CN110133718B - Attenuation anisotropic fluid elastic impedance inversion method - Google Patents

Attenuation anisotropic fluid elastic impedance inversion method Download PDF

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CN110133718B
CN110133718B CN201910407041.5A CN201910407041A CN110133718B CN 110133718 B CN110133718 B CN 110133718B CN 201910407041 A CN201910407041 A CN 201910407041A CN 110133718 B CN110133718 B CN 110133718B
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attenuation
formula
equation
elastic
fracture
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CN110133718A (en
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潘新朋
张广智
周顺心
李林
印兴耀
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China University of Petroleum East China
Central South University
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Central South University
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    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
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Abstract

The invention discloses an attenuation anisotropy fluid elastic impedance inversion method, which comprises the following steps: the method comprises the following steps: acquiring a linear sliding HTI model considering the intrinsic attenuation and fracture induced attenuation of background rocks; step two: establishing a relation equation between the dry elastic modulus and the saturated fluid elastic modulus of the fractured rock; step three: obtaining a real part of complex stiffness of the saturated fluid medium containing the pores and cracks by using the formulas in the first step and the second step; step four: acquiring a PP wave reflection coefficient equation of the dynamic equivalent HTI attenuation medium; step five: acquiring a longitudinal wave reflection coefficient equation; step six: obtaining an azimuth attenuation elastic impedance equation according to the longitudinal wave reflection coefficient equation in the step five; step seven: and inverting the fracture weakness parameter and the fracture induced attenuation parameter by the attenuation elastic impedance difference values in different directions. The inversion method realizes the pre-stack seismic inversion of the background fluid parameters, the fracture characteristic parameters and the attenuation parameters of the fractured reservoir.

Description

Attenuation anisotropic fluid elastic impedance inversion method
Technical Field
The invention relates to the technical field of geophysical exploration of oil and gas resources, in particular to an attenuation anisotropic fluid elastic impedance inversion method.
Background
With the increasing demand for oil and gas in the global scope, the oil and gas exploration direction of geophysicists is gradually changed from the conventional oil and gas reservoir to some special oil and gas reservoirs, wherein the exploration and development of the fractured oil and gas reservoir become the focus of the oil and gas exploration research. Due to the comprehensive influence of factors such as formation pressure and the like, most fractures in the actual formation are high-angle or nearly vertical fractures, and when the fractures develop to a certain scale, transverse wave splitting, azimuth velocity anisotropy characteristics and the like can occur in the propagation of seismic waves in a fractured reservoir and the seismic response of the seismic waves. A single set of vertical cracks developing in the dominant horizontal direction in a homogeneous isotropic background medium can be considered a long wavelength equivalent HTI medium. Therefore, the seismic data are used for describing the seismic response characteristics of the underground medium fractures, and the method has important guiding significance and practical value for exploration and development of fractured reservoirs.
The seismic waves have strong velocity dispersion and attenuation when propagating in an actual fractured reservoir, and the elastic response of the seismic waves has frequency dependence. Previous studies have either only considered intrinsic attenuation of the background medium or only considered the effects of matrix porosity and fluid flow effects; the method establishes an anisotropic fluid elastic impedance inversion method by simultaneously considering the influences of the matrix pore and fluid flow effect, the background intrinsic attenuation and the fracture induced attenuation on the anisotropic pore elasticity approximation theory.
Disclosure of Invention
The present invention is directed to overcoming the above-mentioned deficiencies of the prior art and providing a method for inverting the elastic impedance of a damped anisotropic fluid.
In order to achieve the purpose, the invention adopts the following technical scheme: a method of inverting the elastic impedance of a damped anisotropic fluid, comprising the steps of:
the method comprises the following steps: acquiring a linear sliding HTI model considering the intrinsic attenuation and fracture induced attenuation of background rocks;
step two: establishing a relation equation between the dry elastic modulus and the saturated fluid elastic modulus of the fractured rock;
step three: obtaining a real part of complex stiffness of the saturated fluid medium containing the pores and cracks by using the formulas in the first step and the second step;
step four: acquiring a PP wave reflection coefficient equation of the dynamic equivalent HTI attenuation medium;
step five: acquiring a longitudinal wave reflection coefficient equation;
step six: obtaining an azimuth attenuation elastic impedance equation according to the longitudinal wave reflection coefficient equation in the step five;
step seven: and inverting the fracture weakness parameter and the fracture induced attenuation parameter by the attenuation elastic impedance difference values in different directions.
Preferably, in the first step, the isotropic background modulus parameter and the fracture parameter in the linear sliding HTI model are both expressed in a complex form, and the formula is as follows:
Figure RE-RE-GDA0002085362600000021
in the formula (1), the first and second groups,
Figure RE-RE-GDA0002085362600000022
Figure RE-RE-GDA0002085362600000023
and
Figure RE-RE-GDA0002085362600000024
respectively representing complex longitudinal wave modulus, first and second Lame constants of isotropically attenuating background rock, and
Figure RE-RE-GDA0002085362600000025
Figure RE-RE-GDA0002085362600000026
and
Figure RE-RE-GDA0002085362600000027
representing complex normal and tangential fracture attenuation parameters that induce longitudinal and transverse wave attenuation with fractures along the axis of symmetry
Figure RE-RE-GDA0002085362600000028
And
Figure RE-RE-GDA0002085362600000029
is simply expressed as
Figure RE-RE-GDA0002085362600000031
Model parameters in complex form under the assumption of isotropic viscoelastic background rock
Figure RE-RE-GDA0002085362600000032
And
Figure RE-RE-GDA0002085362600000033
can be expressed as
Figure RE-RE-GDA0002085362600000034
In the formula (3), the first and second groups,
Figure RE-RE-GDA0002085362600000035
and
Figure RE-RE-GDA0002085362600000036
respectively representing the inverse quality factors of the longitudinal wave and the transverse wave of the background;
and (3) simultaneously substituting the notations (2) and (3) into the formula (1) to obtain a linear sliding HTI model considering the intrinsic attenuation and the fracture-induced attenuation of the background rock.
