A method, system, and medium for display stability compensated viscoacoustic reverse-time migration

Abstract

The application relates to a kind of based on display stable compensation viscous anisotropic reverse time migration method, system and medium, comprising: by explicit stable compensation constant fractional order viscous wave equation and perfectly matched layer absorbing boundary condition, from initial time, along time direction forward solution, obtain the seismic wave field value of all time; By explicit stable compensation constant fractional order viscous wave equation and perfectly matched layer absorbing boundary condition, along time negative direction reconstruction seismic wave field;From the maximum time, along time direction negative solution, obtain the seismic wave field value of all time at geophone point;According to seismic wave field and geophone point seismic wave field, obtain underground structure imaging result.It can stably compensate the amplitude attenuation phenomenon, does not produce high frequency abnormal value, in the case where quality factor Q changes sharply with space, amplitude compensation and migration imaging can also be accurately carried out, ensure that stratum phase axis is reasonably and correctly homing.

Description

Technical Field

[0001] This invention relates to a viscoacoustic reverse time migration method, system, and readable medium based on explicit stability compensation, belonging to the field of exploration physical geoscience. Background Technology

[0002] Seismic exploration technology is one of the core technologies for finding oil and gas resources, and seismic wavefield imaging technology plays a pivotal role in seismic exploration. However, as exploration and development continue to deepen, the target areas are gradually moving from shallow to deep layers, and the exploration objects are becoming increasingly complex. Therefore, in order to improve the accuracy of identifying deep underground oil and gas-bearing areas, it is urgent to improve imaging theory methods and imaging accuracy.

[0003] Pre-stack reverse time migration (RTM) based on the two-way wave equation is one of the most popular techniques in the imaging field. This method has a low approximation of seismic waves, is not limited by formation dip angle, and theoretically can accurately image multiple seismic wave fields simultaneously. However, most current RTM techniques often neglect the viscoelastic behavior of the subsurface medium, assuming that seismic waves do not experience energy attenuation or phase shift during propagation. However, since the actual subsurface medium is viscoelastic, seismic waves experience amplitude attenuation and phase shift during propagation, especially in oil and gas-rich formations where amplitude absorption and attenuation are particularly severe. If the viscoelastic effect of the subsurface medium is ignored, the amplitude and phase errors of the seismic waves will accumulate during propagation, severely affecting the final imaging results and making it impossible to accurately identify the location of subsurface oil and gas-bearing areas, thus increasing acquisition costs. Therefore, the viscous acoustic wave RTM imaging method, which considers formation absorption and attenuation, is more realistic.

[0004] Currently, there are two widely used viscous wave equations: one is the viscous wave equation based on the constant Q model, which originates from the constant Q theory proposed by Kjartansson (Constant Q-wave propagation and attenuation, Kjartansson, E., Journal of Geophysical Research Solid Earth, Vol. 84, No. 9, 4737-4748, 1979); the other is the viscous wave equation based on the standard linear body model, which was first introduced into seismic wave propagation theory by Carcione et al. (Wavepropagation simulation in a linear Viscoelastic medium, Carcione, JM, D. Kosloff, and R. Kosloff, Geophysical Journal International, Vol. 95, No. 3, 393-401, 1988). In actual seismic exploration, the effective frequency of seismic signals is mostly below 150Hz. At this frequency, the subsurface medium satisfies the constant quality factor Q condition, meaning the quality factor Q does not change with frequency. Furthermore, compared to the generalized standard linear body model, the amplitude attenuation and phase dispersion effects in the decoupled constant quality factor Q viscous acoustic wave equation are decoupled, and fewer characterization parameters are required. Therefore, compared to the viscous acoustic wave equation based on the standard linear body model, the constant Q decoupled viscous acoustic wave equation better meets the needs of seismic exploration.

