CN116794716B - Frequency dispersion AVO simulation method of mesoscopic fracture rock physical model - Google Patents
Frequency dispersion AVO simulation method of mesoscopic fracture rock physical model Download PDFInfo
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Abstract
The invention discloses a frequency dispersion AVO simulation method of a mesoscopic fracture rock physical model, belonging to the technical field of oil and gas exploration; the method comprises a phase of obtaining a frequency-dependent stiffness matrix of mesoscopic fracture rock and a phase of simulating model dispersion AVO; the frequency-dependent stiffness matrix of the mesoscopic fracture rock can be constructed into corresponding additional flexibility matrixes for different fracture arrangement modes, and the frequency-dependent flexibility matrixes are combined with the normal flexibility of the fracture depending on frequency to obtain corresponding dynamic flexibility matrixes of the dry rock, so that the frequency-dependent stiffness matrixes of the rock are obtained after the fluid characteristics are added; and in the model frequency dispersion AVO simulation stage, the frequency-dependent anisotropy coefficient is obtained based on the frequency-dependent stiffness matrix of the rock, and the multi-interface seismic frequency dispersion AVO simulation record is obtained by combining the frequency-dependent interface reflection coefficient and the seismic source wavelet. The invention solves the problems that rock model construction and dispersion AVO analysis are difficult to be carried out on a mesoscopic crack dynamic model which is randomly distributed.
Description
Technical Field
The invention belongs to the technical field of oil and gas exploration, and particularly relates to a frequency dispersion AVO simulation method of a mesoscopic fracture rock physical model.
Background
Velocity dispersion and energy attenuation (simply dispersion) generally occur as waves pass through the subsurface fluid-containing rock. The current theory regarding the mechanism of this dispersion effect is wave-induced fluid flow (WIFF), and the mechanism of dispersion attenuation occurring in the seismic exploration band is mainly mesoscopic flow.
Mesoscale mainly refers to a scale that is much smaller than the artificial seismic wave wavelength and much larger than the rock pore size, typically in the order of centimeters. There are many reasons for the mesoscale non-uniformity of rock, of which cracking is one of the main factors. In addition, the cracks may have some directionality, resulting in dispersion and attenuation of the waves as well as anisotropy. At present, description of fracture rock, especially mesoscale, most of the considered directional arrangement lacks a modeling scheme for mesoscopic fracture models with complex arrangement and even random arrangement, so that a method capable of constructing mesoscopic fracture dynamic models with random distribution and arrangement and performing dispersion AVO simulation on the constructed models is needed.
Disclosure of Invention
Aiming at the defects in the prior art, the frequency dispersion AVO simulation method of the mesoscopic fracture rock physical model provided by the invention solves the problem that rock model construction and frequency dispersion AVO analysis are difficult to carry out on a mesoscopic fracture dynamic model which is randomly distributed.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the invention provides a frequency dispersion AVO simulation method of a mesoscopic fracture rock physical model, which comprises a frequency-dependent stiffness matrix acquisition stage of mesoscopic fracture rock and a model frequency dispersion AVO simulation stage;
the phase for obtaining the frequency-dependent stiffness matrix of the mesoscopic fracture rock comprises the following steps:
a1, acquiring crack density, number of cracks, radius of the cracks and shear modulus of background rock, and calculating to obtain normal flexibility and tangential flexibility of the cracks;
a2, calculating the normal flexibility of the crack based on the P-wave modulus of the crack-containing rock and the saturated background rock, and obtaining the normal flexibility of the crack depending on the frequency;
a3, calculating a dry rock dynamic flexibility matrix based on tangential flexibility of the cracks, normal flexibility of the cracks depending on frequency and a dry rock background flexibility matrix according to the arrangement mode of the cracks;
a4, calculating to obtain a complete rock frequency-dependent compliance matrix based on the dry rock dynamic compliance matrix and an anisotropic Gassmann equation;
a5, inverting the complete rock frequency-dependent flexibility matrix to obtain a rock frequency-dependent stiffness matrix;
the model dispersion AVO simulation stage comprises the following steps:
B1, obtaining a frequency-dependent stiffness coefficient based on a frequency-dependent stiffness matrix of the rock;
b2, calculating to obtain an anisotropic coefficient dependent on frequency based on the real part of the frequency-dependent stiffness coefficient;
b3, obtaining a reflection coefficient of the frequency-dependent interface based on the anisotropic coefficient and the reflection coefficient equation;
and B4, calculating to obtain the multi-interface seismic dispersion AVO simulation record according to the frequency-dependent interface reflection coefficient and the source wavelet.
The beneficial effects of the invention are as follows: according to the frequency dispersion AVO simulation method of the mesoscopic fracture rock physical model, the frequency dependent fracture flexibility parameter is constructed through the frequency variation rigidity matrix acquisition stage of the mesoscopic fracture rock, and the complex frequency dispersion model can be constructed based on the frequency dependent fracture flexibility parameter; the model constructed by the scheme is not limited to describing HTI media, can construct a dry rock dynamic flexibility matrix which is randomly distributed and arranged in any crack arrangement mode, and is more convenient and quicker than the existing construction method in a calculation method for constructing the model; by introducing the dispersion characteristic, the construction of a fluid-containing dynamic model can be realized, and the diversity of mesoscopic fracture rock physical models is greatly enriched; by analyzing the AOV frequency variation and frequency dependent synthetic seismic recordings of a dispersed rock physical model in a model dispersed AVO simulation phase, more parameters or phenomena can be provided to describe the fluid and fracture conditions of the subsurface rock.
Further, the calculation expressions of the normal compliance and the tangential compliance in A1 are as follows:
wherein,and->The normal and tangential compliance of the dry fracture are shown, respectively, lambda shows the pull Mei Jishu, mu shows the shear modulus of the background rock, e shows the fracture density, N shows the number of cracks, a shows the fracture radius, V shows the rock volume.
The beneficial effects of adopting the further scheme are as follows: the method for calculating the normal flexibility and the tangential flexibility is provided, the normal flexibility and the tangential flexibility of the cracks in the dry rock are obtained according to the related characteristics of the crack density in the rock, the shear modulus of the background rock and the like, and a foundation is provided for obtaining the frequency-dependent normal flexibility of the cracks.
