CN106019375B - A kind of shale gas stratum stratification geophysics evaluation method - Google Patents
A kind of shale gas stratum stratification geophysics evaluation method Download PDFInfo
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Abstract
The present invention relates to unconventionaloil pool field of seismic exploration, discloses a kind of shale gas stratum stratification geophysics evaluation method, comprises the following steps：The first step, characterized based on the theoretical horizontal bedding density anisotropic parameters of rock physicses；Second step, the pre-stack seismic inversion based on Polarisation Anisotropy；3rd step, the horizontal bedding evaluation based on seismic data.The present invention proposes a kind of method of more stable VTI medium anisotropy parametric inversions, pass through the inverting to Polarisation Anisotropy parameter, and the relation between anisotropic parameters and horizontal bedding density is combined, finally realize the horizontal bedding evaluation of shale oil and gas reservoir.Compared with the Polarisation Anisotropy inverting of routine, the inventive method proposes the concept of new stratification density, and consider the relation between shale anisotropic parameters and stratification density, the horizontal bedding of shale is set to evaluate with more intuitively understanding, the exploration and development to shale oil and gas reservoir is significant.
Description
Technical field
The present invention relates to unconventionaloil pool field of seismic exploration, more particularly to a kind of shale gas stratum stratification geophysics is commented
Valency method.
Background technology
The information not available for many poststack data is contained in Prestack seismic data, so pre-stack seismic inversion is extensive
Should be in reservoir prediction and fluid identification.During shale deposition, caused by being deposited due to various deposits on vertical discontinuously,
This stratification construction to be formed that acted on by connate deposit is referred to as horizontal bedding.In other words, due to the presence of horizontal bedding,
Just cause shale that there is the feature of VTI media so that shale shows Polarisation Anisotropy.Anisotropic parameters be weigh it is each to
Different in nature strong and weak important indicator, for the crack elimination of HTI media, fracture spacing refers to the bar number of unit volume internal fissure,
It is to influence the strong and weak principal element of anisotropic parameters.
Seismic inversion is the effective way for obtaining underground medium elastic parameter.According to different, the seismic inversion using seismic data
Post-stack inversion and prestack inversion can be divided into.Post-stack inversion utilizes poststack seismic data, main inverting stratum compressional wave information；Prestack
Shake inverting utilizes the abundant information that Prestack seismic data is included, and in addition to inverting compressional wave information, can also estimate formation shear, rock
Stone modulus, fluid sensitive parameter, physical parameter, anisotropic parameters, even absorption parameter, the information such as density.In pre-stack seismic
It is different according to the earthquake direct problem analytical expression of use in inverting, the prestack inversion based on wave equation can be divided into, based on earthquake
Ripple accurate reflection coefficient equation and its approximate prestack inversion and seismic scattering inverting based on Seismic Wave Scattering coefficient equation etc.,
Wherein, the prestack seismic inversion method based on wave equation is limited by computational efficiency and stability, it is difficult in actual seismic data
Middle inverting obtains legitimate result, and practicality is smaller；It is different according to refutation strategy, based on seismic reflection coefficient equation and its approximately
Prestack inversion method can be divided into AVO invertings, AVA invertings and elastic impedance inverting again.It is different according to underground medium equivalent model, it can divide
For uniform, non-uniform dielectric, isotropism, anisotropic medium, elasticity, viscoelastic media, and mutual group between them
Close medium pre-stack seismic inversion etc..
The existing shale oil and gas reservoir based on Polarisation Anisotropy inverting, only it is merely the anisotropy progress to shale
Evaluation, the relation between anisotropic parameters and horizontal bedding is not built, can not be true simply by anisotropic parameters
Normal incidence realizes that shale horizontal bedding is evaluated.
The content of the invention
The present invention is theoretical based on Schoenberg linear slides, and the extension linear slide derived suitable for VTI media is managed
By describing the Equivalent Elasticity matrix of VTI media also with normal direction " weakness " and tangential " weakness ", finally obtain anisotropic parameters
With the relation between stratification density.And a kind of method of more stable VTI medium anisotropy parametric inversions is proposed, pass through
Inverting to Polarisation Anisotropy parameter, and the relation between anisotropic parameters and horizontal bedding density is combined, it is final to realize
The horizontal bedding evaluation of shale oil and gas reservoir.
