CN106896409B - A kind of varying depth cable ghost reflection drawing method based on wave equation boundary values inverting - Google Patents
A kind of varying depth cable ghost reflection drawing method based on wave equation boundary values inverting Download PDFInfo
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Abstract
The present invention relates to a kind of varying depth cable ghost reflection drawing method based on wave equation boundary values inverting, comprising the following steps: 1) common-shot-gather is extracted to the seismic data of varying depth cable acquisition；2) one-dimensional Fourier transform is carried out to the seismic data of certain big gun in common-shot-gather and obtains the frequency spectrum containing ghost reflection seismic data；3) the corresponding frequency domain seismic data U containing ghost reflection of certain frequencies omega in frequency spectrum is calculatedAB；4) according to geophone station depthCalculate G1And G2；5) according to UABAnd G1And G2Calculate the corresponding pressed frequency domain seismic data F of ghost reflection of frequencies omegaCD；6) the pressed frequency domain seismic data of ghost reflection is obtained to all frequencies omegas on frequency spectrum in the big gun；7) the pressed frequency domain seismic data of ghost reflection is arrived to other big guns in common-shot-gather；8) frequency domain seismic data F pressed to ghost reflectionCDIt carries out inverse Fourier transform and obtains the pressed common-shot-gather of ghost reflection, the present invention can be used in the treatment process of marine varying depth cable acquisition seismic data.
Description
Technical field
The present invention relates to a kind of energy development exploitation methods, specifically about a kind of change based on wave equation boundary values inverting
Depth cable ghost reflection drawing method.
Background technique
Seismic prospecting is the important means of oil-gas exploration, especially exploratory engineering of off-shore petroleum/gas reservoir, since its drilling cost is high, surveys
Other data such as well, geology are few, make have prior effect in seismic prospecting oil-gas exploration at sea.Wide band earthquake number
It can be improved the basic data of mid-deep strata signal-to-noise ratio according to that can be construed to that resolution ratio can either be improved again, improve structure interpretation and storage
The precision and reliability of layer prediction are one of the targets that offshore seismic exploration is pursued.However due to the limitation of various conditions, this
There is no realize well for target.When carrying out offshore seismic exploration, generally requires and focus and receiver are respectively placed in Hai Ping
Face certain depth below, since the contact surface of extra large water and air is a good reflecting surface, receiver is in addition to receiving
To outside the back wave of subsurface interface, ghost relevant to the reflex on sea level, this ghost will be also received
It is exactly ghost reflection.Ghost reflection can generate trap effect to the reflection signal from underground reduces ground so that the frequency band of seismic data narrows
Shake the resolution ratio of section.When the depth of cable is larger, ghost reflection causes false lineups to occur.At sea in seismic prospecting, drag
Cable is the common collecting operation mode in field, generally in same one acquisition, will receive cable and is placed on some depth fixed
On, the depth for receiving wave detector all in cable is all identical.To obtain the higher seismic data of frequency, towing cable should be placed on to the greatest extent
It measures in shallow depth, but at this moment the noise of low-frequency range can be very strong, and towing cable is placed on deeper place and is acquired and can subtract
A small number of noises in, but since the trap of ghost reflection acts on, so that seismic data frequency band narrows.Past, due to oil-gas exploration
Destination layer bury shallower, most of thinner thicknesses need high-resolution seismic data just and can recognize that relatively thin oily
Reservoir, therefore usually towing cable is placed on as far as possible in shallower depth in acquisition, so that first trap wave point of ghost reflection is located at earthquake
Except frequency range required for being imaged.It is smaller and smaller in the probability that middle-shallow layer finds oil-gas reservoir with the development of oil-gas exploration, exploration
Destination layer be increasingly turned to mid-deep strata.But due to the reflection of upper formation, energy subtracts significantly when seismic signal reaches mid-deep strata
Weak, the signal-to-noise ratio of seismic data reduces.Cable is placed in order to improve the signal-to-noise ratio of mid-deep strata when field seismic data acquires
It is acquired in deeper place.This mode is while improving seismic data signal-to-noise ratio, but also the trap of ghost reflection influences
It greatly increases.
