# Magnetic Anomaly Data Detection of Local Marine Geomagnetic Field Model considering Robust Trend Surface Scientific Calculation Algorithm

Authors: Wei Su
Journal: Scientific Programming
 (2022)

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## Abstract

As a momentous part of marine data detection, modeling the marine geomagnetic field and detecting its magnetic data have momentous theoretical and practical value for obtaining its geomagnetic field parameters and characteristic distribution and then carrying out marine environment research. The detection of magnetic anomaly data of local marine geomagnetic field model has become a momentous prerequisite for obtaining key parameter info of local ocean and subsequent development and utilization. On account of this, this paper first analyzes the detection of local marine geomagnetic anomaly data, then studies the theoretical basis of local marine geomagnetic field model, as well as the measurement and modeling of local marine geomagnetic field data, and finally gives the analysis of the detection results of local marine geomagnetic anomaly data considering the robust trend surface.


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## Body

## 1. Introduction

At present, with the continuous rise of the global population and the continuous amelioration of people’s pursuit of living standards, the demand and consumption of various resources from all walks of life are also increasing. In this context, land resources have been unable to effectively meet people’s growing needs, and the ocean, which accounts for two-thirds of the Earth’s surface area, has become the focus of attention and research [1]. The marine environment is relatively complex. In order to fully tap the reserves of marine resources and provide rich and usable data and info support for the development and utilization of marine resources, it is necessary to conduct in-depth exploration, research, and analysis of marine structures. As a momentous part of marine data detection, modeling the marine geomagnetic field and detecting its magnetic data have momentous theoretical and practical value for obtaining its geomagnetic field parameters and characteristic distribution and then carrying out marine environment research.It is necessary and urgent to carry out local marine magnetic data detection in military and civil fields. On the one hand, through the detection of local marine geomagnetic parameters, the data of water depth, foreign language, and gravity field distribution can be obtained, so as to provide momentous hydrological support for the development of marine channels; on the other hand, marine magnetic anomaly data detection is also a momentous carrier and means to obtain seabed landform, material composition, and gravity characteristics. The most intuitive goal of local marine geomagnetic field modeling and magnetic anomaly data detection is to obtain the distribution law and typical characteristics of local marine geomagnetic field. It can be seen that the detection of magnetic anomaly data of local marine geomagnetic field model has become a momentous prerequisite for obtaining key parameter info of local ocean and subsequent development and utilization.In addition, in the field of military utilization, the magnetic anomaly data detection of marine geomagnetic field model can effectively help carry out relevant operations in many aspects as shown in Figure1, so as to ensure the safety of the sea area [2]. In the civil field, with the help of high-precision detection of marine geomagnetic data, momentous resources on the seabed can be found, including sunken ships and minerals. The momentous value of magnetic anomaly data detection of local marine geomagnetic field model makes relevant detection methods and equipment emerge continuously, and fruitful results have been achieved. The magnetic anomaly data detection of marine geomagnetic field involves many aspects, which has high complexity and difficulty. It needs the organic coordination and cooperation between various links; otherwise, it will have a direct adverse impact on the detection results. Therefore, it is very necessary to develop an intelligent, integrated, and reliable detection algorithm.Figure 1
The field of magnetic anomaly data detection of marine geomagnetic field model.The traditional marine geomagnetic field model magnetic anomaly data detection relies on manual intervention and experience, which is not only cumbersome, but also has high time cost, poor accuracy, and reliability [3]. The construction of local marine geomagnetic field model is to establish the magnetic field model in the two dimensions of main magnetic field and abnormal field, so as to intuitively and accurately display and describe the observed data. In addition, the construction of local marine geomagnetic field model needs to be carried out on account of the principles shown in Figure 2, so as to ensure the convenience, feasibility, and expansibility of the algorithm while obtaining a robust marine geomagnetic field model.Figure 2
Construction principles of local marine geomagnetic field model.The detection process of marine magnetic data has typical dynamic characteristics and is easily disturbed and affected by various internal and external factors, resulting in various errors. Compared with the land environment, the marine environment has stronger instability, so there are more interference factors. It is necessary to eliminate the cumulative error to ensure the detection accuracy and the availability of detection data. The traditional detection methods of marine magnetic data have some disadvantages, such as insufficient accuracy and poor anti-interference [4]. The anti-difference trend surface method is used to establish the corresponding function and eliminate the gross error, so as to effectively measure the data while judging the anomaly of marine magnetic data. Therefore, it is of great practical value to carry out the magnetic anomaly data detection of local marine geomagnetic field model on account of the scientific calculation algorithm of robust trend surface of ancient books.


## 2. Detection of Local Marine Geomagnetic Anomaly Data

### 2.1. Typical Characteristics of Local Marine Geomagnetic Field

As the product of the interaction of internal and external currents, the distribution and law of local marine geomagnetic field are quite different in time and space. The Earth’s magnetic field and its dipolarity are mainly caused by the current flowing in the conductive liquid core. The magnetic induction intensity of local marine geomagnetic field can be expressed by (1), where β and α are permeability and magnetic susceptibility, respectively, and β0 is vacuum permeability.(1)B⇀=βH⇀=β01+αH⇀=β0H⇀+M⇀.The local marine geomagnetic field is mainly composed of endogenous and exogenous parts, in which the endogenous field is composed of basic magnetic field and abnormal magnetic field; the external field is mainly composed of stable magnetic field and variable magnetic field, as shown in (2). T0+Tm is the endogenous field, and δT+Tse is the exogenous field. In the process of detecting the local ocean geomagnetic anomaly data, the selection of Ta is often a relative concept because there are great differences in the detection object, the selected local ocean range, and the sea depth of the local ocean.(2)T=T0+Tm+Ta+δT+Tse.Paramagnetic materials will be organically sorted in the direction under the action of external magnetic field, and the value ofα will also change [5]. The detection of local marine geomagnetic anomaly data will help to understand the evolution process of regional marine magnetic field and the variation law of magnetic field intensity and further clarify the structure, expansion, and climate of regional seabed plate.


