Superparamagnetic effect identification and separation method in time domain electromagnetic response

Abstract

The invention relates to a superparamagnetic effect identification and separation method in time domain electromagnetic response. The method comprises the following steps: establishing a double-feature superparamagnetic effect identification model based on a fuzzy support vector machine algorithm; fitting the induction-magnetization effect in power law attenuation in the late period by adopting a Levenberg-Marquardt algorithm to obtain a quasi-superparamagnetic effect, and performing de-equalization and whitening on the quasi-superparamagnetic effect and the total effect as input signals of an independent component analysis algorithm; and selecting a mutual information minimization criterion and a natural gradient algorithm to update and optimize the separation matrix according to the statistical characteristics of the transient electromagnetic signal until the convergence condition is met, and finally separating to obtain the induction response and the superparamagnetic effect. According to the method, the superparamagnetic effect can be effectively identified and accurately separated, the inversion interpretation precision of the time-domain electromagnetic method in superficial superparamagnetic layer exploration is effectively improved, and technical support is provided for the development of the time-domain electromagnetic method in refined detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of geophysical exploration, and particularly relates to a method for identifying and separating superparamagnetic effects in time-domain electromagnetic responses. Background Art

[0002] 1. The transient electromagnetic method is a geophysical exploration method based on the principle of electromagnetic induction. It has the advantages of being fast, economical, and having a large exploration depth. Currently, it has been widely used in fields such as resource exploration, hydrogeological survey, and environmental monitoring. Its principle is to use an artificial loading source to emit a transient current pulse into the ground to generate a primary magnetic field. When the current is suddenly turned off, the primary magnetic field rapidly decays and induces eddy currents in the underground conductive medium; these eddy currents decay over time to generate a secondary magnetic field, which is received by the receiving device.

[0003] 2. The superparamagnetic effect is mainly caused by paramagnetic and ferromagnetic substances. During the detection process of the time-domain electromagnetic method under magnetic geological conditions, during the rising edge stage of the transmitted current, the magnetic particles in the medium change direction and obtain magnetization; after the transmitted current is turned off, the magnetic particles gradually lose their magnetization intensity, and the electromagnetic field observation system will detect an attenuation signal approximately following a -1 power law. This process is called the superparamagnetic effect.

[0004] 3. Under the action of the superparamagnetic layer, if the traditional detection theory and methods are followed and the superparamagnetic effect is ignored, it will lead to large errors in the conductivity interpretation process and the inability to accurately identify magnetic mineral resources. Therefore, achieving effective identification and precise separation of the superparamagnetic effect can promote the development of the time-domain electromagnetic method in the direction of precise detection and provide exploration technical support for solving the contradiction between resource supply and demand in China. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for identifying and separating superparamagnetic effects in time-domain electromagnetic responses, and to achieve effective identification and precise separation of the superparamagnetic effect.

[0006] The present invention is implemented as follows. A method for identifying and separating superparamagnetic effects in time-domain electromagnetic responses, the method comprising:

[0007] 1) Piecewise fit the late power-law attenuation coefficient of time-domain electromagnetic detection data, and calculate the mean and standard deviation;

[0008] Further, in step 1), in order to ensure the fitting accuracy and efficiency of the late attenuation coefficient of time-domain electromagnetic detection data, a time segmentation strategy based on the logarithmic time sampling principle is proposed, so that the time interval increases in a geometric progression, ensuring the balance of the dynamic range of each segment of data points, expressed as:

[0009]

[0010] In the above formula, tk is the time coordinate of the k-th segment, T0 is the starting moment for fitting the late decay data, T max is the ending moment of signal decay, and N is the number of segments.

