The Joint Inversion of Seismic Ambient Noise and Gravity Data in an Ellipsoidal Coordinate System: A Case Study of Gold Deposits in the Jiaodong Peninsula

Abstract

The three-dimensional inversion of geophysical data is an effective method for analyzing underground structures. The seismic method is widely used due to its high resolution. However, the uneven distribution of seismic stations, especially in offshore areas, increases the uncertainty of inversion results. Gravity data are easy to obtain and offer high lateral resolution. For the influence of the Earth’s curvature in large-scale inversion, we first developed the joint inversion method of seismic ambient noise and gravity data in the ellipsoidal coordinate system, achieving the acquisition of large-scale and high-precision underground density and velocity structures. Experiments were conducted to address the uneven distribution of seismic stations, which proved the accuracy of the method. The proposed method was applied to the Jiaodong Peninsula (China) to obtain the transcrustal property distribution, further revealing that gold deposits are formed by the upwelling and condensation of hydrothermal materials, which causes the destruction of the North China Craton caused by the subduction of the Western Pacific Plate. Furthermore, we inverted the high-precision gravity anomaly of Sanshan Island, obtaining the structural distribution and predicting the distribution of offshore gold deposits.

1. Introduction

Natural seismic ambient noise imaging typically provides high vertical resolution but limited horizontal resolution, with the quality of the results being heavily dependent on the distribution of seismic stations [1,2,3,4]. In contrast, gravity data generally offer superior horizontal resolution but exhibit lower vertical resolution. By integrating ambient noise data with gravity data, complementary information in both directions can be leveraged, thereby enhancing the overall resolution of the inversion results.

The joint inversion of gravity and seismic data has undergone many years of development and has gradually formed a well-developed system. Initial applications combining surface wave group velocities with gravity anomalies established self-consistent shear wave velocity–density models of the crust and upper mantle in the Tarim Basin and Junggar Basin, demonstrating that joint inversion can enhance the resolution of shallow structures [5]. Subsequent developments included a method that established an empirical relationship between velocity and density and employed a nonlinear iterative inversion to obtain the final S-wave velocity structure model of the crust in the Shanxi Rift Zone [6]; multi-data joint inversion frameworks jointly inverted the arrival times of locally recorded P and S body waves, phase delays of Rayleigh waves generated by ambient noise, and Bouguer gravity anomalies, producing a 3D image of P and S wave velocities for the upper 25 km of the East African Rift crust [7]. Additionally, surface wave tomography based on Eikonal ray tracing combined with gravity imaging was used to obtain a 3D crustal shear wave velocity model of the eastern Tibetan Plateau [8]. These advances collectively highlight the resolution gains achievable through joint inversion.

In recent years, the application of spherical coordinate systems in gravity modeling and inversion has gained increasing attention, particularly in planetary and large-scale geophysical studies. Methods based on Gauss–Legendre quadrature integration have been developed to calculate the gravity effects of spherical prisms with high accuracy [9]. Building upon this foundation, three-dimensional gravity inversion techniques in spherical coordinates have been successfully applied to planetary data [10]. Forward modeling approaches using tesseroids have further advanced the capability to simulate gravitational fields in spherical geometries with improved fidelity [11]. These advancements have led to the development of fast nonlinear inversion techniques in spherical coordinates, enabling detailed crustal structure interpretations over continental scales [12]. More recently, methods utilizing full gravity gradient tensor data within a spherical coordinate system have been proposed to enhance inversion resolution and stability [13]. In addition, the joint inversion of gravity and vertical gravity gradient data—constrained by density-weighting and cross-gradient methods—have been formulated and applied to lunar geophysical exploration [14].

Seismic tomography in spherical coordinate systems has also been in development in recent years. Initial computational approaches implemented differential ray-tracing algorithms for global seismic phase modeling [15]. Subsequent refinements integrated parametric optimization techniques for ray path determination in multi-layered media [16]. Twenty-first-century innovations introduced wavefront propagation algorithms enabling efficient multi-phase travel-time computations [17], culminating in hybrid methodologies combining optimized pathfinding with domain decomposition strategies. These advancements permitted the simultaneous resolution of 49 global seismic phases within integrated inversion protocols, subsequently applied to multidisciplinary lithospheric investigations [18,19].

In fact, the earth is not a regular sphere but an oblate ellipsoid. Early formulations addressed gravitational field calculations through ellipsoidal prism discretization combined with orthogonal polynomial expansions [20], building upon foundational correction frameworks established in mid-20th-century studies [21]. Seismic propagation analyses further revealed measurable discrepancies between spherical and ellipsoidal models, particularly in ray path geometries and travel time residuals attributable to radial velocity gradients [22]. Recent computational advancements enable comprehensive ellipsoidal coordinate implementations, including partitioned multi-step algorithms for multi-phase seismic ray tracing [23,24,25].

