Full-band espac micro-motion dispersion imaging method and system based on zero-order stroud function

Abstract

The present application relates to a kind of full-band ESPAC microseismic dispersion imaging method and system based on zero-order stroud function.The method comprises: reading the original microseismic signal recorded by microseismic station array, calculating the average cross-correlation spectrum between station pairs;The Hilbert transform is carried out on the average cross-correlation spectrum, and the complex analytical cross-correlation spectrum is constructed;Unified composite kernel function based on zero-order stroud function is constructed, and the unified composite kernel function is combined by zero-order first kind Bessel function and zero-order stroud function;The complex analytical cross-correlation spectrum is fitted in full band using unified composite kernel function, and the fitting energy residual is calculated;Wherein, the fitting process does not need to be segmented in frequency domain, and does not need to identify the zero-crossing frequency of cross-correlation spectrum;Based on the fitting energy residual of all station pairs, generate dispersion energy spectrum, and extract dispersion curve.Can consider low-frequency band large depth detection capability and high-frequency band artifact suppression capability in full band, improve fitting stability.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, and in particular to a full-band ESPAC micro-motion dispersion imaging method and system based on the zero-order Struff function. Background Technology

[0002] Microseismic exploration methods, which acquire surface wave signals from surface vibrations, extract their dispersion characteristics, and then invert the shear wave velocity structure of the subsurface medium, have been widely applied in engineering geological exploration, geothermal resource investigation, and site seismic safety assessment. The Extended Spatial Auto-Correlation (ESPAC) method is one of the core algorithms for microseismic data processing. Traditional ESPAC methods typically employ a zero-order Bessel function of the first kind (…). Fitting the cross-correlation spectrum of station pairs can preserve complete low-frequency information, and the detection depth can reach 3 to 5 times the array radius. However, the traditional ESPAC method has significant drawbacks when processing sparse array data: in the high-frequency band, it is prone to severe crossing artifacts, which interfere with the acquisition of dispersion curves, leading to shallow imaging blurring and seriously affecting interpretation accuracy. To solve the high-frequency artifact problem, the industry has proposed an improved extended spatial autocorrelation method (M-ESPAC), which uses analytic signals and the zeroth-order Hankel function of the first kind. Complex domain fitting can effectively eliminate high-frequency crossover artifacts and improve high-frequency imaging quality. However, due to the von Neumann function... The rapid decline in low frequency bands, the appearance of negative values, and the premature return result in the suppression of long-period signals and a significant reduction in detection depth, which is usually less than twice the array radius.

[0003] To balance the deep-penetration capabilities of traditional ESPAC with the high-frequency artifact suppression capabilities of M-ESPAC, a piecewise fitting method based on the zero-crossing frequency of the cross-correlation spectrum (FM-ESPAC) has been proposed in the existing technology, using... Fitting is used to ensure depth, and H0(1) fitting is switched to eliminate artifacts in the high-frequency band. However, this method is highly dependent on the automatic identification of f01, and is prone to misjudgment in low signal-to-noise ratio data. It usually requires manual intervention to set the starting scanning frequency, which is cumbersome, unstable, and difficult to achieve fully automatic processing in industrial software.

[0004] Therefore, traditional micro-motion data processing methods suffer from high-frequency cross artifacts due to Bessel function fitting, low-frequency response suppression due to Hankel function fitting, and piecewise fitting methods rely on zero-crossing frequency identification and often require manual intervention, resulting in poor stability and an inability to simultaneously achieve both large depth and high-precision imaging. Summary of the Invention

[0005] In order to solve the above-mentioned technical problems, a full-band ESPAC micro-motion dispersion imaging method and system based on the zero-order Struff function is provided. It can simultaneously take into account the low-frequency band deep detection capability and the high-frequency band artifact suppression capability, improve the fitting stability, automation and processing efficiency, and improve the dispersion imaging accuracy and the reliability of stratigraphic inversion.

[0006] A full-band ESPAC micro-motion dispersion imaging method based on a zero-order Struff function, the method comprising:

[0007] Read the original micro-motion signals recorded by the micro-motion array, and calculate the average cross-correlation spectrum between station pairs based on the original micro-motion signals;

[0008] Perform a Hilbert transform on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum;

[0009] A unified composite kernel function based on the zeroth-order Struff function is constructed. The unified composite kernel function is composed of a zeroth-order Bessel function of the first kind and a zeroth-order Struff function.

[0010] The unified composite kernel function is used to perform a full-band unified fitting of the complex analytic cross-correlation spectrum, and the fitting energy residual is calculated; wherein, the fitting process does not require segmentation of the frequency domain, nor does it require identification of the zero-crossing frequencies of the cross-correlation spectrum;

[0011] Based on the fitted energy residuals of all station pairs, a dispersive energy spectrum is generated, and the dispersion curve is extracted.

[0012] In one embodiment, reading the original micro-motion signal recorded by the micro-motion array and calculating the average cross-correlation spectrum between station pairs based on the original micro-motion signal includes:

[0013] The original micro-motion signals of each station are divided into time window signals of preset time lengths;

[0014] Perform Fourier transform on the time window signals of all stations to obtain the frequency domain signals of each station;

[0015] For each station pair, the self-power spectrum and the cross-power spectrum between any two stations are calculated based on the frequency domain signal.

[0016] The average cross-correlation spectrum is obtained by statistically averaging the self-power spectrum and cross-power spectrum.

[0017] In one embodiment, a Hilbert transform is performed on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum, including:

[0018] The average cross-correlation spectrum is used as the real part signal, and a Hilbert transform is performed on the average cross-correlation spectrum to obtain the imaginary part signal orthogonal to the real part signal;

[0019] The real part signal and the imaginary part signal are combined to construct a complex analytic cross-correlation spectrum in complex form.

[0020] In one embodiment, a unified composite kernel function based on a zero-order Struff function is constructed. This unified composite kernel function is composed of a zero-order Bessel function of the first kind and a zero-order Struff function, including:

[0021] Define the dimensionless wavenumber as α = 2πfr / c; where f is the frequency, r is the station spacing, and c is the phase velocity.