### 2.2. Local Marine Geomagnetic Anomaly

The geomagnetic anomaly is mainly caused by the superposition and interference between the local magnetic field of rocks and minerals with magnetism in the shallow crust and the basic magnetic field of the Earth. The magnetic anomaly of local marine geomagnetic field is complex. In order to carry out relevant research, it is usually necessary to simplify the model of local marine geomagnetic field. Firstly, it is assumed that the shape of the local marine geomagnetic body is regular and simple, and the interference between geomagnetic bodies is not considered. Secondly, assuming that the magnetism of the local marine geomagnetic is relatively uniform, there are multiple methods to calculate the local marine geomagnetic field, including Poisson, volume, and area fraction [6]. The calculation of local marine geomagnetic gravity magnetic potential field is shown in (3) and (4), where ρ is density, GA is gravity potential, and C is magnetic potential.(3)GA=Gρ∫∫V∫1rdv,(4)C=−14πGρM⇀•∇GA.On the premise of obtaining the gravitational potential of the local marine geomagnetic field model, the expression of each component of the magnetic field can be obtained. In addition, the process of local marine geomagnetic field magnetic detection is easy to disturb by submarine cables represented by optical cables and cables. Therefore, before detection, it is necessary to accurately locate the submarine cables, so as to avoid the interference of submarine cables with and their influence on the measurement results, so as to better ensure the accuracy of the measured magnetic anomaly data.


### 2.3. Method for Detecting Local Marine Geomagnetic Field

At present, as one of the common means of local marine geomagnetic field detection, towed marine survey ship mainly uses magnetometer to detect the magnetic field. During the working process, the towed detection device is arranged at the stern of the ship and sinks to the seabed at a certain depth [7]. The control, data recording, and analysis components of the detection device are arranged on the mother ship, which can realize the measurement during navigation. The towed cable of the detection ship is often long, so it can detect magnetic anomaly data in a wide range. The detection range of points is usually thousands of square meters. In order to determine the optimal drag cable length, it is necessary to determine the influence of the mother ship on the drag detection device and analyze it, so as to establish the optimal distance between the mother ship and the drag detector. Secondly, the detection orientation shall be determined, the influence of the mother ship shall be analyzed through real-time recording of the measurement data, and the data shall be optimized and corrected.In addition, in the process of local marine geomagnetic field detection, especially the detection of magnetic anomaly data, it is necessary to continuously test the detection depth, so as to determine the best depth. If the submergence is too small, it is easy to be disturbed and affected by the wake of the mother ship, resulting in the decline of detection accuracy. However, too deep submergence is often accompanied by strict requirements on equipment reliability, cost, and realizability [8]. Therefore, it is necessary to comprehensively adjust the diving depth of the detection device and the length of the retracted cable on account of the navigation parameters of the mother ship.


## 2.1. Typical Characteristics of Local Marine Geomagnetic Field

As the product of the interaction of internal and external currents, the distribution and law of local marine geomagnetic field are quite different in time and space. The Earth’s magnetic field and its dipolarity are mainly caused by the current flowing in the conductive liquid core. The magnetic induction intensity of local marine geomagnetic field can be expressed by (1), where β and α are permeability and magnetic susceptibility, respectively, and β0 is vacuum permeability.(1)B⇀=βH⇀=β01+αH⇀=β0H⇀+M⇀.The local marine geomagnetic field is mainly composed of endogenous and exogenous parts, in which the endogenous field is composed of basic magnetic field and abnormal magnetic field; the external field is mainly composed of stable magnetic field and variable magnetic field, as shown in (2). T0+Tm is the endogenous field, and δT+Tse is the exogenous field. In the process of detecting the local ocean geomagnetic anomaly data, the selection of Ta is often a relative concept because there are great differences in the detection object, the selected local ocean range, and the sea depth of the local ocean.(2)T=T0+Tm+Ta+δT+Tse.Paramagnetic materials will be organically sorted in the direction under the action of external magnetic field, and the value ofα will also change [5]. The detection of local marine geomagnetic anomaly data will help to understand the evolution process of regional marine magnetic field and the variation law of magnetic field intensity and further clarify the structure, expansion, and climate of regional seabed plate.


## 2.2. Local Marine Geomagnetic Anomaly

The geomagnetic anomaly is mainly caused by the superposition and interference between the local magnetic field of rocks and minerals with magnetism in the shallow crust and the basic magnetic field of the Earth. The magnetic anomaly of local marine geomagnetic field is complex. In order to carry out relevant research, it is usually necessary to simplify the model of local marine geomagnetic field. Firstly, it is assumed that the shape of the local marine geomagnetic body is regular and simple, and the interference between geomagnetic bodies is not considered. Secondly, assuming that the magnetism of the local marine geomagnetic is relatively uniform, there are multiple methods to calculate the local marine geomagnetic field, including Poisson, volume, and area fraction [6]. The calculation of local marine geomagnetic gravity magnetic potential field is shown in (3) and (4), where ρ is density, GA is gravity potential, and C is magnetic potential.(3)GA=Gρ∫∫V∫1rdv,(4)C=−14πGρM⇀•∇GA.On the premise of obtaining the gravitational potential of the local marine geomagnetic field model, the expression of each component of the magnetic field can be obtained. In addition, the process of local marine geomagnetic field magnetic detection is easy to disturb by submarine cables represented by optical cables and cables. Therefore, before detection, it is necessary to accurately locate the submarine cables, so as to avoid the interference of submarine cables with and their influence on the measurement results, so as to better ensure the accuracy of the measured magnetic anomaly data.


## 2.3. Method for Detecting Local Marine Geomagnetic Field

At present, as one of the common means of local marine geomagnetic field detection, towed marine survey ship mainly uses magnetometer to detect the magnetic field. During the working process, the towed detection device is arranged at the stern of the ship and sinks to the seabed at a certain depth [7]. The control, data recording, and analysis components of the detection device are arranged on the mother ship, which can realize the measurement during navigation. The towed cable of the detection ship is often long, so it can detect magnetic anomaly data in a wide range. The detection range of points is usually thousands of square meters. In order to determine the optimal drag cable length, it is necessary to determine the influence of the mother ship on the drag detection device and analyze it, so as to establish the optimal distance between the mother ship and the drag detector. Secondly, the detection orientation shall be determined, the influence of the mother ship shall be analyzed through real-time recording of the measurement data, and the data shall be optimized and corrected.In addition, in the process of local marine geomagnetic field detection, especially the detection of magnetic anomaly data, it is necessary to continuously test the detection depth, so as to determine the best depth. If the submergence is too small, it is easy to be disturbed and affected by the wake of the mother ship, resulting in the decline of detection accuracy. However, too deep submergence is often accompanied by strict requirements on equipment reliability, cost, and realizability [8]. Therefore, it is necessary to comprehensively adjust the diving depth of the detection device and the length of the retracted cable on account of the navigation parameters of the mother ship.


