CN105954801A - Frequency-conversion-attribute-based reservoir permeability evaluation method - Google Patents

Abstract

The invention provides a frequency-conversion-attribute-based reservoir permeability evaluation method. A response characteristic of a K1 attribute to a permeability change is simulated and analyzed by using a numerical value; and the result demonstrates that the attribute can reflect the permeability change obviously. Moreover, the response characteristics are different under different top and bottom wave impedance differences. For a fluidity attribute, only dominant low frequencies are considered; and high-frequency and low-frequency seismic data are combed for usage by the K1 attribute. In a logging analysis and an application example, the K1 attribute can match the logging data well and can reflect the fluid ability of the fluid of the reservoir effectively. Because the response characteristic of the K1 attribute to a permeability change is simulated and analyzed by using a numerical value, accuracy of reservoir permeability evaluation is improved substantially.

Description

A kind of reservoir permeability appraisal procedure becoming attribute based on frequency

Technical field

The present invention relates to geological technique field, particularly relate to a kind of reservoir permeability appraisal procedure becoming attribute based on frequency.

Background technology

For Petroleum Engineer, a permeability formation parameter that must be paid close attention to beyond doubt.It is true Whether determine a bite well should completion and the foundation of operation.Meanwhile, it is also to creep into oil layer protection, completion perforating Scheme Choice, The basis of the formulation of good drain location and throughput rate and tertiary oil recovery measure.

Affected by existing seismic exploration technique, it is difficult to direct inversion permeability from seismic data.Mobility attribute at present It is verified that reservoir permeability can be reflected indirectly, but affected by the uncertainty of reservoir thickness and dominant frequency, used it Evaluate reservoir permeability and there is uncertain and multi-solution.

Summary of the invention

It is an object of the invention to solve the defect that above-mentioned prior art exists, it is provided that a kind of reservoir becoming attribute based on frequency Permeability appraisal procedure, applies the numerical simulation analysis K1 attribute response characteristic to permeability variation, and the earth improves storage The accuracy that layer permeability is evaluated.

The present invention uses following scheme for achieving the above object:

A kind of reservoir permeability appraisal procedure becoming attribute based on frequency, for the geological condition of different regions, selects suitably Petrophysical model carry out numerical simulation, analyze this area's K1 attribute response characteristic to permeability；Calculate poststack earthquake money The time-frequency spectrum of material；K1 attribute is calculated from time frequency signal；The infiltration of reservoir is evaluated in conjunction with numerical simulation result and log data Rate is distributed.

Further, specifically comprise the following steps that

(1) extraction of K1 attribute

K₁Attribute is the ratio of seismic spectrum high frequency signal and low frequency signal:

$K_1={\mathrm{\Σ}}_{{\mathrm{\ω}}_m}^{{\mathrm{\ω}}_2}\left|S\left(\mathrm{\ω}\right)\right|/{\mathrm{\Σ}}_{{\mathrm{\ω}}_1}^{{\mathrm{\ω}}_m}\left|S\left(\mathrm{\ω}\right)\right|---\left(1\right)$

In formula, S (ω) is seismic spectrum, ω₁、ω_mAnd ω₂It is that the Frequency of seismic signal, crest frequency and height are frequent Rate；

In order to the signal of time domain is converted into time frequency signal, deconvolution Short Time Fourier Transform is utilized to extract seismic data Time frequency signal, the short time discrete Fourier transform of signal x (u) is defined as:

${\mathrm{STFT}}_X(t,f)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(u\right)h*(u-t)e^{(-j2\mathrm{\π}fu)}du---\left(8\right)$

Wherein h (u-t) is window function, and conventional is Gaussian window, and wherein * is conjugate transpose；

Short time discrete Fourier transform spectrum is defined as:

${\mathrm{SPEC}}_X(t,f)={|{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(u\right)h*(u-t)e^{(-j2\mathrm{\π}fu)}du|}^2---\left(9\right)$

For signal x (t), its Wigner-Ville distribution is defined as:

${\mathrm{WVD}}_X(t,f)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x(t+\frac{\mathrm{\τ}}{2})x*(t-\frac{\mathrm{\τ}}{2})e^{(-j2\mathrm{\π}f\mathrm{\τ})}d\mathrm{\τ}---\left(10\right)$

Wigner-Ville is distributed cross term, and it is caused by Wigner-Ville distributed nonlinear；