It is influenced to suppress the trap of ghost reflection, people use various methods in earthquake data acquisition and indoor processing, such as
Upper and lower cable acquisition method is exactly one of.In the 1950s, Haggerty proposes to utilize upper and lower cable acquisition method earliest
The concept of marine streamer data quality is improved, upper and lower cable acquisition method is exactly acquisition vessel while dragging two is placed on different depth
On cable be acquired, deeper towing cable mainly measures low-frequency information, and shallower towing cable fills up the trap wave point of deep towing cable, so
And this will increase the complexity and field operation difficulty of acquisition.Double inspection acquisition methods are the field acquisitions of another ghost reflection compacting
Method, double inspection acquisition methods are examined in water and increase land inspection (velocity detector) except (pressure detector), and two sets of wave detectors are integrated
In the same position of cable, seismic wave caused pressure wavefield and the variation of speed wave field in seawater communication process are recorded respectively,
Optimal proportion merging is carried out to the output signal of two kinds of wave detectors, ghost reflection can be suppressed.The third method of ghost reflection compacting is to become
The acquisition of depth cable, in such acquisition method, cable is placed on the oblique line at non-zero inclination angle or on curved line, so that ghost reflection
Trap wave point is decentralized.For varying depth towing cable collection as a kind of new acquisition method, its purpose is by making different inspections in cable
The trap wave point of wave device disperses, to be conducive to suppress ghost reflection, while the part placement on towing cable far from ship is deep as far as possible, so that low
Frequency range obtains the data of high s/n ratio.Different with the constant depth of tradition acquisition, the depth of towing cable changes with offset distance, drags
The placement depth of the wave detector of different location is different in cable, and the trap frequency of each wave detector is different, to make finally to combine
The result of different wave detectors does not have apparent trap wave point.Processing varying depth acquisition data critical step is the pressure of geophone station ghost reflection
System.The seismic data of varying depth cable acquisition further suppresses ghost reflection for us and provides an extraordinary data basis, but this
Kind data will be can be only achieved compacting ghost reflection by specific processing method and widen the purpose of the frequency band of seismic data.2010,
Soubaras et al. re-starts research to the processing method for the seismic data that varying depth cable acquires, and proposes to pass through joint deconvolution
Method suppresses ghosting, and the basic thought of this method is that varying depth cable data are carried out with offset and mirrored offset, at the two
Joint deconvolution is carried out on the basis of offset data to suppress ghost reflection, achieves preferable effect.2012, Soubaras again will
The advantages of this method is generalized to pre stack data, this method, which is it, regards a kind of special wave as the ghost reflection of receiving point, still
This method needs to complete to deviate twice, increases calculation amount, therefore researcher solves double offset meters using optimization filter operator
The problem of calculation, realizes ghost reflection compacting for pre stack data.Researcher proposes a kind of frequency domain for varying depth cable seismic data
Radon transform method provides a kind of Radon inverse transformation operator based on the ray path of receiving point ghost reflection, this method can with compared with
Then high accuracy prediction ghost reflection subtracts the ghost reflection of prediction from practical received seismic data, and then reach ghost reflection compacting
Purpose.The application of these methods substantially increases the pressing result of ghost reflection, but these methods are all to carry out letter to wave equation
Put forward after change, is adapted to the better simply underground medium of subsurface structure.With the development of oil-gas exploration, the oil-containing of main exploration
Gas stratum becomes increasingly complex, and for the underground medium of this complexity, the precision that the above method suppresses ghost reflection is reduced, and is difficult complete ghost
Wave pressure system.
Summary of the invention
In view of the above-mentioned problems, being suitable for complicated underground medium the object of the present invention is to provide one kind and can be improved ghost reflection pressure
The varying depth cable ghost reflection drawing method based on wave equation boundary values inverting of precision processed.
