CN105093322B - A kind of mirror image boundary calculation method - Google Patents
A kind of mirror image boundary calculation method Download PDFInfo
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Abstract
The invention provides a kind of mirror image boundary calculation method, belong to the digital processing fields such as seismic prospecting data processing.The characteristics of this method is using data edge signal calculates its image signal to carry out flared end；Comprise the following steps：(1) original earthquake alarm collection or trace gather data, i.e. original matrix S are inputted, S size is m sampled point, and the size of n seismic channel, i.e. S is m × n；(2) big matrix S is built1：To original matrix S, H point is respectively expanded along the top in sampled point direction and low side, respectively expands K point along the left side and the right in seismic channel direction, then obtains the geological data after flared end, i.e., big matrix S1, S1Size be (m+2*H) × (n+2*K)；(3) iteration pointwise asks for the new mirror image for expanding data and is worth to big matrix S1；(4) to the big matrix S1Numerical operation is carried out, then the result after computing is removed to the side of expansion, that is, obtains the result after computing.
Description
Technical field
The invention belongs to the digital processing fields such as seismic prospecting data processing, and in particular to a kind of mirror image feature modeling
Method.
Background technology
In geophysical signal processing, because the finiteness of computational fields to use suitable at free boundary
ARTIFICIAL BOUNDARY, Artificial Boundaries are almost related to the links of seismic data processing, and inappropriate ARTIFICIAL BOUNDARY can drop
Low computational accuracy, upset result of calculation, result even in calculating diverging, this logarithm value simulation wave field and Various types of data processing method
In it is particularly important.
Nonreflecting boundary condition is most widely used under normal circumstances, is broadly divided into absorbing boundary, signature analysis
The application of border and progressive solution boundary condition etc., wherein absorbing boundary is than wide, and scientific workers have done greatly in this regard
Work is measured, wherein the most typically having Newtonian damping absorbing boundary condition and PML boundary conditions.Israeli＆Orszag is proposed
Classical Newtonian damping absorbing boundary condition, form is simple, using relatively broad, but its precision and steady in actual use
It is qualitative general, and it is strongly depend on the experience of user.PML is a kind of zero recoil fraction technology grown up in recent years,
PML boundary conditions are generalized to full Euler equations by Hu, and Parrish＆Hu develops into PML suitable for without viscous, oblique mean flow afterwards
Situation.Hu et al. is established on Research foundation before again considers non-conservation suitable for full Euler and Navier-Stok
The popularity of form Euler equations application, the non-linear PML equations of conservation form of Lines equations.In view of non-conservation form
The popularity of Euler equations application, Lin et al. has developed the non-linear PML equations of corresponding non-conservation type, further expands
The use scope of PML boundary conditions.PML boundary conditions have good stability and precision, but are due to that form is more complicated, need
Extra auxiliary variable and equation are introduced, increase is calculated into internal memory and amount of calculation in the application.
Geophysical signal processing in, due to the finiteness of data, often there is border issue, if be not added with border or
Border add it is undesirable if, may cause signal processing results distortion or distortion, produce serious boundary effect.
The content of the invention
It is an object of the invention to solve problem present in above-mentioned prior art, there is provided a kind of mirror image feature modeling side
Method, its image signal is calculated the characteristics of using data edge signal and carries out flared end, traditional boundary pattern is improved, reached preferably
Treatment effect.
The present invention is achieved by the following technical solutions：
A kind of mirror image boundary calculation method, calculates its image signal to carry out flared end the characteristics of using data edge signal；
Methods described includes：
(1) original earthquake alarm collection or trace gather data, i.e. original matrix S are inputted, S size is m sampled point, n
The size of seismic channel, i.e. S is m × n；
(2) big matrix S is built1：
To original matrix S, H point is respectively expanded along the top and bottom in sampled point direction, along the left side and the right side in seismic channel direction
K point is respectively expanded on side, then obtains the geological data after flared end, i.e., big matrix S1, S1Size be (m+2*H) × (n+2*K)；
(3) iteration pointwise asks for the new mirror image for expanding data and is worth to big matrix S1；
(4) to the big matrix S1Numerical operation is carried out, then the result after computing is removed to the side of expansion, that is, obtains computing
Result afterwards.