[0005] Zhu (Q-compensated reverse-time migration, Zhu, T., Harris, JM, and Biondi, B., Geophysics, Vol. 79, No. 3, S77-S87, 2014) proposed a viscous acoustic equation based on a decoupled fractional Laplace operator, building upon the constant Q theory. This equation has advantages such as relatively small computational and storage requirements and ease of implementation, making it a good method for realizing viscous acoustic reverse-time migration. However, this method still faces several problems in its implementation. First, due to the continuous accumulation of the viscosity effect of the medium, the amplitude energy of the imaging results of deep phase axes is extremely weak, making it impossible to accurately identify deep subsurface structures. To solve this problem, Zhu (2014) directly changed the sign of the amplitude attenuation term in the equation for energy compensation. However, using this compensation method generates a large number of high-frequency anomalies during the propagation of seismic waves, reducing the signal-to-noise ratio of the imaging profile and making it impossible to identify effective geological structures. To address the problem of high-frequency anomalies in the compensation, Zhu (2014) introduced an additional low-pass filter. However, selecting the low-pass filter parameters is extremely difficult; furthermore, high-frequency anomalies increase exponentially over time, while the filtering effect of the low-pass filter remains constant. Therefore, this method results in the loss of some high-frequency information. Secondly, solving this viscosity equation currently requires calculating the fractional-order Laplace operator in the wavenumber domain. However, the exponent of the fractional-order operator is related to the quality factor Q, which describes the attenuation of seismic waves, and the quality factor Q varies with the spatial domain location. Therefore, the variable fractional-order Laplace operator is a wavenumber-space hybrid domain problem, but directly solving hybrid domain problems mathematically is very difficult. To address this issue, a feasible approach is to calculate using the average quality factor Q globally. However, this method is only suitable when the quality factor Q varies little with space. When the underground structure is complex, the quality factor Q varies drastically with spatial location, introducing a large average error. Summary of the Invention

[0006] To address the aforementioned problems, the present invention aims to provide a viscoacoustic reverse time migration method, system, and readable medium based on explicit stable compensation. This method can stably compensate for amplitude attenuation without generating high-frequency anomalies. It approximates the variational fractional-order Laplace operator as a constant fractional-order Laplace operator. Even when the quality factor Q varies drastically with space, it can accurately perform amplitude compensation and migration imaging, ensuring the reasonable and correct repositioning of the formation phase axis.

[0007] To achieve the above objectives, the present invention proposes the following technical solution: a viscoacoustic reverse time migration method based on explicit stability compensation, comprising: reading the coordinates of the source and receiver points and generating a Ricker wavelet; generating an explicit stability-compensated constant fractional-order viscoacoustic wave equation based on the Ricker wavelet; solving the source seismic wave field values ​​at all times in the forward direction of time starting from the initial time using the explicit stability-compensated constant fractional-order viscoacoustic wave equation and perfectly matched layer absorbing boundary conditions; reconstructing the source wave field in the negative time direction using the source seismic wave field values ​​as initial conditions using the explicit stability-compensated constant fractional-order viscoacoustic wave equation and perfectly matched layer absorbing boundary conditions; solving the receiver seismic wave field values ​​at all times in the negative time direction starting from the maximum time using the explicit stability-compensated constant fractional-order viscoacoustic wave equation and perfectly matched layer absorbing boundary conditions; and obtaining subsurface structural imaging results based on the source wave field and receiver seismic wave field.

[0008] Furthermore, the constant fractional order viscous acoustic wave equation for explicit stable compensation is obtained by performing two first-order Taylor expansions on the viscous acoustic wave equation for explicit stable compensation, replacing the variable fractional order Laplace operator of the stable compensation equation with a constant fractional order Laplace operator.

[0009] Furthermore, the viscous acoustic wave equation for explicit stable compensation is:

[0010]

[0011]

[0012] in, p is the pressure wave field, t is time, c0 is the medium velocity, Q is the quality factor, ω0 is the reference angular frequency, and β and σ are both parameters for stability compensation.

[0013] Furthermore, the viscous acoustic wave equation for explicit stable compensation is:

[0014]

[0015] Where λ=(ω d / ω0) 2γ ξ is an empirical constant, ω d It is the angular frequency, and α is the compensation coefficient.

[0016] Furthermore, the time derivative of the constant fractional viscous acoustic wave equation for explicit stable compensation is solved using the finite difference method, and the spatial operator is obtained using the pseudospectral method. The accuracy of the time derivative is second-order, and the accuracy of the spatial operator is spectral.

[0017] Furthermore, the constant fractional viscous acoustic wave equation for explicit stability compensation is computed in parallel using multiple GPUs, while the Fourier transform of the spatial derivative is accelerated using CUFFT in the CUDA command.

