CN103645500A - Method for estimating mixed-phase seismic wavelets of frequency domain - Google Patents

Abstract

The invention provides a method for estimating mixed-phase seismic wavelets by using high-order cumulants of frequency domain seismic data. The method can accurately estimate the mixed phase of the seismic wavelets by comprehensively utilizing two-dimensional Fourier transformation, two-dimensional phase unwrapping, linear inversion and the like. Influences imposed on the estimation result of the wavelets by noises are effectively reduced by combining a series of technical processes, and the applicability of the wavelets in a certain space range is improved.

Description

A kind of mixed-phase seismic wavelet evaluation method of frequency field

Technical field

The invention belongs to geophysical exploration technology, relate to the high precision evaluation method of seismic wavelet in seismic prospecting.

Background technology

Seismic wavelet estimation is an important technology in reflection wave seismic prospecting.No matter be that Simulation of Seismic Wave, geological data deconvolution are processed or seismic inversion, all need clear and definite seismic wavelet information.Therefore the estimation result of seismic wavelet needs very high precision.

The seismic wavelet exciting by man-made explosion has fixing spectral amplitude and phase spectrum conventionally.Due to effects such as source effect, distortion in underground medium communication process and decay, the amplitude of seismic wavelet and phase place all can change in underground medium communication process.So the final seismic wavelet observing is common and nonideal minimum phase or zero phase, but more complicated mixed-phase.

The estimating techniques of mixed-phase seismic wavelet can be divided into two classes substantially: first kind technology calculates reflection coefficient by geophysical logging data, using that this carries out wavelet estimation of seismic trace as technology such as constraint zygote wave phase corrections; Equations of The Second Kind technology is utilized the high-order statistic estimation wavelet of geological data itself, does not need other supplementary.Although first kind technology can be carried out wavelet estimation comparatively accurately near seismic trace wellhole position, be difficult to apply it to far away apart from wellhole or lack on the geological data of Log-constrained.The advantage of Equations of The Second Kind technology is in the situation that there is no logging trace constraint, directly to estimate seismic wavelet, so range of application is more extensive.But the validity of such technology is often because method is different, and estimation result is easily subject to the impact of the factors such as noise, Wavelet space variation.

At present, the conventional seismic wavelet estimating techniques based on high-order statistic utilize the Higher Order Cumulants of time domain to estimate sub-wave amplitude and phase place mostly, for example: maximum time postpones square (MTM) method or normalizing semi-invariant (NC) method (Giannakis, 1987).Because said method only utilizes the single high-order statistic of seismic trace to cut into slices, be similar to the high-order statistic of wavelet, therefore in stability, be short of to some extent.In addition, conventionally need to utilize the method for inverting to reduce deviation (Lazear, 1993 between the High Order Moment of seismic wavelet and the Higher Order Cumulants of geological data; Velis and Ulrych, 1996).Although the frequency spectrum of high-order statistic has retained spectral amplitude and the phase spectrum of geological data, the seismic wavelet estimating techniques based on frequency field high-order statistic are actually rare at present.Main cause is that the phase place of the higher-order spectrum that obtains by multidimensional Fourier trans form is normally reeled within the scope of 2 π, and its actual value not.Therefore be difficult to directly be used to the estimation of seismic wavelet phase place.

Summary of the invention

In order to solve the problem existing in above-mentioned background technology, the invention provides a kind of method of utilizing the Higher Order Cumulants estimation mixed-phase seismic wavelet of frequency field geological data.The technology such as the method comprehensive utilization two-dimensional Fourier transform, two-dimensional phase solution twine, linear inversion, can estimate the mixed-phase of seismic wavelet exactly; And effectively reduced the impact of noise on wavelet estimation result in conjunction with a series of techniqueflows, and improved the applicability of wavelet within the scope of certain space.

The present invention is achieved through the following technical solutions:

A mixed-phase seismic wavelet evaluation method for frequency field, comprises the following steps:

(1) to a certain pending two-dimension earthquake section or the selected analysis window of 3-D data volume, by time data volume in window be divided into K group, every group of adjacent seismic trace that data contain identical or approximate equal number, the degree that described adjacent seismic trace changes in spatial dimension according to real data is divided into one group, 5,10,15 or 20 road, then the geological data in every group is joined end to end as pending data x (t);

The object of doing is like this: 1. avoid each road geological data to carry out respectively wavelet estimation process, thereby reduce calculated amount; 2. thereby increase input data volume and strengthen the statistical law relating in subsequent step.