What the step (3) was realized in：
(31) value of clear area is asked for along sampled point direction mirror picture：
S is put into big matrix S1Center, extract S Zhong the i-th roads, it is assumed that the coboundary point in the road is j, then Si,j
For S i-th road the top border a point；To S1For, Si,jIt is its internal point, formula (7) is utilized together to every
The value of clear area is asked for along sampled point direction mirror picture：
Si,j-k=Si,j+k k≤H (7)
The calculating on the border in all roads in sampled point direction is completed, now S size is (m+2*H) × n；
(32) value of clear area is asked for along road direction mirror picture：
S is put into big matrix S1Center, extract S in each road of t value, it is assumed that the left boundary in the road
Point is p, then St,pFor S t Far Left border a point；To S1For, St,pIt is its internal point, to per a period of time
Carve the value for asking for clear area along road direction mirror picture using formula (8)：
St,p-q=St,p+q q≤K (8)
The calculating on the border at road direction all moment is completed, now S size is (m+2*H) × (n+2*K).
The side that the result after computing removes expansion being realized in the step (4)：With big matrix S1Center
The central point as matrix of consequence is put, from the big matrix S after flared end1Middle extraction and original matrix S-phase people having a common goal number and sampled point
Matrix.
Compared with prior art, the beneficial effects of the invention are as follows：From the point of view of simulation seismic data noise attenuation effect, this method tool
There is the obvious advantage for removing boundary effect, have obvious excellent relative to traditional be not added with border, null value and random noise border
Gesture.
Brief description of the drawings
Fig. 1 builds big matrix schematic diagram
The step block diagram of Fig. 2 the inventive method
Original analog trace gather in the denoising effect figure of Fig. 3-1 simulation geological data mirror images border
The trace gather after non-edged circle denoising in the denoising effect figure of Fig. 3-2 simulation geological data mirror images border
In the denoising effect figure of Fig. 3-3 simulation geological data mirror images border plus trace gather after null boundary denoising
In the denoising effect figure of Fig. 3-4 simulation geological data mirror images border plus trace gather after RANDOM BOUNDARY denoising
In the denoising effect figure of Fig. 3-5 simulation geological data mirror images border plus trace gather after the denoising of mirror image border
Original analog trace gather in Fig. 4-1 simulation geological data mirror image border denoising amplification effect figures
The trace gather after non-edged circle denoising in Fig. 4-2 simulation geological data mirror image border denoising amplification effect figures
In Fig. 4-3 simulation geological data mirror image border denoising amplification effect figures plus trace gather after null boundary denoising
In Fig. 4-4 simulation geological data mirror image border denoising amplification effect figures plus trace gather after RANDOM BOUNDARY denoising
In Fig. 4-5 simulation geological data mirror image border denoising amplification effect figures plus trace gather after the denoising of mirror image border
Original analog trace gather in the denoising effect figure of Fig. 5-1 actual seismic data images border
The trace gather after non-edged circle denoising in the denoising effect figure of Fig. 5-2 actual seismic data images border
Trace gather after in the denoising effect figure of Fig. 5-3 actual seismic data images border plus null boundary denoising
Trace gather after in the denoising effect figure of Fig. 5-4 actual seismic data images border plus RANDOM BOUNDARY denoising
Trace gather after in the denoising effect figure of Fig. 5-5 actual seismic data images border plus mirror image border denoising
Original analog trace gather in Fig. 6-1 actual seismic data image border denoising amplification effect figures
The trace gather after non-edged circle denoising in Fig. 6-2 actual seismic data image border denoising amplification effect figures
Trace gather after in Fig. 6-3 actual seismic data image border denoising amplification effect figures plus null boundary denoising
Trace gather after in Fig. 6-4 actual seismic data image border denoising amplification effect figures plus RANDOM BOUNDARY denoising
Trace gather after in Fig. 6-5 actual seismic data image border denoising amplification effect figures plus mirror image border denoising
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings：
The characteristics of a kind of mirror image boundary calculation method described in the invention, foundation margin signal, calculates its image signal and enters
Row flared end, belongs to the first.
