Utilising Macau Science Satellite-1 Data and Comprehensive Datasets to Develop a Lithospheric Magnetic Field Model of the Chinese Mainland

Abstract

We incorporated a comprehensive dataset encompassing recent measurements from satellites such as the Macau Science Satgellite-1 (MSS-1), Swarm, and CHAMP, as well as aero and ocean magnetic measurements, alongside ground-based data from 1936 to 2000. This amalgamation is the basis for constructing a lithospheric magnetic field model of the Chinese mainland, employing the three-dimensional Surface Spline (3DSS) model. Additionally, we used the World Digital Magnetic Anomaly Map (WDMAM)-2.1 and CHAOS-7.13 models to address data gaps horizontally and vertically. To evaluate the efficacy of the new model, we compared it not only with established models such as SHA1050, NGDC720, and LCS-1 but also with the new model excluding the MSS-1 data. The results show a high agreement between the 3DSS model and other global models at a spatial resolution of 0.05°. Furthermore, we inspected the rapid variations in the magnetic field with increasing altitude, demonstrating a smooth transition across the altitudes covered by the three satellites. Error analyses reflected the importance of MSS-1 data, which contributed notably to modelling by capturing finer-scale magnetic structures. The increased data availability correlated positively with the model’s accuracy, as evidenced by the Root Mean Square Error (RMSE), registering an optimal value of 0.02 nT. The new model reveals additional geological details in southern Tibet, northeastern Inner Mongolia, and the adjacent areas of Liaoning and Jilin provinces, which are not discernible in other global models. The relationship between these anomalies and heat flow in northeastern China appears less evident, suggesting a complex interplay of orogenic processes and surface mineralogy in shaping these magnetic signatures.

1. Introduction

The lithospheric magnetic field is an important component of Earth’s magnetic environment, encompassing the magnetic properties of the solid outer layer of the planet known as the lithosphere. This magnetic field is generated by various processes within Earth’s interior, primarily through molten iron and nickel movement in the outer core. Unlike the global geomagnetic field, primarily studied through observations from satellites and ground-based instruments, the lithospheric magnetic field pertains specifically to the magnetic properties of Earth’s crust and upper mantle. Understanding the lithospheric magnetic field is essential for various scientific disciplines, including geology, geophysics, and planetary science, as it provides valuable insights into the composition, structure, and tectonic history of Earth’s lithosphere.

The lithospheric magnetic field of the Chinese mainland is a subject of significant geological interest and study. It is primarily influenced by the distribution of magnetic minerals within the Earth’s crust and their alignment with the Earth’s magnetic field over geological time. Due to the diverse geological history and tectonic activity, the Chinese mainland exhibits a complex lithospheric magnetic field. Regions such as the Tibetan Plateau and the North China Craton display distinct magnetic signatures, reflecting variations in crustal composition, age, and thermal history. These magnetic anomalies are valuable indicators for understanding crustal dynamics, geological evolution, and tectonic processes within the Chinese mainland [1].

The advancement of magnetic satellite technology since 1999, with notable launches such as the Ørsted [2] and CHAMP [3] satellites, has ushered in an era of geomagnetic modelling with high data quality. The subsequent deployment of the Swarm constellations [4] in 2013, consisting of three identical satellites (Alpha, Charlie in lower orbits, and Bravo in a higher orbit), aimed to perfectly explore the Earth’s geomagnetic field and its temporal evolution. These developments have generated numerous geomagnetic field models over the past decades. In the domain of lithospheric magnetic field modelling, efforts can be broadly categorised into comprehensive models, exemplified by the CM series [5,6,7] and CHAOS series [8,9] and sequential models like the MF series [10], LCS-1 [11], and NGDC720 [12]. Advancements in computational capabilities and algorithmic optimisation have enabled these models to achieve high truncation degrees, such as reaching 1050 [13], corresponding to structures with wavelengths of approximately 38 km. A recent milestone in this domain is the successful launch of the Macau Magnetic Satellite-1 (MSS-1) on 21 May 2023, which employs advanced fluxgate and scalar magnetometers mounted on a stable optical bench. MSS-1 operates in lower-latitude orbits, inclined about 41° to the equatorial plane at approximately 450 km [14], and has delivered high-quality magnetic vector and scalar data.