(2) autocorrelation function of computational data x (t), and extract on this basis the spectral amplitude of autocorrelation function, using the approximate spectral amplitude A (ω) as wavelet of the square root of auto-correlation amplitude;

(3) calculate two spectrum B of geological data _x(ω ₁, ω ₂), according to one of following two kinds of modes, calculate:

(a) first calculate three rank semi-invariants of geological data

and it is carried out to two spectrum B that two-dimensional Fourier transform obtains geological data _x(ω ₁, ω ₂);

(b) first calculate the frequency spectrum X (ω) of geological data, then ask the two-dimensional correlation function of X (ω) to obtain two spectrum B _x(ω ₁, ω ₂);

(4) utilize two-dimentional Lp norm phase unwrapping method to recover the actual value of geological data bispectrum phase, specifically adopt following steps:

(a) the two-dimentional bispectrum phase to a coiling

i=0 ..., N, j=0 ..., N, in two directions calculate respectively between adjacent two elements without coiling phase differential with

(b) in order to solve without coiling phase place ψ _i,j, i=0 ..., N, j=0 ..., N, in two directions utilizes Lp norm to set up objective function simultaneously, makes the difference ψ of adjacent 2 of phase place to be asked _{i+1, j}-ψ _i,jand ψ _{i, j+1}-ψ _i,jrespectively with

with

between error minimum;

(c) to objective function, ask local derviation to obtain a nonlinear equation, utilize weight generalized linear inversion method to carry out iterative, in iterative process, make norm p get 0, wherein the weight factor W1 (i of both direction, j) and W2 (i, j) respectively with unknown variable ψ _{i+1, j}-ψ _i,jand ψ _{i, j+1}-ψ _i,jrelevant;

The phase place that makes norm p get estimation in 0 o'clock has the partial gradient value very approaching with true phase place, and p=0 contributes to improve speed of convergence.In addition, in actual solution procedure, the optimization of weight factor being carried out to certain way can improve speed of convergence.

(d) after each iteration finishes, the phase place ψ of check estimation _i,jwith original phase

between local phase residual error, if residual values approaches or equals zero, stop iterative;

(5) according to formula ψ _x(ω ₁, ω ₂)=φ (ω ₁)+φ (ω ₂)-φ (ω ₁+ ω ₂) set up objective function, utilize linear inversion method to solve seismic wavelet phase spectrum φ (ω), wherein: ψ _x(ω ₁, ω ₂) be the bispectrum phase of the geological data of estimation;

(6) the spectral amplitude A (ω) that merges phase spectrum φ (ω) and obtain by step (1) estimation, recycling Fourier inversion obtains seismic wavelet to be asked;

(7), to every group of Data duplication above-mentioned steps (2)-(6) that obtain of integrating in step (1), obtain K with the seismic wavelet of spatial variations;

For example, in order to guarantee the stability of latter earthquake data processing and inverting (deconvolution or wave impedance inversion) result, conventionally to a certain 2-D data section or 3-D data volume, only retain a seismic wavelet.In order to meet the applicability of this wavelet in spatial dimension, need to calculate each wavelet and the related function of other K-1 wavelet, the then addition that estimation obtains.The wavelet with maximum correlation coefficient is the optimum wavelet in spatial dimension.

(8) if there is log data in a certain position of real data, utilize well curve as constraint, and by the wavelet of phasescan method estimation seismic trace near well, then using this result as reference, check utilizes above-mentioned steps (1)-(7) to obtain mixed-phase seismic wavelet.

If two estimation results are close, explanation estimation result is comparatively accurate, and at selected spatial dimension endoadaptation; If two results differ larger, need according to the following parameter of actual conditions adjustment: the norm value in the packet parameter in step (1), step (4), the weight factor in step (4).

