Magnetic field migration imaging method and apparatus

Abstract

A method and device for magnetic field migration imaging comprises the following steps: establishing a forward algorithm of a magnetic field vector or its gradient based on the given subsurface rock m

Description

TECHNICAL FIELD

[0001] The present invention relates to a magnetic field migration imaging method and apparatus, and more particularly, to the field of exploration geophysics. BACKGROUND

[0002] With the advancement of science and technology, various technical methods have been developed to investigate the magnetic susceptibility and spatial distribution of subsurface target bodies by using surface magnetic field data. In the early stages, qualitative interpretation methods such as pole reduction, continuation, and boundary identification were mainly adopted. Subsequently, numerous quantitative inversion algorithms based on potential fields were developed, including two-dimensional (2D) and three-dimensional (3D) interactive fitting inversions and automatic inversion methods.

[0003] Some existing techniques employ the damped least-squares method to solve general nonlinear inversion problems in order to obtain stable solutions. Other existing approaches use the generalized inverse matrix selection method to iteratively invert 2D magnetic anomalies, thereby obtaining relatively accurate results for a finite set of composite plate models. With the continuous progress of computer technology, many new inversion algorithms have emerged, such as 3D smooth regularization inversion, 3D focused inversion, cluster-c-means focused inversion methods, joint inversion methods based on linear correlation constraints, and various 3D potential field gradient inversion techniques.

[0004] However, both 2D and 3D inversion processes are generally complex and timeconsuming, as they heavily depend on prior models and constraint conditions.

[0005] Migration imaging, by contrast, is a high-efficiency data processing technique, which was first developed in the fields of seismic wavefield imaging and electromagnetic field imaging. Mathematically, migration is described as the action of an adjoint operator on the observed data, where the adjoint operator represents the back-propagation function of the seismic or electromagnetic field. Based on the concept of potential-field migration, the present invention proposes a magnetic field migration imaging method and apparatus capable of efficiently reconstructing subsurface magnetic susceptibility distributions. SUMMARY

[0006] The present invention proposes a method and apparatus for magnetic field migration imaging, which enables automatic migration imaging of two-dimensional magnetic field vector data.

[0007] To solve the above-mentioned technical problems, the technical solutions adopted by the present invention are as follows:

[0008] In a first aspect, a magnetic field migration imaging method is provided, comprising: step SI: acquiring any two components or component gradients of the magnetic field above a target body as the observed magnetic field data; step S2: establishing a forward algorithm of a magnetic field vector or its gradient based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation; step S3: deriving an adjoint operator formula for any observed magnetic field based on the forward algorithm of the magnetic field vector; step S4: deriving an adjoint magnetic field from the adjoint operator of the observed magnetic field; step S5: deriving a magnetic susceptibility distribution function of the subsurface space from the adjoint magnetic field, thereby completing the migration imaging of the magnetic field vector; step S6: deriving a magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, thereby completing the migration imaging of the magnetic field gradient.

[0009] According to one possible implementation of the present embodiment, the forward algorithm of the magnetic field vector or its gradient based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation comprises:

[0010] assuming that the magnetization intensity in complex form satisfies:

[0011] 7(0 = 7x(x,z) + i7z(x,z) (1)

[0012] where 7(0denotes the magnetization intensity, <( = x + iz, 7x(x, zjrepresents the x-direction component of the magnetization intensity, 7z(x, z) represents the z-direction component, and i is the imaginary unit, and the magnetic field in the complex plane is defined as:

[0013] H«) = -Hx(x,z) + iH^x^ = Ah(I) = -2 ffr^ds (2)

[0014] where denotes the magnetic field intensity, AH represents the forward operator, and = x' + i;

[0015] Ix(x, z) = Hqy(x, z) cos 0 ; Iz(x, z) = HQy(x, z) sin 0 (3)

[0016] where y is the magnetic susceptibility, 0 is the magnetization angle, and Ho is the magnetic field intensity;

[0017] assuming the survey line lies on the ground (z' = 0), substituting equation (3) into equation (2), the magnetic field intensity on the survey line satisfies:

[0018] W) = —2 ffr—= —2 <4) IS S J lA A T1ZJ

[0019] for the magnetic field gradient = , the following being obtained:

[0020] HtW = -4 J^-^lCOds = -4 / 4 (5)

[0021] where denotes any point on the subsurface magnetic body = x + iz , ^'denotes any point on the ground, = x' + iz', and ds denotes the surface element of the subsurface magnetic body.

[0022]

[0023] 3. The magnetic field migration imaging method according to claim 2, characterised in that the derivation of an adjoint operator formula for any observed magnetic field based on the magnetic field vector forward algorithm comprises:

[0024] assuming that the survey line lies on L and the boundary of the magnetic body is T, introducing the Hilbert space in the complex plane:

[0025] (H, nD = H,fED (6)

[0026] where H denotes the theoretically calculated magnetic field intensity, f denotes the observed magnetic field, and D denotes the subsurface half-space.

[0027] introducing the real plane M:

[0028] (jyy^m = T], y £ M (7)

[0029] where q denotes the magnetization intensity.

[0030] for any observed field f(x'), introducing its adjoint operator then:

[0031] CA^Vd = >M (8)

[0032] expanding and rearranging both sides of the equation yields the adjoint operator of any observed field / (%'):

[0033] AH\f) = -2 f+™(c°s0+isin0^ (xq dx, L J \J J J-co (x-x' + iz)2 J V 7

[0034] the adjoint operator of the magnetic field intensity is:

[0035] = -2 C (10)

[0036] where (x') denotes the mirror magnetic field intensity.

