A method for extracting Love wave dispersion based on Hankel transform

Abstract

The present invention discloses a method for extracting Love wave dispersion based on Hankel transform, specifically relating to the field of seismic exploration technology. The present invention performs a zero-order Bessel transform on Love wave field records collected in the field to obtain the Love wave dispersion energy spectrum, divides the zero-order Bessel function into a first-class Hankel function and a second-class Hankel function, performs a zero-order Hankel transform on the Love wave dispersion energy spectrum and ignores the second-class Hankel function during the transformation process, performs a velocity scan on the Love wave field only in the positive direction of the Love wave wave number, removes cross-aliasing in the Love wave dispersion energy spectrum, obtains a transformed Love wave dispersion energy diagram, extracts the phase velocity values ​​of each extreme point in the Love wave dispersion energy diagram, and obtains the Love wave dispersion curve. The present invention overcomes the cross-aliasing during the velocity scanning of the Love wave wave field record, has high resolution and multi-order resolution, and provides a new dispersion analysis method for multi-component surface wave detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic exploration, and in particular relates to a method for extracting Love wave dispersion based on Hankel transform. Background Art

[0002] As one of the fundamental physical properties of soil, shear wave velocity and its dynamic characteristics are directly related to parameters such as soil lithology, porosity, density, and pore fluid. Surface wave multichannel analysis technology has been widely used to determine shallow surface shear wave velocity structures due to its non-invasive, efficient, low-cost, wide spatial sampling, and high precision. Compared to Rayleigh waves, the phase velocity of Love waves is unaffected by the P-wave velocity. The fewer inversion parameters for Love waves make the inversion process more stable and the resulting shear wave velocity model more reliable.

[0003] High-resolution and multi-mode surface-wave dispersion analysis is a key step in multi-channel surface-wave analysis. However, cross-aliasing occurs when Love-wave wavefield recordings are subjected to velocity scanning. This cross-aliasing directly affects the resolution and multi-mode resolution of the Love-wave dispersion energy spectrum. Therefore, a Love-wave dispersion extraction method is urgently needed to eliminate aliasing and obtain a clear and continuous Love-wave dispersion energy spectrum, thus providing a new dispersion analysis method for the detection of multi-component surface waves. Summary of the Invention

[0004] In order to overcome the problem of cross-aliasing during velocity scanning of Love wave field recording, and solve the problems of low precision and poor continuity of Love wave dispersion energy spectrum, the present invention proposes a Love wave dispersion extraction method based on Hankel transform. This method has high resolution and multi-order resolution capability, and provides a new dispersion analysis method for the detection of multi-component surface waves.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for extracting Love wave dispersion based on Hankel transform specifically comprises the following steps:

[0007] Step 1: Extract the Love wave field record from the multi-channel seismic records collected in the field in the study area, perform zero-order Bessel transform on the Love wave field record, and obtain the Love wave dispersion energy spectrum, as shown in formula (1):

[0008]

[0009] Where r is the offset, k L is the Love wave scanning wave number, u(ω,r) is the Love wave field record at offset r, I is the Love wave dispersion energy spectrum, and J0 is the first kind zero-order Bessel function;

[0010] Step 2: Divide the zero-order Bessel function into two parts: the first-class Hankel function and the second-class Hankel function, as shown in formula (2):

[0011]

[0012] Where k is the wave number; is the first kind of Hankel function, which is used to characterize the inner cylindrical wave solution in the Love wave equation; is the second kind of Hankel function, used to characterize the outer cylindrical wave solution in the Love wave equation; J0 is the first kind of zero-order Bessel function;

[0013] Step 3: Substitute formula (2) into formula (1) and perform zero-order Hankel transform on the Love wave dispersion energy spectrum. Ignore the second-kind Hankel function during the zero-order Hankel transform process and perform velocity scanning on the Love wave field only in the positive direction of the Love wave wave number to remove the cross-aliasing in the Love wave dispersion energy spectrum. The Love wave dispersion energy diagram after the zero-order Hankel transform is obtained. The phase velocity value of each extreme point in the Love wave dispersion energy diagram after the zero-order Hankel transform is extracted, as shown in formula (3):

[0014]

[0015] Where D(ω,v) is the phase velocity of the Love wave; u(ω,r) is the Love wave field record at offset r; ω is the circular frequency of the Love wave, ω = 2πf, and f is the frequency of the Love wave.