The expression formula of generalized S-transform is:

$GST\left(\mathrm{\τ},f\right)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(t\right)\frac{\mathrm{\λ}\left|f\right|p}{\sqrt{2\mathrm{\π}}}{e}^{-\frac{-{\mathrm{\λ}}^2{f}^{2\mathrm{\ρ}}{\left(\mathrm{\τ}-t\right)}^2}{2}}{e}^{-j2\mathrm{\π}ft}dt,\mathrm{\λ}>0,p>0---\left(11\right)$

Generalized S-transform, by introducing two parameter lambda and p, has been transformed the Gauss function of S-transformation, has been regulated Gauss neatly Window function is with the variation tendency of dimensions in frequency f；

The short time discrete Fourier transform of signal x (t) compose into following two dimension convolution form:

$\begin{array}{c}{\mathrm{SPEC}}_X(t,f)={\left|{\mathrm{STFT}}_X(t,f)\right|}^2\\ ={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\mathrm{WVD}}_h(u,v)\×{\mathrm{WVD}}_x(t-u,f-v)dudv\end{array}---\left(12\right)$

Wherein WVD_xAnd WVD_hIt is respectively the Wigner-Ville distribution of signal x (t) and window function h (u), Short-time Fourier The cross term of conversion spectrum is 0 in major part situation；

Seismic signal is brought in above formula, has obtained time-frequency seismic signal, then time frequency signal has been brought in formula (1), Try to achieve K1 attribute.

(2) reservoir permeability evaluation

Understood the K1 attribute general trend of this reservoir by the result of numerical simulation, permeability is with the change of K1 property trends Change.

The present invention, based on double-porosity model, applies the numerical simulation analysis K1 attribute response to permeability variation Feature, result shows that this attribute has significantly reflection for the change of permeability.And meeting under natural impedance difference at the bottom of different top Different response characteristics occurs.Only considering advantage low frequency compared with mobility attribute, high frequency, low-frequency acoustic data are combined and make by K1 attribute With.In log analysis and exemplary application, K1 attribute can coincide and effectively reflect the stream of reservoir fluid with well-log information Kinetic force, applies the numerical simulation analysis K1 attribute response characteristic to permeability variation, and the earth improves reservoir permeability The accuracy evaluated.

Accompanying drawing explanation

Fig. 1 K1 attribute is with the change curve of permeability；

Well A seismic profile is crossed in Fig. 2 certain district marine；

Fig. 3 crosses synthetic seismic record and the horizon calibration of well A；

Fig. 4 well A core experiment porosity and permeability relation；

Fig. 5 crosses the K1 attribute section of well A；

The K1 attribute section of the downward 15ms of Fig. 6 top layer；

The mobility attribute section of the downward 15ms of Fig. 7 top layer.

Detailed description of the invention

For making the object, technical solutions and advantages of the present invention clearer, below technical scheme in the present invention carry out clearly Chu, it is fully described by, it is clear that described embodiment is a part of embodiment of the present invention rather than whole embodiments.Based on Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under not making creative work premise Embodiment, broadly falls into the scope of protection of the invention.

The present invention proposes a set of reservoir permeability evaluation methodology utilizing K1 attribute, this attribute from high-frequency seism signal and Low-frequency acoustic signal extracts.Steps of the method are: first against the geological condition of different regions, select suitable rock Stone physical model carries out numerical simulation, analyzes this area's K1 attribute response characteristic to permeability；Calculate poststack seismic data Time-frequency spectrum；K1 attribute is calculated from time frequency signal；The permeability evaluating reservoir in conjunction with numerical simulation result and log data is divided Cloth, the following is the process of realization:

Step one: first against the geological condition of different regions, selects suitable petrophysical model to carry out numerical simulation, Analyze this area's K1 attribute response characteristic to permeability；

Step 2: calculate the time-frequency spectrum of poststack seismic data；

Step 3: calculate K1 attribute from time frequency signal；

Step 4: combine numerical simulation result and the Permeability Distribution of log data evaluation reservoir.

