CN115330897A - Acoustic logging imaging method based on Matrix Pencil and fully-connected neural network - Google Patents
Acoustic logging imaging method based on Matrix Pencil and fully-connected neural network Download PDFInfo
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Abstract
The invention provides an acoustic logging imaging method based on Matrix Pensil and a fully-connected neural network. The slowness-frequency relation curve is obtained by processing the array sound wave signals by using Matrix Pencil, the operation is simple, the accuracy is high, the anti-noise capability is good, the adopted full-connection neural network algorithm is simple, and the network architecture is easy to build; the method and the device can realize rapid imaging of the logging data under complex working conditions, and can provide a foundation for well cementation quality detection.
Description
Technical Field
The application relates to the field of acoustic logging data processing, in particular to an acoustic logging imaging method based on Matrix pencils and a fully-connected neural network.
Background
The acoustic logging technique is a logging method formed by utilizing the characteristic that different rocks and fluids have different speeds for acoustic wave propagation. Sonic logging can be conventionally used to measure velocity changes along the borehole axis. Wellbore damage and fluid invasion can alter wellbore formation elasticity, thereby affecting the velocity changes obtained by sonic logging. Knowledge of the radial variation of formation velocity near the wellbore helps to recover the original formation velocity and provides important geomechanical information useful for drilling and completion analysis. Therefore, the research on the inversion method of the well bore radial profile has important significance for evaluating the stability of the well wall, judging the invasion of mud and the like.
Currently, methods for imaging using acoustic data include: (1) The method is used for inverting the stratum radial velocity change by utilizing ray tracing, but the arrival time accuracy requirement of the method on the longitudinal wave is high, and errors occur in detection due to the influence of noise factors in practical application, so that the accuracy of describing the radially changed stratum is reduced. (2) The well wall stratum radial tomography is carried out by using a constraint inversion method, but the requirement on a higher frequency band is high, the condition of high-frequency deletion is frequently encountered during actual well logging, and an error is also generated in a constraint inversion result under the condition of high-frequency deletion. (3) Full-wave inversion methods are used to image the velocity radially and circumferentially of the wellbore, but require a relatively accurate initial model to perform well and converge to the desired solution.
In summary, the existing method has high requirements on data when inversion speed changes, thereby affecting the imaging quality of logging data.
Disclosure of Invention
Aiming at the technical problems of high operation difficulty, high possibility of generating errors, high dependency on original data and low logging imaging quality of the existing acoustic logging imaging method, the invention provides the acoustic logging imaging method based on Matrix Pensil and a fully-connected neural network.
In order to achieve the purpose, the technical scheme of the invention is realized as follows: a sonic logging imaging method based on Matrix Pensil and a fully-connected neural network is characterized by comprising the following steps:
the method comprises the following steps: constructing a real geometric model, and forward modeling the real geometric model to obtain array logging signals and a real slowness map of the real geometric model with different sizes under different working conditions;
step two: preprocessing the array logging signals obtained in the first step, analyzing the array logging signals through Matrix Pencil to obtain a slowness-frequency curve, extracting a low-frequency Stoneley wave part from the slowness-frequency curve to serve as a characteristic signal, and forming the characteristic signal into a Matrix to obtain a characteristic signal Matrix;
step three: adjusting a network structure of the fully-connected neural network, inputting the real slowness map obtained in the step one and the characteristic signal matrix obtained in the step two as samples into the fully-connected neural network for training and verification, and constructing an optimal parameter and well logging data inversion imaging model;
step four: and inputting the logging data obtained in the real geometric model test into a logging data inversion imaging model, so as to obtain the imaging of the logging data.
In the first step, the array logging signal is the superposition of various mode waves, and the mode waves comprise longitudinal waves and Stoneley waves.
The method for constructing the real geometric model in the first step comprises the following steps: and constructing a real geometric model comprising a water layer, a steel pipe, a cement layer and a stratum, wherein the radiuses of the water layer, the steel pipe and the cement are randomly generated within the size parameter range of the real well hole, the real geometric model is a uniform isotropic elastic medium, and the properties of medium materials of each part are consistent.
