CN104714253A - AVO/AVA analysis method based on dispersion viscosity wave equation - Google Patents

Abstract

The invention discloses an AVO/AVA analysis method based on a dispersion viscosity wave equation. Reflection coefficients of plane waves on two kinds of dispersive medium interfaces are deduced based on the dispersion viscosity wave equation, the reflection coefficients are not only related to parameters of media but also obviously dependent on the changing of the frequency. For three typical media, the feature that the reflection coefficients change along with the frequency and the incident angle on the medium interfaces is researched, and the results are compared with the reflection coefficients based on the sound wave equation and analyzed. The responses of reflection features dependent on the frequency changing are different in different types of media especially in the low frequency, and important guiding significance is provided for reservoir stratum describing and fluid identification.

Description

A kind of AVO/AVA analytical approach based on disperse viscosity wave equation

Technical field

The invention belongs to field of geophysical exploration, propose in a kind of AVO/AVA based on disperse viscosity wave equation (change of the change/amplitude incident angle of amplitude offset distance) analysis theories and layered medium thereof the method for synthesizing zero inclined VSP (vertical seismic profiling (VSP)) and recording.

Background technology

AVO/AVA analyzes important effect in seismic prospecting, and it is a kind of effective tool of hydrocarbon indication, may be used for the physical parameter of inverting underground medium and identifies fluid.Traditional AVO/AVA analysis theories has been widely used in acoustics, elastic medium and the viscoelastic medium.Carcione et al. have studied the AVO response of hydrocarbon source rock dielectric layer in two kinds of viscoelastic isotropic mediums, consider organic and water exists time the dissipation mechanism that causes; Lam et al. have studied the pulse sound reflection on the flat medium interface with decay and Dispersion; Krebes et al. analyzes the difficult point calculating viscoelastic media midplane wave reflection coefficient and transmission coefficient, and provides the method that three kinds are determined vertical slowness symbol; Linesetal. finding also can produce faint reflection when only there is seismic attenuation difference, and only considering that compared with sound impedance difference, this reflection exists phase shift phenomenon.Innanen etal. have studied in viscoelastic media the problem utilizing AVF (change of amplitude frequency) and AVA inversion medium parameter; It is abnormal that Spectral Decomposition Technique is used for detecting the relevant frequency dispersion of reservoir saturated to gassiness by Odebeatu et al., and this is that non-resilient AVF responds an application example in hydrocarbon reservoir.Bird et al. has developed a kind of nonredundancy S-transformation algorithm of correction that utilizes and has estimated the AVF inversion method that the reflection coefficient relevant to high-selenium corn destination layer is composed; Morozov et al. proposes a kind of generalized definition utilizing matrix differential operator to describe seismic impedance, and have studied the sound impedance of viscoelastic media and relevant principle thereof in detail.

In order to portray dissimilar reservoir better, many scholars also studied the AVO/AVA effect in poroelasticity medium.Tomar et al. have studied elastic medium and contains plane wave reflection and transmission phenomenon on the pore media interface of two kinds of incompatible fluids; Quintal et al., based on one dimension interflow model, as White model, have studied the bass reflex phenomenon on the overdamp thin layer that causes due to interflow; The change (AVF) of amplitude frequency response with the variation characteristic of frequency, and is divided into the response of low frequency dim spot, phase reversal and low frequency bright spot to respond three classes by the amplitude of reflection coefficient when appointing great waves etc. to have studied ripple normal incidence on medium,nondispersive and dispersive medium interface, phasing degree; The impact of the reflection coefficient that the change that Quintal et al. have studied saturation degree in pore media changes for dependent Frequency, result shows the reflection coefficient of fractional saturation dielectric layer with frequency change clearly, especially can cause overdamp in low frequency part saturation degree.

The earthquake low-frequency anomaly phenomenon relevant to hydrocarbon reservoir gets more and more people's extensive concerning, and scholars think that the decay pattern of anomaly in the saturated reservoir of hydro carbons is relevant to velocity dispersion.Experimental result shows that the decay in the complete saturated media of the attenuation ratio of P ripple in fractional saturation rock and dry dielectric layer is large, and this can make in the reflection in some region is that change that is that caused by attenuation change instead of elastic wave impedance causes.Loizou et al. summarizes in acoustic logging and the earthquake band limits different Physical Mechanism relevant with velocity dispersion from decay, great majority are all relevant for the motion of solid skeletal to fluid-phase, and he points out that AVO is closely bound up with existing of the response of frequency change and saturated fluid.

Disperse viscosity wave equation plays a very important role for the explanation abnormal occurrence relevant to hydrocarbon reservoir, so the reflection characteristic that research disperse viscosity ripple depends on frequency change is necessary.

Summary of the invention

The object of the invention is to a kind of method providing AVO/AVA analysis theories and synthesis VSP record based on disperse viscosity wave equation.From disperse viscosity wave equation, disperse viscosity of having derived in detail plane wave incidence, to the reflection coefficient formula on two kinds of dispersive medium interfaces, uses it for the analysis of two aspects on this basis: AVO/AVA analyzes and reflectivity method synthesis VSP record.

To achieve these goals, the technical solution adopted in the present invention comprises the following steps:

1) physical parameter of saturated with fluid dielectric layer involved in disperse viscosity wave equation is provided according to actual geology background condition, physical test of rock and well logging thereof, drilling data;

2) complex velocity of Two-Dimensional Dispersion viscosity ripple, phase velocity, propagation wave-numbers and attenuation coefficient is asked for; Wherein,

Two-Dimensional Dispersion viscosity wave equation is:

$\frac{{\∂}^{2}u}{\∂t^2}+\mathrm{\γ}\frac{\∂u}{\∂t}-\mathrm{\η}(\frac{{\∂}^{3}u}{\∂x^2\∂t}+\frac{{\∂}^{3}u}{\∂z^2\∂t})-{\mathrm{\υ}}^2(\frac{{\∂}^{2}u}{\∂x^2}+\frac{{\∂}^{2}u}{\∂z^2})=0---\left(1\right);$

In formula:

$\mathrm{\γ}=\frac{{\mathrm{\μ}}_f}{K}\frac{{\mathrm{\φ}}_0({\mathrm{\α}}_2-1)}{{\mathrm{\ρ}}_{\mathrm{pf}}}$

$\mathrm{\η}=\frac{1}{{\mathrm{\ρ}}_{\mathrm{\φf}}}[{\mathrm{\ξ}}_f+\frac{4}{3}({\mathrm{\μ}}_f-\frac{{\mathrm{\σ}}_M}{{\mathrm{\φ}}_0}{\mathrm{\α}}_2)]---\left(2\right);$

${\mathrm{\υ}}^2=\frac{K_f}{{\mathrm{\ρ}}_{\mathrm{pf}}}$

In formula (2): K is permeability, K _ffor the body of fluid becomes modulus, μ _ffor the shear viscosity of fluid, ξ _ffor the body degree of becoming sticky of fluid, φ ₀for factor of porosity; ρ _{φ f}=ρ _f-ρ ₁₂(α ₁+ 1), $\begin{array}{cc}{\mathrm{\α}}_1=\frac{{\mathrm{\φ}}_0-{\mathrm{\δ}}_f}{{\mathrm{\δ}}_s},& {\mathrm{\σ}}_M=(1-{\mathrm{\φ}}_0){\mathrm{\μ}}_f[\frac{{\mathrm{\μ}}_M}{(1-{\mathrm{\φ}}_0){\mathrm{\μ}}_s}-1],\end{array}$ μ _m=ε ₀μ _s(1+c), ε ₀=1-φ ₀, c, δ _fand δ _sfor constant; ρ _ffor the mass density of fluid, μ _mfor the modulus of shearing compared with solid in large scale, μ _sfor the modulus of shearing of solid;

3) ask for the reflection coefficient formula of Two-Dimensional Dispersion viscosity wave equation based on Plane wave theory, wherein, reflection coefficient formula is as follows:

$R=\frac{{\mathrm{\ρ}}_2{\tilde{k}}_1\cos {\mathrm{\θ}}_1-{\mathrm{\ρ}}_1{\tilde{k}}_2\cos {\mathrm{\θ}}_2}{{\mathrm{\ρ}}_2{\tilde{k}}_1\cos {\mathrm{\θ}}_1+{\mathrm{\ρ}}_1{\tilde{k}}_2\cos {\mathrm{\θ}}_2}=\frac{{\mathrm{\ρ}}_2{V}_2\cos {\mathrm{\θ}}_1-{\mathrm{\ρ}}_1{V}_1\cos {\mathrm{\θ}}_2}{{\mathrm{\ρ}}_2{V}_2{\cos \mathrm{\θ}}_1+{\mathrm{\ρ}}_1{V}_1{\cos \mathrm{\θ}}_2}---\left(3\right);$

4) formula (3) is utilized to analyze plane wave incidence to the Changing Pattern of the reflection coefficient on two kinds of contiguity medium interfaces with frequency and incident angle.