The following is the process of realization:

1 numerical simulation

K₁Attribute is the ratio of seismic spectrum high frequency signal and low frequency signal:

$K_1={\mathrm{\Σ}}_{{\mathrm{\ω}}_m}^{{\mathrm{\ω}}_2}\left|S\left(\mathrm{\ω}\right)\right|/{\mathrm{\Σ}}_{{\mathrm{\ω}}_1}^{{\mathrm{\ω}}_m}\left|S\left(\mathrm{\ω}\right)\right|---\left(1\right)$

In formula, S (ω) is seismic spectrum, ω₁、ω_mAnd ω₂It is that the Frequency of seismic signal, crest frequency and height are frequent Rate.When seismic wave is propagated in the double porosity media containing fluid, its main decay is because seismic wave and drives the movement of fluid.No The seismic wave of same frequency there will be different decay under the influence of permeability, when during high frequency, seismic wave is through double porosity media, and stream Body have little time reflection, so during high frequency seismic wave propagates in double porosity media decay understand than low frequency time seismic wave decay little Xu Many.

It is carbonate rock for actual work area oil-bearing reservoir, in order to analyze this reservoir permeability to K₁The impact of attribute, Double-porosity model first with the coarse fracture surface of Kozlov.According to the resistance difference of reservoir Yu cap rock, by reservoir Being divided into two classes, model 1 is to become big with permeability value, and cap rock diminishes with the resistance value difference of reservoir；Model 2 is the change with permeability Greatly, cap rock also becomes big with the resistance value difference of reservoir.According to plan, devise the rock skeleton parameter of two class models and split Stitch parameter and cap rock and the speed of bottom and density.Assume that the crack in rock aligns, utilize Kozlov to use The theoretical fracture surface represented in rock of Hertz is contacted by the sags and crests on fracture surface, and combine Thomsen fluid affect because of Son has been derived and there is, by crack, the rock additional compliance expression formula that causes:

$Z_N=\frac{2}{3}Bce{\left(\frac{c}{K^{2}p}\right)}^{\frac{1}{3}}D---\left(2a\right)$

$Z_T=(1-0.5\mathrm{\ν})ce{\left(\frac{2c}{3(1-\mathrm{\ν}){\mathrm{\μ}}^{2}p}\right)}^{\frac{1}{3}}---\left(2b\right)$

$D={\[1+\frac{2}{3}\left(\frac{K_f}{\mathrm{\φ}K}\right)\left(\frac{K_S}{K_S-K_f}\right)BFce\sqrt[3]{\frac{cK}{3p}}\]}^{-1}---\left(2c\right)$

Z in formula_NAnd Z_TIt is the normal direction additional compliance and tangential additional compliance caused due to the existence in crack respectively.D is fluid The factor, B=[(1+ ν)/(1-ν)]^2/3, ν is Poisson's ratio, and e is the density in crack, and c is crack roughness, and K is the body of dry rock Product module amount, P is effective pressure, K_fFor the bulk modulus of fluid, K_SFor the bulk modulus of Rock Matrix, F is the stream that Hudson derives The expression formula of the fluid factor of influence in body connection hole and crack:

$F={\{1+\[\frac{3}{2b}(1-i)\]\[\frac{{\mathrm{\φK}}_f\mathrm{\κ}}{2{\mathrm{\η}}_f\mathrm{\ω}}\]\}}^{-1}---3)$

In formula, b is the average open in crack, and φ is the porosity of perforate, and κ is permeability, and ω is angular frequency, η_fFor stream Bulk viscosity.

Complex velocity calculating formula for seismic wave is formula (4), and in formula, Z is the body change compliance of dry rock, and formula (5) is inverse product The expression formula of prime factor.

$\tilde{V}={\{\[(Z+\widetilde{Z_N})+\frac{4}{3}\mathrm{\μ}\]/\mathrm{\ρ}\}}^2---4)$

$Q^{-1}=\frac{\mathrm{Im}\left(\widetilde{V^2}\right)}{\mathrm{Re}\left(\widetilde{V^2}\right)}---5)$

The physical parameter of two models substitutes in above formula, effective pressure is set to 5Mpa and has obtained compressional wave phase velocity Bring the seismic reflection coefficient calculation method propagated at Layered Viscoelastic isotropic medium that Ursin is derived, its equation into Seeing formula (6), in formula, τ is reservoir time thickness.V₂、ρ₂It is speed and the density of reservoir respectively, ρ₁、ρ₃And V₃It is cap rock and the end respectively The density of layer and speed.