The technical solution adopted by the present invention is：A kind of shale gas stratum stratification geophysics evaluation method, including following step
Suddenly：
The first step, characterized based on the theoretical horizontal bedding density anisotropic parameters of rock physicses：
If the stratification density for the horizontal bedding developed in shale reservoir is η, i.e., developmental level stratification is total in unit volume
Surface area is η, the relational expression in the case of analogy vertical fracture between fracture spacing and anisotropic parameters, obtains stratification density η
With normal direction " weakness " ΔNWith tangential " weakness " ΔTRelation：
In formula (1),η represents stratification density, and K ' and μ ' represent charges bulk modulus in stratification respectively
And modulus of shearing, α represent the depth-width ratio of stratification,
Anisotropic parameters ε, δ and γ and normal direction " weakness " Δ in VTI mediaNWith tangential " weakness " ΔTRelation：
The normal direction " weakness " Δ established according to formula (1)NWith tangential " weakness " ΔTWith stratification density η relation, by formula (1) band
Enter formula (2), the relation that can be obtained between anisotropic parameters ε, γ and δ and stratification density η is as follows：
In formula (3),
Second step, the pre-stack seismic inversion based on Polarisation Anisotropy：
Theoretical according to VTI media seimic wave propagation, the infinitely great anisotropic medium reflectance factor of two half spaces is approximate
Equation is as follows：
In equation (5)WithThe average of upper and lower medium velocity of longitudinal wave, shear wave velocity and density is represented respectively；Δ
VP、ΔVSRepresent the difference of upper and lower medium velocity of longitudinal wave, shear wave velocity and density respectively with Δ ρ；Represent transverse and longitudinal
The ratio of wave velocity mean square；Δ δ=δ2-δ1With Δ ε=ε2-ε1The difference of upper and lower medium anisotropic parameters is represented respectively,
The P wave reflections of VTI media are write as isotropism reflection R in equation (5)isoWith anisotropic emission coefficient
RanisoThe longitudinal wave reflection coefficient approximate formula of sum, as Polarisation Anisotropy inverting：
In formula (6),
Make A=1+tan2θ, B=-8Ksin2θ, C=1-4Ksin2θ, D=sin2θ, E=sin2θtan2θ, obtain：
If elastic impedance represents as follows with reflectance factor：
Δ lnx=Δ x/x are made, joint above-mentioned formula (7) and (8), are then had：
Δ ln (EI)=A Δ ln (VP)+Bln(ΔVS)+C Δs ln (ρ)+D Δ δ+E Δs ε (9),
Formula (9) both sides are integrated simultaneously, and take natural Exponents, then are had：
Introduce three normaliztion constant EI0、VP0、VS0、ρ0、δ0And ε0, to formula (10) normalized, it is changed into：
Natural logrithm is taken to the elastic impedance expression formula both sides of formula (11), then had：
OrderThen have：
Δ EI (θ)=(δ-δ0)D(θ)+(ε-ε0) E (θ) (13),
A relatively large natural number C is multiplied by simultaneously to formula (13) both sides, obtained：
C Δs EI (θ)=C (δ-δ0)D(θ)+C·(ε-ε0) E (θ) (14),
In formula (14), Δ EI (θ) represents the elastic impedance of anisotropy terms,
Using formula (14), by the elastic impedance data of multiple different incidence angles, determine that the anisotropy of VTI media is joined
Number：
The form for being write as matrix has：
The elastic impedance Δ EI (θ) and anisotropic parameters ε and δ of the anisotropy terms on well are obtained according to log,
Now calculate 4 constant coefficient D (θ1)、E(θ1)、D(θ2) and E (θ2), the constant coefficient calculated is updated to formula (15) again
In, obtain trying to achieve the anisotropic parameters of any sample point；
3rd step, the horizontal bedding evaluation based on seismic data：
It is anti-to the angle gathers earthquake record progress Sparse Pulse of different incidence angles respectively by the use of log data as constraint
Drill, obtain the elastic impedance data volume of the VTI media under each incidence angle, then calculate the isotropism background media under each incidence angle
Elastic impedance data volume, and eliminate contribution of the isotropic medium to elastic impedance, " amplification " anisotropic parameters is to elasticity
The influence of impedance, the elastic impedance of anisotropy terms is calculated, finally according to the elasticity of the anisotropy terms under each incidence angle
Resistance difference, the anisotropic parameters in shale reservoir is calculated, the rammell based on seismic data is finally realized according to formula (1)
Reason evaluation.
Compared with the Polarisation Anisotropy inverting of routine, the inventive method proposes the concept of new stratification density, and examines
The relation between shale anisotropic parameters and stratification density is considered, there is the horizontal bedding evaluation of shale and more intuitively manage
Solution, the exploration and development to shale oil and gas reservoir are significant.
Brief description of the drawings
Fig. 1 is main research approach figure.
Fig. 2 anisotropic parameters direct inversion results.
The anisotropic parameters of direct inversion when Fig. 3 is noiseless.
The Anisotropic parameters inversion result of the random noise of Fig. 4 additions 10%.
The Anisotropic parameters inversion result of the random noise of Fig. 5 additions 20%.
Elastic impedance inversion result during 5 ° of incidence angles of Fig. 6 a.
Elastic impedance inversion result during 10 ° of incidence angles of Fig. 6 b.
Elastic impedance inversion result during 15 ° of incidence angles of Fig. 6 c.
Elastic impedance inversion result during 20 ° of incidence angles of Fig. 6 d.
Elastic impedance inversion result during 25 ° of incidence angles of Fig. 6 e.
Fig. 7 anisotropic parameters ε inversion results.