[0011] 2) Using the mean and standard deviation obtained in step 1) as inputs and "whether it is the induction-magnetization effect" as the output, establish a dual-feature superparamagnetic effect recognition model based on the fuzzy support vector machine algorithm;

[0012] Furthermore, in step 2), the overall level and stability of the attenuation coefficient are jointly used to characterize the physical essence of the superparamagnetic effect, and a dual-feature superparamagnetic effect recognition model based on the fuzzy support vector machine algorithm is established. The training set samples are expressed as:

[0013]

[0014] In the above formula, X l is the dual-feature input of the recognition model, is the mean of the power-law attenuation coefficients in each late period, σ l (b) is the standard deviation of the power-law attenuation coefficients in each late period, b is the power-law attenuation coefficient of the late data, yl is the output result. If both and σ l (b) < 0.05, it is considered that the superparamagnetic effect exists, y l = 1, otherwise y l = -1, s l is the fuzzy membership degree, and l is the number of training set samples.

[0015] 3) Adopt the Levenberg-Marquardt algorithm to fit the late data of the induction-magnetization effect of the superparamagnetic layer to obtain the pseudo-superparamagnetic effect;

[0016] Furthermore, in step 3), the construction of the pseudo-superparamagnetic effect uses the Levenberg-Marquardt algorithm. By introducing a dynamic damping factor μ, an adaptive balance mechanism is established between the gradient descent method (when μ is large) and the Gauss-Newton method (when μ is small) in the parameter update equation, which is expressed as:

[0017] θ k+1 = θ k -(J T J + μ k I) -1 J T r(θ k )(3)

[0018] In the above formula, θ k is the parameter vector of the k-th iteration, J is the Jacobian matrix of the residual function r(θ), μ k is the dynamic damping factor, and I is the identity matrix.

[0019] 4) Use the pseudo-superparamagnetic effect and the total response as the input signals of the independent component analysis algorithm, and perform data preprocessing;

[0020] Furthermore, in step 4):

[0021] The data preprocessing includes mean removal and whitening;

[0022] Mean removal means performing a mean removal process on the observed signal to make its mean zero:

[0023]

[0024] In the above formula, X i (t) is the input signal, N is the number of data, is the input signal after mean removal.

[0025] Whitening makes the correlation between input signals zero and simplifies the extraction of subsequent independent components. The steps are as follows:

[0026] C = E(X·X T ), CV = VΛ, X w = Λ -1 / 2 ·V T ·X (5)

[0027] In the above formula, X is the input signal, X T is the transpose of the input matrix, E(·) is the expectation, C is the covariance matrix of the input signal, V is the matrix composed of eigenvectors by columns, Λ is the diagonal matrix composed of eigenvalues, X w is the data after whitening;

[0028] 5) Select the mutual information minimization criterion and the natural gradient algorithm as the independence criterion and optimization algorithm of the independent component analysis algorithm, and update and optimize the separation matrix;

[0029] Furthermore, in step 5), select the mutual information minimization criterion as the independence criterion, which quantifies the statistical dependence between the induction response and the superparamagnetic effect, expressed as:

[0030]

[0031] In the above formula, y is the output signal, x t is the input signal, y t is the induction response and the superparamagnetic effect, W is the separation matrix, ln|det(W)| is the information measure of the separation matrix, and H(·) is the entropy of the discrete random variable.

[0032] Furthermore,

[0033] In step 5), the natural gradient algorithm is selected as the optimization algorithm, which does not require the inverse of the separation matrix and has better convergence and convergence speed, expressed as:

[0034] W(k + 1) = W(k) + α(k)[I - f(y)y T W(k) (7)

[0035] In the above formula, W is the separation matrix, α is the learning rate, f(y) is the activation function, and y is the output signal.