[0022] Construct a unified composite kernel function as follows ;in, It is a zero-order Bessel function of the first kind, which serves as the real part of the unified composite kernel function; is the zero-order Struff function, which serves as the imaginary part of the unified composite kernel function; i is the imaginary unit;

[0023] Taking advantage of the fact that the zeroth-order Struff function approaches zero at the origin, the unified composite kernel function approaches the zeroth-order Bessel function of the first kind in the low-frequency range; taking advantage of the fact that the zeroth-order Struff function approximates the zeroth-order Neumann function of the second kind in the high-frequency range, the unified composite kernel function approaches the zeroth-order Hankel function of the first kind in the high-frequency range.

[0024] In one embodiment, the unified composite kernel function is used to perform a full-band unified fitting of the complex analytic cross-correlation spectrum, and the fitting energy residual is calculated, including:

[0025] For each station pair, the frequency and phase velocity are iterated, and the dimensionless wavenumber is calculated based on the frequency and phase velocity.

[0026] The theoretical composite kernel function is calculated based on the dimensionless wavenumber. ;

[0027] Calculate the complex domain residual modulus between the complex analytic cross-correlation spectrum and the theoretical composite kernel function, and then use the formula... The fitted energy residual was calculated;

[0028] The fitting process uses a uniform fitting across the entire frequency band, without dividing the frequency band or identifying the zero-crossing frequency of the cross-correlation spectrum.

[0029] In one embodiment, the fitting energy is defined as: The higher the energy, the better the fit, and the maximum energy is 1.

[0030] In one embodiment, a dispersive energy spectrum is generated based on the fitted energy residuals of all station pairs, and a dispersion curve is extracted, including:

[0031] The fitted energy residuals of all station pairs are weighted and superimposed to obtain the superimposed energy spectrum;

[0032] The superimposed energy spectrum is sequentially subjected to Gaussian smoothing, normalization, and energy focusing to achieve energy enhancement processing, resulting in a two-dimensional dispersive energy spectrum.

[0033] For each frequency point in the two-dimensional dispersion energy spectrum, the phase velocity corresponding to the maximum energy value at each frequency point is selected and connected to form a continuous dispersion curve.

[0034] A full-band ESPAC micro-motion dispersion imaging system based on a zero-order Struff function, the system comprising:

[0035] The cross-correlation spectrum calculation module is used to read the original micro-motion signals recorded by the micro-motion array and calculate the average cross-correlation spectrum between station pairs based on the original micro-motion signals.

[0036] The transformation module is used to perform a Hilbert transform on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum.

[0037] The function construction module is used to construct a unified composite kernel function based on the zeroth-order Struff function. The unified composite kernel function is composed of a zeroth-order Bessel function of the first kind and a zeroth-order Struff function.

[0038] The fitting energy calculation module is used to perform a unified full-band fitting of the complex analytical cross-correlation spectrum using the unified composite kernel function, and to calculate the fitting energy residual; wherein, the fitting process does not require segmentation of the frequency domain, nor does it require identification of the zero-crossing frequencies of the cross-correlation spectrum;

[0039] The dispersion generation module is used to generate a dispersion energy spectrum based on the fitted energy residuals of all station pairs and extract the dispersion curve.

[0040] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of a full-band ESPAC micro-motion dispersion imaging method based on a zero-order Struff function.

[0041] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a full-band ESPAC micro-motion dispersion imaging method based on a zero-order Struff function.

[0042] The aforementioned full-band ESPAC micro-motion dispersion imaging method and system based on the zero-order Struff function can stably acquire the spatial correlation characteristics of surface waves in micro-motion signals by calculating the average cross-correlation spectrum of the station, thereby improving the signal's anti-interference capability. By constructing a complex analytic cross-correlation spectrum through Hilbert transform of the average cross-correlation spectrum, the real-valued signal is extended into a complex domain signal, preserving the complete amplitude and phase information of the signal. By constructing a unified composite kernel function composed of a zero-order Bessel function of the first kind and a zero-order Struff function, the system can simultaneously take into account low frequencies across the entire frequency band. It features high-depth detection capabilities and high-frequency artifact suppression; it employs a unified composite kernel function for uniform fitting across the entire frequency band, eliminating the need for segmentation and zero-crossing frequency identification, thus avoiding splicing errors, zero-crossing identification errors, and manual intervention issues caused by segmented fitting, thereby improving fitting stability, automation, and processing efficiency; it generates a dispersion energy spectrum and extracts dispersion curves based on the fitted energy residuals from all stations, effectively suppressing random noise and enhancing the true dispersion energy, ultimately obtaining a continuous dispersion curve with a high signal-to-noise ratio, improving dispersion imaging accuracy and stratigraphic inversion reliability. Attached Figure Description

[0043] Figure 1 This is an application environment diagram of the full-band ESPAC micro-motion dispersion imaging method based on the zero-order Struff function in one embodiment.

[0044] Figure 2 This is a flowchart illustrating a full-band ESPAC micro-dispersion imaging method based on a zero-order Struff function in one embodiment.

[0045] Figure 3 This is a waveform comparison diagram of three zero-order special functions in one embodiment;

[0046] Figure 4 This is a schematic diagram of the numerical simulation model and observation array layout for micro-motion exploration in one embodiment;

[0047] Figure 5 This is a schematic diagram illustrating the effects of four different methods—ESPAC, M-ESPAC, FM-ESPAC, and ST-ESPAC—in micro-motion dispersive imaging in one embodiment.

[0048] Figure 6 This is a block diagram of a full-band ESPAC micro-motion dispersion imaging system based on a zero-order Struff function in one embodiment.

[0049] Figure 7 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0051] The full-band ESPAC micro-motion dispersion imaging method based on the zero-order Struff function provided in this application can be applied to, for example... Figure 1 The application environment shown. For example... Figure 1 As shown, the application environment includes computer device 110. Computer device 110 can read the original micro-motion signals recorded by the micro-motion array and calculate the average cross-correlation spectrum between station pairs based on the original micro-motion signals; computer device 110 can perform a Hilbert transform on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum; computer device 110 can construct a unified composite kernel function based on the zero-order Struff function, which is composed of a zero-order Bessel function of the first kind and a zero-order Struff function; computer device 110 can use the unified composite kernel function to perform a unified full-band fitting of the complex analytic cross-correlation spectrum and calculate the fitting energy residual; wherein, the fitting process does not require segmentation of the frequency domain or identification of the zero-crossing frequencies of the cross-correlation spectrum; computer device 110 can generate a dispersion energy spectrum based on the fitting energy residuals of all station pairs and extract the dispersion curve. Computer device 110 can be, but is not limited to, various personal computers, laptops, smartphones, robots, unmanned aerial vehicles, tablets, etc.

