A method and device for multi-modal adaptive fitting of rayleigh wave dispersion curves

Abstract

This invention discloses a multimodal adaptive fitting method and apparatus for Rayleigh surface wave dispersion curves, relating to the field of surface wave exploration technology. The invention first performs multimodal dispersion forward modeling based on subsurface medium model parameters to obtain theoretical velocity values ​​for multiple candidate modes corresponding to each frequency point. Based on the difference between observed and theoretical velocity values, a frequency-mode residual cost matrix is ​​constructed. Simultaneously, a global mode sequence is formed by the selected candidate mode numbers at each frequency point. A total cost function is constructed based on the residual cost matrix and a continuity penalty coefficient. A dynamic programming algorithm is used to globally optimize and solve the total cost function, obtaining the optimal mode sequence across the entire frequency band and determining the target theoretical mode branch corresponding to each frequency point. The optimal residual is then extracted to construct the fitness value. The entire process effectively suppresses unreasonable mode jumps and improves the continuity and stability of dispersion curve fitting. It is applicable to mode matching and fitness calculation in Rayleigh surface wave dispersion curve inversion.

Description

Technical Field

[0001] This invention relates to the field of surface wave exploration technology, and in particular to a multimodal adaptive fitting method and apparatus for Rayleigh surface wave dispersion curves. Background Technology

[0002] Rayleigh surface wave dispersion curve inversion is a common method in near-surface and shallow engineering exploration. Its inversion process generally includes: (1) establishing layered medium model parameters (layer thickness, shear wave velocity, longitudinal wave velocity, density, etc.); (2) performing dispersion forward modeling calculation based on model parameters to obtain the theoretical dispersion curves of the basic order and several higher-order modes; (3) defining the mismatch between the observed dispersion curve and the theoretical curve, and using the mismatch as the objective function / fitness of the optimization or sampling algorithm; (4) updating the model parameters iteratively through intelligent optimization or Bayesian sampling until the mismatch converges; In engineering surveying, the observed dispersion curve often has the following problems: (1) mode aliasing: the picked "observed dispersion curve" does not strictly correspond to a certain fixed mode; (2) mode skipping: as the frequency changes, the observed curve is closer to the higher-order mode than the basic mode in some frequency bands; (3) noise disturbance: causing abnormal residuals at local frequency points, further inducing mode misselection.

[0003] Therefore, in Rayleigh surface wave dispersion curve inversion, the key to the stability of fitness and the reliability of inversion lies in selecting a reasonable mode for each frequency point in the multimodal theoretical curve and maintaining continuity on the frequency axis. Improper handling of this step can directly introduce non-physical jumps, causing spikes and jitters in the objective function, thereby reducing the efficiency of optimization / sampling algorithms. Currently, the commonly used method is forced single-mode fitting, which independently selects the mode branch with the smallest residual for each frequency point. However, although this method has a small local residual, it is prone to frequent mode jumps between adjacent frequency points, resulting in discontinuous and unstable fitting curves. This causes the fitness to spike and jitter with model changes, thereby reducing the convergence efficiency of optimization and sampling algorithms and the reliability of inversion results.

[0004] To address the problems in forced single-mode fitting, researchers proposed a frequency-point greedy mode selection method. This method independently selects the mode with the smallest residual from all theoretical modes and the measured value at each frequency point as the "best-matching mode" for that point. Although this method achieves optimal matching at a single frequency point, the presence of noise and local interference in the Rayleigh surface wave dispersion curve can easily lead to drastic, frequent, and physically meaningless jumps in the mode numbering of adjacent frequency points. Such jumps result in a "combined curve" that, although having a small residual at each point, is a discontinuous curve that is physically impossible to exist as a whole. This ignores the smoothness that the dispersion curve should have on the frequency axis and the physical laws of mode evolution, ultimately leading to a large discrepancy between the inversion results and the actual results. Summary of the Invention

[0005] This invention provides a method and apparatus for multimodal adaptive fitting of Rayleigh surface wave dispersion curves, which can solve the problems existing in the prior art.

