CN109975868A - A kind of wave equation ghost reflection drawing method based on Taylor expansion - Google Patents
A kind of wave equation ghost reflection drawing method based on Taylor expansion Download PDFInfo
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- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
- G01V1/282—Application of seismic models, synthetic seismograms
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- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
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Abstract
The present invention relates to a kind of wave equation ghost reflection drawing method based on Taylor expansion, characterized by the following steps: the seismic data containing ghost reflection (1) is expressed as to the superposition of primary wave and ghost reflection, obtains the primary wave expression formula indicated by ghost reflection operator G；(2) ghost reflection operator G is based on Taylor expansion, obtains the primary wave expression formula indicated by wave field extrapolation matrix F；(3) wave field extrapolation matrix F is calculated, and is substituted into the primary wave expression formula in step (2), obtains the pressed primary wave of ghost reflection.The present invention can be widely applied to the ghost reflection compacting field of seismic data.
Description
Technical field
The present invention relates to a kind of wave equation ghost reflection drawing method based on Taylor expansion belongs to seism processing neck
Domain.
Background technique
At sea during streamer seismic data collection, towing cable is typically disposed in certain depth under sea level, due to sea level
Strong reflection, towing cable collection records very strong ghosting, causes seismic data frequency spectrum that trap effect occurs, greatly affected number
According to quality, this ghosting is generally known as ghost reflection by seismic prospecting.Ghost reflection cannot generally be imaged well, will lead to migrated section
There are a large amount of migration noises.Therefore ghost reflection compacting is a key link of offshore seismic exploration data processing.
Last decade obtains broadband seismic data to effectively suppress ghost reflection, a series of ghost reflection compact techniques occurs.This
A little technologies can be generally divided into two classes: (1) related to acquisition mode, upper and lower source acquisition, the acquisition of upper and lower cable, double inspections acquisition, towing cable
Three-component acquisition, submarine cable acquisition (OBC), the acquisition of varying depth cable etc., mainly cooperate needle by special acquisition mode again
To the processing means of property, realizes effective compacting of ghost reflection, widen the frequency range of seismic data.These special acquisition modes by
The control difficulty increase of focus, cable into many restrictions of field work condition, such as field acquisition implementation process, to draw
Play the significantly promotion of acquisition expense；(2) related to processing technique, common method is that ghost reflection compacting is regarded as an inverting to ask
Topic carries out least square solution.Because ghost reflection operator is directly inverted there are singularity problem, solved to stablize, it is common to do
Method is to carry out regularization constraint, but this method causes ghost reflection compacting precision to reduce, after compacting because of the introducing of regularization term
Data noise is relatively low.
Summary of the invention
In view of the above-mentioned problems, the object of the present invention is to provide a kind of wave equation ghost reflection compacting side based on Taylor expansion
The high-precision compacting of ghost reflection may be implemented in method, the method for the present invention, and compared to traditional ghost reflection drawing method, the present invention suppresses ghost reflection result
More fidelity, signal-to-noise ratio are higher.
To achieve the above object, the present invention takes following technical scheme: a kind of wave equation ghost reflection based on Taylor expansion
Drawing method comprising following steps:
(1) seismic data containing ghost reflection is expressed as to the superposition of primary wave and ghost reflection, is obtained by ghost reflection operator G expression
Primary wave expression formula；
(2) ghost reflection operator G is based on Taylor expansion, obtains the primary wave expression formula indicated by wave field extrapolation matrix F；
(3) wave field extrapolation matrix F is calculated, and is substituted into the primary wave expression formula in step (2), obtains ghost reflection pressure
Primary wave after system.
Further, in the step (2), the primary wave expression formula indicated by wave field extrapolation matrix F are as follows:
P=(1+F+F2+ ...) d,
Wherein, p is primary wave, and d is the seismic data containing ghost reflection.
