Seismic wave forward modeling method, device and equipment in viscoacoustic VTI medium and medium

Abstract

This invention relates to the field of seismic imaging technology and discloses a method, apparatus, equipment, and medium for forward modeling of seismic acoustic waves in a viscoelastic-acoustic (VTI) medium. The method includes: obtaining a desired Q value; calculating the viscoelastic velocity of the seismic acoustic wave based on the desired Q value; fitting parameters of a generalized standard linear body model; constructing a wave equation for the seismic acoustic wave in the VTI medium based on the generalized standard linear body model; and solving the wave equation for the seismic acoustic wave in the VTI medium using the finite difference method and the viscoelastic velocity. This invention solves the problem that traditional seismic simulations cannot simultaneously consider seismic anisotropy and seismic attenuation, significantly improving the accuracy and applicability of seismic simulations, as well as the accuracy of seismic simulations in complex terrain, geology, and oil and gas reservoir areas. It provides a foundation for subsequent high-precision seismic velocity modeling and seismic migration imaging.

Description

Technical Field

[0001] This invention relates to the field of seismic imaging technology, and in particular to a method, apparatus, equipment, and medium for forward modeling seismic acoustic waves in a viscous acoustic VTI medium. Background Technology

[0002] Seismic simulation is a crucial component of seismic imaging and velocity modeling, and accurate seismic simulation can effectively improve the quality of seismic imaging. Common high-precision seismic imaging and modeling are based on pure acoustic equations, without considering the effects of medium anisotropy and seismic attenuation, resulting in a lack of accuracy in imaging and modeling. This is especially true for complex oil and gas reservoirs, where anisotropy and attenuation characteristics are significant, and conventional seismic simulation cannot meet the accuracy requirements.

[0003] Currently, both anisotropic wave theory and seismic attenuation theory have their own theoretical developments. The anisotropic wave equation extends the traditional one-dimensional stress-strain relationship to three dimensions and then simplifies it using medium properties. Theoretically, P-waves and S-waves in anisotropic media cannot be completely decoupled. There are two main categories of effective acoustic wave equations for anisotropic media: one is the pseudo-acoustic wave equation, which directly sets the shear wave velocity to zero and then solves directly using the anisotropic wave equation. However, this method suffers from shear wave interference, leading to numerical instability and compromising simulation accuracy. The more commonly used approach is the pseudo-acoustic wave equation, which is based on the phase velocity dispersion relationship of anisotropic media. This pseudo-acoustic wave equation has relatively better numerical stability and can ensure subsequent imaging quality.

[0004] Viscoelastic wave theory describes the viscous characteristics of a medium's stress-strain relationship based on various mathematical assumptions and combinations of physical components. It typically describes the frequency-dependent characteristics of attenuation in the frequency-wavenumber domain. Common models include the Kolsky model based on a spring and a sticky pot in parallel, the Kelvin-Voigt model, the constant Q model based on fractional derivatives, and the generalized viscoelastic model. In practical applications, the generalized standard linear body model can be effectively solved using the finite difference method, is easily implemented in large-scale GPU parallel computing, and can relatively accurately describe the constant Q attenuation characteristics of earthquakes, thus gaining industrial application.

[0005] However, due to the complex coupling between medium anisotropy and seismic wave attenuation, and the fact that the two theories are different, they cannot be directly integrated at present. This theoretical gap makes it difficult to further improve the accuracy of seismic simulation in viscous acoustic anisotropic media, which in turn affects subsequent seismic imaging and interpretation work. Summary of the Invention

[0006] The purpose of this invention is to provide at least one method, apparatus, device, and medium for forward modeling of seismic acoustic waves in viscous acoustic VTI media, which solves the problem that seismic anisotropy and seismic attenuation cannot be considered simultaneously in traditional seismic simulation. This invention can significantly improve the accuracy and applicability of seismic simulation, as well as the accuracy of seismic simulation in complex terrain, geology, and oil and gas reservoir areas, and provides a foundation for subsequent high-precision seismic velocity modeling and seismic migration imaging.

[0007] To address the aforementioned technical problems, at least one embodiment of the present invention provides a method for forward modeling seismic acoustic waves in a viscous acoustic VTI medium, comprising:

[0008] Obtain the expected Q value;

[0009] Calculate the viscoelastic velocity of seismic sound waves based on the expected Q value;

[0010] Parameters for fitting a generalized standard linear volume model;

[0011] Based on the generalized standard linear body model, the seismic acoustic wave equation in the viscoacoustic VTI medium is constructed.

[0012] The seismic acoustic wave equation in the viscoelastic VTI medium is solved using the finite difference method and the viscoelastic velocity.

[0013] In some optional embodiments, calculating the viscoelastic velocity of the seismic sound wave based on the desired Q value includes:

[0014] Construct a standard linear body to describe the viscoelastic properties of viscoacoustic VTI media;

[0015] The stress relaxation time and strain relaxation time in the standard linear body are determined based on the expected Q value.

