CN110888172A - Coarse medium electromagnetic response resistivity imaging method based on neural network - Google Patents

Coarse medium electromagnetic response resistivity imaging method based on neural network Download PDF

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CN110888172A
CN110888172A CN201911093615.2A CN201911093615A CN110888172A CN 110888172 A CN110888172 A CN 110888172A CN 201911093615 A CN201911093615 A CN 201911093615A CN 110888172 A CN110888172 A CN 110888172A
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嵇艳鞠
吴琼
姜曜
赵雪娇
关珊珊
黎东升
王远
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Abstract

The invention relates to a rough medium electromagnetic response resistivity imaging method based on a neural network, which comprises the steps of substituting a convolution state equation of a rough medium into a Maxwell equation, deriving a rough medium frequency domain electromagnetic response formula of a long wire source, calculating frequency domain earth-air electromagnetic response of a rough medium model, constructing a neural network sample set, carrying out preprocessing such as noise suppression on actually measured flight data of earth-air electromagnetism, converting actually measured time domain electromagnetic data into frequency domain electromagnetic response by adopting a regularization method, determining the roughness β value of an underground medium by combining geological data and rock physical property information of a measuring area, establishing a resistivity imaging optimal neural network based on the rough medium, carrying out parameter extraction on the frequency electromagnetic response by utilizing the neural network to obtain the resistivity of the underground medium, calculating a depth parameter according to a frequency domain rough medium generalized skin depth formula, and finally carrying out resistivity-depth imaging.

Description

Coarse medium electromagnetic response resistivity imaging method based on neural network
Technical Field
The invention relates to the field of geophysical exploration, in particular to a neural network-based rough medium electromagnetic response resistivity imaging method which is suitable for a rough medium model in accordance with an actual geological condition.
Background
In the field of electromagnetic response data imaging in geophysical exploration, resistivity and detection depth are important parameters, and the skin depth of a traditional uniform half-space model does not consider that the conductivity of a subsurface rough medium has dispersion characteristics.
Currently, the Born iterative method proposed by Wang and Chen (1989) is widely used for resistivity imaging studies. Regarding the calculation of the resistivity depth, the Cheney nation (2014) proposed to use the grounded wire source as an excitation, calculating the relevant skin depth.
CN201811362820.X discloses a rapid imaging method for the visual resistivity of an artificial field source frequency domain electric field gradient far zone, which comprises data preprocessing, electric field gradient calculation, electric field gradient visual resistivity calculation, space imaging, corresponding conversion of measurement frequency into visual depth, and drawing a visual resistivity-visual depth cross-section drawing on a measuring line.
CN201410748111.0 discloses a three-dimensional resistivity imaging system, which comprises a host and a plurality of measuring units, wherein the host comprises an upper computer and a lower computer; the measurement unit comprises a sub-station and a plurality of electrodes; the upper computer is communicated with the lower computer through an RS232 bus; the lower computer communicates with the substation through a Controller Area Network (CAN) bus; and the lower computer is communicated with the electrodes through the controller area network CAN bus and the substation.
CN201810762046.5 discloses a human tissue conductivity distribution reconstruction method and system based on a deep learning neural network, the method comprises the following steps: acquiring neural network training data; constructing a neural network; training a neural network by using training data to obtain specific parameters of the neural network; and according to the obtained specific parameters, performing three-dimensional reconstruction on the to-be-reconstructed imaging body to obtain the internal conductivity distribution of the imaging body. The system comprises: the system comprises a data acquisition module, a network construction modeling module, a network training module and an image reconstruction module. According to the invention, the conductivity reconstruction network is obtained by learning the magnetic induction intensities of different positions outside the imaging body, so that the three-dimensional conductivity reconstruction speed and resolution are improved.
However, the resistivity and depth calculation method is based on the homogeneous medium theory, and the actual underground medium has complex heterogeneous characteristics, that is, the actual geological structure is more accurately described by adopting a rough medium model, so that the resistivity and depth calculation results are deviated from the actual results, and the accuracy of the data interpretation result is influenced, so that the method has important significance for researching the resistivity imaging method of electromagnetic response of the rough medium model defined under the actual geological condition.
Disclosure of Invention
The invention aims to provide a rough medium electromagnetic response resistivity imaging method based on a neural network aiming at the defects of the existing resistivity imaging.