In the first step, the method for obtaining the array logging signals and the real slowness map of the real geometric models with different sizes under different working conditions through forward modeling of the real geometric models comprises the following steps: changing the sizes of different real geometric models to obtain a real slowness map, superposing a partial differential equation of a displacement field of the uniform isotropic elastic medium and a parallel vector Green's function defined by the partial differential equation to obtain a displacement field equation, solving the displacement field equation to obtain a displacement field caused by any source under a frequency domain solution, and carrying out Fourier change on the displacement field caused by any source under the frequency domain solution to obtain displacement field information under a time domain solution, namely the obtained array logging signal.
The implementation method of the Matrix Pensil in the second step is as follows: carrying out Fourier transform on a time domain signal of a logging signal to obtain frequency spectrum information of a logging signal waveform, constructing a Hankel parent matrix X through the frequency spectrum information, combining a backward-averaging matrix bundle method and a forward-averaging matrix bundle method to obtain a pole A obtained by a mode wave under the forward-averaging method and a pole B obtained by the mode wave under the backward-averaging method, setting an error range according to the signal-to-noise ratio of the array logging signal, setting the error to be 20%, calculating the phase difference between the pole A and the pole B, and when the phase difference between the pole A and the pole B is smaller than the set error range, averaging the pole A and the pole B to obtain a pole C corresponding to the determined mode wave; and when the phase difference between the pole A and the pole B is larger than the set error range, judging that the pole is a noise signal.
The backward-averaged matrix bundle method is: deleting the head column and the tail column of the Hankel parent matrix X to convert the Hankel parent matrix into two sub-matrices X 0 And X 1 Or deleting the head row and the tail row of the Hankel parent matrix X to convert the Hankel parent matrix into corresponding sub-matrices, and multiplying the Hankel parent matrix X by the left 1 Moore-Penrose generalized inverse matrix [ X ] 1 ] + Converting into a problem of solving matrix eigenvalues, and separating the differentiated fluctuation modes by calibrating poles to obtain poles B; and inverting the sequence of the Hankel parent matrix X to obtain a forward-average matrix bundle method.
In the third step, the method for inputting the true slowness map obtained in the first step and the characteristic signal matrix obtained in the second step as samples into the fully-connected neural network for training and verification comprises the following steps: processing and sampling the characteristic signal matrix obtained in the second step to form a data set, dividing the data set into a training set, a verification set and a test set, training the fully-connected neural network by using the training set of the data set, testing the network structure of the trained fully-connected neural network by using the test set of the data set, setting an activation function and a loss function, simultaneously setting and testing coherent parameters of the fully-connected neural network by using an optimization algorithm, adjusting and seeking optimal parameters, and constructing a logging data inversion imaging model by using the network structure and the optimal parameters of the fully-connected neural network.
The method for dividing the data set into the training set, the verification set and the test set is to randomly select 60% of data in the data set to generate the training set; randomly selecting 20% of data in the rest data to generate a verification set; the remaining 20% of the data generated the test set.
In the third step, the activation function of the fully-connected neural network is a sigmoid function, the loss function is a mean square error function, the optimization algorithm is an Adam algorithm, the fully-connected neural network in the third step comprises an input layer, an output layer and 4 hidden layers, each hidden layer is provided with 16 neurons, the iteration number is 500, the input layer is used for receiving logging signals, the hidden layers are used for extracting the characteristics of the logging signals, and the output layer is used for outputting inversion results.
The method for constructing the logging data inversion imaging model in the third step comprises the following steps: the FCNN hidden layer has L layers, wherein the L layer has g nodes, and the L-1 layer has h nodes. In the forward propagation process, the output of l layers can be written as:
c l ＝f(z l )＝f(W l c l-1 +d l ) (19)
wherein, c l Is the output of the l-th layer, z l Is the inactive output of layer l, W l Is the weight between layer l-1 to layer l, d l Is the deviation of the l-th layer. f is an activation function; l (c) L ) The cost function of the output layer can be expressed as:
L(c L )＝L(f(z L ))＝L(f(W L c L-1 +d L )) (20)
in the back propagation process, the weights and biases are updated to minimize the cost function.
