Fractal distribution magnetic anomaly data inversion method for magnetic source depth based on deep learning

Abstract

The present application relates to the field of processing and interpretation of magnetic anomaly data, and discloses a method for inverting magnetic source depth based on fractal distribution magnetic anomaly data and deep learning. The application adopts a self-attention mechanism to build a neural network model based on feature decoupling. For two-dimensional fractal distribution magnetic anomaly, the deep learning network model designed by the application is used to process power spectrum data. The input of the model is magnetic anomaly data, the power spectrum is extracted by calculation, and position encoding is added in the power spectrum. The LSTM neural network is selected as the encoder to facilitate the processing of long sequence data. The power spectrum sequence data is input into the z t , z b and β encoders for feature decoupling. The decoder is added in the side branch to supervise the accuracy of feature decoupling. Then, the self-attention mechanism is added between the decoupled features, and the feature fusion is performed to regress the magnetic source depth information and realize the inversion of the magnetic source bottom depth. The accuracy problem caused by the selection of window size and wave number by human is solved.

Description

Technical Field

[0001] This invention belongs to the field of magnetic source depth inversion technology of magnetic anomaly data, and is applicable to the processing and interpretation of magnetic anomaly data. Specifically, it is a deep learning-based method for inverting magnetic source depth from fractal distribution magnetic anomaly data. Background Technology

[0002] Magnetic exploration is a commonly used geophysical exploration method. By processing and interpreting the measured magnetic anomaly data, the distribution characteristics of subsurface geological bodies can be reconstructed. Among these methods, magnetic anomaly data can be used to invert the depth information of the subsurface magnetosphere. Currently, the commonly used processing method is to solve for the depth information at the bottom of the magnetic source based on the power spectrum of the magnetic anomaly. However, the choice of inversion method will affect the accuracy of the results.

[0003] Bouligand et al.'s paper "Mapping Curie temperature depth in the western United States with afractal model for crustal magnetization," published in the Journal of Geophysical Research [2009, 114, B11104], estimates the bottom depth directly from the radial average power spectral density function using curve fitting based on the theoretical formula of the radial average power spectrum. This method was applied to measured magnetic anomaly data in the western United States. However, when all three parameters in the power spectrum expression change simultaneously, the method has a very large error.

[0004] The paper "Estimation of Depth to Bottom of Magnetic Sources Using Spectral Methods: Application on Iran's Aeromagnetic Data" published by Kumar et al. in Journal of Geophysical Research: Solid Earth [2020, 125(3)] uses the centroid method to obtain the power spectrum of magnetic anomaly data from a fractal distribution model by applying a windowed Fourier transform. The power spectrum data is then fitted with a straight line in different wavenumber ranges to solve for the bottom depth information. The method is then applied to the measured aeromagnetic data of Iran to estimate the bottom depth.

[0005] Chinese patent CN113064211B discloses a "Curie depth calculation method based on wavelet transform of marine magnetic anomalies." The Curie depth can be considered as the depth of the bottom of the magnetosphere. Wavelet transform is performed on magnetic anomaly data; then, the top depth and average center depth are calculated using the power spectrum to estimate the Curie depth. Utilizing the fourth-order wavelet transform of magnetic anomalies, shallow anomalies are suppressed while deep anomalies are highlighted, thus improving the accuracy of the calculation to a certain extent.

[0006] The above method requires frequency domain transformation of the data during the solution process. The window size of the Fourier transform or wavelet transform will have a great impact on the results. At the same time, improper selection of the straight line fitting interval will also cause errors in the results, making the depth estimation results inaccurate. Summary of the Invention

[0007] The technical problem to be solved by this invention is to provide a method for inverting magnetic source depth from fractal distribution magnetic anomaly data based on deep learning, thereby solving the accuracy problem caused by manually selecting window size and wavenumber.

[0008] This invention is implemented as follows:

[0009] A deep learning-based method for inverting magnetic source depth from fractal magnetic anomaly data, the method comprising:

[0010] a. Generating magnetic anomaly data with fractal distribution of magnetization intensity through simulation;

[0011] b. Design the deep learning network model structure and parameters based on feature decoupling, and initialize the deep learning network model parameters;

[0012] c. Input the magnetic anomaly data into a deep learning network model to calculate the power spectrum. The formula for calculating the radial power spectrum of a layered geological body under vertical magnetization conditions is:

[0013] Where is the radial wavenumber, C is a constant, Δz is the magnetolayer thickness, β is the fractal exponent, and z t z represents the depth of the top of the magnetosphere and the depth of the bottom of the magnetic source. b =z t +Δz; and use the Adam optimization algorithm to minimize the loss function to complete the deep learning network model training, and use the training dataset to test the network performance;

[0014] d. Perform data preprocessing on the measured magnetic anomaly data, and then feed the processed data into a deep learning network model to complete the inversion of the depth of the bottom of the magnetosphere.