[0018] This invention also discloses a system for improving seismic profile resolution based on attenuated synthetic records, comprising: a Ricker wavelet generation module for reading the coordinates of the source and receiver points and generating a Ricker wavelet; a wave equation generation module for generating an explicitly stable compensated constant fractional-order viscous acoustic wave equation based on the Ricker wavelet; and a time-dependent source seismic wave field value calculation module for solving, from the initial time, in a forward direction using the explicitly stable compensated constant fractional-order viscous acoustic wave equation and perfectly matched layer absorbing boundary conditions, to obtain the source seismic wave field values ​​at all times; and a source wave field... The reconstruction module is used to reconstruct the source wavefield along the negative time direction using the source seismic wavefield value as the initial condition and through the explicitly stable compensated constant fractional-order viscous acoustic wave equation and the perfectly matched layer absorbing boundary condition. The reverse-time receiver seismic wavefield value calculation module solves along the negative time direction starting from the maximum time using the explicitly stable compensated constant fractional-order viscous acoustic wave equation and the perfectly matched layer absorbing boundary condition to obtain the receiver seismic wavefield values ​​at all times. The result output module is used to obtain the subsurface structure imaging results based on the source wavefield and the receiver seismic wavefield.

[0019] Furthermore, the constant fractional order viscous acoustic wave equation for explicit stable compensation is obtained by performing two first-order Taylor expansions on the viscous acoustic wave equation for explicit stable compensation, replacing the variable fractional order Laplace operator of the stable compensation equation with a constant fractional order Laplace operator.

[0020] Furthermore, the viscous acoustic wave equation for explicit stable compensation is:

[0021]

[0022]

[0023] in, p is the pressure wave field, t is time, c0 is the medium velocity, Q is the quality factor, ω0 is the reference angular frequency, β and σ are both stability compensation parameters, and λ = (ω d / ω0) 2γ ξ is an empirical constant (taken as 1 / 16 in this paper), ω d It is the angular frequency, and α is the compensation coefficient.

[0024] The present invention also discloses a computer-readable storage medium storing a computer program, which is executed by a processor to implement the adhesive acoustic reverse-time migration method based on explicit stability compensation as described in any of the preceding claims.

[0025] The present invention has the following advantages due to the adoption of the above technical solutions:

[0026] 1. Conventional acoustic wave equations neglect the absorption and attenuation effect of the strata and cannot accurately describe the propagation law of seismic waves underground. Compared with the viscosity-acoustic equation based on the standard linear body, the quality factor Q value in this invention is explicitly expressed in the equation and uses fewer model parameters, which is more conducive to its extension to full waveform inversion and least squares inverse migration.

[0027] 2. By introducing a time-varying stable amplitude compensation term into the wave equation, the problem of high-frequency outliers caused by direct compensation is alleviated without introducing an additional low-pass filter. Furthermore, this algorithm is theoretically easier to solve for the wave field using the finite difference method.

[0028] 3. The present invention uses a constant fractional Laplace operator, which can accurately compensate the wave field point by point even when the quality factor Q value varies drastically with space, providing more accurate input results for the calculation of viscous acoustic reverse time migration;

[0029] 4. The adhesive acoustic reverse time migration imaging process based on explicit stability compensation improves the signal-to-noise ratio and resolution of imaging profiles in complex structural regions, which is beneficial for accurately identifying subsurface structures and predicting reservoir intervals in seismic data interpretation. Attached Figure Description

[0030] Figure 1 This is a flowchart of a viscosity-acoustic reverse-time migration method based on explicit stability compensation in one embodiment of the present invention;

[0031] Figure 2 This is a maximum error diagram for different Q values ​​and frequencies when ζ = 1 / 16 in one embodiment of the present invention; wherein, Figure 2 (a) is the maximum error graph corresponding to the main frequency of 10Hz, 30Hz and 60Hz when Q is 10; Figure 2 (b) is a graph showing the maximum error at main frequencies of 10Hz, 30Hz, and 60Hz when Q is 40. Figure 2 (c) is the maximum error graph corresponding to the main frequency of 10Hz, 30Hz, and 60Hz when Q is 80. Figure 2 (d) is the maximum error graph corresponding to the main frequency of 10Hz, 30Hz and 60Hz when Q is 100;

[0032] Figure 3 Figure 150ms is a snapshot of the wave field of different equations in one embodiment of the present invention. Figure 150ms is a snapshot of the wave field of the acoustic equation, Figure 150ms is a snapshot of the wave field considering the absorption and attenuation properties of the formation, Figure 150ms is a snapshot of the wave field of direct compensation, and Figure 150ms is a snapshot of the wave field of the method of the present invention.

