A method for evaluating the degree of waveform dispersion and a related device

Abstract

The present invention relates to the field of seismic wave exploration technology, and specifically to a method for evaluating the degree of waveform dispersion and a related device. The present invention constructs the first amplitude expected value and the square expected value of the first amplitude absolute value of each frequency, as well as the second amplitude expected value and the second expected value product corresponding to each frequency pair according to the amplitude on the frequency spectrum information of each segmented waveform; constructs the third amplitude expected value and the third expected value product corresponding to each frequency pair; and finally evaluates the degree of dispersion of the original waveform according to the above-mentioned expected values. The present invention only needs to know the amplitude of each frequency to calculate the expected value information required for evaluating the degree of waveform dispersion, without the need to collect additional data, thereby improving the efficiency of evaluating the degree of waveform dispersion. In addition, the present invention quantitatively calculates the data required for evaluating the degree of waveform dispersion based on the amplitude, thereby realizing the quantitative evaluation of the degree of waveform dispersion, thereby improving the accuracy of the evaluation of the degree of waveform dispersion.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic wave exploration, and particularly to a method for evaluating the degree of waveform dispersion and related devices. Background Art

[0002] Collecting seismic waves generated by the vibration of geological structures and analyzing the seismic waves can be used for geological structure imaging, and the better the quality of the dispersion curve, the more favorable the corresponding seismic waveform is for geological structure imaging. According to the theory of background noise tomography, the more dispersed the seismic noise waveform used, the better the quality of the dispersion curve that can be extracted from the seismic noise waveform.

[0003] The prior art estimates the degree of waveform dispersion by analyzing the propagation energy in all propagation directions of the waveform. This method requires a large amount of data, thereby increasing the time required to evaluate the degree of waveform dispersion.

[0004] In summary, the efficiency of the prior art in evaluating the degree of waveform dispersion is low.

[0005] Therefore, the prior art still needs to be improved. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a method for evaluating the degree of waveform dispersion and related devices, which solves the problem of low efficiency in evaluating the degree of waveform dispersion in the prior art.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] In a first aspect, the present invention provides a method for evaluating the degree of waveform dispersion, which includes:

[0009] Determining the respective spectral information corresponding to each segmented waveform of the original waveform, and the frequency information covered by each of the spectral information is the same;

[0010] Constructing a first amplitude expectation value and a first squared amplitude absolute value expectation value corresponding to each frequency based on the amplitudes corresponding to each frequency of each spectral information;

[0011] Constructing a second amplitude expectation value and a product of second expectation values corresponding to each frequency pair based on the amplitude pairs corresponding to each frequency of each spectral information, the frequency pair includes two frequencies, the second amplitude expectation value is determined by the amplitude corresponding to one of the frequencies in the frequency pair and the amplitude corresponding to the other frequency, and the product of the second expectation values is determined by the absolute value of the amplitude corresponding to one of the frequencies in the frequency pair and the absolute value of the amplitude corresponding to the other frequency;

[0012] Construct the third amplitude expectation value and the third expectation value product corresponding to each frequency pair based on the amplitude and the complex conjugate amplitude corresponding to each frequency of each of the spectral information, where the third amplitude expectation value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the complex conjugate amplitude corresponding to the other frequency, and the third expectation value product is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the complex conjugate amplitude corresponding to the other frequency;

[0013] Evaluate the dispersion degree of the original waveform based on the first amplitude expectation value, the first squared absolute value of the amplitude expectation value, the second amplitude expectation value, the second expectation value product, the third amplitude expectation value, and the third expectation value product.

[0014] In one implementation, determining the respective spectral information corresponding to the respective segmented waveforms of the original waveform, where the frequency information covered by each of the spectral information is the same, includes:

[0015] Segment the original waveform at equal time intervals to obtain the equally spaced segmented waveforms in each of the segmented waveforms;

[0016] Apply Fourier transform to each of the equally spaced segmented waveforms to obtain each spectrogram in each of the spectral information of each of the equally spaced segmented waveforms, where the frequency sampling and the frequency length in the frequency information of each of the spectrograms are the same.

[0017] In one implementation, evaluating the dispersion degree of the original waveform based on the first amplitude expectation value, the first squared absolute value of the amplitude expectation value, the second amplitude expectation value, the second expectation value product, the third amplitude expectation value, and the third expectation value product includes:

[0018] Divide the squared absolute value of the first amplitude expectation value by the first squared absolute value of the amplitude expectation value to obtain a first index value;

[0019] Divide the squared absolute value of the second amplitude expectation value by the second expectation value product to obtain a second index value;

[0020] Divide the squared absolute value of the third amplitude expectation value by the third expectation value product to obtain a third index value;

[0021] Evaluate the dispersion degree of the original waveform based on the first index value, the second index value, and the third index value.

[0022] In one implementation, evaluating the dispersion degree of the original waveform based on the first index value, the second index value, and the third index value includes:

[0023] Determine a first root mean square function formed by each of the first index values;

[0024] Determine a second root mean square function formed by each of the second index values;

[0025] Determine a third root mean square function formed by each of the third index values;

[0026] Evaluate the dispersion degree of the original waveform based on the first root mean square function, the second root mean square function, and the third root mean square function.

[0027] In one implementation, the determining of the first root mean square function formed by each of the first index values includes:

[0028] Determine a first index mean value formed by all of the first index values;

[0029] Determine the absolute value of the difference between each of the first index values and a set standard value, denoted as the absolute value of the difference;

[0030] Determine an adjacent index mean value formed by the absolute values of the differences between the adjacent index values of each of the first index values and the set standard value, where the frequencies corresponding to the adjacent index values are adjacent;

[0031] Divide the mean value of the absolute values of the differences between the adjacent indices corresponding to each of the first index values and the set standard value by the mean value of the absolute values of the differences between all the first indices and the set standard value to obtain each weight;

[0032] Obtain the first root mean square function based on each weight of each of the first index values, the absolute value of the difference corresponding to each of the first index values, and the total number of indices formed by each of the first index values.

