CN110687601A - Inversion method for fluid factor and fracture parameter of orthotropic medium - Google Patents

Inversion method for fluid factor and fracture parameter of orthotropic medium Download PDF

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CN110687601A
CN110687601A CN201911059377.3A CN201911059377A CN110687601A CN 110687601 A CN110687601 A CN 110687601A CN 201911059377 A CN201911059377 A CN 201911059377A CN 110687601 A CN110687601 A CN 110687601A
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潘新朋
柳卓
柳建新
张大洲
崔益安
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Abstract

The invention provides an inversion method of orthogonal anisotropy medium fluid factor and fracture parameter. The method comprises the following steps: using a vertical and transverse isotropic medium under a dry rock background, and deducing a stiffness matrix of an orthorhombic symmetrical anisotropic fracture medium according to the fracture weakness; the method comprises the steps of (1) deriving a new expression of saturated fluid rock weak anisotropy approximate stiffness in an orthogonal medium by using the assumptions of weak anisotropy and small crack weakness and combining an anisotropy Gassmann equation; combining a rigidity disturbance and scattering theory to obtain a PP wave linear reflection coefficient with decoupled parameters of fluid and cracks in an orthorhombic symmetrical weak anisotropic medium; and using the logging information as prior information, and stacking azimuth seismic data by using a part of incidence angles under a Bayesian framework to realize elastic impedance prestack inversion along with the change of offset and azimuth. The method can provide reliable results for fluid identification and fracture characterization, and provides technical support for seismic wave propagation research, oil and gas development and seismic disaster prevention.

Description

Inversion method for fluid factor and fracture parameter of orthotropic medium
Technical Field
The invention relates to the technical field of physical inversion, in particular to an inversion method of an orthotropic medium fluid factor and a fracture parameter.
Background
Distinguishing fluid and fracture properties is critical to reservoir exploration and production, and "sweet spot" information of high fracture density properties is needed to locate the position of the well to obtain maximum production. For subsurface fracture detection, azimuthal seismic reflection amplitudes are widely used to estimate fracture properties. Fluid indicators directly estimated from seismic reflection data are one of the hot spots used in fluid identification. For fracture-induced anisotropy, dimensionless fracture compliance or weakness is used to evaluate fracture properties, where normal compliance or weakness exhibits a significant dependence on fluid fill, while tangential compliance or weakness does not vary with fluid content. Thus, the ratio of normal to tangential fracture compliance is taken as the fluid factor of the fractured reservoir. In the prior art, the corresponding normal to tangential weakness ratio is used as a fluid indicator, and g represents the square of the ratio of the S-wave velocity to the P-wave velocity. However, these fracture fluid indicators described above exhibit coupling of fracture density to the fluid fill, leading to uncertainty in the fluid and fracture properties in such fracture background media.
Orthosymmetric anisotropic media can be formed by developing a set of perpendicular fractures in a perpendicular transverse isotropy (VTI) background medium, and two sets of perpendicular orthogonal fractures in an isotropic or VTI background medium. Seismic waves show azimuth velocity changes in the process of propagating in the orthotropic medium, and the anisotropy defined by fracture weakness can represent the azimuth velocity changes.
In view of the above, there is a need for an inversion method of fluid factor and fracture parameters of orthotropic medium to solve the problems in the prior art.
Disclosure of Invention
The invention aims to provide an inversion method of orthogonal anisotropy medium fluid factors and fracture parameters, and provides technical support for seismic wave propagation research, oil and gas development and seismic disaster prevention.
In order to achieve the aim, the invention provides an inversion method of orthogonal anisotropy medium fluid factor and fracture parameter, which comprises the following steps:
the method comprises the following steps: using a vertical and transverse isotropic medium under a dry rock background, and deducing a stiffness matrix of an orthorhombic symmetrical anisotropic fracture medium according to the fracture weakness;
step two: the method comprises the steps of (1) deriving a new expression of saturated fluid rock weak anisotropy approximate stiffness in an orthogonal medium by using the assumptions of weak anisotropy and small crack weakness and combining an anisotropy Gassmann equation;
step three: combining a rigidity disturbance and scattering theory to obtain a PP wave linear reflection coefficient with decoupled parameters of fluid and cracks in an orthorhombic symmetrical weak anisotropic medium;
step four: and using the logging information as prior information, and stacking azimuth seismic data by using a part of incidence angles under a Bayesian framework to realize elastic impedance prestack inversion along with the change of offset and azimuth.
