CN103777237A - Surface elevation smoothing method based on space-variant weighted banding wave-number domain filtering - Google Patents

Abstract

The invention provides a surface elevation smoothing method based on space-variant weighted banding wave-number domain filtering and belongs to the field of seismic exploration data processing. The method comprises the following steps: (1) carrying out space-variant weighted banding on an original elevation signal x(m) to obtain data x(n) after space-variant weighted banding, wherein m is a natural number from 1 to M, n is a natural number from 1 to N, and M and N are natural numbers; (2) carrying out discrete Fourier forward transform on the data x(n) after space-variant weighted banding to obtain X<wavy line>(omega); (3) determining a filter and carrying out low-pass filtering on the X<wavy line>(omega) to obtain after-filtering data X<^>(omega); (4) carrying out discrete Fourier inverse transform on the after-filtering data X<^>(omega) to obtain X<^>(n); (5) removing data in banding positions at the two ends of X<^>(n), wherein the remaining data X<^>(omega) is the required after-filtering smooth elevation data, and X<^>(omega) is output. By the adoption of the method of the invention, filtered and smoothed elevation is enabled to maintain the low/middle-frequency overall change trend of original data, distortion error at both ends of data is weak, and the elevation value of each point is reliable.

Description

A kind of earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering

Technical field

The invention belongs to seismic prospecting data process field, be specifically related to a kind of earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering.

Background technology

Conventionally the analysis of seismic exploration data speed, stack and the migration and imaging techniques based on level reference, in the face of the often actual conditions of acute variation of earthquake data acquisition earth's surface, field, is generally to carry out pre-service by static correction technology.But the static corrections processing error based on earth's surface-consistent hypothesis in the violent situation of the area surface relief of oil-gas exploration is at present just very large, causes seismic wave field distortion, affects imaging effect and quality.People just research and develop the technology such as floating datum processing, wave equation datuming and true earth's surface migration imaging in succession.Three kinds of methods respectively have relative merits, but no matter which kind of method, for the violent and very coarse earth's surface that rises and falls, geological data all carries out suitably smooth conventionally to original ground surface while processing, this is mainly the radio-frequency component in order to eliminate surface elevation change, keeps the middle lower wave number change component of original ground surface.What now people easily expected is to earth's surface adopt suitable level and smooth radius (3D seismic data needs two level and smooth radiuses of orthogonal directions) to carry out not weighting or weighting level and smooth, but in practical application, a problem is that level and smooth radius is difficult for choosing, particularly for 3D seismic data, topographic relief severe degree is often all different in road direction and line direction, and fixing level and smooth radius can not meet earth's surface elevation amplitude of variation in length and breadth to the situation of space-variant.If it is improper that level and smooth radius is chosen, the position low at earth's surface elevation can produce projection by a narrow margin, and can produce depression by a narrow margin in the high position of earth's surface elevation.Such as, for a just profound curve, when adopting 1.5 times of level and smooth radiuses of wavelength to carry out just there will be when smooth this situation.

Have not yet to see the method and technology of the smooth earth's surface of wavenumber domain filtering elevation.

Summary of the invention

The object of the invention is to solve the difficult problem existing in above-mentioned prior art, a kind of earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering is provided, adopt space-variant weighting fringing method, press apart from inequality proportion weighting (being space-variant weighting), consider the impact of both sides different range data on fringing data, make result keep the variation tendency of raw data low frequency component, a little less than the distortion error of data two ends, it is reliable making the each height value after level and smooth.

The present invention is achieved by the following technical solutions:

Based on an earth's surface elevation smoothing method for space-variant weighting fringing wavenumber domain filtering, said method comprising the steps of:

(1) original elevation signal x (m) is carried out to space-variant weighting fringing and obtain the data x (n) after space-variant weighting fringing; M is 1 to M natural number, and n is 1 to N natural number, and M, N are natural number;

(2) the data x (n) after space-variant weighting fringing being carried out to discrete fourier direct transform obtains

(3) determine wave filter and right

carry out low-pass filtering and obtain filtered data

(4) to filtered data

carrying out discrete fourier inverse transformation obtains

(5) remove after the data of fringing position, middle two ends, remaining data

be exactly required filtered level and smooth altitude figures, will

output.