Further, the A2 includes the following steps:
a21, calculating to obtain a time scale parameter and a shape parameter based on the P-wave modulus of the saturated crack-containing rock and the background rock;
the calculation expressions of the time scale parameters and the shape parameters are respectively as follows:
wherein τ andrespectively representing a time scale parameter and a shape parameter, C b Representing P-wave modulus, C, of saturated fractured rock and background rock under high frequency limit conditions 0 The P-wave modulus of saturated crack-containing rock and background rock under the low-frequency limit condition is represented, G represents a low-frequency scale parameter, and T represents a high-frequency scale parameter;
A22, calculating to obtain a flexibility frequency relation based on the time scale parameter and the shape scale parameter;
the calculation expression of the flexibility frequency relation is as follows:
wherein f fra (ω) represents the compliance frequency relationship, i represents the imaginary part of the complex number, ω represents frequency;
a23, calculating the normal flexibility of the crack depending on the frequency based on the flexibility frequency relation and the normal flexibility of the crack;
the frequency-dependent fracture normal compliance is calculated as follows:
wherein Z is N And (ω) represents the fracture normal compliance as a function of frequency.
The beneficial effects of adopting the further scheme are as follows: based on time scale parameters, shape parameters, P-wave modulus of saturated crack-containing rock and background rock under low-frequency and high-frequency limit conditions respectively, and characteristics of fluid, cracks and rock mineral particles, a flexibility frequency relation is obtained, frequency characteristics are given to normal flexibility, and a foundation is provided for constructing a rock dynamic flexibility matrix under the condition that the arrangement modes of the cracks in the vertical direction are different.
Further, the A3 includes the following steps:
a31, acquiring an arrangement mode of cracks in the mesoscopic crack rock physical model;
a32, judging whether the arrangement mode of the cracks is vertical random arrangement, if so, entering A33, otherwise, entering A34;
A33, calculating to obtain an additional flexibility matrix of the vertical random cracks based on tangential flexibility of the cracks and normal flexibility of the cracks depending on frequency, taking the additional flexibility matrix of the vertical random cracks as the additional flexibility matrix depending on frequency, and entering into step A37;
the computational expression of the additional compliance matrix for the vertical random fracture is as follows:
wherein DeltaS (omega) s An additional compliance matrix, Z, representing vertical random cracking N1 (ω) represents the normal compliance of the fracture in terms of frequency when the fracture is vertically randomly arranged,the tangential flexibility of the dry cracks when the cracks are vertically and randomly arranged is shown;
a34, judging whether the vertical direction arrangement mode of the cracks is vertical directional arrangement, if so, entering A35, otherwise, entering A36;
a35, calculating to obtain an additional flexibility matrix of the vertical directional crack based on tangential flexibility of the crack and normal flexibility of the crack depending on frequency, taking the additional flexibility matrix of the vertical directional crack as the additional flexibility matrix depending on frequency, and entering into step A37;
the computational expression of the additional compliance matrix for the vertically oriented fracture is as follows:
wherein DeltaS (omega) d Additional compliance matrix of dry rock, Z, representing fracture orientation N (ω) 2 Represents the normal compliance of the fracture as a function of frequency for vertically oriented alignment of the fracture, The tangential flexibility of the dry cracks when the cracks are vertically aligned is shown;
a36, judging whether the vertical direction arrangement mode of the cracks is vertical and random, if so, entering A37, otherwise, entering A38;
a37, calculating to obtain an additional flexibility matrix of the vertical crack orientation and the random based on the tangential flexibility of the crack and the normal flexibility of the crack depending on the frequency, and taking the additional flexibility matrix of the vertical crack orientation and the random as the additional flexibility matrix depending on the frequency;
the computational expression of the vertical fracture oriented and random additional compliance matrix is as follows:
wherein DeltaS (omega) sd An additional compliance matrix representing vertical fracture orientation and random;
a38, calculating to obtain an additional flexibility matrix completely random to the crack based on tangential flexibility of the crack and normal flexibility of the crack depending on frequency, and taking the additional flexibility matrix completely random to the crack as the additional flexibility matrix depending on frequency;
the computational expression of the fully random additional compliance matrix for the fracture is as follows:
wherein DeltaS (omega) 3 An additional compliance matrix, Z, representing the complete randomness of the fracture N (ω) 3 Indicating the normal compliance of the fracture as a function of frequency when the fracture is fully randomly arranged,the tangential flexibility of the dry cracks when the cracks are completely randomly arranged is shown;
A39, calculating to obtain a dry rock dynamic compliance matrix based on the dry rock background compliance matrix and the additional compliance matrix depending on frequency;
the calculation expression of the dry rock dynamic flexibility matrix is as follows:
wherein S is 0 (ω) represents a dry rock dynamic compliance matrix,representing the dry rock background compliance matrix, deltas (ω) represents the frequency dependent compliance matrix.
The beneficial effects of adopting the further scheme are as follows: the method for calculating the additional flexibility matrix is provided for the situation that the arrangement direction in the vertical direction in the mesoscopic fracture rock physical model is random and the situation that the arrangement direction in the vertical direction in the mesoscopic fracture rock physical model is random are random, the additional flexibility matrix is combined with the dry rock background flexibility matrix, the dry rock dynamic flexibility matrix can be obtained, and a foundation is provided for obtaining the complete rock frequency-dependent flexibility matrix.
Further, the calculation expression of the complete rock frequency-dependent compliance matrix in A4 is as follows:
wherein,and->Respectively represent the compliance tensor of saturated rock, dry rock and mineral particles, +.>Representing the sum of the compliance of the ith row in the dry rock compliance tensor corresponding matrix,/th row>Representing the sum of the compliance of the ith row in the mineral particle compliance tensor corresponding matrix,/>Representing the compliance tensor correspondence of dry rock Flexibility sum of j' th column in matrix,/->Representing the sum of the compliance of the j' th column of the mineral particle compliance tensor corresponding matrix, beta dry Represents the generalized compression coefficient, beta, of fractured dry rock g Representing the compression coefficient, beta, of mineral particles f Representing the compressibility of the fluid, +.>Represents the total porosity, where i '=1, 2,3,4,5,6, j' =1, 2,3,4,5,6.
The beneficial effects of adopting the further scheme are as follows: the dynamic compliance matrix of the dry rock is substituted into an anisotropic Gassmann equation, the residual fluid effect is added, the fluid characteristics can be combined on the basis of the dry rock, the complete rock frequency-dependent compliance matrix is obtained, and a basis is provided for obtaining the frequency-dependent stiffness matrix of the rock and performing frequency dispersion AVO simulation on a constructed rock model.