The geological diversity of China, characterised by its mountains, basins, and deserts, in conjunction with the dynamic variation in plate movements, contributes significantly to the intricate nature of the lithospheric magnetic field. This complexity is exemplified by phenomena such as the strong positive anomalies juxtaposed with neighbouring negative anomalies in western Xinjiang [15] and the distinctive anomaly patterns observed in the country’s southern regions. Before the turn of the millennium, regional magnetic field modelling in China primarily relied on regional modelling techniques (e.g., Taylor polynomial by Le Mouel [16]; Spherical cap harmonic by Haines [17]; Rectangle harmonic by Alldredge [18]; and Surface Spline by An et al. [19]) and regional data sourced mainly from ground observatories and repeat stations [20]; Feng et al. [21]. The inclusion of satellite data, notably following the availability of Ørsted satellite data (Ou et al. [22]; Jiang et al. [23]; Wang et al. [24]; Yang et al. [25]; Feng et al. [26]), marked a pivotal shift in magnetic field studies in China, particularly in investigating large-scale lithospheric fields. In addition to utilising global models, novel methods such as the revised Spherical cap harmonic analysis (RSHA) model (Thébault et al. [27]), the three-dimensional Surface Spline model (3DSS) (Feng et al. [21]), and the depleted-based model (Jiang et al. [23]) have emerged or been updated. When integrated with satellite data or models, these methodologies exhibit enhanced performance in regional analyses, yielding more precise distributions with increased spatial resolution.

However, previous studies exhibit certain limitations, such as the gap between ground-based and satellite-derived data, the rapid decay of the lithospheric field when relying solely on satellite data, and the need for data consistency beyond satellite sources. We propose to address these shortcomings and generate a more robust lithospheric magnetic model of the Chinese mainland through comprehensive datasets from multiple sources. Besides the new MSS-1 data, these sources encompass ground-based data spanning from 1936 to 2000, the most coherent domestic aeromagnetic data available at a 10 km resolution, data from the World Digital Magnetic Anomaly Map (WDMAM v2.1) at a 5 km resolution as curated by Lesur et al. [28], satellite data from missions such as Swarm and CHAMP operating at low orbits, global aeromagnetic and oceanic data including the geographical vicinity of China, and CHAOS-7.13 data to address data gaps. These datasets will be amalgamated using the 3DSS method to construct an integrated Chinese lithospheric field model with high spatial resolutions.

2. Data

This study systematically collected comprehensive datasets encompassing China and its surrounding regions to construct an integrated spatial model. All datasets will be introduced from the ground to the satellite level.

2.1. Ground Data

The ground-based data uniformly covering the entire Chinese mainland have been selected as the foundational dataset, which comprises measurements such as inclination (I), declination (D), horizontal component (H), and vertical component (Z). The Chinese national geomagnetic field surveys were implemented in 1936.0, 1950.0, 1960.0, 1970.0, 1980.0, 1990.0, and 2000.0 and later, the data number detailed in Figure 1. These data were measured and sourced from the Institute of Geology and Geophysics, Chinese Academy of Sciences. The accuracy and quality of data are uniformly processed; for example, the way to mitigate diurnal fluctuations and disturbances at the repeat stations is to refer to the closest geomagnetic observatories.

A selection process was conducted to prioritise data points closely aligned with the lithospheric field of CM4 (Sabaka et al. [5]), which can divide the geomagnetic field into internal (core and crustal fields) and external (ionospheric and magnetospheric fields, and their induced fields) parts. The IGRF13 (Alken et al. [29]) was employed to subtract the core field part from 1936.0 to 1950.0 data points to ensure the integrity and consistency of anomaly data. Similarly, data points from 1960.0 to 2000.0 were adjusted using the CM4 model. Furthermore, efforts were made to mitigate external noise, particularly from large-scale magnetospheric ring currents, by applying the CM4 model. In total, 3137 ground data points were included in the modelling after the data processing.