[0037] According to one possible implementation of the present embodiment, deriving the djoint magnetic field from the adjoint operator of the observed magnetic field comprises:

[0038] since T* being the mirror image of the subsurface magnetic body r located in the lower half-space, (%') being the mirror field generated by F„ expressed as:

[0039] = —2 JJr-4— / -(Ods = -2 Hr.-^r(r)ds=HT.(x') (11)

[0040] where is referred to as the adjoint field, and let P+ denote the complex plane in the upper half-space and P- denote that in the lower half-space, separated by the x-axis, for any point { 6 f, a circle of radius R is drawn, and the portion of the real axis x within the circle is denoted by bR, while the portion within P- is denoted by CR, according to the Cauchy integral formula: [00411 ^.(0=^,,^^+^^ <EP- (12)

[0042] where the integration along the closed contour bR UCR is taken counterclockwise, and the integration along the real-axis segment bR is from right to left;

[0043] as R—>+Infinity, the integral along CR approaches zero, therefore, equation (12) can be rewritten as:

[0044] = ; ^P~ (13)

[0045] from the above, it follows that:

[0046] Hf(x') = HY^x'} (14)

[0047] and further: [0048W(<)=^C^df; ^P~ (15)

[0049] and considering equations (15) and (10), the adjoint magnetic field is obtained as:

[0050] AH*(Hr) = -4to(cos0 + isin0)Ho^ ) Hr*(0 (16)

[0051]

[0052] According to one possible implementation of the present embodiment, deriving the magnetic susceptibility distribution function of the subsurface space from the adjoint magnetic field, thereby completing the migration imaging of the magnetic field vector, comprises:

[0053] the depth weighting function wH equaling the square root of the integral sensitivity SH of the magnetic field complex intensity:

[0054] wH = 7¾ (17)

[0055] SH = Ho (18)

[0056] and the magnetic susceptibility distribution satisfing the following equation:

[0057] y"«) = = knW^^ReA^^H^knW^^ReAn^^H^knW^^ReH^1^ (19)

[0058] where A^H?) = w^A^H^-, A^ = A* and IK*HrHt IK1 AH*Hr lit

[0059] Kh = m2~——---- 2 (20)

[0060] expanding the above yields the subsurface magnetic susceptibility distribution function:

[0061] rJx.z) = 2k^z) C H0dX' + A J T J (21) U H v J J-co [(x-x'Y+Z2]2 U V 7

[0062] According to one possible implementation of the present embodiment, deriving the magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, thereby completing the migration imaging of the magnetic field gradient, comprises:

[0063] the magnetic field gradient being expressed as:

[0064] Ht^ = —4 JJr-^KOds = -4jjr = Hzz(x,z) + iHZx z) (22)

[0065] where Hzz denotes the gradient field of the horizontal component Hx of the magnetization intensity, and Hzx denotes the gradient field of the vertical component Hz of the magnetization intensity;

[0066] the adjoint operator of the magnetic field gradient is: [00671 ^.(0=^ / 27^^, (Cf (23)

[0068] the adjoint field of the magnetic field gradient is:

[0069] = = 2m(cos6 + isin0)Ho^HT*«) (24)

[0070] the migration imaging of the magnetic field gradient is expressed as:

[0071] YT(x. z) = -4kS-w52(z)_ Llx x ) J 4k^WH2 (z) J+00 Ho dx' (25)

[0072] According to one possible implementation of the present embodiment, the principle of the magnetic field migration imaging is as follows: the observation plane serves as a mirror plane, and it is assumed that a virtual “mirror field source” exists in the upper halfspace, with its corresponding potential field referred to as the “mirror field” (mathematically, this is termed the “migration field”), and downward continuation is performed for this migration field; since it is away from the field source, the upward continuation satisfies the first Dirichlet boundary value problem, and the solution of the equation is convergent and stable.

[0073] In a second aspect, a magnetic field migration imaging apparatus is provided, comprising: a magnetic field data acquisition module, configured to acquire any two components or component gradients of the magnetic field above a target body as observed magnetic field data; a forward algorithm establishment module, configured to establish a forward algorithm of a magnetic field vector or its gradient based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation; an adjoint operator derivation module, configured to derive an adjoint operator formula for any observed magnetic field based on the forward algorithm of the magnetic field vector; an adjoint magnetic field derivation module, configured to derive an adjoint magnetic field from the adjoint operator of the observed magnetic field; a magnetic field vector migration imaging module, configured to derive a magnetic susceptibility distribution function of the subsurface space from the adjoint magnetic field, thereby completing the migration imaging of the magnetic field vector; and a magnetic field gradient migration imaging module, configured to derive a magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, thereby completing the migration imaging of the magnetic field gradient.

[0074] In a third aspect, an electronic device is provided. The electronic device comprises a processor, a memory, and a bus; the memory stores machine-readable instructions executable by the processor; when the electronic device is in operation, the processor communicates with the memory via the bus, and executes the machine-readable instructions to perform the steps of the magnetic field migration imaging method.

[0075] In a fourth aspect, a computer-readable storage medium is provided. A computer program is stored on the computer-readable storage medium, and when executed by a processor, the computer program performs the steps of the magnetic field migration imaging method.

[0076] The technical solution provided in the embodiments of the present invention yields the following beneficial effects:

[0077] According to one embodiment of the present invention, a method for magnetic field migration imaging is provided. The method comprises the following steps: step SI: acquiring the basic data of the observed magnetic field, wherein the basic data of the observed magnetic field include rock magnetic susceptibility and magnetization intensity; step S2: establishing a forward algorithm of a magnetic field vector or its gradient based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation; step S3: deriving an adjoint operator formula for any observed magnetic field based on the forward algorithm of the magnetic field vector; step S4: deriving an adjoint magnetic field from the adjoint operator of the observed magnetic field; step S5: deriving a magnetic susceptibility distribution function of the subsurface space from the adjoint magnetic field, thereby completing the migration imaging of the magnetic field vector; step S6: deriving a magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, thereby completing the migration imaging of the magnetic field gradient, step s7: performing magnetic field migration imaging using the magnetic field vector migration imaging formula and the magnetic field gradient migration imaging formula. The invention constructs a magnetic field intensity forward modelling algorithm based on magnetic susceptibility and geomagnetic field strength, and applies it to magnetic vector migration imaging. This approach provides more accurate magnetic field intensity information, thereby improving the quality and anti-interference capability of magnetic vector migration imaging.