To achieve the above object, the present invention takes following technical scheme: a kind of deepening based on wave equation boundary values inverting
Spend cable ghost reflection drawing method, which comprises the following steps: 1) take out to the seismic data of marine field varying depth cable acquisition
Take common-shot-gather；2) one-dimensional Fourier transform is carried out to the seismic data of certain big gun in common-shot-gather, obtained containing ghost reflection
The frequency spectrum of seismic data；3) the corresponding frequency domain seismic data U containing ghost reflection of certain frequencies omega in frequency spectrum is calculatedAB；4) according to defeated
The geophone station depth enteredThe GREEN function G of datum level below seawater face is calculated1With datum level relative to seawater face
Line of symmetry GREEN function G2；5) according to the obtained frequency domain seismic data U containing ghost reflectionABAnd the G being calculated1
And G2, the pressed frequency domain seismic data F of the corresponding ghost reflection of frequencies omega is calculatedCD；6) on frequency spectrum in common-shot-gather
All frequencies omegas carry out step 3)~5) obtain the pressed frequency domain seismic data of ghost reflection；7) to its in common-shot-gather
He carries out step 2)~6 by big gun) obtain the pressed frequency domain seismic data of ghost reflection；8) to the pressed frequency domain earthquake of ghost reflection
Data FCDInverse Fourier transform is carried out, the pressed common-shot-gather of ghost reflection is obtained.
Further, the corresponding frequency domain seismic data U containing ghost reflection of certain frequencies omega in frequency spectrum is calculatedABDetailed process
Are as follows: definition datum level is CD, and seawater face is EF, and varying depth cable is AB, is observed at CD, EC and FD sections, obtained earthquake
Record is respectively uCD、uECAnd uFD, the earthquake record of varying depth cable AB is u in the seawaterAB, according to wave equation theory, by uCD
To uABForward problem be written as the direct problem of scattering form:
u(x,z,t)|(x, z) ∈ EC=uEC (8)
u(x,z,t)|(x,z)∈FD=uFD (9)
The boundary condition for taking seawater face EF is free boundary condition, it may be assumed that
At the time of time t=0, wave field not yet starts to propagate, and primary condition is taken as:
Wherein, u (x, z, t) is displacement wave field, and x, z are respectively coordinate both horizontally and vertically, and v (x, z) is in medium
The speed of (x, z) point, fCDFor by uCDObtained scattering source function is integrated, for practical problem, uECAnd uFDIt can not find out,
Therefore absorbing boundary condition is taken on EC and FD, since forward problem is the propagation problem of the wave considered in the seawater, thus speed
Degree can take constant value, it may be assumed that
Since water meter is negative reflection, reflection coefficient is -1, therefore seismic wave is divided into two parts, and a part is to pass directly up
The wave table broadcast is shown as u1, another part is to be shown as u to the wave table of lower propagation after seawater face EF reflection2, total wave field is expressed as u
=u1+u2, and u1Meet:
u2Meet:
Wherein, C ' D ' is line of symmetry of the benchmark face CD relative to seawater face EF, fC’D’For fCDMirror image function, and fC’D’With
fCDIt is equal in magnitude, at this point, formula (13) and (14) they are the equation in uniform infinite medium, it is equal to formula (13) and (14) both sides
Fourier transformation is taken to obtain about the time:
Formula (15) and (16) are passed through GREEN function representation and solved and is obtained:
Wherein, G1、G2For GREEN function, the receiving point of formula (17) and (18) on varying depth cable AB is also set up, it may be assumed that
Above-mentioned formula (19) and (20) is write as matrix form to obtain:
UAB1=G1FCD (21)
UAB2=-G2FCD (22)
Formula (21) and (22) are merged and obtain the frequency domain seismic data U containing ghost reflectionAB:
UAB=G1FCD-G2FCD=(G1-G2)FCD (23)
Further, according to the geophone station depth of inputThe GREEN function of datum level below seawater face is calculated
G1GREEN function G with datum level relative to the line of symmetry in seawater face2Detailed process are as follows: in equal medium, the meter of GREEN function
Calculate formula are as follows:
Wherein, parameter k=ω/v；Parameter
According to the geophone station depth of inputAnd formula (24) and (25) calculate separately to obtain G1And G2:
Further, according to the frequency domain seismic data U containing ghost reflectionABAnd the G being calculated1And G2, it is calculated
The pressed frequency domain seismic data F of frequencies omega ghost reflectionCDDetailed process are as follows: in formula (23), G1-G2It is a matrix, according to
