameters m. The likelihood function captures the degree of fit between the data d and the forward modeling results of the parameters m. By calculating the likelihood function, we can characterize the posterior probability density distribution of the parameters. It can be expressed as:

$$p(d|m)={(2\pi )}^{-N/2}|\sum d{|}^{-{\displaystyle \frac{1}{2}}}\times \exp [-{\displaystyle \frac{1}{2}}{(d-Gm)}^{\mathrm{T}}{\displaystyle {\sum }_d^{-1}(d-Gm)}]$$

(13)

3. Study Area and Datasets

3.1. Background of the Study Area

The Liaohe Oilfield is located in Liaoning Province in northeastern China, within the Liaohe Delta region (Figure 5). The Liaohe Delta features relatively flat terrain, primarily consisting of plains. The main river flowing through the area is the Liao River. The region experiences a temperate monsoon climate with distinct seasons, with rainfall concentrated in July and August. It is rich in wetland resources, serving as an essential habitat and migration corridor for various rare bird species. Additionally, the region is abundant in mineral resources, especially oil and natural gas, making it a significant petrochemical base in China. The Shuguang Oilfield and Huanxiling Oilfield are two major oil extraction bases within the Liaohe Oilfield. The Shuguang Oilfield is located in the central section of the western slope belt of the Liaohe Basin’s western depression. To date, six oil-bearing formations have been developed, with 44 production units. The proven cumulative oil-bearing area is 185.79 km², and the proven geological reserves exceed 419 million tons. The Huanxiling Oilfield is situated in the southern section of the same geological structure, covering an area of 350 km². Since its inception, 1282 oil wells have been established, with 779 currently operational. The daily liquid production reaches 11,600 tons, and the daily crude oil production is 1486 tons.

3.2. SAR Data and Processing

This study selected the Interferometric Wide (IW) mode and VV polarization SAR dataset provided by the Sentinel-1 satellite platform (

Table 1. Basic parameters of Sentinel-1 images.

Sensor	Orbit	Path	Frame	Waveband	Temporal Coverage	Image
Sentinel-1A	Ascending	98	129	C band(5.6 cm)	January 2021–December 2023	78
Sentinel-1B	Descending	3	455		January 2020–December 2021	45

), which includes 78 ascending SAR images (covering the period from January 2021 to December 2023) and 45 descending SAR images (covering the period from January 2020 to December 2021). The MT-InSAR method was employed to monitor LOS deformation from January 2020 to December 2023, and the MSBAS method was used to conduct two-dimensional deformation monitoring from January 2021 to December 2021. The 30-m resolution Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) was chosen to simulate the topographic phase. Interferometric processing of the SAR data was performed using GAMMA(2017) software. For the selection of interferometric pairs, we set a temporal baseline threshold of 48 days and a spatial baseline threshold of 200 m as the limiting conditions (Figure 6).

4. Result

4.1. MT-InSAR LOS Deformation Analysis

Figure 7 shows the LOS deformation rates extracted from the MT-InSAR processing of the Liaohe Oilfield study area for ascending (Figure 7a) and descending (Figure 7b). The results indicate the presence of two significant subsidence areas within the study area (marked by red boxes), namely the Shuguang Oilfield and the Huanxiling Oilfield. In the Shuguang Oilfield, the maximum LOS subsidence rates from the ascending and descending data are 143 mm/yr and 194 mm/yr, respectively, exhibiting straightforward subsidence troughs. In the Huanxiling Oilfield, the maximum LOS subsidence rates from the ascending and descending data are 71 mm/yr and 85 mm/yr, respectively. These areas show a marked ground deformation trend under long-term oil and gas extraction activities, indicating that underground oil and gas extraction is the primary driving factor. Additionally, comparing these findings with previous deformation monitoring studies, Tang et al. [3] monitored LOS subsidence rates of 177 mm/yr and 69 mm/yr for the Shuguang and Huanxiling oilfields, respectively, between 2017 and 2021. Yu et al. [40] observed LOS subsidence rates of 152 mm/year and 182 mm/year for ascending and descending in the Shuguang Oilfield from 2019 to 2023. This is generally consistent with the magnitude and trend observed in this study. The differences in subsidence rates between the ascending and descending are primarily attributed to the different monitoring time spans.