[0033] In one implementation, the determining of the second root mean square function formed by each of the second index values includes:

[0034] Determine a second index mean value formed by all of the second index values;

[0035] Determine an adjacent index mean value formed by the adjacent index values of each of the second index values, where the frequencies corresponding to the adjacent index values are adjacent;

[0036] Divide the adjacent index mean value corresponding to each of the second index values by the second index mean value to obtain each weight of each of the second index values;

[0037] Determine the absolute value of the difference between each of the second index values and a set standard value, denoted as the absolute value of the difference;

[0038] A second root mean square function is obtained based on the absolute values of the differences corresponding to the respective second index values, the respective weights of the respective second index values, and the square value of the total number of indices constituted by the respective second index values.

[0039] In one implementation, the second amplitude expectation value is the expectation value constituted by the product of the amplitudes corresponding to one of the frequencies of the frequency pair and the amplitude corresponding to the other frequency; the second expectation value product is the product constituted by the expectation value of the square of the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the expectation value of the square of the absolute value of the amplitude corresponding to the other frequency; the third amplitude expectation value is the expectation value constituted by the product of the amplitude corresponding to one of the frequencies of the frequency pair and the complex conjugate amplitude corresponding to the other frequency; the third expectation value product is the product constituted by the expectation value of the square of the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the expectation value of the square of the absolute value of the complex conjugate amplitude corresponding to the other frequency.

[0040] In a second aspect, an embodiment of the present invention further provides an evaluation device for the degree of waveform dispersion, wherein the device includes the following components:

[0041] A spectrum analysis module, configured to determine the respective spectrum information corresponding to the respective segmented waveforms of the original waveform, and the frequency information covered by the respective spectrum information is the same;

[0042] A first expectation value calculation module, configured to construct a first amplitude expectation value and a first expectation value of the square of the absolute value of the amplitude corresponding to each frequency based on the amplitudes corresponding to each frequency of each spectrum information;

[0043] A second expectation value calculation module, configured to construct a second amplitude expectation value and a second expectation value product corresponding to each frequency pair based on the amplitude pairs corresponding to each frequency pair of each spectrum information, the frequency pair includes two frequencies, the second amplitude expectation value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the amplitude corresponding to the other frequency, and the second expectation value product is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the amplitude corresponding to the other frequency;

[0044] A third expectation value calculation module, configured to construct a third amplitude expectation value and a third expectation value product corresponding to each frequency pair based on the amplitudes and the complex conjugate amplitudes of the amplitudes corresponding to each frequency pair of each spectrum information, the third amplitude expectation value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the complex conjugate amplitude corresponding to the other frequency, and the third expectation value product is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the complex conjugate amplitude corresponding to the other frequency;

[0045] A dispersion evaluation module, configured to evaluate the dispersion degree of the original waveform according to the first amplitude expectation value, the first squared absolute value of amplitude expectation value, the second amplitude expectation value, the second product of expectation values, the third amplitude expectation value, and the third product of expectation values.

[0046] In a third aspect, an embodiment of the present invention further provides a terminal device. The terminal device includes a memory, a processor, and an evaluation program for waveform dispersion degree stored in the memory and executable on the processor. When the processor executes the evaluation program for waveform dispersion degree, the steps of the above-described method for evaluating waveform dispersion degree are implemented.

[0047] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium. An evaluation program for waveform dispersion degree is stored on the computer-readable storage medium. When the evaluation program for waveform dispersion degree is executed by a processor, the steps of the above-described method for evaluating waveform dispersion degree are implemented.

[0048] Beneficial effects: The present invention first divides the original waveform to be evaluated into individual segmented waveforms and calculates the spectral information of each segmented waveform. Then, according to the amplitudes corresponding to each frequency on each spectrum, the first amplitude expectation value and the first squared absolute value of amplitude expectation value for each frequency are constructed, and according to the amplitude pairs corresponding to each frequency on each spectrum, the second amplitude expectation value and the second product of expectation values corresponding to each frequency pair are constructed; at the same time, according to the amplitudes and the complex conjugate amplitudes of the amplitudes corresponding to each frequency pair on each spectrum, the third amplitude expectation value and the third product of expectation values corresponding to each frequency pair are constructed; finally, the dispersion degree of the original waveform is evaluated according to the first amplitude expectation value, the first squared absolute value of amplitude expectation value, the second amplitude expectation value, the second product of expectation values, the third amplitude expectation value, and the third product of expectation values. From the above analysis, it can be seen that the present invention only needs to know the amplitudes of each frequency to calculate the expectation value information required for evaluating the waveform dispersion degree, without the need to collect additional data, thereby improving the efficiency of evaluating the waveform dispersion degree. In addition, the present invention quantitatively calculates the data required for evaluating the waveform dispersion degree according to the amplitude, thereby realizing the quantitative evaluation of the waveform dispersion degree, and further improving the evaluation accuracy of the waveform dispersion degree. Description of the Drawings

[0049] Figure 1 is the overall flowchart of the present invention;

[0050] Figure 2 is the original waveform diagram whose dispersion degree needs to be evaluated in the embodiment of the present invention;

[0051] Figure 3 is the simulation diagram of the first index value in the embodiment of the present invention;

[0052] Figure 4 It is the simulation diagram of the second index value in the embodiment of the present invention;

[0053] Figure 5 It is the simulation diagram of the third index value in the embodiment of the present invention;

[0054] Figure 6 It is the internal structure principle block diagram of the terminal device provided by the embodiment of the present invention. Specific embodiments

[0055] The technical solutions in the present invention will be clearly and completely described below in conjunction with the embodiments and the accompanying drawings of the specification. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0056] Through research, it is found that collecting seismic waves generated by the vibration of geological structures and analyzing the seismic waves can be used for geological structure imaging. The better the quality of the dispersion curve, the more favorable the corresponding seismic waveform is for geological structure imaging. According to the theory of ambient noise tomography, the more dispersed the seismic noise waveform used, the more likely it is to extract a dispersion curve with good quality from the seismic noise waveform. The prior art estimates the dispersion degree of the waveform by analyzing the propagation energy in all propagation directions of the waveform. This method requires a large amount of data, thus increasing the time required to evaluate the dispersion degree of the waveform.