G is calculated in formula (25)~(27)1-G2, according to the sinking depth profile of varying depth cable AB when marine field earthquake data acquisition
Obtain geophone station depthFCDIt is free from the frequency domain seismic data of ghost reflection, for amount to be asked；UABWhen being field earthquake-capturing
The obtained frequency domain seismic data containing ghost reflection, is known quantity, obtains the frequency without containing ghost reflection by the solution of formula (23)
Rate domain seismic data FCD。
The invention adopts the above technical scheme, which has the following advantages: 1, the present invention is described using wave equation
The generation process of ghost reflection, thus precision with higher, can describe propagation and ghost of the seismic wave in underground medium well
The generation process of wave.2, the present invention is based on wave equation boundary values inverting, the compacting problem of ghost reflection is attributed to the side of wave equation
It is worth inversion problem, solves the problems, such as that ghost reflection is suppressed using wave equation inversion method, ghost reflection pressing result is good.3, the present invention is directed to
Common-shot-gather carries out ghost reflection compacting, can preferably keep the prestack feature of initial data, and the present invention is carried out in frequency domain,
Each frequency can be handled independently, thus there is preferable concurrency and parallel efficiency is higher, suppressing can be with after ghost reflection
Seismic signal frequency spectrum is widened, the resolution ratio of seismic data is improved, present invention can be widely used to marine varying depth cable acquisition earthquake
In the treatment process of data.
Detailed description of the invention
Fig. 1 is the principle of the present invention schematic diagram, whereinIt is the round of ghost reflection,It is to have
Imitate the round of wave (not including ghost reflection)；
Fig. 2 is implementation flow chart of the invention；
Fig. 3 is the Numerical Experiment without ghost reflection of the pressed Numerical Experiment result of ghost reflection of the present invention and synthesis
Comparative result figure, wherein Fig. 3 (a) is the single-shot trace gather simulated seismogram without ghost reflection of synthesis, and Fig. 3 (b) is synthesis containing ghost
The single-shot trace gather simulated seismogram of wave, Fig. 3 (c) are the pressed single-shot trace gather simulated seismograms of ghost reflection of the present invention；
Fig. 4 is the Numerical Experiment without ghost reflection of the pressed Numerical Experiment frequency spectrum of ghost reflection of the present invention and synthesis
Spectral contrast figure, wherein Fig. 4 (a) is the single-shot trace gather amplitude spectrum without ghost reflection of synthesis, and Fig. 4 (b) is the list containing ghost reflection of synthesis
Big gun trace gather amplitude spectrum, Fig. 4 (c) are the pressed single-shot trace gather amplitude spectrums of ghost reflection of the present invention；
Fig. 5 is the knot before processing result and ghost reflection compacting after practical varying depth cable seismic data of the invention suppresses ghost reflection
Fruit comparison diagram, wherein Fig. 5 (a) is an earthquake single-shot trace gather data of varying depth cable acquisition, and Fig. 5 (b) is present invention compacting ghost
Earthquake single-shot trace gather data after wave.
Specific embodiment
Come to carry out detailed description to the present invention below in conjunction with attached drawing.It should be appreciated, however, that attached drawing has been provided only more
Understand the present invention well, they should not be interpreted as limitation of the present invention.
As shown in Figure 1, seismic wave from O point excitation after to underground propagation, reflected after encountering each subsurface reflective boundary
It upwardly propagating, first passes around datum level CD, seismic wave at this time is free from ghost reflection, and seismic wave continues up propagation, and one
Divide and be propagate directly to varying depth cable AB, another part travels to after the EF of seawater face and propagates down into varying depth by the total reflection of seawater face
Cable AB, this part seismic wave is exactly ghost reflection.Therefore, it had both contained in the seismic wave that varying depth cable AB is received by datum level CD
It is propagate directly to the seismic wave field of varying depth cable AB upwards afterwards, also contains and the seismic wave propagated downwards is totally reflected by seawater face
Field, i.e. ghost reflection.So ghost reflection compacting is exactly the received earthquake record of known varying depth cable AB, such as from the point of view of wave field propagation
What seeks the earthquake record of the datum level CD without containing ghost reflection by inverting.