[0006] This invention provides a multimodal adaptive fitting method for Rayleigh surface wave dispersion curves, comprising the following steps: Collect the observation frequency sequence of the geological area to be measured and the velocity values ​​of the Rayleigh surface wave dispersion curves corresponding to each frequency point; Based on the model parameters of the underground medium model constructed based on the geological area to be measured, multimode dispersion forward modeling is performed on the observed Rayleigh surface wave dispersion curve to obtain the theoretical velocity values ​​of multiple candidate modes corresponding to each frequency point in the observed frequency sequence; the observed velocity values ​​of each candidate mode corresponding to each frequency point are obtained, and the residuals between the observed velocity values ​​and the theoretical velocity values ​​of each candidate mode corresponding to each frequency point are calculated to form a residual cost matrix. From the candidate modes corresponding to each frequency point in the observed frequency sequence, a candidate mode is selected for each frequency point to form a global mode sequence. A continuity penalty coefficient is introduced and multiplied by the magnitude of the mode change between adjacent candidate modes in the global mode sequence. A total cost function is constructed to characterize the quality of the global mode sequence by combining the residual cost matrix. A dynamic programming algorithm is used to globally optimize the total cost function. For each frequency point and its corresponding candidate modes in the observed frequency sequence, the minimum cumulative cost of transitioning from each candidate mode at the previous frequency point to the current candidate mode is obtained, thus obtaining the optimal mode sequence for that frequency point and the optimal mode sequence for the entire frequency band. Based on the optimal mode sequence across the entire frequency band, the target theoretical mode branch corresponding to each frequency point is determined, thereby realizing multi-mode adaptive fitting of the observed Rayleigh surface wave dispersion curve.

[0007] Preferably, obtaining the theoretical velocity values ​​of multiple candidate modes corresponding to each frequency point within the observed frequency sequence includes: Obtain the shear wave velocity of each layer in the subsurface medium model constructed for the geological area to be tested. v S With layer thickness h And based on preset v P and v S The mapping relationship determines the P-wave velocity of each layer. v P And determine the density parameters of each layer based on empirical density relationships. ρ ; Based on the shear wave velocity of each layer v S Layer thickness h P-wave velocities at each layer v P and density parameters of each layer ρ Multimode dispersion forward modeling was performed on the observed Rayleigh surface wave dispersion curves to obtain the theoretical velocity values ​​of each mode corresponding to each frequency point in the observed frequency sequence.

[0008] Preferably, the construction of the residual cost matrix includes: For each frequency point within the observed frequency sequence f i Obtain each frequency point f i Corresponding observed velocity value d i And obtain the frequency point number. j The theoretical velocity values ​​corresponding to each candidate mode c i,j ; Based on the observed velocity value d i Compared with theoretical speed value c i,j Construct the residual cost matrix from the residuals between them E ( i , j The residual cost matrix is ​​expressed as: ; in: E ( i , j ) indicates the first i The frequency point and the first j The residual cost corresponding to each candidate mode.

[0009] Preferably, the process of obtaining the total cost function and then performing a global optimization solution includes: Suppose the observed frequency sequence contains N There are 1 frequency points, each frequency point has 1 frequency point M There are candidate modes, and the global mode sequence is represented as follows: ; in, m i Indicates the first i Candidate mode numbers selected at each frequency point; The total cost function is constructed based on the residual cost matrix and is expressed as follows: ; in: C (m) represents the total cost function; | m i - m i-1 | indicates the variation range of mode numbers between adjacent frequency points. i Indicates the frequency point; mi Indicates the first i Candidate mode numbers selected at each frequency point; N Indicates the number of frequency points; E ( i , j ) indicates the first i The residual cost corresponding to each frequency point and candidate mode; λ This represents the continuity penalty coefficient, used to suppress jumps in mode numbering between adjacent frequency points; The total cost function is globally optimized using a dynamic programming algorithm to calculate the minimum cumulative cost at each frequency point and at the end of each candidate mode, expressed as: ; in: F ( i , j ) indicates up to the th i The frequency point and the first j The minimum cumulative cost at the end of each candidate mode.

[0010] Preferably, in the initial stage of global optimization using dynamic programming algorithm, a starting point constraint is applied to the lowest frequency point, limiting the lowest frequency point to the basic mode. During the dynamic programming solution process, the optimal predecessor mode number of each frequency point is recorded. After the cumulative cost calculation is completed, backtracking is performed from the last frequency point according to the backtracking pointer to obtain the optimal mode sequence of the entire frequency band.