Described step (1) is specific as follows:

If original elevation signal is x (m)=g _m, total M altitude figures; To the initiating terminal of original elevation signal successively fringing N1 and N2 data, the end of a period of original elevation signal is held to fringing N3 and N4 data successively; After fringing is processed, the altitude figures of M originally expands to N data, is denoted as x (n)=g _n, N=N1+N2+M+N3+N4; N1, N2, N3 and N4 are natural number.

N1, N2, N3 and N4 in described step (1) should elevation change predominant wavelength and adjacent altitude figures level interval ratio 1/4 and 1/3 between.When concrete enforcement, in the time of M < 1000, make N2 ≈ 0.1 × M; In the time of M >=1000, make N2 ≈ 100～150; N1 ≈ 0.2 × N2, N3 ≈ N2, N4 ≈ N1.

In described step (1):

I data in N1 data are:

$x_{N1}^i=x_{N2}^1[0.5+0.5*\cos (\mathrm{\&pi;}(N1-i)/N1)],$ I is 1 to N1 natural number;

I data in N2 data are:

$x_{N2}^i=\frac{1}{N2-i}{\mathrm{\&Sigma;}}_{j=1}^{j=N2-i}x\left(j\right),$ I is 1 to N2 natural number;

I data in N3 data are:

$x_{N3}^i=\frac{1}{i}{\mathrm{\&Sigma;}}_{j=M-1}^{j=M}x\left(j\right),$ I is 1 to N3 natural number;

I data in N4 data are:

$x_{N4}^i=x_{N3}^{N3}[0.5+0.5*\cos (\mathrm{\&pi;}*i/N4)],$ I is 1 to N4 natural number.

Described step (2) is specific as follows:

Data x (n) after space-variant weighting fringing is carried out to the result that discrete fourier direct transform obtains is

signal conversion is expressed as follows:

$x\left(n\right)\stackrel{\mathrm{FFT}}{\&DoubleRightArrow;}\tilde{X}\left(\mathrm{\&omega;}\right)$

Described step (3) is specific as follows:

To wavenumber domain

adopt low-pass filter carry out low-pass filtering and obtain filtered data

formula is as follows:

$\hat{X}\left(\mathrm{\&omega;}\right)=\hat{X}\left(\mathrm{\&omega;}\right)\&CenterDot;\tilde{H}\left(\mathrm{\&omega;}\right)$

$\left|\tilde{H}\left(\mathrm{\&omega;}\right)\right|$

Definite method as follows:

In formula, h _k=0.5+0.5*cos (π * k/ (j-i)), k is 0 to j-i integer, j is natural number, j > i, ω _i, ω _jbe respectively foundation

with the scope to the definite ω of the requirement of elevation signal lower wave number.

Described step (4) is specific as follows:

To data carrying out discrete fourier inverse transformation obtains signal intensity is expressed as follows:

$\hat{X}\left(\mathrm{\&omega;}\right)\stackrel{{\mathrm{FFT}}^{-1}}{\&DoubleRightArrow;}\hat{x}\left(n\right).$

Compared with prior art, the invention has the beneficial effects as follows: utilize the inventive method to make elevation after filtering keep the medium and low frequency general morphologictrend of raw data, a little less than the distortion error of data two ends, the height value of each point is reliable, this is for providing reliable basic data based on smooth earth's surface seismic data processing technology, also for similarly requiring reliable filtering technique that practical new approaches are provided to each sample value.

Accompanying drawing explanation

Fig. 1 is the smooth result of earth's surface elevation wavenumber domain filtering in embodiment, and this figure is to not fringing of raw data.

Fig. 2 is the smooth result of earth's surface elevation wavenumber domain filtering in embodiment, and this figure is to raw data fringing, and fringing signal value is zero.

Fig. 3 is the smooth result of earth's surface elevation wavenumber domain filtering in embodiment, and this figure is to raw data fringing, and left side fringing signal value is the data of raw data high order end, and the right fringing signal value is the data of raw data low order end.