[0016] Step 4: Extract the Love wave dispersion curve based on the phase velocity values ​​of each extreme point in the Love wave dispersion energy diagram and analyze the Love wave dispersion characteristics.

[0017] Preferably, in step 1, the Love wave field record includes two components: a tangential Green's function spectrum and a radial Green's function spectrum, as shown in formula (4):

[0018]

[0019] Where u(ω,r) is the Love wave field record at offset r, g TT (ω,k) is the tangential Green's function spectrum, g RR (ω,k) is the radial Green's function spectrum, k is the wave number, and r is the offset;

[0020] Since the Love wave field record contains both the tangential Green's function spectrum and the radial Green's function spectrum, as well as the zero-order Bessel function and the first-order Bessel function, the dispersion energy spectrum obtained by the zero-order Bessel transform of the Love wave field record is divided into two parts, namely:

[0021]

[0022]

[0023] Where I1 is the first part of the Love wave dispersion energy spectrum, I2 is the second part of the Love wave dispersion energy spectrum;

[0024] Since the wave number k and the offset r are independent of each other, exchanging the integration order of the wave number k and the offset r, combined with the orthogonality of the same-order Bessel functions, we can obtain:

[0025]

[0026]

[0027] According to the integral properties of Bessel function, we get:

[0028]

[0029] Substituting formula (9) into formula (8), we get:

[0030]

[0031] According to the Love wave number k→∞, the tangential Green's function spectrum and the radial Green's function spectrum are not only decoupled into a block diagonal matrix, but also converge to the corresponding static solution. At this time, the tangential Green's function spectrum and the radial Green's function spectrum converge to:

[0032]

[0033]

[0034] Where a L , Δ are both intermediate parameters, V S is the shear wave velocity of the ground surface in the actual formation velocity model, V P is the surface P-wave velocity in the actual formation velocity model, μ L is the shear modulus of the ground surface in the actual formation velocity model;

[0035] Calculate the maximum effective wave value k of Love waves in the actual formation velocity model max , as shown in formula (13):

[0036]

[0037] Where h is the formation thickness;

[0038] The maximum effective wave value k of Love wave in the actual formation velocity model max As the dividing point, when the Love wave number k>k maxWhen , substitute formula (11) and formula (12) into formula (10), we get:

[0039]

[0040] Where A is the calculation parameter,

[0041] Since the actual formation velocity model is an elastic medium, when the Love wave number k is equal to the Love wave number eigenvalue, the tangential Green's function spectrum tends to infinity, and when the Love wave number k is equal to the Rayleigh wave number eigenvalue, the radial Green's function spectrum g RR (ω,k) tends to infinity, eliminating the interval [k L ,k max ], we get:

[0042]

[0043] and, middle and

[0044] Where n is the interval [k L ,k max ], m is the number of eigenmodes of Rayleigh waves in the interval [k L ,k max ]The number of eigenmodes of the Nelove wave;

[0045] Based on formula (7) and formula (15), when the Love wave scanning wave number k L When it is equal to the Love-wave wave number eigenvalue, the first part of the Love-wave dispersion energy spectrum I1 is infinite, while the second part of the Love-wave dispersion energy spectrum I2 is finite. The maximum value in the Love-wave dispersion energy spectrum I corresponds to the maximum value in the first part of the Love-wave dispersion energy spectrum I1. Therefore, the Love-wave dispersion curve is extracted using the maximum value in the first part of the Love-wave dispersion energy spectrum.

[0046] Preferably, in step 3, the wave number of cross-aliased frequencies in the Love wave dispersion energy spectrum is inversely proportional to the detection distance and has periodicity.