[0052] In one embodiment, such as Figure 2 As shown, a full-band ESPAC micro-motion dispersion imaging method based on the zeroth-order Struff function is provided, including the following steps:

[0053] Step 202: Read the original micro-motion signals recorded by the micro-motion array, and calculate the average cross-correlation spectrum between station pairs based on the original micro-motion signals.

[0054] Computer equipment can read the micro-motion data of the array and the coordinates of the stations, and calculate the cross-correlation spectrum between the stations.

[0055] In one embodiment, the full-band ESPAC micro-motion dispersion imaging method based on the zero-order Struff function may further include the process of calculating the average cross-correlation spectrum. The specific process includes: dividing the original micro-motion signals of each station into time window signals of each preset time length; performing Fourier transform on the time window signals of all stations to obtain the frequency domain signals of each station; for each station pair, calculating the self-power spectrum and the cross-power spectrum between any two stations based on the frequency domain signals; and performing statistical averaging based on the self-power spectrum and the cross-power spectrum to obtain the average cross-correlation spectrum.

[0056] The computer equipment can read the raw micro-motion time series recorded by each station in the micro-motion array set up in the exploration area. To balance computational efficiency and spectral resolution, the continuous raw micro-motion signal is divided into multiple non-overlapping or overlapping time window signals according to a preset time length. Next, the computer equipment can preprocess the raw micro-motion signal, mainly including detrending processing (eliminating instrument drift), mean removal processing (eliminating DC components), and bandpass filtering processing (filtering out high-frequency noise and low-frequency drift according to the frequency band of the exploration target).

[0057] The computer equipment can perform Fourier transform on the time-window signals of all stations, converting the time-domain signals into frequency-domain signals, and obtaining the complex amplitude information of each station at each frequency point. Then, for each pair of stations, the computer equipment can perform spectral estimation based on the transformed frequency-domain signals, that is, calculate the self-power spectrum of each station and the cross-power spectrum between the two stations. The self-power spectrum can be the product of the frequency-domain signal and its conjugate, reflecting the signal energy at a single point; the cross-power spectrum can be the product of the frequency-domain signal of one station and the conjugate of the frequency-domain signal of another station, used to extract coherence information between the two points.

[0058] To suppress random noise and improve the signal-to-noise ratio, computer equipment can perform statistical averaging of the auto-power spectrum and cross-power spectrum of all calculated time windows. Specifically, the computer equipment can perform linear or geometric averaging of the cross-power spectrum of all time windows to obtain the final average cross-correlation spectrum.

[0059] In this embodiment, specifically, suppose there are n (n≥2) stations in the observation array T, and the station pair is denoted as (A,B) (A,B=1,2,…,n and A≠B). The Fourier transform of stations A and B is S. A S B Then the average cross-correlation spectrum of the stations (A,B) can be expressed as: ;in, , These are the Fourier transforms of the records from stations A and B, respectively. Indicates complex conjugation. Indicates taking the real part, The number of data segments can be determined; the signal-to-noise ratio can be improved by averaging the cross-correlation spectrum multiple times.

[0060] In this embodiment, by using time window segmentation and statistical averaging techniques, random noise in the micro-motion data can be suppressed, and the signal-to-noise ratio of the cross-correlation spectrum can be improved. The output average cross-correlation spectrum provides high-quality basic data for subsequent Hilbert transform and complex kernel function fitting.

[0061] Step 204: Perform a Hilbert transform on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum.

[0062] In the traditional ESPAC method, real functions are used directly. Fitting the real cross-correlation spectrum can easily lead to crossover artifacts in the high-frequency band. To overcome this defect, this embodiment introduces analytic signal processing techniques, using Hilbert transform to extend the real cross-correlation spectrum into a complex analytic cross-correlation spectrum, laying the foundation for subsequent complex domain fitting. That is, in order to eliminate zero-crossing artifacts in the cross-correlation spectrum and extract complete phase information, the computer device can construct an analytic signal using Hilbert transform.

[0063] In one embodiment, the full-band ESPAC micro-motion dispersion imaging method based on the zero-order Struff function may further include the process of constructing an analytic signal through Hilbert transform. The specific process includes: taking the average cross-correlation spectrum as the real part signal and performing a Hilbert transform on the average cross-correlation spectrum to obtain an imaginary part signal orthogonal to the real part signal; combining the real part signal and the imaginary part signal to construct a complex analytic cross-correlation spectrum in complex form.

[0064] The Hilbert transform is a linear integral transform. Its transformation result for real functions is equivalent in the frequency domain to phase shifting the negative frequency components and positive frequency components of the original signal, thereby constructing an imaginary part signal that is orthogonal to the original signal.

[0065] The computer equipment can use the calculated average cross-correlation spectrum as the real part signal of the complex analytic cross-correlation spectrum. The real part signal retains all the information of the original cross-correlation spectrum, including the deep detection capability in the low-frequency band. Moreover, the real part signal is mainly determined by the zeroth-order Bessel function of the first kind, reflecting the standing wave characteristics of Rayleigh surface waves in horizontally layered media.

[0066] In this embodiment, the average cross-correlation spectrum is denoted as... Where r is the station spacing and f is the frequency; the average cross-correlation spectrum is a real function, and its shape approximates a zero-order Bessel function under ideal conditions. Computer equipment can perform a Hilbert transform on the real part of the signal (i.e., the average cross-correlation spectrum) in the frequency domain to obtain an imaginary part signal that is 90 degrees out of phase with the real part in the time domain. Mathematically, this imaginary part signal forms a Hilbert transform pair with the real part signal, ensuring their orthogonality.

[0067] Specifically, the analytic signal obtained by computer equipment through the Hilbert transform can be represented as: ;in, The imaginary unit, The Hilbert transform of the average cross-correlation spectrum forms the imaginary part of the complex analytic cross-correlation spectrum.

[0068] In this embodiment, the traditional real-domain cross-correlation spectrum is extended to the complex domain through the Hilbert transform process, preserving the deep detection information in the low-frequency band and introducing phase continuity in the high-frequency band, thus avoiding the multiple solutions problem caused by the function crossing zero points in the traditional real-domain fitting.

[0069] Step 206: Construct a unified composite kernel function based on the zeroth-order Struff function. The unified composite kernel function is composed of a zeroth-order Bessel function of the first kind and a zeroth-order Struff function.