[0057] To solve the above technical problems, the present invention provides a method and related device for evaluating the degree of waveform dispersion, which solves the problem of low efficiency in evaluating the degree of waveform dispersion in the prior art. Specifically, in implementation, first determine the respective spectral information corresponding to each segmented waveform of the original waveform (the frequency information covered by each spectral information is the same); then, based on the amplitudes corresponding to each frequency of each spectral information, construct the first amplitude expectation value and the first squared amplitude absolute value expectation value corresponding to each frequency; at the same time, based on the amplitude pairs corresponding to each frequency of each spectral information, construct the second amplitude expectation value and the product of the second expectation values corresponding to each frequency pair (the second amplitude expectation value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the amplitude corresponding to the other frequency, and the product of the second expectation values is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the amplitude corresponding to the other frequency), and based on the amplitudes corresponding to each frequency of each spectral information and the complex conjugate amplitudes of the amplitudes, construct the third amplitude expectation value and the product of the third expectation values corresponding to each frequency pair (the third amplitude expectation value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the complex conjugate amplitude corresponding to the other frequency, and the product of the third expectation values is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the complex conjugate amplitude corresponding to the other frequency); finally, evaluate the degree of dispersion of the original waveform based on the first amplitude expectation value, the first squared amplitude absolute value expectation value, the second amplitude expectation value, the product of the second expectation values, the third amplitude expectation value, and the product of the third expectation values.

[0058] For example, a 30-second-long original waveform is collected. The original waveform is equally divided into three segmented waveforms w1, w2, and w3, and the lengths of w1, w2, and w3 are all 10 seconds. Fourier transforms are respectively performed on w1, w2, and w3 to obtain spectrograms P1, P2, and P3 (the abscissa of the spectrogram is frequency, the ordinate is the waveform amplitude, and the spectrogram establishes the corresponding relationship between frequency and amplitude). The frequencies of P1, P2, and P3 are the same (for example, the frequencies are all f1HZ, f2HZ, and f3HZ). The amplitudes corresponding to f1HZ, f2HZ, and f3HZ on P1 are A11, A12, and A13 respectively; the amplitudes corresponding to f1HZ, f2HZ, and f3HZ on P2 are A21, A22, and A23 respectively; the amplitudes corresponding to f1HZ, f2HZ, and f3HZ on P3 are A31, A32, and A33 respectively.

[0059] The first amplitude expectation value corresponding to the frequency f1HZ is The first amplitude expectation value corresponding to the frequency f2HZ is The first amplitude expectation value corresponding to the frequency f3HZ is

[0060] The first squared amplitude absolute value expectation value corresponding to the frequency f1HZ is The expected value of the square of the absolute value of the first amplitude corresponding to the frequency f2 HZ is The expected value of the square of the absolute value of the first amplitude corresponding to the frequency f3 HZ is

[0061] f1 HZ and f2 HZ form a frequency pair, f1 HZ and f3 HZ form a frequency pair, and f2 HZ and f3 HZ form a frequency pair. The expected value of the second amplitude corresponding to the frequency pair of f1 HZ and f2 HZ is The expected value of the second amplitude corresponding to the frequency pair of f1 HZ and f3 HZ is The expected value of the second amplitude corresponding to the frequency pair of f2 HZ and f3 HZ is

[0062] The product of the second expected values corresponding to the frequency pair of f1 HZ and f2 HZ is as follows:

[0063]

[0064] The product of the second expected values corresponding to the frequency pair of f1 HZ and f3 HZ is as follows:

[0065]

[0066] The product of the second expected values corresponding to the frequency pair of f2 HZ and f3 HZ is as follows:

[0067]

[0068] The complex conjugates of the amplitudes A11, A21, and A31 corresponding to f1 HZ are A * 11, A * 21, A * 31; the complex conjugates of the amplitudes A12, A22, and A32 corresponding to f2 HZ are A * 12, A * 22, A * 32; the complex conjugates of the amplitudes A13, A23, and A33 corresponding to f3 HZ are A * 13, A * 23, A * 33.

[0069] The expected value of the third amplitude corresponding to the frequency pair of f1 HZ and f2 HZ is as follows:

[0070] and

[0071] The expected value of the third amplitude corresponding to the frequency pair of f1 HZ and f3 HZ is as follows:

[0072] and

[0073] The third amplitude expectation values corresponding to the frequency pairs f2HZ and f3HZ are as follows:

[0074] and

[0075] The product of the third expectation values corresponding to the frequency pair f1HZ and f2HZ is as follows:

[0076] and

[0077] The product of the third expectation values corresponding to the frequency pair f1HZ and f3HZ is as follows:

[0078] and

[0079] The product of the third expectation values corresponding to the frequency pair f2HZ and f3HZ is as follows:

[0080] and

[0081] Using all the first amplitude expectation values, the absolute value square expectation values of the first amplitude, the second amplitude expectation values, the second expectation value products, the third amplitude expectation values, and the third expectation value products calculated above, the dispersion degree of the 30-second original waveform can be evaluated.

[0082] Exemplary method

[0083] The method for evaluating the waveform dispersion degree in this embodiment can be applied to a terminal device, and the terminal device can be a terminal product with waveform analysis function, such as a computer, etc. In this embodiment, as Figure 1 shown in, the method for evaluating the waveform dispersion degree specifically includes the following steps:

[0084] S100, determine the respective spectrum information corresponding to each segmented waveform of the original waveform, and the frequency information covered by each of the spectrum information is the same.

