1. A ground-air electromagnetic data inversion method based on a high-generalization neural network is characterized by comprising the following steps:

1) acquiring geological data and rock physical property information of a detection region, constructing an abnormal diffusion fractional order model, calculating earth-air electromagnetic response, and establishing an input and output sample set of the electromagnetic response and the abnormal diffusion fractional order model;

2) optimally designing a network structure, selecting a training function and an activating function according to the sample set and the neural network requirements in the step 1;

3) for the neural network with the depth d and the width h constructed in the step 2, each parameter matrix W is limited₁,…W_j…,W_dThe method comprises the steps that a diagonal matrix j belongs to {1, …, d }, and Frobenius specification is at most 1, a proper rank matrix is adopted to replace a parameter matrix with a rank close to 1, and an approximate neural network is obtained, namely the approximate neural network consists of a depth r' network and a univariate function;

4) for the Lipschitz function of the single variable function in the step 3, mapping all the input 0 of the Lipschitz function to the same fixed output a;

5) by passingThe real value loss function limits the Rademacher complexity of the neural network, limits the generalization error of the neural network, and obtains a highly generalized neural network;

6) and 5, inverting the ground-air electromagnetic data by adopting the high-generalization neural network in the step 5, and imaging an inversion result.

2. The method as claimed in claim 1, wherein in step 3, the rank is 1 and the parameter matrix W_r′＝suv^TWhere s, u, v are the matrix W_r′Singular value decomposition, wherein s and v are orthogonal matrixes, and u is a matrix diagonal matrix; an approximate neural network with a rank-1 parameter matrix is represented as

I.e. the network is formed by a depth r' networkAnd univariate functionComposition of where σ_jFor the activation function at level j, r ∈ {1, …, d }, r' ∈ {1, …, r }.

3. The method of claim 1, wherein in step 4, the Lipschitz constant of the univariate function is at mostGamma is a margin parameter, and each parameter matrix has a spectrum norm M (j) at most; mapping input 0 of all j to the same fixed output a;function f is of the typeWherein f (0) ═ a.

4. The method according to claim 1, wherein in step 5,/, is₁,...,l_mIs thatSo that it satisfies the real-valued loss functionx_kFor the data point set k is equal to {1, …, m }, H is a real-valued function class and satisfies L₁(0)＝l₂(0)＝...＝l_m(0)＝a(a∈R)，Rademacher complexityIs at an upper limit of

Wherein c is>0 is a constant, B is the maximum norm, and the Rademacher complexity is limited by adjusting r; and limiting the neural network generalization error through the relation between the Rademacher complexity and the neural network generalization error to obtain the high-generalization neural network.

5. The method of claim 1, wherein said step 6 comprises the steps of:

i, performing actual flight detection according to detection requirements;

II, preprocessing the ground-air electromagnetic data, including baseline correction, superposition, denoising and data sampling;

III, inputting the data in the step II into the high-generalization neural network in the step 5, and extracting multi-parameter information of the resistivity and the abnormal diffusion parameter;

IV, carrying out multi-parameter imaging on the output result of the step III and forming an abnormal diffusion model;

and V, analyzing the imaging result in the step IV to obtain the underground medium information.

Background

In the field of geophysical detection, as instruments are finely detected, the electromagnetic anomalous diffusion phenomenon is gradually observed. The actual underground medium is affected by differential compaction, metamorphism and the like in the process of depositing or diagenesis and the like, so that the stratum has the characteristics of nonlinearity, porous medium and the like, and the actual medium such as polymetallic ore belongs to a polarized medium. The underground medium model is redefined for fine detection aiming at the actual geological complex structure and the abnormal diffusion (slow diffusion and fast diffusion) phenomenon, so that the simultaneous extraction of multiple parameters such as the conductivity and the abnormal diffusion parameters of the rock is particularly important. The neural network inversion method can be realized, so a high-generalization neural network needs to be researched to improve the interpretation precision.

CN110968826A discloses a magnetotelluric deep neural network inversion method based on a spatial mapping technology, which establishes a deep learning neural network through a geoelectric model sample set and a magnetotelluric forward response data set, and quickly and accurately predicts an underground electrical structure. However, the inversion method is an electrical property structure prediction method based on the homogeneous medium theory, and does not consider the electromagnetic anomalous diffusion phenomenon.

CN201810174296.7 discloses a time domain electromagnetic data slow diffusion imaging method of a rough medium model, which is used for solving direct current conductivity and generalized diffusion depth of electric dipole magnetic field response and drawing a resistivity-generalized skin depth map. However, the method does not extract information such as slow diffusion parameters and does not consider polarization medium parameters.