[0015] Further, step a specifically includes:

[0016] a1. Generate a set of three-dimensional white noise arrays such that their magnetization intensity satisfies a normal distribution;

[0017] a2. Transform the three-dimensional white noise array to the frequency domain using Fourier transform, at which point its power spectral density is constant;

[0018] a3. The power spectrum after Fourier transform multiplied by the magnetization intensity.

[0019] a4. Perform an inverse Fourier transform to convert back to a spatial magnetization array, where the magnetization intensity satisfies a fractal distribution.

[0020] Furthermore, step c also includes:

[0021] c1. Add position encoding to the power spectrum, and input the power spectrum sequence data to z respectively. t z b Feature decoupling is performed with the β encoder, and a decoder is added to the side branch to perform auxiliary tasks to supervise the accuracy of feature decoupling; the encoder uses an LSTM neural network with l hidden layers, m hidden units, and n input feature dimensions.

[0022] c2, z is obtained after being extracted by the encoder. t z b The three feature vectors decoupled from the β feature are then used to perform a self-attention mechanism, which is then used to calculate the predicted output value.

[0023] Each prediction result There will be a difference e between the measured value and the actual value. t The obtained errors are summed, and the Adam optimization algorithm is used to continuously update the weights until the total error meets the accuracy requirements. The Adam algorithm parameter update formula is:

[0024]

[0025] Where, m t =η(β1m) t-1 +(1-β1)g t Let v be the first-order momentum. t =β2v t-1 +(1-β2)diag(g t 2 ) is the second momentum, β1 and β2 are the weighted decay coefficients, and ε is the smoothing term to prevent the denominator from being 0;

[0026] c3. Then, the output data is processed through a pooling layer and a regression layer to regress the bottom depth information of the magnetic source.

[0027] Furthermore, step d specifically includes:

[0028] d1. For measured magnetic anomaly data, project the data onto the Mercator coordinate system;

[0029] d2. The projected data is interpolated and expanded to fill in the missing data points, resulting in the processed measured magnetic anomaly data;

[0030] d3. Input the measured magnetic anomaly data into the deep learning network model for calculation to obtain the bottom depth calculation result of the magnetic source.

[0031] Compared with the prior art, the beneficial effects of this invention are as follows:

[0032] This invention first processes power spectrum data for two-dimensional fractal magnetic anomalies using a deep learning network model. The model takes magnetic anomaly data as input, extracts the power spectrum through calculation, adds position encoding to the power spectrum, and uses an LSTM neural network as the encoder. The power spectrum sequence data is then input to z... t z b The features are decoupled from the β encoder, a decoder is added to the side branch to supervise the accuracy of feature decoupling, a self-attention mechanism is added between the decoupled features, feature fusion is then performed, and finally the bottom depth information of the magnetic source is regressed.

[0033] This invention, targeting the characteristics of power spectrum signals, selects a neural network model suitable for processing long-sequence data to construct a complex mapping relationship between magnetic anomaly data and the bottom depth of the magnetic source. Effective information is obtained from the power spectrum of the magnetic anomaly data, enabling the inversion of the bottom depth of the Xi'an magnetic source. Compared with traditional methods, it eliminates the need to consider the impact of Fourier transform or wavelet transform window size on the results, and avoids errors caused by improper selection of intervals in linear fitting. This allows for full utilization of the effective information in the power spectrum, improving the accuracy of the calculation results. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method of the present invention;

[0035] Figure 2 This is a diagram of the network model structure provided in an embodiment of the present invention;

[0036] Figure 3 This is the error curve of the neural network method with respect to the window size provided in the embodiments of the present invention;

[0037] Figure 4 This is a processed magnetic anomaly data diagram provided in an embodiment of the present invention;

[0038] Figure 5 This is a diagram showing the inversion result of the bottom depth data of the magnetic source provided in an embodiment of the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0040] Example

[0041] Reference Figure 1 Combination Figure 2 As shown, a method for inverting magnetic source depth from fractal magnetic anomaly data based on deep learning includes the following steps:

[0042] a. Simulate and generate a magnetic anomaly dataset with fractal magnetization distribution; when assuming perpendicular magnetization, the power spectrum of the magnetic field can be obtained as follows: Where u, v, and w are obtained by frequency domain transformations of x, y, and z. k is the radial wave number. x and k y Let be the wavenumbers in the x and y directions. For a fractal distribution, the power spectrum of the magnetization is expressed as: β represents the fractal index;

[0043] b. Design a deep learning network model structure and parameters based on feature decoupling to address the influence parameters of the power spectrum, and initialize the deep learning network model parameters.