[0085] The original waveform is the waveform whose dispersion degree needs to be evaluated. In one embodiment, the specific process of step S100 is as follows: perform equal-time-interval segmentation on the original waveform to obtain each equally spaced segmented waveform in each segmented waveform; apply Fourier transform to each of the equally spaced segmented waveforms to obtain each spectrum diagram in each of the spectrum information of each of the equally spaced segmented waveforms, and the frequency sampling and frequency length in the frequency information of each of the spectrum diagrams are the same.

[0086] In one embodiment, the original waveform is a seismic waveform recorded by a single station (geophone).

[0087] In the time domain, the time t and amplitude ψ(r, t) of the segmented waveform satisfy the following relationship:

[0088]

[0089] a n is a complex modal amplitude independent of time, u (n) (r) is the eigenfunction of the normal mode, r is the position vector, ω n is the angular frequency corresponding to the nth normal mode, t is the time,

[0090] Performing a Fourier transform on Equation (1) gives:

[0091]

[0092] In Equation (2), it is the result obtained by omitting the position vector r during the Fourier transform of Equation (1).

[0093] denotes the Fourier transform, rect[·] is the rectangular window function, T is the length of the window, and ω is the angular frequency. When T is long enough, the sinc[·] function approximates the Kronecker delta function. At this time, for any ω n and its adjacent frequency ω p , the spectrogram of the corresponding segmented waveform is as follows:

[0094]

[0095] In another embodiment, when the length T of the window is not long enough, the sinc function may not approximate the Kronecker delta function well, and due to spectral leakage, the spectrum φ(ω p ) of the target signal will be inaccurately estimated, resulting in φ(ω p ) not being well used for the analysis of the dispersion degree. Multitaper spectral analysis is a method that can well overcome this spectral leakage. Compared with the single-taper spectral estimation generated by using the rectangular window function, multitaper spectral analysis uses multiple orthogonal window functions, and the required multitaper spectrum is finally constructed by the weighted average of the periodograms of multiple orthogonal window functions, thus reducing the bias caused by spectral leakage. This embodiment uses a multi-sine-taper spectral analysis method, and the number of orthogonal windows used in this method can be unrestricted by the signal bandwidth, thus providing better flexibility and adaptability for the data. The multi-sine-taper spectrum can be expressed by the following formula:

[0096]

[0097] Among them, K is the number of orthogonal windows used, N is the length of the waveform data record, and ψ(t n ) is the waveform record at time t for which the multi-window spectrum is to be calculated, and v n is the sine window function: k (n)

[0098]

[0099] S200. Based on the amplitude φ(ω p ) corresponding to each frequency of each of the spectrum information, construct the first amplitude expectation value E[φ(ω p )] and the first squared absolute value of the amplitude expectation value E[|φ(ω p )| 2 corresponding to each frequency.

[0100] E[φ(ω p )] = E[a p u (p) T

[0101] S300. Based on the amplitude pairs corresponding to each frequency pair of each of the spectrum information, construct the second amplitude expectation value E[φ(ω p )φ(ω q )] and the second expectation value product E[|φ(ω p )| 2 E[|φ(ω q )| 2 . The frequency pair includes two frequencies. The second amplitude expectation value is determined by the amplitude corresponding to one of the frequencies in the frequency pair and the amplitude corresponding to the other frequency. The second expectation value product is determined by the absolute value of the amplitude corresponding to one of the frequencies in the frequency pair and the absolute value of the amplitude corresponding to the other frequency.

[0102] In E[φ(ω p )φ(ω q )], φ(ω p ) is the amplitude corresponding to frequency ω p in the spectrogram, and φ(ω q ) is the amplitude corresponding to frequency ω q in the spectrogram.

[0103] In E[|φ(ω p )| 2 E[|φ(ω q )| 2 , |φ(ω p )| 2 is the absolute value of the amplitude φ(ω pThe square of the absolute value of (), since the amplitude has positive and negative values, the absolute value of the amplitude and the amplitude are not necessarily the same.

[0104] S400, construct the third amplitude expectation value E[φ(ω p )φ * (ω q )] and the product of the third expectation values E[|φ(ω p )| 2 E[|φ * (ω q )| 2 according to the amplitudes corresponding to each frequency of each of the said spectral information and the complex conjugate amplitudes of the amplitudes. The third amplitude expectation value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the complex conjugate amplitude corresponding to the other frequency. The product of the third expectation values is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the complex conjugate amplitude corresponding to the other frequency.

[0105] E[φ(ω p )φ * (ω q )] where φ * (ω q ) is the complex conjugate of φ(ω p )

[0106] S500, evaluate the dispersion degree of the original waveform according to the first amplitude expectation value, the first square of the absolute value of the amplitude expectation value, the second amplitude expectation value, the product of the second expectation values, the third amplitude expectation value, and the product of the third expectation values.

[0107] In one embodiment, step S500 includes steps S501 to S5015 as follows:

[0108] S501, divide the square of the absolute value |E[φ(ω p )]| p )] of the first amplitude expectation value E[φ(ω 2 by the first square of the absolute value of the amplitude expectation value E[|φω p )| 2 to obtain the first index value A(ω p )

[0109]

[0110] A(ω p ) is the first index value corresponding to the frequency ω p

[0111] S502, the second amplitude expectation value E[φ(ωp ) φ(ω q )] the absolute value of |E[φ(ω p ) φ(ω q )]| 2 Square it and divide by the product of the second expected values E[|φ(ω p )| 2 E[|φ(ω q )| 2 to obtain the second index value B(ω p , ω q )

[0112]

[0113] B(ω p , ω q ) is the second index value B corresponding to the frequency pair (ω p , ω q ), and E[φ(ω p ) φ(ω q )] is the expected value of the product of the amplitudes corresponding to the frequency ω p and ω q

[0114] For example, an original waveform is divided into two segmented waveforms, and each segmented waveform contains frequency pairs (f1, f2) and (f3, f4).