[0033] Figure 4This is a wavefield snapshot at 300ms in one embodiment of the present invention;

[0034] Figure 5 This refers to the 150ms time in one embodiment of the present invention. At that time, the wave field snapshots obtained by taking different compensation parameters σ for the constant fractional viscous acoustic wave equation with explicit stable compensation are shown below. Figure 5 (a) is a snapshot of the wave field when the compensation parameter σ is 0.5; Figure 5 (b) is a snapshot of the wave field when the compensation parameter σ is 1. Figure 5 (c) is a snapshot of the wavefield when the compensation parameter σ is 1.5. Figure 5 (d) is a snapshot of the wave field when the compensation parameter σ is 3;

[0035] Figure 6 This is a snapshot of the wave field obtained by taking different stability compensation parameters for the constant fractional-order viscous acoustic wave equation with explicit stability compensation when the compensation parameter is 1 at 150ms in one embodiment of the present invention. Figure 6 (a) is A snapshot of the wave field at that time; Figure 6 (a) is A snapshot of the wave field at that time; Figure 6 (c) is A snapshot of the wave field at that time. Figure 6 (d) is A snapshot of the wave field at that time;

[0036] Figure 7 This is a reverse-time migration imaging image of a complex medium according to an embodiment of the present invention. Figure 7 (a) is an image of the velocity model of the medium; Figure 7 (b) is the imaging effect diagram of the corresponding Q model; Figure 7 (c) is the imaging effect diagram of the uncompensated viscosity equation; Figure 7 (d) is the imaging effect without considering the effect of the quality factor Q; Figure 7 (e) is an image showing the effect of variable fractional order compensation; Figure 7 (f) is a seismic profile obtained by the method in Example 1;

[0037] Figure 8 This is a single-track information map at a horizontal position of 3500km in one embodiment of the present invention. Detailed Implementation

[0038] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention is described in detail through specific embodiments. However, it should be understood that the specific embodiments are provided only for a better understanding of the present invention and should not be construed as limiting the present invention. In the description of the present invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0039] To meet the oil and gas industry's demand for accurate imaging of subsurface elastic media and address the problems of unstable amplitude compensation and difficulty in obtaining the variational fractional Laplace operator in existing technologies for decoupled viscous acoustic equations, this invention proposes a viscous acoustic reverse-time migration method, system, and readable medium based on explicit stable compensation. It employs a constant Q viscous acoustic equation with decoupled amplitude and phase, compensating for amplitude without changing the phase, ensuring correct alignment of the formation phase axis. The wave equation used explicitly expresses the compensation operator within it, making the operator's physical meaning clear and time-varying. It automatically and stably compensates for amplitude energy during wave propagation without generating high-frequency anomalies. This facilitates direct solution of the wave equation using the finite difference method and solves the problem of high-frequency anomalies caused by direct amplitude compensation. By utilizing two first-order Taylor expansions, the variational fractional Laplace operator in the compensation equation is approximated as a constant fractional operator, enabling accurate amplitude compensation and migration imaging even when the Q value varies drastically with space. The following detailed description, with reference to the accompanying drawings and embodiments, illustrates the invention in detail.

[0040] Example 1:

[0041] This embodiment discloses a viscosity-acoustic reverse-time migration method based on explicit stability compensation, such as... Figure 1 As shown, it includes:

[0042] S1 reads the coordinates of the seismic source and receiver points and generates the Ricker wavelet;

[0043] S2 generates a constant fractional-order viscous acoustic wave equation with explicit stability compensation based on the Reich wavelet.

[0044] The process of establishing the constant fractional-order viscous acoustic wave equation for explicit stable compensation is as follows:

[0045] The viscous acoustic wave equation for explicit stable compensation is:

[0046]

[0047]

[0048] in, p is the pressure wave field, t is time, c0 is the medium velocity, Q is the quality factor, ω0 is the reference angular frequency, and β and σ are both parameters for stability compensation.