## 3. Theoretical Basis of Local Ocean Geomagnetic Field Model

### 3.1. Composition of Geomagnetic Field

The characteristics of the geomagnetic field are similar to the magnetic dipole placed in the center of the Earth, and its magnetic field intensity is low. Therefore, the order of magnitude represented by the intensity unit of the geomagnetic field is usually very small, and the variation of the geomagnetic field intensity with place or time is not obvious [9]. Secondly, as a momentous part of the geomagnetic field, its geomagnetic pole, geomagnetic meridian, magnetic declination, and magnetic inclination also have unique properties. Among them, the magnetic inclination of the geomagnetic field is shown in Figure 3.Figure 3
Geomagnetic inclination model.The magnetic line of force is parallel to the horizontal plane only on the geomagnetic equator and produces the intersection angle between the north and south and the horizontal plane in the vertical direction. In addition, the geomagnetic field consists of dipole field, continental magnetic field, magnetic anomaly field, stable magnetic field, and interference change. Among them, dipole field, continental magnetic field, and magnetic anomaly field together constitute the normal field [10]. The basic magnetic field occupies most of the composition of the geomagnetic field, and the variable magnetic field occupies a small part.As the most basic characteristic of geomagnetic field, the Earth’s magnetic field is relatively stable, and it is usually caused by the large-scale closed eddy motion of good conductive fluid in the Earth’s core and thermoelectric current. The spatial distribution of geomagnetic field can be expressed in many different ways, as shown in Table1.Table 1
Representation of spatial distribution of geomagnetic field.
Expression formFeaturesPrimary coverageFormsDetailed expressionOriginal measurement data and general valueGraphsIntuitiveness and visualizationIsomagnetic declination diagram, vector diagram, and section diagramFunctionsConcise and compactPolynomial, spherical harmonic, crown harmonic model


### 3.2. The Levels of Marine Magnetic Survey

According to the measurement requirements of marine magnetic force in Chinese national standards, the measurement levels are divided, mainly including four levels of accuracy measurement. Among them, the first-class accuracy measurement is mainly used in key sea areas and has high requirements for the accuracy and error of the measurement device. Secondly, as a requirement for detailed marine magnetic survey, secondary precision survey is mainly used in relevant areas represented by coastal, inland waterway, and port entrance. In addition, level 3 precision measurement is mainly used for sea areas not covered by level 1 and level 2 measurement areas, while level 4 precision measurement is mainly used for offshore sea areas, such as all other sea areas not covered by level 1, level 2, and level 3 measurement areas.


### 3.3. Mathematical Model Representation of Geomagnetic Field

The magnetic dipole of the geomagnetic field is a system composed of equal magnetic charges at different sign points. The distance between the positive and negative magnetic charges of the geomagnetic dipole is almost negligible compared with the distance between a point in space and the midpoint of the two magnetic charges [11]. The calculation of the magnetic dipole distance of the two magnetic charges and the magnetic potential B far from the magnetic dipole moment center A is shown in (5), and the calculation diagram is shown in Figure 4.Figure 4
Relationship between positive and negative magnetic charges of geomagnetic dipole.(5)T=μ04πQml++μ04π−Qml−=μ0Qm2rcosα4πl2=μ0m⟶cosα4πl2.The representation of the geocentric axial magnetic dipole field is shown in Figure5(a). In this simplified schematic diagram, the geocentric magnetic dipole axis and the Earth axis are superimposed for convenience [12], where R is the radius of the Earth and Mt⟶ is the magnetic moment of the Earth. For A at any position in the local ocean, the magnetic potential is calculated as shown in the following equation:(6)TA=μ0Mt⟶4πR2sinφ.Figure 5
Geocentric axial magnetic dipole field model.
(a)(b)For the geomagnetic model shown in Figure5(b), in order to facilitate intuitive calculation, it is necessary to establish an organic transformation between the coordinates (x, y, z) of point A in the rectangular coordinate system and the Earth spherical coordinates. The component of magnetic induction intensity s of local marine geomagnetic field in rectangular coordinate system is shown in the following formulas:(7)S¯x=−∂TP∂x=μ0Mt⟶4πR3cosφ,(8)S¯y=−∂TP∂y=0,(9)S¯z=−∂TP∂z=2μ0Mt⟶4πR3sinφ.The magnetic induction intensityS of the local marine geomagnetic field is calculated as shown in the following equation:(10)S⟶=SX2+SY2+SZ2=μ04πMtR31+3cos2θ,=μ04πMtR31+3sin2φ.For the geocentric dipole magnetic field, the calculation coordinate system shown in Figure6 is established, where θ0 is the angle between the geocentric magnetic dipole axis and the Earth axis, r is the Earth radius, and Mt⟶ is the magnetic moment of the local marine geomagnetic field. Then, for any point A of the local ocean, its magnetic potential is shown in the following formula:Figure 6
Geocentric dipole magnetic field coordinate system.(11)S=14πMt⟶•r¯r3=14πMtxx+Mtyy+Mtzzr3.On the premise of knowing the Gaussian coefficient, it can further clarify the magnetic induction intensity of local ocean points, and the Gaussian coefficient is confirmed on account of the observed magnetic induction intensity of local ocean points [13]. Further, after the observed value of magnetic induction intensity and Gaussian coefficient are obtained, the magnetic moment, polar angle, and azimuth of the magnetic dipole can be calculated, as shown in the following formulas:(12)θ0=argtanmx2+my2mz,(13)λ0=argtanmymx.


### 3.4. Spherical Harmonic Analysis of Local Marine Geomagnetic Field

The change of geomagnetic field is manifested in short-term change, long-term change of geomagnetic elements, and long-term slow change with time. The stable magnetic field of local marine geomagnetic field comes from the Earth’s interior, which is more concise in the spherical coordinate system. The calculation of its magnetic potential is shown in (14), where gnmandhnm are Gaussian spherical harmonic coefficients. The expansion of the series of local marine physical signals and the spherical harmonic coefficient of geomagnetic field make each term have a specific physical meaning.(14)T=Rμ0∑n=1∞∑m=0nRrn+1•gnmcosMtλ+hnmsinMtλ•A⇀nmcosθs.