[0078] In addition, the introduction of magnetic field intensity adjoint operators, adjoint fields of magnetic field intensity, adjoint operators of magnetic field gradients, and adjoint fields of magnetic field gradients further enriches the information content of the magnetic field and enhances the efficiency of information utilization. Furthermore, the magnetic field intensity forward modelling algorithm and its application exhibit high real-time performance and accuracy, enabling effective handling of complex interference environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] FIG. 1 is a flowchart illustrating a method of magnetic field migration imaging according to an exemplary embodiment of the present invention;

[0080] FIG. 2 is a schematic structural diagram of a magnetic field migration imaging apparatus according to an exemplary embodiment of the present invention;

[0081] FIG. 3 is a schematic diagram illustrating a hypothetical complex plane for a two-dimensional magnetic problem according to an exemplary embodiment of the present invention;

[0082] FIG. 4 is a schematic diagram illustrating background field grids and model grids according to an exemplary embodiment of the present invention;

[0083] FIG. 5 is a schematic diagram illustrating magnetic field vectors and their gradients obtained through forward computation of a theoretical model at the surface according to an exemplary embodiment of the present invention, wherein (a) shows the vertical component Hzand the horizontal component Hxof the magnetic field intensity, and (b) shows the gradients of the vertical and horizontal components of the magnetic field intensity;

[0084] FIG. 6 is a schematic diagram illustrating the definition of an adjoint field according to an exemplary embodiment of the present invention;

[0085] FIG. 7 is a schematic diagram illustrating two magnetic bodies (Model II) buried at the same depth according to an exemplary embodiment of the present invention;

[0086] FIG. 8 is a schematic diagram illustrating the forward-simulated magnetic field and its gradients above Model II in FIG. 7, wherein (a) shows the vertical and horizontal magnetic field components obtained through forward calculation, and (b) shows the gradients of the vertical and horizontal magnetic field components obtained through forward calculation;

[0087] FIG. 9 is a schematic diagram illustrating magnetic field component migration imaging according to an exemplary embodiment of the present invention;

[0088] FIG. 10 is a schematic diagram illustrating magnetic field gradient migration imaging according to an exemplary embodiment of the present invention;

[0089] FIG. 11 is a schematic diagram illustrating measurement of horizontal and vertical magnetic field gradients according to an exemplary embodiment of the present invention;

[0090] FIG. 12 is a graph illustrating a curve of the horizontal magnetic field gradient Hxxalong the X direction according to an exemplary embodiment of the present invention; and

[0091] FIG. 13 is a schematic diagram illustrating migration imaging of measured magnetic field gradient data according to an exemplary embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0092] To more clearly illustrate the technical features of the present invention, specific embodiments are described in detail below with reference to the accompanying drawings.

[0093] As shown in FIG. 1, a method of magnetic field migration imaging provided according to an embodiment of the present invention includes the following steps:

[0094] Step SI: Acquire any two components or component gradients of the magnetic field above a target body as the observed magnetic field data.

[0095] Step S2: Establish a forward algorithm for magnetic field vectors or their gradients based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation.

[0096] Step S3: Derive the adjoint operator formula for any observed magnetic field based on the forward algorithm of the magnetic field vector.

[0097] Step S4: Derive the adjoint magnetic field from the adjoint operator of the observed magnetic field.

[0098] Step S5: Derive the subsurface magnetic susceptibility distribution function from the adjoint magnetic field, thereby completing magnetic field vector migration imaging.

[0099] Step S6: According to the principle of magnetic field vector migration imaging, derive the magnetic susceptibility spatial distribution function of the magnetic field gradient, thereby completing magnetic field gradient migration imaging.

[0100] In one possible implementation of this embodiment, the step of establishing the forward algorithm for magnetic field vectors or their gradients based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation includes the following:

[0101] Assume that the complex form of magnetization intensity satisfies:

[0102] 7«) = 7%(x,z) + i7z(x,z) (1) where / (^denotes the magnetization intensity, the variable = x + iz, Ix(x, z)is the x-component of the magnetization intensity, lz(x, z)is the z-component of the magnetization intensity, and iis the imaginary unit.

[0103] The magnetic field intensity in the complex plane is then defined as: W«) = -Hx(x,z} + iHz{x,z^ = AhW = -2 ffr^ds (2) where H(^')denotes the magnetization intensity, represents the forward operator, and <= x' + i.

[0104] Ix(x, z) = Hoy(x, z)cos 0, 7z(x, z) = Hoy{x, z)sin 0 (3) where y denotes the magnetic susceptibility, 0 denotes the magnetization angle, and Ho denotes the geomagnetic field intensity.

[0105] When the measuring line is located at the ground surface z' = 0, substituting Equation (3) into Equation (2) yields the following expression for the magnetic field intensity along the measuring line:

[0106] HR') = —2 J / r—^IR)ds = —2 (4) IS S J 1 ^A A TLA J For the magnetic field gradient , the following is obtained: Ht^ = -4 ff--^3 I«)ds = —4 ff (cos0 + isin0) Hny ----------— ds (x + iz — x') (5) where $ denotes any point on the subsurface magnetic body $ = x + iz, ^'denotes any point on the ground, $ = x' + iz', and ds denotes the surface element of the subsurface magnetic body.

[0107] As one possible implementation of the present embodiment, based on the magnetic field vector forward algorithm, the adjoint operator formula for any observed magnetic field is derived, comprising:

[0108] Assuming that the survey line lies on L, and the magnetic body boundary is denoted by T, a complex plane in the Hilbert space is introduced as follows:

[0109] (H, nD = SLH^r^'W; HJED (6) where H represents the theoretically calculated magnetic field intensity, f represents the observed magnetic field, and D denotes the subsurface half-space.

[0110] A real plane M is introduced as:

[0111] (77,y)m = HrTl(OY(Ods; T], y £ M (7)

[0112] where r| denotes the magnetization intensity.

[0113] For any observed field / (%'), the adjoint operator of the observed field is introduced, and we have:

[0114] (^(7), / )0 = (7^( / ))^ (8) Expanding and rearranging both sides of the equation yields the adjoint operator of any observed field f(x'~):

[0115] AH\f) = -2 J+°° f* (x') dx' (9) L J J Qx-x' + iz)2 J v J Thus, the adjoint operator of the magnetic field intensity is:

[0116] AH\Hr) = —2 (x') dx' (10) where (%') represents the mirror magnetic field intensity.

