VSP speed modeling method based on Stein variational gradient descent method
By optimizing particle sampling instead of random sampling using the Stein variational gradient descent method, the problems of low computational efficiency and multiple solutions in VSP velocity modeling of traditional full waveform inversion methods are solved, achieving efficient inversion results and reliable wellbore velocity information acquisition.
Patent Information
- Application Number
- CN202511806708.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-03
- Publication Date
- 2026-02-27
AI Technical Summary
Traditional full-waveform inversion methods are computationally inefficient in VSP velocity modeling, and their reliance on random sampling has resulted in unresolved issues of multiple solutions in the inversion process.
The Stein variational gradient descent method is adopted to generate random particles as the initial velocity model by generating Gaussian random field perturbation. The optimal update direction of the particles is calculated in the forward modeling of the wave equation and the regenerating kernel Hilbert space, and the optimized particles replace random sampling.
It improves the computational efficiency of VSP velocity modeling, quantifies the uncertainty of inversion results, and provides reliable wellbore velocity information.
Smart Images
Figure CN121578367A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of geophysical exploration technology, specifically a VSP velocity modeling method based on Stein variational gradient descent. Background Technology
[0002] Vertical seismic profiles (VSPs) serve as a bridge connecting surface seismic, drilling, and geological data. The core idea of VSPs is to receive the response signals from seismic waves through detectors in the well, thereby reflecting the propagation path and stratigraphic information between the source and the detector. This helps in studying the distribution of target bodies such as stratigraphic structure, geological characteristics, and oil and gas reservoirs. Full waveform inversion (FWI) can use VSP data to model the subsurface medium structure. Traditional full waveform inversion methods reduce inversion ambiguity by randomly sampling to explore the global model space, but these methods usually require a large number of samples, resulting in low computational efficiency. Summary of the Invention
[0003] The purpose of this invention is to overcome the shortcomings of the prior art. The VSP velocity modeling method based on Stein variational gradient descent provided by this invention optimizes particles instead of random sampling, effectively improves FWI inversion efficiency, and provides technical support for VSP velocity modeling.
[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a VSP velocity modeling method based on Stein's variational gradient descent method, comprising the following steps:
[0005] S1: Generate a certain number of random particles based on Gaussian random field perturbation as the initial velocity model. ;
[0006] S2: For the initial model Synthetic seismic data were obtained by performing forward modeling of the wave equation. ;
[0007] S3: Calculate the optimal update direction of the particles in the regenerative kernel Hilbert space based on observed and synthetic seismic data;
[0008] S4: Update the particles based on the optimal update direction calculated in step S3;
[0009] S5: Repeat steps S2 to S4 until the maximum number of iterations is reached.
[0010] Further, in step S1, the initial velocity model The specific calculation formula is as follows:
[0011] ; (1)
[0012] ; (2)
[0013] ; (3)
[0014] In the above formula, for and The Matérn covariance function between two points Let V be the variance of the Gaussian distribution. For gamma function, For the smoothness parameter of the random field, For the modified Bessel function of the second kind, for and The distance between two points and This represents the relevant length along the x and y coordinates.
[0015] Furthermore, in step S2, the initial model... Synthetic seismic data were obtained by performing forward modeling of the wave equation. The specific calculation formula is as follows:
[0016] (4)
[0017] ; (5)
[0018] In the above formula, For sound pressure field, Angular frequency, For speed, and The grid spacing is given by the difference coefficients a=0.9903, b=0.8556, c=0.04, and d=0.0162. To synthesize seismic data, For wave field sampling operators.
[0019] Furthermore, in step S3, the optimal update direction of the particles is calculated in the regenerative kernel Hilbert space based on the observed and synthetic seismic data. The specific calculation formula is as follows:
[0020] ; (6)
[0021] ; (7)
[0022] ; (8)
[0023] In the above formula, Let be the likelihood function. For the prior probability density distribution, As the normalization factor, For the posterior probability density distribution, The standard deviation of the data. In order to observe earthquake data, For the direction of particle renewal, This represents the current iteration number. is the current number of particles, N is the total number of particles, and k is the radial basis kernel function.
[0024] Further, in step S4, for the first In the next iteration, based on the optimal direction calculated in step S3, each particle is updated. The specific calculation formula is as follows:
[0025] ; (10)
[0026] In the above formula, Step size, This represents the current iteration number. This represents the current number of particles.
[0027] Furthermore, in step S5, if l has not reached the maximum number of iterations, l = l + 1 is iterated again, and steps S2 to S4 are repeated until the maximum number of iterations is reached.