[0070] Traditional ESPAC methods use a zero-order Bessel function of the first kind, J0(α), as the theoretical fitting kernel. While this preserves complete low-frequency information, it easily introduces crossover artifacts in the high-frequency band under sparse array conditions. The improved M-ESPAC method uses a zero-order Hankel function of the first kind for complex domain fitting, which can effectively eliminate high-frequency crossover artifacts. However, because its imaginary part drops rapidly in the low-frequency band, becomes negative, and prematurely returns to its original position, long-period signals are suppressed, significantly reducing the detection depth. To balance detection depth and artifact suppression, the computer equipment can use a zero-order Bessel function + a zero-order Struff function to form a unified composite kernel function.

[0071] In one embodiment, a full-band ESPAC micro-motion dispersion imaging method based on a zero-order Struff function may further include a process of constructing a unified composite kernel function. The specific process includes: defining the dimensionless wavenumber as α = 2πfr / c; where f is the frequency, r is the station spacing, and c is the phase velocity; and constructing the unified composite kernel function as follows: ;in, It is a zero-order Bessel function of the first kind, and serves as the real part of the unified composite kernel function; Let be the zeroth-order Struff function, which serves as the imaginary part of the unified composite kernel function; i is the imaginary unit; taking advantage of the fact that the zeroth-order Struff function approaches zero at the origin, the unified composite kernel function approaches the zeroth-order Bessel function of the first kind in the low-frequency range; taking advantage of the fact that the oscillation pattern of the zeroth-order Struff function approximates the zeroth-order Neumann function of the second kind in the high-frequency range, the unified composite kernel function approaches the zeroth-order Hankel function of the first kind in the high-frequency range.

[0072] First, the computer equipment can define the dimensionless wavenumber α as the independent variable of the unified composite kernel function. The physical meaning of the dimensionless wavenumber is: the normalized wavenumber corresponding to the station spacing r at a given frequency f and phase velocity c; the mathematical expression is: α = 2πfr / c; where f is the frequency, determined by the frequency sampling points of the cross-correlation spectrum, and its value range covers the exploration target frequency band; r is the station spacing, calculated from the array's geometric coordinates, and has different values ​​for different station pairs; c is the phase velocity, a parameter to be scanned, and its value range is traversed during subsequent fitting. The dimensionless wavenumber comprehensively reflects the relative relationship between wavelength, observation distance, and propagation speed, serving as a crucial bridge connecting physical space and frequency domain space.

[0073] Next, the computer device can construct a unified composite kernel function in complex form based on the dimensionless wavenumber, with the expression: ;in, It is a zero-order Bessel function of the first kind, serving as the real part of the unified composite kernel function. It mainly characterizes the standing wave characteristics of Rayleigh surface waves in shallow media and the deep response in the low-frequency range. is the zeroth-order Struff function, serving as the imaginary part of the unified composite kernel function, used to describe the non-ideal propagation characteristics of the wave field and the scattering effects in the high-frequency band. i is the imaginary unit; the real and imaginary parts are coupled through complex addition to form an analytic composite function across the entire frequency band.

[0074] In this embodiment, the computer device can utilize the mathematical properties of Bessel and Struff functions to unify the specific physical convergence of composite kernel functions across different frequency bands, thereby achieving a unified description across the entire frequency band. Specifically, it utilizes the zeroth-order Struff function. At the origin The mathematical property that the function value approaches zero means that the unified composite kernel function M(α) is mainly composed of its real part in the low-frequency range. Dominance, that is It retains low-frequency, long-period signals and achieves a detection depth of 3-5 times the array radius, enabling the kernel function to accurately reflect the standing wave characteristics of the traditional ESPAC method in the low-frequency band, thus preserving the ability to detect deep geological structures.

[0075] Computer devices can utilize zeroth-order Struff functions In the high frequency band The oscillation pattern approximates the characteristics of the zeroth-order von Neumann function of the second kind, combined with the Bessel function. The high-frequency behavior of the unified composite kernel function M(α) approaches the zeroth-order Hankel function of the first kind in the high-frequency range. This allows the kernel function to simulate the characteristics of traveling wave propagation in the high-frequency band, effectively suppressing the crossover artifacts generated by traditional methods in the high-frequency band.

[0076] In this embodiment, the proposed unified composite kernel function realizes a smooth transition from a low-frequency standing wave model to a high-frequency traveling wave model. It can automatically adapt to changes in the physical properties of the wave field across the entire frequency range without the need for frequency band segmentation and model switching. This not only simplifies the logical structure of the inversion algorithm but also avoids energy cluster splitting or splicing errors caused by improper segmentation point selection, thereby improving the resolution and reliability of dispersion imaging.

[0077] In one embodiment, with a wave velocity v = 800 m / s and a station spacing r = 50 mr, the zero-order Bessel function of the first kind... Zero-order von Neumann function of the second kind Zero-order Struff function For example Figure 3 As shown:

[0078] Zero-order Bessel function of the first kind This is the core kernel function of the traditional ESPAC method, representing the standing wave field of a Rayleigh surface wave in an ideal infinite medium. At frequency 0, its value is 1. As the frequency increases, it exhibits a decaying oscillation pattern with gradually decreasing amplitude and multiple zero-crossing points. In traditional ESPAC, the measured cross-correlation spectrum should approximate under ideal conditions as... The curve is obtained, but due to its damped oscillation characteristics, it is prone to crossover artifacts when fitting at high frequencies.

[0079] Zero-order von Neumann function of the second kind Typically representing a traveling wave field propagating outwards, its function value tends towards negative infinity as the frequency approaches 0, making it difficult to use directly in the low-frequency range (wavelet number) and causing instability in numerical calculations. In the high-frequency range, the oscillation pattern... Similar, but with a 90-degree phase difference. The negative infinity divergence characteristic in the low-frequency band is the fundamental reason for the insufficient low-frequency response and limited detection depth of the M-ESPAC method, which leads to the suppression of low-frequency signals during complex domain fitting.

[0080] Zeroth-order Struff function This is the key function introduced in this application, used to construct the new kernel function, which smoothly increases from 0, without... That singularity solved the problem of instability in low-frequency calculations; the oscillation pattern gradually approached... Combining finiteness and Its phase characteristic is 0 at 0 and it has no singularities, making it suitable as the imaginary part of an analytic signal. use.