2.2. Chinese Aeromagnetic Data

The aeromagnetic measurement data utilised in this study were sourced from China’s Aero Geophysical Survey and Remote Sensing Centre for Natural Resource, spanning 1970 to 2011. These data constitute scalar data grids obtained at an altitude of 1 km, comprising 97,994 valid data points covering an area of 979.6 km² (Xiong et al. [30]). Notably, these data are recognised for their high level of consistency within the Chinese context, representing the most reliable magnetic data available for the region. With a spatial resolution of 10 km × 10 km, these data provide an ideal basis for investigating the national magnetic field, facilitating a detailed analysis of the lithospheric field distribution. Given the computational constraints and the need to balance various data sources, this study selected a total of 12,511 unique aeromagnetic points to construct the model.

2.3. Satellite Data

We use the scalar data from 2 January 2010 to 3 September 2010 from the CHAMP mission between a quasi-dipole (QD) latitude equatorward of ±55° with 1 sec sampling when the orbit was around 280 km. In 2010, the altitude of the CHAMP data was around 280 km, which is suitable for lithospheric field modelling. We used a MAGA_LR_1B_1Hz calibrated data product from the Swarm mission, with a 1 sec sampling from just Swarm-A scalar data from 1 January 2014 to 30 June 2014; during this period, the solar activity was relatively low.

The Macau Science Satellite-1 (MSS-1), positioned in lower-latitude orbits inclined at 41° to the equatorial plane and maintaining an altitude of approximately 450 km, was successfully launched in 2023. This satellite has generated exceptionally high-quality geomagnetic data [14]. Given the initial instability encountered during the early phase of MSS-1 operations, the selected data are dense enough to cover the middle and southern parts of the study area, so we selected a subset of data spanning only 14 days, following careful filtering processes. Ongoing efforts involve the continuous enhancement of data preprocessing and standardisation procedures, with plans for imminent public dissemination. We exclusively utilised vector data for our analysis stemming from the MSS-1 mission, owing to the observed instability in scalar data. Specifically, we focused on vector data points collected between 18 August 2023 and 31 August 2023, within latitudes equatorward of ±41°, each recorded at a 1 sec sampling interval. The satellite data selection criteria mainly follow what is outlined in the CHOAS-7 model [9].

(I) The data from the dark regions (sun at least 10° below the horizon) are chosen.

(II) Kp ≤ 2° and |RC| ≤ 2 nT/h RC index are used.

(III) All vector and scalar data selected are from latitudes equatorward of ±55° QD, which cover the study area.

(IV) The data are chosen for when the average electric field at the magnetopause over the previous 2 h was Em ≤ 0.8 mV/m. The IMF Bz index at the magnetopause, averaged over the previous 2 h, is positive.

The assessment excludes along-track variations, focusing solely on developing a regional model for middle latitudes. Consequently, the large-scale magnetospheric field component is removed from the satellite model.

The scalar data recorded by Swarm-A total 18020804 data points, while the CHAMP scalar data amount to 2226206 data points, and the Swarm vector data comprise 1164392 data points. The accompanying figures (Figure 2, Figure 3 and Figure 4) illustrate the global and regional distributions and the data quantities:

2.4. Global Aero and Oceanic Data

In regions beyond the mainland where domestic measurements are lacking, we aggregated and integrated aero and oceanic data sourced from reputable institutions such as the National Oceanic and Atmospheric Administration (NOAA) (http://www.ngdc.noaa.gov/geomag/aromag.shtml (accessed on 1 May 2024)), the United States Geological Survey (USGS) (http://mrdata.usgs.gov/magnetic/surveys.php (accessed on 1 May 2024)), and the National Science and Technology Infrastructure (NSTI) (https://mds.nmdis.org.cn/pages/dataViewDetail.html?dataSetId=44 (accessed on 1 May 2024)).