[0016] The reference velocity of the seismic acoustic wave in the viscoelastic VTI medium at the reference frequency is determined as the phase velocity, and the viscoelastic velocity of the seismic acoustic wave is calculated based on the phase velocity, the stress relaxation time, and the strain relaxation time.

[0017] In some optional embodiments, the viscoelastic velocity of the seismic acoustic wave is calculated based on the phase velocity, the stress relaxation time, and the strain relaxation time using the following formula:

[0018]

[0019] In the formula, c0 represents the viscoelastic velocity, c r ω represents the reference velocity of seismic acoustic waves in a viscous acoustic VTI medium. r τ represents the reference frequency. ε and τ σ These represent strain relaxation time and stress relaxation time, respectively.

[0020] In some optional embodiments, the parameters for fitting the generalized standard linear volume model include:

[0021] Multiple stress relaxation frequencies are predefined at exponentially equal intervals within a given seismic wavelet frequency band, and the stress relaxation frequencies are determined based on the stress relaxation time.

[0022] At the center of each stress relaxation frequency and stress frequency band, the parameters of the generalized standard linear body model are fitted according to the desired Q value, and multiple strain relaxation times obtained by different orders of fitting under the desired Q value are calculated.

[0023] The actual Q value is calculated using the predefined stress relaxation time and the fitted strain relaxation time.

[0024] When the actual Q value matches the expected Q value, the parameters of the generalized standard linear body model are determined, including the stress relaxation time and strain relaxation time.

[0025] In some optional embodiments, the seismic acoustic wave equation in the viscous acoustic VTI medium is constructed based on the generalized standard linear volume model, including:

[0026] Construct the pure acoustic wave equation in viscous acoustic VTI medium;

[0027] The pure acoustic wave equation is expressed as a set of equations including constitutive equations and wave field propagation equations, and the constitutive equations are transformed into constitutive relations of a generalized standard linear body.

[0028] By introducing a memory variable into the pure acoustic wave equation, the seismic acoustic wave equation in the viscous acoustic VTI medium is obtained.

[0029] In some optional embodiments, the seismic acoustic wave equation in the viscoacoustic VTI medium is as follows:

[0030]

[0031] In the formula, p represents the seismic sound wave field, t represents time, c0 represents the viscoelastic velocity, and γ n Let N represent the nth memory variable, N represent the total number of strain relaxation times or stress relaxation times, and τ represent the intermediate parameter. n =1-τ εn / τ σn , τ εn τ represents the nth strain relaxation time. σn Let S represent the nth stress relaxation time, and let S denote the S operator.

[0032] In some optional embodiments, the seismic acoustic wave equation in the viscoelastic VTI medium is solved using the finite difference method and the viscoelastic velocity, including:

[0033] The wave equation for seismic acoustic waves in the viscous-acoustic VTI medium is transformed into the following calculation formula using the finite difference method:

[0034]

[0035] In the formula, m represents the time step, and Δt represents the time interval.

[0036] At least one embodiment of the present invention also provides a seismic acoustic wave forward modeling device in a viscous acoustic VTI medium, comprising:

[0037] The Q-value acquisition module is used to obtain the expected Q-value.

[0038] The velocity calculation module is used to calculate the viscoelastic velocity of seismic sound waves based on the desired Q value;

[0039] The parameter fitting module is used to fit the parameters of the generalized standard linear body model;

[0040] The equation construction module is used to construct the seismic acoustic wave equation in the viscous acoustic VTI medium based on the generalized standard linear body model.

[0041] The equation solving module is used to solve the seismic acoustic wave equation in the viscoelastic VTI medium using the finite difference method and the viscoelastic velocity.

[0042] At least one embodiment of the present invention also provides an electronic device, comprising:

[0043] At least one processor; and,

[0044] A memory communicatively connected to the at least one processor; wherein,

[0045] The memory stores instructions that can be executed by the at least one processor, which enables the at least one processor to perform the above-described forward modeling method for seismic acoustic waves in viscous VTI media.

[0046] At least one embodiment of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described forward modeling method for seismic acoustic waves in a viscous VTI medium.