The invention has the beneficial effects that: according to the method, matrix Pensil is utilized to process the array logging signals to obtain a slowness-frequency relation curve, low-frequency Stoneley waves are extracted to serve as characteristic signals, array information received by a sensor is converted into a one-dimensional Matrix, the method is simple to operate, high in accuracy and good in noise resistance, the signals are subjected to characteristic extraction in a frequency domain range, errors in time domain signals are eliminated, and the high dependency of a traditional method on original data is reduced; secondly, the input characteristic signals are quickly imaged by using a deep learning method based on the fully-connected neural network, and the relationship between the characteristic signals and a real slowness map is established by using the fully-connected neural network, so that quick and high-resolution imaging can be realized; the method adopted by the invention can converge to a relatively accurate result without an initial model; the activation function of the fully-connected neural network adopts a sigmoid function, because the output of the activation function corresponds to the range of (0,1) and corresponds to the slowness value after the normalization of the real slowness map. The fully-connected neural network has simple algorithm and easy network architecture construction; the method can realize rapid imaging of the logging data under complex working conditions, and can provide a foundation for well cementation quality detection.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a schematic diagram of a borehole with a transducer module and receiver array for measuring sound fields in a multi-layer cylindrical geometry in a cylindrical coordinate system according to the present invention.
FIG. 3 is a borehole size model and its received signals in accordance with the present invention: (a) An actual wellbore model, and (b) an array of received signals corresponding to (a).
Figure 4 is a comparison of the received signal of the same sensor for different cement densities.
FIG. 5 is a slowness-frequency curve of different cement densities after treatment by the Matrix pencil method.
Fig. 6 is a diagram of a fully-connected neural network in accordance with the present invention.
FIG. 7 is a test result diagram of light cement I, (a) is a slowness diagram of a light cement I test real model, (b) is a slowness diagram obtained by the light cement I through FCNN neural network inversion, and (c) is a slowness cross-section comparison diagram of the light cement I.
FIG. 8 is a test result diagram of light cement II, (a) is a slowness diagram of a light cement II test real model, (b) is a slowness diagram obtained by light cement II through FCNN neural network inversion, and (c) is a slowness section comparison diagram of light cement II.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art based on the embodiments of the present invention without inventive step, are within the scope of the present invention.
As shown in figure 1, the invention provides an acoustic logging imaging method based on a fully-connected neural network, which comprises the steps of firstly, constructing a real geometric model, obtaining array logging signals and a real slowness map of the real geometric model with different sizes under different working conditions through forward modeling of the real geometric model, then, carrying out slowness-frequency curve analysis on the array logging signals by using a Matrix Pencil method, extracting low-frequency Stoneley waves as characteristic signals, then, setting parameters of the fully-connected network, inputting the processed characteristic signal array as a sample into the fully-connected neural network for training and verification, storing the training result of the neural network, and imaging a well hole. The method comprises the following specific steps:
the method comprises the following steps: acquiring array acoustic logging signals of different well hole sizes under different working conditions, and constructing a real geometric model, wherein the real geometric model is mainly divided into four parts: the water layer, the steel pipe, the cement layer and the stratum are all regular cylinders, the water layer, the steel pipe, the cement layer and the stratum are sequentially concentrically arranged from inside to outside to form a multi-layer columnar layered medium, and the radius of the water layer, the steel pipe and the cement layer is randomly generated within the size parameter range of a real well hole.
The method for obtaining the real slowness map and the logging signal by processing the real geometric model comprises the following steps:
forward modeling a real geometric model, which is a homogeneous isotropic elastic medium with a certain density ρ and a Lame constant (Lame), and whose displacement field v (r) satisfies the following second-order partial differential equation, as shown in FIG. 2:
where ω is the angular frequency, L is the operator for v, λ and μ denote Lame constants (Lame), ρ denotes the density, v (r) denotes the displacement field, f denotes the volumetric source density,
representing the Nabla operator. The properties of the material in each layer in the geometric model are set to be consistent, and therefore, the medium displacement field in each layer satisfies equation (1).
Defining a dyadic Green function using a partial differential equation
Wherein the dyadic Green function defined by the above formula
Is a tensor, the ith column of the green's function corresponds to the displacement field caused by the unit point force in the ith direction,
for a unit dyad, δ is a Kronecker Delta function, r represents the receive position coordinate, and r' represents the source position coordinate.
By superposition of equations (1) and (2), equation (1) can be written as:
wherein V (r) represents a displacement field, V represents an integration field, d represents an integration sign,
The dyadic green function is expressed and f (r') the volumetric source density.