Further, the stiffness matrix for an orthorhombic symmetric anisotropic fissured medium is as follows:
Figure BDA0002257477050000021
in the formula (1), 0 represents a zero matrix of 3X 3,
Figure BDA0002257477050000022
andas follows:
Figure BDA0002257477050000024
Figure BDA0002257477050000025
in the formula (2), δN、δVAnd deltaHDimensionless crack weakness in different directions; deltaNExpressed as normal weakness, associated with the fluid filling; deltaVAnd deltaHExpressed as vertical and horizontal tangential weakness, respectively, independent of the fluid filling, i.e.
Figure BDA0002257477050000026
And
Figure BDA0002257477050000027
the definition is as follows:
Figure BDA0002257477050000028
wherein Z isNIs normal compliance, ZVAnd ZHVertical and horizontal tangential compliances.
Further, the host rock is characterized by five stiffnesses C of the VTI background medium11b,C13b,C33b,C44bAnd C and66b，C66bto C12b＝C11b-2C66bConstraining; under weak anisotropy assumptions, dimensionless Thomsen-type anisotropy parameters are expressed in the background medium stiffness element of the VTI as:
εb,γb,δbthomsen-type anisotropy parameters representing VTI backgrounds; definition of
Figure BDA0002257477050000032
And
Figure BDA0002257477050000033
assuming that δ is small enough, ignoring second order terms, the expressions δ and δbThe difference between is of the second order, expression
Figure BDA0002257477050000034
Suitable for weak anisotropy.
Further, the weak anisotropy of saturated fluid rock in orthogonal media approximates a new expression of stiffness:
Figure BDA0002257477050000035
wherein two components of the stiffness tensor
Figure BDA0002257477050000036
And μ ═ C44b＝ρβ2Longitudinal wave alpha with dry rockdryRelated to the shear modulus β; lambda [ alpha ]dry＝Mdry-2 μ represents the first ramet parameter, χ ═ λ, of the dry rockdry/Mdry；
For fractured porous rock, the saturation stiffness is expressed as:
Figure BDA0002257477050000037
wherein the content of the first and second substances,
Figure BDA0002257477050000038
and
Figure BDA0002257477050000039
represents saturated gas and fluid saturated stiffness with arbitrary anisotropy; phi denotes the porosity of the fractured porous rock, phibIncluding the porosity and phi of the matrixfFracture porosity; k0Denotes the mineral modulus, KfRepresenting the fluid modulus.
Further, the saturated stiffness matrix element expression of the orthotropic medium:
Figure BDA0002257477050000041
Figure BDA0002257477050000042
Figure BDA0002257477050000043
Figure BDA0002257477050000044
Figure BDA0002257477050000045
Figure BDA0002257477050000047
Figure BDA0002257477050000048
Figure BDA0002257477050000049
wherein the subscript dry denotes the dry rock modulus of the main rock, KdryRepresents the effective bulk modulus of isotropic dry rock; gn(φ)＝(1-Kdry/K0)2Phi and Fn(φ)＝(1-Kdry/K0)·(Kdry/K0) And/phi respectively represent two simplified particle functions.
Further, in consideration of the weak reflection difference, weak anisotropy and small crack weakness of the interface, the first-order disturbance expression of the orthometric symmetric saturated stiffness matrix is as follows:
Figure BDA00022574770500000410
Figure BDA00022574770500000411
Figure BDA00022574770500000412
Figure BDA0002257477050000051
Figure BDA0002257477050000052
Figure BDA0002257477050000053
Figure BDA0002257477050000054
Figure BDA0002257477050000055
disturbance stiffnessLinear with dry rock modulus, fluid bulk modulus, Thomsen type anisotropy parameters; for the case of orthogonal anisotropy, the reflection coefficient is defined as:
Figure BDA0002257477050000058
where θ represents the angle of incidence and the symbol Δ represents the perturbation of the property parameter; xi and etamnAre two parameters related to slowness and polarization vectors.