Fig. 8 anisotropic parameters δ inversion results.
Fig. 9 shale formation stratification inversion of Density results.
Figure 10 N stratum stratification density horizon slice result.
Embodiment
Horizontal bedding is that shale is influenceed in deposition process by factors such as hydrodynamic force, organic matter and depositional environments, is made
Shale has horizontal layered structure after being formed.Fracture spacing is measurement and the research most basic and most important parameter in crack.Ginseng
According to the concept of fracture spacing, the present invention proposes a kind of new physical quantity, i.e. stratification density.Therefore, stratification density can be defined
Concept is the number of stratification in unit volume, and the stratification developmental state of shale formation is characterized using the concept of stratification density.
It is the weight that geophysical work person faces to carry out evaluation to the horizontal bedding of shale formation by earthquake data before superposition
Want problem, in shale the presence of horizontal bedding shale can be equivalent to VTI media, can be obtained by pre-stack seismic inversion
The anisotropic parameters of VTI media, further according to the relation between anisotropic parameters and stratification density, so as to realize shale level
Stratification is evaluated.
The Polarisation Anisotropy inverting of shale, i.e., using Prestack seismic data to the elastic parameter of shale oil and gas reservoir and respectively
Anisotropy parameter carries out inverting, can be anti-by the anisotropic parameters that inverting obtains and the relation of shale horizontal bedding density
Drill to obtain the stratification developmental state of shale formation.
A kind of key step of shale horizontal bedding evaluation method based on Polarisation Anisotropy inverting proposed by the present invention
As shown in Figure 1：
The first step, characterized based on the theoretical horizontal bedding density anisotropic parameters of rock physicses：
Schoenberg linear slide theories are to propose that the model is mainly examined based on Backus sub-layers layered medium models
Consider crack and rock is divided into flexible face parallel to each other, and do not connected between each crack, the model, which is applied to have, linearly to be connected
Continuous border.Transformation of the horizontal bedding to shale is also that subsurface rock is separated from one another into parallel flexible face, and assumes each water
Do not connected between flat bed plane, therefore, shale is transformed into VTI media by horizontal bedding.With reference to Schoenberg linear slides reason
Relation between fracture spacing and elastic matrix, expression formula of the stratification density to VTI dielectric resilient matrixes is derived, so as to structure
Build-up layers manage the relation between density and anisotropic parameters.
It is similar with linear slide theory, horizontal bedding is decomposed into normal direction flexibility ZNWith tangential flexibility ZT.And contain level course
The flexibility matrix S of the shale of reason can be still expressed as：
Wherein, SbFor the flexibility matrix of isotropism background rock,For the flexibility square of horizontal bedding in shale reservoir
Battle array.
Schoenberg (1995) gives the extension Flexibility tensor of single crack group：
For HTI media, symmetry axis x1Axle, i.e. n1(1,0,0).Similarly, for VTI media, its symmetry axis is x3Axle,
That is n3(0,0,1), then have：
s3333f=ZN
And other flexibility components are 0.With routine 6 × 6 matrix representation, i.e.,：11 → 1,22 → 2,33 → 3,
23 → 4,13 → 5,12 → 6.And the coefficient 2 and 4 introduced according to Nye (1985), represent as follows：
sijkl→Spq, p and q are 1,2 or 3；
2sijkl→Spq, p or q have one for 4,5 or 6；
4sijkl→Spq, p and q are 4,5 or 6；
So in shale reservoir horizontal bedding flexibility matrixIt can be expressed as：
The flexibility matrix S of isotropism background rockbLatin America's parameter representation be：
Therefore, the shale elastic matrix C of developmental level stratificationVTIIt can be expressed as：
Still continue to use Hsu etc. (1993) and propose two nondimensional parameter normal direction " weakness " ΔsNWith tangential " weakness " ΔT, for retouching
Rock rigidity variation characteristic caused by horizontal bedding is stated, i.e.,：
Wherein, λ, μ are respectively first, second Lame parameter.
Using the thought of Schoenberg (1995), the extension linear slide theory suitable for HORIZONTAL LAYERED MEDIUM WITH HIGH ACCURACY is obtained.
Therefore, the shale Equivalent Elasticity matrix of developmental level stratification normal direction " weakness " ΔNWith tangential " weakness " ΔTRepresent as follows：
Assuming that the stratification density for the horizontal bedding developed in shale reservoir is η, i.e., developmental level stratification in unit volume
Total surface area is η, the relational expression in the case of analogy vertical fracture between fracture spacing and anisotropic parameters, can obtain stratification
Density η and normal direction " weakness " ΔNWith tangential " weakness " ΔTRelation：
In formula (1),η represents stratification density；K ' and μ ' represents respectively in stratification charges bulk modulus with
Modulus of shearing；α represents the depth-width ratio of stratification.