[0047] This invention provides a method, apparatus, equipment, and medium for forward modeling seismic acoustic waves in viscoelastic VTI media. The method calculates the viscoelastic velocity of seismic acoustic waves based on the desired Q-value; fits the parameters of a generalized standard linear body model; constructs the wave equation for seismic acoustic waves in viscoelastic VTI media based on the generalized standard linear body model; and solves the wave equation using the finite difference method and viscoelastic velocity. This solves the problem of not being able to simultaneously consider seismic anisotropy and seismic attenuation in traditional seismic simulations, significantly improving the accuracy and applicability of seismic simulations, as well as the accuracy of seismic simulations in complex terrain, geology, and oil and gas reservoir areas. It also provides a foundation for subsequent high-precision seismic velocity modeling and seismic migration imaging. Attached Figure Description

[0048] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0049] Figure 1 This is a flowchart of a method for forward modeling seismic acoustic waves in a viscous VTI medium, provided in an embodiment of the present invention;

[0050] Figure 2 This is a schematic diagram of a forward modeling device for seismic acoustic waves in a viscous VTI medium provided in another embodiment of the present invention;

[0051] Figure 3 This is a comparative schematic diagram of a 0.35s wave field snapshot of a uniform anisotropic medium provided in another embodiment of the present invention;

[0052] Figure 4 This is a comparison of seismic traces of a 0.35s wavefield snapshot in a homogeneous anisotropic medium provided by another embodiment of the present invention, (a) spatial waveform comparison; (b) spectral comparison. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the embodiments of the present invention to facilitate a better understanding of the invention. However, the technical solutions claimed in the present invention can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.

[0054] To address the issue that traditional earthquake simulations cannot simultaneously consider seismic anisotropy and seismic attenuation, this invention proposes a forward modeling method for seismic acoustic waves in viscous-acoustic VTI media. This method significantly improves the accuracy and applicability of earthquake simulations, as well as the accuracy of seismic simulations in complex terrain, geology, and oil and gas reservoir areas, providing a foundation for subsequent high-precision seismic velocity modeling and seismic migration imaging. The implementation details of the forward modeling method for seismic acoustic waves in viscous-acoustic VTI media in this embodiment are described below. These details are provided for ease of understanding and are not essential for implementing this solution.

[0055] Example 1

[0056] The forward modeling method for seismic acoustic waves in the viscous acoustic VTI medium of this embodiment can be applied to electronic devices with communication, computing, and data storage capabilities. Its specific process can be as follows: Figure 1 As shown, it includes:

[0057] Step 101: Obtain the expected Q value.

[0058] Here, the expected Q-value of the input can refer to the Q-value model.

[0059] Step 102: Calculate the viscoelastic velocity of the seismic sound wave based on the expected Q value.

[0060] In some specific implementations, the viscoelastic velocity of seismic sound waves is calculated based on the desired Q value, further including:

[0061] Step 102a: Construct a standard linear body to describe the viscoelastic properties of the viscoelastic VTI medium.

[0062] The standard linear body model is a constitutive model used to describe the viscoelastic properties of VTI media. The complex modulus M(ω) of the standard linear body model used to describe the viscoelastic properties of viscoacoustic VTI media can be written in the following form:

[0063]

[0064] In the formula, Let ρ represent the bulk modulus, ρ represent the density, c0 represent the viscoelastic velocity, i represent the imaginary unit, ω represent the angular frequency, and τ represent the bulk modulus. ε and τ σ These represent strain relaxation time and stress relaxation time, respectively.

[0065] Step 102b: Determine the stress relaxation time and strain relaxation time in the standard linear body based on the expected Q value.

[0066] The stress relaxation time and strain relaxation time in the standard linear body model are determined using the following formula based on the expected Q value:

[0067]

[0068] In the formula, Q represents the expected Q value.

[0069] Step 102c: Determine the reference velocity of the seismic acoustic wave in the viscoelastic VTI medium at the reference frequency as the phase velocity, and calculate the viscoelastic velocity of the seismic acoustic wave based on the phase velocity, stress relaxation time, and strain relaxation time.

[0070] The phase velocity of seismic sound waves can be expressed as:

[0071]

[0072] In the formula, v(ω) represents the phase velocity of the seismic sound wave, and the subscript "Re" represents the real part of the complex modulus.

[0073] The physical meaning of phase velocity is the velocity of a certain frequency component in a VTI medium. In practical applications, it has a reference frequency ω. r The reference speed c r Therefore, in practical implementation, the following calculation formula can be used to calculate the viscoelastic velocity of seismic sound waves based on phase velocity, stress relaxation time, and strain relaxation time:

[0074]

[0075] In the formula, c0 represents the viscoelastic velocity, c r ω represents the reference velocity of seismic acoustic waves in a viscous acoustic VTI medium. r Indicates the reference frequency.

[0076] Establishing the viscoelastic velocity of seismic sound waves is essential to ensuring the correct dispersion characteristics of seismic sound waves and guaranteeing that the propagation speed of a viscoelastic wave field is slower than that of a purely elastic wave field.

[0077] Step 103: Fit the parameters of the generalized standard linear body model, including stress relaxation time and strain relaxation time.

[0078] Since the seismic frequency band is relatively narrow and the frequency is relatively low, it can be approximated as a constant Q characteristic in laboratory and field applications. In order to better simulate this constant Q characteristic, a joint model of multiple standard linear bodies is adopted, that is, a generalized standard linear body model.