Ghost reflection compacting is illustrated above by physical angle, ghost reflection compacting is said below by mathematical angle
Bright, propagation of the seismic wave in two-dimensional medium can be used following wave equation to describe:
Wherein u (x, z, t) is displacement wave field, and x, z are respectively coordinate both horizontally and vertically, and v (x, z) is in medium
The speed of (x, z) point, δ () are Dirac δ-function, and g (t) is source function.Assuming that in O point earthquake-wave-exciting, in CD, EC and
FD sections are observed, and obtained earthquake record is respectively uCD、uECAnd uFD.Consider ground in the CDFE of region by earthquake record
The propagation problem of seismic wave, control equation is formula (1), by uCD、uECAnd uFDRespectively as the boundary condition of CD, EC, FD, it may be assumed that
u(x,z,t)|(x,z)∈CD=uCD (2)
u(x,z,t)|(x,z)∈EC=uEC (3)
u(x,z,t)|(x,z)∈FD=uFD (4)
In view of the actual conditions of seismic prospecting, taking the boundary condition of seawater face EF is free boundary condition, it may be assumed that
Primary condition is taken as:
Pass through wave equation formula (1) and its boundary and primary condition formula (2)~(6) the available sea of numerical solution
Earthquake record u in water on varying depth cable ABAB, while one is defined by uCDTo uABWave field forward-propagating process, that is, forward modeling
Problem.And the compacting of ghost reflection is then by uABSolve uCD, this is the anti-of the i.e. wave equation formula (1) of back-propagation process of wave field
Problem is drilled, when solving inversion problem, unknown is the boundary values of wave equation.In art of mathematics, wave equation formula (1) is inclined
Differential form is properly termed as partial differential equation or the differential equation, solves the inversion problem of the equation, can be described as indirect problem.It is above-mentioned
Ghost reflection compacting is by uABSolve uCDProcess, be mathematically the indirect problem for solving the differential equation, also referred to as boundary values indirect problem, ground
It is known as the inverting of wave equation boundary values in seismic exploration.
As shown in Fig. 2, the analysis based on above-mentioned physical angle and mathematical angle, of the invention anti-based on wave equation boundary values
The varying depth cable ghost reflection drawing method drilled, specifically includes the following steps:
1) common-shot-gather is extracted to the seismic data of marine field varying depth cable acquisition, includes ghost reflection number in the trace gather
According to.
2) one-dimensional Fourier transform is carried out to the seismic data of certain big gun in common-shot-gather, obtains the earthquake number containing ghost reflection
According to frequency spectrum.