[0081] Depend on Figure 3 It can be seen that the zeroth-order Struff function It smoothly transitions to zero in the low-frequency range, and its oscillation pattern in the high-frequency range is similar to the zeroth-order von Neumann function of the second kind. Highly consistent. Based on this characteristic, a system is built using... and The unified composite kernel function can achieve continuous fitting across the entire frequency band without introducing low-frequency singularities. It retains the low-frequency, deep-penetration detection capability of traditional ESPAC while also having high-frequency artifact suppression effect, without the need for segmented processing or manual intervention.

[0082] In one embodiment, to clarify the specific manifestations of the insufficient low-frequency response of M-ESPAC, a simulation experiment was conducted based on a two-layer homogeneous geological model to compare the dispersion spectrum differences between ESPAC and M-ESPAC in linear and triangular arrays. The simulated passive source acquisition used a noise numerical simulation method to generate vertical component micromotion records, with the pulse being a 20Hz Ricker wavelet (simulating a fundamental surface wave). The geological model parameters are shown in the table below:

[0083]

[0084] The theoretical dispersion curve was then calculated using the Dunkin' matrix method and compared with the dispersion spectrum of the simulated data. It can be seen that due to the decaying oscillation characteristics of ESPAC, cross artifacts are easily generated when fitting in the high-frequency band; while the M-ESPAC method has insufficient low-frequency response and limited detection depth.

[0085] By designing a nested triangular array, the schematic diagram of the micro-motion exploration numerical simulation model and the observation array layout is shown below. Figure 4 As shown, the diagram is divided into two sub-plots (a) and (b): a triple triangle with radii of 15m, 30m, and 60m respectively, comprising 10 stations, with an observation duration of 10 minutes, a data sampling rate of 500Hz, and noise sources located far from the array center, randomly distributed within a range of 500-2000m from the array. Figure 4 As shown in (a), the geophone is located at the origin of the coordinate system, representing a single seismic geophone (or station); noise sources are widely and randomly distributed, mainly within a circular area with a radius of approximately 2000 meters centered on the geophone. In background noise imaging theory, it is assumed that the noise sources are spatially uniformly distributed (or approximately uniformly distributed). Therefore, the cross-correlation function of the noise recorded by the two stations can be approximated as the Green's function (i.e., the response of seismic wave propagation) between them. Figure 4 (a) illustrates the relationship between a single station and a large number of surrounding noise sources, illustrating the spatial distribution characteristics of the noise field. It shows that, ideally, the noise sources should be evenly distributed over a large area around the detector to ensure that the cross-correlation function can accurately recover the Green's function of the underground medium.

[0086] like Figure 4As shown in (b), there are nine detectors arranged in a concentric circular array, with one detector at the center and eight detectors on three concentric circles of different radii. By using station pairs with different radii, underground structures at different depths can be detected (larger radii correspond to deeper layers, and smaller radii to shallower layers). The distance between any two detectors determines the detectable wavelength range. By calculating the cross-correlation function between all station pairs, the Rayleigh wave dispersion curve can be extracted, and thus the underground shear wave velocity structure can be inverted. Figure 4 (b) The concentric ring design can effectively cover the detection needs from shallow to deep, and is the standard array form for space autocorrelation methods such as ESPAC.

[0087] Step 208: Use a unified composite kernel function to perform a uniform full-band fitting of the complex analytic cross-correlation spectrum and calculate the fitting energy residual; wherein, the fitting process does not require segmentation of the frequency domain and identification of the zero-crossing frequency of the cross-correlation spectrum.

[0088] After constructing a unified composite kernel function, the computer device can also use the unified composite kernel function to perform a unified full-band fitting of the complex analytic cross-correlation spectrum and calculate the fitted energy. Specifically, the computer device can fit the complex analytic cross-correlation spectrum with the unified composite kernel function, and by scanning the phase velocity, find the phase velocity value that best matches the two, thereby constructing a dispersion energy spectrum. There is no need to switch fitting functions between low-frequency and high-frequency bands, nor is there a need to identify the zero-crossing frequency of the cross-correlation spectrum. A unified composite kernel function is used for fitting across the entire frequency range.

[0089] In one embodiment, the provided full-band ESPAC micro-motion dispersion imaging method based on the zero-order Struff function may further include a unified composite kernel function fitting process, specifically including: for each station pair, traversing the frequency and phase velocity, and calculating the dimensionless wavenumber based on the frequency and phase velocity; calculating the theoretical composite kernel function based on the dimensionless wavenumber. ; Calculate the complex domain residual modulus between the complex analytic cross-correlation spectrum and the theoretical composite kernel function, and then use the formula The fitted energy residual was calculated; the fitting process adopted a uniform fitting across the entire frequency band, without dividing the frequency band or identifying the zero-crossing frequency of the cross-correlation spectrum.

[0090] Computer equipment can set the frequency for each station pair. With phase velocity The search range is defined. Within the search range, all frequency-phase velocity combinations are traversed according to a preset step size. For each frequency-phase velocity combination Calculate the corresponding dimensionless wavenumber. Next, the computer equipment can substitute the calculated dimensionless wavenumber into the unified composite kernel function expression. In this process, the theoretical composite kernel function values ​​at the corresponding frequencies and phase velocities are calculated. It is a zero-order Bessel function of the first kind, which can be computed using standard mathematical library functions; It is a zero-order Struff function, which can be calculated by series summation, numerical integration, or table lookup interpolation.

[0091] Next, the computer equipment can compare the obtained complex analytic cross-correlation spectrum with the theoretical composite kernel function. A comparison is then made. Since both are in complex form, the fitting error is measured by calculating the magnitude of the complex difference, and the fitting energy residual is further calculated.

[0092] Specifically, computer equipment can calculate the complex domain residual modulus based on the complex analytic cross-correlation spectrum and the theoretical composite kernel function, and further calculate the fitted energy residual. .in, The complex analytical cross-correlation spectrum is constructed from measured data; The value of the unified composite kernel function is calculated from the theoretical composite kernel function.

[0093] Next, the computer equipment can repeatedly execute the process of calculating the fitted energy residual for all traversed frequencies and phase velocities, generating a two-dimensional fitted energy matrix based on the calculated fitted energy residual. In this process, a unified fitting strategy across the entire frequency range can be adopted, using the same theoretical model for fitting across the entire frequency range, eliminating the need to find the zero-crossing frequencies of the cross-correlation spectrum to divide the low-frequency and high-frequency bands. Since the unified composite kernel function is continuous and smooth in the complex domain, the fitting process directly crosses the zero-crossing points of the function in the real domain, avoiding the fitting instability or failure caused by weak signals near the zero-crossing points.