Preferably, in the second step, the equation of the relationship between the dry elastic modulus and the saturated fluid elastic modulus of the fractured rock is as follows:
Figure RE-RE-GDA0002085362600000037
in the formula (4), the first and second groups,
Figure RE-RE-GDA0002085362600000038
is a complex representation of the effective rigidity elastic matrix of the saturated fluid fractured rock,
Figure RE-RE-GDA0002085362600000039
the method is characterized in that the method is a complex representation of an effective rigidity elastic matrix of the dry fractured rock;
Figure RE-RE-GDA00020853626000000310
is a complex characterized anisotropy-like Biot coefficient, which can be expressed as
Figure RE-RE-GDA00020853626000000311
Wherein, KgRepresenting the effective bulk modulus of the constituent rock solids;
Figure RE-RE-GDA00020853626000000312
is a complex representation of the anisotropic Gassmann pore space modulus, which can be expressed as
Figure RE-RE-GDA00020853626000000313
In the formula (I), the compound is shown in the specification,
Figure RE-RE-GDA00020853626000000314
is a complex characterized anisotropic dry rock-like bulk modulus; phi represents porosity; kappafRepresenting the pore fluid effective bulk modulus.
Preferably, in the third step, the method for obtaining the real part of the complex stiffness of the pore-containing crack medium of the saturated fluid comprises the following steps:
wherein, the real part of the complex-characterized weak anisotropic stiffness matrix of the dry fracture rock can be expressed as
Figure RE-RE-GDA0002085362600000041
In the formula (7), the first and second groups,
Figure RE-RE-GDA0002085362600000042
Figure RE-RE-GDA0002085362600000043
Figure RE-RE-GDA0002085362600000044
Figure RE-RE-GDA0002085362600000045
Figure RE-RE-GDA0002085362600000046
Figure RE-RE-GDA0002085362600000047
and
Figure RE-RE-GDA0002085362600000048
respectively representing comprehensive attenuation factors of the product of background intrinsic longitudinal wave attenuation and transverse wave attenuation and fracture-induced longitudinal wave attenuation;
substituting the formulas (5), (6) and (7) into the formula (4), and obtaining an approximate expression of the real part of the complex stiffness of the saturated fluid medium containing the pore gaps, which is characterized by the modulus of the background dry rock, the flexibility of the dry gaps, the modulus of the fluid, the intrinsic longitudinal and transverse wave attenuation of the background and the induced longitudinal wave attenuation of the gaps, in the seismic frequency range on the basis of the weak anisotropy approximation and the weak intrinsic attenuation approximation of the background
Figure RE-RE-GDA0002085362600000051
In the formula (8), the first and second groups,
Figure RE-RE-GDA0002085362600000052
Figure RE-RE-GDA0002085362600000053
Figure RE-RE-GDA0002085362600000054
Figure RE-RE-GDA0002085362600000055
Figure RE-RE-GDA0002085362600000056
β0＝1-Kdry/Kgis the Biot coefficient;
Kdryrepresenting the bulk modulus of the dry rock.
Preferably, in the fourth step, the method for obtaining the PP wave reflection coefficient equation is as follows:
based on scattering theory, the longitudinal wave reflection coefficient of HTI media can be expressed as:
Figure RE-RE-GDA0002085362600000057
where θ represents the angle of incidence, ρ represents the density term of the homogeneous isotropic background medium,
Figure RE-RE-GDA0002085362600000058
parameter, ξ, representing the disturbance stiffness of saturated rockmnRelated to slowness vectors and polarization vectors;
therefore, by combining the equations (8) and (9), the equation of the reflection coefficient of the PP wave of the dynamic equivalent HTI attenuation medium can be derived, and the expression is
Figure RE-RE-GDA0002085362600000059
In the formula (I), the compound is shown in the specification,
Figure RE-RE-GDA0002085362600000061
Figure RE-RE-GDA0002085362600000062
Figure RE-RE-GDA0002085362600000063
Figure RE-RE-GDA0002085362600000064
Figure RE-RE-GDA0002085362600000065
Figure RE-RE-GDA0002085362600000066
in the formula (10), the first and second groups,
Figure RE-RE-GDA0002085362600000067
representing the azimuth angle, delta representing the difference of each property of the two layers of media, and f is fluid/pore and is a fluid factor; the fracture weakness parameter can be estimated according to logging data and a rock physical model;
preferably, in the fifth step, according to the relationship between the longitudinal wave reflection coefficient of the horizontal interface and the elastic impedance of the azimuthal anisotropy, the longitudinal wave reflection coefficient equation can be expressed as:
Figure RE-RE-GDA0002085362600000068
in the formula (11), the reaction mixture,
Figure RE-RE-GDA0002085362600000069
represents the azimuthal attenuation elastic resistance, and Δ EI (θ, Φ) represents the difference between the elastic resistances of the previous and next layers.
