Elastic guided wave mode decomposition method based on array sound wave signals

Abstract

The invention discloses an elastic guided wave mode decomposition method based on array sound wave signals, and the method comprises the steps: converting a time domain waveform into a frequency domain through fast Fourier transform; accurately estimating the phase and the speed of the array signal by using an amplitude phase estimation method; selecting a mode with the strongest amplitude as a first separation target, and selecting a frequency-amplitude vector near the mode as an initial value of iteration; accurately estimating the amplitude and attenuation of the initial frequency by using an amplitude attenuation method; obtaining an accurate amplitude attenuation value at a target frequency point by using curve interpolation of four adjacent frequency points closest to the target frequency point every time; searching for high frequency and low frequency, and reconstructing a time domain array waveform by using all obtained target mode signal parameters; and subtracting the target mode array waveform from the original array waveform until a required mode is separated. According to the scheme, a new signal processing means is provided for wave field analysis and utilization of a complex multilayer structure medium.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a method for decomposing elastic guided wave modes based on array acoustic wave signals. Background Art

[0002] Based on their propagation mode, elastic waves can be divided into two categories: guided waves and bulk waves. In specific elastic wave applications (such as elastic wave exploration and nondestructive testing), bulk waves and guided waves represent the systematic response of the medium of interest to the excitation source. By analyzing the received waveform signals, relevant physical properties of the medium can be derived.

[0003] Body waves propagate through an infinitely homogeneous medium. They can be categorized as longitudinal and transverse waves, depending on the relationship between particle motion and propagation direction. Each wave propagates at its own speed. The propagation velocity of a body wave signal depends solely on the physical properties of the propagation medium and can be used to directly invert the medium's parameters.

[0004] Guided waves are formed by multiple reflections of elastic waves at discontinuous interfaces of media, which further produce complex interference and geometric dispersion. They can be regarded as elastic waves propagating parallel to the boundary. Typical guided waves include Rayleigh waves propagating on the free surface of semi-infinite solids, Lamb waves propagating in thin plate structures, and Stoneley waves propagating along the interface between solids. Guided wave signals are often complex: (1) Complexity of physical principles: The formation of guided wave signals is affected by boundary conditions and is related to the physical properties of the media on both sides of the boundary. It is difficult to directly use it to invert the medium parameters; (2) Complexity of signal processing: Guided wave signals often have dispersion characteristics. That is, guided waves of different frequency components have different propagation speeds, which leads to a larger time window for guided wave signal propagation, which gradually lengthens as the propagation distance increases, making it easy to overlap with other signals.

[0005] Due to the complexity of waveguide signal processing, their utilization in geophysical exploration remains underutilized. Dispersive waveguides are often considered noise, such as surface waves in seismic exploration and casing and drill collar waves in cased-hole and logging-while-drilling. However, these signals may carry medium information not present in other waveforms, thus requiring further development and utilization. In practical applications, due to the unknown medium properties and distribution in geophysical elastic wave exploration, adaptive control of the acoustic source excitation is difficult, and the excited waveguide signals often exhibit multiple modes. These different modes of waveguide signals alias in the time and frequency domains, hindering elastic wave field analysis and further medium parameter inversion. Current advanced waveform inversion algorithms match measured waveforms to waveforms synthesized in a hypothetical model to ultimately determine the model parameters of the measured object. However, elastic wave signals from different sources alias each other in the actual waveform. When the matching relationship is not appropriate, local minima can occur, leading to algorithm convergence errors. Therefore, the study of array waveform signal mode decomposition methods is conducive to better signal processing and geophysical inversion related to elastic wave exploration, and is conducive to our better development and application of elastic guided waves of different modes.