[0094] In one embodiment, the fitting energy is defined as: The higher the energy, the better the fit, and the maximum energy is 1.

[0095] When the complex analytic cross-correlation spectrum is completely consistent with the theoretical composite kernel function, the analytic signal-complex kernel function approaches zero, and the fitting energy approaches the maximum value of 1, indicating that the theoretical model and the measured data achieve the best match under this frequency-phase velocity combination.

[0096] Through a unified fitting process across the entire frequency band, the dispersion energy calculation from low frequency to high frequency can be completed in one go, which greatly simplifies the algorithm process and eliminates systematic artifacts caused by improper selection of segmentation points or zero-crossing point identification errors.

[0097] Step 210: Generate a dispersion energy spectrum based on the fitted energy residuals of all station pairs, and extract the dispersion curves.

[0098] Computer equipment can fuse, enhance, and visualize the fitting results of all station pairs to form a dispersion energy spectrum that can be interpreted manually or automatically, and extract dispersion curves from it to provide input data for subsequent shear wave velocity inversion.

[0099] In one embodiment, the full-band ESPAC micro-motion dispersion imaging method based on the zero-order Struff function may further include a dispersion curve picking process, specifically including: weighted superposition of the fitted energy residuals of all station pairs to obtain a superimposed energy spectrum; sequentially performing Gaussian smoothing, normalization, and energy focusing on the superimposed energy spectrum to achieve energy enhancement processing and obtain a two-dimensional dispersion energy spectrum; for each frequency point in the two-dimensional dispersion energy spectrum, selecting the phase velocity corresponding to the maximum energy value at each frequency point and connecting them to form a continuous dispersion curve.

[0100] For all station pairs, the computer equipment can perform weighted superposition of the calculated fitted energy residuals. Specifically, for the same frequency-phase velocity grid point, the fitted energies of all station pairs at that point are accumulated or weighted averaged, thereby compressing the multidimensional station pair data into a two-dimensional superimposed energy spectrum. The superposition process can enhance the energy of the effective signal, suppress random noise, and make the dispersive energy clusters more focused.

[0101] Next, the computer equipment can sequentially perform Gaussian smoothing, normalization, and energy focusing on the superimposed energy spectrum to highlight the characteristics of the dispersion curve and improve the signal-to-noise ratio and energy cluster clarity of the dispersion energy spectrum. Specifically, the computer equipment can perform Gaussian smoothing filtering on the superimposed energy spectrum along both the frequency axis and the phase velocity axis to eliminate energy jumps caused by discrete sampling, making the energy distribution more continuous, thus completing the Gaussian smoothing process; the smoothed energy values ​​are then normalized to compress the dynamic range of the energy values ​​to the [0,1] interval, facilitating energy comparison between different frequency bands, thus completing the normalization process; high-energy regions are further sharpened and low-energy backgrounds are suppressed through nonlinear enhancement, ultimately resulting in a clear two-dimensional dispersion energy spectrum, thus completing the energy focusing process.

[0102] For two-dimensional dispersion energy spectra, computer equipment can search for the position of the maximum energy value (i.e. the position with the highest fit) on the phase velocity profile corresponding to each frequency point in the order from low frequency to high frequency, extract the phase velocity value corresponding to the maximum energy value, and connect the coordinate points of the maximum energy value and phase velocity value extracted from all frequency points in sequence to form a continuous dispersion curve, which is used for subsequent S-wave velocity inversion.

[0103] In this embodiment, high signal-to-noise ratio dispersion curves are automatically extracted from the fitting results, and weighted superposition makes full use of the redundant information of multiple station pairs to improve the stability of the inversion results; energy enhancement processing makes the dispersion curves more visually intuitive and facilitates subsequent analysis; and the automatic connection algorithm based on the maximum energy value avoids the subjectivity and inefficiency of relying on human experience for curve tracking in traditional methods, realizing full automation of micro-motion exploration data processing.

[0104] In one embodiment, a full-band ESPAC micro-motion dispersion imaging method based on a zero-order Struff function is provided. It requires no manual setting of the initial scanning frequency or manual intervention in segmentation points, enabling fully automatic and highly robust processing under low signal-to-noise ratio data, achieving fully automated dispersion imaging processing. It is applicable to any one or more combinations of sparse linear arrays, sparse triangular arrays, small-aperture arrays, or nested arrays. It is suitable for underground structure detection under low signal-to-noise ratio micro-motion data conditions, with an effective detection depth reaching 3 to 5 times the array radius. It can be used in any one or more application scenarios in geothermal resource exploration, hydropower engineering investigation, deep geological surveys, or site seismic safety assessment.

[0105] This application provides a full-band ESPAC micro-motion dispersion imaging method (ST-ESPAC) based on a zero-order Struff function. By calculating the average cross-correlation spectrum of the station, it can stably acquire the spatial correlation characteristics of surface waves in micro-motion signals, improving the signal's anti-interference capability. By constructing a complex analytic cross-correlation spectrum through Hilbert transform of the average cross-correlation spectrum, the real-valued signal is extended into a complex domain signal, preserving the complete amplitude and phase information of the signal. By constructing a unified composite kernel function composed of a zero-order Bessel function of the first kind and a zero-order Struff function, it can achieve full-band ESPAC micro-motion dispersion imaging. Within the segment, it simultaneously considers the deep detection capability in the low-frequency band and the artifact suppression capability in the high-frequency band; it adopts a unified composite kernel function for uniform fitting across the entire frequency band, without the need for segmentation or identification of zero-crossing frequencies, avoiding splicing errors, zero-crossing identification errors, and manual intervention problems caused by segmented fitting, thus improving fitting stability, automation, and processing efficiency; based on the energy residuals of the fitted data from all stations, it generates a dispersion energy spectrum and extracts dispersion curves, which can effectively suppress random noise and enhance the true dispersion energy, ultimately obtaining a continuous dispersion curve with a high signal-to-noise ratio, improving the accuracy of dispersion imaging and the reliability of stratigraphic inversion.