The Jiaodong Peninsula, located in the North China Craton, is one of the largest gold-bearing regions in the world, attracting considerable attention due to its vast accumulation of gold. Most of the gold deposits in this area were formed during the Early Cretaceous and are structurally controlled by northeast- to north–northeast-trending faults, which developed within or along the main boundary of granite intrusions and late Archaean metamorphic rocks. The spatial distribution of global orogenic and magmatic–hydrothermal gold deposits is often controlled by the plate tectonic settings of the trench–arc–basin system [26]. While the tectonic–fluid interactions, metallogenic chronology, and ore-forming processes of this province have been extensively characterized [27,28,29,30,31,32,33,34,35], significant debates persist regarding mineralization sources, with some studies proposing inadequacies of existing genetic models [36] and emphasizing linkages to craton destruction events [37]. Systematic analyses integrating mineralization characteristics and tectonic constraints suggest a novel genetic classification for these deposits, supported by sulfur isotopic signatures correlating with Neoproterozoic sedimentary sequences along the Yangtze Craton’s northern margin [38,39,40,41]. Spatial–temporal associations with mafic dike swarms further implicate metasomatized subcontinental lithospheric mantle as a potential metal source [42,43,44,45,46]. Tectono dynamic reconstructions indicate progressive modification of this Proterozoic orogenic belt through multi-stage subduction processes: Paleo-Tethyan slab dynamics preceding the Triassic Yangtze–North China collision, succeeded by Paleo-Pacific plate interactions. Such protracted subduction regimes facilitated mantle wedge metasomatism through slab-derived fluid fluxes, crucially preconditioning regional metallogenic fertility [47,48].

This paper mainly focuses on research on the joint inversion of satellite gravity and ambient noise on a large scale. Considering the uneven distribution of seismic stations and the influence of the Earth’s curvature on a large scale, the joint inversion of satellite gravity and ambient noise in the ellipsoidal coordinate system is carried out. This method is applied to the Jiaodong Peninsula in Shandong Province, obtaining a more detailed underground geological model of this area, which provides a more powerful basis for subsequent interpretation.

2. Methods

2.1. Forward Modeling in the Ellipsoidal Coordinate System

2.1.1. Gravity Anomaly

To better approximate the shape of the earth, ellipsoidal prisms in the ellipsoidal coordinate system (e.g., the blue prism in Figure 1) are used to discretize the underground space.

For the ellipsoidal prism E(r_E, θ_E, ϕ_E) in Figure 1 and observation point P(r, θ, ϕ), the equations of the gravity anomaly and its gradient produced by ellipsoidal prism E at observation point P can be written in the form of the Newtonian integral [9].

$$g_E(r,\theta ,\varphi )=G\rho {\displaystyle \underset{{\varphi }_1}{\overset{{\varphi }_2}{\int }}{\displaystyle \underset{{\theta }_1}{\overset{{\theta }_2}{\int }}{\displaystyle \underset{r_1}{\overset{r_2}{\int }}g(r_E,{\theta }_E,{\varphi }_E,r,\theta ,\varphi )}}}d{r}_{E}d{\theta }_{E}d{\varphi }_E,$$

(1)

where G is the gravitational constant, ρ is the residual density, and g_E may represent either a radial gravity vector component or a gravity tensor gradient component.

The Gauss–Legendre quadrature formulas for the gravity and its gradient of an ellipsoidal prism are can be rewritten as follows:

$$g_E(r,\varphi ,\theta )\approx {\displaystyle \frac{\left({\theta }_2-{\theta }_1\right)\left({\varphi }_2-{\varphi }_1\right)\left(r_2-r_1\right)}{8}}{\displaystyle \sum _{i=1}^{I^r}{\displaystyle \sum _{j=1}^{J^{\varphi }}{\displaystyle \sum _{k=1}^{K^{\theta }}{W}_i^r{W}_j^{\varphi }{W}_k^{\theta }g({\widehat{r}}_{Ei},{\widehat{\varphi }}_{Ej},{\widehat{\theta }}_{Ek},r,\varphi ,\theta )}}},$$

(2)

where $I^r$, $J^{\varphi }$, and $K^{\theta }$ represent the order of the expansion,

$${\widehat{r}}_{Ei}={\displaystyle \frac{r_2-r_1}{2}}{r}_{Ei}+{\displaystyle \frac{r_2+r_1}{2}},$$