[0011] Preferably, after obtaining the optimal mode sequence across the entire frequency band, the optimal residual corresponding to each frequency point is extracted from the residual cost matrix. e i = E ( i , m i The optimal residual at each frequency point will be... e i = E ( i , m i The fitness value is converted into a root mean square (RMS) value, which is expressed as follows: ; in: n d This indicates the normalization factor or the number of data points involved in the fitting.

[0012] This invention also provides a Rayleigh surface wave dispersion curve multimodal adaptive fitting device, comprising: The data module is used to collect the observation frequency sequence of the geological area to be measured and the velocity values ​​of the Rayleigh surface wave dispersion curves corresponding to each frequency point; The residual module is used to perform multimodal dispersion forward modeling on the observed Rayleigh surface wave dispersion curves based on the model parameters of the underground medium model constructed based on the geological area to be measured. It obtains the theoretical velocity values ​​of multiple candidate modes corresponding to each frequency point in the observed frequency sequence; obtains the observed velocity values ​​of each candidate mode corresponding to each frequency point; and calculates the residual between the observed velocity values ​​and the theoretical velocity values ​​of each candidate mode corresponding to each frequency point to form a residual cost matrix. The modality fitting module is used to select a candidate mode from each candidate mode corresponding to each frequency point in the observed frequency sequence to form a global modality sequence. It introduces a continuity penalty coefficient multiplied by the magnitude of the modality change between adjacent candidate modes in the global modality sequence, and constructs a total cost function to characterize the quality of the global modality sequence by combining the residual cost matrix. The total cost function is globally optimized using a dynamic programming algorithm. Specifically, for each frequency point and its corresponding candidate modes in the observed frequency sequence, the minimum cumulative cost of transitioning from each candidate mode at the previous frequency point to the current candidate mode is obtained, thus obtaining the optimal modality sequence for that frequency point and the optimal modality sequence for the entire frequency band. Based on the optimal mode sequence across the entire frequency band, the target theoretical mode branch corresponding to each frequency point is determined, thereby realizing multi-mode adaptive fitting of the observed Rayleigh surface wave dispersion curve.

[0013] This invention also provides an electronic device, including a memory and a processor; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the Rayleigh surface wave dispersion curve multimodal adaptive fitting method as described above.

[0014] This invention also provides a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements the steps of a Rayleigh surface wave dispersion curve multimodal adaptive fitting method as described above.

[0015] This invention provides a method and apparatus for multimodal adaptive fitting of Rayleigh surface wave dispersion curves, which has the following advantages compared with the prior art: This invention constructs a residual cost matrix based on the difference between the observed velocity values ​​at each frequency point in the observed frequency sequence and the theoretical velocity values ​​of multiple candidate modes at the corresponding frequency points. Then, a global modal sequence to be solved is set, and a continuity penalty coefficient is introduced, multiplied by the amplitude of modal changes between each modal sequence. Based on the cost matrix used for path optimization, a total cost function is constructed for globally evaluating the quality of the modal sequences. This process explicitly introduces a penalty term represented by the modal continuity coefficient into the total cost function, and multiplies the penalty term by the amplitude of modal changes between each modal sequence, thus incorporating the amplitude of modal changes as part of the global optimization. This mathematically forces the modal sequence to possess smoothness along the frequency axis, effectively suppressing unreasonable modal jumps. Simultaneously, a dynamic programming algorithm is used for global solution, which can find a globally optimal path from all possible modal combinations that satisfies both the physical laws of modal evolution and the continuity constraint, effectively suppressing unreasonable modal jumps, improving the continuity and stability of the modal trajectory along the frequency axis, making the fitting results more consistent with the modal evolution laws in engineering applications, and ultimately achieving high-precision inversion. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall process of a multimodal adaptive fitting method for Rayleigh surface wave dispersion curves provided in an embodiment of the present invention; Figure 2 A schematic diagram of the observed dispersion curve, the multi-candidate mode theoretical curve, and the target fitting curve determined based on the optimal mode sequence provided in the embodiments of the present invention; Figure 3 This is a schematic diagram of continuous constraint dynamic programming fitting provided in an embodiment of the present invention. Detailed Implementation

[0017] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0018] Rayleigh surface wave dispersion curve inversion is a commonly used method in near-surface and shallow engineering exploration. Its inversion process generally includes: (1) Establish the parameters of the layered medium model (layer thickness, transverse wave velocity, longitudinal wave velocity, density, etc.).