$R(\mathrm{\ω},\mathrm{\τ})=\frac{\widetilde{r_1}+\widetilde{r_2}\exp (-i\mathrm{\ω}\mathrm{\τ}+Q_2^{-1}/2)}{1+\widetilde{r_1}\widetilde{r_2}\exp (-i\mathrm{\ω}\mathrm{\τ}+Q_2^{-1}/2)}---6a)$

$\widetilde{r_1}=\frac{{\mathrm{\ρ}}_2\mathrm{Re}\left(\widetilde{V_2}\right)-{\mathrm{\ρ}}_1{V}_1(1+{\mathrm{iQ}}_2^{-1}/2)}{{\mathrm{\ρ}}_2\mathrm{Re}\left(\widetilde{V_2}\right)+{\mathrm{\ρ}}_1{V}_1(1-{\mathrm{iQ}}_2^{-1}/2)}---6b)$

$\widetilde{r_2}=\frac{{\mathrm{\ρ}}_3{V}_3(1-{\mathrm{iQ}}_2^{-1}/2)-{\mathrm{\ρ}}_2\mathrm{Re}\left(\widetilde{V_2}\right)}{{\mathrm{\ρ}}_2\mathrm{Re}\left(\widetilde{V_2}\right)+{\mathrm{\ρ}}_3{V}_3(1-{\mathrm{iQ}}_2^{-1}/2)}---6c)$

After obtaining reflection coefficient, calculate seismic spectrum according to formula (7).In formula, W (ω) is wavelet spectrum, and its dominant frequency is 30Hz。

S (ω, τ)=R (ω, τ) W (ω) (7)

Then S (ω, τ) is brought in formula (1), calculate model 1 and the K of model 2₁Attribute.

Fig. 1 is shown that K₁Change curve with permeability.When model 1 layer thickness is 25ms, K₁Increase with permeability And reduce；When thickness is 55ms and 85ms, K₁Increase with permeability and increase.When model 2 layer thickness is 25ms, K₁With infiltration Rate increases and increases；When thickness is 55ms, it is 0.001 to 0.02mD section K in permeability₁Increase with permeability and increase, K during 0.02mD to 1000mD₁Increase with permeability and reduce；Layer thickness is 85ms, K₁When variation tendency and thickness are 55ms substantially Unanimously.As seen from the above analysis K₁Attribute is when permeability is higher more than 0.01mD and layer thickness time, and general trend exists Model 1 increases with permeability and increases, increase with permeability in model 2 and reduce.

The extraction of 2 K1 attributes

In order to the signal of time domain is converted into time frequency signal, deconvolution Short Time Fourier Transform is utilized to carry

Taking the time frequency signal of seismic data, the short time discrete Fourier transform of signal x (u) is defined as:

${\mathrm{STFT}}_X(t,f)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(u\right)h*(u-t)e^{(-j2\mathrm{\π}fu)}du---\left(8\right)$

Wherein h (u-t) is window function, and conventional is Gaussian window, and wherein * is conjugate transpose.

Short time discrete Fourier transform spectrum is defined as:

${\mathrm{SPEC}}_X(t,f)={|{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(u\right)h*(u-t)e^{(-j2\mathrm{\π}fu)}du|}^2---\left(9\right)$

For signal x (t), its Wigner-Ville distribution is defined as:

${\mathrm{WVD}}_X(t,f)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x(t+\frac{\mathrm{\τ}}{2})x*(t-\frac{\mathrm{\τ}}{2})e^{(-j2\mathrm{\π}f\mathrm{\τ})}d\mathrm{\τ}---\left(10\right)$

Wigner-Ville is distributed cross term, and it is caused by Wigner-Ville distributed nonlinear.Generalized S-transform Expression formula be:

$GST(\mathrm{\τ},f)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(t\right)\frac{\mathrm{\λ}\left|f\right|p}{\sqrt{2\mathrm{\π}}}{e}^{\frac{-{\mathrm{\λ}}^2{f}^{2p}{(\mathrm{\τ}-t)}^2}{2}}{e}^{-j2\mathrm{\π}ft}dt,\mathrm{\λ}>0,p>0---\left(11\right)$

Generalized S-transform, by introducing two parameter lambda and p, has been transformed the Gauss function of S-transformation, has been regulated Gauss neatly Window function is with the variation tendency of dimensions in frequency f.