The marine and aero data comprise 66435635 and 23826681 data points, respectively. This distribution strategy is illustrated in Figure 5. Including these datasets significantly aids in constraining the modelling efforts beyond the designated study area. This study employed 500 data points each from the marine and aero datasets. Considering data compatibility, only data from similar instruments and repeating tracks were selected. Subsequently, a regional model was constructed and compared with other global models. The data were then categorised into three levels—A, B, and C—and only the level A data were incorporated into the modelling process.

2.5. Satellite Model Data

Two types of complementary data are used in the modelling process. Empirical evidence from experiments shows that the satellite geomagnetic model serves as an effective constraint for the modelling. Consequently, the lithospheric field prediction from the CHAOS-7.13 model was selected for integration. Specifically, a systematic approach was employed to uniformly select 9380 CHAOS predictions covering distances from 0 to 500 km, with each interval spanning 100 km and with a resolution of 0.05°. This selection process significantly mitigates boundary effects by ensuring comprehensive coverage and control over data points, thereby facilitating the creation of a comprehensive integrated model.

The WDMAM 2.1 data with a resolution of 5 km, as detailed in Lesur et al. [28], were selected to provide constraints for modelling at a 5 km level, offering extensive geographical coverage of scalar anomalies. In WDMAM-2.1, the structures corresponding to spherical harmonic (SH) degrees ranging from 16 to 100 were derived from the GRIMM_L120 lithospheric field model, which was downward continued to an altitude of 5 km. A total of 4546 points were ultimately chosen for the modelling process.

To assess the impact of the quantity of data on the regional model, we systematically increased the number of Chinese aero and satellite data points by approximately 1.2 times in four stages, which resulted in the use of 31860, 35113, 39042, and 41227 points (see

Table 1. Four combinations of modelling data.

	Ground Data	Chinese Aero Data	MSS-1 Data	Swarm Data	CHAMP Data	Marine Data	Aero Data	WDMAM Data	CHAOS-7.13 Data	Total
3DSS31860	3137	4900	3261	2571	3065	500	500	4546	9380	31860
3DSS35113	3137	6533	4076	2938	3503	500	500	4546	9380	35113
3DSS39042	3137	9800	4348	3116	3715	500	500	4546	9380	39042
3DSS41277	3137	10889	5017	3427	3831	500	500	4546	9380	41227

) to develop the four 3DSS models. We study only the total intensity throughout this study because the aeromagnetic data are scalar.

3. Methods

3.1. Three-Dimensional Surface Spline Model

The 3DSS model is the empirical model based on numerical interpolating theory. This regional model is very appropriate for modelling the complicated geomagnetic region, so the anomalies with different scales can be significantly reflected [21]. Based on the two-dimensional Surface Spline (2DSS) model proposed by An et al. [19], Feng et al. [21] introduced an altitude variable, thereby extending the model to a three-dimensional context, known as the three-dimensional Surface Spline (3DSS) model. The mathematical formulations for the 3DSS model are outlined as follows:

$$W=a_0+a_{1}x+a_{2}y+a_{3}z+{\displaystyle \sum _{i=1}^M{F}_i{r}_i^2\ln (r_i^2+\epsilon )}$$

(1)

$${\displaystyle \sum _{i=1}^M{F}_i}={\displaystyle \sum _{i=1}^M{x}_i{F}_i}={\displaystyle \sum _{i=1}^M{y}_i{F}_i}={\displaystyle \sum _{i=1}^M{z}_i{F}_i}=0$$

(2)

The variables in the equation include a geomagnetic component denoted as $W$; $x,y,z$ corresponds to the latitude, longitude, and altitude, respectively; $r_i^2={(x_i-x)}^2+{(y_i-y)}^2+{(z_i-z)}^2$; $M$ represents the total number of data points; $a_0,a_1,a_2,a_3$, and $F_i$ are undetermined coefficients; $x_i,y_i,z_i$ denote the latitudes, longitudes, and altitudes of all measurement locations; and $\epsilon$ is a small constant chosen typically as 1 × 10⁻⁷ to control surface curvature changes.