The present invention provides a kind of flared end mode for signal transacting, and implementing step is：
(1) classical absorbing boundary technology
The application of classical absorbing boundary is main in wave-field simulation and wave field description, and the cutoff boundary face of wave field is generally off-site from
Focus, therefore near cutoff boundary face, wave field meets wave equation.Make shown in operator L such as formulas (1).
In formula, x, y and z are spatial coordinates variable, and t is time variable, and v is the spread speed of ripple, and P (x, z, t) is compression
Wave field (P ripples).
Then have near cutoff boundary face：
LP (x, y, z, t)=0 (2)
Operator L is decomposed：
L=L-L+ (3)
Wherein：
If wherein B.Engquuist et al. it has been proved that P any angle is incided on the interface x=0 of the zoning left side
Left outside traveling wave, then have：
L-P (x, y, z, t)=0 (5)
This incidence wave will all be absorbed without causing any reflection, therefore formula (5) can be as on left boundary x=0
Accurate absorbing boundary condition.Similarly, if P is to incide interface x=x on the right of zoning with any angle0On the outer traveling wave in the right side
L+P (x, y, z, t)=0 (6)
The right interface x=x can be used as0On accurate absorbing boundary condition.But L-And L+Right lateral ripple can not be absorbed respectively
With left lateral ripple, therefore they are called individual event wave operator.
A kind of mirror image boundary calculation method of the present invention, is mainly used in border issue during data processing, to by data meter
Data skew caused by calculating border has improvement result.
(2) technical thought and technology are realized
The present invention provides a kind of mirror image border reinforcement technology computing method for data flared end.
Existing Boundary algorithm when being applied to data processing is often present the problem of only alleviate boundary effect, removes
Boundary effect is not thorough, the characteristics of present invention has similitude using adjacent signals, and its mirror image number is asked for using data boundary
According to, and then flared end is carried out to whole data, the big data after flared end is subjected to Various types of data processing again, finally by the knot after processing
Fruit carries out trimming processing, the result data without boundary effect after being handled.
As shown in Fig. 2 the step that implements of the inventive method is：
Step one：Build big matrix
It is assumed that S is original earthquake big gun collection or trace gather data, size is m sampled point, and the size of n seismic channel, i.e. S is m
×n.Newly set up a matrix S1, the matrix is the geological data after flared end, if respectively expanding H along sampled point direction top and bottom
Point, respectively expands K point, then S along the seismic channel direction left side and the right1Size be (m+2*H) × (n+2*K), as shown in Figure 1 shows
It is intended to.
Step 2：The new mirror value for expanding data is asked in iteration pointwise
S is put into big matrix S1Center, extract S Zhong the i-th roads, it is assumed that the coboundary point in the road is j, then Si,j
For S i-th road the top border a point.To S1For, Si,jIt is its internal point, is asked along sampled point direction mirror picture
Take the value of clear area, calculation formula such as formula (7).