CN110673218A discloses a method for extracting polarized medium parameter information in transient electromagnetic response of a grounded conductor, which utilizes a vertical magnetic field less affected by polarization effect to invert and obtain underground resistivity information, and then forward and obtain electric field response, so as to obtain pure polarization response in observed data, and invert and obtain polarization parameter information. However, the method solves parameters such as resistivity, polarizability and the like respectively, so that the research on the inversion method for extracting the actual abnormal diffusion electromagnetic data with multiple parameters is of great significance.

Disclosure of Invention

The invention aims to provide a ground-air electromagnetic data inversion method based on a high-generalization neural network according to actual underground complex media aiming at the defects of the existing electromagnetic data parameter extraction method.

The invention is realized in such a way that a ground-air electromagnetic data inversion method based on a high-generalization neural network comprises the following steps:

1) acquiring geological data and rock physical property information of a detection region, constructing an abnormal diffusion fractional order model, calculating earth-air electromagnetic response, and establishing an input and output sample set of the electromagnetic response and the abnormal diffusion fractional order model;

2) optimally designing a network structure, selecting a training function and an activating function according to the sample set and the neural network requirements in the step 1;

3) for the neural network with the depth d and the width h constructed in the step 2, each parameter matrix W is limited₁,...W_j...,W_dReplacing a parameter matrix with the rank close to 1 by a matrix with the proper rank of 1 to obtain an approximate neural network, namely the approximate neural network consists of a depth r' network and a univariate function, wherein the diagonal matrix j belongs to {1, ·, d } and the Frobenius specification is at most 1;

further, the rank in step 3 is 1 parameter matrix W_r′＝suv^TWhere s, u, v are the matrix W_r′Singular value decomposition, wherein s and v are orthogonal matrixes, and u is a matrix diagonal matrix; an approximate neural network with a rank-1 parameter matrix is represented as

I.e. the network can be considered as a network consisting of depth rAnd univariate functionComposition of where σ_jFor the activation function of the j-th layer, r ∈ { 1., d }, r' ∈ { 1., r }.

4) For the Lipschitz function of the single variable function in the step 3, mapping all the input 0 of the Lipschitz function to the same fixed output a;

further, in step 4, the Lipschitz constant of the univariate function is at mostGamma is a margin parameter, and each parameter matrix has a spectrum norm M (j) at most; mapping input 0 of all j to the same fixed output a;function f is of the typeWherein f (0) ═ a.

5) By passingThe real value loss function limits the Rademacher complexity of the neural network, limits the generalization error of the neural network, and obtains a highly generalized neural network;

further, in step 5,/₁，...l_mIs thatSo that it satisfies the real-valued loss functionx_kFor a data point set k belonging to {1,. eta.,. m }, H is a real-valued function class and satisfies l₁(0)＝l₂(0)＝...＝l_m(0)＝a(a∈R)，Then Rademacher complexityIs at an upper limit ofWherein c is>0 is a constant and B is the maximum norm. Defining a Rademacher complexity by appropriately adjusting r; and limiting the generalization error of the neural network through the relation between the complexity of the Rademacher and the generalization error of the neural network, thus obtaining the high-generalization neural network.

6) And 5, inverting the ground-air electromagnetic data by adopting the high-generalization neural network in the step 5, and imaging an inversion result.

Further, step 6 comprises the following steps:

i, performing actual flight detection according to detection requirements;

II, preprocessing the ground-air electromagnetic data, including baseline correction, superposition, denoising and data sampling;

III, inputting the data in the step II into the high-generalization neural network in the step 5, and extracting multi-parameter information such as resistivity, abnormal diffusion parameters and the like;

IV, carrying out multi-parameter imaging on the output result of the step III and forming an abnormal diffusion model;

and V, analyzing the imaging result in the step IV to obtain the underground medium information.

Has the advantages that: compared with the prior art, the method provided by the invention has the advantages that the Rademacher complexity of the neural network is limited to obtain the high-generalization neural network according to the abnormal diffusion fractional order model aiming at the complex characteristics of the geological structure, the extraction precision of multi-parameter information such as conductivity and abnormal diffusion parameters can be improved, and the practicability of the ground-air electromagnetic detection technology is facilitated. The method provides a new technical support for developing electromagnetic detection and searching resources in China, and is favorable for refinement and practicability of the electromagnetic detection method.

Drawings

FIG. 1 is a flow chart of a method for inverting ground-air electromagnetic data based on a highly generalized neural network;

FIG. 2 is a graph of resistivity versus depth effects for one embodiment of the present invention;

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and detailed description. One of the core ideas of the invention is that the neural network is utilized to extract the ground-air electromagnetic data abnormal diffusion multi-parameter, the Rademacher complexity of the neural network is limited to obtain the highly generalized neural network, and more accurate information of the geological target body is obtained. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

Examples

Take the rough medium slow diffusion model as an example

Referring to fig. 1, a method for inverting ground-air electromagnetic data based on a highly generalized neural network includes: 1) acquiring geological data and rock physical property information of a detection region, constructing an abnormal diffusion fractional order model, and calculating a place