The true geometric model proposed in the present application is a multilayer cylindrical layered medium for which the dyadic Green function in equation (2) is combined
The displacement field caused by an arbitrary source can be solved using equation (3). Where equation (3) is a frequency domain solution and a time domain solution is obtained by fourier transforming equation (3), equation (3) is applicable to any non-uniform isotropic medium.
Due to the medium discontinuity among the water layer, the steel pipe, the cement layer and the stratum in the real geometric model, reflection can occur at the layer interface where the water layer, the steel pipe, the cement layer and the stratum intersect. Meanwhile, since the material properties within each layer are constant, the vector green function is merged in the active layer and the passive layer
There is a difference, in the layer where the point source is located, in the vector green function
Can be divided into two parts: one part corresponds to the main field of the source infinitely extending in the homogeneous medium and the other part corresponds to the interface reflection;
wherein the content of the first and second substances,
for the dyadic green function of the active layer part,
is the dyadic green function of the passive layer part.
And converting the longitudinal wave speeds of the water layer, the steel pipe, the cement and the stratum into slowness to obtain a real slowness map. The real slowness maps under different geometric dimensions can be obtained by changing the dimensions of different real geometric models, and the active layer and the passive layer are subjected to vector-combining Green's functions
Performing superposition and obtaining a dyadic Green function
The solution may be performed to obtain a log signal.
Step two: the method comprises the steps of carrying out Matrix Pensil analysis on logging signals to obtain a slowness-frequency curve, extracting a low-frequency Stoneley wave part of the slowness-frequency curve to serve as a characteristic signal, listing the characteristic signal as a one-dimensional Matrix, extracting the characteristic signal to form a data set, and dividing the data set into a training set, a verification set and a test set, wherein the training set is generated by randomly selecting 60% of data in the data set, the verification set is generated by randomly selecting 20% of data, and the test set is generated by the remaining 20% of data.
The specific method for carrying out Matrix Pencil analysis on the logging signal comprises the following steps:
in the array acoustic logging signal, the logging signals received under different sensors can be regarded as the superposition effect between various mode waves, and the types of the mode waves include but are not limited to longitudinal waves, stoneley waves and the like, which are defined as follows:
wherein, c o The amplitude of the o-th mode wave; q is the number of predicted mode waves; z is the length of the acoustic wave propagation; k is a radical of o The wave number of the o-th mode wave; x (z, ω) is the frequency spectrum of each channel waveform.
Its time domain signal X (z, t) is converted into frequency domain information X (z, ω) using the fourier transform in equation (8):
X(z,ω)＝∫x(z,t)e jωt dt (8)
the spectral information of the mode wave is abbreviated as:
x(n)＝X(z n ,ω 0 )n＝1,2,...,m (9)
wherein m represents the number of sensors for receiving logging signals; x (z) n ,ω 0 ) At a particular frequency ω 0 Next, spectrum information of the waveform obtained by the n sensors.
The Hankel parent matrix constructed by using the waveform frequency spectrum is as follows
Deleting the head column and the tail column of the Hankel parent matrix X to convert the Hankel parent matrix into two sub-matrices X 0 And X 1 The matrix (10) is thus converted into:
and deleting the head row and the tail row of the Hankel parent matrix X to obtain the corresponding sub-matrix. Converting Hankel parent matrix into two sub-matrices X 0 And X 1 The pole phi of the mode waves of different types can be obtained by solving the formula (13), and the pole phi is multiplied by the matrix X 1 Moore-Penrose generalized inverse [ X ] of 1 ]+ may convert equation (13) to equation (14) and convert the problem to solve the problem of the matrix eigenvalues;
([X 0 ]-φ[X 1 ])e＝0 (13)
([X 1 ] + [X 0 ]-φ[I])e＝0 (14)
separating the different mode waves, calibrating the poles of the mode waves according to a self-adaptive algorithm, and placing the same mode wave in an array.