[0079] The complex modulus expression for an arbitrary-order generalized standard linear body model is:

[0080]

[0081] In the formula, N is the number of standard linear bodies. Based on the complex modulus, the quality factor Q can be expressed as:

[0082]

[0083] In the formula, the subscript "Im" represents the imaginary part of the complex modulus.

[0084] In the specific implementation, the parameters for fitting the generalized standard linear volume model further include:

[0085] Step 103a: Define multiple stress relaxation frequencies at equal intervals in an exponential manner within a given seismic wavelet frequency band. The stress relaxation frequencies are determined based on the stress relaxation time.

[0086] Step 103b: At the center of each stress relaxation frequency and stress band range, perform parameter fitting of the generalized standard linear body model according to the desired Q value, and calculate multiple strain relaxation times obtained by fitting at different orders under the desired Q value.

[0087] Step 103c: Calculate the actual Q value using the predefined stress relaxation time and the fitted strain relaxation time.

[0088] Step 103d: If the actual Q value is consistent with the expected Q value, determine the parameters of the generalized standard linear body model, including stress relaxation time and strain relaxation time.

[0089] In one example, N stress relaxation frequencies ω are predefined exponentially at equal intervals within a given seismic wavelet frequency band. n (τ σn =1 / ω n ), and at each stress relaxation frequency ω n At the center interval, parameters are fitted using the least squares method according to the desired Q value. N strain relaxation times are calculated for different orders of fitting under this desired Q value, and then a predefined stress relaxation time τ is used. σn The strain relaxation time τ obtained under the expected Q value εn The actual Q value is calculated by fitting equation (6) and verified. If the actual Q value is consistent with the expected Q value, the parameters of the generalized standard linear body model are determined. Otherwise, the parameters are adjusted until the actual Q value is consistent with the expected Q value. The given seismic wavelet frequency band is, for example, (0, 100) Hz, the exponential interval is, for example, 1 Hz, 10 Hz, 100 Hz, and the center interval position is, for example, the center point 5 Hz in the 0-10 Hz interval. 5 Hz is determined as the new fitting point.

[0090] In practical applications, considering the narrow seismic wavelet frequency band and to balance computational efficiency, N is set to 3.

[0091] Step 104: Construct the seismic acoustic wave equation in the viscous acoustic VTI medium based on the generalized standard linear body model.

[0092] In practical implementation, the seismic acoustic wave equation in viscous acoustic VTI media is constructed based on the generalized standard linear volume model, including:

[0093] Step 104a: Construct the pure acoustic wave equation in the viscous acoustic VTI medium.

[0094] Transversely isotropic (TI) media are common anisotropic media in Earth models. The construction of acoustic wave fields in TI media is constrained by S-wave interference. The pseudo-acoustic equation directly sets the S-wave velocity to zero. Although P-wave accuracy is high, it suffers from strong S-wave interference and numerical instability, making it unsuitable for subsequent seismic migration modeling.

[0095] This embodiment uses a pseudo-acoustic equation to construct a pure acoustic wave equation in a viscous acoustic VTI medium:

[0096]

[0097] In the formula, p represents the sound wave field, v represents the pure sound wave velocity, and t represents time. The S-operator, used to characterize the anisotropy of a medium, can be written as:

[0098]

[0099] In the formula, It is the unit vector in the direction of phase velocity, defined as ε is the wavenumber vector, and δ represents the transverse anisotropy parameter and the longitudinal anisotropy parameter in the Thomsen anisotropy parameters, respectively.

[0100] Step 104b: Express the pure acoustic wave equation in terms of a set of equations including constitutive equations and wave field propagation equations, and transform the constitutive equations into constitutive relations of a generalized standard linear body.

[0101] In one example, the pure acoustic wave equation of equation (7) is divided into the following set of equations according to its physical meaning:

[0102]

[0103] In the formula, E = ρv 2 Representing Young's modulus, in equation (9), p = Eε is the constitutive equation. This is the wave field propagation equation that combines the geometric and kinematic equations. For viscoelastic VTI media, replacing p=Eε with the constitutive relation of the generalized standard linear body model, it is expressed as follows:

[0104]

[0105] In the formula, "*" represents convolution, and G represents the relaxation function, which is expressed as:

[0106]

[0107] In the formula, the intermediate parameter τ n =1-τ εn / τ σn H(t) is the Heaviside function.

[0108] Step 104c: Introduce memory variables into the pure acoustic wave equation to obtain the seismic acoustic wave equation in the viscous acoustic VTI medium.

[0109] Simplifying equation (11) and introducing the memory variable γ, the seismic acoustic wave equation in the viscous acoustic VTI medium is as follows:

[0110]

[0111] In the formula, p represents the seismic sound wave field, t represents time, c0 represents the viscoelastic velocity, and γ n Let τ represent the nth memory variable, N represent the total number of strain relaxation times or stress relaxation times, and τ represent the total number of strain relaxation times or stress relaxation times. εn τ represents the nth strain relaxation time. σn Let S represent the nth stress relaxation time, and let S denote the S operator.