[0036] 6) When the separation matrix meets the convergence condition, the input signal is separated to obtain the induced response and the superparamagnetic effect.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention establishes a dual - feature superparamagnetic effect recognition model based on the fuzzy support vector machine algorithm, realizing the effective recognition of the superparamagnetic effect. A method for constructing the input matrix of independent component analysis based on the Levenberg - Marquardt algorithm is proposed, lifting the restrictions of the input matrix being rank - deficient and the underdetermined blind source separation applied to the single - channel superparamagnetic effect. By analyzing the characteristics of the induced response and the superparamagnetic effect, the mutual information minimization criterion is determined as the independence criterion, and the natural gradient algorithm is used as the optimization algorithm. A superparamagnetic effect separation method based on the natural - gradient - optimized mutual - information - minimization independent component analysis algorithm is proposed, successfully realizing the accurate extraction of the induced response in the superparamagnetic layer and effectively improving the inversion and interpretation accuracy of the time - domain electromagnetic method under magnetic geological conditions. Description of the Drawings

[0038] Figure 1 is the flow chart of the time - domain electromagnetic superparamagnetic effect recognition and separation method based on the FSVM - ICA algorithm;

[0039] Figure 2 is the induced - magnetization effect model with low - resistance anomalies and its pseudo - superparamagnetic effect.

[0040] Figure 3 is the result diagram of the induced response and superparamagnetic effect separated by the present invention; Detailed Embodiments

[0041] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0042] Embodiment

[0043] Combined with Figure 1 shown, a method for recognizing and separating the superparamagnetic effect in the time - domain electromagnetic response includes:

[0044] 1) Simulate the time-domain electromagnetic induction-magnetization effect with a low-resistivity anomaly at a depth of 50 m underground based on the Chikazumi magnetic susceptibility model. Set the layer thicknesses to [30, 50, ∞], the conductivity parameters to [0.01, 0.2, 0.01], and the magnetic susceptibility parameters to [0.2, 0, 0];

[0045] 2) Use the Levenberg-Marquardt algorithm to fit the late-time data of the time-domain electromagnetic signals generated in step 1) to obtain the pseudo-superparamagnetic effect;

[0046] Furthermore, in step 2), the construction of the pseudo-superparamagnetic effect uses the Levenberg-Marquardt algorithm. By introducing a dynamic damping factor μ, an adaptive balance mechanism is established between the gradient descent method (when μ is large) and the Gauss-Newton method (when μ is small) in the parameter update equation, expressed as:

[0047] θ k+1 =θ k -(J T J+μ k I) -1 J T r(θ k )(1)

[0048] In the above formula, θ k is the parameter vector of the k-th iteration, J is the Jacobian matrix of the residual function r(θ), μ k is the dynamic damping factor, and I is the identity matrix.

[0049] 3) For the input matrix composed of the total response and the pseudo-superparamagnetic effect as Figure 2 shown, perform data preprocessing on it;

[0050] Furthermore, in step 3):

[0051] Data preprocessing includes de-mean and whitening;

[0052] De-meaning means performing a de-mean process on the observed signal to make its mean zero:

[0053]

[0054] In the above formula, X i (t) is the input signal, N is the number of data, is the input signal after de-meaning.

[0055] Whitening makes the correlation between input signals zero, simplifying the extraction of independent components later. The steps are as follows:

[0056] C=E(X·X T ),CV=VΛ,X w =Λ -1 / 2 ·VT ·X (3)

[0057] In the above formula, X is the input signal, X T is the transpose of the input matrix, E(·) is the expectation, C is the covariance matrix of the input signal, V is the matrix composed of eigenvectors column by column, Λ is the diagonal matrix composed of eigenvalues, and X w is the whitened data;

[0058] 4) The independent component analysis algorithm based on natural gradient optimization for minimizing mutual information is used to separate the preprocessed data. After the separation matrix iteration reaches the convergence condition, the induced response and superparamagnetic effect are separated.

[0059] 5) The separation result of the time-domain electromagnetic induction - magnetization effect containing low-resistance anomalies is as Figure 3 shown. The separated superparamagnetic effect basically coincides with the total response in the late stage. The average relative error of the calculated separation solution of the induced response is 3.23%, and the interference of the superparamagnetic effect is successfully eliminated.