[0117] As one possible implementation of the present embodiment, the adjoint magnetic field is derived from the adjoint operator of the observed magnetic field, comprising:

[0118] Since E is the mirror image of the magnetic body flocated in the lower half-space, (x')is the mirror field generated by E:

[0119] Ufa') = -2 ff-r^ds =—2 ff —^—P(^,)ds=H[-.(x') (11) IS A J IS A J

[0120] The field H^is defined as the adjoint field. Let P+denote the complex plane in the upper half-space and P~denote that in the lower half-space, separated by the x-axis. For any point G T, draw a circle of radius R; the real-axis segment within the circle is denoted by bR, and the arc portion within P“is denoted by CR. According to Cauchy’s integral formula, we have: [O^JHr.GO =^bR^d?+^c^d<;'; ^p- (12) where the integrals along the closed contour bR U CRare taken in the counterclockwise direction, and the integral along the real-axis segment bRproceeds from right to left. In the limit as R—+Inf inity, the integral over CRtends to zero, and thus Eq. (12) can be rewritten as:

[0122] <EP~ <13) From the above expression, it follows that:

[0123] H^x'} = H^x') (14) and further:

[0124] (er (15) Considering Equations (15) and (10), the adjoint magnetic field can be obtained as:

[0125] = -47ri(cos 0 + isin 0)Ho^(r.)«) (16) As one possible implementation of the present embodiment, the magnetization susceptibility distribution function of the subsurface is derived from the adjoint magnetic field, thereby completing the magnetic field vector migration imaging, comprising:

[0126] The depth weighting function wH equals the square root of the integral sensitivity SHof the complex magnetic field intensity:

[0127] wH = 7¾ (17) 2n Sh = h°jTz~^ (18)

[0128] The magnetization susceptibility distribution satisfies the following formula:

[0129] yW = w^z^ = kHWu\z)ReA^(Hr)=kHw„2(z)ReAH\Hr^ (19)

[0130] where = w^A^XH^; A^ = A^1; rnn1l . II^HrllM L J H WA^H^ Expanding the above formula yields the magnetization susceptibility distribution function of the subsurface:

[0132] = 2k^w^ C Wx' + k^w^2 (z) J+°° (stneHfco*0HJ^ Hdx' (2 i) U n V J J-co [(x-X!)2+Z2]2 U V J

[0133] As one possible implementation of the present embodiment, according to the magnetic field vector migration imaging principle, the spatial magnetization susceptibility distribution function of the magnetic field gradient is derived, thereby completing the magnetic field gradient migration imaging, comprising:

[0134] The magnetic field gradient is given as: = -<-^1(0^ = - HZ^z) + iHzx(X,z) (22)

[0135] where Hzz is the gradient field of the horizontal component Hx of the magnetization intensity, and Hzxis the gradient field of the vertical component Hz.

[0136] The adjoint operator of the magnetic field gradient is:

[0137] HT.K^^f^^^dx'-. (er (23) The adjoint field of the magnetic field gradient is: a2

[0138] = A$Ht = 2m(cos 0 + isin 0)Ho^%*)«) (24) The magnetic field gradient migration imaging is expressed as:

[0139] yT(x >z) = <X~X,) Hodx' - U H V J J-m [(x—X^ + Z2]3 u 4k^vS2(z)J+“ (25)

[0140] As one possible implementation of the present embodiment, the principle of magnetic field migration imaging is as follows: taking the observation plane as a mirror surface, it is assumed that a virtual "mirror field source” exists in the upper half-space. The corresponding potential field is called the mirror field, which is mathematically referred to as the migration field. This migration field is downward continued, and since it is located away from the field source, the upward continuation equation satisfies Dirichlet’s first boundary value problem, with its solution being convergent and stable.

[0141] The present invention provides a magnetic field migration imaging algorithm with high computational efficiency, strong noise resistance, and stable convergence.

[0142] As shown in Figure 2, in a second aspect, an embodiment of the present invention provides a magnetic field migration imaging apparatus, comprising:

[0143] a magnetic field data acquisition module, configured to acquire any two components or component gradients of the magnetic field above the target as observation magnetic field data;

[0144] a forward algorithm construction module, configured to establish the forward algorithm of the magnetic field vector or its gradient based on given subsurface rock magnetization susceptibility or magnetization intensity parameters and magnetic field integral equations;

[0145] an adjoint operator derivation module, configured to derive the adjoint operator formula of any observation magnetic field based on the magnetic field vector forward algorithm;

[0146] an adjoint magnetic field derivation module, configured to derive the adjoint magnetic field from the adjoint operator of the observation magnetic field;

[0147] a magnetic field vector migration imaging module, configured to derive the subsurface magnetization susceptibility distribution function from the adjoint magnetic field, thereby completing the magnetic field vector migration imaging;

[0148] a magnetic field gradient migration imaging module, configured to derive the magnetization susceptibility spatial distribution function of the magnetic field gradient according to the magnetic field vector migration imaging principle, thereby completing the magnetic field gradient migration imaging.

[0149] The magnetic field belongs to a potential field or conservative field. In a potential field, migration imaging essentially determines the location of the field source by downward analytical continuation, and the migration is manifested as a special form of downward continuation of the potential field and its gradient. However, the mathematical equations for downward continuation constitute an ill-posed problem, whose solutions are unstable and easily divergent.

[0150] To overcome this problem, it is assumed that a virtual "mirror field source” exists in the upper half-space with the observation plane as a mirror surface. The corresponding potential field is called a mirror field, mathematically referred to as a migration field. Performing downward continuation on this migration field means it is actually located away from the mirror field source, and this migration process is effectively an upward continuation. Since the mathematical equation for upward continuation satisfies Dirichlet’s first boundary value problem, its solution is convergent and stable. Therefore, this assumption is correct and feasible. The migration field (mirror field) can be derived from the measured field through a migration operator. The adjoint operator can be iterated multiple times, making the iterative potential field migration equivalent to a regularized inversion process, similar to electromagnetic migration iterations.

[0151] Thus, the present invention proposes a magnetic field migration imaging algorithm, whose principle is as follows: taking the observation plane as a mirror, assuming the existence of a virtual "mirror field source” in the upper half-space, with the corresponding potential field called a mirror field or mathematically a migration field, and performing downward continuation on this migration field. Since it is located away from the field source, this is effectively an upward continuation. Because the upward continuation equation satisfies Dirichlet’s first boundary value problem, the solution is convergent and stable.

[0152] After acquiringthe basic field data on site, the specific implementation process of the magnetic field migration imaging is as follows:

[0153] I. Constructing the forward operator of the magnetic vector or its gradient.

[0154] Based on the given subsurface rock magnetization susceptibility or magnetization intensity parameters, as shown in Figure 3, it is assumed that any two orthogonal magnetic vectors or gradients form a complex plane, and the forward algorithm of the magnetic field vector and its gradient is established based on the magnetic field integral equation.