The coefficients can be determined using backward substitution, one of the Gaussian elimination methods, expressed as a form of the upper triangular system $c_i=(b_i-{\displaystyle \sum _{k=i+1}^n{u}_{ik}{c}_k)/u_{ii}},i=n,n-1,\dots ,1$, where $u_{ik} \mathrm{and} b_i$ are upper triangular elements over diagonal and left side values after i steps, n signifies the number of measurement points, and $c_i$ are coefficients.

3.2. Other Models

In addition to the 3DSS model, this study incorporates global geomagnetic models, namely SHA1050, LCS-1, and NGDC720, which employ higher truncation degrees. Thébault et al. [13] developed a global magnetic field model using Swarm, CHAMP data, WDMAM-2 grid data, and the R-SCHA model. They extended N_max to 1050 and achieved excellent agreement with prior models. Their analysis focused on anomalies within the South Atlantic Anomaly (SAA) region, highlighting changes in the sign of secular acceleration in element Z over the Pacific Ocean. The LCS-1 model [11] was exclusively derived from satellite data, featuring coefficients identical to CHAOS-7 for N > 25. The NGDC720 model [12], with N_max = 720, is also included for comparison purposes. Developed by the National Geophysical Data Center (NGDC) of the United States, this model combines data from satellite observations and ground, oceanic, and aeromagnetic surveys.

These models are all founded on spherical harmonic functions or closely related variants such as the LCS-1 and SHA1050 models. They assume that the magnetic scalar potential can be represented as $\mathbf{B}=-\nabla V$ and divided into the sum of internal and external parts.

4. The Distribution of the Lithospheric Magnetic Field

In this section, we show the spatial distribution of the new lithospheric field model at a 1 km level because the aeromagnetic data at such a level are the most consistent. Additionally, we present magnetic field variations at various altitudes and provide a comparative analysis with other global models.

4.1. The Distributions of the Lithospheric Magnetic Field at 1 Km Altitude

Four 3DSS models were constructed utilising different data quantities, as outlined in Table 1, with a spatial resolution of 0.05°. These models were subsequently compared with the NGDC720, SHA1050, and LCS-1 models, along with aeromagnetic survey data, as depicted in Figure 6.

Based on the figures above, it is evident that most figures demonstrate consistency, except for LCS-1, which is characterised by a degree of 185 and reflects a wavelength structure of only 216 km. NGDC and SHA1050 exhibit a high degree of similarity owing to their similar modelling datasets; however, the representation of Tibet’s distribution still needs to be clarified. Upon comparison with aeromagnetic data, after a thorough examination, the 3DSS₄₁₂₂₇ model exhibits the most significant consistency, particularly in the large-scale regions of southwest Xinjiang and the small-scale regions of northeast China. As the modelling data diminish, the structure of the 3DSS models becomes more simplified. Artefacts along the coastline are observed, which result from the incompatibility between the mainland data and various complementary datasets. After all, the 3DSS model still provides a more detailed depiction than global models.

4.2. The Distributions of the Lithospheric Magnetic Field at Different Altitudes

We present the magnetic field distributions at various altitudes to examine the variation in the magnetic field. We test rapid fluctuations near the surface (the colour bars are the same) by plotting the magnetic field at 0.2 km intervals in Figure 7. Moreover, we assess the average change from the surface to satellite levels, where the colour bars differ. Notably, all figures depicted below used a fixed 30° elevation angle.