[0047] The beneficial technical effects brought about by the present invention are:

[0048] The present invention proposes a Love wave dispersion extraction method based on Hankel transform, which uses Hankel transform to extract the dispersion characteristics of Love waves. The Love wave field record is converted from the time-space domain to the frequency-wavenumber domain through an improved zero-order Hankel transform, and the Love wave field is velocity scanned only in the positive wavenumber direction to remove the cross-aliasing in the Love wave dispersion energy spectrum. The Love wave dispersion energy map after the zero-order Hankel transform is obtained, and a clear and continuous Love wave dispersion energy spectrum is obtained. The method solves the problems of low accuracy and poor continuity of the Love wave dispersion energy spectrum, has high resolution and multi-order resolution capability, and provides a new dispersion analysis method for the detection of multi-component surface waves. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a comparison diagram of the Love wave dispersion energy spectrum of the Hankel transform of the present invention. Figure 1 The black dots in the figure are the theoretical phase velocities of Love waves. Figure 1 (a) is the Love wave dispersion energy spectrum after the Hankel function transformation. Figure 1 (b) is the Love wave dispersion energy spectrum after only using the first-type Hankel function transformation.

[0050] Figure 2 Comparison diagram of the zero-order Hankel transform results of the tangential component of displacement at different frequencies and the tangential Green's function spectrum. Figure 2 (a) is a comparison of the zero-order Hankel transform result of the tangential component of the displacement at a frequency of 10 Hz and the tangential Green's function spectrum. Figure 2 (b) is a comparison of the zero-order Hankel transform result of the tangential component of the displacement at a frequency of 20 Hz and the tangential Green's function spectrum. Figure 2 (c) is a comparison of the zero-order Hankel transform result of the tangential component of the displacement at a frequency of 30 Hz and the tangential Green's function spectrum. Figure 2 (d) is a comparison of the zero-order Hankel transform result of the tangential component of the displacement at a frequency of 50 Hz and the tangential Green's function spectrum.

[0051] Figure 3 is the Love wave dispersion energy spectrum processed under different noise conditions. Figure 3 (a) is the Love wave field record containing 20% ​​random noise. Figure 3 (b) is the Love wave field record containing 50% random noise. Figure 3 (c) is the Love wave dispersion energy spectrum obtained by processing the Love wave field record containing 20% ​​random noise using the traditional phase shift method. Figure 3 (d) is the Love wave dispersion energy spectrum obtained by processing the Love wave field record containing 50% random noise using the traditional phase shift method. Figure 3(e) is the Love wave dispersion energy spectrum obtained by processing the Love wave field record containing 20% ​​random noise using the method of the present invention. Figure 3 (f) in the middle is the Love wave dispersion energy spectrum obtained by processing the Love wave field record containing 50% random noise sound using the method of the present invention.

[0052] Figure 4 is the Love wave field record at the selected measuring point. Figure 4 (a) is the Love wave field record at the measuring point L1. Figure 4 Middle (b) is the Love wave field record at measuring point L2.

[0053] Figure 5 Graph showing the processing results of the Love wave field records at measuring points L1 and L2 using the method of the present invention and the traditional phase shift method. Figure 5 (a) is the frequency spectrum of the Love wave obtained by processing the Love wave field record at the measuring point L1 using the traditional phase shift method. Figure 5 (b) is the frequency energy spectrum of the Love wave obtained by processing the Love wave field record at the measuring point L2 using the traditional phase shift method. Figure 5 (c) is the frequency energy spectrum of the Love wave obtained by processing the Love wave field record at the measuring point L1 using the method of the present invention. Figure 5 (d) is the frequency energy spectrum of the Love wave obtained by processing the Love wave field record at the measuring point L2 using the method of the present invention. Figure 5 (e) is the dispersion energy map generated by the method of the present invention after the Love wave field record of the measuring point L1 is normalized in the time domain. Figure 5 (f) in the middle is the dispersion energy map generated by the method of the present invention after the Love wave field record of the measuring point L2 is normalized in the time domain of each channel.