## 3.1. Composition of Geomagnetic Field

The characteristics of the geomagnetic field are similar to the magnetic dipole placed in the center of the Earth, and its magnetic field intensity is low. Therefore, the order of magnitude represented by the intensity unit of the geomagnetic field is usually very small, and the variation of the geomagnetic field intensity with place or time is not obvious [9]. Secondly, as a momentous part of the geomagnetic field, its geomagnetic pole, geomagnetic meridian, magnetic declination, and magnetic inclination also have unique properties. Among them, the magnetic inclination of the geomagnetic field is shown in Figure 3.Figure 3
Geomagnetic inclination model.The magnetic line of force is parallel to the horizontal plane only on the geomagnetic equator and produces the intersection angle between the north and south and the horizontal plane in the vertical direction. In addition, the geomagnetic field consists of dipole field, continental magnetic field, magnetic anomaly field, stable magnetic field, and interference change. Among them, dipole field, continental magnetic field, and magnetic anomaly field together constitute the normal field [10]. The basic magnetic field occupies most of the composition of the geomagnetic field, and the variable magnetic field occupies a small part.As the most basic characteristic of geomagnetic field, the Earth’s magnetic field is relatively stable, and it is usually caused by the large-scale closed eddy motion of good conductive fluid in the Earth’s core and thermoelectric current. The spatial distribution of geomagnetic field can be expressed in many different ways, as shown in Table1.Table 1
Representation of spatial distribution of geomagnetic field.
Expression formFeaturesPrimary coverageFormsDetailed expressionOriginal measurement data and general valueGraphsIntuitiveness and visualizationIsomagnetic declination diagram, vector diagram, and section diagramFunctionsConcise and compactPolynomial, spherical harmonic, crown harmonic model


## 3.2. The Levels of Marine Magnetic Survey

According to the measurement requirements of marine magnetic force in Chinese national standards, the measurement levels are divided, mainly including four levels of accuracy measurement. Among them, the first-class accuracy measurement is mainly used in key sea areas and has high requirements for the accuracy and error of the measurement device. Secondly, as a requirement for detailed marine magnetic survey, secondary precision survey is mainly used in relevant areas represented by coastal, inland waterway, and port entrance. In addition, level 3 precision measurement is mainly used for sea areas not covered by level 1 and level 2 measurement areas, while level 4 precision measurement is mainly used for offshore sea areas, such as all other sea areas not covered by level 1, level 2, and level 3 measurement areas.


## 3.3. Mathematical Model Representation of Geomagnetic Field

The magnetic dipole of the geomagnetic field is a system composed of equal magnetic charges at different sign points. The distance between the positive and negative magnetic charges of the geomagnetic dipole is almost negligible compared with the distance between a point in space and the midpoint of the two magnetic charges [11]. The calculation of the magnetic dipole distance of the two magnetic charges and the magnetic potential B far from the magnetic dipole moment center A is shown in (5), and the calculation diagram is shown in Figure 4.Figure 4
Relationship between positive and negative magnetic charges of geomagnetic dipole.(5)T=μ04πQml++μ04π−Qml−=μ0Qm2rcosα4πl2=μ0m⟶cosα4πl2.The representation of the geocentric axial magnetic dipole field is shown in Figure5(a). In this simplified schematic diagram, the geocentric magnetic dipole axis and the Earth axis are superimposed for convenience [12], where R is the radius of the Earth and Mt⟶ is the magnetic moment of the Earth. For A at any position in the local ocean, the magnetic potential is calculated as shown in the following equation:(6)TA=μ0Mt⟶4πR2sinφ.Figure 5
Geocentric axial magnetic dipole field model.
(a)(b)For the geomagnetic model shown in Figure5(b), in order to facilitate intuitive calculation, it is necessary to establish an organic transformation between the coordinates (x, y, z) of point A in the rectangular coordinate system and the Earth spherical coordinates. The component of magnetic induction intensity s of local marine geomagnetic field in rectangular coordinate system is shown in the following formulas:(7)S¯x=−∂TP∂x=μ0Mt⟶4πR3cosφ,(8)S¯y=−∂TP∂y=0,(9)S¯z=−∂TP∂z=2μ0Mt⟶4πR3sinφ.The magnetic induction intensityS of the local marine geomagnetic field is calculated as shown in the following equation:(10)S⟶=SX2+SY2+SZ2=μ04πMtR31+3cos2θ,=μ04πMtR31+3sin2φ.For the geocentric dipole magnetic field, the calculation coordinate system shown in Figure6 is established, where θ0 is the angle between the geocentric magnetic dipole axis and the Earth axis, r is the Earth radius, and Mt⟶ is the magnetic moment of the local marine geomagnetic field. Then, for any point A of the local ocean, its magnetic potential is shown in the following formula:Figure 6
Geocentric dipole magnetic field coordinate system.(11)S=14πMt⟶•r¯r3=14πMtxx+Mtyy+Mtzzr3.On the premise of knowing the Gaussian coefficient, it can further clarify the magnetic induction intensity of local ocean points, and the Gaussian coefficient is confirmed on account of the observed magnetic induction intensity of local ocean points [13]. Further, after the observed value of magnetic induction intensity and Gaussian coefficient are obtained, the magnetic moment, polar angle, and azimuth of the magnetic dipole can be calculated, as shown in the following formulas:(12)θ0=argtanmx2+my2mz,(13)λ0=argtanmymx.


## 3.4. Spherical Harmonic Analysis of Local Marine Geomagnetic Field

The change of geomagnetic field is manifested in short-term change, long-term change of geomagnetic elements, and long-term slow change with time. The stable magnetic field of local marine geomagnetic field comes from the Earth’s interior, which is more concise in the spherical coordinate system. The calculation of its magnetic potential is shown in (14), where gnmandhnm are Gaussian spherical harmonic coefficients. The expansion of the series of local marine physical signals and the spherical harmonic coefficient of geomagnetic field make each term have a specific physical meaning.(14)T=Rμ0∑n=1∞∑m=0nRrn+1•gnmcosMtλ+hnmsinMtλ•A⇀nmcosθs.


## 4. Measurement and Modeling Methods of Local Marine Geomagnetic Field Data

### 4.1. Measurement Basis of Local Marine Geomagnetic Data

In order to establish an accurate local marine geomagnetic field model, it is necessary to obtain the magnetic data of relevant sea areas efficiently and accurately. The strategy of magnetic data of sea area geomagnetic field model is usually measured in relevant sea areas with the help of detection ships. The relevant principle framework is shown in Figure7. The magnetic data detection ship sinks the detection equipment in the sea area at a certain depth by dragging, so as to reduce the interference of the mother ship with and its adverse impact on the detection process as much as possible. By erecting drag cables with reasonable depth and length, continuous detection can be carried out, so as to obtain detection results that meet the requirements. Finally, by summarizing and fitting the obtained detection data, a more perfect geomagnetic field model of the detection sea area can be established.Figure 7
Magnetic data detection ship towing detection model.