Further, the calculation expression of the anisotropy coefficient in B2 is as follows:
wherein α (ω) represents a first frequency-dependent anisotropy coefficient, c 33 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 3 and column 3 in the frequency-dependent stiffness matrix, ρ represents the medium density, β (ω) represents the frequency-dependent second anisotropy coefficient, c 44 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 4 and column 4 in the frequency-dependent stiffness matrix, ε (ω) represents the third frequency-dependent anisotropy coefficient, c 11 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 1 and column 1 in the frequency-dependent stiffness matrix, γ (ω) represents the fourth frequency-dependent anisotropy coefficient, c 66 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 6 and column 6 in the frequency-dependent stiffness matrix, δ (ω) represents the fifth frequency-dependent anisotropy coefficient, c 13 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 1 and column 3 in the frequency-dependent stiffness matrix, c 55 And (ω) represents the real part of the frequency-dependent stiffness coefficient at row 5 and column 5 in the frequency-dependent stiffness matrix.
The beneficial effects of adopting the further scheme are as follows: the frequency-dependent anisotropic coefficient is obtained by calculating the coefficient in the frequency-dependent stiffness matrix of the rock corresponding to the mesoscopic fracture rock physical model with respect to the medium density, and a foundation is provided for calculating the interface reflection coefficient.
Further, the calculation expression of the reflection coefficient of the variable interface in the B3 is as follows:
Δγ(ω)＝γ 2 (ω)-γ 1 (ω)
Δα(ω)＝α 2 (ω)-α 1 (ω)Δε(ω)＝ε 2 (ω)-ε 1 (ω)Δδ(ω)＝δ 2 (ω)-δ 1 (ω)
ΔZ(ω)＝Z 2 (ω)-Z 1 (ω)Z(ω)＝ρα(ω)
Δμ(ω)＝μ 2 (ω)-μ 1 (ω)μ(ω)＝ρβ(ω) 2
wherein R is pp (ω, ζ, θ) represents the frequency-dependent interface reflection coefficient, ΔZ (ω) represents the difference in vertical P-wave impedance between the lower medium and the upper medium with respect to frequency,represents the average value of the vertical P-wave impedance of the lower medium and the upper medium in relation to frequency, delta alpha (omega) represents the first anisotropy coefficient difference value of the lower medium and the upper medium in relation to frequency,/ >A first anisotropy coefficient average value representing the frequency dependence of the lower medium and the upper medium,/>A second anisotropy coefficient average value representing the frequency dependence of the lower medium and the upper medium, and Δμ (ω) represents a difference in vertical shear modulus of the lower medium and the upper medium with respect to frequency,/>Represents the average value of the vertical transverse wave modulus of the lower medium and the upper medium related to frequency, delta (omega) represents the fifth anisotropy coefficient difference value of the lower medium and the upper medium dependent on frequency, θ represents the incident angle of the P wave, Δε (ω) represents the third anisotropy coefficient difference between the frequency dependence of the lower medium and the upper medium, ζ represents the incident azimuth angle of the P wave, and α 1 (omega) and alpha 2 (omega) represents the first anisotropy coefficient, beta, of the frequency dependence of the upper medium and the lower medium, respectively 1 (omega) and beta 2 (omega) represents the second anisotropy coefficient of the upper medium and the lower medium dependent frequency, respectively ε 1 (omega) and ε 2 (ω) third anisotropy coefficient, δ, representing the frequency dependence of the upper medium and the lower medium, respectively 1 (omega) and delta 2 (ω) fifth anisotropy coefficient of dependence frequency of upper medium and lower medium, γ 1 (omega) and gamma 2 (ω) represents the fourth anisotropy coefficient of the upper medium and the lower medium dependent frequency, respectively, Δγ (ω) represents the fourth anisotropy coefficient difference of the lower medium and the upper medium dependent frequency, Z 1 (omega) and Z 2 (ω) represents the vertical P-wave impedance of the lower medium and the upper medium with respect to frequency, Z (ω) represents the vertical P-wave impedance with respect to frequency, μ 1 Sum mu 2 The vertical shear modulus of the lower medium and the upper medium are shown as a function of frequency, respectively.
The beneficial effects of adopting the further scheme are as follows: substituting the anisotropic coefficient depending on the frequency into the HIT medium P wave reflection coefficient formula to obtain the frequency-dependent interface reflection coefficient, and providing a basis for the seismic record of the AVO simulation result combined with the seismic source wavelet.
Further, the step B4 includes the steps of:
b41, obtaining the reflection coefficient of the interface relative to the frequency based on the reflection coefficient of the frequency-dependent interface;
b42, calculating to obtain a multi-interface seismic dispersion AVO simulation record based on the reflection coefficient and the source wavelet of the interface related to frequency;
the calculation expression of the multi-interface seismic dispersion AVO simulation record is as follows:
wherein x is t (theta) seismic recordings with a time depth t,the unit reflection coefficient of the n-th layer interface is represented, k represents the total layer number of the interface, deltat represents the sampling interval, W (omega) represents the source wavelet, R n (θ, ω) represents the reflection coefficient of the n-th layer interface with respect to frequency, and x represents the convolution operation, FFT -1 Representing the inverse fourier transform.
The beneficial effects of adopting the further scheme are as follows: in the frequency domain, multiplying the frequency-dependent reflection coefficient by the source wavelet, and performing inverse Fourier transform to obtain a synthesized seismic record, dividing a target reservoir according to different time depths for a multi-layer interface to obtain interfaces with different time depths, so that the multi-interface synthesized seismic record can be obtained, and multi-interface seismic dispersion AVO simulation is realized.
Compared with the prior art, the invention has the following advantages:
the frequency dispersion AVO simulation method of the mesoscopic fracture rock physical model provided by the invention can realize dynamic rock simulation of complex fracture conditions, multiple groups of fracture conditions are generated when the rock is subjected to different geological conditions in different periods, and when the fracture arrangement mode of the rock has vertical directional arrangement and vertical random arrangement and completely random arrangement, the calculation method for constructing an additional flexibility matrix depending on frequency can still be provided, and the construction method provided by the invention is based on frequency characteristics, is simple and efficient, but is not precision.
Other advantages that are also present with respect to the present invention will be more detailed in the following examples.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of steps of a method for simulating a frequency dispersion AVO of a mesoscopic fracture petrophysical model in an embodiment of the invention.
FIG. 2 is a schematic view of a horizontal layer with vertically oriented arrangement of cracks in an embodiment of the present invention.