For step (3), should be noted: according to seismic convolution model

x(t)＝w(t)*r(t)+n(t) （1）

Wherein w (t), r (t) and n (t) are respectively seismic wavelet to be asked, fractal sequence and signal noise, if fractal sequence is that non-Gauss is independent identically distributed, two spectrums of geological data have following relation with two spectrums of seismic wavelet:

$B_x({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)={\mathrm{\γ}}_3^r{B}_w({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)---\left(2\right)$

B wherein _w(ω ₁, ω ₂) represent that the two of seismic wavelet compose, the third moment that represents reflection coefficient, if can estimate the bispectrum phase ψ of geological data _x(ω ₁, ω ₂), the phase of seismic wavelet (ω) and ψ _x(ω ₁, ω ₂) just like lower linear relation:

ψ _x(ω ₁,ω ₂)＝φ(ω ₁)+φ(ω ₂)-φ(ω ₁+ω ₂) （3）

But conventionally utilizing the phase place of the function that Fourier transform obtains not is its actual value, but (wrapped) that within the scope of 2 π, reel.Therefore can not directly utilize the phase place of formula (3) estimation seismic wavelet.

Accompanying drawing explanation

Fig. 1 is one and crosses well seismic cross-section, Grey curves sign well curve.

Fig. 2 is for estimating the synthetic seismic data line chart of wavelet.

Fig. 3 is the wavelet amplitude (grey) by step (2) estimation and true wavelet amplitude (black).

Fig. 4 is that two-dimensional phase solution twines procedure chart.(a) for original bispectrum phase (reeling at-π), be (b) the local phase residual error of original bispectrum phase to the scope of π in.(c) – (h) is the scheme of describing according to step (4), the phase result (left side) obtaining by 1,2,3 iteration and corresponding local phase residual error (right side).(i) be the bispectrum phase recovering completely.

Fig. 5 is according to the seismic wavelet phase place (grey) of schematic design estimate in step (5) and true sub-wave phase (black) figure.

The seismic wavelet phase place (grey) that Fig. 6 is the amplitude by merging Fig. 2 and the generation of the phase place in Fig. 5 and true wavelet (black) figure.

In Fig. 7, (a) represents optimum estimation line chart.(b) the wavelet estimated result line chart of presentation graphs 1 Zhong Shi road seismic trace.

In Fig. 8, (a) is for utilizing log data shown in Fig. 1 as retrain and passing through Walden & White(1998) seismic wavelet (left side) and the phase place (right side) of the well lie estimated of method.(b) for utilizing seismic wavelet (left side) and the phase place (right side) of section shown in Fig. 1 that step (1-7) estimation obtains.(c) the well shake of carrying out for the wavelet result of using in (a) is demarcated, and the related coefficient of generated data and True Data is 0.73.(d) the well shake of carrying out for the wavelet result of using in (b) is demarcated, and the related coefficient of generated data and True Data is 0.731.

Embodiment

Below in conjunction with the accompanying drawing explanation specific embodiment of the invention.

(1) as shown in Figure 1, first to a certain selected analysis window (2.2s-2.6s) of well (grey) two-dimension earthquake section of crossing.By time data volume in window be divided into 10 groups, the seismic-data traces in every group is joined end to end as pending data x (t), t=0,1..., N.

(2) autocorrelation function of data x shown in calculating chart 2 (t)

$c\left(t\right)=\underset{\mathrm{\τ}=0}{\overset{N-t}{\mathrm{\Σ}}}x\left(t\right)x(t+\mathrm{\τ})---\left(4\right)$

Utilize Fourier transform to obtain the frequency spectrum of autocorrelation function c (t)

$C\left(\mathrm{\ω}\right)=\underset{t=0}{\overset{N}{\mathrm{\Σ}}}c\left(t\right)\exp (-\mathrm{i\ωt})=R_C\left(\mathrm{\ω}\right)+I_C\left(\mathrm{\ω}\right)i,\mathrm{\ω}=\mathrm{0,1},...M---\left(5\right)$

R wherein _c(ω) and I _c(ω) represent respectively real part and imaginary part.Using the approximate spectral amplitude as wavelet of the square root of above formula amplitude

(result as shown in Figure 3).