Bakul in etc. (2000) give anisotropic parameters ε in vertical fracture HTI(v)、δ(v)And γ(v)It is weak with normal direction
Spend ΔNWith tangential " weakness " ΔTRelation it is as follows.Similarly, anisotropic parameters ε, δ and γ and normal direction " weakness " Δ in VTI mediaN
With tangential " weakness " ΔTRelation：
The normal direction " weakness " Δ established according to formula (1)NWith tangential " weakness " ΔTWith stratification density η relation, by formula (1) band
Enter formula (2), the relation that can be obtained between anisotropic parameters ε, γ and δ and stratification density η is as follows：
Wherein,
Second step：Pre-stack seismic inversion based on Polarisation Anisotropy
Theoretical according to VTI media seimic wave propagation, it is anti-that Ruger establishes the infinitely great anisotropic medium of two half spaces
It is as follows to penetrate coefficient approximate equation：
In formulaWithThe average of upper and lower medium velocity of longitudinal wave, shear wave velocity and density is represented respectively；ΔVP、ΔVS
Represent the difference of upper and lower medium velocity of longitudinal wave, shear wave velocity and density respectively with Δ ρ；Represent transverse and longitudinal wave velocity
The ratio of mean square；Δ δ=δ2-δ1With Δ ε=ε2-ε1The difference of upper and lower medium anisotropic parameters is represented respectively.
The P wave reflections of VTI media can also be write as isotropism reflection R in above formulaisoWith anisotropic emission coefficient
RanisoSum, i.e.,：
Wherein,
Above formula is the longitudinal wave reflection coefficient approximate formula of Polarisation Anisotropy inverting.
Make A=1+tan2θ, B=-8Ksin2θ, C=1-4Ksin2θ, D=sin2θ, E=sin2θtan2θ, it can obtain：
Using Connolly (1999) elastic impedance thought, elastic impedance represents as follows with reflectance factor：
Δ lnx=Δ x/x are made, combines above-mentioned two formula, then has：
Δ ln (EI)=A Δ ln (VP)+Bln(ΔVS)+CΔln(ρ)+DΔδ+EΔε
Above formula both sides are integrated simultaneously, and take natural Exponents, then are had：
In order to eliminate influence of the different P ripples incidence angles to elastic impedance dimension, three normaliztion constant EI are introduced0、
VP0、VS0、ρ0、δ0And ε0, to above formula normalized, it is changed into：
It is intended to obtain the anisotropic parameters of VTI media by prestack inversion, at least needs the elastic impedance number of 5 angles
According to taking natural logrithm to both sides in formula, nonlinear elastic impedance formula be converted into system of linear equations, i.e.,：
The form for being write as matrix then has：
Upper simplification is expressed as：
AX=B (4)
Pass through well lie elastic impedance value and known log data VP、VS, ρ, δ and ε 25 constant coefficient matrixes are calculated
A.Each angle elastic impedance obtained by their joint inversions is substituted into formula (4), it is hereby achieved that any one sampled point of each road
The anisotropic parameters at place.
It is in the stratification evaluation of stratum however, by the elastic impedance data volume of VTI media to anisotropic parameters direct inversion
Indispensable.It is many to influence the factor of VTI medium inversion results, because anisotropic parameters ε and δ is to VTI reflectance factors
Contribution is smaller, passes through the elastic impedance equation Simultaneous Inversion velocity of longitudinal wave V of formula (3)P, shear wave velocity VS, density p, anisotropy ginseng
Number five parameters of ε and δ, it will cause the unstable of inversion result.Fig. 2 is given using based on the derivation of Ruger approximate formulas
Elastic impedance equation, inverting obtain the one-dimensional model of anisotropic parameters, as can be seen from Figure, Anisotropic parameters inversion knot
Fruit is very different with realistic model, does not have correlation between the two, just because of contribution of the anisotropic parameters to reflectance factor
It is too weak, cause this method inversion result inaccurate.Therefore, in order that the anisotropic parameters of inverting has more preferable stability,
This paper presents a kind of new anisotropic parameters Direct Inverse Method.
Why Anisotropic parameters inversion is not sufficiently stable, and is because compared to velocity of longitudinal wave VP, shear wave velocity VSAnd density
The isotropism parameter such as ρ, contributions of the anisotropic parameters ε and δ to reflectance factor are too weak.Therefore, want solve this problem, respectively
Anisotropy parameter is contributed necessary " amplification " reflectance factor.It is directly anti-in the anisotropic parameters of VTI media based on this thought
During drilling, influence of the isotropic medium to reflectance factor can be eliminated, only retains anisotropic parameters to reflectance factor
Contribution.Therefore, comprising anisotropic parameters to only including the contribution quilt " amplification " of anisotropy terms reflectance factor, and carry out accordingly
More stable prestack elastic impedance inverting.