(3)

$${\widehat{\varphi }}_{Ej}={\displaystyle \frac{{\varphi }_2-{\varphi }_1}{2}}{\varphi }_{Ej}+{\displaystyle \frac{{\varphi }_2+{\varphi }_1}{2}},$$

(4)

$${\widehat{\theta }}_{Ek}={\displaystyle \frac{{\theta }_2-{\theta }_1}{2}}{\theta }_{Ek}+{\displaystyle \frac{{\theta }_2+{\theta }_1}{2}},$$

(5)

where $W_i^r$, $W_j^{\varphi }$, and $W_k^{\theta }$ and $r_{Ei}$, ${\theta }_{Ei}$, and ${\varphi }_{Ek}$ are Gaussian coefficients and Gaussian node positions on the [−1, 1] interval.

For the ellipsoidal coordinate system in Figure 1, the earth was assumed as an ellipsoid with one long semi-axis and two short semi-axes of equal length, where the long semi-axis (a), short semi-axis (b), and eccentricity (e) are related as follows:

$${\displaystyle \frac{X_E^2+Y_E^2}{a^2}}+{\displaystyle \frac{Z_E^2}{b^2}}=1,$$

(6)

$$e=\sqrt{1-{\displaystyle \frac{b^2}{a^2}}},$$

(7)

where (X_E, Y_E, Z_E) is the coordinate in the Cartesian coordinate system.

The use of ellipsoidal coordinates increases the complexity of the integration in (2). Nevertheless, the gravity anomaly of an ellipsoidal prism can be accurately approximated using (2), with details provided by Roussel [20].

2.1.2. Seismic Data

The surface wave travel time between two stations, A and B (denoted as t_AB and shown schematically in Figure 2, black dots represent stations), can be expressed in discrete form as follows:

$$t_{AB}(\omega )={\displaystyle \sum _{p=1}^P{S}_p}(\omega )\Delta l_{AB}={\displaystyle \sum _{p=1}^P{\displaystyle \sum _{k=1}^k{v}_{pk}\stackrel{\wedge }{S_k}}}(\omega )\Delta l_{AB},$$

(8)

where $t_{AB}$ is the surface wave travel time between station A and station B; $\omega$ is the frequency; $\Delta l_{AB}$ denotes the ray path between stations; $p$ is the number of surface wave ray path segments; $S_p$ is the phase slowness on the p-th path segment; $v_{pk}$ is the bilinear interpolation coefficient, which is used to interpolate the slowness of regular grid points onto the ray path; and $\widehat{S_k}$ is the slowness of the k-th plane grid point.

We adopt the method of directly performing ambient noise ray-tracing calculations in the ellipsoidal coordinate system. The ray path segment $\Delta l_{AB}$ in (8) can be calculated by using the distance formula between any two points on an ellipsoid:

$$\Delta l_{AB}=\sqrt{{(R_A-z_A)}^2+{(R_B-z_B)}^2-2(R_A-z_A)(R_B-z_B)\cos \gamma },$$

(9)

where $R_A$ and $R_B$ are the distances from station A and station B to the center of the ellipsoid, respectively; $z_A$ and $z_B$ are the depths of the two points; and $\gamma$ is the central angle formed by station A and station B and the center of the sphere. In the ellipsoidal coordinate system, there are

$$R(\theta ,\varphi )={\displaystyle \frac{abc}{\sqrt{{(bc\cos \theta \cos \varphi )}^2+{(ac\cos \theta \sin \varphi )}^2+{(ab\sin \theta )}^2}}},$$

(10)

$$\cos \gamma =\sin {\theta }_i\sin {\theta }_j+\cos {\theta }_i\cos {\theta }_j\cos ({\varphi }_i-{\varphi }_j).$$

(11)

where $a$, $b$, and $c$ are the lengths of the three semi-axes of the ellipsoid; $\varphi \in [-180°,180°]$ is the longitude; and $\theta \in [-90°,90°]$ is the latitude.

2.2. Inversion Method

2.2.1. Single Inversion

For the density inversion of gravity data, we typically use the Tikhonov regularization method to solve for the minimum of the objective function.

$$\Phi ={‖W_{d}Am-g‖}_2^2+\alpha {‖W_m(m-m_{\mathrm{ref}})‖}_2^2\to \min ,$$

(12)

where $W_d={\displaystyle \frac{1}{\sigma }}I$ is the data weighting matrix under a measurement error of $\sigma$, which assigns a greater weight to accurate observations (we considered $W_d=I$ in our experiments); $W_m$ represents the model weighting matrix and is a diagonal matrix. $A$ is the gravity kernel matrix, m is the subsurface residual density distribution, and $g$ is the observed anomaly. $\alpha$ is the Tikhonov regularization parameter, reflecting the balance between data fitting and model constraints, which can be determined using the L-curve method. $m_{\mathrm{ref}}$ is the reference model determined based on prior information. When prior information is insufficient, $m_{ref}$ is generally set to 0.