(3) can estimate by following two kinds of modes two spectrum B of geological data _x(ω ₁, ω ₂):

(a) first calculate three rank semi-invariants of geological data

$c_x^3({\mathrm{\τ}}_1,{\mathrm{\τ}}_2)=m_x^3({\mathrm{\τ}}_1,{\mathrm{\τ}}_2)-m_{\mathrm{Gau}}^3({\mathrm{\τ}}_1,{\mathrm{\τ}}_2)---\left(6\right)$

Wherein $m_x^3({\mathrm{\τ}}_1,{\mathrm{\τ}}_2)=E\left\{x\left(t\right)x(t+{\mathrm{\τ}}_1)x(t+{\mathrm{\τ}}_2)\right\},$ The third moment that represents x (t),

represent a third moment having with the equivalent Gaussian process g (t) of the identical second-order statistic of x (t).Right

carry out two-dimensional Fourier transform and can obtain two spectrums of geological data:

$\begin{array}{c}{B}_x({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)=R_B({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)+I_B({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)i=\underset{\mathrm{\τ}1=-\∞}{\overset{\∞}{\mathrm{\Σ}}}\underset{\mathrm{\τ}2=-\∞}{\overset{\∞}{\mathrm{\Σ}}}{c}_x^3({\mathrm{\τ}}_1,{\mathrm{\τ}}_2)\exp [-j({\mathrm{\ω}}_1{\mathrm{\τ}}_1+{\mathrm{\ω}}_2{\mathrm{\τ}}_2)],\\ \left|{\mathrm{\ω}}_1\right|\≤\mathrm{\π},\left|{\mathrm{\ω}}_2\right|\≤\mathrm{\π},|{\mathrm{\ω}}_1+{\mathrm{\ω}}_2|\≤\mathrm{\π}\end{array}---\left(7\right)$

R wherein _b(ω ₁, ω ₂) and I _b(ω ₁, ω ₂) be respectively real part and the imaginary parts of two spectrums.

(b) first according to formula (5), calculate the frequency spectrum X (ω) of geological data x (t), then calculate two spectrums by following formula:

$B_x({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)=R_B({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)+I_B({\mathrm{\ω}}_1,{\mathrm{\ω}}_2)i=\underset{\mathrm{\ω}1=0}{\overset{M}{\mathrm{\Σ}}}\underset{\mathrm{\ω}2=0}{\overset{M-\mathrm{\ω}1}{\mathrm{\Σ}}}X\left({\mathrm{\ω}}_1\right)X\left({\mathrm{\ω}}_2\right)X^{*}({\mathrm{\ω}}_1+{\mathrm{\ω}}_2),---\left(8\right)$

By above-mentioned two kinds of methods, all can estimate two spectrums of geological data, can need to select according to actual computation.The phase spectrum of two spectrums is:

(4) in order to utilize the phase spectrums of the two spectrums of geological data in formula (3) and the linear relationship between the phase spectrum of seismic wavelet, need to original volume around bispectrum phase

carry out phase unwrapping, recover true phase place ψ _x(ω ₁, ω ₂), concrete scheme following (Fig. 4):

(a) the two-dimentional bispectrum phase to a coiling

i=0 ..., N, j=0 ..., N, in two directions calculate respectively between adjacent two elements without coiling phase differential

with

With

(b) in order to solve without coiling phase place ψ _i,j, i=0 ..., N, j=0 ..., N, in two directions utilizes Lp norm establishing equation objective function simultaneously:

$J=\left|{\mathrm{\ϵ}}^p\right|=\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N}{\mathrm{\Σ}}}{|{\mathrm{\ψ}}_{i+1,j}-{\mathrm{\ψ}}_{i,j}-\mathrm{\Δ}{\mathrm{\ψ}}_{i,j}^r|}^p+\underset{i=0}{\overset{N}{\mathrm{\Σ}}}\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{|{\mathrm{\ψ}}_{i,j+1}-{\mathrm{\ψ}}_{i,j}-\mathrm{\Δ}{\mathrm{\ψ}}_{i,j}^c|}^p---\left(11\right)$

(c) to objective function, ask local derviation to obtain a nonlinear equation, can utilize weight generalized linear inversion method to carry out iterative:

(ψ _i+1,j-ψ _i,j)W1(i,j)+(ψ _i,j+1-ψ _i,j)W2(i,j)- （12）

(ψ _i,j-ψ _i-1,j)×W1(i-1,j)-(ψ _i,j-ψ _i,j-1)W2(i,j-1)＝b(i,j)

Wherein:

$b(i,j)=\mathrm{\Δ}{\mathrm{\ψ}}_{i,j}^r{W}_1(i,j)-\mathrm{\Δ}{\mathrm{\ψ}}_{i-1,j}^r{W}_1(i-1,j)+\mathrm{\Δ}{\mathrm{\ψ}}_{i,j}^c{W}_2(i,j)-\mathrm{\Δ}{\mathrm{\ψ}}_{i-1,j}^c{W}_2(i-1,j)---\left(13\right)$

Weight factor W1 (i, j) and the W2 (i, j) of both direction are respectively:

$W1(i,j)={|{\mathrm{\ψ}}_{i+1,j}-{\mathrm{\ψ}}_{i,j}-\mathrm{\Δ}{\mathrm{\ψ}}_{i,j}^r|}^{p-2},i=0,...,N-1,j=0,...,N$

$W2(i,j)={|{\mathrm{\ψ}}_{i,j+1}-{\mathrm{\ψ}}_{i,j}-\mathrm{\Δ}{\mathrm{\ψ}}_{i,j}^c|}^{p-2},i=0,...,N,j=0,...,N-1---\left(14\right)$

(d) in theory, concerning above formula when norm p gets the value that is greater than 2, although estimation phase place solution ψ _x(ω ₁, ω ₂) whole level and smooth, but can be too near exceptional value, thus the accuracy of result affected; When p equals 2, what solve an equation (13) obtained is non-weight least square solution; And when p is less than 2, the phase place of estimation has the partial gradient value very approaching with true phase place, and contribute to improve speed of convergence.The present invention makes norm p get 0, and at this moment the phase place of estimation has the partial gradient value very approaching with true phase place, and contributes to improve speed of convergence.In addition, in actual solution procedure, weight is carried out to following optimization and can improve speed of convergence:

$W1{(i,j)}_{\mathrm{norm}}=\frac{{\mathrm{\ϵ}}_0}{W1(i,j)+{\mathrm{\ϵ}}_0},W2{(i,j)}_{\mathrm{norm}}=\frac{{\mathrm{\ϵ}}_0}{W2(i,j)+{\mathrm{\ϵ}}_0}---\left(15\right)$

ε wherein ₀be a constant, for example, get in the present invention 0.01.

(e) after each iteration finishes, the phase place ψ of check estimation _i,jwith original phase

between local phase residual error:

If residual values approaches or equals zero, stop iterative.

(5) according to formula (3), set up objective function, utilize linear inversion method to solve seismic wavelet phase spectrum φ (ω):

Wherein $D=\left[\begin{array}{cccccccc}2& -1& 0& 0& ...& .& .& .\\ 1& 1& -1& 0& ...& .& .& .\\ 1& 0& 1& -1& ...& .& .& .\\ .& .& .& .& .& .& .& .\\ 1& 0& 0& .& .& 1& -1& .\\ 1& 0& 0& 0& .& 0& 1& -1\\ 0& 2& 0& -1& .& .& .& .\\ 0& 1& 1& 0& -1& .& .& .\\ .& .& .& .& .& .& .& .\\ 0.& 1& .& .& .& 1& -1& 0\\ .& 1& .& .& .& .& 2& -2\end{array}\right].$ Solve an equation and need to determine border φ (0) and φ (N+1), in the present invention, order

φ(0)＝ψ(0,0)≈2ψ(2,2)-ψ(1,1)，

φ(N+1)＝ψ(N+1,N+1)≈2ψ(N-1,N-1)-ψ(N,N)。（18）

(6) the spectral amplitude A (ω) that merges phase spectrum φ (ω) and obtain by step (1) estimation, recycling Fourier inversion obtains seismic wavelet to be asked.

W(ω)＝A(ω)[cos(φ(ω))+sin(φ(ω))i] （19）

$w\left(t\right)=\frac{1}{2\mathrm{\π}}\underset{\mathrm{\ω}=0}{\overset{M}{\mathrm{\Σ}}}W\left(\mathrm{\ω}\right)\exp \left(\mathrm{i\ωt}\right)---\left(20\right)$