### 4.2. Evaluation Indexes for the Accuracy of Local Marine Geomagnetic Map

As a momentous prerequisite for the high-precision rendering of local marine geomagnetic map, the spatial distribution attribute feature interpolation on account of geomagnetic data has a momentous impact on the effective rendering of geomagnetic map. Secondly, the rationality of the parameters of the local marine geomagnetic field model is judged and analyzed by means of statistics. Although there are many kinds of indicators affecting the accuracy of local marine geomagnetic map, the common evaluation indicators mainly include accuracy index, RMS, ME, SD, and Error Mean.


### 4.3. Data Processing Flow of Local Marine Magnetic Survey

As a momentous procedure to ensure the data processing accuracy of local marine magnetic survey, it is necessary to effectively preprocess the detection data and eliminate unreasonable and missing data records through data preprocessing. The data processing flow of local marine magnetic survey mainly includes several aspects as shown in Table2.Table 2
Data processing features of local marine magnetic survey.
ProcessObjectivesMethodsData quality controlEliminating data jumpsTrend surface filtering, manual interactionDaily variation correctionEliminating the influence of geomagnetic diurnal variationArithmetic mean and translation transformation of observationsShip magnetic correctionEliminating the influence of ship magnetismEight-azimuth measured dataNormal field correctionObtaining geomagnetic anomaly fieldGeomagnetic field modelAccuracy evaluationJudging data qualityLaying repeated and checking survey lines


### 4.4. Construction Method of Local Marine Geomagnetic Field Model

The construction methods of local marine geomagnetic field model include many types and methods. The characteristics of these different modeling methods are shown in Table3. It can be seen from Table 3 that different construction methods of local marine geomagnetic field models have different applicable scenarios, which makes it necessary to organically select appropriate construction strategies on account of the actual situation of the scene in the detection area in the process of constructing local marine geomagnetic field models and detecting magnetic anomaly data [14]. Therefore, how to construct a method with simple process, available precision, and controllable cost has become the focus and difficulty of relevant research and analysis.Table 3
Characteristics of construction method of local marine geomagnetic field model.
MethodsAdvantagesDisadvantagesPolynomial modelSimple and easyThe data fitting accuracy is relatively lowSpherical harmonic analysisSuitable for local geomagnetic field modelingThe resolution cannot accurately reflect local geomagnetic changesSpherical crown harmonic modelDirect construction of spherical crown areaThe data processing is complexMoment harmonic analysis modelSuitable for local geomagnetic field modelingThe resolution cannot accurately reflect local geomagnetic changesFunction modelSuitable for discrete node modelingThe data processing is complex


## 4.1. Measurement Basis of Local Marine Geomagnetic Data

In order to establish an accurate local marine geomagnetic field model, it is necessary to obtain the magnetic data of relevant sea areas efficiently and accurately. The strategy of magnetic data of sea area geomagnetic field model is usually measured in relevant sea areas with the help of detection ships. The relevant principle framework is shown in Figure7. The magnetic data detection ship sinks the detection equipment in the sea area at a certain depth by dragging, so as to reduce the interference of the mother ship with and its adverse impact on the detection process as much as possible. By erecting drag cables with reasonable depth and length, continuous detection can be carried out, so as to obtain detection results that meet the requirements. Finally, by summarizing and fitting the obtained detection data, a more perfect geomagnetic field model of the detection sea area can be established.Figure 7
Magnetic data detection ship towing detection model.


## 4.2. Evaluation Indexes for the Accuracy of Local Marine Geomagnetic Map

As a momentous prerequisite for the high-precision rendering of local marine geomagnetic map, the spatial distribution attribute feature interpolation on account of geomagnetic data has a momentous impact on the effective rendering of geomagnetic map. Secondly, the rationality of the parameters of the local marine geomagnetic field model is judged and analyzed by means of statistics. Although there are many kinds of indicators affecting the accuracy of local marine geomagnetic map, the common evaluation indicators mainly include accuracy index, RMS, ME, SD, and Error Mean.


## 4.3. Data Processing Flow of Local Marine Magnetic Survey

As a momentous procedure to ensure the data processing accuracy of local marine magnetic survey, it is necessary to effectively preprocess the detection data and eliminate unreasonable and missing data records through data preprocessing. The data processing flow of local marine magnetic survey mainly includes several aspects as shown in Table2.Table 2
Data processing features of local marine magnetic survey.
ProcessObjectivesMethodsData quality controlEliminating data jumpsTrend surface filtering, manual interactionDaily variation correctionEliminating the influence of geomagnetic diurnal variationArithmetic mean and translation transformation of observationsShip magnetic correctionEliminating the influence of ship magnetismEight-azimuth measured dataNormal field correctionObtaining geomagnetic anomaly fieldGeomagnetic field modelAccuracy evaluationJudging data qualityLaying repeated and checking survey lines


## 4.4. Construction Method of Local Marine Geomagnetic Field Model

The construction methods of local marine geomagnetic field model include many types and methods. The characteristics of these different modeling methods are shown in Table3. It can be seen from Table 3 that different construction methods of local marine geomagnetic field models have different applicable scenarios, which makes it necessary to organically select appropriate construction strategies on account of the actual situation of the scene in the detection area in the process of constructing local marine geomagnetic field models and detecting magnetic anomaly data [14]. Therefore, how to construct a method with simple process, available precision, and controllable cost has become the focus and difficulty of relevant research and analysis.Table 3
Characteristics of construction method of local marine geomagnetic field model.
MethodsAdvantagesDisadvantagesPolynomial modelSimple and easyThe data fitting accuracy is relatively lowSpherical harmonic analysisSuitable for local geomagnetic field modelingThe resolution cannot accurately reflect local geomagnetic changesSpherical crown harmonic modelDirect construction of spherical crown areaThe data processing is complexMoment harmonic analysis modelSuitable for local geomagnetic field modelingThe resolution cannot accurately reflect local geomagnetic changesFunction modelSuitable for discrete node modelingThe data processing is complex


## 5. Local Marine Magnetic Anomaly Data Detection considering Robust Trend Surface

Local marine magnetic data exploration covers abnormal data and normal data. Magnetic anomaly data are divided into background field and anomaly field. The change of the former is usually stable, while the latter is mainly caused by the accumulation of seabed magnetic minerals, so the change is usually obvious. Due to the small proportion of abnormal data, it is necessary to correct and preprocess the detected data in time to ensure the accuracy of the data.At the composition level of magnetic anomaly data of local ocean, it is mainly composed of background field and anomaly field. Among them, compared with the latter, the magnetic anomaly change of the former is less obvious, while the latter is a sudden change of data caused by various natural substances naturally existing on the seabed, so it will show a sharp change in data display. Secondly, due to the complexity of the detection process of local marine magnetic survey data, it will be disturbed by many factors, so it is inevitable to produce abnormal data. On the other hand, the accuracy control of local marine geomagnetic field model requires controlling the abnormal data content of geostrophic data so that its proportion cannot exceed one-tenth, which requires the preprocessing of local marine magnetic measurement data aiming at the detection of abnormal data.