Fig. 4 is the smooth result of earth's surface elevation wavenumber domain filtering in embodiment, this figure is to raw data fringing, left side fringing signal value is that the data of raw data high order end change to zero according to cosine ratio, and the right fringing signal value is that the data of raw data low order end change to zero according to cosine ratio.

Fig. 5 is the smooth result of earth's surface elevation wavenumber domain filtering in embodiment, and this figure is to raw data fringing, and left side fringing signal value is the mirror image result of raw data left end data, and the right fringing signal value is the mirror image result of raw data right-hand member data.

Fig. 6 is the smooth result of earth's surface elevation wavenumber domain filtering in embodiment, and this figure is to raw data fringing, employing be the inventive method.

Fig. 7 is the step block diagram that the present invention is based on the earth's surface elevation smoothing method of space-variant weighting fringing wavenumber domain filtering.

Embodiment

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

The present invention relates to the seismic data processing technology such as floating datum processing based on smooth earth's surface, wave equation datuming and true earth's surface migration imaging, and each sample value is required to reliable filtering technique.

The inventive method comprises the following steps:

(1) original elevation signal is carried out to space-variant weighting fringing and obtain the data x (n) after space-variant weighting fringing if fail to adopt suitable fringing technology, directly adopt wavenumber domain filtering technology to carry out earth's surface elevation level and smooth, in bounds, there will be many exceptional values, if Fig. 2-Fig. 5 in examples of implementation is result, if adopt inappropriate original signal fringing technology, will make the signal at two ends after filtering produce distortion.

The present invention adopts space-variant weighting fringing method, design that to carry out earth's surface elevation based on wavenumber domain filtering technology novel, reasonably space-variant weighting fringing technology level and smooth, make elevation after filtering keep the medium and low frequency general morphologictrend of raw data, a little less than the distortion error of data two ends, the height value of each point is reliable.

Original elevation signal is x (m)=g _m, m=1,2 ..., M.Total M data.To the initiating terminal of signal successively fringing N1 and N2 data, the end of a period of signal is held to fringing N3 and N4 data successively based on raw data.N1, N2, N3 and N4 choose according to the situation analysis of work area scope and altitude figures variation, generally should elevation change predominant wavelength and adjacent altitude figures level interval ratio 1/4 and 1/3 between, when actual use, according to the technical research and the application experience that become image field Fourier transform fringing, face the size of the number of smoothed data, and test result, when M < 1000 (M is generally greater than hundreds of), conventionally make N2 ≈ 0.1 × M; In the time of M >=1000, conventionally make N2 ≈ 100～150, N1 ≈ 0.2 × N2, N3 ≈ N2, N4 ≈ N1.

I data in N2 data are:

$x_{N2}^i=\frac{1}{N2-i}{\mathrm{\&Sigma;}}_{j=1}^{j=N2-i}x\left(j\right),$ i＝1、2、…、N2

I data in N1 data are:

$x_{N1}^i=x_{N2}^1[0.5+0.5*\cos (\mathrm{\&pi;}(N1-i)/N1)],$ i＝1、2、…、N1

I data in N3 data are

$x_{N3}^i=\frac{1}{i}{\mathrm{\&Sigma;}}_{j=M-1}^{j=M}x\left(j\right),$ i＝1、2、…、N3

I data in N4 data are:

$x_{N4}^i=x_{N3}^{N3}[0.5+0.5*\cos (\mathrm{\&pi;}*i/N4)],$ i＝1、2、…、N4

Like this, after fringing is processed, the altitude figures of M originally just expands to N data, is denoted as x (n)=g _n, n=1,2 ..., N, N=N1+N2+M+N3+N4.