[0054] Figure 6 The extraction results of the fundamental-order dispersion curve and the first higher-order dispersion curve when different processing methods are used for the selected measuring points. Figure 6 (a) shows the extraction results of the dispersion curves of the Love wave fundamental order and the first higher order using two methods for the measurement point L1. Figure 6 Middle (b) shows the extraction results of the dispersion curves of the Love wave fundamental order and the first higher order using two methods for the measurement point L2. DETAILED DESCRIPTION

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0056] The present invention proposes a method for extracting Love wave dispersion based on Hankel transform, which specifically includes the following steps:

[0057] Step 1: Extract the Love wave field record from the multi-channel seismic records collected in the field in the study area, perform zero-order Bessel transform on the Love wave field record, and obtain the Love wave dispersion energy spectrum, as shown in formula (1):

[0058]

[0059] Where r is the offset, k L is the Love wave scanning wave number, u(ω,r) is the Love wave field record at offset r, I is the Love wave dispersion energy spectrum, and J0 is the first kind zero-order Bessel function;

[0060] Since the Love wave field record includes two components: the tangential Green's function spectrum and the radial Green's function spectrum, as shown in formula (4):

[0061]

[0062] Where u(ω,r) is the Love wave field record at offset r, g TT (ω,k) is the tangential Green's function spectrum, g RR (ω,k) is the radial Green's function spectrum, k is the wave number, and r is the offset;

[0063] From formula (4), we can see that the Love wave field record contains not only the tangential Green's function spectrum and the radial Green's function spectrum, but also the zero-order Bessel function and the first-order Bessel function. After performing the zero-order Bessel transform on the Love wave field record, the obtained Love wave dispersion energy spectrum is divided into two parts:

[0064]

[0065]

[0066] Where I1 is the first part of the Love wave dispersion energy spectrum, I2 is the second part of the Love wave dispersion energy spectrum;

[0067] Since the wave number k and the offset r are independent of each other, exchanging the integration order of the wave number k and the offset r, combined with the orthogonality of the same-order Bessel functions, we can obtain:

[0068]

[0069]

[0070] According to the integral properties of Bessel function, we get:

[0071]

[0072] Without loss of generality, ignoring the integral property of Bessel function k=k L hour Substituting formula (9) into formula (8), we get:

[0073]

[0074] Considering that when the Love wave number k is very large, the tangential Green's function spectrum and the radial Green's function spectrum are not only decoupled into a block diagonal matrix, but also converge to the corresponding static solution. That is, when the Love wave number k→∞, the tangential Green's function spectrum and the radial Green's function spectrum are not only decoupled into a block diagonal matrix, but also converge to the corresponding static solution. At this time, the tangential Green's function spectrum and the radial Green's function spectrum converge to:

[0075]

[0076]

[0077] Where a L , Δ are both intermediate parameters, V S is the shear wave velocity of the ground surface in the actual formation velocity model, V P is the surface P-wave velocity in the actual formation velocity model, μ L is the shear modulus of the ground surface in the actual formation velocity model;

[0078] Calculate the maximum effective wave value k of Love waves in the actual formation velocity model max , as shown in formula (13):

[0079]

[0080] Where h is the formation thickness;

[0081] The maximum effective wave value k of Love wave in the actual formation velocity model max As the dividing point, when the Love wave number k>k max When , substitute formula (11) and formula (12) into formula (10), we get:

[0082]

[0083] Where A is the calculation parameter,

[0084] Since the actual formation velocity model is an elastic medium, when the Love wave number k is equal to the Love wave number eigenvalue, the tangential Green's function spectrum tends to infinity, and when the Love wave number k is equal to the Rayleigh wave number eigenvalue, the radial Green's function spectrum g RR (ω,k) tends to infinity, eliminating the interval [k L ,k max ], we get:

[0085]

[0086] and, middle and

[0087] Where n is the interval [k L ,k max ], m is the number of eigenmodes of Rayleigh waves in the interval [k L ,k max ]The number of eigenmodes of the Nelove wave;

[0088] Based on formula (7) and formula (15), when the Love wave scanning wave number k L When the Love wave number is equal to the Love wave eigenvalue, the first part of the Love wave dispersion energy spectrum I1 is infinite, while the second part of the Love wave dispersion energy spectrum I2 is finite, that is, different Love wave scanning wave numbers k L Under these conditions, the maximum value in the Love wave dispersion energy spectrum I corresponds to the maximum value in the first part of the Love wave dispersion energy spectrum I1.