[0155] Assuming that the magnetization intensity in complex form satisfies the following formula:

[0156] 7«) = 7%(x,z) + i7z(x,z) (1)

[0157] where / (^) is the magnetization intensity, = x + iz, Ix(x, z) is the x-component of magnetization intensity, lz(x, z)is the z-component of magnetization intensity, and iis the imaginary unit. Then the magnetic field intensity in the complex plane is defined as:

[0158] = -Hx(x,z} + iH^x^ = AH^ = -2 ffr^ds (2) where A" denotes the forward operator, and = x' + iz'-,

[0159] Ix(x, z) = Hoy(x, z)cos 0;Iz(x, z) = Hoy(x, z)sin 0 (3) where yis the magnetization susceptibility and Hois the geomagnetic field intensity. Assuming the survey line is at z' = Oon the ground, substituting Equation (3) into Equation (2), the magnetic field intensity on the survey line satisfies:

[0160] Hr(O = -4jJr-^l«)ds = -4 / Jr^i^^ (4)

[0161] For the magnetic field gradient HT(0 = the following formula is obtained:

[0162] HX?) = ~4 / Jr~0 l«)ds = —4 JJ H°vds (5)

[0163] where 0s any point in the subsurface magnetic body = x + iz, and 0is any point on the ground (' = x' + iz'. According to Equations (4) and (5), the two-dimensional magnetic field distribution can be calculated, as shown in Figures 4 and 5.

[0164] In Figure 4, the solid grid represents the background field grid, with the calculation region in the X direction ranging from -2050 m to +2050 m with a step of 100 m, and in the Z direction ranging from -50 m to -1050 m with a step of 100 m. The dashed grid represents the model grid, with the model region in the X direction ranging from -1100 m to +1100 m with a step of 100 m, and in the Z direction from 0 to -1000 m with a step of 100 m. The gray-filled cells indicate the location and size of the magnetic body, which has a length of 100 m along the X direction, a depth extent of 200 m, a top burial depth of -400 m, and a center located at x = 50 m. The magnetization susceptibility is 0.4, while the other cells have a magnetization susceptibility of 0. The total magnetic field produced by the magnetic body at the ground (Z = 0) is calculated, including the horizontal component Hx, the vertical component Hz, and their gradient fields Hzzand Hzx.

[0165] Figure 5 shows the forward calculation results. In Figure 5a, the vertical (Hz) and horizontal (Hx} components of the magnetic field intensity are shown, with anomalies mainly distributed between -550 m and +450 m. The magnetic field gradient anomalies are concentrated between -500 m and +400 m, as shown in Figure 5b. From the forward results, the magnetic field gradient anomaly range is narrower and closer to the horizontal position of the magnetic body. Comparing the forward results of Model 2 with Model 1, as the burial depth of the magnetic body increases, the magnetic anomaly amplitude decreases and the lateral range increases, indicating that determining the precise position of the magnetic body becomes more difficult.

[0166] II. Deriving the adjoint operator of any observation magnetic field.

[0167] Based on the magnetic field vector forward algorithm, the specific process for deriving the adjoint operator formula of any observation magnetic field is as follows:

[0168] Assume the survey line is on Land the boundary of the magnetic body is T. Introduce a Hilbert space complex plane:

[0169] CH, nD = iLH^r tt'W; H,f ED (6) where His the theoretically computed magnetic field intensity, / is the observation magnetic field, and Pis the subsurface half-space.

[0170] Introduce the real plane M\

[0171] = rj, y E M (7) where zyis the magnetization intensity.

[0172] For any observation field / (%'), introduce the adjoint operator

[0173] = (8)

[0174] Expanding both sides of the above equation and rearranging, the adjoint operator for any observation field / (x')is obtained as:

[0175] = (x') dx' (9) L J V J J_co (x-x' + iz)2 7 J Then, the adjoint operator of the magnetic field intensity is:

[0176] ^(^) = -2^7^2^-^ (1°) where H^x'^is the mirror magnetic field intensity.

[0177] III. Deriving the adjoint magnetic field from the observation field’s adjoint operator.

[0178] Since Fjs the mirror of the subsurface magnetic body T, H^x'^is the mirror field caused by P:

[0179] 11((+-) = -21 / ,.-^4- / -(0^=-2 / / ,.,-^ / -( / ^ (11) Here, HrJs called the adjoint field. As shown in Figure 6, let P+be the complex plane of the upper half-space, P“be the lower half-space, separated by the x-axis. For any point ( £ F, draw a circle of radius R. The portion of the real axis xinside the circle is denoted by bR, and the part inside the circle in P“is denoted by CR. According to the Cauchy integral formula:

[0180] ^P~ (12) The integration over the closed contourbRUCRis counterclockwise, and the integral over the real axis segment bRis from right to left. Taking the limit as R—+Inf inity, the integral over CRtends to 0, so Equation (12) can be written as:

[0181] Hr.(O (EP~ (13) From the above formula, it follows that:

[0182] H^x') = HrJx') (14) Further:

[0183] WO =7- / ^77^ (15) Considering Equations (15) and (10), the adjoint magnetic field is:

[0184] A(h*\Ht) = -47ri(cos 0 + isin 0)Ho^Hr$(() (16) IV. Deriving the subsurface magnetization susceptibility distribution function from the adjoint magnetic field.

[0185] Let SHbe the integral sensitivity of the magnetic field complex intensity, and wHbe the depth weighting function, equal to the square root of SH\

[0186] wH = (17)

[0187] SH=Ha^ (18) The magnetization susceptibility distribution satisfies the following formula:

[0188] = ^(z)^ = kHw^1(z)ReA^(Hr)=kHw^2 (z)ReAH*(Hr)=kHw^2 (z)ReH^(() (19)

[0189] where

[0190] = = A*w„\ II A^Hr \\2m || w^A^Hr \\2m H WA^HV\\2U II A^w^A^Hv \\2m 1 }

[0191] Expanding the above formula, the subsurface magnetization susceptibility distribution function is obtained:

[0192] Ym(x,z) = + I I A. AC J ”r J e+^tsindHx+cosdH^x-x^z ,, , . k»w" (z)]^---[(x_x,)2+z2]2---Wx (21)

[0193] V. Deriving the magnetization susceptibility distribution function of the magnetic field gradient based on the magnetic field vector migration imaging principle.