FIG. 3 (a) is a graph showing the variation of the interface reflection coefficient with the incident angle, which is numbered H in the embodiment of the present invention.
FIG. 3 (b) is a graph showing the variation of the interface reflection coefficient with frequency, which is numbered H in the example of the present invention.
FIG. 3 (c) is a schematic diagram of simulated recording of the AVO of the interfacial seismic dispersion with the number H in the embodiment of the present invention.
FIG. 3 (d) is a superimposed waveform of the frequency-dependent and frequency-independent interface, designated H, in an embodiment of the invention.
FIG. 4 (a) is a graph showing the variation of the interfacial reflection coefficient with the incident angle, which is numbered M in the embodiment of the present invention.
FIG. 4 (b) is a graph showing the variation of the interfacial reflection coefficient with frequency, which is numbered M in the example of the present invention.
FIG. 4 (c) is a schematic diagram of simulated recording of the AVO of the interfacial seismic dispersion with the number M in the embodiment of the present invention.
FIG. 4 (d) is a superimposed waveform of the frequency dependent and frequency independent interface designated M in an embodiment of the invention.
FIG. 5 (a) is a graph showing the variation of the interface reflection coefficient with the incident angle, which is numbered S in the embodiment of the present invention.
FIG. 5 (b) is a schematic diagram of simulated recording of the AVO of the interfacial seismic dispersion with the number S in the embodiment of the present invention.
FIG. 5 (c) is a superimposed waveform of the frequency dependent and frequency independent interface S in an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by a person skilled in the art without making any inventive effort, are intended to be within the scope of the present invention.
Example 1
As shown in fig. 1, in one embodiment of the present invention, the present invention provides a method for simulating a dispersion AVO of a mesoscopic fracture rock physical model, which includes a phase of obtaining a frequency-dependent stiffness matrix of the mesoscopic fracture rock, and a phase of simulating the model dispersion AVO;
the phase for obtaining the frequency-dependent stiffness matrix of the mesoscopic fracture rock comprises the following steps:
a1, acquiring crack density, number of cracks, radius of the cracks and shear modulus of background rock, and calculating to obtain normal flexibility and tangential flexibility of the cracks;
the calculation expressions of the normal flexibility and the tangential flexibility in the A1 are as follows:
wherein,and->The normal and tangential compliance of the dry fracture are shown, respectively, lambda shows the pull Mei Jishu, mu shows the shear modulus of the background rock, e shows the fracture density, N shows the number of cracks, a shows the fracture radius, V shows the rock volume.
A2, calculating the normal flexibility of the crack based on the P-wave modulus of the crack-containing rock and the saturated background rock, and obtaining the normal flexibility of the crack depending on the frequency;
the A2 comprises the following steps:
a21, calculating to obtain a time scale parameter and a shape parameter based on the P-wave modulus of the saturated crack-containing rock and the background rock;
The calculation expressions of the time scale parameters and the shape parameters are respectively as follows:
wherein τ andrespectively representing a time scale parameter and a shape parameter, C b Representing P-wave modulus, C, of saturated fractured rock and background rock under high frequency limit conditions 0 The P-wave modulus of saturated crack-containing rock and background rock under the low-frequency limit condition is represented, G represents a low-frequency scale parameter, and T represents a high-frequency scale parameter;
the most common slit at present is a coin-shaped slit, and the scheme provides a calculation method for the high-frequency scale parameter and the low-frequency scale parameter of the coin-shaped slit, wherein the calculation expression of the high-frequency scale parameter and the low-frequency scale parameter of the coin-shaped slit is as follows:
wherein alpha is b Biot-Willis coefficients, M, representing background rock b Representing the fluid-solid coupling modulus, g, of the background rock b Represents the ratio of shear modulus to P-wave modulus in background rock, eta represents the fluid viscosity coefficient, mu b Represents the shear modulus of the background rock, L B Representing P-wave modulus, κ of background rock b Represents the permeability of background medium, K b 、K g 、K f The bulk modulus of the dry back Jing Yandan, mineral particles, fluid,representing background void fraction;
a22, calculating to obtain a flexibility frequency relation based on the time scale parameter and the shape scale parameter;
The calculation expression of the flexibility frequency relation is as follows:
wherein f fra (ω) represents the compliance frequency relationship, i represents the imaginary part of the complex number, ω represents frequency;
a23, calculating the normal flexibility of the crack depending on the frequency based on the flexibility frequency relation and the normal flexibility of the crack;
the frequency-dependent fracture normal compliance is calculated as follows:
wherein Z is N And (ω) represents the fracture normal compliance as a function of frequency.
A3, calculating a dry rock dynamic flexibility matrix based on tangential flexibility of the cracks, normal flexibility of the cracks depending on frequency and a dry rock background flexibility matrix according to the arrangement mode of the cracks;
the A3 comprises the following steps:
a31, acquiring an arrangement mode of cracks in the mesoscopic crack rock physical model;
a32, judging whether the arrangement mode of the cracks is vertical random arrangement, if so, entering A33, otherwise, entering A34;
a33, calculating to obtain an additional flexibility matrix of the vertical random cracks based on tangential flexibility of the cracks and normal flexibility of the cracks depending on frequency, taking the additional flexibility matrix of the vertical random cracks as the additional flexibility matrix depending on frequency, and entering into step A37;
the computational expression of the additional compliance matrix for the vertical random fracture is as follows:
Wherein DeltaS (omega) s An additional compliance matrix, Z, representing vertical random cracking N1 (ω) represents the normal compliance of the fracture in terms of frequency when the fracture is vertically randomly arranged,the tangential flexibility of the dry cracks when the cracks are vertically and randomly arranged is shown;
a34, judging whether the vertical direction arrangement mode of the cracks is vertical directional arrangement, if so, entering A35, otherwise, entering A36;
a35, calculating to obtain an additional flexibility matrix of the vertical directional crack based on tangential flexibility of the crack and normal flexibility of the crack depending on frequency, taking the additional flexibility matrix of the vertical directional crack as the additional flexibility matrix depending on frequency, and entering into step A37;
the computational expression of the additional compliance matrix for the vertically oriented fracture is as follows:
wherein the method comprises the steps of，ΔS(ω) d Additional compliance matrix of dry rock, Z, representing fracture orientation N (ω) 2 Represents the normal compliance of the fracture as a function of frequency for vertically oriented alignment of the fracture,the tangential flexibility of the dry cracks when the cracks are vertically aligned is shown;
a36, judging whether the vertical direction arrangement mode of the cracks is vertical and random, if so, entering A37, otherwise, entering A38;
a37, calculating to obtain an additional flexibility matrix of the vertical crack orientation and the random based on the tangential flexibility of the crack and the normal flexibility of the crack depending on the frequency, and taking the additional flexibility matrix of the vertical crack orientation and the random as the additional flexibility matrix depending on the frequency;
The computational expression of the vertical fracture oriented and random additional compliance matrix is as follows:
wherein DeltaS (omega) sd An additional compliance matrix representing vertical fracture orientation and random;
a38, calculating to obtain an additional flexibility matrix completely random to the crack based on tangential flexibility of the crack and normal flexibility of the crack depending on frequency, and taking the additional flexibility matrix completely random to the crack as the additional flexibility matrix depending on frequency;
the computational expression of the fully random additional compliance matrix for the fracture is as follows:
wherein DeltaS (omega) 3 An additional compliance matrix, Z, representing the complete randomness of the fracture N (ω) 3 Indicating the normal compliance of the fracture as a function of frequency when the fracture is fully randomly arranged,indicating a crackTangential compliance of the dry split when the slits are fully randomly arranged;
a39, calculating to obtain a dry rock dynamic compliance matrix based on the dry rock background compliance matrix and the additional compliance matrix depending on frequency;
the calculation expression of the dry rock dynamic flexibility matrix is as follows:
wherein S is 0 (ω) represents a dry rock dynamic compliance matrix,representing the dry rock background compliance matrix, deltas (ω) represents the frequency dependent compliance matrix.