(2) the data x (n) after space-variant weighting fringing is carried out to discrete fourier direct transform

Data x (n) after space-variant weighting fringing is carried out to the result that discrete fourier direct transform obtains is

signal conversion is expressed as follows:

$x\left(n\right)\stackrel{\mathrm{FFT}}{\&DoubleRightArrow;}\tilde{X}\left(\mathrm{\&omega;}\right)$

(3) wave filter is determined and filtering

To wavenumber domain adopt low-pass filter carry out low-pass filtering, eliminate the high wave number composition in elevation variation, result is

$\hat{X}\left(\mathrm{\&omega;}\right)=\hat{X}\left(\mathrm{\&omega;}\right)\&CenterDot;\tilde{H}\left(\mathrm{\&omega;}\right)$

$\left|\tilde{H}\left(\mathrm{\&omega;}\right)\right|$

Definite method as follows:

In formula,

H _k=0.5+0.5*cos (π * k/ (j-i)), k=0,1,2,3 ..., j-i, (j > i), ω _i, ω _jbe respectively foundation with the scope to the definite ω of the requirement of elevation signal lower wave number.

(4) Fourier inversion

To the data after low-pass filtering

carry out discrete fourier inverse transformation, result is

signal intensity be expressed as follows:

$\hat{X}\left(\mathrm{\&omega;}\right)\stackrel{{\mathrm{FFT}}^{-1}}{\&DoubleRightArrow;}\hat{x}\left(n\right)$

(5) output net result:

Remove

after the data (being the data at N1, N2, N3 and N4 place) of fringing position, middle two ends, remaining data

(m=1,2 ..., M) be exactly required filtered level and smooth altitude figures, will

output.

According to the inventive method, the actual altitude figures in certain field is processed, comparing result is asked for an interview Fig. 1 to Fig. 6.Wherein, the former data in Fig. 1 do not have fringing, in the each figure of Fig. 2 to Fig. 6 the left side of raw data and right side all carried out reasonably, similar number ground fringing, just definite method of its value is inconsistent, other disposal routes and parameter are all identical.Fine rule in each figure all represents the original elevation on earth's surface, and solid line all refers to the result of each method filtering after smooth.Fig. 1 does not have fringing, processes the value distortion at postamble sequence two ends obviously, and these data can not be used at all.Fig. 2 fringing signal value is zero, and result is with respect to Fig. 1, and the scope of the burst of distortion value slightly restrains oneself, but the distortion of burst endpoints thereof is still obvious, and data after treatment can not be used at all.Fig. 3 left side fringing signal value is the data of raw data high order end, and the right fringing signal value is the data of raw data low order end, and it is larger that result is affected by burst endpoint value.Fig. 4 left side fringing signal value is that the data of raw data high order end change to zero according to cosine ratio, the right fringing signal value is that the data of raw data low order end change to zero according to cosine ratio, it is larger that result is affected by burst endpoint value, and original fringing data variation to zero has affected the irrational variation tendency of net result.Fig. 5 left side fringing signal value is the mirror image result of raw data left end data, and the right fringing signal value is the mirror image result of raw data right-hand member data.It is larger that result is affected by mirror value variation tendency, and the left side value of right-hand member fringing data obviously has the region of individual low amplitude value, and the results change trend that the right side of burst is processed is nearly level, and this is obviously unreasonable.Fig. 6 adopts space-variant weighting fringing method of the present invention, by considered the impact of both sides different range data on fringing data apart from inequality proportion weighting, makes result keep the variation characteristic of raw data, and data two ends distortion error is the most weak.

The technical requirement earth's surfaces such as the processing of geological data floating datum, wave equation datuming and true earth's surface migration imaging are smooth.With the direct smooth earth's surface of suitable level and smooth radius, because topographic relief severe degree is often all different in road direction and line direction, make level and smooth radius can not meet actual requirement.The present invention provides a kind of earth's surface elevation smoothing technique based on space-variant weighting fringing wavenumber domain filtering, and earth's surface elevation Finite Length Signal is transformed to wavenumber domain, adopts low-pass filtering technique to suppress high wave number composition, reaches the object of level and smooth earth's surface elevation.Adopt space-variant weighting fringing method, by apart from inequality proportion weighting, consider the impact of both sides different range data on fringing data, make result keep the variation characteristic of the medium and low frequency composition of raw data, a little less than the distortion error of data two ends, the each height value after level and smooth is reliable.This is for providing reliable basic data based on smooth earth's surface seismic data processing technology, also for similarly requiring reliable filtering technique that practical new approaches are provided to each sample value.