3) the corresponding frequency domain seismic data U containing ghost reflection of certain frequencies omega in frequency spectrum is calculatedAB。
It is above-mentioned by u according to wave equation theoryCDTo uABForward problem can be written as the direct problem of scattering form:
u(x,z,t)|(x,z)∈EC=uEC (8)
u(x,z,t)|(x,z)∈FD=uFD (9)
The boundary condition for taking seawater face EF is free boundary condition, it may be assumed that
At the time of time t=0, wave field not yet starts to propagate, and primary condition is taken as:
Wherein, fCDFor by uCDIntegrate obtained scattering source function.For practical problem, uECAnd uFDIt can not find out, because
This takes absorbing boundary condition on EC and FD.Since above-mentioned forward problem is the propagation problem of the wave considered in water, thus speed
Degree can take constant value, v (x, z)=v in formula (7), it may be assumed that
Further, since water meter is negative reflection, usual reflection coefficient is -1, therefore seismic wave is segmented into two parts, one
Part is that the wave table propagated directly up is shown as u1, another part is to be shown as after seawater face EF reflection to the wave table of lower propagation
u2, total wave field is expressed as u=u1+u2, and u1Meet:
u2Meet:
Wherein, C ' D ' is line of symmetry of the benchmark face CD relative to seawater face EF, fC’D’For fCDMirror image function, and fC’D’With
fCDIt is equal in magnitude.At this point, formula (13) and (14) they are the equation in uniform infinite medium, it is equal to formula (13) and (14) both sides
Fourier transformation is taken to obtain about the time:
Formula (15) and (16) are passed through GREEN function representation and solved and is obtained:
Wherein, G1、G2For GREEN function, concrete form is forth below.Formula (17) and (18) are on varying depth cable AB
Receiving point is also set up, it may be assumed that
Above-mentioned formula (19) and (20) is write as matrix form to obtain:
UAB1=G1FCD (21)
UAB2=-G2FCD (22)
Formula (21) and (22) are merged and obtain the frequency domain seismic data U containing ghost reflectionAB:
UAB=G1FCD-G2FCD=(G1-G2)FCD (23)
4) according to the geophone station depth of inputThe GREEN function G of datum level CD below the EF of seawater face is calculated1With
GREEN function G of the datum level CD relative to the line of symmetry C ' D ' of seawater face EF2。
In equal medium, the calculation formula of GREEN function are as follows:
Wherein, parameter k=ω/v；Parameter
According to the geophone station depth of inputAnd formula (24) and (25) calculate separately to obtain G1And G2:
5) according to the obtained frequency domain seismic data U containing ghost reflectionABAnd the G being calculated1And G2, frequency is calculated
The pressed frequency domain seismic data F of the corresponding ghost reflection of rate ωCD。
In formula (23), G1-G2It is a matrix, G can be calculated according to formula (25)~(27)1-G2, according to sea
Outside u'eno when earthquake data acquisition varying depth cable AB sinking depth profile, geophone station depth can be obtainedFCDIt is free from
The frequency domain seismic data of ghost reflection, for amount to be asked；UABThe frequency domain containing ghost reflection obtained when being marine field earthquake-capturing
Data are shaken, are known quantity；Pass through the available frequency domain seismic data F without containing ghost reflection of solution of formula (23)CD, to reach
To the purpose of compacting ghost reflection.
6) step 3)~5 are carried out to all frequencies omegas on frequency spectrum in common-shot-gather) obtain the pressed frequency of ghost reflection
Rate domain seismic data.
7) step 2)~6 are carried out to other big guns in common-shot-gather) obtain the pressed frequency domain seismic data of ghost reflection.
8) frequency domain seismic data F pressed to ghost reflectionCDInverse Fourier transform is carried out, the pressed big gun altogether of ghost reflection is obtained
Point trace gather.
As shown in figure 3, the present invention, which analyzes ghost reflection, suppresses forward and backward Numerical Experiment as a result, Fig. 3 (a) is synthesis
Single-shot trace gather simulated seismogram without ghost reflection, Fig. 3 (b) is the single-shot trace gather simulated seismogram containing ghost reflection of synthesis, by Fig. 3
(b) simulated seismogram obtains Fig. 3 (c), comparison diagram 3 (c) and Fig. 3 (a) as can be seen that two after suppressing ghost reflection using the present invention
Width figure is completely the same, and the ghost reflection in explanatory diagram 3 (b) has been pressed, and useful signal is effectively maintained.
As shown in figure 4, Fig. 4 is spectrogram corresponding to each figure in Fig. 3, Fig. 4 (a) is the single-shot road without ghost reflection of synthesis
Collect amplitude spectrum, Fig. 4 (b) is the single-shot trace gather amplitude spectrum containing ghost reflection of synthesis, can be clearly seen that the ghost reflection in Fig. 4 (b)
Trap effect, Fig. 4 (c) is the pressed single-shot trace gather amplitude spectrum of ghost reflection of the present invention, can see trap band from Fig. 4 (c)
Frequency spectrum is recovered.