[0106] The effects of four different methods—ESPAC, M-ESPAC, FM-ESPAC, and ST-ESPAC—on micro-motion dispersive imaging are as follows: Figure 5 As shown, Figure 5 In the diagram, (a), (b), (c), and (d) all represent the dispersive energy spectrum. The horizontal axis represents frequency, the vertical axis represents phase velocity, and the color represents energy. Red / yellow indicates high energy, which means high fit; blue indicates low energy.

[0107] in, Figure 5 (a) shows the ESPAC method. Traditional methods typically use only the zero-order Bessel function as the kernel function. This function has oscillatory characteristics and multiple zero-crossing points. When the phase of the measured data crosses these zero-crossing points, it can lead to multiple solutions in the fitting, resulting in these spurious "crossing artifacts" that severely interfere with the identification of the true dispersion curve. Figure 5 As shown in (a), the energy is intact and the detection depth is large in the low frequency band (<5Hz), but there are obvious cross artifacts (oblique high-energy stripes) in the high frequency band (>15Hz).

[0108] Figure 5 (b) The M-ESPAC method introduces a second-type Bessel function (Neumann function) to address the ambiguity of the zero-order Bessel function. However, the second-type Bessel function exhibits singularity (tending towards infinity) at low frequencies (approaching 0), leading to numerical instability and affecting the fitting accuracy in the low-frequency range. Figure 5 As shown in (b), high-frequency artifacts are completely eliminated, but the energy in the low-frequency band (<5Hz) is significantly weakened or shows a return, limiting the detection depth.

[0109] Figure 5 (c) is the FM-ESPAC method, which combines the advantages of the previous two methods, eliminating artifacts while ensuring accuracy at low frequencies. However, it requires manually defining a "splitter point," i.e., deciding at which frequency to start splicing from... Switch to This requires interaction, and ordinary users may make mistakes, increasing the complexity and subjectivity of the operation. For example... Figure 5 As shown in (c), the piecewise fitting takes into account both low and high frequencies, but it relies on splicing point recognition and has poor stability at low signal-to-noise ratios.

[0110] Figure 5 (d) The ST-ESPAC method proposed in this application uses a unified composite kernel function for continuous fitting across the entire frequency band. This eliminates high-frequency artifacts while preserving low-frequency depth information. Furthermore, the dispersion energy spectrum is smooth and continuous across the entire frequency band, requiring no segmentation or identification of splicing points, thus demonstrating the best overall performance.

[0111] It should be understood that although the steps in the flowchart above are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowchart above may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0112] In one embodiment, such as Figure 6 As shown, a full-band ESPAC micro-motion dispersion imaging system based on a zero-order Struff function is provided, including: a cross-correlation spectrum calculation module 610, a transformation module 620, a function construction module 630, a fitting energy calculation module 640, and a dispersion generation module 650, wherein:

[0113] The cross-correlation spectrum calculation module 610 is used to read the original micro-motion signals recorded by the micro-motion array and calculate the average cross-correlation spectrum between station pairs based on the original micro-motion signals.

[0114] Transformation module 620 is used to perform Hilbert transform on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum.

[0115] Function construction module 630 is used to construct a unified composite kernel function based on the zeroth-order Struff function. The unified composite kernel function is composed of a zeroth-order Bessel function of the first kind and a zeroth-order Struff function.

[0116] The fitting energy calculation module 640 is used to perform a unified full-band fitting of the complex analytic cross-correlation spectrum using a unified composite kernel function and to calculate the fitting energy residual; wherein, the fitting process does not require segmentation of the frequency domain and identification of the zero-crossing frequency of the cross-correlation spectrum;

[0117] The dispersion generation module 650 is used to generate a dispersion energy spectrum based on the fitted energy residuals of all station pairs and extract the dispersion curve.

[0118] In one embodiment, the cross-correlation spectrum calculation module 610 is further configured to divide the original micro-motion signals of each station into time window signals of each preset time length; perform Fourier transform on the time window signals of all stations to obtain the frequency domain signals of each station; for each station pair, calculate the self-power spectrum and the cross-power spectrum between any two stations based on the frequency domain signals; and perform statistical averaging based on the self-power spectrum and the cross-power spectrum to obtain the average cross-correlation spectrum.

[0119] In one embodiment, the transformation module 620 is further configured to use the average cross-correlation spectrum as the real part signal, and perform a Hilbert transform on the average cross-correlation spectrum to obtain an imaginary part signal orthogonal to the real part signal; and combine the real part signal and the imaginary part signal to construct a complex analytic cross-correlation spectrum in complex form.

[0120] In one embodiment, the function construction module 630 is further configured to define the dimensionless wavenumber as α = 2πfr / c; where f is the frequency, r is the station spacing, and c is the phase velocity; and to construct a unified composite kernel function as follows: ;in, It is a zero-order Bessel function of the first kind, and serves as the real part of the unified composite kernel function; Let be the zeroth-order Struff function, which serves as the imaginary part of the unified composite kernel function; i is the imaginary unit; taking advantage of the fact that the zeroth-order Struff function approaches zero at the origin, the unified composite kernel function approaches the zeroth-order Bessel function of the first kind in the low-frequency range; taking advantage of the fact that the oscillation pattern of the zeroth-order Struff function approximates the zeroth-order Neumann function of the second kind in the high-frequency range, the unified composite kernel function approaches the zeroth-order Hankel function of the first kind in the high-frequency range.

[0121] In one embodiment, the fitted energy calculation module 640 is further configured to, for each station pair, iterate through the frequency and phase velocity, and calculate the dimensionless wavenumber based on the frequency and phase velocity; and calculate the theoretical composite kernel function based on the dimensionless wavenumber. ; Calculate the complex domain residual modulus between the complex analytic cross-correlation spectrum and the theoretical composite kernel function, and then use the formula The fitted energy residual was calculated; the fitting process adopted a uniform fitting across the entire frequency band, without dividing the frequency band or identifying the zero-crossing frequency of the cross-correlation spectrum.

[0122] In one embodiment, the fitting energy is defined as: The higher the energy, the better the fit, and the maximum energy is 1.

[0123] In one embodiment, the dispersion generation module 650 is further used to weight and superimpose the fitted energy residuals of all station pairs to obtain a superimposed energy spectrum; to perform Gaussian smoothing, normalization and energy focusing on the superimposed energy spectrum in sequence to achieve energy enhancement processing and obtain a two-dimensional dispersion energy spectrum; for each frequency point in the two-dimensional dispersion energy spectrum, the phase velocity corresponding to the maximum energy value at each frequency point is selected and connected to form a continuous dispersion curve.