Preferably, in the sixth step, the method for obtaining the azimuth attenuation elastic impedance equation from the longitudinal wave reflection coefficient equation of the fifth step is as follows:
in the weak elastic parameter difference (| delta f/f | < 1, | delta mu/mub1 and [ Delta ] rho/rhob< 1), small crack weakness (
Figure RE-RE-GDA00020853626000000610
And isT< 1) and weak attenuation (
Figure RE-RE-GDA00020853626000000611
And is
Figure RE-RE-GDA00020853626000000612
) Under the assumption of the conditions that,
the relative difference in background elastic modulus in equation (11) can be approximately replaced by:
Δf/f≈Δ(lnf)，
Δμ/μb≈Δ(lnμb)，
Δρ/ρb≈Δ(lnρb) And is and
Figure RE-RE-GDA0002085362600000071
under the assumption of continuous change of elastic parameters, crack parameters, attenuation parameters and elastic impedance parameters, delta (ln f) is approximately equal to d (ln f), and delta (ln mu)b)≈d(lnμb)，Δ(lnρb)≈d(lnρb)，
Figure RE-RE-GDA0002085362600000072
ΔT≈dT，
Figure RE-RE-GDA0002085362600000073
And is
Figure RE-RE-GDA0002085362600000074
Substituting the above approximate substitution into equation (11) yields the following equation:
Figure RE-RE-GDA0002085362600000075
the integral of the formula (12) is calculated, and the logarithmic domain azimuth attenuation elastic impedance equation is obtained through corresponding operation, and is expressed as
Figure RE-RE-GDA0002085362600000076
Taking the logarithm of equation (13), the final azimuthal attenuation elastic impedance equation can be expressed as
Figure RE-RE-GDA0002085362600000077
Preferably, in the seventh step, the inversion of the fracture weakness parameter and the fracture-induced attenuation parameter according to the attenuation elastic impedance difference values in different directions includes the following steps:
step 7-1: carrying out difference linearization processing on the attenuation elastic impedance in different directions of the logarithmic domain to obtain a difference linearization expression as shown in the following formula;
Figure RE-RE-GDA0002085362600000078
in formula (15), M is the number of incident angles, N is the number of azimuthal angle differences, and L is the number of reflective interfaces;
Figure RE-RE-GDA0002085362600000081
is the difference in elastic impedance, m, in different directions in the logarithmic domaincQIs the fracture weakness and fracture induced attenuation parameters to be inverted, and Δ X is a positive operator matrix associated with the different azimuth reflection coefficient weight difference operator matrix Δ A, which can be expressed as
Figure RE-RE-GDA0002085362600000082
Figure RE-RE-GDA0002085362600000083
Figure RE-RE-GDA0002085362600000084
Figure RE-RE-GDA0002085362600000085
Figure RE-RE-GDA0002085362600000086
Figure RE-RE-GDA0002085362600000087
Figure RE-RE-GDA0002085362600000088
Figure RE-RE-GDA0002085362600000089
Figure RE-RE-GDA00020853626000000810
Figure RE-RE-GDA00020853626000000811
Figure RE-RE-GDA00020853626000000812
Figure RE-RE-GDA00020853626000000813
Figure RE-RE-GDA00020853626000000814
Step 7-2: performing decorrelation and normalization processing on the difference value linearization expression to obtain a positive problem after decorrelation;
decorrelation and normalization processing among model parameters are considered in inversion of logarithm domain azimuth elastic impedance difference, and a kernel matrix delta X after the decorrelation becomes
Figure RE-RE-GDA0002085362600000091
Dynamic domain model parameter vector mcQBecome into
Figure RE-RE-GDA0002085362600000092
The decorrelated positive problem can be expressed as
Figure RE-RE-GDA0002085362600000093
And 7-3: converting the decorrelated positive problem into a target function;
using the Cauchy probability distribution as the prior probability density function and the Gaussian distribution as the likelihood function, the posterior probability density function is solved using a joint probability density function of the prior probability density function and the likelihood function, i.e.
Figure RE-RE-GDA0002085362600000094
In the formula (17), the reaction is carried out,
Figure RE-RE-GDA0002085362600000095
is the variance of the noise, and is,
Figure RE-RE-GDA0002085362600000096
is the variance of the quasi-static domain model parameter vector. Taking a maximum posterior probability density function of the formula (17), combining with the low-frequency information regularization constraint term of the initial model, and finally representing the target function as
Figure RE-RE-GDA0002085362600000097
In the formula (18), the first and second groups,
Figure RE-RE-GDA0002085362600000098
is a regularization coefficient of the quasi-static domain model parameters;
Figure RE-RE-GDA0002085362600000099
wherein
Figure RE-RE-GDA00020853626000000910
Representing the initial values of the model parameters.
And 7-4: solving an objective function;
the objective function equation (18) is solved to obtain
Figure RE-RE-GDA00020853626000000911
In the formula (18), the reaction mixture,
Figure RE-RE-GDA00020853626000000912
Figure RE-RE-GDA0002085362600000101
Figure RE-RE-GDA0002085362600000102
QCauchyrepresents the Cauchy sparse matrix and the matrix,
Figure RE-RE-GDA0002085362600000103
represents a reflection coefficient;
and 7-5: and (3) carrying out iterative solution on the formula (19) by adopting an iterative reweighted least square optimization algorithm to obtain a dynamic domain model parameter vector, wherein the formula is as follows:
Figure RE-RE-GDA0002085362600000104
the invention has the following beneficial effects:
according to the method, the intrinsic attenuation and the induced attenuation of the fracture rock background are comprehensively considered, a relational equation between the dry elastic modulus and the saturated fluid elastic modulus of the fracture rock represented by a plurality of factors is combined, and an approximate expression of the complex stiffness real part of the saturated fluid medium containing the pores and characterized by the background dry rock modulus, the dry fracture flexibility, the fluid modulus, the background intrinsic longitudinal and transverse wave attenuation and the fracture induced longitudinal wave attenuation is obtained in the seismic frequency range on the basis of the weak anisotropy approximation and the weak background intrinsic attenuation approximation; based on a scattering theory, a PP wave reflection coefficient equation of a dynamic equivalent HTI attenuation medium is deduced, and an azimuth attenuation elastic impedance equation is deduced according to a longitudinal wave reflection coefficient equation under the assumption conditions of weak elastic parameter difference, small crack weakness and weak attenuation and under the assumption conditions of continuous change of elastic parameters, crack parameters, attenuation parameters and elastic impedance parameters; a sparse constraint regularization and low-frequency information constraint regularization azimuth attenuation elastic impedance iterative inversion method is provided, and prestack seismic inversion of background fluid parameters, fracture characteristic parameters and attenuation parameters of a fractured reservoir is realized.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of a method for inverting the elastic impedance of a damped anisotropic fluid according to the present invention;
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The invention is further illustrated with reference to the following figures and examples.