A coarse medium electromagnetic response resistivity imaging method based on a neural network comprises the following steps:
1) substituting the convolution state equation of the rough medium into a Maxwell equation to derive a rough medium frequency domain electromagnetic response formula of the long-wire source;
2) calculating the frequency domain ground-air electromagnetic response of the rough medium model according to the rough medium frequency domain electromagnetic response formula in the step 1, and constructing a neural network sample set;
3) preprocessing ground-air electromagnetic actual measurement flight data, and converting actual measurement time domain electromagnetic response into frequency domain electromagnetic response by adopting a regularization method;
4) acquiring geological data and rock physical property information of a field measuring area, determining a roughness value β of underground media of the measuring area, determining the number of hidden layers, the number of nodes and a training function of a neural network, introducing a sample set serving as input data into the neural network for training, completing neural network training, and determining an optimal neural network for interpreting electromagnetic data of a rough medium;
5) performing parameter extraction on the frequency electromagnetic response of the step 3 by adopting the optimal neural network of the step 4 to obtain the resistivity of the underground medium;
6) and (5) calculating by using a frequency domain rough medium generalized skin-seeking depth formula according to the resistivity of the underground medium obtained in the step (5) to obtain a depth parameter, and performing resistivity-depth imaging on the rough medium.
Further, the step 1 includes substituting a convolution type state equation of the rough medium into a maxwell equation, establishing an electromagnetic field fractional order diffusion equation containing roughness, and obtaining a grounded long-conductor source vertical magnetic field under the rough medium, wherein a calculation expression of the grounded long-conductor source vertical magnetic field is as follows:
Figure BDA0002267613440000031
where I is the emission current, 2L is the length of the earth conductor, rTEThe reflection coefficient, e is the base of the natural logarithm e ≈ 2.718, mu is the magnetic permeability, sigma0For dc conductivity, β is a spatially uniform roughness parameter,
Figure BDA0002267613440000032
omega is the angular frequency, 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.
Further, the step 3 comprises the following steps:
preprocessing acquired time domain electromagnetic response data, including data superposition, noise suppression and data sampling;
II, performing dispersion by a broken line approximation method according to a cosine transform formula;
III, applying constraint conditions to the discrete cosine transform formula in the step II, and obtaining a new objective function by utilizing regularization;
IV, applying the sampled data in the step I, and obtaining an optimal regularization parameter by using an L curve method;
and V, solving the objective function according to the optimal regularization parameter to obtain the frequency domain electromagnetic response.
Further, the cosine transform formula in step 3 is:
Figure BDA0002267613440000041
Figure BDA0002267613440000042
Re[H(ω)]is the real part of the magnetic field component in the frequency domain, Im [ H (ω)]Is an imaginary part of the frequency domain magnetic field component,
Figure BDA0002267613440000043
obtained by induced electromotive force
Figure BDA0002267613440000044
h (t) is the time domain magnetic field response and ω is the angular frequency.
Further, the formula obtained by discretizing the polygonal line approximation method in step 3 is as follows:
Figure BDA0002267613440000045
let Re [ H ]]Forming a vector D with a time domain vector of D, responses D for different time-channelsiComprises the following steps:
Figure BDA0002267613440000046
order to
Figure BDA0002267613440000051
Constructing an objective function:
Φ(D)＝[d-LD]T[d-LD]+λDTWTWD (7)
in the formula (6), λ is a regularization parameter, the model smooth matrix W is I, and I is an identity matrix.
Further, the step 4 comprises the following steps:
a) determining the data of a sample set to be trained according to the working parameters of the time domain electromagnetic system and the roughness information of the experimental region, and calculating the frequency domain electromagnetic response of the rough medium model;
b) determining the number of hidden layers, the number of nodes and a training function of the neural network according to the sample set data;
c) carrying out neural network training on the basis of the electromagnetic response of the numerically simulated rough medium model;
d) and judging whether the training error meets the requirement, if not, returning to the step b).
Further, step 6 attenuates the amplitude of the electromagnetic response to e, defined by the skin depth-1Is called skin depth, then:
Figure BDA0002267613440000052
wherein i-βA + ib, where a, b are real numbers, σ0Is the direct current conductivity.
Has the advantages that: compared with the prior art, the method adopts neural network learning, and can obtain the resistivity value of the detection area more quickly. The corresponding depth can be efficiently and accurately obtained by utilizing the derived frequency domain rough medium generalized skin depth formula. And the actual underground rough medium is considered, the resistivity-depth imaging is accurately and reasonably carried out, and the practicability of the ground-space time domain electromagnetic detection technology is facilitated. Because the skin depth of the traditional uniform half-space model does not consider that the conductivity of the underground rough medium has a frequency dispersion characteristic, the method adopts a neural network method to solve the conductivity, then utilizes a generalized skin depth formula to carry out depth calculation, and finally carries out imaging of resistivity and depth, thereby improving the precision.