From surface elevations up to 1.6 km, a discernible transition in structural complexity is observed at the 1 km level, followed by a subsequent simplification. This pattern correlates with the corresponding changes in data density at these altitudes. Notable shifts in magnetic field characteristics are obvious, such as the rapid magnetic inversion between the positive western region of Tibet and the negative northern region of Heilongjiang as altitude increases. At higher elevations, structural features exhibit relative stability. Beyond 100 km, there is a gradual attenuation in distribution amplitudes, ultimately leading to a stabilised overall distribution pattern. Remarkably, the distributions from the three satellites, particularly that from the MSS-1 satellite, show a high similarity with the structures at other altitudes, indicative of the quality and reliability of the satellite data.

5. The Error Analysis

This section will analyse the differences between the new model and other models. Furthermore, we will evaluate the forward modelling capacity by testing points that are outside the scope of the initial modelling process.

5.1. The Differences Among 3DSS, NGDC720, and SHA1050 Models

Based on the latest MSS-1 satellite data, a heightened focus has been directed towards regions from 41°S to 41°N, significantly impacting the ultimate model’s accuracy. Our initial analysis entails contrasting the distributions of the 3DSS₄₁₂₇₇ models, inclusive and exclusive of MSS-1 data, at an altitude of 457.08 km, which is the average altitude of the MSS-1 data (Figure 8).

The preceding figure illustrates the subtle distinctions between the two models; nevertheless, the new satellite data reveal five small differences below 41°N. Specifically, two differences are observed in the western regions of Tibet and the Jiangsu–Anhui provinces, while other differences are identified in western Xinjiang, eastern Tibet, and the Guangxi–Guangdong provinces. These five differences are roughly discernible in the figure at 1 km altitudes.

For a further comparison, we analyse the grid differences between the 3DSS and the SHA1050 models and present them in Figure 9. Initially, we generate a difference map without imposing any limitations on the values (Figure 9a), followed by applying a limit (Figure 9b) to enhance the visualisation of the finer details.

Figure 9 depicts a comparative analysis between the 3DSS and the highest degree model SHA1050. Figure 9a highlights that the differences are predominantly negligible, hovering around zero, except for a few outlier data points. In contrast, Figure 9b reveals a noticeable increase in anomalies when strength limitations are applied. These positive and negative anomalies are particularly concentrated in the northeastern and northwestern regions of China, notably Tibet, where both global models lack data. This observation suggests that the new model exhibits greater reliability, attributed to its denser data distribution near the surface. Figure 9c indicates the small difference between the two global models.

5.2. Error Test

To evaluate the efficacy of the new model, considering the Surface Spline is a numerical interpolation technique that approximates values across all modelling datasets, we implemented two methodologies. The first involved randomly selecting nine points from a comprehensive dataset and utilising the remaining data to generate models (denote 3DSS₃₁₈₅₁, 3DSS₃₅₁₀₄, 3DSS₃₉₀₃₃, and 3DSS₄₁₂₁₈). Subsequently, we calculated the model forward values of these nine points and compared them against others. The second approach entailed randomly selecting 5%, 10%, 20%, and 33.33% of the data from the four 3DSS models to be absent datasets to mitigate potential coincidences. We then constructed models using the remaining data and evaluated their performance by approximating these absent data and contrasted the forward approximations with those from three global models, as outlined in

Table 2. A comparison of 9 fixed absent points of four 3DSS models. Units: ° and nT.

Latitude	Longitude	Altitude	Absent Data	3DSS31851	3DSS35104	3DSS39033	3DSS41218	CHAOS-7.13	NGDC720	SHA1050
36.94	121.90	0.007	−152.94	−152.94	−153	−153	−152.94	−25.17	43.23	−18.26
35.59	119.21	1.00	201.86	−31.32	166.27	−31	201.86	31.70	−81.73	15.91
48.24	89.97	498.63	−3.45	−3.55	−3.22	−3.01	−3.47	−3.43	−0.94	−3.31
39.56	117.66	306.73	0.84	1.05	1.11	0.98	0.82	0.84	1.88	1.06
37.72	84.85	453.01	3.63	3.69	3.86	4	3.57	3.61	5.44	3.49
29.86	130.79	0	−7.05	−7.04	−7.13	−7.14	−7.05	13.51	4.27	−6.34
26.84	128.39	1.52	−33.17	−33.17	−33.24	−33.25	−33.18	−16.69	−22.16	−7.27
34.15	112.15	5.00	−58.46	−58.46	−58.48	−58.48	−58.46	−31.92	−12.63	−52.71
35.80	112.80	200.00	0.13	0.14	0.22	0.26	0.11	0.13	2.02	0.06

.