A method of inverting the elastic impedance of a damped anisotropic fluid, as shown in fig. 1, comprising the steps of:
the method comprises the following steps: acquiring a linear sliding HTI model considering the intrinsic attenuation and fracture induced attenuation of background rocks;
preferably, in the first step, the isotropic background modulus parameter and the fracture parameter in the linear sliding HTI model are both expressed in a complex form, and the formula is as follows:
Figure RE-RE-GDA0002085362600000111
in the formula (1), the first and second groups,
Figure RE-RE-GDA0002085362600000112
Figure RE-RE-GDA0002085362600000113
and
Figure RE-RE-GDA0002085362600000114
respectively representing complex longitudinal wave modulus, first and second Lame constants of isotropically attenuating background rock, and
Figure RE-RE-GDA0002085362600000115
Figure RE-RE-GDA0002085362600000116
and
Figure RE-RE-GDA0002085362600000117
representing complex normal and tangential fracture attenuation parameters that induce longitudinal and transverse wave attenuation with fractures along the axis of symmetry
Figure RE-RE-GDA0002085362600000121
And
Figure RE-RE-GDA0002085362600000122
is simply expressed as
Figure RE-RE-GDA0002085362600000123
Bringing the expression (2) into the formula (1) to obtain a linear sliding HTI model considering fracture-induced fracture induced attenuation;
model parameters in complex form under the assumption of isotropic viscoelastic background rock
Figure RE-RE-GDA0002085362600000124
And
Figure RE-RE-GDA0002085362600000125
can be expressed as
Figure RE-RE-GDA0002085362600000126
In the formula (3), the first and second groups,
Figure RE-RE-GDA0002085362600000127
and
Figure RE-RE-GDA0002085362600000128
respectively representing the inverse quality factors of the longitudinal wave and the transverse wave of the background;
substituting the public representation (3) into the formula (1) to obtain a linear sliding HTI model considering the intrinsic attenuation of the background rock;
and (3) simultaneously substituting the notations (2) and (3) into the formula (1) to obtain a linear sliding HTI model considering the intrinsic attenuation and the fracture-induced attenuation of the background rock.
Step two: establishing a relation equation between the dry elastic modulus and the saturated fluid elastic modulus of the fractured rock;
preferably, in the second step, the equation of the relationship between the dry elastic modulus and the saturated fluid elastic modulus of the fractured rock is as follows:
Figure RE-RE-GDA0002085362600000129
in the formula (4), the first and second groups,
Figure RE-RE-GDA00020853626000001210
is a complex representation of the effective rigidity elastic matrix of the saturated fluid fractured rock,
Figure RE-RE-GDA00020853626000001211
the method is characterized in that the method is a complex representation of an effective rigidity elastic matrix of the dry fractured rock;
Figure RE-RE-GDA00020853626000001212
is a complex characterized anisotropy-like Biot coefficient, which can be expressed as
Figure RE-RE-GDA00020853626000001213
Wherein, KgRepresenting the effective bulk modulus of the constituent rock solids;
Figure RE-RE-GDA00020853626000001214
is a complex representation of the anisotropic Gassmann pore space modulus, which can be expressed as
Figure RE-RE-GDA0002085362600000131
In the formula (I), the compound is shown in the specification,
Figure RE-RE-GDA0002085362600000132
is a complex characterized anisotropic dry rock-like bulk modulus; phi represents porosity; kappafRepresenting the pore fluid effective bulk modulus.
Step three: obtaining a real part of complex stiffness of the saturated fluid medium containing the pores and cracks by using the formulas in the first step and the second step;
preferably, in the third step, the method for obtaining the real part of the complex stiffness of the pore-containing crack medium of the saturated fluid comprises the following steps:
the prior research shows that the imaginary part of the reflection coefficient represented by a complex number is far smaller than the real part, so that only the derivation of the real part of the reflection coefficient is focused on in the invention, and the imaginary part of the reflection coefficient is ignored;
wherein, the real part of the complex-characterized weak anisotropic stiffness matrix of the dry fracture rock can be expressed as
Figure RE-RE-GDA0002085362600000133
In the formula (7), the first and second groups,
Figure RE-RE-GDA0002085362600000134
Figure RE-RE-GDA0002085362600000135
Figure RE-RE-GDA0002085362600000136
Figure RE-RE-GDA0002085362600000137
Figure RE-RE-GDA0002085362600000138
Figure RE-RE-GDA0002085362600000141
and
Figure RE-RE-GDA0002085362600000142
respectively representing comprehensive attenuation factors of the product of background intrinsic longitudinal wave attenuation and transverse wave attenuation and fracture-induced longitudinal wave attenuation;
Figure RE-RE-GDA0002085362600000143
indicating the case of background dry rock
Figure RE-RE-GDA0002085362600000144
And
Figure RE-RE-GDA0002085362600000145
a ratio;
where the parameters in the formula of the invention with superscript dry all represent parameters in the case of dry rock (no fluid in the pores), for example:
Figure RE-RE-GDA0002085362600000146
complex longitudinal wave modulus of isotropically damped background rock is shown, then
Figure RE-RE-GDA0002085362600000147
Then the complex longitudinal wave modulus of the isotropically attenuated dry background rock is represented;
substituting the formulas (5), (6) and (7) into the formula (4), and obtaining an approximate expression of the real part of the complex stiffness of the saturated fluid medium containing the pore gaps, which is characterized by the modulus of the background dry rock, the flexibility of the dry gaps, the modulus of the fluid, the intrinsic longitudinal and transverse wave attenuation of the background and the induced longitudinal wave attenuation of the gaps, in the seismic frequency range on the basis of the weak anisotropy approximation and the weak intrinsic attenuation approximation of the background
Figure RE-RE-GDA0002085362600000148
In the formula (8), the first and second groups,
Figure RE-RE-GDA0002085362600000149
Figure RE-RE-GDA00020853626000001410
Figure RE-RE-GDA00020853626000001411
Figure RE-RE-GDA00020853626000001412
Figure RE-RE-GDA00020853626000001413
β0＝1-Kdry/Kgis the Biot coefficient;
Kdryrepresenting the bulk modulus of the dry rock.