[0019] (2) Perform dispersion forward modeling based on the model parameters to obtain the theoretical dispersion curves of the basic mode and several higher-order modes.

[0020] (3) Define the mismatch between the observed dispersion curve and the theoretical curve, and use the mismatch as the objective function / fitness of the optimization or sampling algorithm.

[0021] (4) Update the model parameters iteratively through intelligent optimization or Bayesian sampling until the mismatch converges.

[0022] In engineering surveying, the following problems often occur when observing dispersion curves: (1) Modal aliasing: The picked “observation dispersion curve” does not strictly correspond to a certain fixed mode.

[0023] (2) Modal skipping: As the frequency changes, the observed curves are closer to higher-order modes than to the basic mode in some frequency bands.

[0024] (3) Noise disturbance: causes abnormal residuals at local frequency points, further inducing mode misselection.

[0025] Therefore, in surface wave inversion, how to select a reasonable mode for each frequency point in the multimodal theoretical curve and maintain continuity on the frequency axis is a key factor affecting the fitness stability and inversion reliability. If this step is not handled properly, it will directly introduce non-physical jumps, causing spikes and jitters in the objective function, thereby reducing the efficiency of the optimization / sampling algorithm.

[0026] Currently, there are generally two methods for addressing this stage, including: (1) Forced single-mode fitting: The observed curve is fitted as a single mode (e.g., the basic mode).

[0027] Disadvantages: Under complex layered structure conditions, if the observed curves have modal aliasing or step jumps, this method will produce systematic biases, causing the inversion results to deviate from the true structure.

[0028] (2) Greedy mode selection at each frequency point: Select the mode branch with the smallest residual independently at each frequency point.

[0029] Disadvantages: Although the local residuals are small, frequent modal jumps are likely to occur between adjacent frequency points, resulting in discontinuous and unstable fitting curves. This causes the fitness to spike and fluctuate with model changes, thereby reducing the convergence efficiency of optimization and sampling algorithms and the reliability of inversion results.

[0030] To address the problems existing in current methods, this invention introduces a modal continuity penalty and employs dynamic programming to achieve the global optimal selection of the modal sequence across the entire frequency band in the multimodal theoretical dispersion curve. This suppresses unreasonable modal jumps, obtains more continuous and stable fitting results, and constructs a stable root mean square (RMSE) fitness function, improving the convergence efficiency and reliability of surface wave inversion optimization. Figure 1As shown, this invention provides a method for multimodal adaptive fitting and fitness calculation of Rayleigh surface wave dispersion curves based on dynamic programming continuity constraints, specifically including: Step S1: Data acquisition and model parameter construction.

[0031] Obtain the observed frequency sequence and the corresponding observed dispersion curve Simultaneously, shear wave velocities for each layer are extracted based on the parameters of the subsurface medium model to be evaluated. v S With layer thickness h And according to the preset v P and v S The mapping relationship determines the P-wave velocity v P Further determine the density parameters based on empirical density relationships. ρ The longitudinal wave velocity adopts a linear proportional relationship. v P = α · v S Density adopted And set the thickness of the last layer to zero to represent a half space.

[0032] Step S2: Multimodal dispersion forward modeling calculation.

[0033] Based on the subsurface layered medium model parameters obtained in step S1, the dispersion forward modeling module is called to calculate the multimodal theoretical dispersion curve, and the theoretical velocity values ​​of multiple candidate modes corresponding to each frequency point are obtained. c i,j Among these features, the forward modeling results can be converted from velocity to slowness, so that the theoretical curves are uniformly expressed in the form of phase velocity. To enhance engineering robustness, a default theoretical curve can be output when the forward modeling fails, so as to ensure that the process is not interrupted.

[0034] Step S3: Construct the frequency-modal residual cost matrix.

[0035] For each frequency point fi Calculate the observed velocity values ​​respectively. d i Theoretical velocity values ​​of each candidate mode c i,j The residuals between them form the residual cost matrix. E ( i , j ); where the residuals are expressed in absolute form, as follows: .