Further, the linearized reflection coefficient of the fluid and fracture parameter characterization in the orthometric weak anisotropic background medium comprises a fluid/pore term, a shear modulus term, a density term, two Thomsen type anisotropic parameter terms and three weakness parameter terms, and the equation is expressed as:
Figure BDA0002257477050000059
Figure BDA00022574770500000510
wherein the content of the first and second substances,is the azimuth, subscripts dry and sat denote dry and saturation;
Figure BDA00022574770500000512
further, the new parameterized expression of the anisotropy parameters is:
Figure BDA0002257477050000061
Figure BDA0002257477050000062
Figure BDA0002257477050000063
Figure BDA0002257477050000064
Figure BDA0002257477050000065
wherein subscript 0 represents an average of the upper and lower layers; the PP wave reflection coefficient can be approximated as:
Figure BDA0002257477050000066
where EI represents the elastic impedance.
Further, the relative contrast in equation (13) may be approximately replaced by:
Figure BDA0002257477050000067
under the assumption that EI and model parameters vary continuously, the relative contrast can be replaced by a linear differential expression:
further, the elastic impedance change with offset and azimuth (EIVOAz) equation is:
Figure BDA0002257477050000069
the technical scheme of the invention has the following beneficial effects:
in the present invention, to characterize orthorhombic symmetric anisotropic media, an elastic impedance inversion (EIVOAz) with offset and azimuthal variations of decoupling fluid and fracture parameters is proposed. And combining the scattering theory with the disturbance of the orthogonal symmetric fracture medium rigidity matrix, and then obtaining the reflection coefficient of the linearized PP wave according to a mixed fluid/pore item, a shear modulus item, a density item, two Thomsen type anisotropic parameter items and three weakness parameter items. The proposed method can also be generalized to two other orthogonal models (consisting of two orthogonal sets of vertical fractures embedded in the isotropic and VTI backgrounds). A method for estimating fluid and fracture property decoupling using a Bayesian-EIVOAz method. A Bayesian-EIVOAz inversion is implemented using partially angle stacked seismic sections. The method can provide reliable results for fluid identification and fracture characterization, and provides technical support for seismic wave propagation research, oil and gas development and seismic disaster prevention.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1(a) is a schematic diagram of an orthometric symmetric fracture model formed by embedding a set of vertical fractures into a VTI background;
FIG. 1(b) is a schematic diagram of an orthometric symmetric fracture model formed by embedding two sets of orthonormal rotationally invariant vertical fractures into an isotropic background;
FIG. 1(c) is a schematic diagram of an orthosymmetric fracture model formed from two sets of orthorotationally invariant vertical fractures embedded in a VTI background;
fig. 2(a) is a comparison of the exact and approximate components of the orthogonally symmetric gas-containing fracture porous rock stiffness tensor for a gas content of 30%, δ N of 0.1, ε b of 0.05, δ b of 0.02, γ b of 0.1;
fig. 2(b) is a comparison of the exact and approximate components of the orthogonally symmetric gas-containing fracture porous rock stiffness tensor for a gas content of 70%, δ N of 0.1, ε b of 0.05, δ b of 0.02, γ b of 0.1;
fig. 2(c) is a comparison of the exact and approximate components of the orthogonally symmetric gas fracture porous rock stiffness tensors with a gas content of 70%, δ N of 0.2, ε b of 0.05, δ b of 0.02, γ b of 0.1;
fig. 2(d) is a comparison of the exact and approximate components of the orthogonally symmetric gas-containing fracture porous rock stiffness tensor with a gas content of 70%, δ N of 0.1, ε b of 0, δ b of 0, γ b of 0;
FIG. 3(a) is an anisotropic fluid displacement in an orthogonally symmetric fractured porous rock saturated with gas and water;
FIG. 3(b) is an anisotropic fluid displacement in an orthogonally symmetric fractured porous rock saturated with oil and water;
FIG. 4(a) the effect of changes in model parameters Δ f/f on reflectance;
FIG. 4(b) the effect of variation of the model parameter Δ μ/μ on the reflection coefficient;
FIG. 4(c) Effect of variation of model parameters Δ ρ/ρ on reflectance;
FIG. 4(d) model parameters Δ εbThe effect of the change in reflectance;
FIG. 4(e) model parameters Δ δbThe effect of the change in reflectance;
FIG. 4(f) model parameters Δ δNThe effect of the change in reflectance;