As a preferred solution, the background compliance matrix of the rock in this embodiment is obtained from the background stiffness matrix; the parameters in the background stiffness matrix can be obtained through calculation of mineral particle parameters and background porosity of the rock, and can also be obtained through measurement of high-pressure experiments.
A4, calculating to obtain a complete rock frequency-dependent compliance matrix based on the dry rock dynamic compliance matrix and an anisotropic Gassmann equation;
the calculation expression of the complete rock frequency-dependent flexibility matrix in the A4 is as follows:
wherein,and->Respectively represent the compliance tensor of saturated rock, dry rock and mineral particles, +.>Representing the sum of the compliance of the ith row in the dry rock compliance tensor corresponding matrix,/th row>Representing the sum of the compliance of the ith row in the mineral particle compliance tensor corresponding matrix,/>Representing the sum of the compliance of the j' th column in the dry rock compliance tensor corresponding matrix,representing the sum of the compliance of the j' th column of the mineral particle compliance tensor corresponding matrix, beta dry Represents the generalized compression coefficient, beta, of fractured dry rock g Representing the compression coefficient, beta, of mineral particles f Representing the compressibility of the fluid, +.>Represents the total porosity, where i '=1, 2,3,4,5,6, j' =1, 2,3,4,5,6.
A5, inverting the complete rock frequency-dependent flexibility matrix to obtain a rock frequency-dependent stiffness matrix;
the model dispersion AVO simulation stage comprises the following steps:
b1, obtaining a frequency-dependent stiffness coefficient based on a frequency-dependent stiffness matrix of the rock;
b2, calculating to obtain an anisotropic coefficient dependent on frequency based on the real part of the frequency-dependent stiffness coefficient;
The calculation expression of the anisotropy coefficient in the B2 is as follows:
wherein α (ω) represents a first frequency-dependent anisotropy coefficient, c 33 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 3 and column 3 in the frequency-dependent stiffness matrix, ρ represents the medium density, β (ω) represents the frequency-dependent second anisotropy coefficient, c 44 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 4 and column 4 in the frequency-dependent stiffness matrix, ε (ω) represents the third frequency-dependent anisotropy coefficient, c 11 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 1 and column 1 in the frequency-dependent stiffness matrix, γ (ω) represents the fourth frequency-dependent anisotropy coefficient, c 66 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 6 and column 6 in the frequency-dependent stiffness matrix, δ (ω) represents the fifth frequency-dependent anisotropy coefficient, c 13 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 1 and column 3 in the frequency-dependent stiffness matrix, c 55 And (ω) represents the real part of the frequency-dependent stiffness coefficient at row 5 and column 5 in the frequency-dependent stiffness matrix.
B3, obtaining a reflection coefficient of the frequency-dependent interface based on the anisotropic coefficient and the reflection coefficient equation;
the calculation expression of the reflection coefficient of the frequency-dependent interface in the B3 is as follows:
/>
Δγ(ω)＝γ 2 (ω)-γ 1 (ω)
Δα(ω)＝α 2 (ω)-α 1 (ω)Δε(ω)＝ε 2 (ω)-ε 1 (ω)Δδ(ω)＝δ 2 (ω)-δ 1 (ω)
ΔZ(ω)＝Z 2 (ω)-Z 1 (ω)Z(ω)＝ρα(ω)
Δμ(ω)＝μ 2 (ω)-μ 1 (ω)μ(ω)＝ρβ(ω) 2
wherein R is pp (ω, ζ, θ) represents the frequency-dependent interface reflection coefficient, ΔZ (ω) represents the difference in vertical P-wave impedance between the lower medium and the upper medium with respect to frequency, Represents the average value of the vertical P-wave impedance of the lower medium and the upper medium in relation to frequency, delta alpha (omega) represents the first anisotropy coefficient difference value of the lower medium and the upper medium in relation to frequency,/>A first anisotropy coefficient average value representing the frequency dependence of the lower medium and the upper medium,/>A second anisotropy coefficient average value representing the frequency dependence of the lower medium and the upper medium, and Δμ (ω) represents a difference in vertical shear modulus of the lower medium and the upper medium with respect to frequency,/>Represents the average value of the vertical transverse wave modulus of the lower medium and the upper medium related to frequency, delta (omega) represents the fifth anisotropy coefficient difference value of the lower medium and the upper medium dependent on frequency, θ represents the incident angle of the P wave, Δε (ω) represents the third anisotropy coefficient difference between the frequency dependence of the lower medium and the upper medium, ζ represents the incident azimuth angle of the P wave, and α 1 (omega) and alpha 2 (omega) first anisotropy coefficients representing the frequency dependence of the upper medium and the lower medium, respectively，β 1 (omega) and beta 2 (omega) represents the second anisotropy coefficient of the upper medium and the lower medium dependent frequency, respectively ε 1 (omega) and ε 2 (ω) third anisotropy coefficient, δ, representing the frequency dependence of the upper medium and the lower medium, respectively 1 (omega) and delta 2 (ω) fifth anisotropy coefficient of dependence frequency of upper medium and lower medium, γ 1 (omega) and gamma 2 (ω) represents the fourth anisotropy coefficient of the upper medium and the lower medium dependent frequency, respectively, Δγ (ω) represents the fourth anisotropy coefficient difference of the lower medium and the upper medium dependent frequency, Z 1 (omega) and Z 2 (ω) represents the vertical P-wave impedance of the lower medium and the upper medium with respect to frequency, Z (ω) represents the vertical P-wave impedance with respect to frequency, μ 1 Sum mu 2 The vertical shear modulus of the lower medium and the upper medium are shown as a function of frequency, respectively.
