A one-way wave migration method based on a thin-plate approximation for preprocessing viscous acoustic media.
By using an iterative method for preprocessing viscous acoustic media based on thin-plate approximation, the convergence of the Born series is improved, the problem of insufficient imaging accuracy in strongly disturbed media is solved, and efficient migration imaging effect is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-30
- Publication Date
- 2026-03-13
AI Technical Summary
In strongly disturbed media, the convergence speed of the Born series is slow and the calculation error is large. The traditional Born approximation method has insufficient imaging accuracy in strongly disturbed media, making it difficult to achieve efficient and accurate migration imaging.
A preprocessing iterative method based on thin-plate approximation for viscous acoustic media is adopted. By introducing small imaginary components and pre-solution factors, the convergence of the Born series is improved. The velocity model is divided into local calculations using the thin-plate partitioning idea, and equivalent processing is performed using the Kolsky-Futterman model. Migration imaging is performed using cross-correlation imaging conditions.
It achieves efficient and accurate migration imaging in strongly disturbed media, improves computational efficiency and reduces the impact of background Green's function instability on imaging results, and is suitable for one-way wave migration imaging in viscous acoustic media.
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Figure CN120652546B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a geophysical exploration method, specifically a one-way wave migration method based on a thin-plate approximation viscous acoustic medium preprocessing iterative method. Background Technology
[0002] Compared to differential classification operators, integral operators typically utilize perturbation theory to decompose the medium into a superposition of background and perturbation parameters, transforming the scattering problem into a boundary value problem of solving the second kind of Fredholm integral equation. The Lippmann-Schwinger (LS) integral equation can then be obtained using the Green's function. Due to the nonlinearity of the LS equation, the Born scattering series can be obtained using iterative methods. However, the traditional Born series converges slowly in strongly perturbed media, and the first-order Born approximation has relatively large computational errors in such media. Therefore, the Born approximation is only applicable to weakly transversely inhomogeneous media (velocity perturbations less than 10%). To address this issue, researchers have introduced the renormalization concept from quantum scattering theory. By renormalizing the Born series, the convergence of the scattering series in strongly perturbed media can be improved, resulting in a more accurate numerical solution with fewer iterations. In the field of seismic scattering, the renormalization method uses a splitting operator to arrange the scattering series into a series of sub-series and sums some of the sub-series to eliminate the divergence term of the series.
[0003] The purpose of the preprocessing iterative method is to improve the convergence of the Born series, similar to the preprocessing methods used for solving linear equation systems. To obtain a convergent Born series, a small imaginary component is first introduced into the background wavenumber, resulting in an LS equation with a complex wavenumber. The background Green's function corresponding to this LS equation has a damping factor. Then, a preprocessing factor defined by the small imaginary component is used to preprocess the LS equation with the complex wavenumber. Finally, an iterative method is used to solve the preprocessed LS equation, obtaining the Born series improved by the complex wavenumber and preprocessing. Experiments show that the improved Born series is also convergent for strong scattering. However, the convergence rate of the Born series varies depending on the preprocessing factor.
[0004] Therefore, the research direction of this invention is to provide a new migration imaging method that selects an appropriate preprocessing factor and applies the above-mentioned preprocessing iterative method to one-way wave migration imaging of viscous acoustic media, so as to achieve migration imaging with high efficiency and good accuracy. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention provides a one-way wave migration method based on the thin-plate approximation for preprocessing viscous acoustic media, which can effectively solve the above-mentioned technical problems.
[0006] To achieve the above objectives, the technical solution adopted by this invention is: a one-way wave migration method based on the thin-plate approximation for preprocessing viscous acoustic media, comprising the following steps:
[0007] Step 1: Arrange multiple geophones in a row at equal intervals in the area to be detected to form an observation system, and arrange multiple seismic sources in a row at equal intervals and number them.
[0008] Step 2: Excite each seismic source in sequence according to its number, and the observation system acquires the seismic record at the time of excitation of each seismic source.
[0009] Step 3: Set the velocity model parameters for the propagation of seismic scattered waves in the detection area, and determine the absorption and attenuation model for the seismic scattered waves as they propagate in the detection area.
[0010] Step 4: Using the idea of thin plate division, the absorption attenuation model in Step 3 is divided into multiple thin plates along the depth direction, and the velocity parameters and quality factor parameters in each thin plate are determined.
[0011] Step 5: Load the Ricker wavelet at the first source location and use Fourier transform to convert it to the frequency wavenumber domain. Use this as the initial value to calculate and obtain the forward scattering migration wavefield of all thin plates.
[0012] Step 6: Perform a Fourier transform on the seismic record corresponding to the excitation of the first source to convert it to the frequency-wavenumber domain, and use it as the initial value to perform the calculation process in step 5 to obtain the corresponding backpropagation scattering migration wave field.