[0115]

[0116]

[0117] S503. Square the absolute value of the third amplitude expected value |E[φ(ω p ) φ * (ω q )]|, i.e., |E[φ(ω p ) φ * (ω q )]| 2 and divide it by the product of the third expected values E[|φ(ω p )| 2 E[|φ * (ω q )| 2 to obtain the third index value C(ω p , ω q )

[0118]

[0119] φ * (ω q ) is the frequency ω q ​The complex conjugate of the amplitude φ(ω q ).

[0120] Steps S501, S502, and S503 calculate A(ω p ), B(ω p , ω q ), and C(ω p , ω q ). The amplitudes corresponding to the frequencies on each segmented waveform of an original waveform constitute A(ω p ), B(ω p , ω q ), and C(ω p , ω q ). Based on these three indicators of A(ω p ), B(ω p , ω q ), and C(ω p , ω q ), subsequent evaluation can be carried out on whether the original waveform meets the dispersion condition. And using A(ω p ), B(ω p , ω q ), and C(ω p , ω q ) to evaluate whether the original waveform meets the dispersion condition is based on the following reasons:

[0121] For a fully dispersed wave field, the statistics of the modal amplitude (i.e., the amplitude of the waveform in the time domain) need to simultaneously meet the following three conditions:

[0122]

[0123] a p is the amplitude of the waveform at time p, a q is the amplitude of the waveform at time q, is the complex conjugate of a q , F(ω p ) is the power spectral density of the waveform. δ pq is the Kronecker function. When p and q are equal, the value of δ pq is 1; when p and q are not equal, the value of δ pq is 0.

[0124] a p and a q are the a n in formula (1). Therefore, formula (1) can be transformed to obtain a p and a q independent of time. However, since formula (1) involves the eigenfunction u (n) (r), it is difficult to obtain a p and aq , and thus unable to use E[a p = 0, E[a p a q = 0, to determine whether an original waveform satisfies the dispersion condition.

[0125] Therefore, it is necessary to convert the original waveform in the time domain into the original waveform in the frequency domain to avoid the eigenfunction u (n) (r).

[0126] In the time domain, E[a p = 0, and in the frequency domain, it is E[φ(ω p )] = 0. Representing E[φ(ω p )] with a dimensionless quantity gives

[0127]

[0128] Therefore, the difference between the value of A(ω p ) of a waveform and 0 can be used to characterize the dispersion degree of the waveform.

[0129] Substituting φ(ω p ) = a p u (p) T and φ(ω q ) = a q u (q) T into the covariance gives:

[0130] E[φ(ω p )φ(ω q )] = E[a p a q u (p) u (q) T 2

[0131] Since a waveform that satisfies the dispersion condition can make E[a p a q = 0, a waveform for which E[φ(ω p )φ(ω q )] equals 0 can be determined as a dispersion waveform. Therefore, calculating the value of E[φ(ω p )φ(ω q )] for the waveform to be evaluated can determine the degree of closeness to a dispersion waveform, that is, the dispersion degree of the waveform can be evaluated using the value of E[φ(ω p )φ(ω q )] of the waveform to be evaluated. The value of E[φ(ω p [φ(ω q )] can be represented by B(ω p [φ(ω q )]:

[0132]

[0133] Therefore, the difference between the B(ω p , ω q ) value of a waveform and 0 can be used to characterize the dispersion degree of the waveform. If the B(ω p , ω q ) of a waveform is closer to 0, the dispersion degree of the waveform is greater. On the contrary, if the B(ω p , ω q ) of a waveform deviates more from 0, the dispersion degree of the waveform is smaller.

[0134] Applied to covariance, we get:

[0135]

[0136] When p ≠ q, is equivalent to E[φ(ω p )φ * (ω q )] = 0; when p = q, is equivalent to E[φ(ω p )φ * (ω q )] = F(ω p )[u (p) T] 2 . Therefore, the following dimensionless formula C(ω p , ω q ) is defined. For a dispersed waveform, there will be:

[0137]

[0138] When the C(ω p , ω q ) corresponding to any two frequencies of a waveform is closer to 0, it indicates that the dispersion degree of the waveform is greater; on the contrary, when the C(ω p , ω q ) corresponding to any two frequencies of a waveform is less close to 0, it indicates that the dispersion degree of the waveform is smaller.

[0139] Through steps S501, S502, and S503, the first index value A(ω p ), the second index value B(ω p , ω q ), and the third index value C(ω p , ω q) By traversing all possible frequencies and calculating the above three index values corresponding to each frequency for comprehensive analysis, the dispersion degree of the waveform can be accurately and quantitatively evaluated. Subsequently, the subsequent S504 to S5015 are precisely the comprehensive analysis of the above three index values for each frequency.

[0140] In S504, determine the mean value of the first index mean[A] composed of all the first index values.

[0141] mean[A] is the average value of A(ω corresponding to multiple frequencies on each waveform segmented from the original waveform. p ) For example, if there are three A(ω corresponding to three frequencies. p ) Calculate the mean value of these three A(ω. p ) which is mean[A].

[0142] In S505, determine the absolute value of the difference between each of the first index values and a set standard value, denoted as the absolute value of the difference a. m .

[0143]

[0144] For example, if the first index value corresponding to the waveform frequency m whose dispersion degree needs to be evaluated is and its corresponding standard value is The standard value is the first index value corresponding to a standard dispersion waveform.

[0145] In S506, determine the mean value of the absolute values of the differences between the adjacent index values of each of the first index values and the set standard value, which is the adjacent index mean. The frequencies corresponding to the adjacent index values are adjacent.

[0146] a m represents the absolute value of the difference between the first index value corresponding to the frequency m and the set standard value; the frequencies j - s, j - s + 1,... j + s are the adjacent frequencies of the frequency m, and a j-s , a j-s+1 ,..., a j+s is the absolute value of the difference between each adjacent index value and the set standard value. m

[0147] In S507, divide the mean value of the absolute values of the differences between the adjacent indexes corresponding to each of the first index values and the set standard value by the mean value of the absolute values of the differences between all the first indexes and the set standard value mean[A] to obtain each weight w. j .