Drawings
FIG. 1 is a flow chart of a method for coarse media electromagnetic response resistivity imaging based on a neural network;
FIG. 2 shows a time-frequency transformation effect diagram of the present invention, where (a) is a real part and (b) is an imaginary part;
FIG. 3 is a graph of resistivity imaging effects of one embodiment of the present invention; wherein a is a theoretical model, and b is resistivity imaging of a rough medium electromagnetic response resistivity imaging method calculation result based on a neural network.
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 invention utilizes the neural network to extract the resistivity, and utilizes the frequency domain rough medium generalized skin depth formula to calculate the depth, so as to carry out accurate resistivity-depth imaging on the detection area, thereby obtaining more accurate information of the geological target body. 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
Referring to fig. 1, a method for imaging the electromagnetic response resistivity of a rough medium based on a neural network comprises the following steps:
1) substituting the convolution state equation of the rough medium into a Maxwell equation to derive a rough medium frequency domain electromagnetic response formula of the long-wire source;
the ground-air electromagnetic system lays a grounded long-wire source on the ground, so that the electromagnetic response of the coarse-medium long-wire source needs to be calculated. The central point of the long wire source is arranged at the coordinate origin, the field source line extends to-L and L along the x axis, and the vertical magnetic field of the grounded long wire source in the rough medium lower-layer-shaped earth can be obtained, and the expression is as follows:
Figure BDA0002267613440000071
wherein R ═ x [ (x-x')2+y2]1/2. In the ground-air electromagnetic system, a signal received by the receiving coil is induced electromotive force, and according to faraday's law of electromagnetic induction, equation (1) can be rewritten as follows:
Figure BDA0002267613440000072
wherein S is the receive coil effective area.
2) Calculating the frequency domain ground-air electromagnetic response of the rough medium model according to the rough medium frequency domain electromagnetic response formula in the step 1, and constructing a neural network sample set;
establishing sample set data, mainly comprising a training set, a verification set and a test set, and carrying out normalization processing on the sample set data. The sample set data is randomly disassembled into three parts, namely training data (Train), verification data (Validation) and Test data (Test).
3) Preprocessing ground-air electromagnetic actual measurement flight data, and converting actual measurement time domain electromagnetic response into frequency domain electromagnetic response by adopting a regularization method;
the fourier transform of the frequency response for step-off can be calculated using a sine or cosine transform. Sine or cosine transform is a commonly used digital filtering technique that enables frequency-time transformation,
Figure BDA0002267613440000073
Figure BDA0002267613440000081
wherein Re [ H (omega)]Is the real part of the electromagnetic field component, Im [ H (ω)]Is a virtual part of the electromagnetic field component.
Figure BDA0002267613440000082
Can be obtained by inducing electromotive force
Figure BDA0002267613440000083
Adopting broken line approximation method to make formulas (3) and (4)) Carrying out dispersion:
Figure BDA0002267613440000084
Figure BDA0002267613440000085
the time domain electromagnetic response can be obtained by frequency domain response calculation from equations (5), (6). It can be written in matrix form, taking equation (5) as an example. Let N discrete frequency responses Re [ H ]]Forming a vector D, M discrete time domain responses being a vector D, for tiResponse d of time-channeliIs composed of
Figure BDA0002267613440000086
Coefficient of order
Figure BDA0002267613440000087
Then the matrix form of equation (5) is
d＝LD (9)
Wherein d can pass
Figure BDA0002267613440000088
And (4) obtaining. Knowing the number M of time domain responses and the number N of frequency domain responses that one desires to obtain, is usually different, results in the inability to directly obtain a solution in the conventional sense of equation (9). A regularization algorithm is adopted for solving the D selection, and a stable solution can be obtained by adding proper constraint and is converted into an optimal regularization problem. The frequency domain response in electromagnetic measurements is continuously smooth with an objective function of:
Φ(D)＝[d-LD]T[d-LD]+λDTWTWD (10)
in the formula, λ is a regularization parameter, the model smooth matrix W is I, and I is an identity matrix. There are many ways to select the optimal regularization, and the present embodiment selects the L-curve method. The method is based on the data error level being unknownAnd obtaining the regularization parameter by the heuristic method. Residual norm lLD-d non-woven counting phosphor2And norm number | | D | | non-woven phosphor2And the curve is expressed by a log-log scale, wherein the maximum value of the curvature on the log-log curve is a regularization parameter value.