For ambient noise inversion, the goal is to obtain a solution that minimizes the residuals $\delta t_i(\omega )$ between the observed arrival times $t_i^{obs}(\omega )$ and the calculated arrival times $t_i^{pre}(\omega )$ at all frequencies, which can be written as follows:

$$t=Gv,$$

(13)

where $t$ represents the travel time residual data at all frequencies, $G$ is the kernel function matrix, and $v$ is the velocity model parameter to be determined. We minimize the following objective function:

$${\Phi }_v={‖t-Gv‖}_2^2+\lambda {‖Lv‖}_2^2\to \min ,$$

(14)

where $L=\left[\begin{array}{l}{D}_x\\ D_y\\ D_z\end{array}\right]$ is the smoothing operator constructed by combining the first-order finite difference operators along the x, y, and z axes. D_x, D_y, and D_z are the finite difference matrices that approximate the spatial gradients of the model parameters. $\lambda$ is the weight parameter of the regularization term of the model.

2.2.2. Joint Inversion

Three principal methodologies exist for the joint inversion of gravity and seismic data: sequential inversion, simultaneous inversion, and cross-gradient constrained joint inversion.

Sequential inversion initially implements separate inversions for seismic and gravity datasets and then employs the velocity–density conversion relationship to update the initial models for subsequent iterations until convergence is achieved. While theoretically feasible, this method demonstrates critical limitations by relying solely on empirical velocity–density correlations as its constraint mechanism. Lithologically identical rock units exhibit variable velocity–density relationships across different structural domains and depth intervals. Impropetuous density–velocity conversions inevitably introduce model artifacts, particularly when utilizing empirical relationships derived from low-resolution initial models. Data inaccuracies in the first-stage inversion become geometrically amplified through iterative conversion processes, ultimately diminishing the secondary dataset’s contribution to final model optimization.

Simultaneous inversion frameworks integrate seismic velocity (shown in Figure 2b) and gravity kernels within a unified parameter space through a composite kernel formulation:

$$\left[\begin{array}{c}{G}_s\\ G_g\end{array}\right]\delta {\beta }_i=\left[\begin{array}{c}\delta t\\ \delta g\end{array}\right],$$

(15)

where $G_s$ and $G_g$ represent the kernel function matrix of surface wave dispersion travel times and Bouguer gravity anomalies with respect to shear wave velocity, respectively, while $\delta {\beta }_i$ denotes the parameters of the subsurface velocity and residual density model.

Seismic velocity and density are structurally correlated in the Earth’s crust, particularly in crystalline basement and upper mantle regions, which provides a basis for structural constraints in joint inversion [49]. First, the velocity model is converted into a density model. The density anomaly $\Delta \rho$ from the upper surface of the crust to the reference Moho depth (30 km) is defined as $\Delta \rho =\rho -{\rho }_c$, where ${\rho }_c=2.67 (\mathrm{g}/\mathrm{c}{\mathrm{m}}^3)$. The density anomaly $\Delta \rho$ below 30 km is defined as $\Delta \rho =\rho -{\rho }_m$, where ${\rho }_m=3.27 (\mathrm{g}/\mathrm{c}{\mathrm{m}}^3)$.

For joint inversion, we consider the cross gradients of gravity and ambient noise, which are defined as follows:

$${\psi }_1(m)={‖D_{obs}-D_{cal}‖}_2^2+{\lambda }_1^2{‖W_m\left(\Delta \rho -\Delta {\rho }_P\right)‖}_2^2+{\alpha }_1^2{‖\nabla \Delta \rho \wedge \nabla \Delta V_P‖}_2^2,$$

(16)

$${\psi }_2(m)={‖D_{vobs}-D_{vcal}‖}_2^2+{\lambda }_2^2{‖\left(\Delta v-\Delta v_{apr}\right)‖}_2^2+{\alpha }_2^2{‖\nabla \Delta \rho \wedge \nabla \Delta V_P‖}_2^2,$$