[0028] Beneficial effects: The VSP velocity modeling method based on Stein variational gradient descent disclosed in this invention generates a certain number of random particles as the initial velocity model based on Gaussian random field perturbation. The initial model is subjected to forward modeling of the wave equation to obtain synthetic seismic data. The optimal update direction of the particles is calculated in the regenerating kernel Hilbert space based on the observed and synthetic seismic data. By introducing the Stein variational strategy, the optimized particles are used instead of random sampling, which provides technical support for VSP velocity modeling, solves the problem of dependence on the initial model in traditional full waveform inversion methods, improves the computational efficiency of the inversion method, and quantifies the uncertainty of the inversion results. Attached Figure Description
[0029] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.
[0030] In the attached diagram:
[0031] Figure 1 This is a flowchart of the VSP velocity modeling method based on Stein variational gradient descent method of the present invention;
[0032] Figure 2 This invention relates to a layered model and initial particles;
[0033] Figure 3This is a comparison chart of the zero-bias VSP inversion results and velocity curves at the well location in this invention;
[0034] Figure 4 This invention resamples the Marmousi2 velocity model and initial particles;
[0035] Figure 5 The results of VSP inversion of the Marmousi2 model in this invention;
[0036] Figure 6 This is a comparison diagram of velocity curves at the well location in the Marmousi2 model of this invention. Detailed Implementation
[0037] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following text is only used to describe the implementation of the VSP velocity modeling method based on Stein variational gradient descent method of the present invention, and does not strictly limit the scope of protection of the present invention.
[0038] Furthermore, the technical solutions of the various embodiments can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.
[0039] Example 1: As Figure 1 As shown, this invention discloses a VSP velocity modeling method based on Stein's variational gradient descent method, including the following steps:
[0040] S1: Generate a certain number of random particles based on Gaussian random field perturbation as the initial velocity model. ;
[0041] S2: For the initial model Synthetic seismic data were obtained by performing forward modeling of the wave equation. ;
[0042] S3: Calculate the optimal update direction of the particles in the regenerative kernel Hilbert space based on observed and synthetic seismic data;
[0043] S4: Update the particles based on the optimal update direction calculated in step S3;
[0044] S5: Repeat steps S2 to S4 until the maximum number of iterations is reached.
[0045] In Embodiment 1, in step S1, the initial velocity model The specific calculation formula is as follows:
[0046] ; (1)
[0047] ; (2)
[0048] ; (3)
[0049] In the above formula, for and The Matérn covariance function between two points Let V be the variance of the Gaussian distribution. For gamma function, For the smoothness parameter of the random field, For the modified Bessel function of the second kind, The distance between two points. and This represents the relevant length along the x and y coordinates.
[0050] In Example 1, in step S2, the initial model is... Synthetic seismic data were obtained by performing forward modeling of the wave equation. The specific calculation formula is as follows:
[0051] (4)
[0052] ; (5)
[0053] In the above formula, For sound pressure field, Angular frequency, For speed, and Let be the grid spacing, i and j be the indices in the x and y directions respectively, and the difference coefficients be a = 0.9903, b = 0.8556, c = 0.04, and d = 0.0162. To synthesize seismic data, For wave field sampling operators.
[0054] In Example 1, in step S3, the optimal update direction of the particles is calculated in the regenerative kernel Hilbert space based on the observed and synthetic seismic data. The specific calculation formula is as follows:
[0055] ; (6)
[0056] ; (7)
[0057] ; (8)
[0058] In the above formula, Let be the likelihood function. For the prior probability density distribution, As the normalization factor, Let m be the posterior probability density distribution, and m be the model parameters. The standard deviation of the data. In order to observe earthquake data, For the direction of particle renewal, This represents the current iteration number. is the current number of particles, N is the total number of particles, and k is the radial basis kernel function.
[0059] In Embodiment 1, in step S4, for the first... In the next iteration, based on the optimal direction calculated in step S3, each particle is updated. The specific calculation formula is as follows:
[0060] ; (10)
[0061] In the above formula, Step size, This represents the current iteration number. This represents the current number of particles.
[0062] In Example 1, in step S5, if l has not reached the maximum number of iterations, l = l + 1 and iterates again, repeating steps S2 to S4 until the maximum number of iterations is reached.
[0063] Example 2: Figure 2 The layered model shown in a and Figure 4 The Marmousi2 model shown in Figure a was used to test the VSP velocity modeling method based on Stein variational gradient descent in this invention using both the layered model and the Marmousi2 model. The grid spacing was 10m, the source was a Ricker wavelet with a main frequency of 20Hz, the shot point of the layered model was located at the top of the model at 120m, and a single shot was used for excitation. The shot point of the Marmousi2 model was at x=50m, the shot spacing was 60m, and a total of 49 shots were used. A well position was set at the center of the model for observation.
[0064] In Example 2, 50 random models obtained by highly smoothing a real model and superimposing a Gaussian random field were used as initial particles. Figure 2 b and Figure 4b shows the effect after adding initial particles to the layered model and Marmousi2 model. Inversion was performed on the 2~35Hz frequency band with a frequency interval of 3Hz. The three frequencies were grouped together and inverted in ascending order. The inversion model obtained at the low frequency was used as the initial model for the next group of inversion frequencies. Each group of frequencies was inverted 100 times. The model inversion results were obtained using the above method, and the velocity curve at the well location was extracted and compared with the true value to verify the effectiveness of the method.