FIG. 4(g) model parameter Δ δVThe effect of the change in reflectance;
FIG. 4(h) model parameter Δ δTThe effect of the change in reflectance;
FIG. 5 is a flow chart for establishing an orthometric symmetric petrophysical model to estimate anisotropic logging information;
FIG. 6(a) is a synthetic seismic angle gather with signal-to-noise ratio of 10000;
FIG. 6(b) is a synthetic seismic angle gather with a signal-to-noise ratio of 5;
FIG. 6(c) is a synthetic seismic angle gather with a signal-to-noise ratio of 2;
FIG. 7(a) estimates fluid/porosity term, shear modulus and density parameters using a synthetic angle gather with a signal-to-noise ratio of 10000;
FIG. 7(b) estimates Thomsen type quasi-anisotropy parameters using synthetic angle gathers with a signal-to-noise ratio of 10000;
FIG. 7(c) estimates fracture pseudo-weakness using a synthetic angle gather with a signal-to-noise ratio of 10000;
FIG. 8(a) estimates fluid/porosity term, shear modulus and density parameters using a synthetic angle gather with a signal-to-noise ratio of 5;
FIG. 8(b) estimates Thomsen-type quasi-anisotropy parameters using synthetic angle gathers with a signal-to-noise ratio of 5;
FIG. 8(c) estimates fracture pseudo-weakness using a synthetic angle gather with a signal-to-noise ratio of 5;
FIG. 9(a) estimates fluid/porosity term, shear modulus and density parameters using a synthetic angle gather with a signal-to-noise ratio of 2;
FIG. 9(b) estimates Thomsen-type quasi-anisotropy parameters using synthetic angle gathers with a signal-to-noise ratio of 2;
FIG. 9(c) estimates fracture pseudo-weakness using a synthetic angle gather with a signal-to-noise ratio of 2;
FIG. 10(a) is a comparison of original and composite angle gathers at a signal-to-noise ratio of 10000;
FIG. 10(b) is a comparison of the original and composite angle gathers at a signal-to-noise ratio of 5;
FIG. 10(c) is a comparison of the original and synthesized angle gathers at a signal-to-noise ratio of 2;
fig. 11(a) is data of an input azimuth angle of 22.5 °;
fig. 11(b) is data of an input azimuth angle of 67.5 °;
fig. 11(c) is data input with a third azimuth angle of 112.5 °;
fig. 11(d) is data in which the fourth azimuth angle is 157.5 °;
fig. 12(a) is data of which the output azimuth angle is 22.5 °;
fig. 12(b) is data of output azimuth angle 67.5 °;
fig. 12(c) is a graph that outputs data of a third azimuth angle of 112.5 °;
fig. 12(d) is data for outputting the fourth azimuth angle of 157.5 °;
FIG. 13(a) is the inversion of the fluid/porosity term f;
FIG. 13(b) is the inversion of the S-wave modulus μ;
fig. 13(c) is an inversion result of the density ρ;
FIG. 14(a) is an inverse Thomsen-type anisotropy parameterqεb；
FIG. 14(b) is an inverse Thomsen-type anisotropy parameterqδb；
FIG. 15(a) fracture parameters normal fault pseudo-weaknessqδNThe inversion result of (2);
FIG. 15(b) crack parameters perpendicular to tangential crack pseudo-weaknessqδVThe inversion result of (2);
FIG. 15(c) fracture parameters horizontal tangential fracture pseudo-weaknessqδHThe inversion result of (2);
FIG. 16(a) comparison between original and estimated curves for fluid term, shear modulus term, and density term;
FIG. 16(b) comparison between two Thomsen-type anisotropy parameter terms raw and estimated curves;
FIG. 16(c) comparison between three weak term raw and estimated curves.
Detailed Description
Embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways, which are defined and covered by the claims.
Example 1:
referring to fig. 1 to 16, a method for inverting the fluid factor and fracture parameter of an orthotropic medium comprises the following steps:
the method comprises the following steps: using a vertical and transverse isotropic medium under a dry rock background, and deducing a stiffness matrix of an orthorhombic symmetrical anisotropic fracture medium according to the fracture weakness;
the horizontal lamellae that develop vertical cracks can be considered long wavelength equivalent orthotropic media. When assuming a dry rock skeleton is a porous rock against a VTI background made up of a set of horizontal fractures perpendicular to the x-axis, the dry rock stiffness tensor is as follows:
Figure BDA0002257477050000101
0 represents a 3 x 3 zero matrix,
Figure BDA0002257477050000102
and
Figure BDA0002257477050000103
as follows:
Figure BDA0002257477050000104
Figure BDA0002257477050000105
here, δN、δVAnd deltaHAre different from each otherThe dimensionless crack weakness of the direction; deltaNExpressed as normal weakness, associated with the fluid filling; deltaVAnd deltaHExpressed as vertical and horizontal tangential weakness, respectively, independent of the fluid filling, i.e.