B4, calculating to obtain a multi-interface seismic dispersion AVO simulation record according to the frequency-dependent interface reflection coefficient and the source wavelet;
the step B4 comprises the following steps:
b41, obtaining the reflection coefficient of the interface relative to the frequency based on the reflection coefficient of the frequency-dependent interface;
b42, calculating to obtain a multi-interface seismic dispersion AVO simulation record based on the reflection coefficient and the source wavelet of the interface related to frequency;
the calculation expression of the multi-interface seismic dispersion AVO simulation record is as follows:
wherein x is t (theta) seismic recordings with a time depth t,represents the unit reflection coefficient of the n-th layer interface, and k represents the total layer number of the interface Δt represents the sampling interval, W (ω) represents the source wavelet, R n (θ, ω) represents the reflection coefficient of the n-th layer interface with respect to frequency, and x represents the convolution operation, FFT -1 Representing the inverse fourier transform.
The invention adds the relaxation function to the crack parameters to construct the crack flexibility parameters depending on the frequency, and the improvement is convenient for constructing the complex dispersion model. The method can realize the construction of a mesoscopic crack dynamic model which is randomly distributed, and the corresponding formula form is simpler than the previous model.
Based on the petrophysical model modeling of the invention, the simulation of the related AVO seismic records is realized, and a petrophysical foundation can be provided for forward modeling of earthquake and logging data and interpretation work.
Based on the related frequency dispersion rock physical model, the AVO frequency variation and the frequency-related synthetic seismic records are analyzed, and more parameters or phenomena can be provided for describing the fluid and crack conditions of underground rock, so that the method has important significance.
Example 2
As shown in fig. 2, in a practical example of the present invention, a horizontal layer is designed, and the upper layer is dense mudstone and isotropic; the lower layer was sandstone, containing fluids and fractures, with the fractures vertically aligned (HTI type alignment), with the mudstone parameters and the sandstone background rock parameters as shown in table 1:
TABLE 1
In this embodiment, the background rock parameters are constant;
the horizontal layer-related fracture fluid parameters are shown in table 2:
TABLE 2
In this embodiment, according to the method for simulating the dispersion AVO of the mesoscopic fracture petrophysical model provided in embodiment 1, the designed horizontal layer is subjected to the dispersion AVO simulation by using the 25Hz rake wavelet and the characteristic frequency in table 2, so as to obtain the multi-interface seismic dispersion AVO simulation record of a series of models in table 2.
When the sandstone parameter is taken as a model H, the characteristic frequency is about 158Hz and is larger than the main frequency of 25Hz of the Rake wavelet. As shown in fig. 3 (a), there is no significant reflection coefficient dispersion from 1Hz to 60 Hz; as shown in fig. 3 (b), the interface reflection coefficient is negative at normal incidence, and as the incident angle increases, the reflection coefficient becomes positive and further increases; as shown in fig. 3 (c), the 0.3s is the frequency-dependent dynamic model simulation result, the 0.7s is the frequency-independent low-frequency limit result simulated by the Gassmann equation, and the rightmost one is the result after the superposition of the angle gathers; as shown in fig. 3 (d), the dynamic model and Gassmann low frequency limit results were observed to be nearly identical in the oscillogram in the synthetic seismic record.
When the sandstone parameter is taken as the model M, the characteristic frequency is about 40Hz, which is similar to the main frequency of the Rake wavelet. In fig. 4 (a), it is observed that a significant reflection coefficient dispersion occurs from 1Hz to 60Hz with the change of the incident angle; as shown in fig. 4 (b), in the synthetic seismic record, a difference occurs between the dynamic model using the scheme at 0.3s and the low frequency limit result simulated by the Gassmann equation at 0.7 s; as shown in fig. 4 (c), the superimposed waveform of the dynamic model angle gather is distorted, and the waveform is not symmetrical any more; as shown in fig. 4 (d), the dispersion difference exhibited at an incident angle of 40 ° was larger than that of the small-angle incident, and the same phenomenon was observed in the subsequent simulation.
The sandstone parameter is taken as a model S, and the characteristic frequency is about 2 Hz. As shown in fig. 5 (a), the dispersion of the reflection coefficient is no longer noticeable after 20 Hz; as shown in fig. 5 (b), in the synthetic seismic record, the dynamic model and the low frequency limit static model difference further increase; as shown in fig. 5 (c), the amplitude value of the angle gather of the dynamic model is small, the amplitude polarities of the near and far tracks of the dynamic model are opposite, and after superposition, the amplitude of the superimposed tracks is weak.
And calculating to obtain the multi-interface seismic dispersion AVO simulation record of the sandstone M and the mudstone when the azimuth angle is 45 degrees and 90 degrees by adopting the same method. The proportions of the large azimuthal angle (parallel to the crack direction) dispersion differences increase in the variation of the reflection coefficient at the interfaces of the comparative model M at the azimuth planes of 0 degrees, 45 degrees and 90 degrees, but are smallest in the numerical difference. This is because the dispersion is strongest when incident on the vertical fracture surface, and is weakest when parallel to the fracture surface. For the waveform distortion phenomenon, it is also observed that the waveform distortion decreases with increasing azimuth angle.
When the characteristic frequency is near the main frequency of the seismic wavelet, the dispersion effect is obvious on the seismic section, and the characteristic frequency is mainly reflected in the waveform amplitude difference and waveform distortion. As the characteristic frequency is smaller, the difference between the result after considering the dispersion and the result using the conventional Gassmann equation static model is larger. It should be noted that the dispersion on the seismic profile is not significant when the characteristic frequency is about an order of magnitude greater than the dominant frequency of the seismic survey wavelet, and the effect of the dispersion can be ignored. However, in the case of well-to-seismic joints, the effect of dispersion has to be taken into account. In directional HTI fracture media, the dispersion phenomenon over the seismic section gradually diminishes as the azimuth angle increases. That is, it is intended to observe a significant waveform distortion phenomenon in the fracture medium, and the phenomenon is most significant in a cross section perpendicular to the fracture direction.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within the scope of the present invention.