[0049] In the formula For phase delay term, For amplitude compensation, and For phase correction, For the stable amplitude term. Among them,

[0050] The wave equation (1) contains amplitude stabilization compensation terms with explicit physical meaning. Therefore, seismic waves can stably compensate for amplitude attenuation during propagation without generating high-frequency anomalies, eliminating the need for a low-pass filter during wavefield extension. Furthermore, compared to implicit compensation methods, this embodiment does not require additional calculation of the stabilization operator in the wavenumber domain. However, the wave equation (1) still has a problem: the fractional-order operator in the wave equation is a mixed-domain operator that varies between the wavenumber and spatial domains, and it is mathematically very difficult to directly obtain the mixed-domain operator. To address this problem, this embodiment uses two first-order Taylor expansions to approximate the variable fractional-order Laplace operator of the stabilization compensation equation as a constant fractional-order Laplace operator. The specific process is as follows:

[0051] First, assuming the seismic wave propagates in a homogeneous medium, substituting the plane wave equation into the wave equation (1), we obtain the frequency-wavenumber domain equation:

[0052]

[0053] in, It is a wave field in the wavenumber domain, where k is the wavenumber.

[0054] This embodiment uses fractional operators. Taking an example, we approximate the formula to obtain the following expression:

[0055]

[0056] in, w d =2πf d f d Main frequency, k d The dominant wavenumber.

[0057] right A first-order Taylor expansion yields:

[0058]

[0059] Since the wavenumber distribution of seismic waves follows a normal distribution, the wavenumber in the seismic wavefield is approximately equal to the dominant wavenumber; and since the Q value is generally greater than 10 in practical applications, γ < 0.0318. It can be transformed into:

[0060]

[0061] Where ξ is an empirical constant, preferably 1 / 16 in this embodiment, obtained through a first-order Taylor expansion. Can Modified to

[0062] Will Substituting into formula (6), we get:

[0063]

[0064] Substituting formula (7) into formula (4), formula (4) can be approximated as:

[0065]

[0066] Using the same method to approximate the remaining fractional terms in formula (3), we can obtain the approximate wave equation:

[0067]

[0068]

[0069] Where ξ is an empirical constant and α is a compensation coefficient.

[0070] S3 uses a constant fractional-order viscous acoustic wave equation with explicit stability compensation and a perfectly matched layer absorbing boundary condition to suppress boundary reflections. It solves the source seismic wave field values ​​at all times in the forward direction of time, starting from the initial moment.

[0071] The absorbing boundary condition employs a fully matched layer to absorb boundary reflections in the numerical simulation.

[0072] S4 uses the source seismic wave field value as the initial condition, and suppresses boundary reflection through the constant fractional-order viscous acoustic wave equation with explicit stability compensation and the perfectly matched layer absorbing boundary condition, and reconstructs the source wave field along the negative time direction.

[0073] S5 uses a constant fractional-order viscous acoustic wave equation with explicit stability compensation and a perfectly matched layer absorbing boundary condition to suppress boundary reflections. It solves in the negative time direction starting from the maximum moment to obtain the seismic wave field values ​​of the receiver at all moments.

[0074] S6 obtains subsurface structural imaging results based on the source wavefield and receiver wavefield. Specifically, it processes the source and receiver wavefield information of all shots using imaging conditions, and obtains the subsurface structural imaging results after denoising.

[0075] In this embodiment, the time derivative of the constant fractional viscous acoustic wave equation for explicit stable compensation is solved using the finite difference method, and the spatial operator is obtained using the pseudospectral method. The accuracy of the time derivative is second-order, and the accuracy of the spatial operator is spectral. The constant fractional viscous acoustic wave equation for explicit stable compensation is computed in parallel using multiple GPUs (Graphics Processing Units), and the Fourier transform of the spatial derivative is accelerated using the CUDA (Compute Unified Device Architecture) command CUFFT (CUDA FastFourier Transform).

[0076] This embodiment achieves stable compensation using viscous-acoustic reverse-time migration. It maintains good stability and accuracy even when calculating complex media.

[0077] Example 2:

[0078] Based on the same inventive concept, this embodiment verifies the correctness of the results of the embodiment. A homogeneous model is designed with the following parameters: model size of 200*200 grid points, velocity of c0 = 2000 m / s, spatial step size of 20 m, and ω is set. d =ω0λ=1, the formula for calculating the wave number is as follows;

[0079]

[0080] Where, k ix is the spatial position of the wavenumber, ix is ​​the spatial position in the x-direction, and nx is the number of sampling points in the x-direction.