[0036] in, iIndicates the frequency point number. j Indicates the candidate mode number.

[0037] Step S4: Construct the total cost function that includes continuous penalties and solve it using dynamic programming.

[0038] Define modal sequence ,in Indicates the first i The modal numbers selected at each frequency point are determined; the total cost function is constructed and expressed as: .

[0039] in: C (m) represents the total cost function, | m i - m i-1 | indicates the variation range of mode numbers between adjacent frequency points. i For frequency points, m i Indicates the first i The candidate mode number selected at each frequency point. N The number of frequency points, E ( i , j ) indicates the first i The residual cost corresponding to each frequency point and candidate mode; λ This is a continuity penalty coefficient used to suppress large changes in the mode numbering of adjacent frequency points.

[0040] A dynamic programming algorithm is used to globally optimize and solve the total cost function. For the ... i The frequency point and the first j There are candidate modes, and the cumulative cost satisfies:

[0041] .

[0042] in, F ( i , j ) indicates up to the th i The frequency point and the first j The minimum cumulative cost at the end of each candidate mode. By recording the optimal predecessor mode number and backtracking from the last frequency point after the calculation is completed, the optimal mode sequence for the entire frequency band can be obtained.

[0043] The preceding mode number corresponding to the minimum cumulative cost is recorded as the path pointer for subsequent backtracking; wherein, a starting point constraint is applied to the lowest frequency point: the lowest frequency point is limited to the basic mode to enhance path stability and conform to engineering priors.

[0044] Step S5: Backtrack to obtain the optimal modal trajectory.

[0045] After calculating the cumulative cost for all frequency points, starting from the last frequency point, backtracking point by point according to the path pointer recorded in step S4, the optimal mode sequence for the entire frequency band is obtained. The modal trajectory.

[0046] Step S6: Extract the optimal residual and calculate the fitness.

[0047] Based on the full-band optimal mode sequence, extract the frequency-point optimal residual from the residual cost matrix. e i = E ( i , m i ).

[0048] The optimal residual at each frequency point is calculated as the fitness value and output for use by the optimization / inversion algorithm; the fitness value is expressed in root mean square form as follows: .

[0049] in: nd The fitness value can be used as a normalization factor or the number of data points involved in the fitting process; it can also be used as the objective function input for subsequent intelligent optimization algorithms or Bayesian sampling algorithms.

[0050] like Figure 2 As shown in the figure, the observed dispersion curve, the multi-candidate mode theoretical curve, and the target fitting curve determined based on the optimal mode sequence are presented. It can be seen that by performing global path optimization among the multi-modal theoretical curves, the target fitting curve obtained by this invention can maintain good overall continuity and stability while maintaining high local fitting accuracy.

[0051] like Figure 3 As shown, the optimal modal trajectory obtained by the continuous constraint dynamic programming fitting in this invention has good overall continuity on the frequency axis and the residual distribution at each frequency point is relatively stable, which helps to reduce the peaks and jitters in the fitness curve and improve the stability and reliability of the subsequent inversion optimization process.

[0052] This invention simultaneously calculates the multimodal residuals at each frequency point, forming a cost map that can be used for path optimization, thus realizing the construction of the frequency-mode residual cost matrix; this invention integrates mode switching cost ( λ | m i - m i-1|) By introducing an objective function and explicitly suppressing unreasonable step skips, this invention constructs a total cost function that includes a continuous penalty term. It obtains the modal sequence with the minimum total cost across the entire frequency band and obtains the optimal modal trajectory through backtracking, achieving dynamic programming for global solution of the optimal modal trajectory. This invention extracts residuals from the optimal trajectory and forms an RMSE fitness score for inversion iteration, enabling the construction of a fitness function based on the optimal modal trajectory. This invention ensures engineering stability by using the lowest frequency point basic order constraint and the default output for forward modeling failures, achieving the setting of optimal starting point constraints and fault tolerance mechanisms.

[0053] The advantages of this invention are: ① Suppressing unreasonable modal jumps: Continuity penalty and dynamic programming global optimization avoid frequent jumps caused by point-by-point greedy algorithms; ② Improved fitting continuity and stability: Modal trajectories are more continuous on the frequency axis, and the fitting is more in line with engineering constraints; ③ More robust fitness: Reduced peaks and jitter in the fitness function, which is conducive to the stable convergence of intelligent optimization / sampling algorithms; ④ Improved inversion efficiency and reliability: Stable solutions are easier to obtain under the same iteration budget, reducing the probability of false convergence.