[0124] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 7As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used for communication with external terminals via a network connection. When executed by the processor, the computer program implements a full-band ESPAC micro-dispersion imaging method based on a zero-order Struff function. The display screen can be a liquid crystal display (LCD) or an electronic ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0125] Those skilled in the art will understand that Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0126] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a full-band ESPAC micro-motion dispersion imaging method based on a zero-order Struff function.

[0127] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of a full-band ESPAC micro-motion dispersion imaging method based on a zero-order Struff function.

[0128] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0129] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0130] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A full-band ESPAC micro-motion dispersion imaging method based on a zero-order Struff function, characterized in that, The method includes: Read the original micro-motion signals recorded by the micro-motion array, and calculate the average cross-correlation spectrum between station pairs based on the original micro-motion signals; Perform a Hilbert transform on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum; A unified composite kernel function based on the zeroth-order Struff function is constructed. The unified composite kernel function is composed of a zeroth-order Bessel function of the first kind and a zeroth-order Struff function. The unified composite kernel function is used to perform a full-band unified fitting of the complex analytic cross-correlation spectrum, and the fitting energy residual is calculated; wherein, the fitting process does not require segmentation of the frequency domain, nor does it require identification of the zero-crossing frequencies of the cross-correlation spectrum; Based on the fitted energy residuals of all station pairs, a dispersive energy spectrum is generated, and the dispersion curve is extracted.

2. The full-band ESPAC micro-motion dispersion imaging method based on the zeroth-order Struff function according to claim 1, characterized in that, Read the original micro-motion signals recorded by the micro-motion array, and calculate the average cross-correlation spectrum between station pairs based on the original micro-motion signals, including: The original micro-motion signals of each station are divided into time window signals of preset time lengths; Perform Fourier transform on the time window signals of all stations to obtain the frequency domain signals of each station; For each station pair, the self-power spectrum and the cross-power spectrum between any two stations are calculated based on the frequency domain signal. The average cross-correlation spectrum is obtained by statistically averaging the self-power spectrum and cross-power spectrum.

3. The full-band ESPAC micro-motion dispersion imaging method based on the zeroth-order Struff function according to claim 1, characterized in that, Perform a Hilbert transform on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum, including: The average cross-correlation spectrum is used as the real part signal, and a Hilbert transform is performed on the average cross-correlation spectrum to obtain the imaginary part signal orthogonal to the real part signal; The real part signal and the imaginary part signal are combined to construct a complex analytic cross-correlation spectrum in complex form.

4. The full-band ESPAC micro-motion dispersion imaging method based on the zeroth-order Struff function according to claim 1, characterized in that, A unified composite kernel function based on the zeroth-order Struff function is constructed. This unified composite kernel function is composed of a zeroth-order Bessel function of the first kind and a zeroth-order Struff function, including: Define the dimensionless wavenumber as α = 2πfr / c; where f is the frequency, r is the station spacing, and c is the phase velocity. Construct a unified composite kernel function as follows ;in, It is a zero-order Bessel function of the first kind, which serves as the real part of the unified composite kernel function; is the zero-order Struff function, which serves as the imaginary part of the unified composite kernel function; i is the imaginary unit; Taking advantage of the fact that the zeroth-order Struff function approaches zero at the origin, the unified composite kernel function approaches the zeroth-order Bessel function of the first kind in the low-frequency range; taking advantage of the fact that the zeroth-order Struff function approximates the zeroth-order Neumann function of the second kind in the high-frequency range, the unified composite kernel function approaches the zeroth-order Hankel function of the first kind in the high-frequency range.

5. The full-band ESPAC micro-motion dispersion imaging method based on the zeroth-order Struff function according to claim 4, characterized in that, The complex analytic cross-correlation spectrum is uniformly fitted across the entire frequency band using the unified composite kernel function, and the fitted energy residual is calculated, including: For each station pair, the frequency and phase velocity are iterated, and the dimensionless wavenumber is calculated based on the frequency and phase velocity. The theoretical composite kernel function is calculated based on the dimensionless wavenumber. ; Calculate the complex domain residual modulus between the complex analytic cross-correlation spectrum and the theoretical composite kernel function, and then use the formula... The fitted energy residual was calculated; The fitting process uses a uniform fitting across the entire frequency band, without dividing the frequency band or identifying the zero-crossing frequency of the cross-correlation spectrum.

6. The full-band ESPAC micro-motion dispersion imaging method based on the zeroth-order Struff function according to claim 5, characterized in that, The fitting energy is defined as: The higher the energy, the better the fit, and the maximum energy is 1.

7. The full-band ESPAC micro-motion dispersion imaging method based on the zeroth-order Struff function according to claim 1, characterized in that, Based on the fitted energy residuals of all station pairs, a dispersive energy spectrum is generated, and dispersion curves are extracted, including: The fitted energy residuals of all station pairs are weighted and superimposed to obtain the superimposed energy spectrum; The superimposed energy spectrum is sequentially subjected to Gaussian smoothing, normalization, and energy focusing to achieve energy enhancement processing, resulting in a two-dimensional dispersive energy spectrum. For each frequency point in the two-dimensional dispersion energy spectrum, the phase velocity corresponding to the maximum energy value at each frequency point is selected and connected to form a continuous dispersion curve.

8. A full-band ESPAC micro-motion dispersion imaging system based on a zero-order Struff function, characterized in that, The system includes: The cross-correlation spectrum calculation module is used to read the original micro-motion signals recorded by the micro-motion array and calculate the average cross-correlation spectrum between station pairs based on the original micro-motion signals. The transformation module is used to perform a Hilbert transform on the average cross-correlation spectrum to construct a complex analytic cross-correlation spectrum. The function construction module is used to construct a unified composite kernel function based on the zeroth-order Struff function. The unified composite kernel function is composed of a zeroth-order Bessel function of the first kind and a zeroth-order Struff function. The fitting energy calculation module is used to perform a unified full-band fitting of the complex analytical cross-correlation spectrum using the unified composite kernel function, and to calculate the fitting energy residual; wherein, the fitting process does not require segmentation of the frequency domain, nor does it require identification of the zero-crossing frequencies of the cross-correlation spectrum; The dispersion generation module is used to generate a dispersion energy spectrum based on the fitted energy residuals of all station pairs and extract the dispersion curve.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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