(7) as shown in Figure 7, every group of Data duplication step (2)-(6) to integrating in step (1), can obtain 10 with the seismic wavelet of spatial variations.For example, in order to guarantee the stability of latter earthquake data processing and inverting (deconvolution or wave impedance inversion) result, the 2-D data section shown in Fig. 1 is only retained to a seismic wavelet.In order to meet the applicability of this wavelet in spatial dimension, need to calculate each wavelet and the related function of other 9 wavelets, the then addition that estimation obtains.The wavelet with maximum correlation coefficient is the optimum wavelet in spatial dimension.(8) shown in Fig. 8 a, be to utilize the log data shown in Fig. 1 as the seismic wavelet that retrains and pass through the method estimation of Walden & White.Shown in Fig. 8 b is to utilize above-mentioned steps (1-7) estimation to obtain mixed-phase seismic wavelet.Two groups of results are carried out respectively to well shake demarcates: in wellhole position, estimation wavelet and the reflection coefficient obtaining by well curve calculation are carried out to convolution.Synthetic geological data and true geological data are carried out to correlation analysis, and by relatively finding, the result of two kinds of distinct methods generations is reliable (related coefficient is respectively 0.73 and 0.71) all.Therefore confirmed the validity of the method for the invention.

Claims (1)

1. a mixed-phase seismic wavelet evaluation method for frequency field, comprises the following steps:

(1) to a certain pending two-dimension earthquake section or the selected analysis window of 3-D data volume, by time data volume in window be divided into K group, every group of adjacent seismic trace that data contain identical or approximate equal number, the degree that described adjacent seismic trace changes in spatial dimension according to real data is divided into one group, 5,10,15 or 20 road, then the geological data in every group is joined end to end as pending data x (t);

(2) autocorrelation function of computational data x (t), and extract on this basis the spectral amplitude of autocorrelation function, using the approximate spectral amplitude A (ω) as wavelet of the square root of auto-correlation amplitude;

(3) calculate two spectrum B of geological data _x(ω ₁, ω ₂), according to one of following two kinds of modes, calculate:

(a) first calculate three rank semi-invariants of geological data

and it is carried out to two spectrum B that two-dimensional Fourier transform obtains geological data _x(ω ₁, ω ₂);

(b) first calculate the frequency spectrum X (ω) of geological data, then ask the two-dimensional correlation function of X (ω) to obtain two spectrum B _x(ω ₁, ω ₂);

(4) utilize two-dimentional Lp norm phase unwrapping method to recover the actual value of geological data bispectrum phase, specifically adopt following steps:

(a) the two-dimentional bispectrum phase to a coiling

i=0 ..., N, j=0 ..., N, in two directions calculate respectively between adjacent two elements without coiling phase differential

with

(b) in order to solve without coiling phase place ψ _i,j, i=0 ..., N, j=0 ..., N, in two directions utilizes Lp norm to set up objective function simultaneously, makes the difference ψ of adjacent 2 of phase place to be asked _{i+1, j}-ψ _i,jand ψ _{i, j+1}-ψ _i,jrespectively with

with between error minimum;

(c) to objective function, ask local derviation to obtain a nonlinear equation, utilize weight generalized linear inversion method to carry out iterative, in iterative process, make norm p get 0, wherein two

The weight factor W1 (i, j) of individual direction and W2 (i, j) respectively with unknown variable ψ _{i+1, j}-ψ _i,jand ψ _{i, j+1}-ψ _i,jrelevant;

(d) after each iteration finishes, the phase place ψ of check estimation _i,jwith original phase

between local phase residual error, if residual values approaches or equals zero, stop iterative;

(5) according to formula ψ _x(ω ₁, ω ₂)=φ (ω ₁)+φ (ω ₂)-φ (ω ₁+ ω ₂) set up objective function, utilize linear inversion method to solve seismic wavelet phase spectrum φ (ω), wherein: ψ _x(ω ₁, ω ₂) be the bispectrum phase of the geological data of estimation;

(6) the spectral amplitude A (ω) that merges phase spectrum φ (ω) and obtain by step (2) estimation, recycling Fourier inversion obtains seismic wavelet to be asked;

(7), to every group of Data duplication above-mentioned steps (2)-(6) that obtain of integrating in step (1), obtain K with the seismic wavelet of spatial variations;

(8) if there is log data in a certain position of real data, utilize well curve as constraint, and by the wavelet of phasescan method estimation seismic trace near well, then using this result as reference, check utilizes above-mentioned steps (1)-(7) to obtain mixed-phase seismic wavelet.

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