[0054] The optimal mode sequence across the entire frequency band obtained by dynamic programming in this invention has good overall stability. Therefore, the residual sequence extracted based on this optimal trajectory is usually more stable. When the fitness function constructed in this way changes with the model parameters, its spikes and jitters can be suppressed to a certain extent, thus providing a more stable search space for subsequent inversion optimization.

[0055] The continuity penalty term set in this invention is equivalent to a smoothing filter in the frequency domain. It forces the mode sequence to remain continuous, making it difficult for a single noise point to induce a mode jump. Even if the residual of a certain mode is very small due to noise at a certain frequency, dynamic programming will comprehensively consider the mode continuity of the preceding and following frequencies. Only when the fitting benefit brought by the mode selection is sufficient to compensate for the continuity penalty will it be adopted. This mechanism is inherently noise-resistant, making the optimal mode trajectory insensitive to random noise.

[0056] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A multimodal adaptive fitting method for Rayleigh surface wave dispersion curves, characterized in that, Includes the following steps: Collect the observation frequency sequence of the geological area to be measured and the velocity values ​​of the Rayleigh surface wave dispersion curves corresponding to each frequency point; Based on the model parameters of the underground medium model constructed based on the geological area to be measured, multimode dispersion forward modeling is performed on the observed Rayleigh surface wave dispersion curve to obtain the theoretical velocity values ​​of multiple candidate modes corresponding to each frequency point in the observed frequency sequence; the observed velocity values ​​of each candidate mode corresponding to each frequency point are obtained, and the residuals between the observed velocity values ​​and the theoretical velocity values ​​of each candidate mode corresponding to each frequency point are calculated to form a residual cost matrix. From the candidate modes corresponding to each frequency point in the observed frequency sequence, a candidate mode is selected for each frequency point to form a global mode sequence. A continuity penalty coefficient is introduced and multiplied by the magnitude of the mode change between adjacent candidate modes in the global mode sequence. A total cost function is constructed to characterize the quality of the global mode sequence by combining the residual cost matrix. A dynamic programming algorithm is used to globally optimize the total cost function. For each frequency point and its corresponding candidate modes in the observed frequency sequence, the minimum cumulative cost of transitioning from each candidate mode at the previous frequency point to the current candidate mode is obtained, thus obtaining the optimal mode sequence for that frequency point and the optimal mode sequence for the entire frequency band. Based on the optimal mode sequence across the entire frequency band, the target theoretical mode branch corresponding to each frequency point is determined, thereby realizing multi-mode adaptive fitting of the observed Rayleigh surface wave dispersion curve.

2. The Rayleigh surface wave dispersion curve multimodal adaptive fitting method according to claim 1, characterized in that, The process of obtaining the theoretical velocity values ​​of multiple candidate modes corresponding to each frequency point within the observed frequency sequence includes: Obtain the shear wave velocity of each layer in the subsurface medium model constructed for the geological area to be tested. v S With layer thickness h And based on preset v P and v S The mapping relationship determines the P-wave velocity of each layer. v P And determine the density parameters of each layer based on empirical density relationships. ρ ; Based on the shear wave velocity of each layer v S Layer thickness h P-wave velocities at each layer v P and density parameters of each layer ρ Multimode dispersion forward modeling was performed on the observed Rayleigh surface wave dispersion curves to obtain the theoretical velocity values ​​of each mode corresponding to each frequency point in the observed frequency sequence.

3. The Rayleigh surface wave dispersion curve multimodal adaptive fitting method according to claim 2, characterized in that, The construction of the residual cost matrix includes: For each frequency point within the observed frequency sequence f i Obtain each frequency point f i Corresponding observed velocity value d i And obtain the frequency point number. j The theoretical velocity values ​​corresponding to each candidate mode c i,j ; Based on the observed velocity value d i Compared with theoretical speed value c i,j Construct the residual cost matrix from the residuals between them E ( i , j The residual cost matrix is ​​expressed as: ； in: E ( i , j ) indicates the first i The frequency point and the first j The residual cost corresponding to each candidate mode.