Further, in the step (3), method that wave field extrapolation matrix F is calculated, comprising the following steps:
(3.1) by towing cable face Γ0Record wave field p (r ') along Z axis upward continuation to sea level Γ1, sea level is calculated
Γ1Wave field p (r) at upper r, the wave field p (r) are indicated using record wave field p (r ') and its integrated form of normal derivative；
(3.2) set the medium between towing cable face and sea level be it is uniform, then approximation obtains towing cable face Γ0Record wave field
The normal derivative of p (r ')；
(3.3) Green's function is indicated under three-dimensional situation, obtains the three-dimensional expression formula of Green's function；
(3.4) by towing cable face Γ obtained in step (3.2) and step (3.3)0Record wave field p (r ') normal derivative
And the three-dimensional expression formula of Green's function substitutes into step (3.1), obtains the wave field p on the sea level without normal derivative at r
(r) integral equation；
(3.5) wave field p (r) integral equation on the sea level in step (3.4) at r is subjected to discretization, can be obtained
Wave field extrapolation matrix F.
Further, in the step (3.1), sea level Γ1Wave field p (r) at upper r are as follows:
Wherein, G (r, r ') is Green's function,Indicate normal derivative.
Further, in the step (3.2), the normal derivative of wave field p (r ') is recorded are as follows:
Wherein, angle of the θ between boundary normal direction and propagation path r-r ',For background wave number, c0For back
Scape speed, ω are angular frequency.
Further, in the step (3.3), the three-dimensional expression formula of Green's function are as follows:
Further, in the step (3.4), the integral side of the wave field p (r) on the sea level without normal derivative at r
Journey are as follows:
Wherein, r=| r-r ' |,
The invention adopts the above technical scheme, which has the following advantages: the present invention uses the wave based on Taylor expansion
Dynamic equation is indicated the seismic data containing ghost reflection, avoids singularity problem when directly inverting to ghost reflection operator,
Simultaneously avoid in conventional method due to introduce regularization term caused by ghost reflection compacting precision it is low, data noise compares after compacting
Low disadvantage, the present invention calculate simply, suppress ghost reflection result more fidelity, and signal-to-noise ratio is higher, can be widely applied to ghost reflection compacting
Technical field.
Detailed description of the invention
Fig. 1 is rate pattern, upward triangle expression focus in figure, downward triangle expression wave detector；
Fig. 2 a is recording containing ghost reflection for wave equation synthesis；
Fig. 2 b is wave equation synthesis without ghost reflection record (as reference)；
Fig. 3 a is to suppress ghost reflection result using conventional method；
Fig. 3 b is to suppress ghost reflection result using the method for the present invention.
Specific embodiment
The present invention is described in detail below with reference to the accompanying drawings and embodiments.
A kind of wave equation ghost reflection drawing method based on Taylor expansion provided by the invention, comprising the following steps:
(1) seismic data containing ghost reflection is expressed as to the superposition of primary wave and ghost reflection, is obtained by ghost reflection operator G expression
Primary wave expression formula.
Seismic data with ghost reflection can be considered as the superposition of primary wave p and ghost reflection g, i.e.,
D=p+g=(I+RF) p=Gp (1)
Wherein, F indicates that wave field extrapolation matrix, R indicate the reflection coefficient on sea level, usually assumes that being equal to -1, G indicates ghost reflection
Operator.It is recorded in order to obtain without ghost reflection, needs to invert to ghost reflection operator G, directly inverting to ghost reflection operator G, there are unusual
Property (denominator 0), it is common practice on denominator plus a regularization term, i.e.,
Wherein, ε is a small positive number.Formula (2) is conventional ghost reflection compacting algorithm, and this method overcomes singularity
Stable ghost reflection compacting may be implemented in problem, but because the operator of formula (2) is not fully equal to the inverse of ghost reflection operator, because
It is lower that this ghost reflection suppresses precision.
(2) ghost reflection operator G is based on Taylor expansion, obtains the primary wave expression formula indicated by wave field extrapolation matrix F.
It, can be by following Taylor expansion back and forth by formula (1) it is found that inverse 1/ (I-F) of ghost reflection operator G=(I-F)
Keep away singularity problem:
Formula (3) are substituted into formula (1), obtain the primary wave p expression formula indicated by wave field extrapolation matrix F:
P=(1+F+F2+…)d (4)
It is found that formula (4) is a kind of stable inversion operator, solves and need explicit characterization wave field extrapolation matrix F.