Reflectance factor approximate formula in VTI media given below, according to above-mentioned thought, eliminate isotropic medium pair
The contribution of reflectance factor, it can obtain：
With reference to the thought for eliminating isotropic medium contribution, natural logrithm is taken to the elastic impedance expression formula both sides of above formula,
Then have：
OrderThen have：
Δ EI (θ)=(δ-δ0)D(θ)+(ε-ε0)E(θ)
In order to protrude the fine difference between anisotropic parameters, above formula both sides are multiplied by simultaneously one it is relatively large from
So number C, so not only " has amplified " difference between anisotropic parameters, and also ensure that the stabilization for solving linear equation
Property.Therefore, above formula is changed into：
C Δs EI (θ)=C (δ-δ0)D(θ)+C·(ε-ε0)E(θ)
C represents relatively large natural number in formula；Δ EI (θ) represents the elastic impedance of anisotropy terms；Using above formula, lead to
Cross the elastic impedance data of multiple different incidence angles, it may be determined that the anisotropic parameters of VTI media：
The form for being write as matrix has：
The elastic impedance Δ EI (θ) and anisotropic parameters ε of the anisotropy terms on well can be obtained according to log
And δ, it can now calculate 4 constant coefficient D (θ1)、E(θ1)、D(θ2) and E (θ2).The constant coefficient calculated is updated to again
In formula, it can obtain trying to achieve the anisotropic parameters of any sample point.The anisotropy ginseng that this method can not only be stablized
Number, also has higher noise immunity.
In order to verify the feasibility and stability of the elastic impedance direct inversion anisotropic parameters for utilizing anisotropy terms,
The A wells for choosing the actual seismic work area of east shale oil and gas reservoir carry out one-dimensional model tentative calculation, when Fig. 3 gives noiseless,
The anisotropic parameters obtained using the elastic impedance Δ EI Direct Inverse Methods of anisotropy terms, can be seen by comparison diagram 2
Go out, when noiseless, the anisotropic parameters and realistic model that are obtained using the elastic impedance Δ EI direct inversions of anisotropy terms
The goodness of fit is very high, has good feasibility.
In order to further verify the stability of this method, different degrees of random noise is added, random noise obeys Gauss
Anisotropic parameters inversion result when distribution, Fig. 4 and Fig. 5 sets forth the random noise of addition 10% and 20%.Light/dark balance
Curve represents inversion result, and aterrimus curve represents realistic model.In the feelings of addition random noise it can be seen from Fig. 4 and Fig. 5
Under condition, anisotropic parameters still has the preferable goodness of fit.So as to demonstrate the elastic impedance inverting for utilizing anisotropy terms
The stability and feasibility of anisotropic parameters.
3rd step：Horizontal bedding evaluation based on Polarisation Anisotropy inverting
Using the thought for eliminating isotropic term contribution, by the use of log data as constraint, respectively to different incidence angles
Angle gathers earthquake record carries out Sparse Pulse Inversion, obtains the elastic impedance data volume of the VTI media under each incidence angle, then calculate
The elastic impedance data volume of isotropism background media under each incidence angle, and eliminate tribute of the isotropic medium to elastic impedance
Offer, influence of " amplification " anisotropic parameters to elastic impedance, the elastic impedance of anisotropy terms is calculated, it is last according to each
The elastic impedance difference of anisotropy terms under incidence angle, the anisotropic parameters in shale reservoir is calculated, finally realizes shale
Stratification is evaluated.
Fig. 6 sets forth incidence angle for 5 °, 10 °, 15 °, 20 ° and 25 ° when, the elastic impedance for eliminating isotropic term is anti-
Result is drilled, i.e. only contribution result schematic diagram of the anisotropic parameters to elastic impedance.From fig. 6 it can be seen that at each angle
The elastic impedance inversion result and the overall trend of log data that the incident lower inverting of degree obtains coincide substantially.And enter in low-angle
The resolution ratio of elastic impedance inversion result is substantially better than the elastic impedance inversion result of wide-angle when penetrating.
Anisotropic parameters is the important indicator of Representation Level stratification in VTI media, is intended to carry out level course to shale formation
Reason evaluation, needs to characterize the anisotropic parameters of VTI media first.By obtaining the anisotropy terms under different incidence angles
, can be to realize that anisotropy is joined with reference to least-squares algorithm after elastic impedance data, and to anisotropic parameters direct inversion
Number direct inversion.
Fig. 7 and 8 sets forth anisotropic parameters ε and δ inversion result.It is each to different it can be seen from Fig. 7 and Fig. 8
Property parameter ε and δ are on the occasion of meeting the anisotropic parameters changing rules of VTI media.When anisotropy be present in shale formation,
ε and δ are embodied, and both overall variation trend is basically identical, this phenomenon and result of log interpretation performance one
Cause, thereby confirm the accuracy of Anisotropic parameters inversion, data support is provided for the stratification evaluation of shale.