[0081] The optimal ζ value, which minimizes the maximum error, is determined by the following formula:

[0082]

[0083] Among them, E sum It is the approximate total error, f e (k) is the term on the left-hand side of Formula 8, f a (k) is the term on the right side of the equation in Formula 8, where k is the wave number.

[0084]

[0085]

[0086] The calculation results of the optimal ζ values ​​for different frequencies and Q values ​​are shown in Table 1.

[0087] To obtain the accuracy of the wave equation approximation when ζ is 1 / 16, the following formula is used to test the maximum error E for different Q values ​​and frequencies. max .

[0088]

[0089] The calculation results are as follows Figure 2 As shown in Table 2.

[0090] Table 1. Optimal ζ values ​​for different frequencies and Q values.

[0091]

[0092] Table 2. Maximum error for different Q values ​​and frequencies when ζ = 1 / 16.

[0093]

[0094] According to Table 1, Table 2 and Figure 2 It can be seen that: (1) the optimal ζ is related to the Q value and is independent of the frequency; (2) as the Q value increases, the optimal ζ continuously decreases; (3) as shown in Table 2, the maximum error is less than 1 percent when using ζ = 1 / 16. Therefore, the approximate results in this embodiment can meet the requirements of wave field simulation.

[0095] The accuracy of simulating seismic wave propagation was tested using a uniform velocity model, a wave equation considering formation absorption and attenuation, a directly compensated wave equation, and a constant fractional viscous acoustic wave equation with explicit stable compensation in Example 1.

[0096] The velocity of the uniform model is c0 = 2000 m / s, with 200 grids in both the horizontal and vertical directions and a grid spacing of 10 m. The number of absorbing boundary layers is 100. A Ricker wavelet with a dominant frequency of 20 Hz is used as the excitation source, with a time sampling interval of 1 ms, and the source is placed at the center of the model. If the Q value is extremely large, the constant fractional-order viscous acoustic wave equation with explicit stability compensation in this embodiment degenerates into an acoustic wave equation. Figure 3 This is a snapshot of the wave field for different wave equations at 150ms. Figure 3 (a) is a snapshot of the wave field of the acoustic wave equation; Figure 3 (b) is a snapshot of the wave field of the wave equation considering the absorption and attenuation properties of the formation; Figure 3 (c) is a snapshot of the wave field of the wave equation for direct compensation; Figure 3 (d) is a snapshot of the wave field of the constant fractional-order viscous acoustic wave equation with explicit stable compensation, where β takes the value 2.

[0097]

[0098] Figure 4 A snapshot of the wavefield at 300 ms for the constant fractional-order viscous acoustic wave equation with explicit stability compensation. Figure 3(a)-(d) The constant fractional viscous acoustic wave equation with explicit stable compensation in Example 1 can effectively decouple the amplitude attenuation and phase delay effects, and effectively compensate for the amplitude energy without changing the phase. Figure 4 This demonstrates that the absorbing boundary conditions of the method in Example 1 can effectively eliminate artificial boundary reflection errors. Figure 5 Wave field snapshots obtained for the constant fractional viscous acoustic wave equation with different compensation parameters for explicit stability compensation. Figure 5 (a) is a snapshot of the wave field when the compensation parameter σ is 0.5; Figure 5 (b) is a snapshot of the wave field when the compensation parameter σ is 1. Figure 5 (c) is a snapshot of the wavefield when the compensation parameter σ is 1.5. Figure 5 (d) is a snapshot of the wave field when the compensation parameter σ is 3. Figure 6 These are snapshots of the wave field obtained by taking different stability compensation parameters for the constant fractional-order viscous acoustic wave equation with explicit stability compensation when the compensation parameter is 1 at 150ms. Figure 6 (a) is A snapshot of the wave field at that time; Figure 6 (a) is A snapshot of the wave field at that time; Figure 6 (c) is A snapshot of the wave field at that time. Figure 6 (d) is A snapshot of the wave field at that time; via Figure 5 , Figure 6 It can be seen that the lower the stability order β, the larger the stability factor σ, and the stronger the compensated amplitude energy.