Described step 1) in, physical parameter comprises density, velocity of wave propagation, disperse attenuation coefficient, viscosity attenuation coefficient; Wherein, disperse attenuation coefficient and viscosity attenuation coefficient are determined by the modulus of shearing of permeability, factor of porosity, solid, the body degree of becoming sticky of fluid, the shear viscosity of fluid.

Described step 2) in, the concrete grammar asking for the complex velocity of Two-Dimensional Dispersion viscosity ripple, phase velocity, propagation wave-numbers and attenuation coefficient is:

The mathematical description of Two-Dimensional Dispersion viscosity wave equation is:

$\frac{{\∂}^{2}u}{\∂t^2}+\mathrm{\γ}\frac{\∂u}{\∂t}-\mathrm{\η}(\frac{{\∂}^{3}u}{\∂x^2\∂t}+\frac{{\∂}^{3}u}{\∂z^2\∂t})-{\mathrm{\υ}}^2(\frac{{\∂}^{2}u}{\∂x^2}+\frac{{\∂}^{2}u}{\∂z^2})=0---\left(1\right)$

In formula: u is wave field function; γ and η is respectively disperse and viscosity attenuation coefficient, and the density, viscosity etc. of their factor of porosity, permeability and fluids with rock are relevant; υ is velocity of wave propagation in medium,nondispersive; X and t is respectively room and time variable;

If the harmonic plane wave solution of Two-Dimensional Dispersion viscosity wave equation (1) is:

$u(x,z,t)=e^{i(\mathrm{\ωt}-{\tilde{k}}_{x}x-{\tilde{k}}_{z}z)}---\left(2\right)$

For the sake of simplicity, if plane wave amplitude is 1; In above formula, the wave number of horizontal direction and vertical direction is followed successively by ω is angular frequency; And for complex wave number, can be written as

$\tilde{k}=k+\mathrm{i\α}---\left(3\right)$

In formula: k is propagation wave-numbers; α attenuation coefficient, and

Formula (2) is substituted into formula (1), obtains

$-{\mathrm{\ω}}^2+\mathrm{\γ}\left(\mathrm{i\ω}\right)+\mathrm{\η}{\tilde{k}}^2\left(\mathrm{i\ω}\right)+{\mathrm{\υ}}^2{\tilde{k}}^2=0---\left(4\right)$

The complex wave number obtaining disperse viscosity ripple from formula (4) is:

$\begin{array}{c}{\tilde{k}}^2=\frac{{\mathrm{\ω}}^2-\mathrm{i\γ\ω}}{{\mathrm{\υ}}^2+\mathrm{i\η\ω}}=\frac{({\mathrm{\υ}}^2{\mathrm{\ω}}^2-\mathrm{\γ\η}{\mathrm{\ω}}^2)-i(\mathrm{\η}{\mathrm{\ω}}^3+\mathrm{\γ\ϖ}{\mathrm{\υ}}^2)}{{\mathrm{\υ}}^4+{\mathrm{\η}}^2{\mathrm{\ω}}^2}\\ ={\tilde{K}}_R+i{\tilde{K}}_I\end{array},---\left(5\right)$

In formula: ${\tilde{K}}_R=\frac{{{\mathrm{\υ}}^2\mathrm{\ω}}^2-\mathrm{\γ\η}{\mathrm{\ω}}^2}{{\mathrm{\υ}}^4+{\mathrm{\η}}^2{\mathrm{\ω}}^2},$ ${\tilde{k}}_I=-\frac{\mathrm{\η}{\mathrm{\ω}}^3+\mathrm{\γ\ω}{\mathrm{\υ}}^2}{{\mathrm{\υ}}^4+{\mathrm{\η}}^2{\mathrm{\ω}}^2}$ Be respectively real part and imaginary part;

Again according to formula (3):

${\tilde{k}}^2=k^2+i2k\mathrm{\α}-{\mathrm{\α}}^2---\left(6\right)$

Convolution (5) and formula (6), obtain propagation wave-numbers k and attenuation coefficient α is respectively:

$k=\±\sqrt{\frac{{\tilde{K}}_R+\sqrt{{\tilde{K}}_R^2}+{\tilde{K}}_I^2}{2}}---\left(7\right)$

$\mathrm{\α}=\frac{{\tilde{K}}_I}{2k}=\±\frac{{\tilde{K}}_I}{2\sqrt{\frac{{\stackrel{\text{~}}{K}}_R+\sqrt{{\tilde{K}}_R^2}+{\tilde{K}}_{\text{'}I}^2}{2}}}---\left(8\right)$

Symbol in formula (7) and formula (8) is determined by the attenuation characteristic of disperse viscosity ripple, and propagation wave-numbers and attenuation coefficient all not only with the relating to parameters of medium, also depend on the change of frequency;

The complex velocity of disperse viscosity ripple obtains from formula (4):

$V=\frac{\mathrm{\ω}}{\tilde{k}}=\sqrt{\frac{{\mathrm{\υ}}^2+\mathrm{i\η\ω}}{1-i\frac{\mathrm{\γ}}{\mathrm{\ω}}}}---\left(9\right)$

Pass then between phase velocity and complex velocity is:

$V_p={\left(\mathrm{Re}\left(\frac{1}{V}\right)\right)}^{-1}---\left(10\right)\·$

Described step 3) in, the reflection coefficient formula asking for Two-Dimensional Dispersion viscosity wave equation is specifically adopted with the following method:

When disperse viscosity plane wave incidence can occur to launch and transmission to during two kinds of contiguity medium interfaces, upper and lower layer medium represents with footmark 1,2 respectively, and is called medium 1 and medium 2 according to this, and interface is positioned at z=0 place;

With pressure P=P (x, z; T) represent wave field, in uniform dielectric, the velocity of displacement of wave field is

$v=(\▿P)/\left(\mathrm{i\ω\ρ}\right)---\left(11\right)$

In formula: ρ is the density of medium;

If the plane of incidence of ripple and xz planes overlapping, therefore

$\begin{array}{ccc}{\tilde{k}}_{\mathrm{xj}}={\tilde{k}}_j\sin {\mathrm{\θ}}_j,& {\tilde{k}}_{\mathrm{zj}}={\tilde{k}}_j\cos {\mathrm{\θ}}_j,& j=\mathrm{1,2}\end{array}----\left(12\right)$

In formula: for complex wave number, V is ripple complex velocity in media as well; θ ₁for incident angle, θ ₂for angle of transmission;

Being taken into and penetrating wave amplitude is 1, and note wave reflection coefficient is R, and transmission coefficient is T, then total wave field of medium 1 and medium 2 is respectively

$P_1=e^{i{\tilde{k}}_1(x\sin {\mathrm{\θ}}_1-z\cos {\mathrm{\θ}}_1)}+R{e}^{i{\tilde{k}}_1(x\sin {\mathrm{\θ}}_1+z\cos {\mathrm{\θ}}_1)}---\left(13\right)$

$P_2={\mathrm{Te}}^{i{\tilde{k}}_2(x\sin {\mathrm{\θ}}_2-z\cos {\mathrm{\θ}}_2)}---\left(14\right)$