To analyze the temporal and spatial subsidence characteristics of the two subsiding oilfield areas, profiles were selected for both the east-west and north-south directions from the ascending and descending deformation rate maps. Specifically, profiles AA’ (east-west) and BB’ (north-south) for the Shuguang Oilfield, and profiles CC’ (east-west) and DD’ (north-south) for the Huanxiling Oilfield were analyzed (Figure 8a–d). The profile results indicate that in the Shuguang Oilfield area, the east-west pro-file AA’ (Figure 8e) shows the ascending subsidence rate peaking at 2.5 km with a maximum subsidence rate of 143 mm/yr, while the descending subsidence rate peaks at 3.5 km with a maximum subsidence rate of 194 mm/yr. In the north-south profile BB’ (Figure 8f), the maximum subsidence rate peaks show a difference of approximately 50 mm/yr between the two datasets. However, the spatial distribution trends of deformation are relatively consistent for ascending and descending. In the Huanxiling Oil-field area, the east-west profile CC’ (Figure 8g) and the north-south profile DD’ (Figure 8h) reveal that the deformation results from ascending and descending are pretty consistent in terms of subsidence amount and profile subsidence trends. The profile results from the two subsiding areas demonstrate certain differences in the distribution and magnitude of the subsidence centers between the ascending and descending. These differences may be attributed to the ascending and descending incident angles and differences in the monitoring period.

The study also selected two characteristic points along the east-west profile lines in the Shuguang Oilfield and Huanxiling Oilfield areas to analyze the temporal characteristics of subsidence. Firstly, the time series results for the P1 characteristic point in the Shuguang Oilfield (Figure 9a) indicate that the descending track data exhibit linear and uniform subsidence from 2020 to 2021, with a relatively stable subsidence rate. Similarly, the ascending track data show a linear subsidence rate from 2021 to 2023, with a slight deceleration trend observed in 2023. For the P2 characteristic point in the Huanxiling Oilfield area (Figure 9b), the time series results for ascending and descending indicate an annual periodic variation in subsidence. The overall periodic trend is characterized by accelerated subsidence in the first half of the year and a more moderate subsidence trend in the second half. This periodic characteristic may be related to the cyclical increase and decrease in production during oil and gas extraction in the Huanxiling Oilfield, leading to periodic changes in subsidence. The subsidence characteristics in both the Shuguang and Huanxiling Oilfield areas demonstrate a certain regularity in time and space, reflecting the significant impact of oilfield extraction activities on surface subsidence.

4.2. Two-Dimensional Deformation Monitoring and Analysis

The InSAR deformation results obtained from ascending and descending track data can only reflect one-dimensional LOS deformation. More is needed to fully explain the deformation mechanisms in complex areas for regions like the Shuguang Oilfield, which exhibit large-gradient, wide-area bowl-shaped subsidence, so the horizontal deformation must be addressed.

This study utilized the overlapping time intervals of ascending and descending track data to perform MSBAS processing, extracting vertical and east-west horizontal deformation for the Shuguang and Huanxiling oilfields from January to December 2021 (Figure 10a–d). The results show that the maximum vertical deformation rate reaches −221 mm/yr in the Shuguang Oilfield. In terms of horizontal deformation, there is a clear trend of eastward deformation on the west side of the subsidence trough and westward deformation on the east side, with the deformation converging towards the center of the subsidence trough, where there is almost no horizontal deformation. The maximum eastward deformation is 90 mm/yr, and the maximum westward deformation is 97 mm/yr. For the Huanxiling Oilfield, the two-dimensional deformation results indicate that the maximum vertical deformation rate at the center of the subsidence trough is −94 mm/yr. In the horizontal direction, the maximum eastward deformation rate is 43 mm/yr, and the maximum westward deformation rate is 46 mm/yr. We also conducted a comparative analysis with historical research results from the study area. Gong et al. [41] monitored the vertical and horizontal deformations of the Shuguang Oilfield within the Liaohe Oilfield from 2017 to 2020. Their results indicated significant horizontal displacement, with a maximum vertical subsidence rate of 198 mm/year and a maximum horizontal deformation rate of 62 mm/year. Although there are some differences in the vertical and horizontal deformation values between this study and previous research, the overall trend of two-dimensional deformation is consistent. Furthermore, our study reveals more pronounced deformation in both vertical and horizontal directions, indicating that the deformation trend in the Shuguang Oilfield has become increasingly significant as extraction activities continue.

