A double-path wave migration imaging method for VTI medium based on De Wolf approximation

Abstract

The application discloses a VTI medium double-way wave migration imaging method based on De Wolf approximation, and comprises the following steps: firstly, dividing a model into multiple thin plates; then, based on a seismic source, sequentially calculating and obtaining a positive transmission down-going migration wave field and a positive transmission first up-going migration wave field of each thin plate from a minimum depth to a maximum depth; then, calculating a positive transmission up-going migration wave field of each thin plate at different positions from the maximum depth to the minimum depth and adding the reserved positive transmission first up-going migration wave field, so as to finally obtain the positive transmission up-going migration wave field of all the thin plates; then, based on seismic records, obtaining reverse transmission down-going and up-going migration wave fields according to the above calculation process; finally, obtaining all imaging results by using a cross-correlation imaging condition. Not only the down-going migration wave field information can be used, but also the up-going migration wave field information can be used; a double-way wave migration operator is formed by two one-way migration operators, the influence of anisotropic parameters on migration imaging results can be corrected, and finally the migration imaging precision of steeply dipping structures is effectively improved.

Description

Technical Field

[0001] This invention relates to a geophysical exploration method, specifically a VTI medium two-way wave migration imaging method based on the DeWolf approximation. Background Technology

[0002] As oil and gas exploration gradually expands into deeper, deeper water, and unconventional areas, the anisotropy of media has attracted widespread attention from academia and industry. Research on anisotropic media parameters is crucial for improving the accuracy of detection in ultra-deep and deep-sea waters, small-scale targets, and reservoir (fluid) changes. Studies show that most sedimentary rocks exhibit anisotropic characteristics. VTI (Transversely Isotropic Media with Avertically Axis of Symmetry) is an approximate representation of the anisotropic characteristics of actual Earth media (subsurface sedimentary strata are mostly layered, exhibiting lateral isotropic characteristics) and a longitudinally anisotropic model, characterized by a vertical axis of symmetry. Compared to other anisotropic media models, wave field propagation in VTI media is relatively easy to describe and more consistent with reality; therefore, it is often used in seismic migration imaging studies in VTI media.

[0003] The DeWolf approximation splits the scattering potential into forward scattering and backscattering potentials, and renormalizes the incident wave field and Green's function into a forward scattering field and a forward propagation Green's function. The forward scattering field is the sum of an infinite sequence of subsequences including all forward scattering fields, and the forward propagation Green's function is the sum of similar subsequences including all forward scattering corrections to the Green's function. This method aims to address the problem of large calculation errors in the Born approximation when the forward accumulation effect is strong. In 2025, a paper titled "AVTI medium prestack migration method based on the DeWolf approximation" was published in the journal *Computers and Geosciences*. This paper utilizes the one-way wave DeWolf approximation method to achieve pre-stack migration imaging of VTI media, effectively correcting the influence of anisotropic parameters on migration imaging. However, due to the tilt angle limitation of the one-way wave operator, the imaging accuracy is relatively low when constructing images at steep tilt angles.

[0004] To overcome this problem, the research direction of this invention is to provide a new offset imaging method that can effectively improve the imaging accuracy of steeply tilted structures while ensuring computational efficiency. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a VTI medium two-way wave migration imaging method based on the DeWolf approximation. This method combines downlink and uplink migration field information and constructs a two-way wave migration operator using two unidirectional migration operators and performs cross-correlation, thereby effectively improving the imaging accuracy of steep-tilt structures.

[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 parameters and anisotropy parameters of the VTI medium model for the propagation of seismic scattered waves in the detection area.

[0010] Step 4: Using the idea of ​​thin plate division, the VTI medium model from Step 3 is divided into multiple thin plates along the depth direction, and the velocity parameters and anisotropy parameters within each thin plate are determined.

[0011] Step 5: Load the Rack 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 down-propagation offset wavefield and forward up-propagation offset wavefield of all thin plates.

[0012] 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 reverse propagation downlink migration wavefield and reverse propagation uplink migration wavefield of all thin plates.

[0013] Step 7: Using cross-correlation imaging conditions, perform migration imaging on the forward and reverse propagation downlink and uplink migration wavefields 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 anisotropy parameters of the VTI medium model are also specified. and The expression is:

[0018] (1)

[0019] in and These are the maximum speed and the minimum speed, respectively.

[0020] Furthermore, step five specifically includes:

[0021] A. The velocity parameters within the j-th thin plate and anisotropy parameters and Decomposed into background parameters and disturbance parameters, where the background parameters include background velocity. and background anisotropy parameters and The disturbance parameters include velocity disturbances. and anisotropic parameter perturbation and .