[0112] Since the seismic acoustic wave equation in the viscous acoustic VTI medium is constructed based on the constitutive relation of the generalized standard linear body, it reflects the seismic acoustic wave attenuation effect in the viscous acoustic VTI medium.

[0113] Step 105: Solve the seismic acoustic wave equation in the viscoelastic VTI medium using the finite difference method and viscoelastic velocity.

[0114] In practical implementation, the finite difference method and viscoelastic velocity are used to solve the seismic acoustic wave equation in the viscoacoustic VTI medium, including:

[0115] The wave equation for seismic acoustic waves in viscous-acoustic VTI media is transformed into the following calculation formula using the finite difference method:

[0116]

[0117] In the formula, m represents the time step, and Δt represents the time interval.

[0118] The spatial derivative can be divided into:

[0119]

[0120] In the formula, p x Let (i,j,k) represent the first derivative in space, and (i,j,k) represent the grid space position. i This represents the finite difference coefficients.

[0121] The unit vector in the S operator can be calculated as:

[0122]

[0123] Thus, the seismic acoustic wave equation in the viscous VTI medium has been solved, the forward modeling has been completed, and the seismic acoustic wave field value at each time step has been obtained.

[0124] In this embodiment, the construction of the seismic acoustic wave equation in the viscoacoustic VTI medium and the efficient and accurate forward modeling of the seismic wave field in complex anisotropic and attenuated coupled media are demonstrated. By introducing the generalized standard linear volume model into the pseudo-acoustic wave equation of the viscoacoustic VTI medium, the layered anisotropy characteristics and constant Q attenuation features of seismic wave propagation can be accurately simulated. Furthermore, finite difference solutions can be directly performed in the time-space domain, which is beneficial for large-scale GPU parallel computing and improves the applicability of the algorithm. This achieves high-precision simulation of seismic waves in complex anisotropic and attenuated coupled underground media, providing strong support for subsequent migration imaging and velocity modeling.

[0125] Example 2

[0126] Another embodiment of the present invention relates to a seismic acoustic wave forward modeling device in a viscous VTI medium. The implementation details of this embodiment's seismic acoustic wave forward modeling device are described below. The following details are provided for ease of understanding and are not essential for implementing this solution. A schematic diagram of the seismic acoustic wave forward modeling device in this embodiment can be seen as follows: Figure 2 As shown, it includes a Q-value acquisition module 201, a velocity calculation module 202, a parameter fitting module 203, an equation construction module 204, and an equation solving module 205.

[0127] Q-value acquisition module 201 is used to acquire the expected Q-value;

[0128] The velocity calculation module 202 is used to calculate the viscoelastic velocity of the seismic sound wave based on the desired Q value;

[0129] The parameter fitting module 203 is used to fit the parameters of the generalized standard linear body model;

[0130] Equation building module 204 is used to construct the seismic acoustic wave equation in viscous acoustic VTI medium based on the generalized standard linear body model;

[0131] Equation solving module 205 is used to solve the seismic acoustic wave equation in viscoelastic VTI media using the finite difference method and viscoelastic velocity.

[0132] In this embodiment, the expected Q value can refer to the Q-value model.

[0133] In some specific implementations, the viscoelastic velocity of seismic sound waves is calculated based on the desired Q value, further including:

[0134] A standard linear body is constructed to describe the viscoelastic properties of the viscoelastic VTI medium; the stress relaxation time and strain relaxation time in the standard linear body are determined based on the expected Q value; the reference velocity of the seismic acoustic wave in the viscoelastic VTI medium at the reference frequency is determined as the phase velocity, and the viscoelastic velocity of the seismic acoustic wave is calculated based on the phase velocity, stress relaxation time and strain relaxation time.

[0135] The standard linear body model is a constitutive model used to describe the viscoelastic properties of VTI media. The complex modulus M(ω) of the standard linear body model used to describe the viscoelastic properties of viscoacoustic VTI media can be written in the following form:

[0136]

[0137] In the formula, Let ρ represent the bulk modulus, ρ represent the density, c0 represent the viscoelastic velocity, i represent the imaginary unit, ω represent the angular frequency, and τ represent the bulk modulus. ε and τ σ These represent strain relaxation time and stress relaxation time, respectively.

[0138] The stress relaxation time and strain relaxation time in the standard linear body model are determined using the following formula based on the expected Q value:

[0139]

[0140] In the formula, Q represents the expected Q value.

[0141] The phase velocity of seismic sound waves can be expressed as:

[0142]

[0143] In the formula, v(ω) represents the phase velocity of the seismic sound wave, and the subscript "Re" represents the real part of the complex modulus.