[0006] In terms of signal mode separation, some mature methods have emerged. In 1998, the empirical mode decomposition (EMD) algorithm was proposed, recursively decomposing a signal into modes with distinct spectral bands. This method decomposes the signal based on the time-scale characteristics of the data itself and does not require any basis functions, fundamentally different from Fourier and wavelet transforms, which rely on harmonic and wavelet basis functions. Over the following decade, this method has been refined by various researchers and widely used in many fields. However, it still suffers from limitations such as sensitivity to noise and sampling frequency, and the potential for modal aliasing. In 2014, the intrinsic mode functions were redefined, ultimately enabling a non-recursive method (Variational Mode Decomposition (VMD)) to separate all modes simultaneously, which is less susceptible to noise and sampling frequency. However, these methods primarily apply to one-dimensional time-domain signals and do not utilize spatial information. This results in poor consistency of decomposition results across different receivers when applied to array signal processing, and the decomposition results are less effective in practical applications of guided wave mode decomposition. Pattern decomposition methods based on array signals are primarily implemented through transform-domain filtering, such as Radon transforms and fk filters. However, these transform-domain filtering methods introduce artifacts for data with low spatial sampling frequencies, and artifacts of some patterns can overlap with true images of other patterns, making them ineffective in separating the true patterns. Consequently, they perform poorly with data with high source frequencies or low spatial sampling frequencies, such as acoustic logging data. With the advancement of computing power and the exponential growth of exploration seismic and borehole acoustic field data, data-driven intelligent wavefield separation research has garnered increasing attention. In the field of speech segmentation, this problem was first proposed and has been more maturely developed. In the field of elastic wave exploration, many researchers have also conducted research on signal decomposition using deep learning methods. However, the inherent limitations of deep learning methods, such as poor interpretability and high computing and data requirements, have limited their practical application. Summary of the Invention

[0007] In view of the shortcomings of the above methods in the application of elastic guided wave mode decomposition with attenuation characteristics under sparse spatial sampling, the present invention provides an elastic guided wave mode decomposition method based on array acoustic wave signals.

[0008] The present invention is implemented by adopting the following technical solution: a method for decomposing elastic guided wave modes based on array acoustic wave signals, comprising the following steps: Step S1: Use fast Fourier transform to convert the time domain waveform into the frequency domain; Step S2: Accurately estimate the phase and velocity of the array signal using the amplitude-phase estimation method to obtain a rough estimate of the amplitude; Step S3: Select the mode with the strongest amplitude as the first separation target, and select the frequency-amplitude vector near the mode as the initial value of the iteration; Step S4: Substituting the initial value of the iteration, using the amplitude attenuation estimation method to solve the optimization, and accurately estimating the amplitude and attenuation of the initial frequency; Step S5: Repeat step S4 for the four frequency points adjacent to the initial frequency point, with the initial value of each iteration being the precise value at the nearest frequency point; Step S6: For the target frequency point, each time, the curve interpolation of the four adjacent frequency points closest to it is used to obtain the iterative initial value of the next frequency point, and further obtain the accurate amplitude attenuation value at the target frequency point; Step S7: Repeat step S6 to search for high and low frequencies until no valid convergence value can be found in the iterations of high and low frequencies; Step S8: Reconstruct the time domain array waveform using all the obtained target pattern signal parameters. If the pattern is the one to be used, stop; otherwise, proceed to the next step. Step S9: Subtract the target pattern array waveform from the original array waveform, and repeat steps S3 to S8 until the desired pattern is separated.

[0009] Specifically, the one-dimensional array signal model in the frequency domain of step S1 is expressed as: ; in, The Fourier transform spectrum of the corresponding receiver at frequency The spectrum value at , the receiver spacing is , is the receiver sequence number, and ; For a certain frequency , coexistence There are waves propagating at different speeds, and their slownesses are ; At the same time, it has exponential decay, and the decay exponent is ; The amplitude and phase of the harmonic at the first receiver are expressed as complex numbers The noise is ; , expressed as: amplitude and phase The multiplication form, is a positive real number and a complex number with magnitude 1.

[0010] Specifically, in the one-dimensional array signal model, the spatial variation of the phase is uniquely determined by the magnitude of the phase velocity, that is, ; The spatial variation of the amplitude is uniquely determined by the attenuation size, that is, ;in, and Represents a function.

[0011] Specifically, the amplitude attenuation estimation method in step S4 specifically includes: Assuming a decay exponential If exists, then the following vector exists: ; The received array signal is amplified according to the exponential law, the exponentially decaying signal model is corrected to a non-attenuating model, and the signal after lossless filtering is estimated: ,in, , , ; Modify the intermediate variables using the amplitude-phase estimation method: , ; ; Modify the estimated value of the filter : ; in, , represents an intermediate variable; ; , and Both represent intermediate variables.

[0012] Specifically, it also includes: The filtered estimated signal Expressed as slowness Ingredients and other ingredients : ; Constructing the optimization problem: ; Solve the optimization problem to get the estimated values of amplitude and attenuation 、 .