By being VTI media by shale Approximate Equivalent, eliminate influence of the isotropic term to reflectance factor, only retain it is each to
Influence of the different in nature item to anisotropic parameters, inverting obtains the elastic impedance of anisotropy terms, and combines the principle of least square, right
Anisotropic parameters ε and δ direct inversion.Above being derived by the relation of anisotropic parameters and stratification density η can be expressed as：
Therefore, anisotropic parameters ε and δ, convolution above-mentioned two are obtained using anisotropy terms elastic impedance direct inversion
Formula, it is assumed that charges and inclusion are not present between each horizontal bedding, and it is isotropic medium to think between each stratification, then μ '
=0, and：
Then tangential " weakness " ΔTIt can represent：
It is poor that the formula of anisotropic parameters two is made, and can then have：
The relation between stratification density and anisotropic parameters can be obtained by above formula to obtain：
Fig. 9 gives the stratification density using anisotropic parameters estimation shale formation, realizes that shale horizontal bedding is evaluated
Purpose, Figure 10 give along N stratum stratification density horizon slice show result.It can be seen that stratification density
The strong and weak sign of horizontal bedding, in shale formation, the larger place of anisotropic parameters, the stratification density of shale also compared with
Greatly, the overall trend of stratification density and anisotropic parameters is basically identical, in area of the horizontal bedding compared with development, shale it is each to
Anisotropic parameter is also relatively strong, and this is consistent with the basic condition of actual underground medium.
Claims (1)
1. a kind of shale gas stratum stratification geophysics evaluation method, it is characterised in that it comprises the following steps：
The first step, characterized based on the theoretical horizontal bedding density anisotropic parameters of rock physicses：
If the stratification density for the horizontal bedding developed in shale reservoir is η, i.e., the total surface of developmental level stratification in unit volume
Product is η, the relational expression in the case of analogy vertical fracture between fracture spacing and anisotropic parameters, obtains stratification density η and method
To " weakness " ΔNWith tangential " weakness " ΔTRelation：
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<mi>&pi;</mi>
<mi>&alpha;</mi>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
<mi>&eta;</mi>
<mo>,</mo>
<msub>
<mi>&Delta;</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>16</mn>
<mrow>
<mn>3</mn>
<mo>&lsqb;</mo>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
<mi>g</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mn>4</mn>
<msup>
<mi>&mu;</mi>
<mo>&prime;</mo>
</msup>
</mrow>
<mrow>
<mi>&pi;</mi>
<mi>&alpha;</mi>
<mi>&mu;</mi>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
<mi>&eta;</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
In formula (1),η represents stratification density, and K ' and μ ' represent charges bulk modulus in stratification and cut respectively
Shear modulu, α represent the depth-width ratio of stratification, and λ is the first Lame parameter, and μ is the second Lame parameter,
Anisotropic parameters ε, δ and γ and normal direction " weakness " Δ in VTI mediaNWith tangential " weakness " ΔTRelation：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&epsiv;</mi>
<mo>=</mo>
<mn>2</mn>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>g</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>&Delta;</mi>
<mi>N</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>&delta;</mi>
<mo>=</mo>
<mn>2</mn>
<mi>g</mi>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>g</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>&Delta;</mi>
<mi>N</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&Delta;</mi>
<mi>T</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>&gamma;</mi>
<mo>=</mo>
<mfrac>
<msub>
<mi>&Delta;</mi>
<mi>T</mi>
</msub>
<mn>2</mn>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
The normal direction " weakness " Δ established according to formula (1)NWith tangential " weakness " ΔTWith stratification density η relation, formula (1) is brought into public affairs
Formula (2), the relation that can be obtained between anisotropic parameters ε, γ and δ and stratification density η are as follows：
<mrow>
<mi>&eta;</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>12</mn>
<mi>K</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
<mrow>
<mn>32</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mn>2</mn>
<mi>K</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mi>&epsiv;</mi>
<mo>-</mo>
<mi>&delta;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
In formula (3),
Second step, the pre-stack seismic inversion based on Polarisation Anisotropy：
It is theoretical according to VTI media seimic wave propagation, the infinitely great anisotropic medium reflectance factor approximate equation of two half spaces
It is as follows：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>R</mi>
<mrow>
<mi>P</mi>
<mi>P</mi>
</mrow>
<mrow>
<mi>V</mi>
<mi>T</mi>
<mi>I</mi>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;V</mi>
<mi>P</mi>
</msub>
</mrow>
<msub>
<mover>
<mi>V</mi>
<mo>&OverBar;</mo>
</mover>
<mi>P</mi>
</msub>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>&rho;</mi>
</mrow>
<mi>&rho;</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;V</mi>
<mi>P</mi>
</msub>
</mrow>