(17)

where $\Delta \rho$ is the density anomaly; $\Delta {\rho }_P$ is the a priori density anomaly; $D_{obs}$ and $D_{cal}$ are the measured Bouguer gravity anomaly and the theoretical Bouguer gravity anomaly, respectively; ${\lambda }_1$ and ${\alpha }_1$ are the regularization weights of the density model fitting term and the cross-gradient term, respectively; $\Delta v$ is the velocity; $\Delta v_{apr}$ is the velocity a priori model; $D_{vobs}$ and $D_{vcal}$ are the actual dispersion data and the theoretical dispersion data, respectively; ${\lambda }_2$ and ${\alpha }_2$ are the regularization weights of the velocity model fitting term and the cross-gradient term, respectively; and $W_m$ is the depth weighting operator applied to the model, which is calculated by integrating the gravity kernel function $G_g$ over the discretized subsurface grids and the position of each observation point (Portniaguine and Zhdanov [50]). For a research area with $N_{obs}$ observation points and M_grid discretized subsurface grids, the matrix operator $W_m$, as defined in [51], is a diagonal matrix, whose diagonal entries are defined as follows:

$$W_k={\left({\displaystyle \sum _{i=1,Nobs}{G_g}_{i,k}^2}\right)}^{{\displaystyle \frac{1}{2}}},$$

(18)

As shown in (18), $W_m$ dimensions vary with the depth of the discretized subsurface grid. It is used to mitigate the influence of depth variation on the inversion results.

The cross-gradient inversion strategy of the two datasets is inverted separately. After each iteration, the cross-gradient terms of ${\psi }_1$ and ${\psi }_2$ are updated based on the current velocity and density distribution. This process is repeated until the convergence criterion is satisfied. This strategy allows the structural correlation between the two properties to be progressively enforced while maintaining flexibility in handling differences in data type.

As indicated in (17) and (18), we employed L2-norm for the inversion because in the absence of prior information, L2-norm regularization cannot fully restore the true density of geological bodies but can still recover relatively accurate boundaries. In such scenarios, L1- or L0-norm inversions—lacking constraints from prior information—would produce erroneous results in both density estimates and spatial positioning [52,53]. The stopping criteria for the inversion are defined as reaching a maximum of 100 iterations or achieving a data misfit less than 0.01.

2.3. Model Tests

To evaluate the application effect of the method, we established a dual geological body model with unevenly distributed stations. The research area ranges from 115.0° E to 116.3° E and from 34.0° N to 34.8° N with a depth of 40 km. It is divided into 32 × 16 × 8 blocks, and each block has a size of 0.05° × 0.05° × 5 km. Among them, the density anomaly of the model is uniformly 0.6 g/cm³ (Figure 3a), and the velocities are 3.3 km/s and 4.5 km/s (Figure 3b). The shape and size range of the density anomaly body are consistent with the high-velocity anomaly body in the low-velocity layer. The resulting gravity anomaly is shown in Figure 3c, and the station distribution and ray density in the model area are shown in Figure 3d. Considering the background of our inversion, we focus on the case of missing seismic data and insufficient a priori information. At this point, it is not possible to obtain an accurate initial model, so in this case, we set the initial model of gravity to 0 mGal. For seismic data, in the model test, our initial model has a single interface at 30 km.

Figure 4a,b show vertical slices of the inversion results from the ambient noise and gravity-only inversions, respectively. Figure 4c,d display slices from the sequential inversion (ambient noise followed by gravity). Compared with standalone inversions, the ambient noise imaging results exhibit improved horizontal resolution due to the incorporation of gravity data, but the resolution at the upper interfaces of geological bodies is reduced. For the sequential gravity inversion results, the vertical resolution in shallow sections is enhanced, and the results at the bottom show better convergence compared to standalone inversions. Figure 4e,f present vertical slices of the background noise and gravity inversion results from the data-constrained simultaneous inversion. Compared with sequential inversion, the ambient noise imaging results maintain higher resolution at the upper interfaces of shallow geological bodies while improving horizontal resolution. However, the gravity results exhibit severe smearing effects despite enhanced vertical resolution in shallow sections. Figure 4g,h show slices of the cross-gradient structure-constrained joint inversion of velocity and density. Compared with simultaneous inversion, the ambient noise results show no significant differences, while the gravity inversion results effectively mitigate the smearing issues observed in simultaneous inversion. Additionally, the cross-gradient approach improves vertical resolution in shallow sections and yields better converged results.

We define the precision of the four methods for comparison using the following formula:

$$P=\left|{\displaystyle \frac{m}{\max (m)}}\cdot \left(\max (m_{\mathrm{true}})-m_{\mathrm{true}}\right)\right|,$$

(19)

where $m$ represents the experimental result, $m_{\mathrm{true}}$ represents the true model, $max\left(m\right)$ represents the maximum value of the experimental result $m$, and $max(m_{\mathrm{true}})$ represents the maximum value of the true model $m_{\mathrm{true}}$.