The short time discrete Fourier transform spectrum of signal x (t) can be to be write as the form of following two dimension convolution:

$\begin{array}{c}{\mathrm{SPEC}}_X(t,f)={\left|{\mathrm{STFT}}_X(t,f)\right|}^2\\ ={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\mathrm{WVD}}_h(u,v)\×{\mathrm{WVD}}_x(t-u,f-v)dudv\end{array}---\left(12\right)$

Wherein WVD_xAnd WVD_hIt is respectively the Wigner-Ville distribution of signal x (t) and window function h (u).Short-time Fourier The cross term of conversion spectrum is 0 in major part situation.

(5-15) formula also can be write as:

S_X=W_X**W_h (13)

Wherein S_XIt is the short time discrete Fourier transform spectrum of signal x (u), W_hIt is the Wigner-Ville distribution of signal x (u), W_hIt is The Wigner-Ville distribution of window function h (u), * * represents two dimension convolution.

It is desirable that deconvolution result W_x ^-Have and be distributed W with Wigner-Ville_xClose time frequency resolution, but due to short Time fourier transform spectrum and decrease cross term.

If it is known that window function h (u), it is possible to know that Wigner-Ville is distributed W_h.Obtain from short time discrete Fourier transform spectrum Take W_x ^-It it is a deconvolution problem.Seismic signal is brought in above formula, obtained time-frequency seismic signal, then by time frequency signal band Enter in formula (1), try to achieve K1 attribute.

3 reservoir permeability evaluations

As a example by actual marine three dimensional seismic data, Fig. 2 crosses well A seismic profile for certain district marine, and green solid lines is mesh Layer, well A bores chance industry stream oil in carbonate reservoir, and section indicated by Fig. 2 Green arrow is containing the oil reservoir of 85 meters, sapphirine Log be deep lateral resistivity, it can be seen that the resistivity of the oily section that height oozes high hole can be significantly raised, permeability Can reach 700mD, porosity reaches 31%.Fig. 3 was synthetic seismic record and the horizon calibration of well A, Article 1 log Being sound impedance, Article 2 log is deep lateral resistivity.Can from Fig. 4 figure that crosses of permeability (porosity with) Going out, it is complicated that relation is oozed in the hole of this reservoir, although totally presents porosity and rises the trend that high permeability also raises, but same hole Permeability value under Du is also changeable.

Because reservoir is carbonate rock, cap rock is clastic rock, so this reservoir meets the situation of model 1 in literary composition, i.e. with oozing The change of rate is big thoroughly, and cap rock reduces with the natural impedance difference of reservoir, be it will be seen that the K of this reservoir by the result of numerical simulation₁Belong to Property general trend should increase with the increase of permeability.

Utilize deconvolution Fourier transformation to calculate the time-frequency spectrum of this seismic data, after having picked up advantage frequency range, bring public affairs into Formula 1 calculates K₁Attribute.Fig. 5 was the K of well A₁Attribute profile, the warm colour region in figure and well-log information middle and high infiltration height hole Oil-bearing layer match.Fig. 6 is K₁Attribute prolongs the section (Lycoperdon polymorphum Vitt mark is without geological data region) of 15ms under the top layer.Section In two dashed region drilling well carbonate rock target zone all bore chance industry stream oil.Black dotted lines is well A region, should The daily oil production of well is up to 783.1 sides；Navy blue dotted line is well B region, and this well core intersection reaches 62 meters of thickness, permeability Reaching 700mD, porosity reaches 28%, and daily oil production is 94.9 sides.The carbonic acid of two wellblocks is it will be seen that by well-log information Rock salt reservoir fluid mobility is strong, and permeability is big.Can be seen that be K in black dotted lines and blue dotted line₁Attribute is all and K₁Belong to Property with log data coincide, show the distribution of high permeability high quality carbon Carbonate Reservoir.And in the mobility attribute of Fig. 7 is cut into slices The fluid ability that reservoir in well B district is stronger is not shown in blue dashed region

Can be seen that according to above-mentioned techniqueflow in the result of numerical simulation and demonstrate that K1 attribute can reflect the change of permeability Change, the overall change with permeability in model 1 of K1 attribute is big and becomes big, and in model 2, the overall change with permeability diminishes greatly. Because K1 attribute make use of the seismic signal of high and low frequency simultaneously, relatively mobility attribute is advantageously, more can reflect reservoir permeability Distribution.