[0013] Specifically, the step S8 of reconstructing the time domain array waveform is as follows: ; ; in, That is the time domain waveform of the mode signal at the nth receiver.

[0014] The beneficial effects of the present invention are as follows: the present invention proposes a new mode wave decomposition algorithm based on signal estimation theory. The algorithm uses the apparent velocity difference of different mode waves under the receiver array to perform mode decomposition. This method draws on the idea of parameter estimation method, estimates the important parameters in the signal model to realize the reconstruction of the mode wave, and further estimates the amplitude and attenuation using optimization methods on the basis of the amplitude and phase estimation method, and finally reconstructs the array waveform of a specific mode. It provides a new signal processing means for the wave field analysis and utilization of complex multi-layer structure media, especially for the utilization of mode waves with important physical significance and the extraction of weaker mode waves. It provides a new method. This method can be applied to signal processing in applications such as borehole acoustic wave remote detection, acoustic logging wellbore integrity evaluation, seismic surface wave exploration, and ultrasonic non-destructive testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0016] Figure 1 This is a decomposition diagram of the neutral waveguide mode in an embodiment of the present invention; Figure 2 This is a structural diagram of a cased well model in an embodiment of the present invention; Figure 3 This is a medium parameter chart in an embodiment of the present invention; Figure 4 This is a synthetic array acoustic wave signal diagram in an embodiment of the present invention; Figure 5 Schematic diagram of the theoretical structure of the synthetic data in an embodiment of the present invention; Figure 6 The result of the L2 mode and PR1 mode separation in the embodiment of the present invention; Figure 7 This is a diagram showing the results of the In-ST mode and L3 mode wave separation in an embodiment of the present invention; Figure 8 PR2 mode and AD-ST mode wave separation results in an embodiment of the present invention; Figure 9 This is a diagram showing the L1 mode wave splitting result in an embodiment of the present invention; Figure 10This is a graph of experimental data in Example 2 of the present invention; Figure 11 Schematic diagram of the pseudo-Rayleigh wave separated in Example 2 of the present invention; Figure 12 This is a simulation model diagram in Example 3 of the present invention; Figure 13 This is a diagram of simulated physical parameters in Example 3 of the present invention; Figure 14 This is a diagram showing the results of applying the algorithm in Example 3 of the present invention. DETAILED DESCRIPTION

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0018] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0019] The following is combined with Figures 1 to 14 , some embodiments of the present invention are described in detail. In the absence of conflict, the following embodiments and features in the embodiments can be combined with each other.

[0020] The present invention proposes a method for decomposing elastic guided wave modes based on array acoustic wave signals. In a preferred embodiment, the method comprises the following steps: Step S1: Use fast Fourier transform to convert the time domain waveform into the frequency domain; Step S2: Accurately estimate the phase and velocity of the array signal using the amplitude-phase estimation method to obtain a rough estimate of the amplitude; Step S3: Select the mode with the strongest amplitude as the first separation target, and select the frequency-amplitude vector near the mode as the initial value of the iteration; Step S4: Substituting the initial value of the iteration, using the amplitude attenuation estimation method to solve the optimization, and accurately estimating the amplitude and attenuation of the initial frequency; Step S5: Repeat step S4 for the four frequency points adjacent to the initial frequency point, with the initial value of each iteration being the precise value at the nearest frequency point; Step S6: For the target frequency point, each time, the curve interpolation of the four adjacent frequency points closest to it is used to obtain the iterative initial value of the next frequency point, and further obtain the accurate amplitude attenuation value at the target frequency point; Step S7: Repeat step S6 to search for high and low frequencies until no valid convergence value can be found in the iterations of high and low frequencies; Step S8: Reconstruct the time domain array waveform using all the obtained target pattern signal parameters. If the pattern is the one to be used, stop; otherwise, proceed to the next step. Step S9: Subtract the target pattern array waveform from the original array waveform, and repeat steps S3 to S8 until the desired pattern is separated.

