Micro-motion exploration frequency dispersion curve extraction method, equipment and medium

Abstract

The invention discloses a micro-motion exploration frequency dispersion curve extraction method, device and medium, and relates to the technical field of micro-motion exploration, and the method comprises the following steps: S1, calculating the average cross-correlation spectrum of each station pair according to the recorded data of a plurality of stations in an observation array; s2, aiming at the average cross-correlation spectrum of each station pair, identifying a first intersection point frequency of the average cross-correlation spectrum and a frequency axis; s3, based on the first intersection point frequency, performing piecewise fitting on the average cross-correlation spectrum to extract a phase velocity: for a frequency band not greater than the first intersection point frequency, performing fitting by adopting a zero-order Bessel function J0; and for a frequency band of which the frequency is greater than the frequency of the first intersection point, performing fitting by adopting a first-class zero-order Hankel function H0 (1). In a single method, the contradiction of artifact interference in a high frequency band and insufficient detection depth in a low frequency band in the prior art is overcome at the same time, the accuracy and reliability of frequency dispersion curve extraction under the sparse array condition are improved, and the detection depth of micro-motion exploration is effectively expanded.

Description

Technical Field

[0001] This invention relates to the field of micro-motion exploration technology, and in particular to a method, equipment, and medium for extracting micro-motion exploration dispersion curves based on adaptive piecewise fitting of cross-correlation spectra. Background Technology

[0002] Microseismic exploration, as a passive source geophysical method, has been widely used in urban engineering surveys, shallow geological structure detection, and mineral resource exploration due to its advantages such as convenient observation, no need for artificial seismic sources, and strong anti-interference capabilities. This method is based on surface wave signals excited by natural field sources, extracts Rayleigh wave dispersion curves through array observations, and then inverts the subsurface shear wave velocity structure.

[0003] Spatial autocorrelation (SPAC) is a classic dispersion curve extraction technique in micro-motion exploration. Aki first proposed using the relationship between the autocorrelation function and the zero-order Bessel function of station pair records to estimate phase velocity. Subsequently, Ling et al. proposed the Extended Spatial Autocorrelation (ESPAC) method, which constructs a dispersion spectrum by directly fitting the cross-correlation spectrum of station pairs to the zero-order Bessel function J0. However, in practical applications, especially when the spatial distribution of the observation array is sparse, the ESPAC method is prone to producing so-called "crossing artifacts" in the high-frequency band. This means that the J0 curves of different velocities intersect with the cross-correlation spectrum to form false energy bands, severely interfering with the accurate identification and acquisition of dispersion curves.

[0004] To overcome the aforementioned high-frequency crossover artifact problem, Xi et al. proposed an improved extended spatial autocorrelation (M-ESPAC) method. This method constructs an analytic signal with a cross-correlation spectrum through Hilbert transform and employs a first-order zero Hankel function H0. ( ¹ ) The J0 function was replaced for fitting. This improvement effectively eliminated crossover artifacts in the high-frequency band, significantly improved the imaging quality of the dispersion spectrum, and laid a good foundation for subsequent automated acquisition.

[0005] However, further practical exploration applications have revealed that, when the dispersion curves extracted based on the M-ESPAC method are converted to depth according to half-wavelength theory, the effective detection depth is typically only about twice the array radius. This depth is significantly lower than the detection depth level of 3-5 times the array radius that the traditional ESPAC method can usually achieve. In applications such as geothermal exploration that require detection at greater depths, this limitation of the M-ESPAC method in terms of depth detection capability is particularly prominent.

[0006] In summary, the existing technologies present the following contradictions: the traditional ESPAC method, while possessing good low-frequency response and deep detection potential, is severely affected by high-frequency cross artifacts under sparse array conditions; while the improved M-ESPAC method, although effectively suppressing high-frequency artifacts, loses some low-frequency information, thus limiting its inversion detection depth.

[0007] Therefore, there is an urgent need for a new method that can balance high-frequency imaging quality with low-frequency response capability, thereby extending the effective detection depth while ensuring the clarity of the dispersion spectrum. Summary of the Invention

[0008] The technical problem to be solved by this invention is to resolve the core technical contradiction that existing micro-motion exploration methods cannot simultaneously achieve high-frequency cross-artifact-free imaging and sufficient low-frequency response (i.e., sufficient detection depth) under sparse array conditions.

[0009] In a first aspect, to solve the above-mentioned technical problems, a method for extracting dispersion curves in micro-motion exploration is provided, comprising the following steps: S1. Calculate the average cross-correlation spectrum of each station pair based on the recorded data from multiple stations in the observation array; S2. For the average cross-correlation spectrum of each station pair, identify the first intersection frequency with the frequency axis. ; S3, Based on the frequency of the first intersection point The average cross-correlation spectrum is piecewise fitted to extract the phase velocity: For frequencies not greater than the first intersection point frequency The frequency band is fitted using the zero-order Bessel function J0; For frequencies greater than the frequency of the first intersection point The frequency band uses the first-order zero Hankel function H0. (1) Perform fitting.