Fig. 2 is a time-frequency transformation effect diagram according to an embodiment of the present invention, where a is a comparison between a time-frequency transformation real part result and theoretical frequency domain real part data, and b is a comparison between a time-frequency transformation imaginary part result and theoretical frequency domain imaginary part data, and the result is in accordance with the embodiment.
4) Acquiring geological data and rock physical property information of a field measuring area, determining a roughness value β of underground media of the measuring area, determining the number of hidden layers, the number of nodes and a training function of a neural network, introducing a sample set serving as input data into the neural network for training, completing neural network training, and determining an optimal neural network for interpreting electromagnetic data of a rough medium;
when a neural network is established, the following neural network parameters are set.
(a) Hidden layer number and node number in BP neural network
Input parameter of neural network is taui，αiThat is, the number of nodes of the input layer of the network is 2; output parameter is rhoi，hiI.e. the number of output layer nodes of the network is 2. According to the principle that the network is compact as much as possible (the number of hidden layers and the number of nodes are reduced as much as possible) under the precision requirement condition to be met, an optimization scheme is set to establish the neural network based on an empirical formula and trial and error. The number of the hidden layers of the selected network is 2, and the number of the nodes is respectively selected to be 8 and 5.
(b) Determining a training function for a neural network
In order to obtain a good-performance neural network, several more commonly used training functions are selected to train the sample set data, and the training functions are Scaled conjugate gradient method (Scaled), BFGS Quasi-Newton method (BFGS Quasi-Newton method), Levenberg-Marquardt algorithm (LM algorithm). The training errors are compared, as shown in table 1, to obtain the optimal training function. As can be seen from the table, the LM algorithm has a smaller training error than the other algorithms, whichThe training effect of the algorithm is better, so the LM algorithm is selected to train the sample set. When Mean Square Error (MSE) is less than 10-5Then, the training performance of the BP neural network can be satisfied.
TABLE 1 training errors for different training functions
Number of iterations Scaled conjugate gradient method BFGS quasi-Newton method LM algorithm
50 0.0049 0.0051 1.14e-5
100 0.00061 0.00078 2.76e-6
150 0.00032 0.00033 1.74e-6
200 0.00012 0.00011 5.82e-7
(c) Setting of training parameters
I. Transfer function
The transfer function of the hidden layer selects a sigmoid (tansig) function to realize the mapping of complex nonlinear relations in the neural network.
II. Target error
The training performance of the network is satisfied when the training error meets the target error requirement, and theoretically, the smaller the target error is set, the better the network training performance is. However, if the target error setting is too small, it may make the network training time longer, thereby generating an "overfitting" phenomenon. Therefore, it is necessary to select the proper target error value to ensure the training efficiency.
The system can automatically transmit verification data serving as input data into the neural network when the neural network is trained, the network is verified by using the system, if the verification output error is continuously calculated for multiple times, the verification output error is not reduced or even increased, namely the training error is not reduced, the network performance cannot be improved after the training, and the training needs to be stopped to avoid the over-fitting condition. The validation data is applied to validate the performance of the current training network. And transmitting the processed sample set serving as input data into a neural network for training.
5) Performing parameter extraction on the frequency electromagnetic response of the step 3 by adopting the optimal neural network of the step 4 to obtain the resistivity of the underground medium;
and (4) bringing the processed data into a trained neural network system, and calculating the resistivity value by using a neural network model of the rough medium.
6) And (5) calculating by using a frequency domain rough medium generalized skin-seeking depth formula according to the resistivity of the underground medium obtained in the step (5) to obtain a depth parameter, and performing resistivity-depth imaging on the rough medium.
The wave number k of the rough medium model is known as:
k2＝-μσ0s1-β(11)
the wave number k is complex, i.e.In the form written as k-m-in, where m, n are both real numbers. Is provided with i-βA + ib, where a, b are both real numbers, are derived
Figure BDA0002267613440000111
Figure BDA0002267613440000112
According to the definition of skin depth, when the electromagnetic wave amplitude is attenuated to e-1When the propagation distance is the skin depth, the following are:
Figure BDA0002267613440000121
after obtaining the roughness and resistivity values of the subsurface medium, the generalized skin depth, i.e., the generalized skin depth of the rough medium, can be calculated using equation (14) based on the measured frequency, when β is 0,
Figure RE-GDA0002367570150000122
fig. 3 is a resistivity imaging effect diagram of an abnormal body model with roughness of 0.1 according to an embodiment of the invention shown in fig. 1, wherein a is a theoretical model, b is resistivity imaging of a calculation result of a neural network-based rough medium electromagnetic response resistivity imaging method, and the result accords with the practical situation of the embodiment, so that a new thought and a new method are provided for field high-precision explanation of an electromagnetic exploration 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.