[0194] Using the same method, the migration imaging correlation functions based on the magnetic field vector gradient can be obtained:

[0195] Magnetic field gradient:

[0196] MG = -4jJr-^I(Qds = -4jJr^^^ = Hzz(x,z) + iHzx(x,z) (22)

[0197] Adjoint operator of the magnetic field gradient: [019S]HT.«)=++”^dx'; (EF Adjoint field of the magnetic field gradient: a2

[0199] = A*tHt = 27ri(cos 6 + isin (24) Migration imaging of the magnetic field gradient (magnetization susceptibility distribution function):

[0200] yJ,(x >z) = 0 H V [(X-x')2+z2]3 0 4k;>H2(z)f+c"^^^ (25) 0 H V J [(x—x^+z2]3 0 v J

[0201] VI. Testing and validation of magnetic field migration imaging.

[0202] 1) Testing with theoretical model forward data

[0203] The theoretical model is shown in Figure 7: two magnetic bodies have a top burial depth of 400 m, a horizontal separation of 1800 m, magnetization susceptibility of 0.4, length along the x-direction of 100 m, and depth extent of approximately 200 m. The center of the left magnetic body is located atx = —950 m, and the center of the right magnetic body is located at x = +950 m.

[0204] Through forward calculation, the vertical and horizontal magnetic field components, i.e., Hz and Hx, were obtained as shown in Figure 8a, as well as the gradients of vertical and horizontal magnetic field components, i.e., Hzx and Hxx, as shown in Figure 8b. It can be observed that although the two magnetic bodies are relatively far apart, both magnetic field components are still affected to some extent; for example, the Hz anomaly shows poor symmetry, and the minimum of the Hx anomaly is larger than its maximum.

[0205] Applying the magnetic field migration imaging to the above magnetic field component data yields the results shown in Figures 9 and 10. As shown in Figure 9, the maximum magnetization susceptibility of subsurface units obtained from magnetic field migration imaging is 0.15, which is smaller than the theoretical model value of 0.4. The centers of the two magnetic bodies match the centers of the magnetic bodies in the model. As shown in Figure 10, the magnetic field gradient migration imaging accurately corresponds to the locations of the magnetic bodies. The maximum magnetization susceptibility of the unit magnetic bodies is 0.1, consistent with the model body locations, but with slightly smaller susceptibility values. It can also be observed that the inversion results of the magnetic field gradient converge better than those of the magnetic field itself.

[0206] 2) Testing with physical experimental data for migration imaging

[0207] To further verify the adaptability of the migration imaging algorithm to measured data, an actual observation was conducted outdoors using a magnetometer on an iron block of size 5x5x5 cm3, as shown in Figure 11. The survey line was oriented east-west, with a total length of 3.0 m, a point spacing of 0.1 m, a height above ground of 0.3 m, and a probe spacing of 0.6 m. The magnetic field gradient value was defined as the difference between probe 1 and probe 2. For the horizontal gradient Ha, the two probes on the left in Figure 11 were placed horizontally; for the vertical gradient Hzx, the two probes on the right in Figure 11 were placed vertically.

[0208] To eliminate part of the measurement error, each measurement point was observed three times, and the average value was taken as the final value, forming the magnetic field gradient curve as shown in Figure 12. The horizontal magnetic field gradient Hxx exhibits a maximum and a minimum. When the magnetic probes are far from the target body, Hxx varies between —27 and —40 nT / m. When the first probe approaches the iron block, the magnetic field gradient increases, reaching a maximum of 206.37 nT / m. When the iron block is located between the two probes, the horizontal magnetic field gradient is close to 0 nT. When the second probe passes over the iron block, the gradient reaches the minimum value of —283.97 nT / m. The large difference in amplitude between the two extreme values may be due to inconsistent sensitivity between the two probes, or distance errors between the probes and the iron block during measurement, as the probes are only 0.3 m from the block.

[0209] For the vertical magnetic field observation, the magnetic field gradient Hzx values at both ends of the survey line are between —40 and —110 nT / m. When the probe passes over the iron block, a minimum of —267.97 nT / m occurs, with the anomaly being approximately symmetric on both sides. In addition, large jumps in the measurement data on the right side of the survey line indicate significant external interference. The noise-to-minimum ratio is approximately 27.7%.

[0210] According to the migration imaging principle and the particularity of the mirror field and its corresponding original field, the Hxx of the mirror field equals that of the original field, but it is opposite to Hzx. By using the mirror field, the adjoint operator can be obtained, and the magnetization susceptibility distribution can be determined. Applying migration imaging to the measured data, the results are shown in Figure 13. The target body is clearly imaged, with a maximum susceptibility of approximately 0.05. Its lateral center position is generally consistent with the magnetic body, located between 1.4-1.6 m. The top burial depth of the target body from migration imaging is 0.5 m, while the model’s top burial depth is 0.3 m, showing some deviation, indicating that this method has limited depth resolution. As can be seen from Figure 12, although the right side of the vertical magnetic field Hzx curve is strongly affected by noise, the migration imaging still performs well, demonstrating the strong anti-noise capability of this algorithm.

[0211] This invention conducted numerical simulations and physical experiments to study the migration imaging algorithm. Multiple model examples were constructed to verify the effectiveness of two-dimensional magnetic field and gradient migration imaging. Grid division was optimized, and tests with different noise data were performed to verify algorithm robustness. Physical experiments provided measured magnetic field data, confirming that the algorithm is stable and reliable.

[0212] The present invention realizes automatic migration imaging of two-dimensional magnetic field vector data with strong anti-interference capability.

[0213] An embodiment of the present invention provides an electronic device, which includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the device is in operation, the processor communicates with the memory via the bus and executes the machine-readable instructions to perform the steps of any of the magnetic field migration imaging methods described above.

[0214] Specifically, the aforementioned memory and processor may be general-purpose memory and processor, without further limitation. When the processor executes a computer program stored in the memory, it is capable of performing the magnetic field migration imaging method as described above.

[0215] Those skilled in the art can understand that the structure of the electronic device does not constitute a limitation. The device may include more or fewer components than illustrated, or certain components may be combined, separated, or arranged differently.

[0216] In some embodiments, the electronic device may further include a touchscreen, which can be used to display a graphical user interface (e.g., the startup interface of an application) and receive user operations on the graphical user interface (e.g., the operation to start the application). Specifically, the touchscreen may include a display panel and a touch panel. The display panel can be configured using LCD (Liquid Crystal Display), OLED (Organic Light-Emitting Diode), or other forms. The touch panel collects contact or non-contact operations performed by the user on or near it and generates pre-set operation commands. For example, the user may use a finger, stylus, or any suitable object or accessory to operate on or near the touch panel.