[0089] Therefore, the maximum value of the first part of the Love wave dispersion energy spectrum I1 corresponds to the Love wave dispersion curve, and the Love wave dispersion curve is extracted using the maximum value in the first part of the Love wave dispersion energy spectrum.

[0090] Step 2: Divide the zero-order Bessel function into two parts: the first-class Hankel function and the second-class Hankel function, as shown in formula (2):

[0091]

[0092] Where k is the wave number; is the first kind of Hankel function, which is used to characterize the inner cylindrical wave solution in the Love wave equation; is the second kind of Hankel function, which is used to characterize the outer cylindrical wave solution in the Love wave equation; J0 is the first kind of zero-order Bessel function.

[0093] From formula (2), we can get the first kind of Hankel function and the Hankel function of the second kind The inner cylindrical wave solution and the outer cylindrical wave solution of the two-dimensional wave equation are described respectively, so the Hankel transform can be understood as a velocity scan of the Love wave field in the positive direction (+k) and the reverse direction (-k) of the Love wave.

[0094] Step 3: Since cross-aliasing will occur when the first-order Hankel function is used to perform velocity scanning on the Love wave field record, and the wave number corresponding to the cross-aliasing is inversely proportional to the detection distance and has a certain periodicity, in order to avoid the generation of cross-aliasing, formula (2) is substituted into formula (1) to perform zero-order Hankel transform on the Love wave dispersion energy spectrum. In the zero-order Hankel transform process, the second-order Hankel function is ignored, and the Love wave field is only velocity-scanned in the positive direction of the Love wave wave number to remove the cross-aliasing in the Love wave dispersion energy spectrum. The Love wave dispersion energy map after the zero-order Hankel transform is obtained. The phase velocity value of each extreme point in the Love wave dispersion energy map after the zero-order Hankel transform is extracted, as shown in formula (3):

[0095]

[0096] Where D(ω,v) is the phase velocity of the Love wave; u(ω,r) is the Love wave field record at offset r; ω is the circular frequency of the Love wave, ω = 2πf, and f is the frequency of the Love wave.

[0097] Step 4: Extract the Love wave dispersion curve based on the phase velocity values ​​of each extreme point in the Love wave dispersion energy diagram and analyze the Love wave dispersion characteristics.

[0098] Example 1

[0099] In this embodiment, the discrete wavenumber method is used to simulate the seismic wave field record caused by the point source. The offset distance of the simulated shot gather record is set to 5m, the array length is set to 200m, and the trace spacing is set to 5m. The Love wave field record is simulated and the dispersion energy spectrum obtained by performing Hankel transformation on the Love wave field record using the Hankel function generates cross-aliasing, as shown in the following example: Figure 1 (a), while the method of the present invention only uses the first-class Hankel function to perform velocity scanning energy enhancement on the Love wave field record to eliminate cross-aliasing, as shown in Figure 1 As shown in (b), the dispersion energy spectrum obtained after eliminating cross-aliasing is clearer and continuous, which is more conducive to picking up the dispersion curve in the higher frequency band.

[0100] Example 2

[0101] A Love wave dispersion extraction method based on Hankel transform proposed in the present invention is applied to a double-layered formation model. The parameters of the double-layered formation model are shown in Table 1.

[0102] Table 1 Parameters of the double-layered stratum model

[0103]

[0104] For the viscoelastic model, the attenuation of the medium will cause the singularity in the Green's function spectrum to disappear, making the value of the surface wave at infinity become finite.