[0060] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for identifying and separating superparamagnetic effect in time-domain electromagnetic response, characterized in that: The method includes: 1) Fit the late power-law attenuation coefficient of the time-domain electromagnetic detection data piecewise and calculate the mean and standard deviation; 2) Taking the mean and standard deviation obtained in step 1) as input and "whether it is an induction-magnetization effect" as output, a dual-feature superparamagnetic effect recognition model based on fuzzy support vector machine algorithm is established; 3) The Levenberg-Marquardt algorithm is used to fit the induction-magnetization effect that decays in a specific power law in the late stage to obtain the pseudo-superparamagnetic effect; 4) The pseudo-superparamagnetic effect and the total response are used as input signals of the independent component analysis algorithm, and de-meaning and whitening are performed; 5) Select the mutual information minimization criterion and the natural gradient algorithm as the independence criterion and optimization algorithm of the independent component analysis algorithm to update and optimize the separation matrix; 6) When the separation matrix meets the convergence condition, the input signal is separated to obtain the induction response and superparamagnetic effect.

2. The method for identifying and separating superparamagnetic effect in time-domain electromagnetic response according to claim 1, characterized in that: In step 1), in order to ensure the fitting accuracy and efficiency of the late attenuation coefficient of the time-domain electromagnetic late detection data, a time segmentation strategy based on the logarithmic time sampling principle is proposed to make the time interval grow geometrically and ensure the dynamic range of each data point is balanced, which is expressed as: In the above formula, t k is the time coordinate of the kth segment, T0 is the starting time of fitting the late decay data, T max is the end time of signal attenuation, and N is the number of segments.

3. The method for identifying and separating superparamagnetic effect in time-domain electromagnetic response according to claim 1, characterized in that: In step 2), the overall level and stability of the attenuation coefficient are used to jointly characterize the physical nature of the superparamagnetic effect, and a dual-feature superparamagnetic effect recognition model based on the fuzzy support vector machine algorithm is established. The training set samples are expressed as: In the above formula, X l is the dual feature input of the recognition model, is the mean value of the power law attenuation coefficient in each period of the late period, σ l (b) is the standard deviation of the power-law attenuation coefficient of each period in the late period, b is the power-law attenuation coefficient of the late data, and yl is the output result. If both satisfy And σ l (b)<0.05, then the superparamagnetic effect is considered to exist, y l =1, otherwise y l =-1,s l is the fuzzy membership, and l is the number of samples in the training set.

4. The method for identifying and separating superparamagnetic effect in time-domain electromagnetic response according to claim 1, characterized in that: The construction of the pseudo-superparamagnetic effect in step 3) adopts the Levenberg-Marquardt algorithm. By introducing the dynamic damping factor μ, the parameter update equation establishes an adaptive balance mechanism between the gradient descent method (when μ is large) and the Gauss-Newton method (when μ is small), which is expressed as: i k+1 =θ k -(J T J+m k I) -1 J T r(θ k ) In the above formula, θ k is the parameter vector of the kth iteration, J is the Jacobian matrix of the residual function r(θ), μ k is the dynamic damping factor and I is the identity matrix.

5. The method for identifying and separating superparamagnetic effect in time-domain electromagnetic response according to claim 1, characterized in that: In step 5), the mutual information minimization criterion is selected as the independence criterion, and the statistical dependence between the induction response and the superparamagnetic effect is quantified, which is expressed as: In the above formula, y is the output signal, x is t is the input signal, y t is the inductive response and superparamagnetic effect, W is the separation matrix, ln|det(W)| is the information measure of the separation matrix, and H(·) is the entropy of the discrete random variable.

6. The method for identifying and separating superparamagnetic effect in time-domain electromagnetic response according to claim 1, characterized in that: In step 5), the natural gradient algorithm is selected as the optimization algorithm. It does not need to invert the separation matrix, and has better convergence and convergence speed, which can be expressed as: W(k+1)=W(k)+α(k)[I-f(y)y T ]W(k) In the above formula, W is the separation matrix, α is the learning rate, f(y) is the activation function, and y is the output signal.

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