Figure BDA0002257477050000106
And
Figure BDA0002257477050000107
they are defined as follows:
Figure BDA0002257477050000108
wherein Z isNIs normal compliance, ZVAnd ZHVertical and horizontal tangential compliances.
The main rock is characterized by five stiffnesses C of the VTI background medium11b,C13b,C33b,C44bAnd C and66b(Accept C)12b＝C11b-2C66bConstrained). Under weak anisotropy assumptions, dimensionless Thomsen-type anisotropy parameters may be expressed in the background medium stiffness element of the VTI.
Figure BDA0002257477050000109
Figure BDA0002257477050000111
εb,γb,δbThomsen type anisotropy parameters representing VTI background. Definition of
Figure BDA0002257477050000112
And
Figure BDA0002257477050000113
it is then assumed that if δ is small enough, the second order term can be ignored. Thus, the expressions δ and δbThe difference between is of the second order, expression
Figure BDA0002257477050000114
May be suitable for weak anisotropy conditions.
Step two: the assumption of weak anisotropy and small crack weakness is utilized, and an anisotropy Gassmann equation is combined to derive a new expression of approximate weak anisotropy rigidity of saturated fluid rock in an orthogonal medium:
Figure BDA0002257477050000115
Figure BDA0002257477050000116
wherein two components of the stiffness tensor
Figure BDA0002257477050000117
And μ ═ C44b＝ρβ2Longitudinal wave alpha with dry rockdryRelated to the shear modulus β; lambda [ alpha ]dry＝Mdry-2 μ represents the first ramet parameter, χ ═ λ, of the dry rockdry/Mdry. It is emphasized that the stiffness tensor components used by the embodiments are not density normalized, but rather stress elements.
For fractured porous rock, the saturation stiffness can be expressed in this form:
wherein
Figure BDA0002257477050000119
And
Figure BDA00022574770500001110
meaning saturated gas (or dry rock) and fluid saturation with arbitrary anisotropyAnd stiffness. Phi denotes the porosity of the fractured porous rock, phibIncluding the porosity and phi of the matrixfFracture porosity. K0Denotes the mineral modulus, KfRepresenting the fluid modulus.
Since the fluid bulk modulus is typically much smaller than the mineral bulk modulus and the stiffness is approximated using the weak anisotropy of linearized dry rock, we derive the saturated stiffness matrix element expression for orthotropic media:
Figure BDA00022574770500001111
Figure BDA0002257477050000121
Figure BDA0002257477050000122
Figure BDA0002257477050000123
Figure BDA0002257477050000124
Figure BDA0002257477050000125
Figure BDA0002257477050000126
Figure BDA0002257477050000127
wherein the subscript dry represents the dry rock modulus of the host rock, e.g., KdryRepresenting the effective bulk modulus of isotropic dry rock. Gn(φ)＝(1-Kdry/K0)2Phi and Fn(φ)＝(1-Kdry/K0)·(Kdry/K0) And/phi respectively represent two simplified particle functions.
Figure 2 shows a comparison between the exact (equation 6) and approximate (equations 7a-7i) components of the stiffness tensor to demonstrate the accuracy of the derived stiffness of the fluid saturated fracture porous background medium with orthogonal symmetry (assuming that the fracture porous rock is uniformly saturated with water and gas).
From the comparative analysis of fig. 2a and 2b, it was found that the difference between the exact stiffness and the approximate stiffness decreased with increasing gas saturation, and from fig. 2b and 2c, we found that the difference increased with decreasing normal weakness. Even with the Thomsen type anisotropy parameter zero, the difference is still small (fig. 2b and 2 d). The results show that the approximate stiffness derived by the invention is reasonable for the case of a gas-bearing fractured porous reservoir with weak anisotropy and small weakness.
The derived approximate values of the elastic stiffness equations (7a) - (7i) can be used to analyze the influence of fracture density and water saturation on stiffness when the fracture is oil-, water-or gas-bearing. Fig. 3a and 3b illustrate anisotropic fluid displacement in an orthorhombic symmetric fractured porous rock.