4. The Rayleigh surface wave dispersion curve multimodal adaptive fitting method according to claim 3, characterized in that, After the total cost function is obtained, it is solved through global optimization, including: Suppose the observed frequency sequence contains N There are 1 frequency points, each frequency point has 1 frequency point M There are candidate modes, and the global mode sequence is represented as follows: ； in, m i Indicates the first i Candidate mode numbers selected at each frequency point; The total cost function is constructed based on the residual cost matrix and is expressed as follows: ； in: C (m) represents the total cost function; | m i - m i-1 | indicates the variation range of mode numbers between adjacent frequency points. i Indicates the frequency point; m i Indicates the first i Candidate mode numbers selected at each frequency point; N Indicates the number of frequency points; E ( i , j ) indicates the first i The residual cost corresponding to each frequency point and candidate mode; λ This represents the continuity penalty coefficient, used to suppress jumps in mode numbering between adjacent frequency points; The total cost function is globally optimized using a dynamic programming algorithm to calculate the minimum cumulative cost at each frequency point and at the end of each candidate mode, expressed as: ； in: F ( i , j ) indicates up to the th i The frequency point and the first j The minimum cumulative cost at the end of each candidate mode.

5. The Rayleigh surface wave dispersion curve multimodal adaptive fitting method according to claim 4, characterized in that, In the initial stage of global optimization using dynamic programming algorithm, a starting point constraint is applied to the lowest frequency point, which is limited to the basic mode. During the dynamic programming solution process, the optimal predecessor mode number of each frequency point is recorded. After the cumulative cost calculation is completed, backtracking is performed from the last frequency point according to the backtracking pointer to obtain the optimal mode sequence of the entire frequency band.

6. The Rayleigh surface wave dispersion curve multimodal adaptive fitting method according to claim 5, characterized in that, After obtaining the optimal mode sequence across the entire frequency band, the optimal residual corresponding to each frequency point is extracted from the residual cost matrix. e i = E ( i , m i The optimal residual at each frequency point will be... e i = E ( i , m i The fitness value is converted into a root mean square (RMS) value, which is expressed as follows: ； in: n d This indicates the normalization factor or the number of data points involved in the fitting.

7. A multimodal adaptive fitting device for Rayleigh surface wave dispersion curves, characterized in that, include: The data module is used to collect the observation frequency sequence of the geological area to be measured and the velocity values ​​of the Rayleigh surface wave dispersion curves corresponding to each frequency point; The residual module is used to perform multimodal dispersion forward modeling on the observed Rayleigh surface wave dispersion curves based on the model parameters of the underground medium model constructed based on the geological area to be measured. It obtains the theoretical velocity values ​​of multiple candidate modes corresponding to each frequency point in the observed frequency sequence; obtains the observed velocity values ​​of each candidate mode corresponding to each frequency point; and calculates the residual between the observed velocity values ​​and the theoretical velocity values ​​of each candidate mode corresponding to each frequency point to form a residual cost matrix. The modality fitting module is used to select a candidate mode from each candidate mode corresponding to each frequency point in the observed frequency sequence to form a global modality sequence. It introduces a continuity penalty coefficient multiplied by the magnitude of the modality change between adjacent candidate modes in the global modality sequence, and constructs a total cost function to characterize the quality of the global modality sequence by combining the residual cost matrix. The total cost function is globally optimized using a dynamic programming algorithm. Specifically, for each frequency point and its corresponding candidate modes in the observed frequency sequence, the minimum cumulative cost of transitioning from each candidate mode at the previous frequency point to the current candidate mode is obtained, thus obtaining the optimal modality sequence for that frequency point and the optimal modality sequence for the entire frequency band. Based on the optimal mode sequence across the entire frequency band, the target theoretical mode branch corresponding to each frequency point is determined, thereby realizing multi-mode adaptive fitting of the observed Rayleigh surface wave dispersion curve.

8. An electronic device, characterized in that, include: Memory and processor; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the Rayleigh surface wave dispersion curve multimodal adaptive fitting method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, Used to store a computer program, which, when executed by a processor, implements the steps of a Rayleigh surface wave dispersion curve multimodal adaptive fitting method as described in any one of claims 1 to 6.

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