Step four: acquiring a PP wave reflection coefficient equation of the dynamic equivalent HTI attenuation medium;
preferably, in the fourth step, the method for obtaining the PP wave reflection coefficient equation is as follows:
based on scattering theory, the longitudinal wave reflection coefficient of HTI media can be expressed as:
Figure RE-RE-GDA0002085362600000151
where θ represents the angle of incidence, ρ represents the density term of the homogeneous isotropic background medium,
Figure RE-RE-GDA0002085362600000152
parameter, ξ, representing the disturbance stiffness of saturated rockmnRelated to slowness vectors and polarization vectors;
thus, in combination with equations (8) and (9), a dynamic equivalent HTI attenuation can be derivedEquation of PP wave reflection coefficient of medium, specifically, for equation (9)
Figure RE-RE-GDA0002085362600000153
Is subjected to derivation and then is subjected to ximnThe formula (10) can be obtained by multiplying and neglecting small terms, and the expression is
Figure RE-RE-GDA0002085362600000154
In the formula (I), the compound is shown in the specification,
Figure RE-RE-GDA0002085362600000155
Figure RE-RE-GDA0002085362600000156
Figure RE-RE-GDA0002085362600000157
Figure RE-RE-GDA0002085362600000158
Figure RE-RE-GDA0002085362600000159
Figure RE-RE-GDA00020853626000001510
in the formula (10), the first and second groups,
Figure RE-RE-GDA00020853626000001511
representing the azimuth angle, delta representing the difference of each property of the two layers of media, and f is fluid/pore and is a fluid factor; the fracture weakness parameter can be estimated according to logging data and a rock physical model;
Figure RE-RE-GDA0002085362600000161
representing the background saturated fluid case
Figure RE-RE-GDA0002085362600000162
And
Figure RE-RE-GDA0002085362600000163
a ratio;
wherein the parameters with superscript sat in the present invention all represent parameters in the case of saturated fluids.
Step five: acquiring a longitudinal wave reflection coefficient equation;
preferably, in the fifth step, according to the relationship between the longitudinal wave reflection coefficient of the horizontal interface and the elastic impedance of the azimuthal anisotropy, the longitudinal wave reflection coefficient equation can be expressed as:
Figure RE-RE-GDA0002085362600000164
in the formula (11), the reaction mixture,
Figure RE-RE-GDA0002085362600000165
represents the azimuth attenuation elastic impedance, and delta EI (theta, phi) represents the difference between the elastic impedance of the upper layer and the elastic impedance of the lower layer;
where the longitudinal wave is a p-wave and pp means that both incident and reflected are p-waves.
Step six: obtaining an azimuth attenuation elastic impedance equation according to the longitudinal wave reflection coefficient equation in the step five;
preferably, in the sixth step, the method for obtaining the azimuth attenuation elastic impedance equation from the longitudinal wave reflection coefficient equation of the fifth step is as follows:
in the weak elastic parameter difference (| delta f/f | < 1, | delta mu/mub1 and [ Delta ] rho/rhob< 1), small crack weakness (
Figure RE-RE-GDA0002085362600000166
And isT< 1) and weak attenuation (
Figure RE-RE-GDA0002085362600000167
And is
Figure RE-RE-GDA0002085362600000168
) Under the assumption of the conditions that,
the relative difference in background elastic modulus in equation (11) can be approximately replaced by:
Δf/f≈Δ(lnf)，
Δμ/μb≈Δ(lnμb)，
Δρ/ρb≈Δ(lnρb) And is and
Figure RE-RE-GDA0002085362600000169
under the assumption of continuous change of elastic parameters, crack parameters, attenuation parameters and elastic impedance parameters, delta (ln f) is approximately equal to d (ln f), and delta (ln mu)b)≈d(lnμb)，Δ(lnρb)≈d(lnρb)，
Figure RE-RE-GDA00020853626000001610
ΔT≈dT，
Figure RE-RE-GDA0002085362600000171
And is
Figure RE-RE-GDA0002085362600000172
Substituting the above approximate substitution into equation (11) yields the following equation:
Figure RE-RE-GDA0002085362600000173
the integral of the formula (12) is calculated, and the logarithmic domain azimuth attenuation elastic impedance equation is obtained through corresponding operation, and is expressed as
Figure RE-RE-GDA0002085362600000174
Taking the logarithm of equation (13), the final azimuthal attenuation elastic impedance equation can be expressed as
Figure RE-RE-GDA0002085362600000175
Step seven: and inverting the fracture weakness parameter and the fracture induced attenuation parameter by the attenuation elastic impedance difference values in different directions.