[0022] B. Load the Ricker wavelet at the location of the first hypocenter. And it is transformed to the frequency wavenumber domain using Fourier transform. ;make The initial value is, i.e. .

[0023] C. Perform phase-shifting calculations in the frequency-wavenumber domain, including both frequency-wavenumber domain calculations and phase-shifting calculations. , , , .

[0024] (2)

[0025] (3)

[0026] (4)

[0027] (5)

[0028] in:

[0029] (6)

[0030] in for The corresponding transverse wavenumber, , .

[0031] D. Will , , and Transformed into the frequency space domain as follows , , and After correction, the above values ​​are substituted into formulas (7) and (8) to obtain the forward downward offset field of all thin plates. And the forward transmission of the first upward offset wave field .

[0032] (7)

[0033] (8)

[0034] in .

[0035] E. After calculating to the bottom of the model, the forward-propagating upward migration wave field of the second thin plate, sorted from deepest to shallowest. As its forward uplink offset wave field The initial value is calculated according to formula (7) (when calculating the upward wave, the imaginary part i needs to be multiplied by a sign), and the previous forward propagation upward offset wave field of the thin plate is added. The calculation continues using the initial values ​​of the adjacent thin plates above them; until the top of the model, the forward propagation upward migration wavefield of all thin plates is obtained. .

[0036] Furthermore, the calculation formula for cross-correlation imaging in step seven is as follows:

[0037] (9)

[0038] Where * represents the conjugate, and W represents the cutoff frequency.

[0039] Compared to traditional VTI medium one-way wave migration methods based on the DeWolf approximation, this invention first employs the concept of thin-plate partitioning, dividing the model parameters into individual thin plates. This approach not only effectively improves computational efficiency but also enhances the accuracy of subsequent calculations by utilizing each thin plate. Then, based on the seismic source, the forward down-propagation migration wavefield and the first forward up-propagation migration wavefield are calculated sequentially for each thin plate from the deepest to the deepest point. Next, the forward up-propagation migration wavefield is calculated for each thin plate at different locations, from the deepest point to the shallowest point. The first forward up-propagation migration wavefield of each thin plate is added to the previous value as the initial value for the next thin plate, and this process is repeated to obtain the forward up-propagation migration wavefield for all thin plates. Then, the reverse down-propagation migration wavefield and the reverse up-propagation migration wavefield are obtained based on the seismic record following the same calculation process. Finally, all imaging results are obtained using cross-correlation imaging conditions. This invention can utilize both downlink and uplink wavefield information; by using two unidirectional migration operators to form a two-way wave migration operator, it can correct the influence of anisotropic parameters on migration imaging results, and ultimately effectively improve the migration imaging accuracy of steep-tilt structures. Attached Figure Description

[0040] Figure 1 This is the overall flowchart of the present invention.

[0041] Figure 2 These are the velocity model parameters and anisotropy parameters of this invention embodiment.

[0042] Where (a) are velocity model parameters; and (b) are anisotropic parameters. Parameters; (c) Anisotropy parameter;

[0043] Figure 3 This is the offset imaging result of an embodiment of the present invention.

[0044] (a) shows the results of one-way wave imaging; (b) shows the results of two-way wave imaging. Detailed Implementation

[0045] The present invention will be further described below.

[0046] like Figure 1 As shown, the present invention includes the following steps:

[0047] 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.

[0048] 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. .

[0049] Step 3: Set the velocity parameters and anisotropy parameters of the VTI medium model for the propagation of seismic scattered waves in the detection area. Specifically, the velocity model parameters are as follows: ,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 anisotropy parameters of the VTI medium model are also specified. and The expression is:

[0050] (1)

[0051] in and These are the maximum speed and the minimum speed, respectively.

[0052] Step 4: Using the idea of ​​thin plate partitioning, the VTI medium model from Step 3 is divided into multiple thin plates along the depth direction, totaling j plates. The thickness of each thin plate is dp, which is usually the thickness of one mesh, dz. , and Represent the velocity parameters and anisotropy parameters within a thin plate, respectively. Figure 2 As shown.

[0053] 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 downshifting offset wavefield and forward upshifting offset wavefield of all thin plates are obtained through calculation, specifically:

[0054] A. The velocity parameters within the j-th thin plate and anisotropy parameters and Decomposed into background parameters and disturbance parameters, where the background parameters include background velocity. and background anisotropy parameters and The disturbance parameters include velocity disturbances. and anisotropic parameter perturbation and .

[0055] B. Load the Ricker wavelet at the location of the first hypocenter. And it is transformed to the frequency wavenumber domain using Fourier transform. ;make The initial value is, i.e. .