<msub>
<mover>
<mi>V</mi>
<mo>&OverBar;</mo>
</mover>
<mi>P</mi>
</msub>
</mfrac>
<mo>-</mo>
<mn>8</mn>
<mi>K</mi>
<mfrac>
<mrow>
<msub>
<mi>&Delta;V</mi>
<mi>S</mi>
</msub>
</mrow>
<msub>
<mover>
<mi>V</mi>
<mo>&OverBar;</mo>
</mover>
<mi>S</mi>
</msub>
</mfrac>
<mo>-</mo>
<mn>4</mn>
<mi>K</mi>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>&rho;</mi>
</mrow>
<mover>
<mi>&rho;</mi>
<mo>&OverBar;</mo>
</mover>
</mfrac>
<mo>+</mo>
<mi>&Delta;</mi>
<mi>&delta;</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;V</mi>
<mi>P</mi>
</msub>
</mrow>
<msub>
<mover>
<mi>V</mi>
<mo>&OverBar;</mo>
</mover>
<mi>P</mi>
</msub>
</mfrac>
<mo>+</mo>
<mi>&Delta;</mi>
<mi>&epsiv;</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<msup>
<mi>&theta;tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In equation (5)WithThe average of upper and lower medium velocity of longitudinal wave, shear wave velocity and density is represented respectively；ΔVP、Δ
VSRepresent the difference of upper and lower medium velocity of longitudinal wave, shear wave velocity and density respectively with Δ ρ；Represent transverse and longitudinal wave velocity
The ratio of mean square；Δ δ=δ2-δ1With Δ ε=ε2-ε1The difference of upper and lower medium anisotropic parameters is represented respectively,
The P wave reflections of VTI media are write as isotropism reflection R in equation (5)isoWith anisotropic emission coefficients RanisoIt
With the as longitudinal wave reflection coefficient approximate formula of Polarisation Anisotropy inverting：
<mrow>
<msubsup>
<mi>R</mi>
<mrow>
<mi>P</mi>
<mi>P</mi>
</mrow>
<mrow>
<mi>V</mi>
<mi>T</mi>
<mi>I</mi>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>R</mi>
<mrow>
<mi>i</mi>
<mi>s</mi>
<mi>o</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>R</mi>
<mrow>
<mi>a</mi>
<mi>n</mi>
<mi>i</mi>
<mi>s</mi>
<mi>o</mi>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
1
In formula (6),
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>a</mi>
<mi>n</mi>
<mi>i</mi>
<mi>s</mi>
<mi>o</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mi>&Delta;&delta;sin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mi>&Delta;&epsiv;sin</mi>
<mn>2</mn>
</msup>
<msup>
<mi>&theta;tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>,</mo>
</mrow>
Make A=1+tan2θ, B=-8K sin2θ, C=1-4K sin2θ, D=sin2θ, E=sin2θtan2θ, obtain：
<mrow>
<msubsup>
<mi>R</mi>
<mrow>
<mi>P</mi>
<mi>P</mi>
</mrow>
<mrow>
<mi>V</mi>
<mi>T</mi>
<mi>I</mi>
</mrow>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mi>A</mi>
<mfrac>
<mrow>
<msub>
<mi>&Delta;V</mi>
<mi>P</mi>
</msub>
</mrow>
<msub>
<mi>V</mi>
<mi>P</mi>
</msub>
</mfrac>
<mo>+</mo>
<mi>B</mi>
<mfrac>
<mrow>
<msub>
<mi>&Delta;V</mi>
<mi>S</mi>
</msub>
</mrow>
<msub>
<mi>V</mi>
<mi>S</mi>
</msub>
</mfrac>
<mo>+</mo>
<mi>C</mi>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>&rho;</mi>
</mrow>
<mi>&rho;</mi>
</mfrac>
<mo>+</mo>
<mi>D</mi>
<mi>&Delta;</mi>
<mi>&delta;</mi>
<mo>+</mo>
<mi>E</mi>
<mi>&Delta;</mi>
<mi>&epsiv;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
If elastic impedance represents as follows with reflectance factor：
<mrow>
<mi>R</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>&ap;</mo>
<mfrac>
<mrow>
<mi>E</mi>
<mi>I</mi>
<msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>E</mi>
<mi>I</mi>
<msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mi>n</mi>
</msub>
</mrow>
<mrow>
<mi>E</mi>
<mi>I</mi>
<msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mi>E</mi>
<mi>I</mi>
<msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mi>n</mi>
</msub>
</mrow>
</mfrac>
<mo>&ap;</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>E</mi>
<mi>I</mi>
</mrow>
<mrow>
<mi>E</mi>
<mi>I</mi>
</mrow>
</mfrac>
<mo>&ap;</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>&Delta;</mi>
<mi>l</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>E</mi>
<mi>I</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
Δ ln x=Δ x/x are made, joint above-mentioned formula (7) and (8), are then had：
Δ ln (EI)=A Δ ln (VP)+B ln(ΔVS)+C Δs ln (ρ)+D Δ δ+E Δs ε (9),
Formula (9) both sides are integrated simultaneously, and take natural Exponents, then are had：
<mrow>
<mi>E</mi>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>V</mi>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msup>
<mi>tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</msubsup>
<msubsup>
<mi>V</mi>
<mi>S</mi>
<mrow>
<mo>-</mo>
<mn>8</mn>
<msup>
<mi>Ksin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
</mrow>
</msubsup>
<msup>
<mi>&rho;</mi>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mn>4</mn>
<msup>
<mi>Ksin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
</mrow>
</msup>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>&delta;sin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>+</mo>
<msup>
<mi>&epsiv;sin</mi>
<mn>2</mn>
</msup>
<msup>
<mi>&theta;tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
Introduce three normaliztion constant EI0、VP0、VS0、ρ0、δ0And ε0, to formula (10) normalized, it is changed into：
<mrow>
<mfrac>
<mrow>
<mi>E</mi>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>EI</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>V</mi>
<mi>P</mi>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>P</mi>
<mn>0</mn>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msup>
<mi>tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>V</mi>
<mi>S</mi>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>S</mi>
<mn>0</mn>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>8</mn>
<msup>
<mi>Ksin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
</mrow>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>&rho;</mi>