Preferably, in the seventh step, the inversion of the fracture weakness parameter and the fracture-induced attenuation parameter according to the attenuation elastic impedance difference values in different directions includes the following steps:
step 7-1: carrying out difference linearization processing on the attenuation elastic impedance in different directions of the logarithmic domain to obtain a difference linearization expression as shown in the following formula;
Figure RE-RE-GDA0002085362600000176
in formula (15), M is the number of incident angles, N is the number of azimuthal angle differences, and L is the number of reflective interfaces;
Figure RE-RE-GDA0002085362600000177
is the difference in elastic impedance, m, in different directions in the logarithmic domaincQIs the fracture weakness and fracture induced attenuation parameters to be inverted, and Δ X is a positive operator matrix associated with the different azimuth reflection coefficient weight difference operator matrix Δ A, which can be expressed as
Figure RE-RE-GDA0002085362600000181
Figure RE-RE-GDA0002085362600000182
Figure RE-RE-GDA0002085362600000183
Figure RE-RE-GDA0002085362600000184
Figure RE-RE-GDA0002085362600000185
Figure RE-RE-GDA0002085362600000186
Figure RE-RE-GDA0002085362600000187
Figure RE-RE-GDA0002085362600000188
Figure RE-RE-GDA0002085362600000189
Figure RE-RE-GDA00020853626000001810
Figure RE-RE-GDA00020853626000001811
Figure RE-RE-GDA00020853626000001812
Figure RE-RE-GDA00020853626000001813
Step 7-2: performing decorrelation and normalization processing on the difference value linearization expression to obtain a positive problem after decorrelation;
decorrelation and normalization processing among model parameters are considered in inversion of logarithm domain azimuth elastic impedance difference, and a kernel matrix delta X after the decorrelation becomes
Figure RE-RE-GDA00020853626000001814
Dynamic domain model parameter vector mcQBecome into
Figure RE-RE-GDA00020853626000001815
The decorrelated positive problem can be expressed as
Figure RE-RE-GDA00020853626000001816
And 7-3: converting the decorrelated positive problem into a target function;
using the Cauchy probability distribution as the prior probability density function and the Gaussian distribution as the likelihood function, the posterior probability density function is solved using a joint probability density function of the prior probability density function and the likelihood function, i.e.
Figure RE-RE-GDA0002085362600000191
Here the bayesian principle is applied: the posterior distribution is equal to prior probability multiplied by likelihood function, and the positive problem after decorrelation is processed;
in the formula (17), the reaction is carried out,
Figure RE-RE-GDA0002085362600000192
is the variance of the noise, and is,
Figure RE-RE-GDA0002085362600000193
is the variance of the quasi-static domain model parameter vector. The maximum a posteriori probability density function is taken for equation (17),combining with the low-frequency information regularization constraint term of the initial model, and performing logarithm transformation to finally express the objective function as
Figure RE-RE-GDA0002085362600000194
In the formula (18), the first and second groups,
Figure RE-RE-GDA0002085362600000195
is a regularization coefficient of the quasi-static domain model parameters;
Figure RE-RE-GDA0002085362600000196
wherein
Figure RE-RE-GDA0002085362600000197
Representing the initial values of the model parameters.
And 7-4: solving an objective function;
the objective function equation (18) is solved to obtain
Figure RE-RE-GDA0002085362600000198
In the formula (18), the reaction mixture,
Figure RE-RE-GDA0002085362600000199
Figure RE-RE-GDA00020853626000001910
Figure RE-RE-GDA0002085362600000201
QCauchyrepresents the Cauchy sparse matrix and the matrix,
Figure RE-RE-GDA0002085362600000202
represents a reflection coefficient;
and 7-5: and (3) carrying out iterative solution on the formula (19) by adopting an iterative reweighted least square optimization algorithm to obtain a dynamic domain model parameter vector, wherein the formula is as follows:
Figure RE-RE-GDA0002085362600000203
the reliability of the azimuth attenuation elastic impedance inversion method provided by the invention is verified by using the synthesized azimuth prestack seismic gather: when the synthetic gather does not contain noise or contains proper noise, the inversion result of the model parameters inverted by the inversion method is well matched with actual data. Compared with the original gather, the difference between the azimuth angle gather synthesized by the model parameter inversion result and the original gather is small, and the feasibility of the azimuth attenuation elastic impedance inversion method is further verified.
According to the method, the intrinsic attenuation and the induced attenuation of the fracture rock background are comprehensively considered, a relational equation between the dry elastic modulus and the saturated fluid elastic modulus of the fracture rock represented by a plurality of factors is combined, and an approximate expression of the complex stiffness real part of the saturated fluid medium containing the pores and characterized by the background dry rock modulus, the dry fracture flexibility, the fluid modulus, the background intrinsic longitudinal and transverse wave attenuation and the fracture induced longitudinal wave attenuation is obtained in the seismic frequency range on the basis of the weak anisotropy approximation and the weak background intrinsic attenuation approximation; based on a scattering theory, a PP wave reflection coefficient equation of a dynamic equivalent HTI attenuation medium is deduced, and an azimuth attenuation elastic impedance equation is deduced according to a longitudinal wave reflection coefficient equation under the assumption conditions of weak elastic parameter difference, small crack weakness and weak attenuation and under the assumption conditions of continuous change of elastic parameters, crack parameters, attenuation parameters and elastic impedance parameters; a sparse constraint regularization and low-frequency information constraint regularization azimuth attenuation elastic impedance iterative inversion method is provided, and prestack seismic inversion of background fluid parameters, fracture characteristic parameters and attenuation parameters of a fractured reservoir is realized.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the present invention, and it should be understood by those skilled in the art that various modifications and changes may be made without inventive efforts based on the technical solutions of the present invention.