[0010] Furthermore, the first intersection frequency in S2 The identification methods include: S21. Smooth the average cross-correlation spectrum; S22. In the smoothed cross-correlation spectrum, determine the frequency range corresponding to the first change in value from positive to negative. ; S23, Based on the frequency range The first intersection frequency is calculated by interpolation based on the corresponding cross-correlation spectrum value and the corresponding cross-correlation spectrum value. ; S4. The piecewise fitting results of all the stations at the same frequency and phase velocity are superimposed and normalized to generate the average dispersion spectrum of the entire observation array.

[0011] Furthermore, the interpolation in S23 is a linear interpolation, which satisfies the formula:

[0012] In the formula, and These are the left and right endpoint frequencies of the first interval in which the cross-correlation spectrum changes from positive to negative; and Frequency and The cross-correlation spectrum value after smoothing.

[0013] Furthermore, in S3, the first-order zero Hankel function H0 is used. (1) Before performing the fitting, the following also includes: The average cross-correlation spectrum is extended into a complex analytic signal using the Hilbert transform.

[0014] Furthermore, S3 specifically includes: For frequencies not greater than The phase velocity is extracted by minimizing the first fitting difference function in the frequency band, where the first fitting difference function is the norm of the difference between the average cross-correlation spectrum and the zero-order Bessel function J0. For frequencies greater than In the frequency band, the phase velocity is extracted by minimizing the second fitting difference function, where the second fitting difference function is the sum of the complex analytic signal and the first kind of zero-order Hankel function H0. (1) The norm of the difference.

[0015] Further, S4 calculates the average dispersion spectrum using the following formula:

[0016] In the formula, The total number of the station pairs; Let be the phase velocity to be searched; This represents the first fitting difference function; This represents the second fit difference function.

[0017] A second aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method.

[0018] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method.

[0019] Compared with the prior art, the embodiments of the present invention have the following beneficial effects: This invention introduces the first intersection frequency of the cross-correlation spectrum. For the adaptive piecewise fitting mechanism of the threshold, a zero-order Bessel function J0 is used for fitting in the low-frequency range to maintain the deep response capability of the traditional ESPAC method, and a first-order zero-order Hankel function H0 is used in the high-frequency range. (1) Fitting is performed to inherit the advantages of the M-ESPAC method in eliminating cross artifacts, thereby overcoming the contradiction between existing technologies having artifact interference in the high-frequency band and insufficient detection depth in the low-frequency band in a single method. This improves the accuracy and reliability of dispersion curve extraction under sparse array conditions and effectively extends the detection depth of micro-motion exploration. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart of the FM-ESPAC method disclosed in this invention; Figure 2 The present invention discloses a cross-correlation spectrum-based method. Piecewise fitting diagram; Figure 3 The present invention discloses a cross-correlation spectrum-based method. Segmented fitting diagram (single station pair) before and after comparison; Figure 4 This is the dispersion diagram of the adaptive piecewise fitting array disclosed in this invention; Figure 5 The following is a dispersion comparison diagram of a Line 2 sparse linear array with 5 channels disclosed in a specific embodiment, wherein: (a) represents the ESPAC dispersion spectrum; (b) represents the M-ESPAC dispersion spectrum; and (c) represents the FM-ESPAC dispersion spectrum. Detailed Implementation

[0022] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] This invention provides a method for extracting micro-motion exploration dispersion curves based on adaptive piecewise fitting of cross-correlation spectrum, called the FM-ESPAC method. Figure 1 The complete processing flow of the FM-ESPAC method of this invention is shown. The flowchart clearly reveals the core idea of ​​this invention to organically integrate two traditional fitting strategies into an automated process, which includes core steps such as data input, cross-correlation spectrum calculation, feature frequency identification, adaptive piecewise fitting, and dispersion spectrum generation. The specific implementation steps of this invention are described in detail below.

[0024] S1. Calculate the average cross-correlation spectrum of each station pair based on the recorded data from multiple stations in the observation array.

[0025] In this scheme, let there be n (n≥2) stations in the observation array T, and let the station pair be denoted as (A, B) (A, B=1,2,…,n and A≠B). The Fourier transforms of stations A and B are SA and SB, respectively. Then the average cross-correlation spectrum of the station pair (A, B) can be expressed as:

[0026] In the formula, , 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 is determined. This step aims to improve the signal-to-noise ratio by averaging the cross-correlation spectrum multiple times.