φ o (ω+Δω)＝φ n (ω+Δω) (15)
Wherein n satisfies:
|φ n (ω+Δω)-φ o ω|＜|φ j (ω+Δω)-φ o ω|(j≠n) (16)
the method is a backward-averaging matrix bundle method, and a forward-averaging matrix bundle method is obtained by inverting the sequence of the parent matrix X. The final problem becomes the following problem of solving the eigenvalues of the matrix:
([X 0 ] + [X 1 ]-φI)e＝0 (17)
combining the forward-averaging matrix beam method and the backward-averaging matrix beam method to obtain a pole group A obtained by different mode waves under the forward-averaging method and a pole group B obtained by the mode waves under the backward-averaging method; when the phase difference between the pole group A and the pole group B is smaller than a set error range, averaging the poles to obtain a pole group C corresponding to the finally determined mode wave, and if the phase difference between the pole group A and the pole group B is larger than the set error range, judging that the point is a noise signal:
wherein phi o 、
And
the pole groups corresponding to the finally determined mode wave and the pole groups obtained by the forward averaging and backward averaging methods respectively are respectively used. And (5) drawing by using the pole group data to obtain a slowness-frequency curve.
And extracting a low-frequency Stoneley wave part from the slowness-frequency curve as a characteristic signal, listing the characteristic signal into a one-dimensional matrix, and dividing the length of the characteristic signal matrix to keep the dimensions of all the characteristic signals consistent. Then, sampling the characteristic signals to form a data set A, dividing the data set A into different parts according to different purposes, wherein 60% of the data set A is randomly selected for training, namely a training set is generated; randomly selecting 20% of data in the data set A for error estimation and parameter optimization in the training process, namely generating a verification set; the remaining 20% of the data is used to test the performance of the neural network, i.e. to generate a test set.
Fig. 3 shows a borehole size model and received signals thereof, fig. 3 (a) shows a borehole model under one size, which includes four parts of a water layer, a steel pipe, a cement layer and a stratum, fig. 3 (b) shows array logging signals under corresponding working conditions, the abscissa shows time, the ordinate shows sensor serial numbers from near to far, and the logging signals mainly consist of wave components such as longitudinal waves and stoneley waves. FIG. 4 is a comparison of the received signals of the same sensor at different cement densities, with different cement parameters as shown in Table 1. It can be seen by observation that the waveforms at different cement densities are mixed together and the amplitude of the sound wave does not vary significantly, so detection by the amplitude of the sound wave in the conventional sense is not reliable. FIG. 5 is a slowness-frequency curve of different cement densities after treatment by the Matrix pencil method. According to the change of the stoneley wave, the slowness value of the stoneley wave shows a decreasing trend along with the increase of the cement density, so that the low-frequency stoneley wave can be taken as a characteristic signal.
TABLE 1 Density parameters of different cements
The method utilizes Matrix Pensil to process the array sound wave signals to obtain a slowness-frequency relation curve, extracts low-frequency Stoneley waves as characteristic signals, converts array information received by the sensor into a one-dimensional Matrix, is simple to operate, high in accuracy and good in noise resistance, extracts the characteristics of the signals in a frequency domain range, eliminates errors in time domain signals, and reduces high dependency of a traditional method on original data.
Step three: adjusting a network structure of the fully-connected neural network, inputting the real slowness map obtained in the step one and the characteristic signal matrix obtained in the step two as samples into the fully-connected neural network for training and verification, and constructing an optimal parameter and well logging data inversion imaging model; FIG. 6 is a diagram of a fully-connected neural network architecture, including an input layer, several hidden layers, and an output layer. The input layer is used for receiving logging signals, the hidden layer is used for extracting the characteristics of the logging signals, and the output layer is used for outputting inversion results. The specific method comprises the following steps:
as shown in fig. 6, 4 hidden layers of the fully-connected neural network are set, each hidden layer has 16 neurons, the number of iterations is 500, and the number of samples of the same training batch is 16. The activation function is a sigmoid function, the loss function is a mean square error function, and the optimization algorithm is an Adam algorithm.
The hidden layer of the FCNN has an L layer, wherein the L layer has g nodes, and the L-1 layer has h nodes. In the forward propagation process, the output of l layers can be written as:
c l ＝f(z l )＝f(W l c l-1 +d l ) (19)
wherein, c l Is the output of the l-th layer, z l Is the inactive output of layer l, W l Is the weight between layer l-1 to layer l, d l Is the deviation of the l-th layer. f is the activation function.