[0099] The superiority of one imaging method in the following example is tested using a complex Marmousi2 model:

[0100] One method from Example 1 is used to perform reverse time migration imaging tests on the complex Marmousi2 model. Figure 7 (a) is an image of the velocity model of the medium; Figure 7 (b) is the imaging effect diagram of the corresponding Q model; Figure 7 (c) is the imaging effect diagram of the uncompensated viscosity equation; Figure 7 (d) is the imaging effect without considering the effect of the quality factor Q; Figure 7 (e) is an image showing the effect of variable fractional order compensation; Figure 7 (f) is a seismic profile obtained using the method described in Example 1. From Figure 7As can be seen, in practice, without amplitude compensation, the imaging results of deep layers are very weak due to the absorption and attenuation effect of the strata; if the phase axis of the imaging result obtained by solving the fractional-order operator using the average Q value method is misaligned, it is impossible to correctly identify the structural location; the imaging results obtained using this patent have accurate spatial positioning of the structural bodies and clear fault edges, achieving accurate imaging of complex structures, proving the correctness and superiority of the method in this embodiment. The single-channel information extracted in this embodiment is as follows: Figure 8 As shown, through Figure 8 It is known that the existing methods have problems such as uneven energy compensation, low resolution, and phase shift of the structure, which makes it impossible to correctly image the underground structure. The method in Example 1 solves the above problems and obtains a more accurate and realistic underground structure map.

[0101] Example 3:

[0102] Based on the same inventive concept, this embodiment discloses a system for improving seismic profile resolution based on attenuation synthetic records, including:

[0103] The Lake wavelet generation module is used to read the coordinates of the seismic source and receiver points and generate Lake waves.

[0104] The wave equation generation module is used to generate a constant fractional-order viscous acoustic wave equation with explicit stability compensation based on the Ricker wavelet.

[0105] The forward-clockwise source seismic wave field value calculation module is used to solve the source seismic wave field value in the forward direction of time from the initial time using the constant fractional-order viscous acoustic wave equation with explicit stability compensation and the perfectly matched layer absorbing boundary condition, so as to obtain the source seismic wave field value at all times.

[0106] The source wavefield reconstruction module is used to reconstruct the source wavefield along the negative time direction by taking the source seismic wavefield value as the initial condition and using the constant fractional-order viscous acoustic wave equation with explicit stability compensation and the perfectly matched layer absorbing boundary condition.

[0107] The reverse-time receiver seismic wave field value calculation module uses the constant fractional-order viscous acoustic wave equation with explicit stability compensation and the perfectly matched layer absorbing boundary condition to solve in the negative time direction starting from the maximum time, and obtains the receiver seismic wave field values ​​at all times.

[0108] The results output module is used to obtain subsurface structural imaging results based on the source wavefield and receiver seismic wavefield.

[0109] The constant fractional order viscous acoustic wave equation for explicit stable compensation is obtained by performing two first-order Taylor expansions on the viscous acoustic wave equation for explicit stable compensation, and replacing the variable fractional order Laplace operator of the stable compensation equation with the constant fractional order Laplace operator.

[0110] The viscous acoustic wave equation for explicit stable compensation is:

[0111]

[0112]

[0113] in, p is the pressure wave field, t is time, c0 is the medium velocity, Q is the quality factor, ω0 is the reference angular frequency, β and σ are both stability compensation parameters, and ξ is an empirical constant (taken as 1 / 16 in this paper). w d =2πf d f d Main frequency, k d The dominant wavenumber is α, and the compensation coefficient is α.

[0114] Example 4:

[0115] Based on the same inventive concept, this embodiment discloses a computer-readable storage medium storing a computer program, which is executed by a processor to implement any of the above-mentioned adhesive acoustic reverse time migration methods based on explicit stability compensation.

[0116] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0117] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0118] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0119] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific embodiments of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention. The above content is only a specific embodiment of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be covered within the protection scope of this application. Therefore, the protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A viscosity-acoustic reverse-time migration method based on explicit stability compensation, characterized in that, include: Read the coordinates of the seismic source and receiver points and generate the Ricker wavelet; The constant fractional-order viscous acoustic wave equation with explicit stability compensation is generated based on the described Lake wavelet. By using the explicit stability compensation constant fractional-order viscous acoustic wave equation and the perfectly matched layer absorbing boundary condition, the source seismic wave field values ​​at all times are obtained by solving in the forward direction along the time direction starting from the initial time. Using the source seismic wave field value as the initial condition, the source wave field is reconstructed along the negative time direction through the explicit stability compensation constant fractional-order viscous acoustic wave equation and the perfectly matched layer absorbing boundary condition. By using the constant fractional-order viscous acoustic wave equation with explicit stability compensation and the perfectly matched layer absorbing boundary condition, the seismic wave field values ​​at all receiver points are obtained by solving in the negative time direction starting from the maximum time. The subsurface structural imaging results were obtained based on the source wavefield and the receiver wavefield.