### 5.1. Detection Method of Local Marine Magnetic Anomaly Data

The typical methods of detecting local marine magnetic anomaly data include gross error elimination method on account of the correction number of observed values, quality control method represented by robust trend surface method, and so on. Among them, the abnormal data quality control method on account of robust trend surface includes several typical methods, such as threshold filtering, 3D visual sliding surface fitting, and least squares trend surface. The threshold filtering method is not suitable for the complex detection scene with the change of geomagnetic field. The sliding surface fitting can better balance the accuracy and workload. In addition, the least squares trend surface detection method is sensitive to the selection of order, which needs to be balanced and determined in combination with the actual fluctuation of magnetic measurement data.The detection method of local marine magnetic anomaly data usually needs data correction and gross error elimination on account of observation data, but it is easy to misjudge the data in the process of correction, resulting in the distortion of detection data. Therefore, using the robust trend surface calculation algorithm to control the data quality can effectively judge and locate the abnormal data, so as to establish an effective premise for the elimination of gross error data. Secondly, the robust trend surface calculation algorithm can better control the data quality, accurately judge and eliminate gross error data, and ensure the availability of detection data. The commonly used data quality control methods considering robust trend surface calculation include threshold filtering, 3D visual sliding surface fitting, and least squares trend surface. The principle of threshold filtering method is to judge whether the magnetic field strength can be effectively adopted by designing the magnetic field strength threshold. The advantage of threshold filtering method is that it can dynamically adjust the threshold according to the severity of local ocean magnetic field change, so as to effectively remove the gross error data, so it can better adapt to the actual background field of regional ocean.However, for the sea area with complex magnetic field changes, the threshold filter has the defect that the detection data is not accurate enough, which requires a lot of manual operations, resulting in poor practical availability of the calculation algorithm. Therefore, 3D visual sliding surface fitting is used to detect and integrate potential abnormal data, and 3D view is used for fitting to comprehensively judge the abnormality of data [15]. In addition, the magnetic anomaly of local marine geomagnetic field often has trend characteristics, so the data fitting trend is used to effectively detect and control the magnetic anomaly data. The least squares trend surface is formally used to detect the magnetic anomaly area by fitting the trend surface. This method has strong detection ability in the case of small outliers, but with the increase of the number of outliers, the detection accuracy of magnetic anomaly data will decrease significantly. In addition, selecting an appropriate calculation order is also the key to ensure the detection accuracy of this method. Dynamically selecting a reasonable order on account of the fluctuation of the detection value of local marine magnetic data can effectively avoid the overload or loss of abnormal data.


### 5.2. Principle of Robust Trend Surface Calculation Algorithm

The robust trend surface calculation algorithm uses mathematical surfaces to simulate the spatial distribution trend and variation law of the elements of the local marine geomagnetic field model. Using the function fitting of the least squares method, the trend surface is fused to effectively eliminate the interference and influence of the abnormal data, so as to find out the spatial distribution trend of the element data of the local marine geomagnetic field model. In order to ensure the data fitting accuracy of the constructed local marine geomagnetic field model, it is necessary to reduce the residual value of the model and ameliorate its trend value as much as possible, as shown in (15), whereAixi,yi is the magnetic anomaly detection data of local marine geomagnetic field, Ai¯¯xi,yi is the trend surface fitting value, and δi is the residual value. In order to ameliorate the detection accuracy, it is necessary to increase Ai¯¯xi,yi as much as possible and reduce the value of δi.(15)Aixi,yi=Ai¯¯xi,yi+δi.Secondly, with the help of regression analysis, the trend surface is obtained through the magnetic anomaly detection data of local marine geomagnetic field, and the sum of squares of residuals is reduced as much as possible. In addition, the fitting degree of trend surface analysis is positively correlated with the effect of local marine geomagnetic field model, so it is necessary to test the appropriateness of trend surface analysis. In the process of multiple rounds of iteration of countermeasure data, by continuously reducing the weight function value of untrusted measurement points, ameliorate the accuracy of calculating the coefficients of trend surface model, further ameliorate the rationality of local marine geomagnetic field countermeasure trend surface model, and finally realize the effective detection and judgment of abnormal data.


### 5.3. Advantages of Abnormal Data Quality Control on account of Robust Trend Surface

The traditional detection of local marine geomagnetic anomaly data represented by least squares still has great room for improvement in stability, accuracy, anti-interference, and reliability, so it has utilization limitations. The robust trend surface detection method can effectively identify multisource abnormal data. It not only has a good effect on the judgment accuracy of data abnormality, but also is not sensitive to the amount of abnormal data. It has significant utilization advantages in both stability and reliability.