Then, L (c) L ) The cost function of the output layer can be expressed as:
L(c L )＝L(f(z L ))＝L(f(W L c L-1 +d L )) (20)
in the back propagation process, the weights and biases are updated to minimize the cost function.
Step four: the logging data obtained in the actual test is input into the logging data inversion imaging model, and the imaging of the logging data can be obtained. As shown in fig. 7, the test results of the light cement i are shown, fig. 7 (a) is a slowness map of a real model of the light cement i, fig. 7 (b) is a slowness map of the light cement i obtained through FCNN neural network inversion, and fig. 7 (c) is a slowness cross-section comparison map of the light cement i. As can be seen by comparing fig. 7 (a) and fig. 7 (b), the test results of water layer radius, steel pipe radius, cement radius, formation radius, etc. are very similar to the real model, and the error is small. Fig. 7 (c) shows a cross section taken from the real model to be split. As can be seen from the comparison, the inverted predicted value is approximately consistent with the actual result, and the slowness information of each layer can be captured. Fig. 8 shows the test results of light cement ii, and it can be seen by comparing fig. 8 (a) and fig. 8 (b) that the slowness of the FCNN method in each layer is not much different from the true model, and an accurate, stable and uniform borehole inversion result can be given. FIG. 8 (c) shows a slowness profile, similar to the results in FIG. 7, where the predicted values after inversion are roughly consistent with the actual results. From the results of fig. 7 and 8, it can be seen that the acoustic logging imaging method based on the fully-connected neural network can image different cements.
The invention uses the deep learning method based on the fully-connected neural network to quickly image the input characteristic signal, and establishes the relation between the characteristic signal and the real slowness map by using the fully-connected neural network, thereby realizing quick and high-resolution imaging.
The invention can image different stratum parameters, can also image the situation of the existence of the micro-ring, can identify and position the micro-ring, and has strong universality and wide application range. The fully-connected neural network has simple algorithm and easy network architecture construction; by the method, the logging data can be rapidly imaged under complex working conditions, and a foundation can be provided for well cementation quality detection.
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, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (10)
1. A sonic logging imaging method based on Matrix Pensil and a fully-connected neural network is characterized by comprising the following steps:
the method comprises the following steps: constructing a real geometric model, and forward modeling the real geometric model to obtain array logging signals and a real slowness map of the real geometric model with different sizes under different working conditions;
step two: preprocessing the array logging signals obtained in the first step, analyzing the array logging signals through Matrix Pencil to obtain a slowness-frequency curve, extracting a low-frequency Stoneley wave part from the slowness-frequency curve to serve as a characteristic signal, and forming the characteristic signal into a Matrix to obtain a characteristic signal Matrix;
step three: adjusting a network structure of the fully-connected neural network, inputting the real slowness diagram obtained in the step one and the characteristic signal matrix obtained in the step two as samples into the fully-connected neural network for training and verification, and constructing an optimal parameter and well logging data inversion imaging model;
step four: and inputting the logging data obtained in the real geometric model test into a logging data inversion imaging model, so as to obtain the imaging of the logging data.
2. The Matrix Pencil and fully-connected neural network-based sonic logging imaging method of claim 1, wherein the array logging signal in step one is a superposition of various types of mode waves, and the mode waves include longitudinal waves and stoneley waves.
3. The sonic logging imaging method based on Matrix pencils and the fully connected neural network as claimed in claim 2, wherein the method for constructing the real geometric model in the first step is: and constructing a real geometric model comprising a water layer, a steel pipe, a cement layer and a stratum, wherein the radiuses of the water layer, the steel pipe and the cement are randomly generated within the size parameter range of the real well hole, the real geometric model is a uniform isotropic elastic medium, and the properties of medium materials of each part are consistent.
4. The sonic logging imaging method based on Matrix pencils and fully-connected neural networks as claimed in claim 2 or 3, wherein the method for obtaining the array logging signals and the true slowness map of the true geometric model with different sizes under different working conditions through forward modeling of the true geometric model in the step one comprises: changing the sizes of different real geometric models to obtain a real slowness map, superposing a partial differential equation of a displacement field of the uniform isotropic elastic medium and a dyadic Green function defined by the partial differential equation to obtain a displacement field equation, solving the displacement field equation to obtain a displacement field caused by any source under frequency domain solution, and carrying out Fourier transformation on the displacement field caused by any source under the frequency domain solution to obtain displacement field information under time domain solution, namely the obtained array logging signal.