2. The adhesive acoustic reverse-time migration method based on explicit stability compensation as described in claim 1, characterized in that, The constant fractional order viscous acoustic wave equation for explicit stable compensation is obtained by performing two first-order Taylor expansions on the viscous acoustic wave equation for explicit stable compensation, and replacing the variable fractional order Laplace operator of the stable compensation equation with the constant fractional order Laplace operator.

3. The adhesive acoustic reverse-time migration method based on explicit stability compensation as described in claim 2, characterized in that, The viscous acoustic wave equation for explicit stable compensation is: in, , p It is a pressure wave field, where t is time. It is the velocity of the medium. For quality factors, It is the reference angular frequency. and These are all parameters for stable compensation.

4. The viscosity-acoustic reverse-time migration method based on explicit stability compensation as described in claim 3, characterized in that, The viscous acoustic wave equation for explicit stable compensation is: in, , These are empirical constants. It is angular frequency. This is the compensation coefficient.

5. The adhesive acoustic reverse-time migration method based on explicit stability compensation as described in any one of claims 1-4, characterized in that, The time derivative of the constant fractional viscous acoustic wave equation for explicit stable compensation is solved using the finite difference method, and the spatial operator is obtained using the pseudospectral method. The accuracy of the time derivative is second-order, and the accuracy of the spatial operator is spectral.

6. The adhesive acoustic reverse-time migration method based on explicit stability compensation as described in any one of claims 1-4, characterized in that, The constant fractional viscous acoustic wave equation for explicit stability compensation is computed in parallel using multiple GPUs, while the Fourier transform of the spatial derivative is accelerated using CUFFT in the CUDA command.

7. A viscosity-acoustic reverse-time migration system based on explicit stability compensation, characterized in that, include: The Lake wavelet generation module is used to read the coordinates of the seismic source and receiver points and generate Lake waves. A wave equation generation module is used to generate a constant fractional-order viscous acoustic wave equation with explicit stability compensation based on the Ricker wavelet. The forward-clockwise source seismic wave field value calculation module is used to solve the source seismic wave field value in the forward direction of time starting from the initial time using the explicit stability compensation constant fractional order viscous acoustic wave equation and the perfectly matched layer absorbing boundary condition to obtain the source seismic wave field value at all times. The source wavefield reconstruction module is used to reconstruct the source wavefield along the negative time direction by taking the source seismic wavefield value as the initial condition and through the explicit stability compensation constant fractional-order viscous acoustic wave equation and the perfectly matched layer absorbing boundary condition. The reverse-time receiver seismic wave field value calculation module uses the constant fractional-order viscous acoustic wave equation with explicit stability compensation and the perfectly matched layer absorbing boundary condition to solve in the negative time direction starting from the maximum time, and obtains the receiver seismic wave field values ​​at all times. The results output module is used to obtain subsurface structural imaging results based on the source wavefield and receiver seismic wavefield.

8. The adhesive acoustic reverse-time migration system based on explicit stability compensation as described in claim 7, characterized in that, The constant fractional order viscous acoustic wave equation for explicit stable compensation is obtained by performing two first-order Taylor expansions on the viscous acoustic wave equation for explicit stable compensation, and replacing the variable fractional order Laplace operator of the stable compensation equation with the constant fractional order Laplace operator.

9. The adhesive acoustic reverse-time migration system based on explicit stability compensation as described in claim 8, characterized in that, The viscous acoustic wave equation for explicit stable compensation is: in, , p It is a pressure wave field, where t is time. It is the velocity of the medium. For quality factors, It is the reference angular frequency. and These are all parameters for stable compensation. , This is an empirical constant (taken as 1 / 16 in this paper). It is angular frequency. This is the compensation coefficient.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that is executed by a processor to implement the adhesive acoustic reverse-time migration method based on explicit stability compensation as described in any one of claims 1-6.

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