The normal velocity component that can be obtained particle in medium 1 and medium 2 by (11) formula is respectively

$v_{1z}=\frac{\frac{\∂P_1}{\∂z}}{\mathrm{i\ω}{\mathrm{\ρ}}_1}=\frac{-i{\tilde{k}}_1\cos {\mathrm{\θ}}_1{e}^{i{\tilde{k}}_1(x\sin {\mathrm{\θ}}_1-z\cos {\mathrm{\θ}}_1)}+R\left(i{\tilde{k}}_1\cos {\mathrm{\θ}}_1\right)e^{i{\tilde{k}}_1(x\sin {\mathrm{\θ}}_1+z\cos {\mathrm{\θ}}_1)}}{\mathrm{i\ω}{\mathrm{\ρ}}_1}---\left(15\right)$

$v_{2z}=\frac{\frac{\∂P_2}{\∂z}}{\mathrm{i\ω}{\mathrm{\ρ}}_2}=-\frac{i{\tilde{k}}_2\cos {\mathrm{\θ}}_{2}T{e}^{i{\tilde{k}}_2(x\sin {\mathrm{\θ}}_2-z\cos {\mathrm{\θ}}_2)}}{\mathrm{i\ω}{\mathrm{\ρ}}_2}---\left(16\right)$

Then utilize ripple to incide boundary condition on medium interface: pressure and normal velocity on interface continuously, namely

[P ₁＝P ₂]| _z＝0(17)

[ν _1z＝ν _2z]| _z＝0(18)

Reflection coefficient is obtained as follows from (14)-(18) formula:

$R=\frac{{\mathrm{\ρ}}_2{\tilde{k}}_1\cos {\mathrm{\θ}}_1-{\mathrm{\ρ}}_1{\tilde{k}}_2\cos {\mathrm{\θ}}_2}{{\mathrm{\ρ}}_2{\tilde{k}}_1\cos {\mathrm{\θ}}_1+{\mathrm{\ρ}}_1{\tilde{k}}_2\cos {\mathrm{\θ}}_2}=\frac{{\mathrm{\ρ}}_2{V}_2\cos {\mathrm{\θ}}_1-{\mathrm{\ρ}}_1{V}_1\cos {\mathrm{\θ}}_2}{{\mathrm{\ρ}}_2{V}_2{\cos \mathrm{\θ}}_1+{\mathrm{\ρ}}_1{V}_1{\cos \mathrm{\θ}}_2}---\left(19\right)$

In formula: $V_j=\frac{\mathrm{\ω}}{{\tilde{k}}_j}=\sqrt{\frac{{\mathrm{\υ}}_j^2+i{\mathrm{\η}}_j\mathrm{\ω}}{1-i\frac{{\mathrm{\γ}}_j}{\mathrm{\ω}}}}$ (j=1,2) are complex velocity, angle of transmission θ ₂with incidence angle θ ₁between relation determined by snell law, that is:

$\cos {\mathrm{\θ}}_2=\sqrt{1-\frac{V_2^2}{V_1^2}}{\sin }^2{\mathrm{\θ}}_1---\left(20\right)$

Expression (19) the formula impedance of reflection coefficient is expressed as:

$R=\frac{Z_2-Z_1}{Z_1+Z_2}---\left(21\right)$

In formula: with be respectively the impedance of medium 1 and medium 2.

Compared with prior art, the present invention has following beneficial effect:

The reflection coefficient that the present invention obtains not only with medium parameter, incident angle is relevant, also with frequency dependence, this is for explaining the reflex depending on frequency change observed in actual and experiment, as: low frequency companion shadow phenomenon, the low frequency amplitude observed in the saturated reservoir of hydro carbons strengthens, whilst on tour delay phenomenon, provide a kind of effective way, also namely in the saturated reservoir of hydro carbons, reflection wave strengthens at low frequency occurrence amplitude, the phenomenon of phase shifts, and there is no this phenomenon at dry dielectric layer, the medium parameter of the saturated reservoir of hydro carbons and the medium parameter of dry dielectric layer is utilized to analyze the amplitude of gained reflection coefficient of the present invention whether consistent with the phenomenon actually observed with the variation tendency of frequency with phase place.The reflection coefficient that gained of the present invention depends on frequency change is not only relevant with the density of medium, velocity of wave propagation, also relevant with oil and gas reservoir Reservoir Characters parameter (as: factor of porosity, permeability), fluid parameter (as: viscosity of fluid and density), characteristic parameter and the amplitude of fluid parameter to reflection coefficient and the affecting laws of phase place is preserved by analyzing reservoir, set up reflection coefficient and reservoir preserves contacting between characteristic parameter, fluid parameter, portraying for oil and gas reservoir in oil-gas exploration provides a kind of effective method with fluid identification.In addition, the theoretical model great majority that in common seismic exploration, AVO/AVA technology adopts are ACOUSTIC WAVE EQUATION, Time Migration of Elastic Wave Equation, viscoelasticity wave equation.And most important Reservoir Characters parameter is the factor of porosity of medium, permeability, saturation degree and fluid parameter etc. in fine and close reservoir exploration, these conventional dielectric models cannot meet the demands, need to consider the wave traveling model in multi phase porous medium.Theory of the present invention is disperse viscosity wave equation, this class equation considers above-mentioned Reservoir Characters parameter to the impact of wave traveling rule, is thus conducive to the identification of fluid in complex oil and gas reservoir (as: fine and close oil and gas reservoir) based on the AVO/AVA method of this equation.

Accompanying drawing explanation

The reflection and transmission schematic diagram of disperse viscosity plane wave on single interface in Fig. 1 the present invention

The amplitude of Fig. 2 disperse viscosity plane wave reflection coefficient on dry sand rock and moisture saturated media interface and phasing degree are with the variation relation of incident angle, frequency; Wherein, the amplitude that (a) is reflection coefficient, (b) is for phasing degree is with the variation relation of incident angle, frequency;

The amplitude of Fig. 3 disperse viscosity plane wave reflection coefficient on dry sand rock and oil-containing saturated media interface and phasing degree are with the variation relation of incident angle, frequency; Wherein, the amplitude that (a) is reflection coefficient, (b) is for phasing degree is with the variation relation of incident angle, frequency;

The amplitude of Fig. 4 disperse viscosity plane wave reflection coefficient on oil-containing saturated media and moisture saturated media interface and phasing degree are with the variation relation of incident angle, frequency; Wherein, the amplitude that (a) is reflection coefficient, (b) is for phasing degree is with the variation relation of incident angle, frequency;

Under Fig. 5 different frequency on dry sand rock and moisture saturated media interface the amplitude of reflection coefficient and phasing degree with the variation relation of incident angle; Wherein, the amplitude that (a) is reflection coefficient, (b) is for phasing degree is with the variation relation of incident angle, frequency;

Under Fig. 6 different frequency on dry sand rock and oil-containing saturated media interface the amplitude of reflection coefficient and phasing degree with the variation relation of incident angle; Wherein, the amplitude that (a) is reflection coefficient, (b) is for phasing degree is with the variation relation of incident angle, frequency;

Under Fig. 7 different frequency on oil-containing saturated media and moisture saturated media interface the amplitude of reflection coefficient and phasing degree with the variation relation of incident angle; Wherein, the amplitude that (a) is reflection coefficient, (b) is for phasing degree is with the variation relation of incident angle;

Synthesis VSP record under the little decay of Fig. 8, moderate fading and overdamp situation; Wherein, (a), (b), (c) is respectively the synthesis VSP record under little decay, moderate fading and overdamp situation; (d), (e), (f) is respectively for (a) around thin layer, (b), the amplification display of (c) composite traces;

Fig. 9 degree of depth is the seismologic record at 620m (in the middle of thin layer) place;

Figure 10 degree of depth is the seismologic record at 560m (above thin layer) place.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described in detail:

The present invention is based on the AVO/AVA analytical approach of disperse viscosity wave equation, comprise the following steps:

1. ask for the complex velocity of disperse viscosity ripple, phase velocity, velocity of propagation and attenuation coefficient

The mathematical description of Two-Dimensional Dispersion viscosity wave equation is:

$\frac{{\∂}^{2}u}{\∂t^2}+\mathrm{\γ}\frac{\∂u}{\∂t}-\mathrm{\η}(\frac{{\∂}^{3}u}{\∂x^2\∂t}+\frac{{\∂}^{3}u}{\∂z^2\∂t})-{\mathrm{\υ}}^2(\frac{{\∂}^{2}u}{\∂x^2}+\frac{{\∂}^{2}u}{\∂z^2})=0---\left(1\right)$

In formula: u is wave field function; γ, η are respectively disperse and viscosity attenuation coefficient, and the density, viscosity etc. of their factor of porosity, permeability and fluids with rock are relevant; υ is velocity of wave propagation in medium,nondispersive; X, t are respectively room and time variable.