Claims (7)

1. An inversion method of damping anisotropic fluid elastic impedance is characterized by comprising the following steps:
the method comprises the following steps: acquiring a linear sliding HTI model considering the intrinsic attenuation and fracture induced attenuation of background rocks;
step two: establishing a relation equation between the dry elastic modulus and the saturated fluid elastic modulus of the fractured rock;
step three: obtaining a real part of complex stiffness of the saturated fluid medium containing the pores and cracks by using the formulas in the first step and the second step;
step four: acquiring a PP wave reflection coefficient equation of the dynamic equivalent HTI attenuation medium;
step five: acquiring a longitudinal wave reflection coefficient equation;
step six: obtaining an azimuth attenuation elastic impedance equation according to the longitudinal wave reflection coefficient equation in the step five;
step seven: inverting the fracture weakness parameter and the fracture induced attenuation parameter by the attenuation elastic impedance difference values in different directions;
in the seventh step, the inversion of the fracture weakness parameter and the fracture induced attenuation parameter is carried out by the attenuation elastic impedance difference values in different directions, and the inversion comprises the following steps:
step 7-1: carrying out difference linearization processing on the attenuation elastic impedance in different directions of the logarithmic domain to obtain a difference linearization expression as shown in the following formula;
Figure FDA0002719940290000011
in formula (15), M is the number of incident angles, N is the number of azimuthal angle differences, and L is the number of reflective interfaces;
Figure FDA0002719940290000012
is the difference in elastic impedance, m, in different directions in the logarithmic domaincQIs the fracture weakness and fracture induced attenuation parameters to be inverted, and Δ X is a positive operator matrix associated with the different azimuth reflection coefficient weight difference operator matrix Δ A, which can be expressed as
Figure FDA0002719940290000013
Figure FDA0002719940290000014
Figure FDA0002719940290000021
Figure FDA0002719940290000022
Figure FDA0002719940290000023
Figure FDA0002719940290000024
Figure FDA0002719940290000025
Figure FDA0002719940290000026
Figure FDA0002719940290000027
Figure FDA0002719940290000028
Figure FDA0002719940290000029
Figure FDA00027199402900000210
Step 7-2: performing decorrelation and normalization processing on the difference value linearization expression to obtain a positive problem after decorrelation;
decorrelation and normalization processing among model parameters are considered in inversion of logarithm domain azimuth elastic impedance difference, and a kernel matrix delta X after the decorrelation becomes
Figure FDA00027199402900000212
Dynamic domain model parameter vector mcQBecome into
Figure FDA00027199402900000213
The decorrelated positive problem can be expressed as
Figure FDA00027199402900000214
And 7-3: converting the decorrelated positive problem into a target function;
using the Cauchy probability distribution as the prior probability density function and the Gaussian distribution as the likelihood function, the posterior probability density function is solved using a joint probability density function of the prior probability density function and the likelihood function, i.e.
Figure FDA0002719940290000031
In the formula (17), the reaction is carried out,
Figure FDA0002719940290000032
is the variance of the noise, and is,
Figure FDA0002719940290000033
is the variance of the quasi-static domain model parameter vector; taking a maximum posterior probability density function of the formula (17), combining with the low-frequency information regularization constraint term of the initial model, and finally representing the target function as
Figure FDA0002719940290000034
In the formula (18), the first and second groups,
Figure FDA00027199402900000311
is a regularization coefficient of the quasi-static domain model parameters;
Figure FDA0002719940290000035
wherein
Figure FDA0002719940290000036
Representing initial values of model parameters;
and 7-4: solving an objective function;
the objective function equation (18) is solved to obtain
Figure FDA0002719940290000037
In the formula (18), the reaction mixture,
Figure FDA0002719940290000038
Figure FDA0002719940290000039
Figure FDA00027199402900000310
QCauchyrepresents the Cauchy sparse matrix and the matrix,
Figure FDA00027199402900000312
represents a reflection coefficient;
and 7-5: and (3) carrying out iterative solution on the formula (19) by adopting an iterative reweighted least square optimization algorithm to obtain a dynamic domain model parameter vector, wherein the formula is as follows:
Figure FDA0002719940290000041
2. the method of claim 1, wherein in the first step, the isotropic background modulus parameter and the fracture parameter in the linear sliding HTI model are both expressed in complex form, and the formula is as follows:
Figure FDA0002719940290000042
in the formula (1), the first and second groups,
Figure FDA0002719940290000043
Figure FDA0002719940290000044
and
Figure FDA0002719940290000045
respectively representing complex longitudinal wave modulus, first and second Lame constants of isotropically attenuating background rock, and
Figure FDA0002719940290000046
Figure FDA0002719940290000047
and
Figure FDA0002719940290000048
representing complex normal and tangential fracture attenuation parameters that induce longitudinal and transverse wave attenuation with fractures along the axis of symmetry
Figure FDA0002719940290000049
And
Figure FDA00027199402900000410
is simply expressed as
Figure FDA00027199402900000411
Model parameters in complex form under the assumption of isotropic viscoelastic background rock
Figure FDA00027199402900000412
And
Figure FDA00027199402900000413
can be expressed as
Figure FDA00027199402900000414
In the formula (3), the first and second groups,
Figure FDA00027199402900000415
and
Figure FDA00027199402900000416
respectively representing the inverse quality factors of the longitudinal wave and the transverse wave of the background;
and (3) simultaneously substituting the notations (2) and (3) into the formula (1) to obtain a linear sliding HTI model considering the intrinsic attenuation and the fracture-induced attenuation of the background rock.