(3) wave field extrapolation matrix F is calculated, and is substituted into the primary wave expression formula in step (2), obtains ghost reflection pressure
Primary wave after system.
Specifically, the following steps are included:
(3.1) by towing cable face Γ0Record wave field p (r ') along Z axis upward continuation to sea level Γ1, sea level is calculated
Γ1Wave field p (r) at upper r, wherein Z axis indicates depth direction, and X-axis and Y-axis indicate horizontal direction.
Wave field p (r) is indicated using record wave field p (r ') and its integrated form of normal derivative, it may be assumed that
Wherein, G (r, r ') is Green's function,Indicate normal derivative.
(3.2) assume the medium (i.e. sea water layer) between towing cable face and sea level be it is uniform, then can approximation obtain towing cable
Face Γ0Record wave field p (r ') normal derivative.
In order to calculate the wave field u (r) at r, need to know towing cable face Γ0Upper wave field u (r ') and its normal derivative
But usually we only record wave field value p (r '), lack the record of normal derivative.In order to carry out real data using equation (5)
Wave field extrapolation, need to simplify formula (5).Ignore towing cable face Γ0With sea level Γ1Between multiple reflections, marking wave
The normal derivative of field p (r ') can be with approximate representation are as follows:
Wherein, angle of the θ between boundary normal direction and propagation path r-r ',For background wave number, c0For back
Scape speed, ω are angular frequency.
(3.3) Green's function is indicated under three-dimensional situation, obtains its calculating formula:
(3.4) by towing cable face Γ obtained in step (3.2) and step (3.3)0Record wave field p (r ') normal derivative
And the three-dimensional expression formula of Green's function substitutes into step (3.1), obtains the wave field p on the sea level without normal derivative at r
(r) integral equation:
Wherein, r=| r-r ' |,
(3.5) wave field p (r) integral equation on the sea level in step (3.4) at r is subjected to discretization, can be obtained
Wave field extrapolation matrix F.
Wave field p (r) integral equation is subjected to discretization, is obtained:
P (r)=Fp (r ') (9)
In conjunction with formula (8) and (9), wave field extrapolation matrix F can be obtained.
The method of the present invention is described further combined with specific embodiments below.
1) Wave equation forward modeling
As shown in Figure 1, being the half space rate pattern of input, wherein the upward triangle in direction indicates focus, focus letter
Number is the Ricker wavelet of dominant frequency 15Hz.Wave detector (the downward triangle in direction in figure) is located under sea level depth z=50m
It sets.It chooses suitable parameter and carries out forward simulation, available earthquake record as shown in Figure 2, wherein Fig. 2 a indicates to contain ghost reflection
Earthquake record, Fig. 2 b indicate be free of ghost reflection earthquake record.Sea surface ghost (ghost is apparent that from earthquake record
Wave) it is superimposed upon on primary wave.The purpose of wave equation ghost reflection compacting is obtained from the earthquake record containing ghost reflection shown in Fig. 2 a
To the earthquake record for being free of ghost reflection shown in Fig. 2 b.
2) compacting of high-precision ghost reflection is realized based on formula (4)
As shown in Figure 3a and Figure 3b shows, the method for the present invention and conventional method (based on equation (2)) is respectively adopted to shown in Fig. 2 a
Earthquake record containing ghost reflection carry out ghost reflection compacting, wherein the ghost reflection compacting result of conventional method is as shown in Figure 3a, side of the present invention
The ghost reflection compacting result of method is as shown in Figure 3b.By being compared with Fig. 2 b, it can be seen that wave equation ghost proposed by the present invention
Wave drawing method can carry out high-precision ghost reflection compacting, and pressed record is almost completely the same with desired result.From section
The upper conventional algorithm that can be seen that can restore primary wave, but there are more noises for output result, this is because regularization
The introducing bring of item.
The result of Numerical Experiment illustrates having for wave equation ghost reflection compact technique of the application based on Taylor expansion
Effect property and superiority.