By calculating $P$ through statistical analysis in statistical precision ranges, we can evaluate the precision of each method, as shown in Figure 5.

Figure 5a shows that when station distribution is uneven, the results of the seismic-only inversion are inaccurate, with most of the mistakes occurring in regions lacking seismic stations. Incorporating gravity data significantly enhances the accuracy of seismic inversion. From the statistical probability distributions, all three joint inversion methods yield better performance in velocity structure recovery. For gravity inversion, as shown in Figure 5b, a comparison of the statistical results from the three joint inversion methods reveals that the cross-gradient inversion recovers the largest number of grid cells within the 0–0.1 statistical precision range, followed by simultaneous inversion, while sequential inversion performs the worst. In contrast, within the 0.3–0.4 statistical precision range, the cross-gradient method yields the fewest grids, sequential inversion yields more, and the number from simultaneous inversion is nearly the same as that of the gravity-only inversion. Therefore, the cross-gradient method demonstrates the best performance in recovering the residual density structure. Based on the above statistical results, it can be concluded that the cross-gradient inversion presents the best results.

3. Real Data Inversion

3.1. Geological Background

The Jiaodong gold deposit region is a giant gold mineralization region formed in the Late Mesozoic within the pre-Cambrian metamorphic basement. The Jiaodong Peninsula is located in the eastern part of the Tan-Lu Fault Zone in the eastern North China Craton. The North China Craton, formed around 1.85 Ga, consists of Archaean to Proterozoic metamorphic basement rocks covered by Mesoproterozoic to Cenozoic sedimentary cover rocks (Figure 6). During the Mesozoic, the left-lateral Tan-Lu Fault, which trends north–northeast, displaced the Jiaodong terrane and the Sulu orogenic belt to their current positions. Mesozoic plutonic and volcanic rocks are widely exposed in the eastern part of the North China Craton. During this period, several extensional sedimentary basins and metamorphic core complexes developed. The Jiaodong Peninsula itself is divided into three tectonic units: the Jiaobei terrane, the Sulu orogenic belt, and the Jiaolai basin. The main lithology of the Jiaobei terrane consists of pre-Cambrian basement rocks and Jurassic to Early Cretaceous granitoids. Most of the gold deposits are located in the Jiaobei terrane, with a few smaller deposits distributed along the northern margin of the Jiaolai basin and the Sulu orogenic belt.

3.2. Data

3.2.1. Gravity Data

We adopted the Bouguer gravity anomaly (Figure 7) based on EIGEN6C4 obtained from International Centre for Global Earth Models (ICGEM). The map extends from 115° E to 123° E longitude and from 34° N to 39° N latitude, with a resolution of 0.05°.

The overall EIGEN6C4 Bouguer gravity anomaly in the Jiaodong region of Shandong shows a pattern of higher values in the east and lower values in the west, reflecting the characteristic that the Moho depth in the eastern part of the region is higher than that in the western part. The deposit is located at the edge of a high-value anomaly and lies between two major faults (the Tan-Lu Fault and the Wulian-Yantai Fault). The gradient of EIGEN6C4 Bouguer gravity clearly reflects the directions of the two faults.

3.2.2. Seismic Data

In this study, the lithospheric structure of Shandong was imaged using continuous seismic ambient noise data recorded by 47 broadband seismic stations (Figure 8). The data were collected from January 2014 to January 2015, with a sampling rate of 100 Hz. Based on the empirical Green’s functions (EGFs) from Yao et al., we estimated the inter-station Rayleigh wave phase velocity dispersion for all available station pairs. These Green’s functions were constructed from long-duration noise cross-correlation functions (NCFs). In this study, only vertical component records were considered to extract the Rayleigh wave phase velocity.

3.3. Results

In this study, we performed joint inversion of gravity and seismic data for the Jiaodong Bay region in Shandong using a cross-gradient-based inversion method in an ellipsoidal coordinate system. For the seismic data, our initial model was obtained from CRUST1.0 [54]. Four profiles near the gold deposits (AA’, BB’, CC’, and DD’) were selected, and the locations of these profiles and the inversion results are shown in Figure 9.

For marine-to-land profiles with uneven station distribution, such as DD’, the inclusion of gravity data can improve the inversion results, particularly in the coastal areas where results tend to be poor. Reciprocally, the good ambient noise quality in land areas helps enhance inversion accuracy for gravity data in land regions, indirectly improving the inversion results for gravity data in marine areas. A comparison of the results from the four profiles shows that the velocity results correspond well with the density results. The velocity profile results indicate that the Moho depth in the Jiaodong Bay area is approximately 30 km, with the Moho depth being slightly shallower in the eastern coastal region compared to the western land area. This is consistent with the characteristics reflected in the satellite EIGEN6C4 Bouguer gravity anomalies.