Si,j-k=Si,j+k k≤H (7)
S is obtained thus, it is possible to calculatei,j-1=Si,j+1,Si,j-2=Si,j+2,…,Si,j-H=Si,j+H, pointwise asks for nil trace
Value.Calculating successively by road repetition above, obtains clear area again, completes the calculating on the border in all roads in sampled point direction, this
When S size be (m+2*H) × n.After the flared end algorithm for completing sampled point direction, Zai Yan roads direction is entered with same method to it
Row mirror image flared end, now S size is (m+2*H) × (n+2*K), specific as follows：
S is put into big matrix S1Center, extract S in each road of t value, it is assumed that the left boundary in the road
Point is p, then St,pFor S t Far Left border a point；To S1For, St,pIt is its internal point, to per a period of time
Carve the value for asking for clear area along sampled point direction mirror picture using formula (8)：
St,p-q=St,p+q q≤K (8)
Each moment repeats, i.e. the t1 moment is complete, then calculates the t2 moment, calculates one by one, as shown in figure 1, K is horizontal expansion
Side, H is longitudinal flared end, completes the calculating on all borders in road direction, and now S size is (m+2*H) × (n+2*K).
Step 3：Numerical operation is carried out to the big data after flared end
After the algorithm for completing step 2, data will become the matrix that a size is (m+2*H) × (n+2*K), to the square
Battle array carry out numerical operation (it is common as linear Solving Nonlinear Equation, matrix operation, interpolation, numerical integration, be fitted, ask extreme value,
Mathematic(al) manipulation and filtering etc., according to the difference of purpose, using different numerical operation methods, the present invention is made using medium filtering
For an application verification to presently disclosed method.), the result after computing is removed into the side of expansion (with the center of big matrix
Point extracts the matrix with original matrix identical size as the central point of matrix of consequence from the big matrix after flared end.), i.e.,
Obtain the result after computing.The present invention is analyzed this algorithm and application effect using medium filtering.
By theoretical model and actual seismic data test, this method removes boundary effect substantially, is directed to stronger
Property.
Such as Fig. 3-1 to Fig. 3-5 is simulation geological data mirror image border denoising effect figure, and Fig. 3-1 is original analog trace gather, altogether
There are 2 reflecting layer, respectively at 1000ms and 2000ms, totally 3000 sampling points, 27 roads, sample rate is 1ms, and the noise of addition is
Random noise.Fig. 3-2 is that non-edged circle directly carries out the trace gather after medium filtering denoising, it can be seen that the trace gather noise after denoising
Than improving, but boundary has signal distortion phenomenon.Fig. 3-3 is to add the trace gather after null boundary denoising, it can be seen that after denoising
Signal to noise ratio is equally improved, and the signal of boundary still has a phenomenon of distortion, and the value of boundary almost levels off to zero.Fig. 3-4
To add the trace gather after RANDOM BOUNDARY denoising, it can be seen that the trace gather signal to noise ratio after denoising is improved, the boundary effect of boundary compared with
Gently.Fig. 3-5 adds the trace gather after the denoising of mirror image border, and trace gather shows that the effect of boundary further mitigates.In order to more clearly show
Show boundary effect, enlarged drawing 3-1 is simulation geological data mirror image border denoising amplification effect figure to Fig. 3-5, Fig. 4-1 to Fig. 4-5,
Fig. 4-1 is original analog trace gather, and Fig. 4-2 is that non-edged circle directly carries out the trace gather after medium filtering denoising, the red of boundary
Inframe signal there occurs obvious distortion, and this is very unfavorable to subsequent treatment, and Fig. 4-3 is to add the road after null boundary denoising
Collection, in red block signal have level off to zero phenomenon, the loss to signal is more serious, Fig. 4-4 for plus RANDOM BOUNDARY denoising after
Trace gather, the boundary effect of boundary is lighter, Fig. 4-5 for plus the denoising of mirror image border after trace gather, trace gather shows the effect of boundary
Should further it mitigate, denoising effect is obvious.