## 5.1. Detection Method of Local Marine Magnetic Anomaly Data

The typical methods of detecting local marine magnetic anomaly data include gross error elimination method on account of the correction number of observed values, quality control method represented by robust trend surface method, and so on. Among them, the abnormal data quality control method on account of robust trend surface includes several typical methods, such as threshold filtering, 3D visual sliding surface fitting, and least squares trend surface. The threshold filtering method is not suitable for the complex detection scene with the change of geomagnetic field. The sliding surface fitting can better balance the accuracy and workload. In addition, the least squares trend surface detection method is sensitive to the selection of order, which needs to be balanced and determined in combination with the actual fluctuation of magnetic measurement data.The detection method of local marine magnetic anomaly data usually needs data correction and gross error elimination on account of observation data, but it is easy to misjudge the data in the process of correction, resulting in the distortion of detection data. Therefore, using the robust trend surface calculation algorithm to control the data quality can effectively judge and locate the abnormal data, so as to establish an effective premise for the elimination of gross error data. Secondly, the robust trend surface calculation algorithm can better control the data quality, accurately judge and eliminate gross error data, and ensure the availability of detection data. The commonly used data quality control methods considering robust trend surface calculation include threshold filtering, 3D visual sliding surface fitting, and least squares trend surface. The principle of threshold filtering method is to judge whether the magnetic field strength can be effectively adopted by designing the magnetic field strength threshold. The advantage of threshold filtering method is that it can dynamically adjust the threshold according to the severity of local ocean magnetic field change, so as to effectively remove the gross error data, so it can better adapt to the actual background field of regional ocean.However, for the sea area with complex magnetic field changes, the threshold filter has the defect that the detection data is not accurate enough, which requires a lot of manual operations, resulting in poor practical availability of the calculation algorithm. Therefore, 3D visual sliding surface fitting is used to detect and integrate potential abnormal data, and 3D view is used for fitting to comprehensively judge the abnormality of data [15]. In addition, the magnetic anomaly of local marine geomagnetic field often has trend characteristics, so the data fitting trend is used to effectively detect and control the magnetic anomaly data. The least squares trend surface is formally used to detect the magnetic anomaly area by fitting the trend surface. This method has strong detection ability in the case of small outliers, but with the increase of the number of outliers, the detection accuracy of magnetic anomaly data will decrease significantly. In addition, selecting an appropriate calculation order is also the key to ensure the detection accuracy of this method. Dynamically selecting a reasonable order on account of the fluctuation of the detection value of local marine magnetic data can effectively avoid the overload or loss of abnormal data.


## 5.2. Principle of Robust Trend Surface Calculation Algorithm

The robust trend surface calculation algorithm uses mathematical surfaces to simulate the spatial distribution trend and variation law of the elements of the local marine geomagnetic field model. Using the function fitting of the least squares method, the trend surface is fused to effectively eliminate the interference and influence of the abnormal data, so as to find out the spatial distribution trend of the element data of the local marine geomagnetic field model. In order to ensure the data fitting accuracy of the constructed local marine geomagnetic field model, it is necessary to reduce the residual value of the model and ameliorate its trend value as much as possible, as shown in (15), whereAixi,yi is the magnetic anomaly detection data of local marine geomagnetic field, Ai¯¯xi,yi is the trend surface fitting value, and δi is the residual value. In order to ameliorate the detection accuracy, it is necessary to increase Ai¯¯xi,yi as much as possible and reduce the value of δi.(15)Aixi,yi=Ai¯¯xi,yi+δi.Secondly, with the help of regression analysis, the trend surface is obtained through the magnetic anomaly detection data of local marine geomagnetic field, and the sum of squares of residuals is reduced as much as possible. In addition, the fitting degree of trend surface analysis is positively correlated with the effect of local marine geomagnetic field model, so it is necessary to test the appropriateness of trend surface analysis. In the process of multiple rounds of iteration of countermeasure data, by continuously reducing the weight function value of untrusted measurement points, ameliorate the accuracy of calculating the coefficients of trend surface model, further ameliorate the rationality of local marine geomagnetic field countermeasure trend surface model, and finally realize the effective detection and judgment of abnormal data.


## 5.3. Advantages of Abnormal Data Quality Control on account of Robust Trend Surface

The traditional detection of local marine geomagnetic anomaly data represented by least squares still has great room for improvement in stability, accuracy, anti-interference, and reliability, so it has utilization limitations. The robust trend surface detection method can effectively identify multisource abnormal data. It not only has a good effect on the judgment accuracy of data abnormality, but also is not sensitive to the amount of abnormal data. It has significant utilization advantages in both stability and reliability.


## 6. Detection Results of Local Marine Magnetic Anomaly Data considering Robust Trend Surface

### 6.1. Detection and Location of Local Marine Magnetic Anomaly Data

Firstly, in the process of detecting local marine geomagnetic anomaly data, the scope of the survey area should be confirmed on account of the detection objectives and expected results. Only when the target of the exploration task is clear can the complete range contour of the whole exploration area be determined effectively. Secondly, due to the large range of the detection area, in order to effectively describe and express the detection area, it is necessary to condense the information of the detection area and realize the effective representation of the magnetic field information data of the exploration area through equal proportion reduction. In addition, the process of determining the reduction scale should combine the data attributes of the area to be detected, select a reasonable scale, and determine a scientific projection method.Considering the robust trend surface, the detection of local marine magnetic anomaly data first needs to accurately locate the magnetic target on account of the geomagnetic profile of the survey line. Firstly, in the process of detection, if there are dense local marine geomagnetic intensity isolines, it could preliminarily locate the magnetic target. Secondly, the geomagnetic profile is obtained by establishing the survey line index, and the data are identified to reflect the dynamic changes of local marine geomagnetic profile. In addition, by scanning the most significant area of magnetic anomaly, its position is mapped, and finally the accurate target orientation is obtained.In the process of local marine magnetic anomaly data detection considering the robust trend surface, in order to ensure the data accuracy, it is necessary to continuously ameliorate the robust trend surface model coefficient and reduce the anomaly weight value. The robust trend surface model is relatively more reasonable in the process of detecting magnetic anomaly data and can more accurately detect and locate the magnetic anomaly data of local marine geomagnetic field model.


### 6.2. Elimination of Ship Magnetic Interference in Marine Magnetic Anomaly Data Detection

The process of local marine magnetic anomaly data detection will inevitably be disturbed and affected by the detection mother ship. In order to eliminate the influence of the mother ship’s magnetism on the detection data results and eliminate unnecessary systematic errors, it is necessary to eliminate and correct the ship’s magnetic interference. The common methods to eliminate the magnetic interference of the mother ship mainly include the ship magnetic eight-azimuth test, Fourier series method, four-heading method, and example calculation. Among them, the ship magnetic eight-azimuth test uses the magnetic field to measure the course of the carrier ship and correct the ship magnetic azimuth of the magnetic survey data of the local ocean, which has high correction efficiency, but it is not as accurate as Fourier series method and four-heading correction method.