[0027] S2. For the average cross-correlation spectrum of each station pair, identify the first intersection frequency with the frequency axis. .

[0028] The first intersection frequency in this scheme This is the key threshold for achieving adaptive segmentation. Since the original cross-correlation spectrum may contain noise, step S2 specifically includes: S21, regarding the average cross-correlation spectrum A 5-point moving average method is used for smoothing (the window size can be adjusted according to the actual data noise level) to reduce noise interference.

[0029] S22. Traverse the smoothed cross-correlation spectrum and find the first time its value changes from positive to negative (i.e., ... The frequency range corresponding to ) .

[0030] S23, Based on frequency range The corresponding cross-correlation spectrum values ​​are used to calculate the first intersection frequency through interpolation. .

[0031] In this scheme, the interpolation is linear interpolation, which satisfies the formula:

[0032] In the formula, and These are the left and right endpoint frequencies of the first interval in which the cross-correlation spectrum changes from positive to negative; and Frequency and The smoothed cross-correlation spectrum value can be used to accurately calculate the first intersection frequency through linear interpolation. If the cross-correlation curve does not intersect the frequency axis throughout its entire length, then 90% of the highest frequency is taken as the first intersection frequency. (This situation is quite rare in actual data).

[0033] S3, Based on the frequency of the first intersection point Piecewise fitting of the average cross-correlation spectrum is used to extract the phase velocity: This step is the core of the FM-ESPAC method. First, the average cross-correlation spectrum is analyzed using the Hilbert transform. Perform analytic continuation to construct a complex analytic signal. This prepares for subsequent high-frequency band fitting:

[0034] Then, at the first intersection frequency To define the boundaries, different functions are used for fitting different frequency bands: a) For the low-frequency band, i.e., for frequencies not greater than the first intersection point frequency For the frequency band, the zero-order Bessel function J0 used in the traditional ESPAC method is employed for fitting. Specifically, the phase velocity is extracted by minimizing the first fitting difference function, which is the norm of the difference between the average cross-correlation spectrum and the zero-order Bessel function J0, and satisfies the expression:

[0035] b) For the low-frequency band, for frequencies greater than the first intersection frequency The frequency band uses the first-order zero Hankel function H0 of the M-ESPAC method. (1) The fitting process involves extracting the phase velocity by minimizing the second fitting difference function, which is the sum of the complex analytic signal and the first-order zero Hankel function H0. (1) The norm of the difference satisfies the expression:

[0036] Use analytical signals With the first kind of zeroth order Hankel function H0 (1)Performing complex-domain fitting can effectively avoid high-frequency "crossing artifacts".

[0037] Among them, the first-order zero Hankel function H0 is used. (1) Before fitting, the average cross-correlation spectrum is extended into a complex analytic signal using Hilbert transform.

[0038] like Figure 2 The cross-correlation spectrum shown A schematic diagram of piecewise fitting. The figure shows a typical cross-correlation spectrum curve, and its first intersection with the horizontal axis (frequency axis) is the critical threshold frequency. .exist The low-frequency region on the left indicates that a zero-order Bessel function J0 was used for fitting; in The high-frequency region on the right indicates the use of the first-order zero Hankel function H0. (1) Perform fitting.

[0039] S4. The piecewise fitting results of all stations at the same frequency and phase velocity are superimposed and normalized to generate the average dispersion spectrum of the entire observation array.

[0040] The formula for calculating the average dispersion spectrum is:

[0041] In the formula, The total number of stations; Let be the phase velocity to be searched; Represents the first fit difference function; This represents the second fit difference function.

[0042] This proposal addresses the technical contradiction between ESPAC (high-frequency cross artifacts in sparse arrays) and M-ESPAC (insufficient low-frequency response and low inversion depth) in micro-motion exploration by proposing the FM-ESPAC method. This method uses the frequency of the first intersection of the cross-correlation spectrum and the frequency axis. To achieve adaptive segmentation thresholds, the low-frequency band is fitted with the zeroth-order Bessel function J0 of ESPAC to preserve the low-frequency response, while the high-frequency band is fitted with the first-order zeroth-order Hankel function H0 of M-ESPAC. (1) Fitting eliminates crossover artifacts.

[0043] In a specific example, such as Figure 3 As shown, taking a specific pair of stations as an example, the matching between the piecewise fitting model and the actual cross-correlation spectrum data is compared. It can be observed that by using... J0 and H0 are used as boundaries respectively. (1) By fitting the function, the obtained theoretical model curve can better match the shape of the actual data curve across the entire frequency band, especially the phase change characteristics when crossing zero, which verifies the rationality and necessity of the segmentation strategy.