BORDER PROCESSING effect analysis is carried out to actual seismic data using the method for the present invention, such as Fig. 5-1 to Fig. 5-5 institutes
Show, Fig. 5-1 is original analog trace gather, Fig. 5-2 is that non-edged circle directly carries out the trace gather after medium filtering denoising, it can be seen that no
Only there is distortion phenomenon on border, and whole denoising section effect is also undesirable, and Fig. 5-3 is to add the trace gather after null boundary denoising, border
The signal at place has loss phenomenon, and denoising effect makes moderate progress, and Fig. 5-4 is to add the trace gather after RANDOM BOUNDARY denoising, the side of boundary
Boundary's effect is lighter, and denoising effect further improves, and Fig. 5-5 is adds the trace gather after the denoising of mirror image border, and trace gather, which is shown almost, not to be had
Boundary effect, substantially, the injury to useful signal is also smaller for denoising effect.Fig. 6-1 to Fig. 6-5 is the actual seismic money after amplification
Expect BORDER PROCESSING effect, contrast is found, plus Fig. 6-5 denoising effects on mirror image border are best, almost without boundary effect, signal to noise ratio
It is greatly improved.
The characteristics of purpose of the present invention is using data edge signal calculates its image signal and carries out flared end, improves tradition
Boundary scheme, has reached preferable treatment effect.The characteristics of present invention has similitude using adjacent signals, utilizes data boundary
Its mirror image data is asked for, and then flared end is carried out to whole data, the big data after flared end Various types of data processing is subjected to again, finally
Result after processing is subjected to trimming processing, the result data without boundary effect after being handled.
Above-mentioned technical proposal is one embodiment of the present invention, for those skilled in the art, at this
On the basis of disclosure of the invention application process and principle, it is easy to make various types of improvement or deformation, this is not limited solely to
Invent the method described by above-mentioned embodiment, therefore previously described mode is preferred, and and without limitation
The meaning of property.
Claims (3)
1. a kind of mirror image boundary calculation method, it is characterised in that：The characteristics of methods described utilizes data edge signal calculates its mirror
Flared end is carried out as signal；
Methods described includes：
(1) original earthquake alarm collection or trace gather data, i.e. original matrix S are inputted, S size is m sampled point, n earthquake
The size in road, i.e. S is m × n；
(2) big matrix S is built1：
To original matrix S, H point is respectively expanded along the top and bottom in sampled point direction, it is each along the left side and the right in seismic channel direction
Expand K point, then obtain the geological data after flared end, i.e., big matrix S1, S1Size be (m+2*H) × (n+2*K)；
(3) iteration pointwise asks for the new mirror image for expanding data and is worth to big matrix S1；
(4) to the big matrix S1Numerical operation is carried out, then the result after computing is removed to the side of expansion, that is, is obtained after computing
As a result.
2. mirror image boundary calculation method according to claim 1, it is characterised in that：What the step (3) was realized in：
What the step (3) was realized in：
(31) value of clear area is asked for along sampled point direction mirror picture：
S is put into big matrix S1Center, extract S Zhong the i-th roads, it is assumed that the coboundary point in the road is j, then Si,jExist for S
One point in the i-th road the top border；To S1For, Si,jIt is its internal point, is adopted together using formula (7) edge to every
Ask for the value of clear area sampling point direction mirror picture：
Si,j-k=Si,j+k k≤H (7)
The calculating on the border in all roads in sampled point direction is completed, now S size is (m+2*H) × n；
(32) value of clear area is asked for along road direction mirror picture：
S is put into big matrix S1Center, extract the value in each road of t in S, it is assumed that the left boundary point in the road is
P, then St,pFor S t Far Left border a point；To S1For, St,pIt is its internal point, it is equal to each moment
The value of clear area is asked for along road direction mirror picture using formula (8)：
St,p-q=St,p+q q≤K (8)
The calculating on the border at road direction all moment is completed, now S size is (m+2*H) × (n+2*K).
3. mirror image boundary calculation method according to claim 1, it is characterised in that：In the step (4) by after computing
Result remove what the side of expansion was realized in：With big matrix S1Central point matrix as a result central point, after flared end
Big matrix S1Middle extraction and original matrix S-phase people having a common goal number and the matrix of sampled point.
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