If the harmonic plane wave solution of Two-Dimensional Dispersion viscosity wave equation (1) is:

$u(x,z,t)=e^{i(\mathrm{\ωt}-{\tilde{k}}_{x}x-{\tilde{k}}_{z}z)}---\left(2\right)$

For the sake of simplicity, if plane wave amplitude is 1.In above formula, the wave number of horizontal direction and vertical direction is followed successively by ω is angular frequency; And for complex wave number, can be written as

$\tilde{k}=k+\mathrm{i\α}---\left(3\right)$

In formula: k is propagation wave-numbers; α attenuation coefficient, and

Formula (2) is substituted into formula (1), obtains

$-{\mathrm{\ω}}^2+\mathrm{\γ}\left(\mathrm{i\ω}\right)+\mathrm{\η}{\tilde{k}}^2\left(\mathrm{i\ω}\right)+{\mathrm{\υ}}^2{\tilde{k}}^2=0---\left(4\right)$

The complex wave number obtaining disperse viscosity ripple from formula (4) is:

$\begin{array}{c}{\tilde{k}}^2=\frac{{\mathrm{\ω}}^2-\mathrm{i\γ\ω}}{{\mathrm{\υ}}^2+\mathrm{i\η\ω}}=\frac{({\mathrm{\υ}}^2{\mathrm{\ω}}^2-\mathrm{\γ\η}{\mathrm{\ω}}^2)-i(\mathrm{\η}{\mathrm{\ω}}^3+\mathrm{\γ\ϖ}{\mathrm{\υ}}^2)}{{\mathrm{\υ}}^4+{\mathrm{\η}}^2{\mathrm{\ω}}^2}\\ ={\tilde{K}}_R+i{\tilde{K}}_I\end{array}---\left(5\right)$

In formula: ${\tilde{K}}_R=\frac{{{\mathrm{\υ}}^2\mathrm{\ω}}^2-\mathrm{\γ\η}{\mathrm{\ω}}^2}{{\mathrm{\υ}}^4+{\mathrm{\η}}^2{\mathrm{\ω}}^2},$ ${\tilde{k}}_I=-\frac{\mathrm{\η}{\mathrm{\ω}}^3+\mathrm{\γ\ω}{\mathrm{\υ}}^2}{{\mathrm{\υ}}^4+{\mathrm{\η}}^2{\mathrm{\ω}}^2}$ Be respectively real part and imaginary part.

Again according to formula (3), obtain:

${\tilde{k}}^2=k^2+i2k\mathrm{\α}-{\mathrm{\α}}^2---\left(6\right)$

Convolution (5) and formula (6), obtain propagation wave-numbers k and attenuation coefficient α is respectively:

$k=\±\sqrt{\frac{{\tilde{K}}_R+\sqrt{{\tilde{K}}_R^2}+{\tilde{K}}_I^2}{2}}---\left(7\right)$

$\mathrm{\α}=\frac{{\tilde{K}}_I}{2k}=\±\frac{{\tilde{K}}_I}{2\sqrt{\frac{{\stackrel{\text{~}}{K}}_R+\sqrt{{\tilde{K}}_R^2}+{\tilde{K}}_{\text{'}I}^2}{2}}}---\left(8\right)$

Symbol in formula (7) and formula (8) is determined by the attenuation characteristic of disperse viscosity ripple, and propagation wave-numbers and attenuation coefficient all not only with the relating to parameters of medium, also depend on the change of frequency.

The complex velocity of disperse viscosity ripple obtains from formula (4):

$V=\frac{\mathrm{\ω}}{\tilde{k}}=\sqrt{\frac{{\mathrm{\υ}}^2+\mathrm{i\η\ω}}{1-i\frac{\mathrm{\γ}}{\mathrm{\ω}}}}---\left(9\right)$

Therefore, the pass between its phase velocity and complex velocity is:

$V_p={\left(\mathrm{Re}\left(\frac{1}{V}\right)\right)}^{-1}---\left(10\right)\·$

See from formula (7)-formula (10): 1. disperse viscosity velocity of wave propagation is plural number, and changes with the change of frequency, the fluctuation described by therefore disperse viscosity wave equation dissipates.The complex wave number of 2. disperse viscosity ripple, complex velocity, phase velocity all change with frequency change.3., when disperse attenuation coefficient γ and viscosity attenuation parameter η is zero, corresponding phase velocity and wave number are phase velocity under the sound wave situation of usual indication and wave number; 4. the stickiness due to the factor of porosity of disperse attenuation coefficient γ and viscosity attenuation coefficient η and medium, permeability and fluid is relevant, so the Reservoir Characters of phase velocity and decay and reservoir has certain contacting, this has very large application potential in practice.

2. derivation disperse viscosity plane wave incidence is to the reflection coefficient on two kinds of contiguity medium interfaces

When disperse viscosity plane wave incidence can occur to launch and transmission to during two kinds of contiguity medium interfaces, upper and lower layer medium represents with footmark 1,2 respectively, and is called medium 1 and medium 2 according to this, and interface is positioned at z=0 place, as shown in Figure 1.

Suppose do not have fluid to spread from a kind of medium to another kind of medium, in this case the reflection at interface, the acquiring method of transmission coefficient and Aki and Richards and Brekhovskikh method similar, with these methods unlike wave number and speed, they are plural number and depend on the change of frequency under disperse viscosity wave equation situation.Provide the derivation of reflection coefficient below.

With pressure P=P (x, z; T) represent wave field, in uniform dielectric, the velocity of displacement of wave field is

$v=(\▿P)/\left(\mathrm{i\ω\ρ}\right)---\left(11\right)$

In formula: ρ is the density of medium.

For the sake of simplicity, the factor e of Time-Dependent is omitted under discussion ^{-i ω t}.If the plane of incidence of ripple and xz planes overlapping, therefore

$\begin{array}{ccc}{\tilde{k}}_{\mathrm{xj}}={\tilde{k}}_j\sin {\mathrm{\θ}}_j,& {\tilde{k}}_{\mathrm{zj}}={\tilde{k}}_j\cos {\mathrm{\θ}}_j,& j=\mathrm{1,2}\end{array}----\left(12\right)$

In formula: for complex wave number, V is ripple complex velocity in media as well; θ ₁for incident angle, θ ₂for angle of transmission.