<msub>
<mi>&rho;</mi>
<mn>0</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mn>4</mn>
<msup>
<mi>Ksin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
</mrow>
</msup>
<mo>&times;</mo>
<mfrac>
<mrow>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>&delta;sin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>+</mo>
<msup>
<mi>&epsiv;sin</mi>
<mn>2</mn>
</msup>
<msup>
<mi>&theta;tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&delta;</mi>
<mn>0</mn>
</msub>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>+</mo>
<msub>
<mi>&epsiv;</mi>
<mn>0</mn>
</msub>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<msup>
<mi>&theta;tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
Natural logrithm is taken to the elastic impedance expression formula both sides of formula (11), then had：
<mrow>
<mi>ln</mi>
<mfrac>
<mrow>
<mi>E</mi>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>EI</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mi>A</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mi>ln</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>V</mi>
<mi>P</mi>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>P</mi>
<mn>0</mn>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>B</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mi>ln</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>V</mi>
<mi>S</mi>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>S</mi>
<mn>0</mn>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mi>ln</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mi>&rho;</mi>
<msub>
<mi>&rho;</mi>
<mn>0</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>&delta;</mi>
<mo>-</mo>
<msub>
<mi>&delta;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>D</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>&epsiv;</mi>
<mo>-</mo>
<msub>
<mi>&epsiv;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>E</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
OrderThen have：
Δ EI (θ)=(δ-δ0)D(θ)+(ε-ε0) E (θ) (13),
A relatively large natural number C is multiplied by simultaneously to formula (13) both sides, obtained：
C Δs EI (θ)=C (δ-δ0)D(θ)+C·(ε-ε0) E (θ) (14),
In formula (14), Δ EI (θ) represents the elastic impedance of anisotropy terms,
Using formula (14), by the elastic impedance data of multiple different incidence angles, the anisotropic parameters of VTI media is determined：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>C</mi>
<mo>&CenterDot;</mo>
<mi>&Delta;</mi>
<mi>E</mi>
<mi>I</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>C</mi>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mi>&delta;</mi>
<mo>-</mo>
<msub>
<mi>&delta;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>D</mi>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>C</mi>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mi>&epsiv;</mi>
<mo>-</mo>
<msub>
<mi>&epsiv;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>E</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>C</mi>
<mo>&CenterDot;</mo>
<mi>&Delta;</mi>
<mi>E</mi>
<mi>I</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>C</mi>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mi>&delta;</mi>
<mo>-</mo>
<msub>
<mi>&delta;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>D</mi>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>C</mi>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mi>&epsiv;</mi>
<mo>-</mo>
<msub>
<mi>&epsiv;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>E</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
</mrow>
The form for being write as matrix has：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>D</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>E</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>D</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>E</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>&CenterDot;</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&delta;</mi>
<mo>-</mo>
<msub>
<mi>&delta;</mi>
<mn>0</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>&epsiv;</mi>
<mo>-</mo>
<msub>
<mi>&epsiv;</mi>
<mn>0</mn>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>&Delta;</mi>
<mi>E</mi>
<mi>I</mi>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>&Delta;</mi>
<mi>E</mi>
<mi>I</mi>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
The elastic impedance Δ EI (θ) and anisotropic parameters ε and δ of the anisotropy terms on well are obtained according to log, now
Calculate 4 constant coefficient D (θ1)、E(θ1)、D(θ2) and E (θ2), the constant coefficient calculated is updated in formula (15) again, obtained
To the anisotropic parameters for trying to achieve any sample point；
3rd step, the horizontal bedding evaluation based on seismic data：
By the use of log data as constraint, Sparse Pulse Inversion is carried out to the angle gathers earthquake record of different incidence angles respectively, obtained
The elastic impedance data volume of VTI media under to each incidence angle, then calculate the bullet of the isotropism background media under each incidence angle
Property impedance data body, and contribution of the isotropic medium to elastic impedance is eliminated, " amplification " anisotropic parameters is to elastic impedance
Influence, the elastic impedances of anisotropy terms is calculated, finally according to the elastic impedance of the anisotropy terms under each incidence angle
Difference, the anisotropic parameters in shale reservoir is calculated, finally realize that the shale stratification based on seismic data is commented according to formula (1)
Valency.
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