[0144] The physical meaning of phase velocity is the velocity of a certain frequency component in a VTI medium. In practical applications, it has a reference frequency ω. r The reference speed c r Therefore, in practical implementation, the following calculation formula can be used to calculate the viscoelastic velocity of seismic sound waves based on phase velocity, stress relaxation time, and strain relaxation time:

[0145]

[0146] In the formula, c0 represents the viscoelastic velocity, c rω represents the reference velocity of seismic acoustic waves in a viscous acoustic VTI medium. r Indicates the reference frequency.

[0147] Establishing the viscoelastic velocity of seismic sound waves is essential to ensuring the correct dispersion characteristics of seismic sound waves and guaranteeing that the propagation speed of a viscoelastic wave field is slower than that of a purely elastic wave field.

[0148] Since the seismic frequency band is relatively narrow and the frequency is relatively low, it can be approximated as a constant Q characteristic in laboratory and field applications. In order to better simulate this constant Q characteristic, a joint model of multiple standard linear bodies is adopted, that is, a generalized standard linear body model.

[0149] The complex modulus expression for an arbitrary-order generalized standard linear body model is:

[0150]

[0151] In the formula, N is the number of standard linear bodies. Based on the complex modulus, the quality factor Q can be expressed as:

[0152]

[0153] In the formula, the subscript "Im" represents the imaginary part of the complex modulus.

[0154] In the specific implementation, the parameters for fitting the generalized standard linear volume model further include:

[0155] Multiple stress relaxation frequencies are predefined at exponentially equal intervals within a given seismic wavelet frequency band. These frequencies are determined based on stress relaxation times. At each stress relaxation frequency and the center of the stress band, parameters of a generalized standard linear body model are fitted according to the desired Q value. Multiple strain relaxation times obtained from fitting at different orders under the desired Q value are calculated. The actual Q value is calculated using the predefined stress relaxation times and the fitted strain relaxation times. If the actual Q value matches the desired Q value, the parameters of the generalized standard linear body model are determined, including the stress relaxation times and strain relaxation times.

[0156] In one example, N stress relaxation frequencies ω are predefined exponentially at equal intervals within a given seismic wavelet frequency band. n (τ σn =1 / ω n ), and at each stress relaxation frequency ω n At the center interval, parameters are fitted using the least squares method according to the desired Q value. N strain relaxation times are calculated for different orders of fitting under this desired Q value, and then a predefined stress relaxation time τ is used. σn The strain relaxation time τ obtained under the expected Q value εnThe actual Q value is calculated by fitting equation (6) and verified. If the actual Q value is consistent with the expected Q value, the parameters of the generalized standard linear body model are determined. Otherwise, the parameters are adjusted until the actual Q value is consistent with the expected Q value. The given seismic wavelet frequency band is, for example, (0, 100) Hz, the exponential interval is, for example, 1 Hz, 10 Hz, 100 Hz, and the center interval position is, for example, the center point 5 Hz in the 0-10 Hz interval. 5 Hz is determined as the new fitting point.

[0157] In practical applications, considering the narrow seismic wavelet frequency band and to balance computational efficiency, N is set to 3.

[0158] In the specific implementation, the seismic acoustic wave equation in the viscous acoustic VTI medium is constructed based on the generalized standard linear body model, including: constructing the pure acoustic wave equation in the viscous acoustic VTI medium; expressing the pure acoustic wave equation as a set of equations including constitutive equations and wave field propagation equations, and transforming the constitutive equations into constitutive relations of the generalized standard linear body; introducing memory variables into the pure acoustic wave equation to obtain the seismic acoustic wave equation in the viscous acoustic VTI medium.

[0159] Transversely isotropic (TI) media are common anisotropic media in Earth models. The construction of acoustic wave fields in TI media is constrained by S-wave interference. The pseudo-acoustic equation directly sets the S-wave velocity to zero. Although P-wave accuracy is high, it suffers from strong S-wave interference and numerical instability, making it unsuitable for subsequent seismic migration modeling.

[0160] This embodiment uses a pseudo-acoustic equation to construct a pure acoustic wave equation in a viscous acoustic VTI medium:

[0161]

[0162] In the formula, p represents the sound wave field, v represents the pure sound wave velocity, and t represents time. The S-operator, used to characterize the anisotropy of a medium, can be written as:

[0163]

[0164] In the formula, It is a unit vector in the direction of phase velocity, defined as ε is the wavenumber vector, and δ represents the transverse anisotropy parameter and the longitudinal anisotropy parameter in the Thomsen anisotropy parameters, respectively.

[0165] In one example, the pure acoustic wave equation of equation (7) is divided into the following set of equations according to its physical meaning:

[0166]

[0167] In the formula, E = ρv 2 Representing Young's modulus, in equation (9), p = Eε is the constitutive equation. This is the wave field propagation equation that combines the geometric and kinematic equations. For viscoelastic VTI media, replacing p=Eε with the constitutive relation of the generalized standard linear body model, it is expressed as follows:

[0168]

[0169] In the formula, "*" represents convolution, and G represents the relaxation function, which is expressed as:

[0170]

[0171] In the formula, the intermediate parameter τ n =1-τ εn / τ σn H(t) is the Heaviside function.