In Figure 9, it can be observed that between the Tan-Lu Fault and the Wulian-Yantai Fault, there is a distinct high-velocity, high-density body beneath the mineralized region, with its upper boundary located at approximately 10 km depth. Similar high-velocity, high-density bodies with depths ranging from 10 km to 20 km are also identified in the other three profiles near the two faults. This study suggests that the subduction of the western Pacific Plate caused significant upwelling of asthenospheric material, leading to the destruction of the North China Craton. The hot material, rising through fractures, reached depths of 10–20 km, contributing to the formation of gold deposits. The high-velocity, high-density bodies observed in the inversion results may represent the pathways through which the asthenospheric material ascended. This leads to a deep dynamic model for Jiaodong gold deposits.

3.4. Further Inversion

To further establish the relationship between metallogenic tectonics and gold deposits, we selected the gravity anomaly data from Sanshan Island for single inversion. Sanshan Island, located in the northwest of the Jiaodong Peninsula (the black rectangle in Figure 6), is characterized by diverse and complex geological conditions. The peninsula hosts a wide distribution of Precambrian cratonic metamorphic basement rock series, magmatic intrusions from multiple tectonic–magmatic periods, and brittle fracture structures formed since the Mesozoic, predominantly oriented in the NNE and NE directions. These factors collectively contribute to the region’s richness in gold deposits. Jiaodong gold deposits are sourced primarily from Archean mantle-derived metamorphic rock series and Jurassic crust-derived remelting granites, such as Linglong granite. Early Cretaceous magmatic activity provided the necessary heat to activate gold-bearing fluids, while the fault structures served as pathways and spaces for the migration and enrichment of gold.

The survey area is located in the coastal shallow sea area of Laizhou Bay in Shandong Province, specifically in the northern sea area of Sanshan Island. Seabed gravity data are obtained using an INO gravimeter (Sintrex, Quebec, QC, Canada), and the 1:50,000 Bouguer gravity anomaly is shown in Figure 10.

To obtain a more accurate understanding of the regional structure, we first applied the TILT (tilt derivative [55]) to the anomaly. Based on the Bouguer gravity anomalies and TILT results, we identified the fault distribution, as shown in Figure 11.

$$TDR=\mathrm{atan}{\displaystyle \frac{\frac{\partial m}{\partial z}}{\sqrt{{\left(\frac{\partial m}{\partial x}\right)}^2+{\left(\frac{\partial m}{\partial y}\right)}^2}}}.$$

(20)

In the Jiaodong Peninsula, gold deposits larger than 100 tons are mainly concentrated along the F1 fault and the known onshore segments of the F8 and F10 faults, while the portions of F8 and F10 within our study area extend into the sea and currently lack confirmed mineralization. Based on the fault division shown in Figure 11 and the inversion results shown in Figure 12, Figure 13 and Figure 14, it can be inferred that the overall depth scale of the northeast fractures is larger and the depth scale of the northwest fractures is smaller, which can be categorized into three types of fractures. Small-scale fractures are minor faults characterized by insignificant density changes on either side of the fractures. They are not associated with mineralization and thus hold limited relevance for further exploration. Mesoscale fractures exhibit significant density differences on both sides and act as shallow upward migration pathways for mineralized materials. These structures are associated with mineralization and warrant attention, particularly at the intersections of multiple mesoscale fractures, which provide more favorable transport and accumulation spaces for mineralized materials. Large-scale fractures exhibit substantial density contrasts on either side of the faults. These fractures serve as key indicators of mineralized zones. The gravity field in these areas is characterized by southward-bending gravity anomaly contours, accompanied by pronounced residual gravity anomalies. This suggests the presence of granite intrusions within the metamorphic zone along these fractures, making them significant for understanding the region’s mineralization processes.

To further evaluate the effectiveness of the joint inversion method, we compared the inversion results along three profiles (L1, L2, and L3), as shown in Figure 15. For each profile, the left panel presents the joint inversion result from Section 3.3, while the right panel compares the inversion results between two methods, limited to the 0–5 km depth range.

The comparison reveals that the joint inversion results exhibit better structural continuity and more clearly defined anomaly boundaries than the gravity-only results. In the joint inversion profiles, the density anomalies are more coherent and better aligned with the expected geological features. These findings demonstrate that the incorporation of seismic information, even when station coverage is sparse, significantly improves the resolution and geological interpretability of the inversion results.