Claims (7)

1. A rough medium electromagnetic response resistivity imaging method based on a neural network is characterized by comprising the following steps:
1) substituting the convolution state equation of the rough medium into a Maxwell equation to derive a rough medium frequency domain electromagnetic response formula of the long-wire source;
2) calculating the frequency domain ground-air electromagnetic response of the rough medium model according to the rough medium frequency domain electromagnetic response formula in the step 1, and constructing a neural network sample set;
3) preprocessing ground-air electromagnetic actual measurement flight data, and converting actual measurement time domain electromagnetic response into frequency domain electromagnetic response by adopting a regularization method;
4) acquiring geological data and rock physical property information of a field measuring area, determining a roughness value β of underground media of the measuring area, determining the number of hidden layers, the number of nodes and a training function of a neural network, transmitting a sample set as input data into the neural network for training, completing neural network training, and determining an optimal neural network which can be used for rough medium electromagnetic data interpretation;
5) adopting the optimal neural network in the step 4 to extract parameters of the frequency electromagnetic response in the step 3 to obtain the resistivity of the underground medium;
6) and (5) calculating by using a frequency domain rough medium generalized skin depth formula according to the resistivity of the underground medium obtained in the step (5) to obtain a depth parameter, and performing resistivity-depth imaging on the rough medium.
2. The method of claim 1, wherein the step 1 comprises substituting a convolution type state equation of the rough medium into Maxwell's equation to establish an electromagnetic field fractional order diffusion equation with roughness to obtain the grounded long-lead source vertical magnetic field under the rough medium, and the calculation expression of the grounded long-lead source vertical magnetic field is as follows:
Figure FDA0002267613430000011
where I is the emission current, 2L is the length of the earth conductor, rTEThe reflection coefficient is, e is the base of the natural logarithm, e is approximately equal to 2.718, mu is the magnetic conductivity, sigma0For dc conductivity, β is the spatially uniform roughness parameter,
Figure FDA0002267613430000021
omega is the angular frequency, 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.
3. The method of claim 1, wherein said step 3 comprises the steps of:
preprocessing acquired time domain electromagnetic response data, including data superposition, noise suppression and data sampling;
II, performing dispersion by a broken line approximation method according to a cosine transform formula;
III, applying constraint conditions to the discrete cosine transform formula in the step II, and utilizing regularization to obtain a new objective function;
IV, applying the sampled data in the step I, and obtaining an optimal regularization parameter by using an L curve method;
and V, solving the objective function according to the optimal regularization parameter to obtain the frequency domain electromagnetic response.
4. The method of claim 3,
the cosine transform formula in step 3:
Figure FDA0002267613430000022
Figure FDA0002267613430000023
Re[H(ω)]is the real part of the magnetic field component in the frequency domain, Im [ H (ω)]Is the imaginary part of the frequency domain magnetic field component,
Figure FDA0002267613430000024
obtained by induced electromotive force
Figure FDA0002267613430000025
h (t) is the time domain magnetic field response and ω is the angular frequency.
5. The method of claim 3,
the formula obtained after the polygonal line approximation method in the step 3 is dispersed is as follows:
Figure FDA0002267613430000026
let Re [ H ]]Forming a vector D with a time domain vector of D, responses D for different time-channelsiComprises the following steps:
Figure FDA0002267613430000031
order to
Figure FDA0002267613430000032
Constructing an objective function:
Φ(D)＝[d-LD]T[d-LD]+λDTWTWD (7)
in the formula (6), λ is a regularization parameter, the model smooth matrix W is I, and I is an identity matrix.
6. The method of claim 1, wherein said step 4 comprises the steps of:
a) determining the data of a sample set to be trained according to the working parameters of the time domain electromagnetic system and the roughness information of the experimental region, and calculating the frequency domain electromagnetic response of the rough medium model;
b) determining the number of hidden layers, the number of nodes and a training function of the neural network according to the sample set data;
c) carrying out neural network training on the basis of the electromagnetic response of the numerically simulated rough medium model;
d) and judging whether the training error meets the requirement, if not, returning to the step b).
7. The method of claim 1 wherein step 6 is defined in terms of skin depth and the magnitude of the electromagnetic response is attenuated to e-1Is called skin depth, then:
Figure FDA0002267613430000033
wherein i-βA + ib, where a, b are real numbers, σ0Is the direct current conductivity.
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