[0013] Step 7: Using cross-correlation imaging conditions, perform migration imaging on the forward-propagating and backward-propagating migration wave fields obtained in Steps 5 and 6 to obtain the imaging results of the first source.
[0014] Step 8: Repeat steps 5 to 7 for each seismic source in sequence according to the source number to obtain the imaging results of each source.
[0015] Step 9: Superimpose the imaging results of all seismic sources to obtain the final offset imaging result of the detection area.
[0016] Furthermore, in step one, a coordinate system is established with the X-axis along the deployment direction of each detector and seismic source and the Z-axis perpendicular to the deployment direction (i.e., the depth direction of the detection area), with the origin at (0.0, 0.0); the number of detectors is nx, the distance between adjacent detectors is dr, and the position of the first detector is (0.0, 0.0); the number of seismic sources is ns, the distance between adjacent seismic sources is ds, and the position of the first seismic source is (0.0, 0.0); the dominant frequency of the wavelet is fHz; the sampling interval is set to lms; and the sampling time length is nt.
[0017] Furthermore, the velocity model parameters in step three are: ,in The coordinate parameters are defined as follows: the grid parameter for the X-axis is nx, the grid parameter for the Z-axis is nz, and the grid spacings are dx and dz, respectively. The quality factor parameters are calculated based on the velocity model parameters. The specific calculation formula is as follows:
[0018] (1)
[0019] in The unit is km / s; the absorption attenuation model is the Kolsky-Futterman model, and its compensation formula is expressed as follows:
[0020] (2)
[0021] in For complex velocity, Reference frequency The corresponding approximate speed value.
[0022] Furthermore, step five specifically includes:
[0023] A. Within each thin plate, the velocity is decomposed into background velocity and disturbance velocity, i.e. ,in The background velocity within the thin plate; The disturbance velocity within the thin plate is given; then the quality factor parameter is decomposed into background parameters. and disturbance parameters ,Right now .
[0024] B. Solving for the imaginary components within the thin plate. and pre-solution factor .
[0025] C As boundary conditions, phase shift compensation is performed in the frequency-wavenumber domain to obtain the background wavefield. The formula for calculating the background wave field is:
[0026] (3)
[0027] in Let x be the transverse wavenumber in the x-direction. For grid spacing, For vertical wavenumber, .
[0028] D. Transform to the frequency space domain For phase shift correction and compensation, the continuation formula is:
[0029] (4)
[0030] in: .
[0031] E. The formula for calculating the forward-propagating scattering migration wave field of the (j+1)th thin plate is as follows:
[0032] (5)
[0033] in For the background wave field, For the (j+1)th thin plate, , , , The background Green function.
[0034] Substituting the result obtained in step D into formula (5), we obtain the forward scattering offset wave field after the correction of the (j+1)th thin plate:
[0035] (6)
[0036] F. Using the forward-propagating scattering offset wave field calculated by formula (6) as the boundary condition for the next thin plate, repeat steps A to E to calculate the forward-propagating scattering offset wave field of the next thin plate. Repeat this process until the forward scattering offset wavefields of all the thin plates are obtained.
[0037] Furthermore, the calculation formula for cross-correlation imaging in step seven is as follows:
[0038] (7)
[0039] Where * represents the conjugate, and W represents the cutoff frequency.
[0040] Compared with existing technologies, this invention first obtains actual seismic records; secondly, it uses an iterative preprocessing extension operator based on thin-plate approximation for viscous acoustic media to calculate the forward-scattering migration field, and then uses the observed data as boundary conditions to calculate the backscattering migration field of the seismic records; finally, it uses cross-correlation imaging conditions to perform scattered wave imaging, obtaining the final migration imaging field. Throughout the process, to avoid the influence of the instability of the Green's function in the strongly disturbed medium background on the imaging results, a small imaginary attenuation component is introduced to improve the divergence problem of the Born series in strongly disturbed media, and a pre-solution factor is used to further accelerate the computational efficiency. To avoid solving large iterative matrices, the velocity model is divided into thin plates using the idea of thin-plate partitioning, thereby transforming global calculations into local calculations, and then constructing an iterative preprocessing extension operator based on thin-plate approximation for viscous acoustic media. In addition, considering the complexity of the actual medium, the Kolsky-Futterman model is used to make the actual model equivalent, which is more consistent with the actual situation. Through the above process, a migration imaging with high efficiency and good accuracy is finally achieved. Attached Figure Description
[0041] Figure 1 This is the overall flowchart of the present invention.
[0042] Figure 2 These are the velocity model parameters and quality factor parameters of this invention embodiment.