We also plotted profiles L1 and L2 across the two subsidence troughs to analyze the spatial distribution of vertical and east-west deformations. The blue and red lines in the profiles represent the changes in deformation rates in the vertical and east-west directions, respectively. The profile deformation in the Shuguang Oilfield (Figure 11a) shows that the maximum vertical subsidence rate is at 2.2 km, which coincides with the center of the subsidence trough, and the subsidence rate gradually decreases from the center towards both the east and west sides. In the east-west direction, the eastward deformation rate peaks at 1.2 km, while the westward deformation rate peaks at 3.1 km. At the location with the maximum vertical deformation rate, i.e., 2.2 km at the center of the trough, the east-west deformation rate is almost zero. This is a typical deformation characteristic of subsidence trough, where the horizontal deformation increases from the edges towards the center of the trough and then decreases, ultimately resulting in no horizontal deformation at the center, only vertical deformation. The profile deformation in the Huanxiling Oilfield (Figure 11b) indicates that the maximum vertical subsidence rate is between 0.3–0.6 km. The east-west deformation results show that the eastward deformation rate continuously increases before 0.3 km and gradually decreases, approaching zero around 0.4 km, and then shifts to westward deformation after crossing the trough center. The overall vertical and east-west deformation trends and characteristics are consistent with the subsidence trough results in the Shuguang Oilfield. Therefore, for deformation monitoring of such oilfields, more is needed to analyze one-dimensional LOS deformation; the contribution of horizontal deformation must be addressed. This underscores the necessity of using two-dimensional deformation decomposition to monitor such high-gradient deformation in oilfields. Figure 11c,d further illustrates the three-dimensional effects of the subsidence troughs in the Shuguang and Huanxiling oilfields, providing a more intuitive view of the deformation distribution characteristics of the two subsidence troughs. The three-dimensional vertical effects in the Shuguang Oilfield region also confirm that the ground subsidence in this area is a typical circular, uniform subsidence trough caused by oil extraction activities.

To explore the spatiotemporal evolution characteristics of the Shuguang and Huanxiling oilfields, we extracted the time series of cumulative vertical deformation (Figure 11a) and east-west deformation (Figure 12b) in the study area from January 2021 to December 2021. The cumulative vertical deformation time series results indicate a clear subsidence trend in the Shuguang Oilfield area. Over time, the subsidence area gradually expanded outward, and the amount of subsidence at the center increased, reaching a maximum of 210 mm by 10 December 2021. In the Huanxiling Oilfield area, there was an accelerated subsidence trend from January to May 2021, a stabilization period from May to September, and another accelerated subsidence trend until December 2021. The temporal subsidence characteristics are consistent with the LOS time series characteristics observed in the ascending and descending. In the cumulative east-west deformation time series results, the Shuguang Oilfield shows significant east-west deformation, with maximum eastward and westward horizontal deformations of 78 mm and 82 mm, respectively. In the Huanxiling Oilfield, the maximum horizontal deformations in the east and west directions are around 40 mm, with the westward deformation being more extensive than the eastward deformation. Overall, the westward horizontal deformation is more prominent.

4.3. Reservoir Model Inversion for Two-Dimensional Observations

Ground deformation in oilfield regions directly manifests changes in reservoir parameters such as pore pressure, geometry, and location. Therefore, using two-dimensional deformation results obtained from InSAR technology, combined with geophysical models and inversion algorithms, allows for a more comprehensive understanding of the state changes in oilfield reservoirs. In the reservoir parameter inversion process, the vertical and east-west two-dimensional deformations in the subsidence trough area of the Shuguang Oilfield obtained by the MSBAS method were used as the inversion observations. The CDM and nonlinear Bayesian inversion methods were employed for reservoir parameter inversion. After 1 million iterations, the reservoir parameters converged, and the optimal fitting parameters were obtained. These optimal fitting reservoir parameters were then used for forward modeling to simulate two-dimensional ground deformation. We selected a reference baseline point with coordinates [121.81E, 41.13N] for the reservoir parameter inversion and set the Poisson’s ratio v = 0.25. To improve inversion efficiency, quadtree subsampling was applied to the vertical and east-west two-dimensional observation results.