[0021] In Example 1, the feasibility of the algorithm is verified using analytically calculated cased well monopole array acoustic logging data. In the calculation, a monopole sound source is used to excite Ricker wavelets with a center frequency of 10kHz. The model structure and medium parameters are as follows: Figure 2 、 Figure 3 The calculation results are shown as Figure 4 As shown. Theoretically, the pattern composition of the array acoustic wave signal is as follows Figure 5 The specific implementation steps of the array acoustic wave mode separation method are as follows: Step 1: Use the fast Fourier transform method to transform the time domain waveform into the frequency domain. The one-dimensional array signal model in the frequency domain is as follows: ; The Fourier transform spectrum of the corresponding receiver at frequency The spectrum value at , the receiver spacing is , is the receiver serial number, for a certain frequency (This point will not be emphasized later because the algorithm is completed at a fixed frequency), coexistence There are waves propagating at different speeds, and their slownesses are ; At the same time, it has exponential decay, and the decay exponent is ; The amplitude and phase of the harmonic at the first receiver are expressed as complex numbers The noise is For the convenience of the following description, we will Expressed as: Amplitude and phase In the form of multiplication, is a positive real number, is a complex number with magnitude 1.

[0022] ; .

[0023] Step 2: It is not difficult to see from the signal model that for the aliased signal in the frequency domain, the main parameters we care about include: phase, phase velocity, amplitude, and attenuation. In this one-dimensional propagation signal model, the harmonic component with a fixed frequency propagates at a certain phase velocity. The phase velocity uniquely determines the spatial variation of the phase, that is, The attenuation size uniquely determines the spatial variation of the amplitude, that is, .

[0024] Therefore, when estimating the two sets of parameters—phase and phase velocity, and amplitude and attenuation—there is strong independence between parameters in different sets, while there is strong coupling between parameters in the same set. For phase and phase velocity, the traditional APES method can be used.

[0025] Step 3: Select the mode with the strongest amplitude as the first separation target, and select the frequency-amplitude vector near this mode as the initial value for subsequent method iterations. The strongest mode is selected as the first separation target because, in the algorithm, for each target mode to be separated, the remaining modes are noise. Selecting the strongest mode as the separation target each time yields the highest signal-to-noise ratio. The amplitude value estimated by the APES (amplitude phase estimation) method cannot be directly used based on the target mode because the original APES algorithm signal model does not account for signal attenuation, which leads to inaccurate amplitude estimates.

[0026] Step 4: Substitute the initial value of the iteration and use the amplitude attenuation estimation method to solve the optimization problem and accurately estimate the amplitude and attenuation of the initial frequency. The specific description is as follows: Assuming a decay exponential If exists, then the following vector exists: ; The received array signal is amplified according to the exponential law, and the exponentially decaying signal model can be corrected to a non-attenuating model, and the signal after lossless filtering can be estimated: ; ; , .

[0027] Note that the filter here It can be estimated by the APES method, but compared with the original method, the estimated result of this filter is related to the attenuation parameter. Therefore, the optimization problem of APES here can be corrected by attenuation compensation as follows: , ; ; It can be proved by mathematical derivation that this modification will not affect the transformation of the problem into the problem of filter Finally, the estimated value of the filter is It can be calculated by the following formula: ; in, ; ; .

[0028] For the estimated signal after filtering We can express this as slowness Ingredients and other ingredients , ; Constructing the optimization problem: ; Solving this problem yields estimates of the amplitude and attenuation 、 .

[0029] Step 5: Repeat step 4 for four frequency points adjacent to the initial frequency point, using the exact value at the nearest frequency point as the initial value for each iteration. In step 4, we only estimate the result for a single frequency point. Complete reconstruction of the time-domain waveform requires iterating over all frequencies. To reduce unnecessary computational effort, the parameters of adjacent frequency points generally do not change dramatically due to the continuity of the function. Therefore, when selecting the initial value for the iteration, we can directly use the exact value of the adjacent point. Then, we can apply this to the algorithm executed in step 4 to obtain the exact value.

[0030] Step 6: For each target frequency point, interpolate the curves of the four closest neighboring frequency points to obtain the iterative initial value for the next frequency point, and further determine the precise amplitude attenuation value at the target frequency point. The principle is similar to that of step 5, but interpolation is used to obtain a reasonable initial value, thereby reducing the computational effort required to select the initial value.

[0031] Step 7: Repeat step 6, searching for high and low frequencies, until no valid convergence value is found in both high and low frequency iterations. This completes the parameter estimation for a complete model.

[0032] Step 8: Reconstruct the time domain array waveform using all the obtained target pattern signal parameters. Specifically, the implementation is as follows: ; ; That is the time domain waveform of the mode signal at the nth receiver.

[0033] If the mode is the one you want to use, stop; otherwise, proceed to the next step.