Being taken into and penetrating wave amplitude is 1, and note wave reflection coefficient is R, and transmission coefficient is T, then total wave field of medium 1 and medium 2 is respectively

$P_1=e^{i{\tilde{k}}_1(x\sin {\mathrm{\θ}}_1-z\cos {\mathrm{\θ}}_1)}+R{e}^{i{\tilde{k}}_1(x\sin {\mathrm{\θ}}_1+z\cos {\mathrm{\θ}}_1)}---\left(13\right)$

$P_2={\mathrm{Te}}^{i{\tilde{k}}_2(x\sin {\mathrm{\θ}}_2-z\cos {\mathrm{\θ}}_2)}---\left(14\right)$

The normal velocity component that can be obtained particle in medium 1 and medium 2 by formula (11) is respectively

$v_{1z}=\frac{\frac{\∂P_1}{\∂z}}{\mathrm{i\ω}{\mathrm{\ρ}}_1}=\frac{-i{\tilde{k}}_1\cos {\mathrm{\θ}}_1{e}^{i{\tilde{k}}_1(x\sin {\mathrm{\θ}}_1-z\cos {\mathrm{\θ}}_1)}+R\left(i{\tilde{k}}_1\cos {\mathrm{\θ}}_1\right)e^{i{\tilde{k}}_1(x\sin {\mathrm{\θ}}_1+z\cos {\mathrm{\θ}}_1)}}{\mathrm{i\ω}{\mathrm{\ρ}}_1}---\left(15\right)$

$v_{2z}=\frac{\frac{\∂P_2}{\∂z}}{\mathrm{i\ω}{\mathrm{\ρ}}_2}=-\frac{i{\tilde{k}}_2\cos {\mathrm{\θ}}_{2}T{e}^{i{\tilde{k}}_2(x\sin {\mathrm{\θ}}_2-z\cos {\mathrm{\θ}}_2)}}{\mathrm{i\ω}{\mathrm{\ρ}}_2}---\left(16\right)$

Then utilize ripple to incide boundary condition on medium interface: pressure and normal velocity on interface continuously, namely

[P ₁＝P ₂]| _z＝0(17)

[ν _1z＝ν _2z]| _z＝0(18)

As follows from formula (14)-formula (18) obtains reflection coefficient:

$R=\frac{{\mathrm{\ρ}}_2{\tilde{k}}_1\cos {\mathrm{\θ}}_1-{\mathrm{\ρ}}_1{\tilde{k}}_2\cos {\mathrm{\θ}}_2}{{\mathrm{\ρ}}_2{\tilde{k}}_1\cos {\mathrm{\θ}}_1+{\mathrm{\ρ}}_1{\tilde{k}}_2\cos {\mathrm{\θ}}_2}=\frac{{\mathrm{\ρ}}_2{V}_2\cos {\mathrm{\θ}}_1-{\mathrm{\ρ}}_1{V}_1\cos {\mathrm{\θ}}_2}{{\mathrm{\ρ}}_2{V}_2{\cos \mathrm{\θ}}_1+{\mathrm{\ρ}}_1{V}_1{\cos \mathrm{\θ}}_2}---\left(19\right)$

In formula: $V_j=\frac{\mathrm{\ω}}{{\tilde{k}}_j}=\sqrt{\frac{{\mathrm{\υ}}_j^2+i{\mathrm{\η}}_j\mathrm{\ω}}{1-i\frac{{\mathrm{\γ}}_j}{\mathrm{\ω}}}}$ (j=1,2) are complex velocity, angle of transmission θ ₂with incidence angle θ ₁between relation determined by snell law, that is:

$\cos {\mathrm{\θ}}_2=\sqrt{1-\frac{V_2^2}{V_1^2}}{\sin }^2{\mathrm{\θ}}_1---\left(20\right)$

The expression formula (19) of reflection coefficient is expressed as with impedance:

$R=\frac{Z_2-Z_1}{Z_1+Z_2}---\left(21\right)$

In formula: with be respectively the impedance of medium 1 and medium 2.

In sound wave situation, its wave number k=ω/c (c is sound velocity of wave propagation) for real number and sound phase velocity of wave and frequency have nothing to do, therefore sound wave is without frequency dispersion; The reflection coefficient of sound wave is identical with formula (19) in form, but it does not rely on the change of frequency yet.But, for disperse viscosity ripple, its wave number (V is the complex velocity of disperse viscosity ripple) and reflection coefficient are plural number and change with frequency change, and thus it is frequency dispersion.

3. utilize the reflection coefficient synthesis VSP record obtained

How the disperse viscosity wave reflection coefficient research that utilization is tried to achieve above makes evenly, zero inclined VSP record in isotropy stratiform medium.Method for making is recorded roughly the same based on VSP in the imperfectly elastic media that method and the Ganley of disperse viscosity wave equation making VSP record propose, both due to describe medium physical quantity difference make the calculating of wave number and attenuation coefficient different, physical quantity involved in imperfectly elastic media is the speed of each layer and density and corresponding Q value, and the physical quantity used in disperse viscosity wave equation is except the velocity and density of each layer, also have disperse and viscosity attenuation coefficient.

Provide the detailed step of the inclined VSP record of reflectivity method synthesis zero based on disperse viscosity wave equation below:

A) the complex velocity V (ω) under each frequency is asked, that is:

$V\left(\mathrm{\ω}\right)=\sqrt{\frac{{\mathrm{\υ}}^2+\mathrm{i\η\ω}}{1-i\frac{\mathrm{\γ}}{\mathrm{\ω}}}}---\left(22\right)$

B) formula (7) and formula (8) is utilized to ask propagation wave-numbers k under each frequency and attenuation coefficient α (ω);

C) calculate on each bed interface, the reflection under each frequency, transmission coefficient:

$R_j\left(\mathrm{\ω}\right)=\frac{{\mathrm{\ρ}}_{j+1}{V}_{j+1}\left(\mathrm{\ω}\right)-{\mathrm{\ρ}}_j{V}_j\left(\mathrm{\ω}\right)}{{\mathrm{\ρ}}_{j+1}{V}_{j+1}\left(\mathrm{\ω}\right)+{\mathrm{\ρ}}_j{V}_j\left(\mathrm{\ω}\right)}---\left(\text{23}\right)$

$T_j\left(\mathrm{\ω}\right)=\frac{2{\mathrm{\ρ}}_{j+1}{V}_{j+1}\left(\mathrm{\ω}\right)}{{\mathrm{\ρ}}_{j+1}{V}_{j+1}\left(\mathrm{\ω}\right)+{\mathrm{\ρ}}_j{V}_j\left(\mathrm{\ω}\right)}---\left(\text{24}\right)$

In formula: j=1,2 ... N is medium level number.

When ω → 0, medium is without frequency dispersion, and medium 1 with the reflection on medium 2 interphase, transmission coefficient is:

$R=\frac{{\mathrm{\ρ}}_2{\mathrm{\υ}}_2-{\mathrm{\ρ}}_1{\mathrm{\υ}}_1}{{\mathrm{\ρ}}_2{\mathrm{\υ}}_2+{\mathrm{\ρ}}_1{\mathrm{\υ}}_1}---\left(25\right)$

$T=\frac{2{\mathrm{\ρ}}_2{\mathrm{\υ}}_2}{{\mathrm{\ρ}}_2{\mathrm{\υ}}_2+{\mathrm{\ρ}}_1{\mathrm{\υ}}_1}---\left(26\right)$

D) each layer transmission matrix coefficient A is calculated _j(ω):

$A_j=\frac{1}{T_j}\left[\begin{array}{cc}{e}^{{\mathrm{\α}}_j\mathrm{\Δ}{z}_j}{e}^{i{k}_j\mathrm{\Δ}{z}_j}& R_j{e}^{{\mathrm{\α}}_j\mathrm{\Δ}{z}_j}{e}^{i{k}_j\mathrm{\Δ}{z}_j}\\ R_j{e}^{-{\mathrm{\α}}_j\mathrm{\Δ}{z}_j}{e}^{-i{k}_j\mathrm{\Δ}{z}_j}& e^{-{\mathrm{\α}}_j\mathrm{\Δ}{z}_j}{e}^{-i{k}_j\mathrm{\Δ}{z}_j}\end{array}\right],\underset{n=1}{\overset{n=N}{\mathrm{\Π}}}{A}_n=\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right]---\left(27\right)$

E) the uplink and downlink ripple U of each layer is calculated _j(ω), D _j(ω);

$\left[\begin{array}{c}{D}_{j+1}\left(\mathrm{\ω}\right)\\ U_{j+1}\left(\mathrm{\ω}\right)\end{array}\right]=\underset{k=1}{\overset{k=j}{\mathrm{\Π}}}{A}_k^{-1}\left[\begin{array}{c}{D}_1\left(\mathrm{\ω}\right)\\ U_1\left(\mathrm{\ω}\right)\end{array}\right]---\left(28\right)$

$U_1\left(\mathrm{\ω}\right)=\frac{A_{21}\left(\mathrm{\ω}\right)}{A_{11}\left(\mathrm{\ω}\right)+A_{21}\left(\mathrm{\ω}\right)R_0\left(\mathrm{\ω}\right)}$

$D_1\left(\mathrm{\ω}\right)=1-R_0\left(\mathrm{\ω}\right)U_1\left(\mathrm{\ω}\right)---\left(29\right)$

$D_{N+1}\left(\mathrm{\ω}\right)=-\frac{1}{A_{11}\left(\mathrm{\ω}\right)+A_{21}\left(\mathrm{\ω}\right)R_0\left(\mathrm{\ω}\right)}$

In formula :-R ₀(ω) be the reflection coefficient of Free Surface.