Last it is noted that above example is only in order to illustrate technical scheme, it is not intended to limit；Although With reference to previous embodiment, the present invention is described in detail, it will be understood by those within the art that: it still may be used So that the technical scheme described in foregoing embodiments to be modified, or wherein portion of techniques feature is carried out equivalent； And these amendment or replace, do not make appropriate technical solution essence depart from various embodiments of the present invention technical scheme spirit and Scope.

Claims (2)

1. the reservoir permeability appraisal procedure becoming attribute based on frequency, it is characterised in that: for the geological condition of different regions, Select suitable petrophysical model to carry out numerical simulation, analyze this area's K1 attribute response characteristic to permeability；Calculate folded The time-frequency spectrum of rear seismic data；K1 attribute is calculated from time frequency signal；Store up in conjunction with numerical simulation result and log data evaluation The Permeability Distribution of layer.

The reservoir permeability appraisal procedure becoming attribute based on frequency the most according to claim 1, it is characterised in that concrete steps As follows:

(1) extraction of K1 attribute

K₁Attribute is the ratio of seismic spectrum high frequency signal and low frequency signal:

$K_1={\mathrm{\Σ}}_{{\mathrm{\ω}}_m}^{{\mathrm{\ω}}_2}\left|S\left(\mathrm{\ω}\right)\right|/{\mathrm{\Σ}}_{{\mathrm{\ω}}_1}^{{\mathrm{\ω}}_m}\left|S\left(\mathrm{\ω}\right)\right|---\left(1\right)$

In formula, S (ω) is seismic spectrum, ω₁、ω_mAnd ω₂It is the Frequency of seismic signal, crest frequency and higher frequency；

In order to the signal of time domain is converted into time frequency signal, deconvolution Short Time Fourier Transform is utilized to extract the time-frequency of seismic data Signal, the short time discrete Fourier transform of signal x (u) is defined as:

${\mathrm{STFT}}_X(t,f)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(u\right)h*(u-t)e^{(-j2\mathrm{\π}fu)}du---\left(8\right)$

Wherein h (u-t) is window function, and conventional is Gaussian window, and wherein * is conjugate transpose；

Short time discrete Fourier transform spectrum is defined as:

${\mathrm{SPEC}}_X(t,f)=|{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(u\right)h*(u-t)e^{(-j2\mathrm{\π}fu)}du{|}^2---\left(9\right)$

For signal x (t), its Wigner-Ville distribution is defined as:

${\mathrm{WVD}}_X(t,f)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x(t+\frac{\mathrm{\τ}}{2})x*(t-\frac{\mathrm{\τ}}{2})e^{(-j2\mathrm{\π}f\mathrm{\τ})}d\mathrm{\τ}---\left(10\right)$

Wigner-Ville is distributed cross term, and it is caused by Wigner-Ville distributed nonlinear；

The expression formula of generalized S-transform is:

$GST(\mathrm{\τ},f)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}x\left(t\right)\frac{\mathrm{\λ}\left|f\right|p}{\sqrt{2\mathrm{\π}}}{e}^{\frac{-{\mathrm{\λ}}^2{f}^{2p}{(\mathrm{\τ}-t)}^2}{2}}{e}^{-j2\mathrm{\π}ft}dt,\mathrm{\λ}>0,p>0---\left(11\right)$

Generalized S-transform, by introducing two parameter lambda and p, has transformed the Gauss of S-transformation

Window function, regulation Gauss function is with the variation tendency of dimensions in frequency f neatly；

The short time discrete Fourier transform of signal x (t) compose into following two dimension convolution form:

$\begin{array}{c}{\mathrm{SPEC}}_X\left(t,f\right)=|{\mathrm{STFT}}_X\left(t,f\right){|}^2\\ ={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\mathrm{WVD}}_h\left(u,v\right)\×{\mathrm{WVD}}_x\left(t-u,f-v\right)dudv\end{array}---\left(12\right)$

Wherein WVD_xAnd WVD_hIt is respectively the Wigner-Ville distribution of signal x (t) and window function h (u), short time discrete Fourier transform The cross term of spectrum is 0 in major part situation；

Seismic signal is brought in above formula, obtained time-frequency seismic signal, then time frequency signal has been brought in formula (1), try to achieve K1 attribute.

(2) reservoir permeability evaluation

Understood the K1 attribute general trend of this reservoir by the result of numerical simulation, permeability becomes with the change of K1 property trends Change.