[0056] C. Perform phase-shifting calculations in the frequency-wavenumber domain, including both frequency-wavenumber domain calculations and phase-shifting calculations. , , , .

[0057] (2)

[0058] (3)

[0059] (4)

[0060] (5)

[0061] in:

[0062] (6)

[0063] in for The corresponding transverse wavenumber, , .

[0064] D. Will , , and Transformed into the frequency space domain as follows , , and After correction, the above values ​​are substituted into formulas (7) and (8) to obtain the forward downward offset field of all thin plates. And the forward transmission of the first upward offset wave field .

[0065] (7)

[0066] (8)

[0067] in .

[0068] E. After calculating to the bottom of the model, the forward-propagating upward migration wave field of the second thin plate, sorted from deepest to shallowest. As its forward uplink offset wave field The initial value is calculated according to formula (7) (when calculating the upward wave, the imaginary part i needs to be multiplied by a sign), and the previous forward propagation upward offset wave field of the thin plate is added. The calculation continues using the initial values ​​of the adjacent thin plates above them; until the top of the model, the forward propagation upward migration wavefield of all thin plates is obtained. .

[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 reverse propagation downlink offset wavefield. and reverse transmission uplink wave field .

[0070] Step 7: Using cross-correlation imaging conditions, perform migration imaging on the forward and reverse propagation downlink and uplink migration wavefields obtained in Steps 5 and 6 to obtain the imaging results of the first source. The specific calculation formula is as follows:

[0071] (9)

[0072] Where * represents the complex 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] (10).

[0076] Figure 3As can be seen from the comparison between existing single-path imaging and the two-path imaging of the present invention, the imaging of the present invention is more refined.

[0077] 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 VTI medium two-way wave migration imaging method based on the DeWolf approximation, 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 parameters and anisotropy parameters of the VTI medium model for the propagation of seismic scattered waves in the detection area; Step 4: Using the idea of ​​thin plate partitioning, the VTI medium model from Step 3 is divided into multiple thin plates along the depth direction, and the velocity parameters and anisotropy parameters within each thin plate are determined. Step 5: Load the Rack wavelet at the first source location and convert it to the frequency wavenumber domain using Fourier transform. Use this as the initial value to calculate and obtain the forward down-propagation offset wavefield and forward up-propagation 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 reverse propagation downlink migration wavefield and reverse propagation uplink migration wavefield of all thin plates. Step 7: Using cross-correlation imaging conditions, perform migration imaging on the forward and reverse propagation downlink and uplink migration 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 VTI medium two-way wave migration imaging method based on the DeWolf approximation 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 the layout, 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 fHz, the sampling interval is set to 1ms, and the sampling time length is nt.

3. The VTI medium two-way wave migration imaging method based on the DeWolf approximation 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 anisotropy parameters of the VTI medium model are also specified. and The expression is: （1） in and These are the maximum speed and the minimum speed, respectively.

4. The VTI medium two-way wave migration imaging method based on the DeWolf approximation according to claim 1, characterized in that, Step five specifically involves: A. The velocity parameters within the j-th thin plate and anisotropy parameters and Decomposed into background parameters and disturbance parameters, where the background parameters include background velocity. and background anisotropy parameters and The disturbance parameters include velocity disturbances. and anisotropic parameter perturbation and ; B. Load the Ricker wavelet at the location of the first hypocenter. And it is transformed to the frequency wavenumber domain using Fourier transform. ,make The initial value is, i.e. ; C. Perform phase-shifting calculations in the frequency-wavenumber domain, including both frequency-wavenumber domain calculations and phase-shifting calculations. , , , ; （2） （3） （4） （5） in: （6） in for The corresponding transverse wavenumber, , ; D. Will , , and Transformed into the frequency space domain as follows , , and After correction, the above values ​​are substituted into formulas (7) and (8) to obtain the forward downward offset field of all thin plates. And the forward transmission of the first upward offset wave field : （7） （8） in ; E. After calculating to the bottom of the model, the forward-propagating upward migration wave field of the second thin plate, sorted from deepest to shallowest. As its forward uplink offset wave field The initial value is calculated according to formula (7), and the forward propagation of the thin plate during the first upward offset wave field is added. The calculation continues using the initial values ​​of the adjacent thin plates above them; until the top of the model, the forward propagation upward migration wavefield of all thin plates is obtained. .

5. The VTI medium two-way wave migration imaging method based on the DeWolf approximation according to claim 1, characterized in that, The calculation formula for cross-correlation imaging in step seven is as follows: （9） Where * represents the conjugate, and W represents the cutoff frequency.

Images