[0105] Set the circular frequency ω and scanning wave number k of the Love wave in the double-layered stratum model L , the frequency of the Love wave is set to 10Hz, 20Hz, 30Hz and 50Hz in turn, and the comparison results of the zero-order Hankel transform and the tangential Green's function spectrum of the displacement tangential component at different frequencies are obtained (the imaginary parts of both), as shown in Figure 2 As shown in the figure, the results show that the overall difference between the zero-order Hankel transform of the tangential component of the displacement and the tangential Green's function spectrum of the tangential component of the displacement is small, and the two are basically consistent at the maximum value, that is, the zero-order Hankel transform of the tangential component of the displacement and the tangential Green's function spectrum of the tangential component of the displacement are both equal to the theoretical phase velocity of the Love wave, which verifies that the zero-order Hankel transform can be used to effectively obtain the Love wave dispersion characteristics.

[0106] Since the Love wave field records collected in actual applications contain certain noise, which affects the imaging quality of the Love wave dispersion energy spectrum, it is necessary to conduct noise resistance testing. Taking the double-layered stratum model in Table 1 as an example, 20% random noise and 50% random noise are added to the simulated Love wave field records, as shown in Figure 1. Figure 3 (a) and Figure 3 As shown in (b), the noise is calculated using the following formula:

[0107] Data=Signal+2×(0.5-RND)×mean(max(Signal))×Noise (16)

[0108] Where Data is the noise data, Signal is the simulated Lovewave wavefield data, Noise is the noise level, and mean(max(Signal)) is the average of the maximum values ​​of each channel in the Lovewave wavefield data.

[0109] Figure 3 (c) is the Love wave dispersion energy diagram generated by the traditional phase shift method. Figure 3 (e) is the Love wave dispersion energy diagram generated by the method of the present invention. By comparison, it can be seen that due to the high-frequency interference of noise, it is almost impossible to obtain effective dispersion information in the high-frequency band (>40Hz). Compared with the Love wave field record containing 20% ​​random noise, the dispersion energy spectrum corresponding to the Love wave field record containing 50% random noise is more interfered with at high frequencies, and its effective frequency band is narrower. By comparison Figure 3 (c) Figure 3 (d) and Figure 3 (e) Figure 3 (f) It can be seen that the anti-noise performance of the Love wave dispersion energy spectrum obtained by the method of the present invention is better than that of the Love wave dispersion energy spectrum obtained by the conventional phase shift method.

[0110] Application Experiment

[0111] A Love wave dispersion extraction method based on Hankel transform proposed in the present invention was applied on the dirt road of the Xiaoyi River embankment in Gaoyang County, south of Xiongan New Area, and an ideal Love wave dispersion extraction effect was achieved.

[0112] When acquiring Love wave field records, a single-ended excitation method was used to generate Love waves. To strengthen the coupling between the pile and the ground, multiple steel bars were inserted through the pile and into the ground. During excitation, multiple people stood on the pile to provide counterweight. The pile's long axis and hammering direction were aligned with the geophone's direction (perpendicular to the survey line). Each measurement point was struck five times in the same direction. The horizontal geophone's main frequency was set to 4 Hz, the geophone spacing dx to 2 meters, the minimum offset to 10 meters, the array length to 90 meters, the sampling rate to 0.5 ms, and the sampling length to 1 second.

[0113] Two measuring points L1 and L2 are selected on the survey line. The distance between measuring points L1 and L2 is 120m. The Love wave field records at measuring points L1 and L2 are measured, as shown in the following figure: Figure 4 (a) and Figure 4 As shown in (b), by observing the Love wave field records at measuring points L1 and L2, it can be seen that the Love wave is well developed and the signal-to-noise ratio is high. The Love wave field records at measuring points L1 and L2 are processed using the traditional phase shift method to obtain the frequency energy spectrum of the Love wave, as shown in Figure 5 (a) and Figure 5 As shown in (b), the Love wave field records at the measuring points L1 and L2 are processed by the method of the present invention to obtain the frequency energy spectrum of the Love wave, as shown in FIG. Figure 5 (c) and Figure 5 (d) shown. Figure 5 The black dots in the figure represent the dispersion curve automatically picked from the peak values ​​of each frequency point in the dispersion energy diagram generated using the phase-shift method. The dashed black line represents the maximum wavelength that can be resolved using a linear arrangement, i.e., the line v / f = 100 m. Since the Love wave field recording trace spacing is small, according to the Nyquist theorem, the maximum wavenumber is twice the Nyquist wavenumber, which is 1 / dx. This means that the minimum resolvable wavelength is equal to dx. This shows that the picked dispersion curve is not affected by spatial sampling aliasing.