Step three: and (3) combining the rigidity disturbance and the scattering theory to obtain the PP wave linearization reflection coefficient of decoupling the fluid and fracture parameters in the orthorhombic symmetrical weak anisotropic medium.
In consideration of the weak reflection difference value, weak anisotropy and small crack weakness of the interface, the invention deduces a first-order disturbance expression of an orthometric symmetric saturated stiffness matrix:
Figure BDA0002257477050000132
Figure BDA0002257477050000134
Figure BDA0002257477050000136
Figure BDA0002257477050000137
Figure BDA0002257477050000138
disturbance stiffness
Figure BDA00022574770500001310
Linear with dry rock modulus, fluid bulk modulus, Thomsen type anisotropy parameters.
For the case of orthogonal anisotropy, the reflection coefficient can be defined as:
Figure BDA00022574770500001311
where θ represents the angle of incidence and the symbol Δ represents the perturbation of the property parameter. Xi and etamnAre two parameters related to slowness and polarization vectors.
By utilizing the method and the derived equation, the linearized reflection coefficient of the fluid and fracture parameter characterization in the orthometric weak anisotropic background medium is derived, wherein the linearized reflection coefficient comprises a fluid/pore term, a shear modulus term, a density term, two Thomsen type anisotropic parameter terms and three weak parameter terms. The equation is expressed as:
Figure BDA0002257477050000142
Figure BDA0002257477050000143
is the azimuth, the subscripts dry and sat denote dry and saturation.
Figure BDA0002257477050000144
The proposed method can also be generalized to two other orthogonal models consisting of two perpendicular orthogonal sets of cracks embedded in isotropic and VTI background media (fig. 1b and 1 c). The corresponding linearized PP wave reflection coefficient is shown in appendix b.
FIG. 4 illustrates the effect of model parameter variation in orthogonal background media on the amplitude of PP wave reflection. It was found that the reflectivity of the fluid/aperture term contributed to the reflection coefficient at both low and high angle incidence (fig. 4 a). However, the contribution of the shear modulus term and the density term at small angles is larger than the far angle of incidence (fig. 4b and 4 c). The contribution of the Thomsen-type anisotropy parameters does not change with azimuthal angle (fig. 4d and 4e), but the crack weakness causes PP wave reflection to change not only with angular but also with azimuthal angle (fig. 4f, 4g and 4 h).
Step four: and using the logging information as prior information, and stacking azimuth seismic data by using a part of incidence angles under a Bayesian framework to realize elastic impedance prestack inversion along with the change of offset and azimuth.
In order to estimate the anisotropic parameters stably, the invention proposes a new parameterized expression of the anisotropic parameters:
Figure BDA0002257477050000146
Figure BDA0002257477050000147
Figure BDA0002257477050000148
Figure BDA0002257477050000149
wherein the subscript 0 represents the average number of upper and lower layers.
The PP wave reflection coefficient can be approximated as:
Figure BDA0002257477050000151
where EI represents the elastic impedance.
The relative contrast in equation (13) above may be approximately replaced by:
Figure BDA0002257477050000152
under the assumption that EI and model parameters vary continuously, the relative contrast can be replaced by a linear differential expression:
Figure BDA0002257477050000153
finally, an elastic impedance change with offset and azimuth (EIVOAz) equation is derived:
this inverse problem is solved iteratively based on the proposed Bayesian-EIVOAz inversion.
Example 2:
the proposed Bayesian-EIVOAz inversion method for verifying fluid and fracture separation is exemplified by well log data in gas-containing fractured porous background media. Anisotropic logging information is first estimated using a petrophysical model. The process of constructing an orthometric symmetric fractured porous background medium petrophysical model, as shown in FIG. 5, is used to estimate anisotropic logging information. Fig. 6a, 6b and 6c show synthetic azimuth seismic data. The six azimuth angles are 0 °, 30 °, 60 °, 90 °, 120 °, and 150 °, respectively. Then, a Bayesian-EIVOAz inversion is implemented that separates the fluid factor and fracture properties. The raw, initial and inverse logs of the model parameters are shown separately in fig. 7. It can be seen from the inversion results that the model parameters are reasonably estimated even if the initial model is relatively smooth. We further implemented EIVOAz inversion using noisy synthetic data by adding random gaussian noise to the noiseless synthetic data with different signal-to-noise ratios (SNRs) of 5:1 (fig. 6b) and 2:1 (fig. 6c), the inversion results being shown in fig. 8 and 9, respectively. As with the noise case, the model parameters are reasonably estimated and are feasible for application of the present embodiment. However, due to the different contributions of the seismic amplitude reflections of the PP waves, the accuracy of the estimation of the quasi-anisotropy parameters and of the fracture quasi-weakness proposed by Thomsen (1986) is inferior to that of the background elastic modulus. 10a, 10b, and 10c are synthetic seismic data simulated by the estimates and convolution models. The error is relatively small compared to the raw and synthetic data, enough to justify the applicability of the proposed EIVOAz inversion method.