F) composite traces of each degree of depth in calculated rate territory:

X _j+1(ω)＝U _j+1(ω)+D _j+1(ω)(30)

G) inverse Fourier transform is done to formula (30), obtain the composite traces in time domain;

H) to earth's surface j=0, ground composite traces is calculated:

X ₁(ω)＝U ₁(ω)+D ₁(ω)＝(1-R ₀)U ₁(ω)+1(31)

The present invention is based on the method for the inclined VSP record of disperse viscosity wave equation synthesis zero, to five layer fluid saturated media models synthesis VSP records, point little decay, moderate fading and overdamp three kinds of case study disperse attenuation coefficient and viscosity attenuation coefficient are for the impact of reflection coefficient and composite traces.This amplitude observed from seismologic record is decayed and the change of phase place plays a very important role for the geological data and identification fluid explaining oil-bearing reservoir.In addition, this technical scheme is easy to realize, workable.

The present invention is based on disperse viscosity wave equation and propose in a kind of AVO/AVA analysis theories and layered medium thereof the method for synthesizing zero inclined VSP record, concrete implementation step is respectively:

1) physical parameter of saturated with fluid dielectric layer is provided according to actual geology background condition, physical test of rock and well-log information thereof etc.;

2) formula (7)-Shi (10) is utilized to ask for the complex velocity of disperse viscosity ripple, phase velocity, propagation wave-numbers and attenuation coefficient

3) disperse viscosity wave reflection coefficient formula (19) of deriving is utilized to analyze plane wave incidence to the Changing Pattern of the reflection coefficient on two kinds of contiguity medium interfaces with frequency and incident angle;

4) design stratiform saturated with fluid dielectric model, utilize formula (22)-Shi (31) to calculate the VSP record of this model.Designing five layer fluid saturated media models in the present invention, is the damping layer that 60m is thick in the middle of this model, considers three kinds of situation synthesis VSP records.

Numerical simulation result is analyzed

The present invention is based on disperse viscosity wave equation and derive plane wave incidence to the reflection coefficient on two kinds of dispersive medium interfaces, first have studied reflection coefficient on the extended media variation relation with incident angle and frequency, secondly give a kind of synthesis zero method that inclined VSP records for disperse viscosity wave equation.

1. on medium interface reflection coefficient with the variation characteristic of incident angle and frequency

The present invention have studied disperse viscosity wave reflection characteristic on three kinds of extended medias, i.e. dry sand rock and moisture saturated media interface, dry sand rock and oil-containing saturated media interface and oil-containing saturated media and moisture saturated media interface, and medium parameter is as shown in table 1.

Table 1 dielectric model parameter

Fig. 2-4 are respectively the amplitude of reflection coefficient in these three kinds of situations and the phase place variation relation with frequency and incident angle.Fig. 2 shows that dry sand rock and the amplitude containing reflection coefficient on water-saturated rock medium interface increase with frequency and increase; In its phase angle variations more complicated of low frequency (<10Hz), and when high frequency is less than critical angle (70.62 °) when incident angle, phasing degree increases with frequency and reduces; When the angle of incidence is larger than a critical angle, its phasing degree changes with frequency hardly, but increases along with incident angle and increase.Fig. 3 shows that the amplitude of reflection coefficient on dry sand rock and oil-containing saturated media interface increases with frequency and reduces, but increases with incident angle and increase; Its phasing degree increases with frequency and increases.Fig. 4 shows that the amplitude of reflection coefficient on oil-containing saturated media and moisture saturated media interface increases with frequency and increases, and also increases along with incident angle and increases; At upper frequency, when incident angle is less than critical angle (49.5 °), its phasing degree is close to zero, and when the angle of incidence is larger than a critical angle, its phasing degree changes with frequency change hardly.

In order to more clearly analyze the variation relation of reflection coefficient with incident angle of disperse viscosity ripple dependent Frequency change on these three kinds of medium interfaces, it is 5Hz that Fig. 5-7 sets forth in frequency, 10Hz, 20Hz, during 30Hz and 50Hz, in above-mentioned three kinds of situations, the amplitude of reflection coefficient and phasing degree are with the variation relation of incident angle, in order to contrast with acoustic medium situation, give also the amplitude of sound wave reflection coefficient on these three kinds of medium interfaces and the phasing degree change curve with incident angle in figure.As can be seen from Fig. 5-7: on dry sand rock and moisture saturated media, oil-containing saturated media and moisture saturated media interface, the amplitude of disperse viscosity wave reflection coefficient is less than the amplitude of acoustic reflection coefficient, in little incident angle (0-50 °) scope, both amplitudes all increase with frequency and increase (as shown in Fig. 5 (a), 7 (a)); But on oil-containing saturated media and moisture saturated media interface, the amplitude of reflection coefficient increases with frequency and reduces (as Suo Shi Fig. 7 (a)) when low frequency (<10Hz), larger incident angle.On this two media interface, the phasing degree of reflection coefficient is contrary with the phasing degree in sound wave situation, especially when incident angle is greater than critical angle, and phasing degree reversal development more obvious (as shown in Fig. 5 (b), 7 (b)).On the other hand, on dry sand rock and oil-containing saturated media interface, the amplitude of reflection coefficient increases with frequency and reduces, and the degree of its changes in amplitude is smaller (as Suo Shi Fig. 6 (a)); At low frequency (<10Hz), its phasing degree increases with frequency and reduces, and in lower frequency range, its phasing degree increases with frequency and increases (as Suo Shi Fig. 6 (b)).

2. synthesize VSP record in homogeneous layered medium

The calculation procedure utilizing above-mentioned synthesis VSP to record is simulated for five layers of homogeneous layered saturated with fluid medium that contains, and is the damping layer that 60m is thick in the middle of this model, and consider three kinds of situations synthesis VSP records below, three groups of corresponding parameter lists are as shown in table 2-4.In order to study disperse, viscosity attenuation coefficient for the impact of thin bed reflections, we establish in these three groups of parameters is only that the attenuation parameter of thin intermediate is different, and other parameter is identical.Phone spacing is 10m, and time sampling interval is 1ms, and focus is the Ricker wavelet of 20Hz.

Table 2 five layer fluid saturated media model parameter (little decay situation)

Table 3 five layer fluid saturated media model parameter (moderate fading's situation)

Table 4 five layer fluid saturated media model parameter (overdamp situation)

Fig. 8 (a), (b), c () is respectively the synthesis VSP record in these three kinds of situations, in order to the reflection of thin layer more clearly can be studied, Fig. 8 (d), (e), (f) is respectively in thin layer peripheral region Fig. 8 (a), b (), (c) amplifies later record.Fig. 9 and Figure 10 is respectively the seismologic record that the degree of depth is 620m (in the middle of thin layer) and 560m (above thin layer).

Be clear that from Fig. 8-10 disperse attenuation coefficient and viscosity attenuation coefficient have a great impact for theogram, the amplitude decay and the phase place that show as seismologic record change.When the attenuation parameter in dielectric layer is larger, the attenuation degree of composite traces is larger.When attenuation parameter is smaller, the reflection wave at thin intermediate place can be clearly visible (as Fig. 8 (a), shown in 9 (a)), but when attenuation parameter is larger, reflection wave from thin layer is visible hardly, its attenuation degree larger (as Suo Shi Fig. 8 (c), Figure 10 (c)).In addition, when the attenuation parameter of dielectric layer is different, all can there is obvious change (as Fig. 8 (d), (e), shown in (f) and Figure 10) in the amplitude of the seismologic record received above thin layer and waveform.