The above table exhibits four 3DSS modelling values that demonstrate notable similarity and outperform global models. Optimal performance is achieved when more data are utilised, as indicated by the red column. Differences in ground data modelling arise from using varied measurement techniques and equipment, leading to inconsistency. The Root Mean Square Error (RMSE) values of seven models about absent data are 82.44 nT, 12.58 nT, 82.33 nT, 0.02 nT, 76.39 nT, 123.12 nT, and 81.72 nT, respectively. The errors may come from the different data treatments, the uneven points’ distribution in the horizontal and vertical directions, and the estimation of the external noises.

A random selection of varying percentages of modelling data is designated as absent data (test data). The subsequent analysis focuses solely on comparing the four 3DSS models, as detailed in

Table 3. The RMSE comparison of the different percentages of absent points. Units: ° and nT.

	3DSS1	3DSS2	3DSS3	3DSS4
5%	111.83	108.88	115.49	103.07
10%	109.13	105.00	105.80	98.96
20%	115.08	108.48	108.50	106.31
33.33%	114.97	117.61	108.34	109.95

, stemming from the first approach’s results. Specifically, the labels 3DSS₁, 3DSS₂, 3DSS₃, and 3DSS₄ correspond to 5%, 10%, 20%, and 33.33% absent points of the datasets 3DSS₃₁₈₆₀, 3DSS₃₅₁₁₃, 3DSS₃₉₀₄₂, and 3DSS₄₁₂₂₇, respectively.

The table above compares RMSEs for four different percentages of absent points. The model with more data shows slightly better performance than the other models. As the percentage of absent data increases, the RMSEs slightly increased by about 5.84%, implying that the new model is not very sensitive to the amount of data. For a clearer understanding of the results, the variations across different percentages are presented in Figure 10.

The presented figure illustrates the variation among the four models. It is found that the more absent data correlate with higher RMSE values. Furthermore, the model trained on a larger dataset exhibits decreased RMSE values, and vice versa. In conclusion, the 3DSS₄₁₂₇₇ model demonstrates superior precision within the study area.

6. Discussion

The lithospheric magnetic field arises from the induced and residual magnetic properties of crustal rocks [31], which are influenced by the geological structures of the Earth, particularly in mountainous regions and basins [32]. Regional magnetic anomalies are primarily attributed to magnetic geological formations at both surface and deeper crustal levels, reflecting variations in thickness, changes in magnetic mineral composition, and the spatial morphology of these magnetic formations. Satellite-derived magnetic anomalies indicate ancient, cold, and rigid stable blocks characterised by deep and thick magnetic layers in regions with low heat flow. The occurrence of large-scale satellite magnetic anomalies is predominantly associated with ancient shield areas. Magnetic anomalies observed closer to the Earth’s surface, such as aeromagnetic, are linked to magnetic sources of a certain scale (typically thousands of square kilometres or larger) situated below the Curie isothermal point (above the Curie isothermal surface).

Significant heat flow values may be associated with a shallow Curie surface. This notion was proposed by Gao et al. [33], who indicated a strong correlation between the topography of the Curie surface and heat flow values. Consequently, the relationship between heat flow and the magnetic field can be investigated through comparison. This study compares our new model with SHA1050 (Figure 11). Additionally, considering the well-documented correspondence between heat flow and the Curie point, which in turn influences the lithospheric field, we present the heat flow distribution of China based on 1230 measurements. Notably, 88.5% of the data collected aligns well with expectations, indicating high reliability in our results.