Technique scheme is one embodiment of the present invention, for those skilled in the art, the invention discloses on the basis of application process and principle, be easy to make various types of improvement or distortion, and be not limited only to the described method of the above-mentioned embodiment of the present invention, therefore previously described mode is just preferred, and does not have restrictive meaning.

Claims (7)

1. the earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering, is characterized in that: said method comprising the steps of:

(1) original elevation signal x (m) is carried out to space-variant weighting fringing and obtain the data x (n) after space-variant weighting fringing; M is 1 to M natural number, and n is 1 to N natural number, and M, N are natural number;

(2) the data x (n) after space-variant weighting fringing being carried out to discrete fourier direct transform obtains

(3) determine wave filter and right

carry out low-pass filtering and obtain filtered data

(4) to filtered data

carrying out discrete fourier inverse transformation obtains

(5) remove

after the data of fringing position, middle two ends, remaining data

be exactly required filtered level and smooth altitude figures, will

output.

2. the earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering according to claim 1, is characterized in that: described step (1) is specific as follows:

If original elevation signal is x (m)=g _m, total M altitude figures; To the initiating terminal of original elevation signal successively fringing N1 and N2 data, the end of a period of original elevation signal is held to fringing N3 and N4 data successively; After fringing is processed, the altitude figures of M originally expands to N data, is denoted as x (n)=g _n, N=N1+N2+M+N3+N4; N1, N2, N3 and N4 are natural number.

3. the earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering according to claim 2, is characterized in that: in described step (1), in the time of M < 1000, make N2 ≈ 0.1 × M; In the time of M >=1000, make N2 ≈ 100～150; N1 ≈ 0.2 × N2, N3 ≈ N2, N4 ≈ N1.

4. the earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering according to claim 3, is characterized in that: in described step (1):

I data in N1 data are:

$x_{N1}^i=x_{N2}^1[0.5+0.5*\cos (\mathrm{\&pi;}(N1-i)/N1)],$ I is 1 to N1 natural number;

I data in N2 data are:

$x_{N2}^i=\frac{1}{N2-i}{\mathrm{\&Sigma;}}_{j=1}^{j=N2-i}x\left(j\right),$ I is 1 to N2 natural number;

I data in N3 data are:

$x_{N3}^i=\frac{1}{i}{\mathrm{\&Sigma;}}_{j=M-1}^{j=M}x\left(j\right),$ I is 1 to N3 natural number;

I data in N4 data are:

$x_{N4}^i=x_{N3}^{N3}[0.5+0.5*\cos (\mathrm{\&pi;}*i/N4)],$ I is 1 to N4 natural number.

5. the earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering according to claim 4, is characterized in that: described step (2) is specific as follows:

Data x (n) after space-variant weighting fringing is carried out to the result that discrete fourier direct transform obtains is

signal conversion is expressed as follows:

$x\left(n\right)\stackrel{\mathrm{FFT}}{\&DoubleRightArrow;}\tilde{X}\left(\mathrm{\&omega;}\right).$

6. the earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering according to claim 5, is characterized in that: described step (3) is specific as follows:

To wavenumber domain

adopt low-pass filter

carry out low-pass filtering and obtain filtered data

formula is as follows:

$\hat{X}\left(\mathrm{\&omega;}\right)=\hat{X}\left(\mathrm{\&omega;}\right)\&CenterDot;\tilde{H}\left(\mathrm{\&omega;}\right)$

$\left|\tilde{H}\left(\mathrm{\&omega;}\right)\right|$

Definite method as follows:

In formula, h _k=0.5+0.5*cos (π * k/ (j-i)), k is 0 to j-i integer, j is natural number, j > i, ω _i, ω _jbe respectively foundation

with the scope to the definite ω of the requirement of elevation signal lower wave number.

7. the earth's surface elevation smoothing method based on space-variant weighting fringing wavenumber domain filtering according to claim 6, is characterized in that: described step (4) is specific as follows:

To data

carrying out discrete fourier inverse transformation obtains

signal intensity is expressed as follows:

$\hat{X}\left(\mathrm{\&omega;}\right)\stackrel{{\mathrm{FFT}}^{-1}}{\&DoubleRightArrow;}\hat{x}\left(n\right).$

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