Above content is only and technological thought of the present invention is described; protection scope of the present invention can not be limited with this; every technological thought proposed according to the present invention, any change that technical scheme basis is done, within the protection domain all falling into claims of the present invention.

Claims (4)

1., based on an AVO/AVA analytical approach for disperse viscosity wave equation, it is characterized in that, comprise the following steps:

1) physical parameter of saturated with fluid dielectric layer involved in disperse viscosity wave equation is provided according to actual geology background condition, physical test of rock and well logging thereof, drilling data;

2) complex velocity of Two-Dimensional Dispersion viscosity ripple, phase velocity, propagation wave-numbers and attenuation coefficient is asked for; Wherein, Two-Dimensional Dispersion viscosity wave equation is:

$\frac{{\&PartialD;}^{2}u}{{\&PartialD;t}^2}+\mathrm{\&gamma;}\frac{\&PartialD;u}{\&PartialD;t}-\mathrm{\&eta;}(\frac{{\&PartialD;}^{3}u}{{\&PartialD;x}^2\&PartialD;t}+\frac{{\&PartialD;}^{3}u}{{\&PartialD;z}^2\&PartialD;t})-{\mathrm{\&upsi;}}^2(\frac{{\&PartialD;}^{2}u}{{\&PartialD;x}^2}+\frac{{\&PartialD;}^{2}u}{{\&PartialD;z}^2})=0---\left(1\right);$

In formula:

$\begin{array}{c}\mathrm{\&gamma;}=\frac{{\mathrm{\&mu;}}_f}{K}\frac{{\mathrm{\&phi;}}_0({\mathrm{\&alpha;}}_2-1)}{{\mathrm{\&rho;}}_{\mathrm{pf}}}\\ \mathrm{\&eta;}=\frac{1}{{\mathrm{\&rho;}}_{\mathrm{\&phi;f}}}[{\mathrm{\&xi;}}_f+\frac{4}{3}({\mathrm{\&mu;}}_f-\frac{{\mathrm{\&sigma;}}_M}{{\mathrm{\&phi;}}_0}{\mathrm{\&alpha;}}_2)]\\ {\mathrm{\&upsi;}}^2=\frac{K_f}{{\mathrm{\&rho;}}_{\mathrm{pf}}}\end{array}---\left(2\right);$

In formula (2): K is permeability, K _ffor the body of fluid becomes modulus, μ _ffor the shear viscosity of fluid, ξ _ffor the body degree of becoming sticky of fluid, φ ₀for factor of porosity; ρ _{φ f}=ρ _f-ρ ₁₂(α ₁+ 1), ${\mathrm{\&rho;}}_{\mathrm{pf}}={\mathrm{\&rho;}}_f-\frac{{\mathrm{\&rho;}}_{12}}{{\mathrm{\&phi;}}_0}({\mathrm{\&alpha;}}_2-1),$ ${\mathrm{\&alpha;}}_2=\frac{{\mathrm{\&delta;}}_f}{{\mathrm{\&delta;}}_s},$ ${\mathrm{\&alpha;}}_1=\frac{{\mathrm{\&phi;}}_0-{\mathrm{\&delta;}}_f}{{\mathrm{\&delta;}}_s},$ ${\mathrm{\&sigma;}}_M=(1-{\mathrm{\&phi;}}_0){\mathrm{\&mu;}}_f\left[(\frac{{\mathrm{\&mu;}}_M}{(1-{\mathrm{\&phi;}}_0){\mathrm{\&mu;}}_s}-1)\right],$ μ _m=ε ₀μ _s(1+c), ε ₀=1-φ ₀, c, δ _fand δ _sfor constant; ρ _ffor the mass density of fluid, μ _mfor the modulus of shearing compared with solid in large scale, μ _sfor the modulus of shearing of solid;

3) ask for the reflection coefficient formula of Two-Dimensional Dispersion viscosity wave equation based on Plane wave theory, wherein, reflection coefficient formula is as follows:

$R=\frac{{\mathrm{\&rho;}}_2{\tilde{k}}_1\cos {\mathrm{\&theta;}}_1-{\mathrm{\&rho;}}_1{\tilde{k}}_2\cos {\mathrm{\&theta;}}_2}{{\mathrm{\&rho;}}_2{\tilde{k}}_1\cos {\mathrm{\&theta;}}_1+{\mathrm{\&rho;}}_1{\tilde{k}}_2\cos {\mathrm{\&theta;}}_2}=\frac{{\mathrm{\&rho;}}_2{V}_2\cos {\mathrm{\&theta;}}_1-{\mathrm{\&rho;}}_1{V}_1\cos {\mathrm{\&theta;}}_2}{{\mathrm{\&rho;}}_2{V}_2\cos {\mathrm{\&theta;}}_1+{\mathrm{\&rho;}}_1{V}_1\cos {\mathrm{\&theta;}}_2}---\left(3\right);$

4) formula (3) is utilized to analyze plane wave incidence to the Changing Pattern of the reflection coefficient on two kinds of contiguity medium interfaces with frequency and incident angle.

2. the AVO/AVA analytical approach based on disperse viscosity wave equation according to claim 1, is characterized in that: described step 1) in, physical parameter comprises density, velocity of wave propagation, disperse attenuation coefficient, viscosity attenuation coefficient; Wherein, disperse attenuation coefficient and viscosity attenuation coefficient are determined by the modulus of shearing of permeability, factor of porosity, solid, the body degree of becoming sticky of fluid, the shear viscosity of fluid.

3. the AVO/AVA analytical approach based on disperse viscosity wave equation according to claim 1, it is characterized in that: described step 2) in, the concrete grammar asking for the complex velocity of Two-Dimensional Dispersion viscosity ripple, phase velocity, propagation wave-numbers and attenuation coefficient is:

The mathematical description of Two-Dimensional Dispersion viscosity wave equation is:

$\frac{{\&PartialD;}^{2}u}{{\&PartialD;t}^2}+\mathrm{\&gamma;}\frac{\&PartialD;u}{\&PartialD;t}-\mathrm{\&eta;}(\frac{{\&PartialD;}^{3}u}{{\&PartialD;x}^2\&PartialD;t}+\frac{{\&PartialD;}^{3}u}{{\&PartialD;z}^2\&PartialD;t})-{\mathrm{\&upsi;}}^2(\frac{{\&PartialD;}^{2}u}{{\&PartialD;x}^2}+\frac{{\&PartialD;}^{2}u}{{\&PartialD;z}^2})=0---\left(1\right)$

In formula: u is wave field function; γ and η is respectively disperse and viscosity attenuation coefficient, and the density, viscosity etc. of their factor of porosity, permeability and fluids with rock are relevant; υ is velocity of wave propagation in medium,nondispersive; X and t is respectively room and time variable;

If the harmonic plane wave solution of Two-Dimensional Dispersion viscosity wave equation (1) is:

$u(x,z,t)=e^{i(\mathrm{\&omega;t}-{\tilde{k}}_{z}z)}---\left(2\right)$

For the sake of simplicity, if plane wave amplitude is 1; In above formula, the wave number of horizontal direction and vertical direction is followed successively by ω is angular frequency; And for complex wave number, can be written as

$\tilde{k}=k+\mathrm{i\&alpha;}---\left(3\right)$

In formula: k is propagation wave-numbers; α attenuation coefficient, and

Formula (2) is substituted into formula (1), obtains

$-{\mathrm{\&omega;}}^2+\mathrm{\&gamma;}\left(\mathrm{i\&omega;}\right)+\mathrm{\&eta;}{\tilde{k}}^2\left(\mathrm{i\&omega;}\right)+{\mathrm{\&upsi;}}^2{\tilde{k}}^2=0---\left(4\right)$

The complex wave number obtaining disperse viscosity ripple from formula (4) is:

$\begin{array}{c}{\tilde{k}}^2\frac{{\mathrm{\&omega;}}^2-\mathrm{i\&gamma;\&omega;}}{{\mathrm{\&upsi;}}^2+\mathrm{i\&eta;\&omega;}}=\frac{({\mathrm{\&upsi;}}^2{\mathrm{\&omega;}}^2-\mathrm{\&gamma;}{\mathrm{\&eta;\&omega;}}^2)-i({\mathrm{\&eta;\&omega;}}^2+{\mathrm{\&gamma;\&omega;\&upsi;}}^2)}{{\mathrm{\&upsi;}}^4+{\mathrm{\&eta;}}^2{\mathrm{\&omega;}}^2}\\ {\tilde{K}}_R+i{\tilde{K}}_I\end{array}---\left(5\right)$

In formula: ${\tilde{K}}_R=\frac{{\mathrm{\&upsi;}}^2{\mathrm{\&omega;}}^2-\mathrm{\&gamma;\&eta;}{\mathrm{\&omega;}}^2}{{\mathrm{\&upsi;}}^4+{\mathrm{\&eta;}}^2{\mathrm{\&omega;}}^2},$ ${\tilde{K}}_I=\frac{{\mathrm{\&eta;\&omega;}}^2-\mathrm{\&gamma;}{\mathrm{\&omega;\&upsi;}}^2}{{\mathrm{\&upsi;}}^4+{\mathrm{\&eta;}}^2{\mathrm{\&omega;}}^2},$ Be respectively real part and imaginary part;

Again according to formula (3):

${\tilde{k}}^2=k^2+i2\mathrm{k\&alpha;}-{\mathrm{\&alpha;}}^2---\left(6\right)$

Convolution (5) and formula (6), obtain propagation wave-numbers k and attenuation coefficient α is respectively:

$k=\&PlusMinus;\sqrt{\frac{{\tilde{K}}_R+\sqrt{{\tilde{K}}_R^2+{\tilde{K}}_I^2}}{2}}---\left(7\right)$

$\mathrm{\&alpha;}=\frac{{\tilde{K}}_I}{2k}=\&PlusMinus;\frac{{\tilde{K}}_I}{2\sqrt{\frac{{\tilde{K}}_R+\sqrt{{\tilde{K}}_R^2+{\tilde{K}}_I^2}}{2}}}---\left(8\right)$

Symbol in formula (7) and formula (8) is determined by the attenuation characteristic of disperse viscosity ripple, and propagation wave-numbers and attenuation coefficient all not only with the relating to parameters of medium, also depend on the change of frequency;

The complex velocity of disperse viscosity ripple obtains from formula (4):

$V=\frac{\mathrm{\&omega;}}{\tilde{k}}=\sqrt{\frac{{\mathrm{\&upsi;}}^2+\mathrm{i\&eta;\&omega;}}{1-i\frac{\mathrm{\&gamma;}}{\mathrm{\&omega;}}}}---\left(9\right)$

Pass then between phase velocity and complex velocity is:

$V_p={\left(\mathrm{Re}\left(\frac{1}{V}\right)\right)}^{-1}---\left(10\right).$

4. the AVO/AVA analytical approach based on disperse viscosity wave equation according to claim 1, is characterized in that: described step 3) in, the reflection coefficient formula asking for Two-Dimensional Dispersion viscosity wave equation is specifically adopted with the following method:

When disperse viscosity plane wave incidence can occur to launch and transmission to during two kinds of contiguity medium interfaces, upper and lower layer medium represents with footmark 1,2 respectively, and is called medium 1 and medium 2 according to this, and interface is positioned at z=0 place;

With pressure P=P (x, z; T) represent wave field, in uniform dielectric, the velocity of displacement of wave field is

$v=(\&dtri;P)/\left(\mathrm{i\&omega;\&rho;}\right)---\left(11\right)$

In formula: ρ is the density of medium;

If the plane of incidence of ripple and xz planes overlapping, therefore

${\tilde{k}}_{\mathrm{xj}}={\tilde{k}}_j\sin {\mathrm{\&theta;}}_j,{\tilde{k}}_{\mathrm{zj}}={\tilde{k}}_j\cos {\mathrm{\&theta;}}_j,j=\mathrm{1,2}---\left(12\right)$

In formula: for complex wave number, V is ripple complex velocity in media as well; θ ₁for incident angle, θ ₂for angle of transmission;

Being taken into and penetrating wave amplitude is 1, and note wave reflection coefficient is R, and transmission coefficient is T, then total wave field of medium 1 and medium 2 is respectively

$P_1=e^{1{\tilde{k}}_1(x\sin {\mathrm{\&theta;}}_1-z\cos {\mathrm{\&theta;}}_1)}+{\mathrm{Re}}^{i{\tilde{k}}_1(x\sin {\mathrm{\&theta;}}_1+z\cos {\mathrm{\&theta;}}_1)}---\left(13\right)$

$P_2={\mathrm{Te}}^{i{\tilde{k}}_2(x\sin {\mathrm{\&theta;}}_2-z\cos {\mathrm{\&theta;}}_2)}---\left(14\right)$

The normal velocity component that can be obtained particle in medium 1 and medium 2 by (11) formula is respectively

$v_{1z}=\frac{\frac{{\&PartialD;P}_1}{\&PartialD;z}}{\mathrm{i\&omega;}{\mathrm{\&rho;}}_1}=\frac{-i{\tilde{k}}_1\cos {\mathrm{\&theta;}}_1{e}^{i{\tilde{k}}_1(x\sin {\mathrm{\&theta;}}_1-z\cos {\mathrm{\&theta;}}_1)}+R\left(i{\tilde{k}}_1\cos {\mathrm{\&theta;}}_1\right)e^{i{\tilde{k}}_1(x\sin {\mathrm{\&theta;}}_1+z\cos {\mathrm{\&theta;}}_1)}}{{\mathrm{i\&omega;\&rho;}}_1}---\left(15\right)$

$v_{2z}=\frac{\frac{{\&PartialD;P}_2}{\&PartialD;z}}{\mathrm{i\&omega;}{\mathrm{\&rho;}}_2}=\frac{-i{\tilde{k}}_2\cos {\mathrm{\&theta;}}_{2}T{e}^{i{\tilde{k}}_2(x\sin {\mathrm{\&theta;}}_2-z\cos {\mathrm{\&theta;}}_2)}}{{\mathrm{i\&omega;\&rho;}}_2}---\left(16\right)$

Then utilize ripple to incide boundary condition on medium interface: pressure and normal velocity on interface continuously, namely

[P ₁＝P ₂]| _z＝0(17)

[ν _1z＝ν _2z]| _z＝0(18)

Reflection coefficient is obtained as follows from (14)-(18) formula:

$R=\frac{{\mathrm{\&rho;}}_2{\tilde{k}}_1\cos {\mathrm{\&theta;}}_1-{\mathrm{\&rho;}}_1{\tilde{k}}_2\cos {\mathrm{\&theta;}}_2}{{\mathrm{\&rho;}}_2{\tilde{k}}_1\cos {\mathrm{\&theta;}}_1+{\mathrm{\&rho;}}_1{\tilde{k}}_2\cos {\mathrm{\&theta;}}_2}=\frac{{\mathrm{\&rho;}}_2{V}_2\cos {\mathrm{\&theta;}}_1-{\mathrm{\&rho;}}_1{V}_1\cos {\mathrm{\&theta;}}_2}{{\mathrm{\&rho;}}_2{V}_2\cos {\mathrm{\&theta;}}_1+{\mathrm{\&rho;}}_1{V}_1\cos {\mathrm{\&theta;}}_2}---\left(19\right)$

In formula: for complex velocity, angle of transmission θ ₂with incidence angle θ ₁between relation determined by snell law, that is:

$\cos {\mathrm{\&theta;}}_2=\sqrt{1-\frac{V_2^2}{V_1^2}{\sin }^2{\mathrm{\&theta;}}_1}---\left(20\right)$

Expression (19) the formula impedance of reflection coefficient is expressed as:

$R=\frac{Z_2-Z_1}{Z_1+Z_2}---\left(21\right)$

In formula: with be respectively the impedance of medium 1 and medium 2.