After carefully examining and referring to the aeromagnetic distribution, three distinct differences are denoted by red ellipses and circles. The first is the positive magnetic anomaly belt in southern Tibet (red ellipse) identified by the 3DSS model, which extends from northwest to southeast and includes a positive and negative magnetic anomaly extreme (29°24′N, 90°16′E), with intensities exceeding |400|nT. This magnetic anomaly stripe, prominently tracing the Gangdise Mountains, primarily arises from orogenic terrain features and magnetic minerals within the shallow lithospheric field [26]. The spatial alignment of this belt with heat flow patterns indicates a potential association with superficial ferromagnetic minerals such as Titanium magnetite, suggesting that the source of the lithospheric magnetic field may not be deeply rooted and could be influenced by near-surface geological compositions. However, the SH-based model fails to reflect this belt.

The second difference is located in the northeastern region of Inner Mongolia, where the predominant characteristic of the geological structure manifests through an east–west zoning pattern [34]. This zoning is observed in the Hailar Basin and the Erlian Basin, situated on the western flank of the Greater Khingan Mountains (red circle), where some Quaternary and Tertiary strata occur; its distribution is highly similar to the magnetic anomalies [35]. These geological features are often correlated with igneous rocks, frequently occurring in conjunction with geological structures such as faults, folds, and orogenic belts. Notably, the gradient zones delineated by positive and negative magnetic anomalies align with the zones where there are shallow igneous rocks or deep magnetic basement uplifts.

The third difference is located in the adjacent areas of Liaoning and Jilin provinces, where the magnetic field orientation within the Mudanjiang Dandong magnetic field areas predominantly aligns with the north–east and east–west directions. Large negative anomalies characterise these regions, with closely spaced positive anomalies distributed locally. These anomalies are primarily attributed to magnetic granite [36]. Wavelet analysis shows that the prevailing magnetic anomalies in the northeast region are predominantly negative. Moreover, the depth from the Curie isothermal surface within this area ranges from 10 to 23 km, with the northern area exhibiting greater thickness. The relationship between the observed anomalies in northeastern China and the associated heat flow remains to be seen, necessitating further heat measurements to elucidate these connections more comprehensively.

While the new model shows notable capability in accurately representing the lithospheric magnetic field over China, including middle and small-scale magnetic structures, several limitations of the 3DSS model warrant attention: 1. There is a challenge in attaining a pure lithospheric magnetic field, as it necessitates the evaluation of not only the main field and large-scale magnetospheric field but also factors such as small-scale ocean tidal flow and residual external fields (e.g., F region current, Polar Electrojet (PEJ) currents, the noise that remains in the filtered satellite data). 2. The modelling data are constrained by computational power, highlighting the need to enhance modelling algorithms to enable the inclusion of a greater volume of data, which is a challenge. 3. The data density influences the depiction of structures at different altitudes, emphasising the necessity for denser datasets.

7. Conclusions

We utilised the most recent MSS-1 satellite data, integrating with CHAMP, Swarm, ground-based measurements, and aeromagnetic data as a comprehensive dataset to mitigate uncertainties stemming from limited constraints. Additionally, we selected CHAOS and WDMAM data to create an integrated regional lithospheric magnetic field model. After examining the data’s distribution across various altitudes, conducting error tests, and performing preliminary geological analyses, we can draw two conclusions.

1. The new 3DSS model provides a satisfactory representation of the lithospheric field. The number of modelling data points at different altitudes influences the model’s level of detail but does not alter its fundamental structure.

2. MSS-1 data accounted for 12.17% and 40.87% of the total modelling data and satellite data, respectively. These data significantly contributed to the overall modelling accuracy, given its low-latitude orbit and exceptional measurement quality. Comparative analysis between models with and without MSS-1 data revealed that satellite data can effectively capture smaller and mid-sized magnetic structures.

The launch of the MSS-1 satellite means a promising opportunity to refine the model. However, the current data availability, both vector and scalar, could be improved due to instability in measurements and correction processes during the initial phase. It is anticipated that more MSS-1 data will become accessible shortly, thereby facilitating improvements.