4.3.1. The Inversion of Reservoir Parameter for CDM

Using the CDM for reservoir parameter inversion of the two-dimensional deformation results in the Shuguang area, the optimal fitting parameters and confidence intervals were obtained, as shown in

Table 2. Inversion results of the CDM.

	Compound Dislocation Model (CDM)
	X (m)	Y (m)	Depth (m)	ωX (°)	ωY (°)	ωZ (°)	a (m)	b (m)	c (m)	Opening (m)
Optimal value	−145.48	392.85	1523.69	−15.68	−10.77	35.03	683.51	1258.52	99.91	−0.49
Confidence Interval (2.5%)	−206.19	337.04	1441.75	−21.53	−16.08	30.54	471.69	1153.19	44.78	−0.81
Confidence Interval (97.5%)	−107.48	507.96	1721.92	−11.80	−6.55	38.95	796.44	1350.80	99.50	−0.41

. The oil layer center projected onto the surface relative plane is located at −145.478 m east and −392.847 m north, with an inverted oil layer depth of 1523.69 m. The model’s clockwise rotation angles around the x, y, and z axes are −15.6795°, −10.769°, and 35.0323°, respectively. The semi-axes of the inverted model are 683.508 m (a-axis), 1258.52 m (b-axis), and 99.9126 m (c-axis), indicating that the underground reservoir has an oblate Ellipsoidal shape with the long semi-axis almost parallel to the horizontal plane. Figure 13 illustrates the three-dimensional effect of the reservoir parameters in the CDM inversion model. Figure 14 presents the inversion results of the CDM, where (a) and (d) show the observed vertical and east-west deformations, (b) and (e) show the vertical and east-west deformations simulated by the CDM, and (c) and (f) display the residuals between the observed and simulated deformations in the vertical and east-west directions. The results show that the vertical deformations simulated by CDM at the subsidence centers and edges agree with the observed deformations. The simulated horizontal deformation aligns with the overall trend of the observed deformation, although there are some differences at the points of maximum deformation. The residual distribution for vertical and horizontal deformations shows that the areas with larger residuals are mainly located at the edges, possibly due to noise. Overall, the inversion results demonstrate high accuracy and reliability.

4.3.2. Reservoir Parameter Inversion Using Other Physical Models

To evaluate the effectiveness of the CDM in the inversion of oilfield reservoir parameters, this study also compares it with commonly used geophysical inversion models, including the Mogi model, the Ellipsoidal model, and the Okada model.

The Mogi model [36] is a simple yet effective approach for inverting surface deformation caused by pressure changes in underground reservoirs. It primarily involves four parameters: the center position of the point source (X, Y), reservoir depth, and volume change. The Ellipsoidal model, introduced by Yang et al. in 1988 [38], derives from the analytical calculation of a semi-elastic space with a finite-size and arbitrarily oriented prolate spheroidal cavity. This model includes parameters such as the three-dimensional coordinates of the ellipsoid center, the lengths of the major and minor axes, the orientation and inclination of the major axis, and the pressure change. The Okada model, developed by Okada in 1985 [37], is based on analyzing ground deformation induced by faults in an elastic half-space. This model is characterized by seven inversion parameters: reservoir location, length, width, depth, strike, and the openness of the dislocation surface. The following sections present the inversion results for these three models, providing a comparative analysis of their performance.

Table 3. Inversion results of the Mogi model.

	Mogi Model
	X (m)	Y (m)	Depth (m)	Volume Change (m3)
Optimal value	−67.32	316.356	1397.51	−1.42 × 106
Confidence Interval (2.5%)	−96.73	281.51	1347.23	−1.53 × 106
Confidence Interval (97.5%)	−42.98	351.44	1455.06	−1.32 × 106

presents the best-fit parameters and the 95% confidence intervals obtained from the Mogi model inversion, where the inverted depth is 1397.51 m, and the volume change is −1.42 × 10⁶ m³. Figure 15 illustrates the inversion results of the Mogi model and the residuals between the model and the observed values. The Mogi model inversion simulates vertical deformation as a circular pattern. Significant discrepancies are observed in the fit for the subsidence trough center and its edges. The simulated east-west deformation shows an angular deviation from the observed deformation in the central region of the subsidence trough. The residual distribution reveals substantial deviations in the vertical deformation residuals over a wide area. These results indicate that the Mogi model is more suitable for parameter inversion in regions where deformation characteristics approximate a circular shape. However, when applied to areas with elliptical or other more complex ground deformation characteristics, it exhibits considerable errors.