Claims (7)
1. A frequency dispersion AVO simulation method of a mesoscopic fracture rock physical model is characterized by comprising a frequency-dependent stiffness matrix acquisition stage of mesoscopic fracture rock and a model frequency dispersion AVO simulation stage;
the phase for obtaining the frequency-dependent stiffness matrix of the mesoscopic fracture rock comprises the following steps:
a1, acquiring crack density, number of cracks, radius of the cracks and shear modulus of background rock, and calculating to obtain normal flexibility and tangential flexibility of the cracks;
a2, calculating the normal flexibility of the crack based on the P-wave modulus of the crack-containing rock and the saturated background rock, and obtaining the normal flexibility of the crack depending on the frequency;
a3, calculating a dry rock dynamic flexibility matrix based on tangential flexibility of the cracks, normal flexibility of the cracks depending on frequency and a dry rock background flexibility matrix according to the arrangement mode of the cracks;
the A3 comprises the following steps:
a31, acquiring an arrangement mode of cracks in the mesoscopic crack rock physical model;
A32, judging whether the arrangement mode of the cracks is vertical random arrangement, if so, entering A33, otherwise, entering A34;
a33, calculating to obtain an additional flexibility matrix of the vertical random cracks based on tangential flexibility of the cracks and normal flexibility of the cracks depending on frequency, taking the additional flexibility matrix of the vertical random cracks as the additional flexibility matrix depending on frequency, and entering into step A37;
the computational expression of the additional compliance matrix for the vertical random fracture is as follows:
wherein DeltaS (omega) s An additional compliance matrix, Z, representing vertical random cracking N1 (ω) represents the normal compliance of the fracture in terms of frequency when the fracture is vertically randomly arranged,the tangential flexibility of the dry cracks when the cracks are vertically and randomly arranged is shown;
a34, judging whether the vertical direction arrangement mode of the cracks is vertical directional arrangement, if so, entering A35, otherwise, entering A36;
a35, calculating to obtain an additional flexibility matrix of the vertical directional crack based on tangential flexibility of the crack and normal flexibility of the crack depending on frequency, taking the additional flexibility matrix of the vertical directional crack as the additional flexibility matrix depending on frequency, and entering into step A37;
the computational expression of the additional compliance matrix for the vertically oriented fracture is as follows:
Wherein DeltaS (omega) d Additional compliance matrix of dry rock, Z, representing fracture orientation N2 (ω) represents the normal compliance of the fracture as a function of frequency when the fracture is vertically aligned,the tangential flexibility of the dry cracks when the cracks are vertically aligned is shown;
a36, judging whether the vertical direction arrangement mode of the cracks is vertical and random, if so, entering A37, otherwise, entering A38;
a37, calculating to obtain an additional flexibility matrix of the vertical crack orientation and the random based on the tangential flexibility of the crack and the normal flexibility of the crack depending on the frequency, and taking the additional flexibility matrix of the vertical crack orientation and the random as the additional flexibility matrix depending on the frequency;
the computational expression of the vertical fracture oriented and random additional compliance matrix is as follows:
wherein DeltaS (omega) sd An additional compliance matrix representing vertical fracture orientation and random;
a38, calculating to obtain an additional flexibility matrix completely random to the crack based on tangential flexibility of the crack and normal flexibility of the crack depending on frequency, and taking the additional flexibility matrix completely random to the crack as the additional flexibility matrix depending on frequency;
the computational expression of the fully random additional compliance matrix for the fracture is as follows:
wherein DeltaS (omega) 3 An additional compliance matrix, Z, representing the complete randomness of the fracture N (ω) 3 Indicating the normal compliance of the fracture as a function of frequency when the fracture is fully randomly arranged,the tangential flexibility of the dry cracks when the cracks are completely randomly arranged is shown;
a39, calculating to obtain a dry rock dynamic compliance matrix based on the dry rock background compliance matrix and the additional compliance matrix depending on frequency;
the calculation expression of the dry rock dynamic flexibility matrix is as follows:
wherein S is 0 (ω) represents a dry rock dynamic compliance matrix,representing a dry rock background compliance matrix, Δs (ω) representing a frequency dependent compliance matrix;
a4, calculating to obtain a complete rock frequency-dependent compliance matrix based on the dry rock dynamic compliance matrix and an anisotropic Gassmann equation;
a5, inverting the complete rock frequency-dependent flexibility matrix to obtain a rock frequency-dependent stiffness matrix;
the model dispersion AVO simulation stage comprises the following steps:
b1, obtaining a frequency-dependent stiffness coefficient based on a frequency-dependent stiffness matrix of the rock;
b2, calculating to obtain an anisotropic coefficient dependent on frequency based on the real part of the frequency-dependent stiffness coefficient;
b3, obtaining a reflection coefficient of the frequency-dependent interface based on the anisotropic coefficient and the reflection coefficient equation;
and B4, calculating to obtain the multi-interface seismic dispersion AVO simulation record according to the frequency-dependent interface reflection coefficient and the source wavelet.
2. The method for simulating the dispersion AVO of the mesoscopic fracture petrophysical model according to claim 1, wherein the calculation expressions of the normal compliance and the tangential compliance in the A1 are as follows:
wherein,and->The normal and tangential compliance of the dry fracture are shown, respectively, lambda shows the pull Mei Jishu, mu shows the shear modulus of the background rock, e shows the fracture density, N shows the number of cracks, a shows the fracture radius, V shows the rock volume.
3. The method of simulating a frequency-dispersive AVO of a mesoscopic fracture petrophysical model according to claim 2, wherein the A2 comprises the steps of:
a21, calculating to obtain a time scale parameter and a shape parameter based on the P-wave modulus of the saturated crack-containing rock and the background rock;
the calculation expressions of the time scale parameters and the shape parameters are respectively as follows:
wherein τ andrespectively representing a time scale parameter and a shape parameter, C b Representing P-wave modulus, C, of saturated fractured rock and background rock under high frequency limit conditions 0 The P-wave modulus of saturated crack-containing rock and background rock under the low-frequency limit condition is represented, G represents a low-frequency scale parameter, and T represents a high-frequency scale parameter;
a22, calculating to obtain a flexibility frequency relation based on the time scale parameter and the shape parameter;
The calculation expression of the flexibility frequency relation is as follows:
wherein f fra (ω) represents the compliance frequency relationship, i represents the imaginary part of the complex number, ω represents frequency;
a23, calculating the normal flexibility of the crack depending on the frequency based on the flexibility frequency relation and the normal flexibility of the crack;
the frequency-dependent fracture normal compliance is calculated as follows:
wherein Z is N And (ω) represents the fracture normal compliance as a function of frequency.