3. The method for inverting the elastic impedance of the damping anisotropic fluid according to claim 2, wherein in the second step, the equation of the relationship between the dry elastic modulus and the saturated elastic modulus of the fractured rock is as follows:
Figure FDA0002719940290000051
in the formula (4), the first and second groups,
Figure FDA0002719940290000052
is a complex representation of the effective rigidity elastic matrix of the saturated fluid fractured rock,
Figure FDA0002719940290000053
the method is characterized in that the method is a complex representation of an effective rigidity elastic matrix of the dry fractured rock;
Figure FDA0002719940290000054
is a complex characterized anisotropy-like Biot coefficient, which can be expressed as
Figure FDA0002719940290000055
Wherein, KgRepresenting the effective bulk modulus of the constituent rock solids;
Figure FDA0002719940290000056
is a complex representation of the anisotropic Gassmann pore space modulus, which can be expressed as
Figure FDA0002719940290000057
In the formula (I), the compound is shown in the specification,
Figure FDA0002719940290000058
is a complex characterized anisotropic dry rock-like bulk modulus; phi represents porosity; kappafRepresenting the pore fluid effective bulk modulus.
4. The method for inverting the elastic impedance of the damped anisotropic fluid as set forth in claim 3, wherein in the third step, the method for obtaining the real part of the complex stiffness of the interstitial fracture medium of the saturated fluid comprises the following steps:
wherein, the real part of the complex-characterized weak anisotropic stiffness matrix of the dry fracture rock can be expressed as
Figure FDA0002719940290000059
In the formula (7), the first and second groups,
Figure FDA0002719940290000061
Figure FDA0002719940290000062
Figure FDA0002719940290000063
Figure FDA0002719940290000064
Figure FDA0002719940290000065
Figure FDA0002719940290000066
and
Figure FDA0002719940290000067
respectively representing comprehensive attenuation factors of the product of background intrinsic longitudinal wave attenuation and transverse wave attenuation and fracture-induced longitudinal wave attenuation;
substituting the formulas (5), (6) and (7) into the formula (4), and obtaining an approximate expression of the real part of the complex stiffness of the saturated fluid medium containing the pore gaps, which is characterized by the modulus of the background dry rock, the flexibility of the dry gaps, the modulus of the fluid, the intrinsic longitudinal and transverse wave attenuation of the background and the induced longitudinal wave attenuation of the gaps, in the seismic frequency range on the basis of the weak anisotropy approximation and the weak intrinsic attenuation approximation of the background
Figure FDA0002719940290000068
In the formula (8), the first and second groups,
Figure FDA0002719940290000069
Figure FDA00027199402900000610
Figure FDA00027199402900000611
Figure FDA00027199402900000612
Figure FDA00027199402900000613
β0＝1-Kdry/Kgis the Biot coefficient;
Kdryrepresenting the bulk modulus of the dry rock.
5. The method for inverting the damped anisotropic fluid elastic impedance as claimed in claim 4, wherein in the fourth step, the method for obtaining the PP wave reflection coefficient equation is as follows:
based on scattering theory, the longitudinal wave reflection coefficient of HTI media can be expressed as:
Figure FDA0002719940290000071
where θ represents the angle of incidence, ρ represents the density term of the homogeneous isotropic background medium,
Figure FDA0002719940290000072
parameter, ξ, representing the disturbance stiffness of saturated rockmnRelated to slowness vectors and polarization vectors;
therefore, by combining the equations (8) and (9), the equation of the reflection coefficient of the PP wave of the dynamic equivalent HTI attenuation medium can be derived, and the expression is
Figure FDA0002719940290000073
In the formula (I), the compound is shown in the specification,
Figure FDA0002719940290000074
Figure FDA0002719940290000075
Figure FDA0002719940290000076
Figure FDA0002719940290000077
Figure FDA0002719940290000078
Figure FDA0002719940290000079
in the formula (10), the first and second groups,
Figure FDA00027199402900000710
representing the azimuth angle, delta representing the difference of each property of the two layers of media, and f is fluid/pore and is a fluid factor; fracture weakness parameters may be estimated from well log data and petrophysical models.
6. The method of inverting an attenuating anisotropic fluid elastic impedance of claim 5, wherein in step five, based on the relationship between the horizontal interface longitudinal wave reflection coefficient and the azimuthal anisotropic elastic impedance, the longitudinal wave reflection coefficient equation is expressed as:
Figure FDA0002719940290000081
in the formula (11), the reaction mixture,
Figure FDA0002719940290000082
represents the azimuthal attenuation elastic resistance, and Δ EI (θ, Φ) represents the difference between the elastic resistances of the previous and next layers.
7. The method for inverting the damped anisotropic fluid elastic impedance as claimed in claim 6, wherein in step six, the method for obtaining the azimuthal damped elastic impedance equation from the longitudinal wave reflection coefficient equation of step five is as follows:
in the weak elastic parameter difference (| delta f/f | < 1, | delta mu/mub1 and [ Delta ] rho/rhobLess than 1) small crack weakness
Figure FDA0002719940290000083
And weak attenuation
Figure FDA0002719940290000084
Under the assumption of the conditions that,
the relative difference in background elastic modulus in equation (11) can be approximately replaced by:
Δf/f≈Δ(lnf)，
Δμ/μb≈Δ(lnμb)，
Δρ/ρb≈Δ(lnρb) And is and
Figure FDA0002719940290000085
under the assumption of continuous change of elastic parameters, crack parameters, attenuation parameters and elastic impedance parameters, delta (ln f) is approximately equal to d (ln f), and delta (ln mu)b)≈d(lnμb)，Δ(lnρb)≈d(lnρb)，
Figure FDA0002719940290000086
ΔT≈dT，
Figure FDA0002719940290000087
And is
Figure FDA0002719940290000088
Substituting the above approximate substitution into equation (11) yields the following equation:
Figure FDA0002719940290000091
the integral of the formula (12) is calculated, and the logarithmic domain azimuth attenuation elastic impedance equation is obtained through corresponding operation, and is expressed as
Figure FDA0002719940290000092
Taking the logarithm of equation (13), the final azimuthal attenuation elastic impedance equation can be expressed as
Figure FDA0002719940290000093
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