Example 3:
referring to fig. 13-16, this example demonstrates a method for estimating fluid and fracture properties using the Bayesian-EIVOAz method, using actual data from the sikawa basin as an example. The four azimuth seismic data input are 22.5 degrees, 67.5 degrees, 112.5 degrees and 157.5 degrees respectively. The Bayesian-EIVOAz inversion is performed using the partial angle stack seismic profile shown in fig. 11, with the average angles of incidence of the near, medium and far angle stacks being 5 ° (ranging from 0 ° -10 °), 15 ° (ranging from 10 ° -20 °), and 25 ° (ranging from 20 ° -30 °), respectively. The inverted azimuthal elastic impedance profile is shown in fig. 12.
The estimated separation flow factor and fracture parameters are shown in figures 13, 14 and 15. And (3) adopting a white curve and an elliptic right well as an initial model, and adopting a gas-containing response left well as the verification of the initial model. It is readily found that estimates of fluid parameters and fracture parameters reflect well the hydrocarbon response and fracture development zones.
To further test the reliability of the estimated model parameters, the original model parameters and the estimated model parameters were compared on the right well (fig. 16). In an orthorhombic symmetric fractured-porous reservoir, the estimated model parameters were found to fit well with the original curve, thus illustrating the utility of the proposed Bayesian-EIVOAz method.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. An inversion method of fluid factors and fracture parameters of an orthotropic medium is characterized by comprising the following steps:
the method comprises the following steps: using a vertical and transverse isotropic medium under a dry rock background, and deducing a stiffness matrix of an orthorhombic symmetrical anisotropic fracture medium according to the fracture weakness;
step two: the method comprises the steps of (1) deriving a new expression of saturated fluid rock weak anisotropy approximate stiffness in an orthogonal medium by using the assumptions of weak anisotropy and small crack weakness and combining an anisotropy Gassmann equation;
step three: combining a rigidity disturbance and scattering theory to obtain a PP wave linear reflection coefficient with decoupled parameters of fluid and cracks in an orthorhombic symmetrical weak anisotropic medium;
step four: and using the logging information as prior information, and stacking azimuth seismic data by using a part of incidence angles under a Bayesian framework to realize elastic impedance prestack inversion along with the change of offset and azimuth.
2. The method for inverting the fluid factor and fracture parameters of the orthotropic medium according to claim 1, wherein the stiffness matrix of the orthotropic symmetric anisotropic fracture medium is as follows:
in the formula (1), 0 represents a zero matrix of 3X 3,
Figure FDA0002257477040000012
andas follows:
Figure FDA0002257477040000014
in the formula (2), δN、δVAnd deltaHDimensionless crack weakness in different directions; deltaNExpressed as normal weakness, associated with the fluid filling; deltaVAnd deltaHExpressed as vertical and horizontal tangential weakness, respectively, independent of the fluid filling, i.e.
Figure FDA0002257477040000015
And
Figure FDA0002257477040000016
the definition is as follows:
Figure FDA0002257477040000021
wherein Z isNIs normal compliance, ZVAnd ZHVertical and horizontal tangential compliances.
3. An orthotropic fluid factor and fracture parameter inverse of claim 2The method is characterized in that the main rock is characterized by five rigidities C of VTI background medium11b,C13b,C33b,C44bAnd C and66b，C66bto C12b＝C11b-2C66bConstraining; under weak anisotropy assumptions, dimensionless Thomsen-type anisotropy parameters are expressed in the background medium stiffness element of the VTI as:
Figure FDA0002257477040000022
εb,γb,δbthomsen-type anisotropy parameters representing VTI backgrounds; definition of
Figure FDA0002257477040000023
And
Figure FDA0002257477040000024
assuming that δ is small enough, ignoring second order terms, the expressions δ and δbThe difference between is of the second order, expression
Figure FDA0002257477040000025
Suitable for weak anisotropy.