[0034] Step 9: Subtract the target pattern array waveform from the original array waveform, and then repeat steps 3-8 until the required pattern is separated. The final separation result is as follows Figure 6-9 shown.

[0035] Example 2: This implementation case is to apply the patented method to separate pseudo-Rayleigh waves on experimental data. The experimental data was obtained by measuring a proportional cased well under laboratory conditions using an array full-wavelength acoustic logging instrument. The metal casing was bonded to the simulated formation material using lightweight cement. The data and the separated pseudo-Rayleigh waves are as follows: Figure 10 shown.

[0036] (1) The APES method is used to calculate the spectrum of the array signal in the frequency-phase velocity domain, and the frequency and phase velocity corresponding to the maximum point of the spectrum are selected as the initial values.

[0037] (2) Substitute the initial value of the iteration and use the amplitude attenuation estimation method to solve the optimization problem and accurately estimate the amplitude and attenuation of the initial frequency.

[0038] (3) Repeat step 4 for the four frequency points adjacent to the initial frequency point. The initial value of each iteration is the exact value at the nearest frequency point.

[0039] (4) The interpolation method is used to extend the initial value to high frequency and low frequency respectively, and then the amplitude attenuation estimation method is used to solve the accurate amplitude and attenuation values.

[0040] (5) Reconstruct the time domain waveform using the estimated parameters. The reconstructed pseudo-Rayleigh wave is as follows: Figure 11 shown.

[0041] Example 3: This embodiment is to apply the patented method to simulated data to separate the stronger direct wave, thereby achieving the effect of strengthening the weaker reflected wave. The simulated data is calculated by the finite difference method, and the simulated physical model is as follows: Figure 12 The relevant physical parameters are shown in Figure 13 shown.

[0042] (1) The APES method is used to calculate the spectrum of the array signal in the frequency-phase velocity domain. The mode with the strongest energy and positive velocity is selected as the separation object, and the frequency and velocity corresponding to the maximum value of the spectrum are selected as the initial values.

[0043] (2) Substitute the initial value of the iteration and use the amplitude attenuation estimation method to solve the optimization problem and accurately estimate the amplitude and attenuation of the initial frequency.

[0044] (3) Repeat step 4 for the four frequency points adjacent to the initial frequency point. The initial value of each iteration is the exact value at the nearest frequency point.

[0045] (4) The interpolation method is used to extend the initial value to high frequency and low frequency respectively, and then the amplitude attenuation estimation method is used to solve the accurate amplitude and attenuation values.

[0046] (5) Reconstruct the time domain waveform using the estimated parameters. The reconstructed direct wave is similar to the original waveform as shown in Figure 14 As shown in the left figure, the enhanced reflected wave is Figure 14 As shown in the picture on the right.

[0047] This invention discloses an array-based elastic guided wave mode decomposition algorithm capable of decomposing dispersive guided wave modes of varying physical significance. This algorithm can be used in applications including ultrasonic nondestructive testing, seismic exploration and imaging, and acoustic well logging. For example, using full-wavelength logging data from cased-hole acoustic well logging, this method can separate different-order L-mode waves, pseudo-Rayleigh waves, and Stoneley waves in the wellbore. The specific implementation steps include: 1. Using the fast Fourier transform method to convert the time domain waveform to the frequency domain; 2. Using the amplitude phase estimation method to accurately estimate the phase and velocity of the array signal and obtain a rough estimate of the amplitude; 3. Selecting the mode with the strongest amplitude as the first separation target and selecting the frequency-amplitude vector near this mode as the initial value for subsequent method iterations; 4. Substituting the initial value for the iteration, solving the optimization problem using the amplitude attenuation estimation method to accurately estimate the amplitude and attenuation of the initial frequency; 5. Repeating step 4 for the four frequency points adjacent to the initial frequency point, with the initial value of each iteration being the precise value at the nearest frequency point; 6. For each target frequency point, interpolating the curves of the four closest adjacent frequency points to obtain the initial value for the next frequency point, and further obtaining the precise amplitude attenuation value at the target frequency point; 7. Repeating step 6, searching towards high and low frequencies, until no valid convergence value is found in the high and low frequency iterations; 8. Reconstructing the time domain array waveform using all the obtained target mode signal parameters. If the mode is the desired mode, stop; otherwise, proceed to the next step; 9. The target mode array waveform is subtracted from the original array waveform, and steps 3-8 are repeated until the desired mode is isolated. This invention provides a new signal processing method for wavefield analysis and utilization in complex multilayered media, particularly for utilizing physically significant mode waves and extracting weaker mode waves. This method can be applied to signal processing in applications such as borehole acoustic remote detection, acoustic logging wellbore integrity assessment, seismic surface wave exploration, and ultrasonic nondestructive testing.