The optimal parameters and confidence intervals obtained from the Ellipsoidal model inversion are presented in

Table 4. Inversion results of the Ellipsoidal model.

	Ellipsoidal Model
	X	Y	Depth (m)	Major Semi-Axis (m)	Minor Semi-Axis (m)	Strike (°)	Dip (°)	DP/mu
Optimal value	−89.98	296.51	1234.21	1460.69	15.78	44.92	0.03	−0.003
Confidence Interval (2.5%)	−115.57	259.86	1170.30	1374.69	15.17	42.20	0.01	−0.004
Confidence Interval (97.5%)	−63.37	324.53	1293.26	1535.54	47.91	44.98	1.55	−0.001

. The inverted major axis length is 1460 m, with an azimuth angle of 44°, indicating an orientation 44° east of north, and the inverted reservoir depth is 1234 m. The inversion results of the Ellipsoidal model (Figure 16) indicate that the model can generally simulate the shape and deformation distribution of the subsidence trough in both vertical and horizontal directions. The residual results show that, although the Ellipsoidal model fits the vertical deformation well, there are still significant residuals in the edge areas where large deformations are observed.

The optimal parameters and confidence intervals obtained from the Okada model inversion are shown in

Table 5. Inversion results of the Okada model.

	Okada Model
	X (m)	Y (m)	Length (m)	Width (m)	Depth (m)	Strike (°)	Opening (°)
Optimal value	345.21	−84.38	2342.87	1120.42	1721.07	38.40	−0.70
Confidence Interval (2.5%)	211.92	−198.60	2152.86	801.36	1565.38	33.51	−0.99
Confidence Interval (97.5%)	484.81	38.09	2508.11	1447.12	1827.79	43.84	−0.48

. The optimal parameter results indicate that the inverted reservoir depth is 1721 m, the reservoir length is 2342 m, and the reservoir width is 1120 m. The strike is 38°, similar to the angle obtained from the Ellipsoidal model inversion. Figure 17 presents the inversion results of the Okada model. The results demonstrate that the Okada model performs well in simulating vertical and horizontal deformations. The residual distribution results are similar to the CDM inversion, showing good overall agreement. However, compared to the CDM, the Okada model exhibits minor deviations in the vertical deformation simulation, particularly in the central subsidence area, where there are small discrepancies between the modeled and observed deformations.

5. Discussion

5.1. Comparison of Inversion Model Performance

To compare the fitting performance of each model at the subsidence center, we selected a profile line L1 running from west to east through the subsidence trough. This profile effectively illustrates the spatial characteristics of vertical (Figure 18a) and east-west (Figure 18b) deformation. The fitting results of the deformation distributions along the profile line for the four inversion models—vertical (Figure 18c) and east-west (Figure 18d)—show that all four models exhibit similar deformation trends and directions in both the vertical and east-west directions. In the vertical deformation fitting results, the models show identical fitting performance on the west side of the subsidence center, up to 2 km. The CDM aligns more closely with the observed deformation at the subsidence center (2.2 km) and on the east side. Near 3 km, the fitting performance of the CDM shows a more significant advantage over the other three models. The differences among the four models are smaller in the horizontal deformation fitting results, with the overall trends being largely consistent. The comparative analysis indicates that while all models can capture the general deformation trends, the CDM is closer to the observed vertical deformation, especially around the subsidence center.

In the reservoir parameter inversion results, the residuals between the modeled and observed deformation are critical indicators of the inversion quality. The mean, standard deviation, and root mean square error (RMSE) of the residuals, respectively, reflect the central tendency, dispersion, and predictive accuracy of the residual distribution. Through statistical analysis of the vertical (Figure 19a) and east-west (Figure 19b) residuals, the histogram distributions show that all four models exhibit characteristics of normal distribution, with the CDM demonstrating the highest peak and greater concentration. In the vertical deformation residual statistics, the CDM shows significant advantages. The CDM has a residual mean of 0.006 mm, a residual standard deviation of 10.591 mm, and a root-mean-square error of 10.59 mm, all of which are better than the other three models. In the east-west deformation residual statistics, the residual mean value of CDM is 2.761 mm, the standard deviation is 12.134 mm, and the RMSE is 12.443 mm, slightly lower in residual accuracy than the Ellipsoidal model. However, the histogram of residuals for CDM exhibits a higher peak and a more concentrated residual distribution. Overall, in the inversion of reservoir parameters for the subsidence trough in the Shuguang Oilfield region, the CDM shows the best-fitting performance in the two-dimensional deformation field, followed by the Okada and Ellipsoidal models. Due to the Mogi model being a point source inversion model, it performs poorly in inverting elliptical deformation characteristics.