[0172] Simplifying equation (11) and introducing the memory variable γ, the seismic acoustic wave equation in the viscous acoustic VTI medium is as follows:

[0173]

[0174] In the formula, p represents the seismic sound wave field, t represents time, c0 represents the viscoelastic velocity, and γ n Let τ represent the nth memory variable, N represent the total number of strain relaxation times or stress relaxation times, and τ represent the total number of strain relaxation times or stress relaxation times. εn τ represents the nth strain relaxation time. σn Let S represent the nth stress relaxation time, and let S denote the S operator.

[0175] Since the seismic acoustic wave equation in the viscous acoustic VTI medium is constructed based on the constitutive relation of the generalized standard linear body, it reflects the seismic acoustic wave attenuation effect in the viscous acoustic VTI medium.

[0176] In practical implementation, the seismic acoustic wave equation in the viscoelastic VTI medium is solved using the finite difference method and viscoelastic velocity, including: transforming the seismic acoustic wave equation in the viscoelastic VTI medium into the following calculation formula using the finite difference method:

[0177]

[0178] In the formula, m represents the time step, and Δt represents the time interval.

[0179] The spatial derivative can be divided into:

[0180]

[0181] In the formula, px Let (i,j,k) represent the first derivative in space, and (i,j,k) represent the grid space position. i This represents the finite difference coefficients.

[0182] The unit vector in the S operator can be calculated as:

[0183]

[0184] Thus, the seismic acoustic wave equation in the viscous VTI medium has been solved, the forward modeling has been completed, and the seismic acoustic wave field value at each time step has been obtained.

[0185] In this embodiment, the construction of the seismic acoustic wave equation in the viscoacoustic VTI medium and the efficient and accurate forward modeling of the seismic wave field in complex anisotropic and attenuated coupled media are demonstrated. By introducing the generalized standard linear volume model into the pseudo-acoustic wave equation of the viscoacoustic VTI medium, the layered anisotropy characteristics and constant Q attenuation features of seismic wave propagation can be accurately simulated. Furthermore, finite difference solutions can be directly performed in the time-space domain, which is beneficial for large-scale GPU parallel computing and improves the applicability of the algorithm. This achieves high-precision simulation of seismic waves in complex anisotropic and attenuated coupled underground media, providing strong support for subsequent migration imaging and velocity modeling.

[0186] It is worth mentioning that all modules involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this invention, this embodiment does not introduce units that are not closely related to solving the technical problem proposed by this invention; however, this does not mean that other units are absent from this embodiment.

[0187] Example 3

[0188] Another embodiment of the present invention relates to an electronic device, comprising:

[0189] At least one processor; and,

[0190] A memory that is communicatively connected to at least one processor; wherein,

[0191] The memory stores instructions that can be executed by at least one processor, which enables the at least one processor to perform the aforementioned forward modeling method for seismic acoustic waves in viscous VTI media.

[0192] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0193] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0194] Example 4

[0195] Another embodiment of the present invention relates to a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described forward modeling method for seismic acoustic waves in a viscous VTI medium.

[0196] Another embodiment of the present invention relates to a computer program product, including a computer program that, when executed by a processor, implements the above-described forward modeling method for seismic acoustic waves in viscous VTI media.

[0197] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0198] Example 5

[0199] Another embodiment of the present invention relates to an application example.

[0200] A VTI medium seismic wave simulation was performed in a homogeneous model using the method described in the above embodiments. The anisotropy parameters were ε = 0.3 and δ = 0.05. The source was a Ricker wavelet with a dominant frequency of 15 Hz, excited at the center point of the model. Pure acoustic waves were simulated for Q = 100, 30, and 10, respectively. A wavefield snapshot of 0.35 s is shown below. Figure 3 As shown, the wavefield snapshot exhibits significant anisotropy, with the horizontal propagation distance exceeding that in the vertical direction, and no numerical dispersion or instability is observed. Furthermore, as attenuation increases (Q value decreases), the amplitude attenuation and dispersion effects gradually intensify.

[0201] Figure 4 Figure (a) in the image records the horizontal waveform in the wave field snapshot. It shows obvious amplitude attenuation and dispersion effects, and the waveform is complete with no extra side lobes and no numerical instability. Figure 4 Figure (b) shows the corresponding spectrum, revealing that as Q decreases, the energy decreases significantly and the dominant frequency shifts to lower frequencies, which is consistent with physical laws and demonstrates the correctness of this method.