[0043] Figure 3 This is the offset imaging result of an embodiment of the present invention. Detailed Implementation
[0044] The present invention will be further described below.
[0045] like Figure 1 As shown, the present invention includes the following steps:
[0046] Step 1: Arrange multiple geophones in a row at equal intervals in the required detection area to form an observation system, and arrange multiple seismic sources in a row at equal intervals and number them. Establish a coordinate system with the X-axis along the direction of each geophone and seismic source and the Z-axis perpendicular to the direction of arrangement, with the origin at (0.0, 0.0). The number of geophones is nx, the distance between adjacent geophones is dr, and the position of the first geophone is (0.0, 0.0). The number of seismic sources is ns, the distance between adjacent seismic sources is ds, and the position of the first seismic source is (0.0, 0.0). The dominant frequency of the wavelet is fHz, the sampling interval is 1ms, and the sampling time length is nt.
[0047] Step 2: Each seismic source is excited sequentially according to its number. The observation system acquires the seismic records at the time of excitation of each source. .
[0048] Step 3: Set the velocity model parameters for the seismic scattered waves propagating in the detection area, and determine the absorption and attenuation model for the seismic scattered waves as they propagate in the detection area, such as... Figure 2 As shown, specifically: the velocity model parameters are ,in The coordinate parameters are defined as follows: the grid parameter for the X-axis is nx, the grid parameter for the Z-axis is nz, and the grid spacings are dx and dz, respectively. The quality factor parameters are calculated based on the velocity model parameters. The specific calculation formula is as follows:
[0049] (1)
[0050] in The unit is km / s; the absorption attenuation model is the Kolsky-Futterman model, and its compensation formula is expressed as follows:
[0051] (2)
[0052] in For complex velocity, Reference frequency The corresponding approximate speed value.
[0053] Step 4: Using the idea of thin plate partitioning, the absorption attenuation model in Step 3 is divided into multiple thin plates along the depth direction, a total of j plates, with a plate thickness of dp, which is usually the thickness of one mesh dz. and These represent the velocity parameter and quality factor parameter within a thin plate, respectively.
[0054] Step 5: Load the Ricker wavelet at the location of the first seismic source. (t is a time parameter), and then transformed to the frequency and wavenumber domain using Fourier transform. ( Using the angular frequency as an initial value, the forward scattering offset wave field of all thin plates is obtained through calculation, specifically:
[0055] A. Within each thin plate, the velocity is decomposed into background velocity and disturbance velocity, i.e. ,in The background velocity within the thin plate; The disturbance velocity within the thin plate is given; then the quality factor parameter is decomposed into background parameters. and disturbance parameters ,Right now .
[0056] B. Solving for the imaginary components within the thin plate. and pre-solution factor .
[0057] C As boundary conditions, phase shift compensation is performed in the frequency-wavenumber domain to obtain the background wavefield. The formula for calculating the background wave field is:
[0058] (3)
[0059] in Let x be the transverse wavenumber in the x-direction. For grid spacing, For vertical wavenumber, .
[0060] D. Transform to the frequency space domain For phase shift correction and compensation, the continuation formula is:
[0061] (4)
[0062] in: .
[0063] E. The formula for calculating the forward-propagating scattering migration wave field of the (j+1)th thin plate is as follows:
[0064] (5)
[0065] in For the background wave field, For the (j+1)th thin plate, , , , The background Green function.
[0066] Substituting the result obtained in step D into formula (5), we obtain the forward scattering offset wave field after the correction of the (j+1)th thin plate:
[0067] (6).
[0068] F. Using the forward-propagating scattering offset wave field calculated by formula (6) as the boundary condition for the next thin plate, repeat steps A to E to calculate the forward-propagating scattering offset wave field of the next thin plate. This process is repeated until the maximum depth of the model is reached, obtaining the forward scattering offset wavefield of all thin plates.
[0069] Step 6: Perform a Fourier transform on the seismic record corresponding to the excitation of the first hypocenter to convert it to the frequency-wavenumber domain. Using this as the initial value, the calculation process in step five is performed to obtain the corresponding backpropagation scattering offset wavefield. .
[0070] Step 7: Using cross-correlation imaging conditions, perform migration imaging on the forward-propagating and backward-propagating migration wavefields obtained in Steps 5 and 6 to obtain the imaging results of the first source. The calculation formula for cross-correlation imaging is as follows:
[0071] (7)
[0072] Where * represents the conjugate, and W represents the cutoff frequency.
[0073] Step 8: Repeat steps 5 to 7 for each seismic source, arranged sequentially by source number, to obtain the imaging results for each source, as follows: , … .
[0074] Step 9: Superimpose the imaging results of all seismic sources, as shown below. Figure 3 As shown, the final offset imaging result of the detection area is obtained. The specific formula is as follows:
[0075] (8).