The method comprises the following steps of (1) carrying out null electromagnetic response, and establishing an input and output sample set of an electromagnetic response and an abnormal diffusion fractional order model;

defining a conductivity expression of a coarse medium slow diffusion fractional order model as

σ(ω)＝m₁σ₀+m₂σ₀(iω)^-β (1)

Where ω is the angular frequency, σ₀Is direct current conductivity, m₁,m₂Beta is a spatially uniform roughness parameter. Substituting the conductivity into Maxwell equation to derive a long-conductor source vertical magnetic field expression, wherein according to Faraday's law of electromagnetic induction, the formula of ground-air electromagnetic response induced electromotive force of the electrical source is as follows:

wherein I is the emission current and ω isAngular frequency, μ is permeability, S is effective area of the receiving coil, 2L is length of the grounding wire, r_TEAs reflection coefficient, e ≈ 2.718, J₁Is a Bessel function first-order expression, and R is a receiving-transmitting distance R ═ x-x')²+y²]^1/2X is the x coordinate of the receiving point, y is the y coordinate of the receiving point, z is the z coordinate of the receiving point, and λ, x' are the integrated variables.

And (3) setting conductivity parameters of the coarse medium slow diffusion fractional order model according to geological data and rock physical property information of the detection area, calculating ground-air electromagnetic response by applying a formula (2), and establishing a sample set of the electromagnetic response and the model. 2) Optimally designing a network structure, selecting a training function and an activating function according to the sample set and the neural network requirements in the step 1;

3) for the neural network with the depth d and the width h constructed in the step 2, each parameter matrix W is limited₁,...W_j...,W_dReplacing a parameter matrix with the proper rank of 1 for a diagonal matrix (j belongs to { 1.,. d }) and Frobenius specification of at most 1 to obtain an approximate neural network, namely the approximate neural network consists of a depth r' network and a univariate function;

in order neural networkThe product of the Schatten p-norm is bounded ((S))Arbitrary p<Infinity), then the parameter matrix W₁,...W_j...,W_dAt least one parameter matrix is close to 1 in rank, namely the parameter matrix can be replaced by a proper rank 1 matrix in the r' layer to obtain an approximate neural network. Rank 1 parameter matrix W_r′＝suv^TWhere s, u, v are the matrix W_r′Singular value decomposition, wherein s and v are orthogonal matrixes, and u is a matrix diagonal matrix; an approximate neural network with a rank-1 parameter matrix is represented as

I.e. the network can be considered as a network consisting of depth rAnd univariate functionComposition of where σ_jFor the activation function of the j-th layer, r ∈ { 1., d }, r' ∈ { 1., r }.

4) For the Lipschitz function of the single variable function in the step 3, mapping all the input 0 of the Lipschitz function to the same fixed output a;

the Lipschitz constant of the univariate function is at mostGamma is a margin parameter, and each parameter matrix has a spectrum norm M (j) at most; mapping input 0 of all j to the same fixed output a;function f is of the typeWherein f (0) ═ a.

5) By passingThe real value loss function limits the Rademacher complexity of the neural network, limits the generalization error of the neural network, and obtains a highly generalized neural network;

for theIs thatSo that it satisfies the real-valued loss functionx_kFor a set of data points (k e){1,.. m }), H is a real-valued function class and satisfies l₁(0)＝l₂(0)＝...＝l_m(0)＝a(a∈R)，Then Rademacher complexityIs at an upper limit ofWherein c is>0 is a constant and B is the maximum norm. Let each parameter matrix W of neural network_jSatisfy | | W_j||_F≤M_F(j) (Frobenius norm boundary M_F(1),...,M_F(r)) and has a 1-Lipschitz positive homogeneous element activation function, then

WhereinIgnoring the logarithmic factor and replacing the minimum value by the first parameter, the limit being at most

If II_jM_F(j) And II_jM_F(j) If/Γ is limited by a constant, then a highly generalized convolutional neural network will result.

6) And 5, inverting the ground-air electromagnetic data by adopting the high-generalization neural network in the step 5, and imaging an inversion result.

The step 6 comprises the following steps:

i, performing actual flight detection according to detection requirements;

II, preprocessing the ground-air electromagnetic data, including baseline correction, superposition, denoising and data sampling;

III, inputting the data in the step II into the high-generalization neural network in the step 5, and extracting multi-parameter information such as resistivity, abnormal diffusion parameters and the like;

IV, carrying out multi-parameter imaging on the output result of the step III and forming an abnormal diffusion model;

and V, analyzing the imaging result in the step IV to obtain the underground medium information.

Fig. 2 is a resistivity-depth effect graph of the embodiment of the invention shown in fig. 1, and the result accords with the practical situation of the embodiment, so that a new thought and method are provided for high-precision inversion of measured data of the ground-air electromagnetic detection method.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.