[0202] This invention utilizes a generalized standard linear body for forward modeling of seismic acoustic waves in viscous-acoustic VTI media, improving the accuracy of seismic simulation and thus enhancing the resolution and reliability of subsequent high-precision seismic modeling and reverse-time migration imaging. A method for determining the parameters of the generalized standard linear body in VTI media is established, effectively characterizing the seismic attenuation effect in viscous-acoustic VTI media. By incorporating the relaxation function of the generalized standard linear body into the anisotropic pure acoustic wave equation, the wave equation for viscous-acoustic VTI media is obtained, avoiding the instability of anisotropic acoustic wave simulation and achieving a stable and effective simulation, thereby improving the accuracy of seismic simulation.

[0203] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A method for seismic wave forward modeling in a viscoacoustic VTI medium, characterized in that, include: Obtain the expected Q value; Calculate the viscoelastic velocity of seismic sound waves based on the expected Q value; Parameters for fitting a generalized standard linear volume model; Based on the generalized standard linear body model, the seismic acoustic wave equation in the viscoacoustic VTI medium is constructed. The seismic acoustic wave equation in the viscoelastic VTI medium is solved using the finite difference method and the viscoelastic velocity.

2. The method of claim 1, wherein, Calculating the viscoelastic velocity of seismic sound waves based on the expected Q value includes: Construct a standard linear body to describe the viscoelastic properties of viscoacoustic VTI media; The stress relaxation time and strain relaxation time in the standard linear body are determined based on the expected Q value. The reference velocity of the seismic acoustic wave in the viscoelastic VTI medium at the reference frequency is determined as the phase velocity, and the viscoelastic velocity of the seismic acoustic wave is calculated based on the phase velocity, the stress relaxation time, and the strain relaxation time.

3. The method of claim 2, wherein, The viscoelastic velocity of the seismic acoustic wave is calculated using the following formula, based on the phase velocity, the stress relaxation time, and the strain relaxation time: In the formula, c0 represents the viscoelastic velocity, c r ω represents the reference velocity of seismic acoustic waves in a viscous acoustic VTI medium. r τ represents the reference frequency. ε and τ σ These represent strain relaxation time and stress relaxation time, respectively.

4. The method of claim 1, wherein, The parameters for fitting the generalized standard linear volume model include: Multiple stress relaxation frequencies are predefined at exponentially equal intervals within a given seismic wavelet frequency band, and the stress relaxation frequencies are determined based on the stress relaxation time. At the center of each stress relaxation frequency and stress frequency band, the parameters of the generalized standard linear body model are fitted according to the desired Q value, and multiple strain relaxation times obtained by different orders of fitting under the desired Q value are calculated. The actual Q value is calculated using the predefined stress relaxation time and the fitted strain relaxation time. When the actual Q value matches the expected Q value, the parameters of the generalized standard linear body model are determined, including the stress relaxation time and strain relaxation time.

5. The method of claim 1, wherein, Based on the generalized standard linear volume model, the seismic acoustic wave equation in viscous acoustic VTI medium is constructed, including: Construct the pure acoustic wave equation in viscous acoustic VTI medium; The pure acoustic wave equation is expressed as a set of equations including constitutive equations and wave field propagation equations, and the constitutive equations are transformed into constitutive relations of a generalized standard linear body. By introducing a memory variable into the pure acoustic wave equation, the seismic acoustic wave equation in the viscous acoustic VTI medium is obtained.

6. The method of forward modeling of seismic acoustic waves in a viscoacoustic anisotropic medium according to claim 5, wherein, The seismic acoustic wave equation in the viscoacoustic VTI medium is as follows: In the formula, p represents the seismic sound wave field, t represents time, c0 represents the viscoelastic velocity, and γ n Let N represent the nth memory variable, N represent the total number of strain relaxation times or stress relaxation times, and τ represent the intermediate parameter. n =1-τ εn / τ σn , τ εn τ represents the nth strain relaxation time. σn Let S represent the nth stress relaxation time, and let S denote the S operator.

7. The method of claim 6, wherein, Solving the seismic acoustic wave equation in the viscoelastic VTI medium using the finite difference method and the viscoelastic velocity includes: The wave equation for seismic acoustic waves in the viscous-acoustic VTI medium is transformed into the following calculation formula using the finite difference method: In the formula, m represents the time step, and Δt represents the time interval.

8. A forward modeling device for seismic acoustic waves in a viscous VTI medium, characterized in that, include: The Q-value acquisition module is used to obtain the expected Q-value. The velocity calculation module is used to calculate the viscoelastic velocity of seismic sound waves based on the desired Q value; The parameter fitting module is used to fit the parameters of the generalized standard linear body model; The equation construction module is used to construct the seismic acoustic wave equation in the viscous acoustic VTI medium based on the generalized standard linear body model. The equation solving module is used to solve the seismic acoustic wave equation in the viscoelastic VTI medium using the finite difference method and the viscoelastic velocity.

9. An electronic device, comprising: include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the forward modeling method for seismic acoustic waves in viscous VTI media as described in any one of claims 1 to 7.

10. A computer readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the forward modeling method for seismic acoustic waves in the viscous VTI medium as described in any one of claims 1 to 7.

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