[0114] It should be noted that for the sake of convenience in describing this embodiment, the order of the dispersion curve is simply given in order according to the velocity value, and the problem of mislabeling of the order of the surface wave dispersion curve is not considered. Figure 5 (a) and Figure 5 (c) It can be seen that the imaging of the second high-order mode of Love wave by the method of the present invention is clearer and more continuous. Figure 5 (b) and Figure 5(d) It can be seen that the imaging of the first and second high-order modes of Love waves using this method is clearer and more continuous. Figure 5 (a) and Figure 5 The fundamental order dispersion curve and the first higher order dispersion curve in (c) are as follows: Figure 6 As shown in (a), although there is a deviation between the two, the average difference is 1.547m / s, and the maximum difference is 21.8m / s at the 4Hz low-frequency end. This is because the low-frequency band has large side lobes of scattered energy, resulting in a large error. The maximum deviation between the first and highest orders is 4.9m / s, and the maximum relative error is 2.68%. Therefore, it is verified that the imaging results of the two methods for the Love wave fundamental order and the first and highest orders are basically consistent. Then extract Figure 5 (b) and Figure 5 The fundamental order dispersion curve and the first higher order dispersion curve in (d) are as follows: Figure 6 As shown in (b), the results of extracting the dispersion curves of the Love wave fundamental order and the first higher order using the two methods for the measuring point L2 are basically consistent.

[0115] Generally, the original Love-wave wavefield records need to be normalized in the time domain before surface wave dispersion analysis. Since the phase-shift method only focuses on phase information, the amplitude spectrum of the original Love-wave wavefield records after Fourier transform is performed on the original Love-wave wavefield records does not participate in the dispersion analysis calculation. Therefore, it is not necessary to perform time-domain normalization before using the phase-shift method to perform dispersion analysis on time-domain seismic records. However, the method of the present invention combines the amplitude spectrum and phase spectrum of the original Love-wave wavefield records at the same time. Therefore, time-domain normalization may affect the dispersion analysis results of this method. Figure 5 (e) and Figure 5 (f) represents the dispersion energy diagram generated by the method of the present invention after the Love wave field records of the measuring points L1 and L2 are normalized in the time domain of each channel. Figure 5 (c) and Figure 5 (d) A comparison shows that time-domain normalization alters the amplitude spectrum of the original seismic signal, resulting in the second-highest-order energy at L1 and the first-highest-order energy at L2 being strong only within a narrow frequency band, resulting in relatively poor overall continuity of their dispersion energy. Furthermore, time-domain normalization causes the fundamental-order dispersion energy peak to be slightly higher overall.

[0116] Therefore, in practical applications, in order to ensure the best possible dispersion analysis effect, the method of the present invention can be used to perform dispersion analysis on the original shot gather records and the time-normalized shot gather records respectively, and the better dispersion analysis results can be selected for the subsequent surface wave inversion process.

[0117] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for extracting Love wave dispersion based on Hankel transform, characterized in that: The specific steps include: Step 1: Extract the Love wave field record from the multi-channel seismic records collected in the field in the study area, perform zero-order Bessel transform on the Love wave field record, and obtain the Love wave dispersion energy spectrum, as shown in formula (1): Where r is the offset, k L is the Love wave scanning wave number, u(ω,r) is the Love wave field record at offset r, I is the Love wave dispersion energy spectrum, and J0 is the first kind zero-order Bessel function; Step 2: Divide the zero-order Bessel function into two parts: the first-class Hankel function and the second-class Hankel function, as shown in formula (2): Where k is the wave number; is the first kind of Hankel function, which is used to characterize the inner cylindrical wave solution in the Love wave equation; is the second kind of Hankel function, used to characterize the outer cylindrical wave solution in the Love wave equation; J0 is the first kind of zero-order Bessel function; Step 3: Substitute formula (2) into formula (1) and perform zero-order Hankel transform on the Love wave dispersion energy spectrum. Ignore the second-kind Hankel function during the zero-order Hankel transform process and perform velocity scanning on the Love wave field only in the positive direction of the Love wave wave number to remove the cross-aliasing in the Love wave dispersion energy spectrum. The Love wave dispersion energy diagram after the zero-order Hankel transform is obtained. The phase velocity value of each extreme point in the Love wave dispersion energy diagram after the zero-order Hankel transform is extracted, as shown in formula (3): Where D(ω,v) is the phase velocity of the Love wave; u(ω,r) is the Love wave field record at offset r; ω is the circular frequency of the Love wave, ω = 2πf, and f is the frequency of the Love wave. Step 4: Extract the Love wave dispersion curve based on the phase velocity values ​​of each extreme point in the Love wave dispersion energy diagram and analyze the Love wave dispersion characteristics.