[0076] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A one-way wave migration method based on a thin-plate approximation for preprocessing viscous acoustic media using an iterative method, characterized in that, Includes the following steps: Step 1: Arrange multiple geophones in a row at equal intervals in the area to be detected to form an observation system, and arrange multiple seismic sources in a row at equal intervals and number them. Step 2: Excite each seismic source in sequence according to its number, and the observation system acquires the seismic record at the time of excitation of each seismic source; Step 3: Set the velocity model parameters for the propagation of seismic scattered waves in the detection area, and determine the absorption and attenuation model for the seismic scattered waves as they propagate in the detection area; Step 4: Using the idea of thin plate division, the absorption attenuation model in Step 3 is divided into multiple thin plates along the depth direction, and the velocity parameters and quality factor parameters in each thin plate are determined. Step 5: Load the Ricker wavelet at the first source location and use Fourier transform to convert it to the frequency wavenumber domain. Use this as the initial value to calculate and obtain the forward scattering offset wavefield of all thin plates. Step 6: Perform Fourier transform on the seismic record corresponding to the excitation of the first source to convert it to the frequency-wavenumber domain, and use it as the initial value to perform calculations using the calculation process in Step 5 to obtain the corresponding backpropagation scattered migration wave field. Step 7: Use cross-correlation imaging conditions to perform migration imaging on the forward-propagating and backward-propagating migration wave fields obtained in Steps 5 and 6 to obtain the imaging results of the first source. Step 8: Repeat steps 5 to 7 for each seismic source in sequence according to the source number to obtain the imaging results of each source. Step 9: Superimpose the imaging results of all seismic sources to obtain the final offset imaging result of the detection area.
2. The one-way wave migration method based on the thin-plate approximation of the viscous acoustic medium pretreatment iterative method according to claim 1, characterized in that, In step one, a coordinate system is established with the X-axis along the direction of each detector and seismic source and the Z-axis perpendicular to the direction of deployment, with the origin at (0.0, 0.0). There are nx detectors, the distance between adjacent detectors is dr, and the position of the first detector is (0.0, 0.0). There are ns seismic sources, the distance between adjacent seismic sources is ds, and the position of the first seismic source is (0.0, 0.0). The dominant frequency of the wavelet is f Hz, the sampling interval is set to l ms, and the sampling time length is nt.
3. The one-way wave migration method based on the thin-plate approximation of viscous acoustic medium pretreatment iterative method according to claim 1, characterized in that, The velocity model parameters in step three are: ,in The coordinate parameters are defined as follows: the grid parameter for the X-axis is nx, the grid parameter for the Z-axis is nz, and the grid spacings are dx and dz, respectively. The quality factor parameters are calculated based on the velocity model parameters. The specific calculation formula is as follows: （1） The absorption attenuation model is the Kolsky-Futterman model, and its compensation formula is expressed as follows: （2） in For complex velocity, Reference frequency The corresponding approximate speed value.
4. The one-way wave migration method based on the thin-plate approximation of the viscous acoustic medium pretreatment iterative method according to claim 1, characterized in that, Step five specifically involves: A. Within each thin plate, the velocity is decomposed into background velocity and disturbance velocity, i.e. ,in The background velocity within the thin plate; The disturbance velocity within the thin plate is given; then the quality factor parameter is decomposed into background parameters. and disturbance parameters ,Right now ; B. Solving for the imaginary components within the thin plate. and pre-solution factor ; C As boundary conditions, phase shift compensation is performed in the frequency-wavenumber domain to obtain the background wavefield. The formula for calculating the background wave field is: （3） in Let x be the transverse wavenumber in the x-direction. For grid spacing, For vertical wavenumber, ; D. Transform to the frequency space domain For phase shift correction and compensation, the continuation formula is: （4） in: ; E. The formula for calculating the forward-propagating scattering migration wave field of the (j+1)th thin plate is as follows: （5） in For the background wave field, For the (j+1)th thin plate, , , , Green function for background; Substituting the result obtained in step D into formula (5), we obtain the forward scattering offset wave field after the correction of the (j+1)th thin plate: （6） F. Using the forward-propagating scattering offset wave field calculated by formula (6) as the boundary condition for the next thin plate, repeat steps A to E to calculate the forward-propagating scattering offset wave field of the next thin plate. Repeat this process until the forward scattering offset wavefields of all the thin plates are obtained.
5. The one-way wave migration method based on the thin-plate approximation of viscous acoustic medium pretreatment iterative method according to claim 1, characterized in that, The calculation formula for cross-correlation imaging in step seven is as follows: （7） Where * represents the conjugate, and W is the cutoff frequency. This is the backpropagation scattering offset wave field.