[0044] c. Input the magnetic anomaly data into a deep learning network model to calculate the power spectrum. Assuming constant vertical magnetization, the formula for calculating the radial power spectrum of a layered geological body yields the following power spectrum sequence data: Let C be the radial wavenumber, and C be a constant. Three parameters affect the radial power spectrum: the magnetosphere thickness Δz, the fractal index β, and the magnetosphere top depth z. t The depth z at the bottom of the magnetic source b =z t +Δz; The Adam optimization algorithm is used to minimize the loss function to complete the training of the deep learning network model, and the network performance is tested using the training dataset.

[0045] d. Perform data preprocessing on the measured magnetic anomaly data, and then feed the processed data into a deep learning network model to realize the inversion of the depth of the bottom of the magnetosphere.

[0046] Furthermore, step a specifically includes:

[0047] a1. First, generate a set of three-dimensional white noise arrays, ensuring that their magnetization intensity follows a normal distribution;

[0048] a2. Transform the white noise array of this dimension to the frequency domain using Fourier transform. At this time, its power spectral density should be constant.

[0049] a3. The power spectrum after Fourier transform multiplied by the magnetization intensity.

[0050] a4. Perform an inverse Fourier transform to convert back to a spatial magnetization array. The magnetization at this point satisfies a fractal distribution. Use the formula... The magnetic anomaly values ​​of the model are calculated, where β = 1, 2, ..., ! ! represents double factorial. This method yields the magnetic anomaly of a half-space medium model with an infinitely extending lower base, while the magnetic anomaly of a layered model can be calculated by the difference between the magnetic anomaly values ​​of two models with different upper top depths.

[0051] Furthermore, step c specifically includes:

[0052] c1. Calculate the power spectrum based on the input magnetic anomaly, add position codes to the power spectrum sequence data, and input the power spectrum sequence data to z. t z b Feature decoupling is performed between the β encoder and the network, while a decoder is added as a side branch to perform an auxiliary task and supervise the accuracy of feature decoupling. The encoder uses an LSTM neural network with l hidden layers, m hidden units, and n input feature dimensions. The LSTM network contains three gate structures; the input gates control whether the current data is connected to the unit state, and the calculation formula is as follows:

[0053] i t =σ(θ) i ·[h t-1 ,x t ]+b i );

[0054]

[0055] In the formula, all θ represent parameters that need to be updated, and x... t This indicates the input at that moment. This represents the cell state of the storage unit, σ represents the sigmoid function, and h t b represents the hidden layer state variable. i and b c The bias vector is the input gate output.

[0056] The forget gate integrates the new input and the historical input into a vector, which is then multiplied by the sigmoid function and applied to the cell state. The calculation formula is as follows:

[0057] f t =σ(θ) f ·[h t-1 ,x t ]+b f)

[0058] Where f t Represents the previous moment c t-1 The proportion of information discarded in the middle, b f The bias vector is used as the output gate. Based on the historical information and the new input, the output gate integrates the vector, extracts information using the sigmoid function, and then maps it to the (-1,1) interval using the Tanh function.

[0059] The output gate extracts information from the vector formed by integrating historical information and new input using the sigmoid function, and then maps it to the (-1,1) interval using the Tanh function. The calculation formula is as follows:

[0060] o t =σ(θ) o ·[h t-1 ,x t ]+b o );

[0061] h t =o t ×tanh(c t );

[0062] Among them, c t This indicates the state of the cell at that moment, o t This indicates the output at that moment, b o Let b be the bias vector. i and b c Given the bias vector, the result of the input gate output after calculation is:

[0063] c2. Three feature vectors z are extracted by the encoder. t z b By adding a self-attention mechanism between the three feature vectors, the model can better capture the global dependencies that exist in long sequence data, thereby improving the model's performance and completing feature re-fusion.

[0064] For the input sequence {a 1 ,a 2 ,a 3 ,...,a n The formula for calculating the similarity weight between two vectors is as follows:

[0065] q j =a 1 ×W q ;

[0066] k j =a j ×W k ;

[0067] α 1,j =q 1 ·k j ;

[0068] In the formula, α represents the similarity weight between vectors, and W q W k The weight matrix is ​​continuously updated based on learning. This process is repeated for each input vector to obtain a similarity weight sequence {α}. 1,1 ,α 1,2 ,...,α 1,n The weights are normalized using the soft-max function, mapping them to the (0,1) interval to obtain the coefficient weights α′. 1,j :

[0069]

[0070] Multiply the input sequence by a new vector W. v Then, the values ​​of the vector are weighted and summed according to the coefficient weights to obtain the self-attention output matrix b. 1 :

[0071] v j =a 1 ×W v ;

[0072] b 1 =∑ j α′ 1,j v j ;

[0073] Repeat the above steps to obtain the complete self-attention output matrix, and then obtain the prediction result.