[0217] Additionally, the touch panel may include a touch detection device and a touch controller. The touch detection device detects the user’s touch position and gesture and converts the signal resulting from the touch operation to the touch controller. The touch controller receives touch information from the touch detection device, converts it into information that the processor can handle, and sends it to the processor. It can also receive commands from the processor and execute them. The touch panel may be implemented using resistive, capacitive, infrared, surface acoustic wave technologies, or any future-developed technology. Furthermore, the touch panel may cover the display panel. The user can operate on or near the touch panel according to the graphical user interface displayed on the display panel. After detecting the operation, the touch panel transmits the input to the processor, which then provides corresponding visual output on the display panel. The touch panel and display panel may be implemented as two separate components or integrated together.

[0218] Corresponding to the above application startup method, an embodiment of the present invention further provides a storage medium, which stores a computer program. When executed by a processor, the program performs the steps of any of the magnetic field migration imaging methods described above.

[0219] The application startup device provided in the present embodiment may be specific hardware on a device or software / firmware installed on the device. The principles and technical effects of the device are the same as those of the method embodiments described above. For brevity, the device embodiment description refers to the corresponding method embodiment. Those skilled in the art can understand that for convenience and simplicity, the specific working process of the described systems, devices, and units may refer to the corresponding processes in the above method embodiments and will not be repeated here.

[0220] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the embodiments may be implemented entirely in hardware, entirely in software, or in a combination of software and hardware. The embodiments may also be provided in the form of a computer program product stored on one or more computer-readable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.), containing computer-usable program code.

[0221] In the embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. The described device embodiments are illustrative. For example, the module division represents a logical function division; in practical implementation, other divisions may be used. Multiple modules or components may be combined or integrated into another system; some features may be omitted or not executed. The coupling or direct / communication connection between the shown or discussed modules may be via communication interfaces, or indirect coupling / communication, which maybe electrical, mechanical, or other forms.

[0222] Modules described as separate components may or may not be physically separated. Components shown as modules may or may not be physical modules; they may reside in a single location or be distributed across multiple network modules. Part or all of the modules may be selected according to actual needs to achieve the objectives of the present embodiment.

[0223] Further, functional modules in the embodiments provided may be integrated into one processing module, exist separately, or two or more modules may be integrated into one module.

[0224] The present application is described with reference to flowcharts and / or block diagrams of the methods, devices (systems), and computer program products provided herein. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and combinations thereof, may be implemented by computer program instructions. These instructions can be provided to a general-purpose computer, dedicated computer, embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by a computer or other programmable device create a device for performing the functions specified in one or more flows or blocks of the flowchart or block diagram.

[0225] These computer program instructions may also be stored in a computer-readable storage medium, which can guide the computer or other programmable devices to operate in a specific manner, producing a manufactured product including the instruction device, which performs the functions specified in one or more flows or blocks of the flowchart or block diagram.

[0226] These computer program instructions may also be loaded onto a computer or other programmable device, so that executing a series of operations on the computer or device produces computer-implemented processing, thereby providing steps to achieve the functions specified in one or more flows or blocks of the flowchart or block diagram.

[0227] Finally, it should be noted that the above embodiments are provided to illustrate the technical solutions of the present invention and not to limit it. Although the invention has been described in detail with reference to the above embodiments, those skilled in the art can make modifications or equivalent substitutions to the specific embodiments of the invention without departing from the spirit and scope of the invention, and all such modifications or substitutions are intended to be encompassed within the scope of the claims of the present invention.

Claims

What is claimed is:

1. A magnetic field migration imaging method, comprising:step SI: acquiring any two components or component gradients of the magnetic field above a target body as the observed magnetic field data;step S2: establishing a forward algorithm of a magnetic field vector or its gradient based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation;step S3: deriving an adjoint operator formula for any observed magnetic field based on the forward algorithm of the magnetic field vector;step S4: deriving an adjoint magnetic field from the adjoint operator of the observed magnetic field;step S5: deriving a magnetic susceptibility distribution function of the subsurface space from the adjoint magnetic field, thereby completing the migration imaging of the magnetic field vector;step S6: deriving a magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, thereby completing the migration imaging of the magnetic field gradient.

2. The magnetic field migration imaging method according to claim 1, characterised in that the forward algorithm of the magnetic field vector or its gradient based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation comprises:assuming that the magnetization intensity in complex form satisfies:KO = Ix&z) + ilz(x,z) (1)where KOdenotes the magnetization intensity, = x + iz, Ix(x, z)represents the x-direction component of the magnetization intensity, / z(x, z) represents the z-direction component, and i is the imaginary unit, and the magnetic field in the complex plane is defined as:W«) = -Hx(x,z') + iH^x^ = Ah(I) = -2 ffr^ds (2)where H(^')denotes the magnetic field intensity, represents the forward operator, and ( = x' + i',Ix(x, z) = Hoy(x, z) cos 9 ; Iz(x, z) = Hoy(%, z) sin 0 (3)where y is the magnetic susceptibility, 0 is the magnetization angle, and Ho is the magnetic field intensity;assuming the survey line lies on the ground (z' = 0), substituting equation (3) into equation (2), the magnetic field intensity on the survey line satisfies:= = (4)’J JJr (x-x'+iz)2 v 7for the magnetic field gradient HT(O = the following being obtained:«r(?) = ^ / Jf-^KOds = —4jJ1 1 (x+iz-x'^where denotes any point on the subsurface magnetic body = x + iz, ^'denotes any point on the ground, ( = x' + iz', and ds denotes the surface element of the subsurface magnetic body.

3. The magnetic field migration imaging method according to claim 2, characterised in that the derivation of an adjoint operator formula for any observed magnetic field based on the magnetic field vector forward algorithm comprises:assuming that the survey line lies on L and the boundary of the magnetic body is T, introducing the Hilbert space in the complex plane:nD = HJED (6)where H denotes the theoretically calculated magnetic field intensity, f denotes the observed magnetic field, and D denotes the subsurface half-space.introducing the real plane M:GmOm = iir9(OY(Ods; T], yEM (7)where q denotes the magnetization intensity.for any observed field f(x'), introducing its adjoint operator then:(AHM,nD = (y.A»\n) M (8)expanding and rearranging both sides of the equation yields the adjoint operator of any observed field f(x'y.AH\f) = -2- +co (cos 6 + i sin 9)Hoy (x—x' + iz)2f* (x’) dx'(9)the adjoint operator of the magnetic field intensity is:+°° {cos 9 + i sin 9)HoyHf(x')dx'(10)where (x') denotes the mirror magnetic field intensity.