### 6.3. Detection and Verification Analysis of Local Marine Magnetic Anomaly Data

In order to verify the detection effect of local marine magnetic anomaly data considering robust trend surface, further experimental analysis and verification are needed. Select a sea area for field detection and inspection, and select gn-3765 towed marine magnetic anomaly detection device for relevant detection work. In order to eliminate the influence of data gross error, the detection data are corrected, and finally the isoline distribution map of magnetic anomaly data in the detection area is obtained. Secondly, the interference degree of gross error data on trend surface fitting is further verified by mixing less (usually no more than 9%) gross error with the detected local marine magnetic anomaly data.Firstly, the mixed local marine magnetic anomaly data is used as a new input to detect the robust trend surface, and the detection results are compared with the least squares trend surface. Secondly, the abnormal values in the two detection results are removed, and the difference of magnetic abnormal values before and after mixing is further obtained and compared. The results are shown in Table4.Table 4
Comparison of detection results of marine magnetic anomaly data.
Gross error number & proportionLeast squares trend surfaceRobust trend surfaceNumber foundNumber of testsRoot mean square errorNumber of foundNumber of testsRoot mean square error21 (2%)21595.146821375.173442 (4%)42915.367142795.391363 (6%)56865.598456855.606284 (8%)62695.812271975.865495 (9%)77786.136185996.1446105 (10%)89976.4164961106.4561It can be seen from the data in Table4 that the detection accuracy of the least squares trend surface decreases significantly with the increase of gross error content, which is not only prone to missed detection, but also unstable. Considering the robust trend surface, the detection of local marine magnetic anomaly data is not advanced, which has high detection accuracy, and its accuracy stability remains good with the increase of the number of gross errors. Therefore, considering the robust trend surface, the local marine geomagnetic field model can more effectively meet the practical utilization scenarios.


## 6.1. Detection and Location of Local Marine Magnetic Anomaly Data

Firstly, in the process of detecting local marine geomagnetic anomaly data, the scope of the survey area should be confirmed on account of the detection objectives and expected results. Only when the target of the exploration task is clear can the complete range contour of the whole exploration area be determined effectively. Secondly, due to the large range of the detection area, in order to effectively describe and express the detection area, it is necessary to condense the information of the detection area and realize the effective representation of the magnetic field information data of the exploration area through equal proportion reduction. In addition, the process of determining the reduction scale should combine the data attributes of the area to be detected, select a reasonable scale, and determine a scientific projection method.Considering the robust trend surface, the detection of local marine magnetic anomaly data first needs to accurately locate the magnetic target on account of the geomagnetic profile of the survey line. Firstly, in the process of detection, if there are dense local marine geomagnetic intensity isolines, it could preliminarily locate the magnetic target. Secondly, the geomagnetic profile is obtained by establishing the survey line index, and the data are identified to reflect the dynamic changes of local marine geomagnetic profile. In addition, by scanning the most significant area of magnetic anomaly, its position is mapped, and finally the accurate target orientation is obtained.In the process of local marine magnetic anomaly data detection considering the robust trend surface, in order to ensure the data accuracy, it is necessary to continuously ameliorate the robust trend surface model coefficient and reduce the anomaly weight value. The robust trend surface model is relatively more reasonable in the process of detecting magnetic anomaly data and can more accurately detect and locate the magnetic anomaly data of local marine geomagnetic field model.


## 6.2. Elimination of Ship Magnetic Interference in Marine Magnetic Anomaly Data Detection

The process of local marine magnetic anomaly data detection will inevitably be disturbed and affected by the detection mother ship. In order to eliminate the influence of the mother ship’s magnetism on the detection data results and eliminate unnecessary systematic errors, it is necessary to eliminate and correct the ship’s magnetic interference. The common methods to eliminate the magnetic interference of the mother ship mainly include the ship magnetic eight-azimuth test, Fourier series method, four-heading method, and example calculation. Among them, the ship magnetic eight-azimuth test uses the magnetic field to measure the course of the carrier ship and correct the ship magnetic azimuth of the magnetic survey data of the local ocean, which has high correction efficiency, but it is not as accurate as Fourier series method and four-heading correction method.


## 6.3. Detection and Verification Analysis of Local Marine Magnetic Anomaly Data

In order to verify the detection effect of local marine magnetic anomaly data considering robust trend surface, further experimental analysis and verification are needed. Select a sea area for field detection and inspection, and select gn-3765 towed marine magnetic anomaly detection device for relevant detection work. In order to eliminate the influence of data gross error, the detection data are corrected, and finally the isoline distribution map of magnetic anomaly data in the detection area is obtained. Secondly, the interference degree of gross error data on trend surface fitting is further verified by mixing less (usually no more than 9%) gross error with the detected local marine magnetic anomaly data.Firstly, the mixed local marine magnetic anomaly data is used as a new input to detect the robust trend surface, and the detection results are compared with the least squares trend surface. Secondly, the abnormal values in the two detection results are removed, and the difference of magnetic abnormal values before and after mixing is further obtained and compared. The results are shown in Table4.Table 4
Comparison of detection results of marine magnetic anomaly data.
Gross error number & proportionLeast squares trend surfaceRobust trend surfaceNumber foundNumber of testsRoot mean square errorNumber of foundNumber of testsRoot mean square error21 (2%)21595.146821375.173442 (4%)42915.367142795.391363 (6%)56865.598456855.606284 (8%)62695.812271975.865495 (9%)77786.136185996.1446105 (10%)89976.4164961106.4561It can be seen from the data in Table4 that the detection accuracy of the least squares trend surface decreases significantly with the increase of gross error content, which is not only prone to missed detection, but also unstable. Considering the robust trend surface, the detection of local marine magnetic anomaly data is not advanced, which has high detection accuracy, and its accuracy stability remains good with the increase of the number of gross errors. Therefore, considering the robust trend surface, the local marine geomagnetic field model can more effectively meet the practical utilization scenarios.


## 7. Conclusion

Through the detection of local marine geomagnetic parameters, the data of water depth, foreign language, and gravity field distribution can be obtained, so as to provide momentous hydrological support for the development of marine channels; on the other hand, marine magnetic anomaly data detection is also a momentous carrier and means to obtain seabed landform, material composition, and gravity characteristics. The most intuitive goal of local marine geomagnetic field modeling and magnetic anomaly data detection is to obtain the distribution law and typical characteristics of local marine geomagnetic field. In this paper, the detection method of local marine geomagnetic field is analyzed through the detection of local marine geomagnetic field magnetic anomaly data. By analyzing the theoretical basis of local marine geomagnetic field model, the mathematical model representation of geomagnetic field is studied. Finally, through the measurement, modeling, and analysis of local marine geomagnetic field data, the effectiveness of local marine geomagnetic field model and magnetic anomaly data detection considering robust trend surface is verified.



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*Source: 4055976-2022-05-09.xml*