4. The method for simulating a frequency dispersion AVO of a mesoscopic fracture petrophysical model according to claim 1, wherein the calculation expression of the complete rock frequency-dependent compliance matrix in A4 is as follows:
wherein,and->Respectively represent the compliance tensor of saturated rock, dry rock and mineral particles, +.>Representing the sum of the compliance of the ith row in the dry rock compliance tensor corresponding matrix,/th row>Representing the sum of the compliance of the ith row in the mineral particle compliance tensor corresponding matrix,/>Representing the sum of the compliance of the j' th column in the dry rock compliance tensor corresponding matrix,/>Representing the sum of the compliance of the j' th column of the mineral particle compliance tensor corresponding matrix, beta dry Represents the generalized compression coefficient, beta, of fractured dry rock g Representing the compression coefficient, beta, of mineral particles f Representing the compressibility of the fluid, +.>Represents the total porosity, where i '=1, 2,3,4,5,6, j' =1, 2,3,4,5,6.
5. The method for simulating a frequency dispersion AVO of a mesoscopic fracture petrophysical model of claim 4, wherein the calculated expression of the anisotropy coefficient in B2 is as follows:
wherein α (ω) represents a first frequency-dependent anisotropy coefficient, c 33 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 3 and column 3 in the frequency-dependent stiffness matrix, ρ represents the medium density, and β (ω) is shown in the tableShowing a second frequency dependent anisotropy coefficient, c 44 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 4 and column 4 in the frequency-dependent stiffness matrix, ε (ω) represents the third frequency-dependent anisotropy coefficient, c 11 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 1 and column 1 in the frequency-dependent stiffness matrix, γ (ω) represents the fourth frequency-dependent anisotropy coefficient, c 66 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 6 and column 6 in the frequency-dependent stiffness matrix, δ (ω) represents the fifth frequency-dependent anisotropy coefficient, c 13 (ω) represents the real part of the frequency-dependent stiffness coefficient at row 1 and column 3 in the frequency-dependent stiffness matrix, c 55 And (ω) represents the real part of the frequency-dependent stiffness coefficient at row 5 and column 5 in the frequency-dependent stiffness matrix.
6. The method for simulating a frequency dispersion AVO of a mesoscopic fracture petrophysical model according to claim 5, wherein the calculation expression of the frequency interface reflection coefficient in B3 is as follows:
Δγ(ω)＝γ 2 (ω)-γ 1 (ω)
Δα(ω)＝α 2 (ω)-α 1 (ω) Δε(ω)＝ε 2 (ω)-ε 1 (ω) Δδ(ω)＝δ 2 (ω)-δ 1 (ω)
ΔZ(ω)＝Z 2 (ω)-Z 1 (ω) Z(ω)＝ρα(ω)
Δμ(ω)＝μ 2 (ω)-μ 1 (ω) μ(ω)＝ρβ(ω) 2
wherein R is pp (ω, ζ, θ) represents the frequency-dependent interface reflection coefficient, ΔZ (ω) represents the difference in vertical P-wave impedance between the lower medium and the upper medium with respect to frequency,represents the average value of the vertical P-wave impedance of the lower medium and the upper medium in relation to frequency, delta alpha (omega) represents the first anisotropy coefficient difference value of the lower medium and the upper medium in relation to frequency,/>A first anisotropy coefficient average value representing the frequency dependence of the lower medium and the upper medium,/>A second anisotropy coefficient average value representing the frequency dependence of the lower medium and the upper medium, and Δμ (ω) represents a difference in vertical shear modulus of the lower medium and the upper medium with respect to frequency,/>Represents the average value of the vertical transverse wave modulus of the lower medium and the upper medium related to frequency, delta (omega) represents the fifth anisotropy coefficient difference value of the lower medium and the upper medium dependent on frequency, θ represents the incident angle of the P wave, Δε (ω) represents the third anisotropy coefficient difference between the frequency dependence of the lower medium and the upper medium, ζ represents the incident azimuth angle of the P wave, and α 1 (omega) and alpha 2 (omega) represents the first anisotropy coefficient, beta, of the frequency dependence of the upper medium and the lower medium, respectively 1 (omega) and beta 2 (omega) represents the second anisotropy coefficient of the upper medium and the lower medium dependent frequency, respectively ε 1 (omega) and ε 2 (ω) third anisotropy coefficient, δ, representing the frequency dependence of the upper medium and the lower medium, respectively 1 (omega) and delta 2 (ω) fifth anisotropy coefficient of dependence frequency of upper medium and lower medium, γ 1 (omega) and gamma 2 (ω)A fourth anisotropy coefficient representing the frequency dependence of the upper medium and the lower medium, respectively, Δγ (ω) representing a fourth anisotropy coefficient difference between the frequency dependence of the lower medium and the upper medium, Z 1 (omega) and Z 2 (ω) represents the vertical P-wave impedance of the lower medium and the upper medium with respect to frequency, Z (ω) represents the vertical P-wave impedance with respect to frequency, μ 1 Sum mu 2 The vertical shear modulus of the lower medium and the upper medium are shown as a function of frequency, respectively.
7. The method of simulating a frequency-dispersive AVO of a mesoscopic fracture petrophysical model of claim 6, wherein B4 comprises the steps of:
b41, obtaining the reflection coefficient of the interface relative to the frequency based on the reflection coefficient of the frequency-dependent interface;
b42, calculating to obtain a multi-interface seismic dispersion AVO simulation record based on the reflection coefficient and the source wavelet of the interface related to frequency;
The calculation expression of the multi-interface seismic dispersion AVO simulation record is as follows:
wherein x is t (theta) seismic recordings with a time depth t,the unit reflection coefficient of the n-th layer interface is represented, k represents the total layer number of the interface, deltat represents the sampling interval, W (omega) represents the source wavelet, R n (θ, ω) represents the reflection coefficient of the n-th layer interface with respect to frequency, and x represents the convolution operation, FFT -1 Representing the inverse fourier transform. />
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