[0048] For the sake of simplicity, the aforementioned embodiments are described as a series of actions. However, those skilled in the art should be aware that this application is not limited by the order of the actions described, because according to this application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are preferred embodiments, and the actions involved are not necessarily required by this application.

[0049] The above embodiments describe the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Without departing from the spirit and scope of the present invention, modifications and variations made by those skilled in the art without departing from the spirit and scope of the present invention should be within the scope of protection of the appended claims.

Claims

1. A method for decomposing elastic guided wave modes based on array acoustic wave signals, characterized in that: The following steps are involved: Step S1: Use fast Fourier transform to convert the time domain waveform into the frequency domain; Step S2: Accurately estimate the phase and velocity of the array signal using the amplitude-phase estimation method to obtain a rough estimate of the amplitude; Step S3: Select the mode with the strongest amplitude as the first separation target, and select the frequency-amplitude vector near the mode as the initial value of the iteration; Step S4: Substituting the initial value of the iteration, using the amplitude attenuation estimation method to solve the optimization, and accurately estimating the amplitude and attenuation of the initial frequency; Step S5: Repeat step S4 for the four frequency points adjacent to the initial frequency point, with the initial value of each iteration being the precise value at the nearest frequency point; Step S6: For the target frequency point, each time, the curve interpolation of the four adjacent frequency points closest to it is used to obtain the iterative initial value of the next frequency point, and further obtain the accurate amplitude attenuation value at the target frequency point; Step S7: Repeat step S6 to search for high and low frequencies until no valid convergence value can be found in the iterations of high and low frequencies; Step S8: Reconstruct the time domain array waveform using all the obtained target pattern signal parameters. If the pattern is the one to be used, stop; otherwise, proceed to the next step. Step S9: Subtract the target pattern array waveform from the original array waveform, and repeat steps S3 to S8 until the desired pattern is separated.

2. The elastic guided wave mode decomposition method based on array acoustic wave signals according to claim 1, characterized in that: The one-dimensional array signal model in the frequency domain of step S1 is expressed as: ； in, The Fourier transform spectrum of the corresponding receiver at frequency The spectrum value at , the receiver spacing is , is the receiver sequence number, and ; For a certain frequency , coexistence There are waves propagating at different speeds, and their slownesses are ; At the same time, it has exponential decay, and the decay exponent is ; The amplitude and phase of the harmonic at the first receiver are expressed as complex numbers The noise is ; , expressed as: amplitude and phase The multiplication form, is a positive real number, is a complex number with magnitude 1.

3. The elastic guided wave mode decomposition method based on array acoustic wave signals according to claim 2, characterized in that: In the one-dimensional array signal model, the spatial variation of the phase is uniquely determined by the phase velocity, that is, ; The spatial variation of the amplitude is uniquely determined by the attenuation size, that is, ;in, and Represents a function.

4. The elastic guided wave mode decomposition method based on array acoustic wave signals according to claim 1, characterized in that: The amplitude attenuation estimation method in step S4 specifically includes: Assuming a decay exponential If exists, then the following vector exists: ； The received array signal is amplified according to the exponential law, the exponentially decaying signal model is corrected to a non-attenuating model, and the signal after lossless filtering is estimated: ,in, ， , ； Modify the intermediate variables using the amplitude-phase estimation method: ； ； Modify the estimated value of the filter : ； in, , represents an intermediate variable; ； , and Both represent intermediate variables.

5. The elastic guided wave mode decomposition method based on array acoustic wave signals according to claim 4, characterized in that: Also includes: The filtered estimated signal Expressed as slowness Ingredients and other ingredients : ； Constructing the optimization problem: ； Solve the optimization problem to get the estimated values of amplitude and attenuation 、 .

6. The elastic guided wave mode decomposition method based on array acoustic wave signals according to claim 1, characterized in that: The step S8 of reconstructing the time domain array waveform is specifically as follows: ； ； in, That is the time domain waveform of the mode signal at the nth receiver.

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