2. The method for extracting Love wave dispersion based on Hankel transform according to claim 1, characterized in that: In step 1, the Love wave field record includes two components: the tangential Green's function spectrum and the radial Green's function spectrum, as shown in formula (4): Where u(ω,r) is the Love wave field record at offset r, g TT (ω,k) is the tangential Green's function spectrum, g RR (ω,k) is the radial Green's function spectrum, k is the wave number, and r is the offset; Since the Love wave field record contains both the tangential Green's function spectrum and the radial Green's function spectrum, as well as the zero-order Bessel function and the first-order Bessel function, the dispersion energy spectrum obtained by the zero-order Bessel transform of the Love wave field record is divided into two parts, namely: Where I1 is the first part of the Love wave dispersion energy spectrum, I2 is the second part of the Love wave dispersion energy spectrum; Since the wave number k and the offset r are independent of each other, exchanging the integration order of the wave number k and the offset r, combined with the orthogonality of the same-order Bessel functions, we can obtain: According to the integral properties of Bessel function, we get: Substituting formula (9) into formula (8), we get: According to the Love wave number k→∞, the tangential Green's function spectrum and the radial Green's function spectrum are not only decoupled into a block diagonal matrix, but also converge to the corresponding static solution. At this time, the tangential Green's function spectrum and the radial Green's function spectrum converge to: Where a L , Δ are both intermediate parameters, V S is the shear wave velocity of the ground surface in the actual formation velocity model, V P is the surface P-wave velocity in the actual formation velocity model, μ L is the shear modulus of the ground surface in the actual formation velocity model; Calculate the maximum effective wave value k of Love waves in the actual formation velocity model max , as shown in formula (13): Where h is the formation thickness; The maximum effective wave value k of Love wave in the actual formation velocity model max As the dividing point, when the Love wave number k>k max When , substitute formula (11) and formula (12) into formula (10), we get: Where A is the calculation parameter, Since the actual formation velocity model is an elastic medium, when the Love wave number k is equal to the Love wave number eigenvalue, the tangential Green's function spectrum tends to infinity, and when the Love wave number k is equal to the Rayleigh wave number eigenvalue, the radial Green's function spectrum g RR (ω,k) tends to infinity, eliminating the interval [k L ,k max ], we can get the eigenvalues ​​of all surface wave numbers in : and, middle and Where n is the interval [k L ,k max ], m is the number of eigenmodes of Rayleigh waves in the interval [k L ,k max ]The number of eigenmodes of the Nelove wave; Based on formula (7) and formula (15), when the Love wave scanning wave number k L When it is equal to the Love-wave wave number eigenvalue, the first part of the Love-wave dispersion energy spectrum I1 is infinite, while the second part of the Love-wave dispersion energy spectrum I2 is finite. The maximum value in the Love-wave dispersion energy spectrum I corresponds to the maximum value in the first part of the Love-wave dispersion energy spectrum I1. Therefore, the Love-wave dispersion curve is extracted using the maximum value in the first part of the Love-wave dispersion energy spectrum.

3. The method for extracting Love wave dispersion based on Hankel transform according to claim 1, characterized in that: In step 3, the number of cross-aliased waves in the Love wave dispersion energy spectrum is inversely proportional to the detection distance and has periodicity.

Images