5.2. Comprehensive Analysis of Inversion Results for the CDM

In oilfield reservoir parameter inversion, while the Mogi, Ellipsoidal, and Okada models are widely used, their applicability in complex geological environments is limited due to constraints in rotational parameter freedom. For instance, the Mogi model can be seen as a simplified version of the CDM with three equal axes, and the Okada model corresponds to the CDM with two non-zero axes. Although the Okada model allows free rotation in one direction, it lacks rotational freedom perpendicular to the free surface, limiting its application in certain scenarios. In contrast, the CDM, which consists of three orthogonal rectangular dislocations, offers complete rotational freedom, allowing it to represent any triaxial Ellipsoidal shape and theoretically simulate deformation in any direction in space. This characteristic enhances the CDM’s ability to comprehensively map the complex relationship between subsurface reservoir parameters and ground deformation. Furthermore, the CDM can express oilfield reservoir parameters from multiple angles, improving its adaptability and accuracy in regions with complex ground deformation. Introducing two-dimensional deformation fields into reservoir parameter inversion increases the nonlinear inversion constraints, further enhancing the efficiency and accuracy of the inversion. To verify the feasibility and adaptability of the CDM in two-dimensional deformation field reservoir parameter inversion, we conducted a comparative analysis of the CDM with the Mogi, Ellipsoidal, and Okada models in the Shuguang Oilfield. The study revealed that the CDM outperformed the other models in fitting the observed vertical and east-west two-dimensional deformation. The residual distribution and accuracy results also showed clear advantages for the CDM. These findings confirm the superiority of the CDM in complex oilfield reservoir parameter inversion. However, due to the lack of measured data and detailed geological information, this analysis is limited to evaluating model fitting and residual accuracy based on the existing two-dimensional deformation field data. Future research should consider more comprehensive datasets and geological information to validate further and optimize the performance of the CDM in practical applications.

6. Conclusions

This study focuses on the Liaohe Oilfield as the research area, using Sentinel-1 ascending and descending SAR images from January 2020 to December 2023 to monitor ground deformation attributable to oil extraction activities. We extracted two-dimensional deformation information, both vertical and horizontal, across the investigated area. The CDM was also employed for reservoir parameter inversion and modeling of the Shuguang Oilfield. The main conclusions are as follows:

• Subsidence troughs have been identified in the concentrated extraction zones of the Shuguang and Huanxiling oilfields, with notably more significant subsidence observed in the Shuguang Oilfield. Comparative analysis with previous research results reveals that the subsidence trends in recent years align consistently, indicating ongoing and stable subsidence in these areas due to continuous oil extraction activities.
• The results of the two-dimensional deformation analysis reveal that the Shuguang Oil-field area experiences a maximum vertical subsidence rate of 221 mm/yr. The maximum eastward deformation rate is 90 mm/yr, and the maximum westward deformation rate is 97 mm/yr. The vertical deformation pattern forms an elliptical subsidence trough, while the east-west deformation distribution clearly shows horizontal displacement towards the subsidence center. In the Huanxiling Oilfield area, the maximum vertical subsidence rate is 94 mm/yr, with an eastward deformation rate of 43 mm/yr and a westward de-formation rate of 46 mm/yr.
• The CDM, with its complete rotational freedom and comprehensive inversion parameters, can simulate deformation accurately in any space direction. This allows for a more accurate depiction of the complex mapping relationship between subsurface reservoir parameters and ground deformation. Based on these advantages, we introduced two-dimensional deformation fields for parameter inversion and conducted comparative analyses of different models. The comparative analysis results indicate that the CDM demonstrates better inversion performance and adaptability in the study area, verifying its higher reliability for reservoir parameter inversion in this region.