[0148]

[0149] S508, according to each weight w j and the absolute value of the difference corresponding to each of the first index values and the total number of indicators M composed of each of the first index values, the first root mean square function PA is obtained.

[0150]

[0151] S509, determine the second index mean value mean[B] composed of all the second index values.

[0152] B(ω p , ω q ) in formula (6) is just the second index value corresponding to a frequency pair (ω p , ω q ). Arrange the second index values corresponding to all the frequency pairs in rows and columns to form the matrix B. Finding the mean value of each element of the matrix B is to find the mean value mean[B] composed of the second index values corresponding to each frequency pair.

[0153] S5010, determine the adjacent index mean value composed of the adjacent index values of each of the second index values The frequency corresponding to the adjacent index value is adjacent.

[0154] S5011, divide the adjacent index mean value corresponding to each of the second index values by the second index mean value to obtain each weight w of each of the second index values jk .

[0155]

[0156] S5012, determine the absolute value of the difference between each of the second index values and a set standard value Denote it as the absolute value of the difference.

[0157] S5013, according to the absolute value of the difference corresponding to each of the second index values, each weight of each of the second index values, and the square value of the total number of indicators M composed of each of the second index values, obtain the second root mean square function PB.

[0158]

[0159] The element in the j-th row and k-th column of the matrix B is the true second index value of the waveform whose diffusion degree is to be evaluated, is the second index value as the standard corresponding to .

[0160] S5014. Determine the third root mean square function PC formed by each of the said third index values.

[0161] The third root mean square function PC can be obtained by simply replacing the second index value in the PB expression with the third index value.

[0162] S5015. Evaluate the dispersion degree of the original waveform based on the first root mean square function PA, the second root mean square function PB, and the third root mean square function PC.

[0163] When PA, PB, and PC are all less than 0.05, it is determined that the waveform to be evaluated is completely dispersed; when PA, PB, and PC are all less than 0.2, it is determined that the waveform to be evaluated is relatively dispersed. For different problems, these thresholds of dispersion degree can be adjusted.

[0164] The following takes a seismic waveform in the seismic data recorded by a seismic instrument that needs to evaluate the dispersion degree as an example (as Figure 2 shown, the waveform length is 30 s, the sampling rate is 500 Hz, Figure 2 for the waveform after normalization), and illustrates the detailed process of evaluating the dispersion degree of the waveform of the present invention:

[0165] Step 1: Divide this segment of the waveform into 30 non - overlapping sub - waveforms each with a length of 1 s.

[0166] Step 2: Use the following formula to apply multi - taper spectral analysis to each sub - waveform to obtain their spectra. For any sub - waveform, the length N of the waveform data record is 500, and the number K of orthogonal windows used is 1.

[0167]

[0168]

[0169] Step 3: Substitute the spectra of all the obtained sub - waveforms into formulas (8), (9), and (10) to calculate conditions A, B, and C.

[0170] Step 4: Substitute A into formula (11), and substitute B and C into formula (12) respectively to calculate their corresponding indices P A , P B and P C . Among them, the scale s of the multi - scale root mean square function is 13.

[0171] Step 5: Obtain as Figure 3 ( Figure 3 where the abscissa is the frequency and the ordinate is the first index value A corresponding to each frequency, Figure 3 the P in AThe image corresponding to the first index value A (equal to 0.053), as shown in Figure 4 ( Figure 4 P in B The image corresponding to the second index value B (equal to 0.047), as shown in Figure 5 ( Figure 5 P in C The image corresponding to the third index value C (equal to 0.047).

[0172] In summary, the present invention first divides the original waveform to be evaluated into each segmented waveform and calculates the spectral information of each segmented waveform. Then, according to the amplitudes corresponding to each frequency on each spectrum, the first amplitude expectation value and the first squared absolute value of amplitude expectation value of each frequency are constructed, and according to the amplitude pairs corresponding to each frequency on each spectrum, the second amplitude expectation value and the product of the second expectation values corresponding to each frequency pair are constructed; at the same time, according to the amplitudes and the complex conjugate amplitudes of the amplitudes corresponding to each frequency pair on each spectrum, the third amplitude expectation value and the product of the third expectation values corresponding to each frequency pair are constructed; finally, based on the first amplitude expectation value, the first squared absolute value of amplitude expectation value, the second amplitude expectation value, the product of the second expectation values, the third amplitude expectation value, and the product of the third expectation values, the dispersion degree of the original waveform is evaluated. From the above analysis, it can be seen that the present invention only needs to know the amplitudes of each frequency to calculate the expectation value information required for evaluating the waveform dispersion degree, without the need to collect additional data, thereby improving the efficiency of evaluating the waveform dispersion degree. In addition, the present invention quantitatively calculates the data required for evaluating the waveform dispersion degree according to the amplitude, thereby realizing the quantitative evaluation of the waveform dispersion degree, and further improving the evaluation accuracy of the waveform dispersion degree.

[0173] The present invention does not need to calculate the eigenfunction of the earth model, and the most complex calculation involved is to obtain the spectrum of the signal. The final technical effect is to present the images of three conditions A, B, and C describing whether the seismic waveform is dispersed, and the indexes marked with the dispersion degree corresponding to these three conditions. Therefore, the present invention is an efficient and quantitative method.

[0174] Exemplary device

[0175] This embodiment also provides an apparatus for evaluating the dispersion degree of a waveform, and the apparatus includes the following components:

[0176] A spectrum analysis module, configured to determine the spectral information corresponding to each segmented waveform of the original waveform, and the frequency information covered by each of the spectral information is the same;

[0177] The first expected value calculation module is used to construct the first amplitude expected value and the first squared absolute value of amplitude expected value corresponding to each frequency according to the amplitude corresponding to each frequency of each of the spectrum information.