5. The sonic logging imaging method based on Matrix pencils and fully-connected neural networks as claimed in claim 4, wherein the implementation method of Matrix pencils in step two is as follows: carrying out Fourier transform on a time domain signal of a logging signal to obtain frequency spectrum information of a logging signal waveform, constructing a Hankel parent matrix X through the frequency spectrum information, combining a backward-averaging matrix bundle method and a forward-averaging matrix bundle method to obtain a pole A obtained by a mode wave under the forward-averaging method and a pole B obtained by the mode wave under the backward-averaging method, setting an error range according to the signal-to-noise ratio of the array logging signal, setting the error to be 20%, calculating the phase difference between the pole A and the pole B, and when the phase difference between the pole A and the pole B is smaller than the set error range, averaging the pole A and the pole B to obtain a pole C corresponding to the determined mode wave; and when the phase difference between the pole A and the pole B is larger than the set error range, judging that the pole is a noise signal.
6. The Matrix Pencil and fully-connected neural network-based sonic logging imaging method of claim 5, wherein the backward-averaged Matrix bundle method is: deleting the head column and the tail column of the Hankel parent matrix X to convert the Hankel parent matrix into two sub-matrices X 0 And X 1 Or deleting the head row and the tail row of the Hankel parent matrix X to convert the Hankel parent matrix into corresponding sub-matrices, and multiplying the Hankel parent matrix X by the left 1 Moore-Penrose generalized inverse matrix [ X ] 1 ] + Converting into a problem of solving matrix eigenvalues, and separating the differentiated fluctuation modes by calibrating poles to obtain poles B; and inverting the sequence of the Hankel parent matrix X to obtain a forward-average matrix bundle method.
7. The sonic logging imaging method based on Matrix pencils and fully-connected neural networks as claimed in claim 6, wherein the method for inputting the true slowness map obtained in the step one and the characteristic signal Matrix obtained in the step two as samples into the fully-connected neural network for training and verification in the step three is as follows: processing and sampling the characteristic signal matrix obtained in the second step to form a data set, dividing the data set into a training set, a verification set and a test set, training the fully-connected neural network by using the training set of the data set, testing the network structure of the trained fully-connected neural network by using the test set of the data set, setting an activation function and a loss function, simultaneously setting and testing coherent parameters of the fully-connected neural network by using an optimization algorithm, adjusting and seeking optimal parameters, and constructing a logging data inversion imaging model by using the network structure and the optimal parameters of the fully-connected neural network.
8. The Matrix Pencil and fully connected neural network-based sonic logging imaging method of claim 7, wherein the method of dividing the data set into a training set, a validation set, and a test set generates the training set for randomly selecting 60% of the data in the data set; randomly selecting 20% of data in the rest data to generate a verification set; the remaining 20% of the data generated the test set.
9. The acoustic logging imaging method based on Matrix pencils and the fully-connected neural network according to any one of claims 5 to 8, characterized in that the activation function of the fully-connected neural network in step three is a sigmoid function, the loss function is a mean square error function, the optimization algorithm is an Adam algorithm, the fully-connected neural network in step three comprises an input layer, an output layer and 4 hidden layers, each hidden layer has 16 neurons, the number of iterations is 500, the input layer is used for receiving logging signals, the hidden layers are used for extracting the features of the logging signals, and the output layer is used for outputting inversion results.
10. The sonic logging imaging method based on Matrix pencils and the fully-connected neural network of claim 9, wherein the method for constructing the logging data inversion imaging model in step three is as follows: the hidden layer of the FCNN is provided with an L layer, wherein the L layer is provided with g nodes, and the L-1 layer is provided with h nodes; in the forward propagation process, the output of l layers can be written as:
c l ＝f(z l )＝f(W l c l-1 +d l ) (19)
wherein, c l Is the output of the l-th layer, z l Is the inactive output of layer l, W l Is the weight between layer l-1 to layer l, d l Is the deviation of the l-th layer; f is an activation function; l (c) L ) The cost function of the output layer can be expressed as:
L(c L )＝L(f(z L ))＝L(f(W L c L-1 +d L )) (20)
in the back propagation process, the weights and biases are updated to minimize the cost function.
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