The various embodiments described above are merely to illustrate the present invention, wherein the structure of each component, connection type and manufacture craft etc. are all
It can be varied, all equivalents and improvement carried out based on the technical solution of the present invention should not exclude
Except protection scope of the present invention.
Claims (7)
1. a kind of wave equation ghost reflection drawing method based on Taylor expansion, it is characterised in that the following steps are included:
(1) seismic data containing ghost reflection is expressed as to the superposition of primary wave and ghost reflection, obtains indicating primary by ghost reflection operator G
Wave expression formula；
(2) ghost reflection operator G is based on Taylor expansion, obtains the primary wave expression formula indicated by wave field extrapolation matrix F；
(3) wave field extrapolation matrix F is calculated, and is substituted into the primary wave expression formula in step (2), after obtaining ghost reflection compacting
Primary wave.
2. a kind of wave equation ghost reflection drawing method based on Taylor expansion as described in claim 1, it is characterised in that: described
In step (2), the primary wave expression formula indicated by wave field extrapolation matrix F are as follows:
P=(1+F+F2+ ...) d,
Wherein, p is primary wave, and d is the seismic data containing ghost reflection.
3. a kind of wave equation ghost reflection drawing method based on Taylor expansion as described in claim 1, it is characterised in that: described
In step (3), method that wave field extrapolation matrix F is calculated, comprising the following steps:
(3.1) by towing cable face Γ0Record wave field p (r ') along Z axis upward continuation to sea level Γ1, sea level Γ is calculated1
Wave field p (r) at upper r, the wave field p (r) are indicated using record wave field p (r ') and its integrated form of normal derivative；
(3.2) set the medium between towing cable face and sea level be it is uniform, then approximation obtains towing cable face Γ0Record wave field p (r ')
Normal derivative；
(3.3) Green's function is indicated under three-dimensional situation, obtains the three-dimensional expression formula of Green's function；
(3.4) by towing cable face Γ obtained in step (3.2) and step (3.3)0Record wave field p (r ') normal derivative and
The three-dimensional expression formula of Green's function substitutes into step (3.1), obtains the wave field p's (r) on the sea level without normal derivative at r
Integral equation；
(3.5) wave field p (r) integral equation on the sea level in step (3.4) at r is subjected to discretization, wave field can be obtained
Extended Matrix F.
4. a kind of wave equation ghost reflection drawing method based on Taylor expansion as claimed in claim 3, it is characterised in that: described
In step (3.1), sea level Γ1Wave field p (r) at upper r are as follows:
Wherein, G (r, r ') is Green's function,Indicate normal derivative.
5. a kind of wave equation ghost reflection drawing method based on Taylor expansion as claimed in claim 3, it is characterised in that: described
In step (3.2), the normal derivative of wave field p (r ') is recorded are as follows:
Wherein, angle of the θ between boundary normal direction and propagation path r-r ',For background wave number, c0For background speed
Degree, ω is angular frequency.
6. a kind of wave equation ghost reflection drawing method based on Taylor expansion as claimed in claim 3, it is characterised in that: described
In step (3.3), the three-dimensional expression formula of Green's function are as follows:
7. a kind of wave equation ghost reflection drawing method based on Taylor expansion as claimed in claim 3, it is characterised in that: described
In step (3.4), the integral equation of the wave field p (r) on the sea level without normal derivative at r are as follows:
Wherein, r=| r-r ' |,
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| CN111830566A (en) * | 2020-06-12 | 2020-10-27 | 中国海洋大学 | Parameter matching virtual reflection suppression method and marine seismic exploration system |
| CN114355450A (en) * | 2022-03-21 | 2022-04-15 | 中国石油大学(华东) | Method, system and equipment for suppressing ghost waves of marine plough type cable full waveform inversion |
| CN117148443A (en) * | 2023-10-27 | 2023-12-01 | 胜利信科(山东)勘察测绘有限公司 | Shallow profile data signal-to-noise ratio enhancement method based on ghost wave extraction and conversion |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111830566A (en) * | 2020-06-12 | 2020-10-27 | 中国海洋大学 | Parameter matching virtual reflection suppression method and marine seismic exploration system |
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