[0178] The second expected value calculation module is used to construct the second amplitude expected value and the second product of expected values corresponding to each frequency pair according to the amplitude pairs corresponding to each frequency pair of each of the spectrum information. The frequency pair includes two frequencies. The second amplitude expected value is determined by the amplitude corresponding to one of the frequencies in the frequency pair and the amplitude corresponding to the other frequency. The second product of expected values is determined by the absolute value of the amplitude corresponding to one of the frequencies in the frequency pair and the absolute value of the amplitude corresponding to the other frequency.

[0179] The third expected value calculation module is used to construct the third amplitude expected value and the third product of expected values corresponding to each frequency pair according to the amplitude and the complex conjugate amplitude of the amplitude corresponding to each frequency pair of each of the spectrum information. The third amplitude expected value is determined by the amplitude corresponding to one of the frequencies in the frequency pair and the complex conjugate amplitude corresponding to the other frequency. The third product of expected values is determined by the absolute value of the amplitude corresponding to one of the frequencies in the frequency pair and the absolute value of the complex conjugate amplitude corresponding to the other frequency.

[0180] The dispersion evaluation module is used to evaluate the dispersion degree of the original waveform according to the first amplitude expected value, the first squared absolute value of amplitude expected value, the second amplitude expected value, the second product of expected values, the third amplitude expected value, and the third product of expected values.

[0181] Based on the above embodiments, the present invention further provides a terminal device, and its principle block diagram can be as Figure 6 shown. The terminal device includes a processor, a memory, a network interface, a display screen, and a temperature sensor connected through a system bus. Among them, the processor of the terminal device is used to provide computing and control capabilities. The memory of the terminal device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the terminal device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it realizes a method for evaluating the dispersion degree of a waveform. The display screen of the terminal device can be a liquid crystal display screen or an electronic ink display screen. The temperature sensor of the terminal device is pre-set inside the terminal device and is used to detect the operating temperature of the internal device.

[0182] Those skilled in the art can understand, Figure 6The principle block diagram shown only shows the block diagram of some structures related to the solution of the present invention, and does not constitute a limitation on the terminal device to which the solution of the present invention is applied. The specific terminal device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0183] In one embodiment, a terminal device is provided. The terminal device includes a memory, a processor, and an evaluation program for the degree of waveform dispersion stored in the memory and executable on the processor. When the processor executes the evaluation program for the degree of waveform dispersion, the following operation instructions are implemented:

[0184] Determine the respective spectrum information corresponding to each segmented waveform of the original waveform, and the frequency information covered by each of the spectrum information is the same;

[0185] Based on the amplitudes corresponding to each frequency of each spectrum information, construct the first amplitude expectation value and the first squared absolute value expectation value corresponding to each frequency;

[0186] Based on the amplitude pairs corresponding to each frequency pair of each spectrum information, construct the second amplitude expectation value and the product of the second expectation values corresponding to each frequency pair. The frequency pair includes two frequencies. The second amplitude expectation value is determined by the amplitude corresponding to one of the frequencies in the frequency pair and the amplitude corresponding to the other frequency, and the product of the second expectation values is determined by the absolute value of the amplitude corresponding to one of the frequencies in the frequency pair and the absolute value of the amplitude corresponding to the other frequency;

[0187] Based on the amplitudes and the complex conjugate amplitudes of the amplitudes corresponding to each frequency pair of each spectrum information, construct the third amplitude expectation value and the product of the third expectation values corresponding to each frequency pair. The third amplitude expectation value is determined by the amplitude corresponding to one of the frequencies in the frequency pair and the complex conjugate amplitude corresponding to the other frequency, and the product of the third expectation values is determined by the absolute value of the amplitude corresponding to one of the frequencies in the frequency pair and the absolute value of the complex conjugate amplitude corresponding to the other frequency;

[0188] Evaluate the degree of dispersion of the original waveform based on the first amplitude expectation value, the first squared absolute value expectation value, the second amplitude expectation value, the product of the second expectation values, the third amplitude expectation value, and the product of the third expectation values.

[0189] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include non-volatile and / or volatile memories. Non-volatile memories can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memories 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), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0190] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the degree of waveform dispersion, characterized in that: include: Determine each spectrum information corresponding to each segmented waveform of the original waveform, wherein each spectrum information includes the same frequency information; According to the amplitude corresponding to each frequency of each of the spectrum information, construct a first amplitude expected value and a first amplitude absolute value square expected value corresponding to each frequency; According to the amplitude pairs corresponding to the frequency pairs of each of the frequency spectrum information, construct a second amplitude expected value and a second expected value product corresponding to each frequency pair, wherein the frequency pair includes two frequencies, the second amplitude expected value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the amplitude corresponding to the other frequency, and the second expected value product is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the amplitude corresponding to the other frequency; According to the amplitude corresponding to each frequency pair of each of the frequency spectrum information and the complex conjugate amplitude of the amplitude, construct a third amplitude expected value corresponding to each frequency pair and a third expected value product, wherein the third amplitude expected value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the complex conjugate amplitude corresponding to the other frequency, and the third expected value product is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the complex conjugate amplitude corresponding to the other frequency; Evaluate the degree of diffusion of the original waveform according to the first amplitude expected value, the first amplitude absolute value square expected value, the second amplitude expected value, the second expected value product, the third amplitude expected value, and the third expected value product; The step of evaluating the diffusion degree of the original waveform according to the first amplitude expected value, the first amplitude absolute value square expected value, the second amplitude expected value, the second expected value product, the third amplitude expected value, and the third expected value product comprises: Divide the square of the absolute value of the first expected amplitude value by the expected value of the square of the absolute value of the first amplitude value to obtain a first index value; Divide the square of the absolute value of the second amplitude expected value by the product of the second expected value to obtain a second index value; Divide the square of the absolute value of the third expected amplitude value by the product of the third expected value to obtain a third index value; The diffusion degree of the original waveform is evaluated according to the first index value, the second index value, and the third index value.