4. The magnetic field migration imaging method according to claim 3, characterised in that deriving the adjoint magnetic field from the adjoint operator of the observed magnetic field comprises:since T* being the mirror image of the subsurface magnetic body T located in the lower half-space, (%') being the mirror field generated by T*, expressed as:H((x') = -2^-^(1^ = -2^^1^)^=^,(^ (11)IS x J IS )where Hr„ is referred to as the adjoint field, and let P+ denote the complex plane in the upper half-space and P- denote that in the lower half-space, separated by the x-axis, for any point ( E f, a circle of radius R is drawn, and the portion of the real axis x within the circle is denoted by bR, while the portion within P- is denoted by CR, according to the Cauchy integral formula:+ ^P~ (12)2711 \ 27TI ck s —Swhere the integration along the closed contour bRUCR is taken counterclockwise, and the integration along the real-axis segment bR is from right to left;as R—+Infinity, the integral along CR approaches zero, therefore, equation (12) can be rewritten as:(13)from the above, it follows that:H*v{x'}=H^{x'} (14)and further:= (er (15)and considering equations (15) and (10), the adjoint magnetic field is obtained as:AH*(Hr) = —4m(cos0 + isin0)Ho^) Hr*(0 (16)5. The magnetic field migration imaging method according to claim 4, characterised in that deriving the magnetic susceptibility distribution function of the subsurface space from the adjoint magnetic field, thereby completing the migration imaging of the magnetic field vector, comprises:the depth weighting function wH equaling the square root of the integral sensitivity SH of the magnetic field complex intensity:wh = (17)s«=h°J¥ (18)and the magnetic susceptibility distribution satisfying the following equation: = =kHw^1(z)ReA^(Hr)=kHw^2 (z)ReAH*(Hr)=kHw^2 (z)ReH^(() (19)where A^^Hy = w^A^^y, A% = A * Wy1' andK = no)expanding the above yields the subsurface magnetic susceptibility distribution function:Z A 07 w -2z \ r+oo (cos0Hx-sin0HA[(x-x'y-z2] .. , ,r,„(x,z) = 2k^wH2(z)f_m i——-H«dx +U H V J ^X~x')2 + Z2]2 u6. The magnetic field migration imaging method according to claim 5, characterised in that deriving the magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, thereby completing the migration imaging of the magnetic field gradient, comprises:the magnetic field gradient being expressed as:= -4^77¼10^ = ~4^ ds = H^ + iH^x^(22)where Hzz denotes the gradient field of the horizontal component Hx of the magnetization intensity, and Hzx denotes the gradient field of the vertical component Hz of the magnetization intensity;the adjoint operator of the magnetic field gradient is:=— f+C°^^dx'; (EP~ (23)the adjoint field of the magnetic field gradient is:a2H™ = = 2ni(cos6 + isin6)H0 — (24)the migration imaging of the magnetic field gradient is expressed as:Ym(x ’ z) =-4k;>Hyz) -0 H V 7 J_oo [(x-x')2 + z2]3 04k™WH2(z) / +°° (25)U H V J [(x—X^+Z2]3 U7. The magnetic field migration imaging method according to any one of claims 1-6, characterised in that the principle of the magnetic field migration imaging is as follows: the observation plane serves as a mirror plane, and it is assumed that a virtual “mirror field source” exists in the upper half-space, with its corresponding potential field referred to as the “mirror field” (mathematically, this is termed the “migration field”), and downward continuation is performed for this migration field; since it is away from the field source, the upward continuation satisfies the first Dirichlet boundary value problem, and the solution of the equation is convergent and stable.

8. A magnetic field migration imaging apparatus, comprising:a magnetic field data acquisition module, configured to acquire any two components or component gradients of the magnetic field above a target body as observed magnetic field data;a forward algorithm establishment module, configured to establish a forwardalgorithm of a magnetic field vector or its gradient based on the given subsurface rock magnetic susceptibility or magnetization intensity parameters and the magnetic field integral equation;an adjoint operator derivation module, configured to derive an adjoint operator formula for any observed magnetic field based on the forward algorithm of the magnetic field vector;an adjoint magnetic field derivation module, configured to derive an adjoint magnetic field from the adjoint operator of the observed magnetic field;a magnetic field vector migration imaging module, configured to derive a magnetic susceptibility distribution function of the subsurface space from the adjoint magnetic field, thereby completing the migration imaging of the magnetic field vector; anda magnetic field gradient migration imaging module, configured to derive a magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, thereby completing the migration imaging of the magnetic field gradient.

9. An electronic device, characterised in that it comprises a processor, a memory, and a bus; the memory stores machine-readable instructions executable by the processor; when the electronic device is in operation, the processor communicates with the memory via the bus, and executes the machine-readable instructions to perform the steps of the magnetic field migration imaging method according to any one of claims 1-7.

10. A computer-readable storage medium, characterised in that a computer program is stored thereon, and when executed by a processor, the computer program performs the steps of the magnetic field migration imaging method according to any one of claims 1-7.T +44(0)30 0300 2000Search report under Section 17 of the Patents Act 1977Application No.: GB2517812.0Claims searched: 1-10Date search completed: 12 February 2026International classificationSubclass and subgroup Valid from G01V3 / 38 01 / 01 / 2006Field of searchWorldwide search of patent documents classified in the following areas of the IPC: G01VDatabases used in the preparation of this search report:SEARCH-NPL; SEARCH-PATENTDocuments considered to be relevantPatent literat Category ure Relevant to claims Document of relevance A, P - CN 119087527 A (SHANDONG COAL GEOLOGICAL SURVEY AND RES INSTITUTE) - - Non-patent li Category terature Relevant to claims Document of relevance A Categories - IEEE Transactions on Magnetics, 50, 6, 01 / 06 / 2014, Xu Xin et al., Migration Transformation of Full-Vectorial 3-D Magnetic Field Via Parameterized Complex Intensity, pages 1-7, ISSN 0018-9464, -T +44(0)30 0300 2000Letter or symbol Description X Document indicating lack of novelty or inventive step. Y Document indicating lack of inventive step, if combined with another document of the same category. & Member of the same patent family. A Document indicating technological background. P Document published on or after the priority date but before the filing date of the present application. E Earlier application published on or after the filing date of the present application.

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