[0044] Figure 4 An example of a synthesized dispersion spectrum generated using the method of this invention (FM-ESPAC) is shown. In the figure, the horizontal axis represents frequency, the vertical axis represents phase velocity, and energy intensity is represented by color intensity. It can be seen that the dispersion energy clusters are continuous and clear, without any messy cross-artifact interference. This figure is a visual representation of the final output of the method of this invention, demonstrating its effectiveness in extracting high-quality dispersion curves.

[0045] To verify the effectiveness of the present invention, Figure 5 This document provides a comparison map of the dispersion of the sparse array along Line 2 of the 36th Chinese Antarctic Scientific Expedition. Through a real-world exploration case study, the map compares the processing results of this invention (FM-ESPAC) with those of two existing methods (ESPAC and M-ESPAC).

[0046] Figure 5 In (a) ESPAC dispersion spectrum: it can be seen that there are a large number of obliquely crossed false energy bands (i.e., cross artifacts) in the high frequency band, which seriously interfere with the identification of the true dispersion curve.

[0047] Figure 5 In (b) M-ESPAC dispersion spectrum: high-frequency cross artifacts are basically eliminated, and energy clusters are more focused. However, in the low-frequency range (below about 2.5 Hz), the dispersion energy shows an abnormal "rebound", indicating low-frequency response distortion, resulting in a shallower effective detection depth.

[0048] Figure 5 (c) FM-ESPAC dispersion spectrum: This method balances the quality of both high and low frequency bands, effectively suppressing high-frequency artifacts while retaining clear, continuous energy clusters that extend normally towards lower frequencies in the low-frequency band. It reliably extracts complete dispersion curves from low frequencies (approximately 0.7 Hz) to high frequencies, thus supporting the inversion of deeper geological structures. This comparison strongly demonstrates that the FM-ESPAC method can eliminate high-frequency crossover artifacts in the dispersion spectrum through the core logic of M-ESPAC while preserving low-frequency information from ESPAC to meet the inversion depth requirements. The FM-ESPAC method shows significant advantages in situations with sparse arrays and insufficient spatial sampling.

[0049] The present invention also protects an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described method.

[0050] The present invention also protects a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the above-described method.

[0051] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for extracting dispersion curves in micro-motion exploration, characterized in that, Includes the following steps: S1. Calculate the average cross-correlation spectrum of each station pair based on the recorded data from multiple stations in the observation array; S2. For the average cross-correlation spectrum of each station pair, identify the first intersection frequency with the frequency axis. ; S3, Based on the frequency of the first intersection point The average cross-correlation spectrum is piecewise fitted to extract the phase velocity: For frequencies not greater than the first intersection point frequency The frequency band is fitted using the zero-order Bessel function J0; For frequencies greater than the frequency of the first intersection point The frequency band uses the first-order zero Hankel function H0. (1) Perform fitting; S4. The piecewise fitting results of all the stations at the same frequency and phase velocity are superimposed and normalized to generate the average dispersion spectrum of the entire observation array.

2. The method for extracting dispersion curves in micro-motion exploration according to claim 1, characterized in that, The first intersection frequency in S2 The identification methods include: S21. Smooth the average cross-correlation spectrum; S22. In the smoothed cross-correlation spectrum, determine the frequency range corresponding to the first change in value from positive to negative. ; S23, Based on the frequency range The first intersection frequency is calculated by interpolation based on the corresponding cross-correlation spectrum value and the corresponding cross-correlation spectrum value. .

3. The method for extracting dispersion curves in micro-motion exploration according to claim 2, characterized in that, The interpolation in S23 is a linear interpolation, which satisfies the formula: In the formula, and These are the left and right endpoint frequencies of the first interval in which the cross-correlation spectrum changes from positive to negative; and Frequency and The cross-correlation spectrum value after smoothing.

4. The method for extracting dispersion curves in micro-motion exploration according to claim 1, characterized in that, In S3, the first-order zero Hankel function H0 is used. (1) Before performing the fitting, the following also includes: The average cross-correlation spectrum is extended into a complex analytic signal using the Hilbert transform.

5. The method for extracting dispersion curves in micro-motion exploration according to claim 4, characterized in that, S3 specifically includes: For frequencies not greater than The phase velocity is extracted by minimizing the first fitting difference function in the frequency band, where the first fitting difference function is the norm of the difference between the average cross-correlation spectrum and the zero-order Bessel function J0. For frequencies greater than In the frequency band, the phase velocity is extracted by minimizing the second fitting difference function, where the second fitting difference function is the sum of the complex analytic signal and the first kind of zero-order Hankel function H0. (1) The norm of the difference.

6. The method for extracting dispersion curves in micro-motion exploration according to claim 5, characterized in that, S4 calculates the average dispersion spectrum using the following formula: In the formula, The total number of the station pairs; Let be the phase velocity to be searched; This represents the first fitting difference function; This represents the second fitting difference function.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-6.

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