2. The method for evaluating waveform dispersion as claimed in claim 1, characterized in that: The determining of each spectrum information corresponding to each segmented waveform of the original waveform, wherein each spectrum information has the same frequency information, includes: Divide the original waveform into equally spaced time intervals to obtain equally spaced divided waveforms in each divided waveform; Fourier transform is applied to each of the equally spaced waveforms to obtain each spectrum graph in each of the spectrum information of each of the equally spaced waveforms, and the frequency sampling and frequency length in the frequency information of each of the spectrum graphs are the same.

3. The method for evaluating waveform dispersion as claimed in claim 1, characterized in that: The step of evaluating the diffusion degree of the original waveform according to the first index value, the second index value, and the third index value includes: Determine a first root mean square function composed of each of the first indicator values; Determine a second root mean square function composed of each of the second indicator values; Determine a third root mean square function composed of each of the third indicator values; The dispersion degree of the original waveform is evaluated according to the first root mean square function, the second root mean square function, and the third root mean square function.

4. The method for evaluating waveform dispersion as claimed in claim 3, characterized in that: The determining of a first root mean square function formed by the first indicator values ​​comprises: Determine a first indicator mean value composed of all the first indicator values; Determine the absolute value of the difference between each of the first indicator values ​​and the set standard value, recorded as the absolute value of the difference; Determine an adjacent index mean value formed by the absolute value of the difference between the adjacent index values ​​of each of the first index values ​​and the set standard value, the frequencies corresponding to the adjacent index values ​​are adjacent; Divide the average of the absolute values ​​of the differences between the adjacent indicators corresponding to the respective first indicator values ​​and the set standard values ​​by the average of the absolute values ​​of the differences between all the first indicators and the set standard values ​​to obtain the respective weights; A first root mean square function is obtained according to each weight, the absolute value of the difference corresponding to each first indicator value, and the total number of indicators formed by each first indicator value.

5. The method for evaluating waveform dispersion as claimed in claim 3, characterized in that: The determining of a second root mean square function formed by each of the second indicator values ​​comprises: Determine a second indicator mean value composed of all the second indicator values; Determine an adjacent index mean value formed by adjacent index values ​​of each of the second index values, where the frequencies corresponding to the adjacent index values ​​are adjacent; Divide the adjacent index means corresponding to each of the second index values ​​by the second index mean to obtain each weight of each of the second index values; Determine the absolute value of the difference between each of the second indicator values ​​and the set standard value, and record it as the absolute value of the difference; A second root mean square function is obtained according to the absolute values ​​of the differences corresponding to the second indicator values, the weights of the second indicator values, and the square value of the total number of indicators constituted by the second indicator values.

6. The method for evaluating waveform dispersion according to any one of claims 1 to 5, characterized in that: The second expected amplitude value is an expected value formed by the product of the amplitude corresponding to one of the frequencies in the frequency pair and the amplitude corresponding to the other frequency; the second expected value product is the product of the expected value of the square of the absolute value of the amplitude corresponding to one of the frequencies in the frequency pair and the expected value of the square of the absolute value of the amplitude corresponding to the other frequency; the third expected amplitude value is the expected value formed by the product of the amplitude corresponding to one of the frequencies in the frequency pair and the complex conjugate amplitude corresponding to the other frequency; the third expected value product is the product of the expected value of the square of the absolute value of the amplitude corresponding to one of the frequencies in the frequency pair and the expected value of the square of the complex conjugate amplitude corresponding to the other frequency.

7. A device for evaluating the degree of waveform dispersion, characterized in that: The device comprises the following components: A spectrum analysis module, used to determine each spectrum information corresponding to each segmented waveform of the original waveform, wherein each spectrum information includes the same frequency information; A first expected value calculation module, used for constructing a first amplitude expected value and a first amplitude absolute value square expected value corresponding to each frequency according to the amplitude corresponding to each frequency of each of the spectrum information; A second expected value calculation module, configured to construct a second amplitude expected value and a second expected value product corresponding to each frequency pair according to the amplitude pair corresponding to each frequency pair of each of the spectrum information, wherein the frequency pair includes two frequencies, the second amplitude expected value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the amplitude corresponding to the other frequency, and the second expected value product is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the amplitude corresponding to the other frequency; A third expected value calculation module, configured to construct a third amplitude expected value and a third expected value product corresponding to each frequency pair according to the amplitude corresponding to each frequency pair of each frequency spectrum information and the complex conjugate amplitude of the amplitude, wherein the third amplitude expected value is determined by the amplitude corresponding to one of the frequencies of the frequency pair and the complex conjugate amplitude corresponding to the other frequency, and the third expected value product is determined by the absolute value of the amplitude corresponding to one of the frequencies of the frequency pair and the absolute value of the complex conjugate amplitude corresponding to the other frequency; a dispersion evaluation module, configured to evaluate the degree of dispersion of the original waveform according to the first amplitude expected value, the first amplitude absolute value square expected value, the second amplitude expected value, the second expected value product, the third amplitude expected value, and the third expected value product; The step of evaluating the diffusion degree of the original waveform according to the first amplitude expected value, the first amplitude absolute value square expected value, the second amplitude expected value, the second expected value product, the third amplitude expected value, and the third expected value product comprises: Divide the square of the absolute value of the first expected amplitude value by the expected value of the square of the absolute value of the first amplitude value to obtain a first index value; Divide the square of the absolute value of the second amplitude expected value by the product of the second expected value to obtain a second index value; Divide the square of the absolute value of the third expected amplitude value by the product of the third expected value to obtain a third index value; The diffusion degree of the original waveform is evaluated according to the first index value, the second index value, and the third index value.

8. A terminal device, characterized in that: The terminal device includes a memory, a processor, and a waveform dispersion degree evaluation program stored in the memory and executable on the processor. When the processor executes the waveform dispersion degree evaluation program, the steps of the waveform dispersion degree evaluation method as described in any one of claims 1 to 5 are implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a waveform dispersion degree evaluation program, and when the waveform dispersion degree evaluation program is executed by a processor, the steps of the waveform dispersion degree evaluation method according to any one of claims 1 to 5 are implemented.

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