4. The method for inverting the fluid factor and the fracture parameter of the orthotropic medium according to claim 3, wherein the new expression of the approximate stiffness of the weak anisotropy of the saturated fluid rock in the orthotropic medium is as follows:
Figure FDA0002257477040000026
wherein two components of the stiffness tensor
Figure FDA0002257477040000031
And μ ═ C44b＝ρβ2Longitudinal wave alpha with dry rockdryRelated to the shear modulus β; lambda [ alpha ]dry＝Mdry-2 μ represents the first ramet parameter, χ ═ λ, of the dry rockdry/Mdry；
For fractured porous rock, the saturation stiffness is expressed as:
Figure FDA0002257477040000032
wherein the content of the first and second substances,
Figure FDA0002257477040000033
and
Figure FDA0002257477040000034
represents saturated gas and fluid saturated stiffness with arbitrary anisotropy; phi denotes the porosity of the fractured porous rock, phibIncluding the porosity and phi of the matrixfFracture porosity; k0Denotes the mineral modulus, KfRepresenting the fluid modulus.
5. The method for inverting the fluid factor and the fracture parameter of the orthotropic medium according to claim 4, wherein the saturated stiffness matrix element expression of the orthotropic medium is as follows:
Figure FDA0002257477040000035
Figure FDA0002257477040000036
Figure FDA0002257477040000038
Figure FDA00022574770400000310
Figure FDA00022574770400000312
Figure FDA00022574770400000313
wherein the subscript dry denotes the dry rock modulus of the main rock, KdryRepresents the effective bulk modulus of isotropic dry rock; gn(φ)＝(1-Kdry/K0)2Phi and Fn(φ)＝(1-Kdry/K0)·(Kdry/K0) And/phi respectively represent two simplified particle functions.
6. The inversion method of the fluid factor and fracture parameter of the orthotropic medium according to claim 5, wherein the first-order disturbance expression of the orthotropic symmetric saturated stiffness matrix considering the weak reflection difference, the weak anisotropy and the weak small fracture of the interface is as follows:
Figure FDA0002257477040000041
Figure FDA0002257477040000042
Figure FDA0002257477040000043
Figure FDA0002257477040000044
Figure FDA0002257477040000045
Figure FDA0002257477040000046
Figure FDA0002257477040000047
Figure FDA0002257477040000049
disturbance stiffness
Figure FDA00022574770400000410
Linear with dry rock modulus, fluid bulk modulus, Thomsen type anisotropy parameters; for the case of orthogonal anisotropy, the reflection coefficient is defined as:
Figure FDA00022574770400000411
where θ represents the angle of incidence and the symbol Δ represents the perturbation of the property parameter; xi and etamnAre two parameters related to slowness and polarization vectors.
7. The method of claim 6, wherein the linearized reflection coefficients of the fluid and fracture parameter characterization in the orthometric weak anisotropic background medium comprise a fluid/pore term, a shear modulus term, a density term, two Thomsen-type anisotropy parameter terms and three weakness parameter terms, and the equation is expressed as:
Figure FDA0002257477040000051
Figure FDA0002257477040000052
wherein the content of the first and second substances,
Figure FDA0002257477040000053
is the azimuth, subscripts dry and sat denote dry and saturation;
Figure FDA0002257477040000054
8. the method of claim 7, wherein the new parameterized expression of the anisotropy parameters is:
Figure FDA0002257477040000055
Figure FDA0002257477040000057
Figure FDA0002257477040000058
Figure FDA0002257477040000059
wherein subscript 0 represents an average of the upper and lower layers; the PP wave reflection coefficient can be approximated as:
Figure FDA00022574770400000510
where EI represents the elastic impedance.
9. The method of claim 8, wherein the relative contrast in equation (13) is approximately replaced by:
Figure FDA0002257477040000061
under the assumption that EI and model parameters vary continuously, the relative contrast can be replaced by a linear differential expression:
10. the method of claim 9, wherein the elastic impedance change with offset and azimuth (EIVOAz) equation is:
Figure FDA0002257477040000063
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