[0074] Each prediction result There will be a difference e between the measured value and the actual value. t The obtained errors are summed, and the Adam optimization algorithm is used to continuously update the weights until the total error meets the accuracy requirements. At this point, the model training is complete. The Adam algorithm parameter update formula is:

[0075]

[0076] Where, m t =η(β1m) t-1 +(1-β1)g t Let v be the first-order momentum. t =β2v t-1 +(1-β2)diag(g t 2) is the second-order momentum, β1 and β2 are the weight decay coefficients, η is the learning rate, and ε is the smoothing term to prevent the denominator from being 0;

[0077] c3. Then, by passing the output data through the pooling layer and the regression layer, the depth information of the bottom of the magnetic source can be regressed.

[0078] Furthermore, step d specifically includes:

[0079] d1. For measured magnetic anomaly data, the data needs to be projected onto the universal transverse Mercator coordinate system to prevent data distortion.

[0080] d2. The projected data is interpolated and expanded to fill in the missing data points, resulting in the processed measured magnetic anomaly data;

[0081] d3. Input the measured data into the network for calculation to obtain the calculated depth of the bottom of the magnetic source.

[0082] Figure 3 The mean absolute error of the neural network under different window sizes was tested, and error curves of the neural network method with different window sizes were obtained. Figure 3 As can be seen, the method of the present invention does not require manually selecting the window size based on the bottom depth, and can obtain more accurate inversion results in practical applications. Figure 4 This is a preprocessed image of magnetic anomaly data. Figure 5 This is a result image showing the depth of the bottom of the magnetic source derived from this data.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for inverting magnetic source depth from fractal distribution magnetic anomaly data based on deep learning, characterized in that, The method includes: a. Generating magnetic anomaly data with fractal distribution of magnetization intensity through simulation; b. Design the deep learning network model structure and parameters based on feature decoupling, and initialize the deep learning network model parameters; c. Input the magnetic anomaly data into a deep learning network model to calculate the power spectrum. The formula for calculating the radial power spectrum of a layered geological body under vertical magnetization conditions is: Where is the radial wavenumber, C is a constant, Δz is the magnetolayer thickness, β is the fractal exponent, and z t z represents the depth of the top of the magnetosphere and the depth of the bottom of the magnetic source. b =z t +Δz; and use the Adam optimization algorithm to minimize the loss function to complete the deep learning network model training, and use the training dataset to test the network performance; d. Perform data preprocessing on the measured magnetic anomaly data, and then feed the processed data into a deep learning network model to complete the inversion of the depth of the bottom of the magnetosphere.

2. The method for inverting magnetic source depth from fractal distribution magnetic anomaly data based on deep learning as described in claim 1, characterized in that, Step a specifically includes: a1. Generate a set of three-dimensional white noise arrays such that their magnetization intensity satisfies a normal distribution; a2. Transform the three-dimensional white noise array to the frequency domain using Fourier transform, at which point its power spectral density is constant; a3. The power spectrum after Fourier transform multiplied by the magnetization intensity. a4. Perform an inverse Fourier transform to convert back to a spatial magnetization array, where the magnetization intensity satisfies a fractal distribution.

3. The method for inverting magnetic source depth from fractal distribution magnetic anomaly data based on deep learning as described in claim 1, characterized in that, Step c further includes: c1, add position coding in power spectrum, respectively, power spectrum sequence data to z t , z b and β encoder decouples the features, and adds a decoder to the side branch to assist in the task of supervising the accuracy of feature decoupling; the encoder selects an LSTM neural network, sets the network hidden layer number to l layers, the hidden unit number to m, and the input feature dimension to n; c2, z is obtained after being extracted by the encoder. t z b The three feature vectors decoupled from the β feature are then used to perform a self-attention mechanism, which is then used to calculate the predicted output value. Each prediction result There will be a difference e between the measured value and the actual value. t The obtained errors are summed, and the Adam optimization algorithm is used to continuously update the weights until the total error meets the accuracy requirements. The Adam algorithm parameter update formula is: Where, m t =η(β1m) t-1 +(1-β1)g t Let v be the first-order momentum. t =β2v t-1 +(1-β2)diag(g t 2 ) is the second momentum, β1 and β2 are the weighted decay coefficients, and ε is the smoothing term to prevent the denominator from being 0; c3. Then, the output data is processed through a pooling layer and a regression layer to regress the bottom depth information of the magnetic source.

4. The method for inverting magnetic source depth from fractal distribution magnetic anomaly data based on deep learning as described in claim 1, characterized in that, Step d specifically includes: d1. For measured magnetic anomaly data, project the data onto the Mercator coordinate system; d2. The projected data is interpolated and expanded to fill in the missing data points, resulting in the processed measured magnetic anomaly data; d3. Input the measured magnetic anomaly data into the deep learning network model for calculation to obtain the bottom depth calculation result of the magnetic source.

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