However, due to the differences in data resolution, large-scale satellite gravity data are more sensitive to deep structures and thus contribute to an increased understanding of the genesis of gold deposits. In contrast, small-area gravity data exhibit higher resolution and are more sensitive to shallow geological bodies, enabling the detection of more accurate shallow fault information. Therefore, in discussion, the delineation of gold mineralization zones in the Sanshan Island area is based on the higher-resolution results obtained from the single gravity inversion.

4. Discussion

Considering existing research findings and the distribution of gold deposits, we focused our study on the main deposit-controlling fault (F1). To further interpret the characteristics of the ore-controlling structures, three profiles were selected within the study area to reveal the features of the faults, as shown in Figure 16.

To obtain results in more detail, we calculated the gradients through the squared sum of the residual density inversion results in the x, y, and z directions, respectively. The calculation was performed as shown in (21). To better present the results, the gradient values were normalized.

$$m_{grad}=\sqrt{{\left({\displaystyle \frac{\partial m_g}{\partial x}}\right)}^2+{\left({\displaystyle \frac{\partial m_g}{\partial y}}\right)}^2+{\left({\displaystyle \frac{\partial m_g}{\partial z}}\right)}^2}.$$

(21)

The F1 fault is the main ore-controlling fault in the area, located in the central part of the surveyed region. It extends into the sea at both the southern and northern ends, with an overall strike of NE and a dip towards SE, controlling an area of approximately 43 km. In the middle section of the fault, it exhibits a large-scale gravity anomaly with significant horizontal variation in both the Bouguer gravity anomaly and TILT, reflecting a gravity gradient belt.

L1 passes through known gold deposits on land. According to the interpretation results of L1, F1 shows variations in the dip angle with depth. Studies on the metallogenic tectonics of terrestrial gold deposits indicate that gold mineralization is predominantly concentrated in relatively flat segments of faults, particularly in transition zones between high-angle and low-angle fault segments. These zones are considered favorable sites for gold enrichment [56]. In contrast, the F8 fault is relatively upright, making it less conducive to gold enrichment.

The southern segment of F1 exhibits the characteristics of a gravity gradient belt, extending approximately along a 220° strike. It intersects with the F9 fault and continues southward, being displaced by the F6 fault. The gravity field characteristics show that the gravity anomaly contour lines bend southward in the same direction, indicating granite intrusion along the fault within the metamorphic rock zone. L2 is positioned in the southern part of F1, crossing four faults: F1, F2, F3, and F4. It can be observed that F1 still exhibits variations in steepness with depth. Additionally, F3 and F4 show similar characteristics, indicating the potential presence of large-scale gold deposits in this area.

F1 extends from the northern section of the Sanshan Island gold mine into the sea and is displaced by two NW-trending faults, F17 and F21. On the Bouguer gravity anomaly map, it shows synchronous bending of the contour lines, reflecting the characteristic of the fault being cut by later NW-trending fault displacements. L3 is located in the north of F1 and crosses through four faults: F1, F16, F19, and F20. It can be observed that, except for F1, the other three faults are relatively vertical and do not possess characteristics for mineralization.

Based on the explanation above, we made a prediction of the gold deposits in the sea area around Sanshan Island, as shown in Figure 17.

5. Conclusions

We apply the joint inversion method of satellite gravity and teleseismic ambient noise cross-gradient in an ellipsoidal coordinate system to conduct a genesis analysis of the giant gold deposits in the Jiaodong Bay region, Shandong. Due to the lack of seismic stations in the coastal areas, the imaging resolution of ambient noise is insufficient. By incorporating satellite Bouguer gravity anomaly data, a more detailed underground material distribution can be obtained. The joint inversion results show that between the two major fault zones—the Tan-Lu Fault and the Wulian-Yantai Fault—near the known gold deposits, there is a high-velocity, high-density body, with its upper boundary located at approximately a 15 km depth. This result is in good agreement with the proposed mineralization mechanism model. Therefore, it is speculated that the upwelling of gold-bearing hydrothermal materials, induced by the subduction of the Pacific Plate, led to the destruction of the North China Craton. These hydrothermal fluids then migrated upwards along the fractures, reaching around 15 km, where they cooled and formed giant gold deposits [57,58,59]. The high-velocity, high-density body in the joint inversion results is likely the pathway for the upward migration of the hydrothermal materials. In addition, we further inverted the gravity anomalies in the Sanshan Island area, identified the fault distribution, and predicted the locations of gold deposits in the offshore region.