[0065] In Example 2, the initial particles were subjected to forward modeling of the wave equation using a finite difference scheme to obtain synthetic data.
[0066] In Example 2, for each frequency band, the optimal update direction of the particles is calculated using observational data and synthetic data. The particles are iteratively updated until the maximum number of iterations is met. The inversion results of the layered model and the Marmousi2 model are as follows: Figure 3 and Figure 5 As shown, where Figure 3 a and Figure 3 b represents a comparison of the zero-bias VSP inversion results and the velocity curve at the well location, as shown in the figure. Figure 3 As shown in figure a, the zero-biased VSP inversion results agree well with the layered model. Figure 3 b indicates that the wellbore velocity distribution has a high degree of consistency with the actual model, and the layered interface is clear, such as... Figure 5 As shown, the wellbore inversion results of the Marmousi2 model still have a high degree of matching with the model, verifying the applicability and reliability of the method of the present invention in complex models.
[0067] In Example 2, as Figure 3 b and Figure 6 As shown, the velocity curves at the well location are compared with the true values. The correlation coefficients of the layered model and the Marmousi2 model are 0.9956 and 0.9873, respectively, indicating that the velocity values at the well location are highly fitted to the true values. This verifies the reliability of the inversion results and the effectiveness of the method used. The VSP velocity modeling method based on Stein variational gradient descent of this invention introduces particles to represent the model space. By transforming the gradient information of the objective function into the regenerative kernel Hilbert space, the optimal update direction of the particles is calculated. Thus, optimizing the particles instead of random sampling can efficiently invert and obtain reliable well perimeter velocity information.
[0068] The above description only describes the present invention and its embodiments. This description is not restrictive. Those skilled in the art will realize that the embodiments described herein are to help readers understand the principles of the present invention and should be understood as not limiting the scope of protection of the present invention to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention based on the technical teachings disclosed in the present invention, and these modifications and combinations are still within the scope of protection of the present invention.
Claims
1. A VSP velocity modeling method based on Stein's variational gradient descent method, characterized in that, Includes the following steps: S1: Generate a certain number of random particles based on Gaussian random field perturbation as the initial velocity model. ; S2: For the initial model Synthetic seismic data were obtained by performing forward modeling of the wave equation. ; S3: Calculate the optimal update direction of the particles in the regenerative kernel Hilbert space based on observed and synthetic seismic data; S4: Update the particles based on the optimal update direction calculated in step S3; S5: Repeat steps S2 to S4 until the maximum number of iterations is reached.
2. The VSP velocity modeling method based on Stein variational gradient descent as described in claim 1, characterized in that: In step S1, the initial velocity model The specific calculation formula is as follows: ； （1） ； （2） ； （3） In the above formula, for and The Matérn covariance function between two points Let V be the variance of the Gaussian distribution. For gamma function, For the smoothness parameter of the random field, For the modified Bessel function of the second kind, for and The distance between two points and This represents the relevant length along the x and y coordinates.
3. The VSP velocity modeling method based on Stein variational gradient descent as described in claim 2, characterized in that: In step S2, the initial model is... Synthetic seismic data were obtained by performing forward modeling of the wave equation. The specific calculation formula is as follows: ；（4） ； （5） In the above formula, For sound pressure field, Angular frequency, For speed, and Let be the grid spacing, i and j be the indices in the x and y directions respectively, and the difference coefficients be a = 0.9903, b = 0.8556, c = 0.04, and d = 0.0162. To synthesize seismic data, For wave field sampling operators.
4. The VSP velocity modeling method based on Stein variational gradient descent as described in claim 3, characterized in that: In step S3, the optimal update direction of the particles is calculated in the regenerative kernel Hilbert space based on the observed and synthetic seismic data. The specific calculation formula is as follows: ； （6） ； （7） ； （8） In the above formula, Let be the likelihood function. For the prior probability density distribution, As the normalization factor, Let m be the posterior probability density distribution, and m be the model parameters. The standard deviation of the data. In order to observe earthquake data, For the direction of particle renewal, This represents the current iteration number. is the current number of particles, N is the total number of particles, and k is the radial basis kernel function.
5. The VSP velocity modeling method based on Stein variational gradient descent as described in claim 4, characterized in that: In step S4, for the first In the next iteration, based on the optimal direction calculated in step S3, each particle is updated. The specific calculation formula is as follows: ； （10） In the above formula, Step size, This represents the current iteration number. This represents the current number of particles.
6. The VSP velocity modeling method based on Stein variational gradient descent as described in claim 5, characterized in that: In step S5, if l has not reached the maximum number of iterations, l = l + 1 and iterates again, repeating steps S2 to S4 until the maximum number of iterations is reached.