As shown in figure 5, Fig. 5 is to carry out ghost reflection to practical varying depth cable seismic data using the present invention to suppress forward and backward place
Comparative result is managed, Fig. 5 (a) is an earthquake single-shot trace gather data of varying depth cable acquisition, can clearly be seen in the diagram
To ghost reflection, Fig. 5 (b) is the earthquake single-shot trace gather data suppressed after ghost reflection with the present invention, and comparing this two width figure can clearly see
It arrives, the ghost reflection in original earthquake single-shot data that treated through the invention is suppressed well, while original earthquake single-shot
Significant wave in data is kept well.
The various embodiments described above are merely to illustrate the present invention, and wherein each step etc. of method may be changed, all
The equivalents and improvement carried out based on the technical solution of the present invention, should not exclude protection scope of the present invention it
Outside.
Claims (4)
1. a kind of varying depth cable ghost reflection drawing method based on wave equation boundary values inverting, which comprises the following steps:
1) common-shot-gather is extracted to the seismic data of marine field varying depth cable acquisition；
2) one-dimensional Fourier transform is carried out to the seismic data of certain big gun in common-shot-gather, obtains the seismic data containing ghost reflection
Frequency spectrum；
3) the corresponding frequency domain seismic data U containing ghost reflection of certain frequencies omega in frequency spectrum is calculatedAB；
4) according to the geophone station depth of inputThe GREEN function G of datum level below seawater face is calculated1With datum level phase
For the GREEN function G of the line of symmetry in seawater face2；
5) according to the obtained frequency domain seismic data U containing ghost reflectionABAnd the G being calculated1And G2, frequencies omega is calculated
The corresponding pressed frequency domain seismic data F of ghost reflectionCD；
6) step 3)~5 are carried out to all frequencies on frequency spectrum in common-shot-gather) with obtaining the pressed frequency domain of ghost reflection
Shake data；
7) step 2)~6 are carried out to other big guns in common-shot-gather) obtain the pressed frequency domain seismic data of ghost reflection；
8) frequency domain seismic data F pressed to ghost reflectionCDInverse Fourier transform is carried out, the pressed common-source point road of ghost reflection is obtained
Collection.
2. a kind of varying depth cable ghost reflection drawing method based on wave equation boundary values inverting as described in claim 1, feature
It is, calculates the corresponding frequency domain seismic data U containing ghost reflection of certain frequencies omega in frequency spectrumABDetailed process are as follows:
Definition datum level is CD, and seawater face is EF, and varying depth cable is AB, is observed at CD, EC and FD sections, obtained earthquake
Record is respectively uCD、uECAnd uFD, the earthquake record of varying depth cable AB is u in the seawaterAB, according to wave equation theory, by uCD
To uABForward problem be written as the direct problem of scattering form:
U (x, z, t) |(x, z) ∈ EC=uEC (8)
U (x, z, t) |(x, z) ∈ FD=uFD (9)
The boundary condition for taking seawater face EF is free boundary condition, it may be assumed that
At the time of time t=0, wave field not yet starts to propagate, and primary condition is taken as:
Wherein, u (x, z, t) is displacement wave field, and x, z are respectively coordinate both horizontally and vertically, and v (x, z) is in medium (x, z)
The speed of point, fCDFor by u0DObtained scattering source function is integrated, for practical problem, uECAnd uFDIt can not find out, therefore
Absorbing boundary condition is taken on EC and FD, since forward problem is the propagation problem of the wave considered in the seawater, thus speed can be with
Take constant value, it may be assumed that
Since water meter is negative reflection, reflection coefficient is -1, therefore seismic wave is divided into two parts, and a part is propagated directly up
Wave table is shown as u1, another part is to be shown as u to the wave table of lower propagation after seawater face EF reflection2, total wave field is expressed as u=u1+
u2, and u1Meet:
u2Meet:
Wherein, C ' D ' is line of symmetry of the benchmark face CD relative to seawater face EF, fC’D’For fCDMirror image function, and fC’D’With fCDGreatly
It is small equal, at this point, formula (13) and (14) they are the equation in uniform infinite medium, to formula (13) and (14) both sides about
Time takes Fourier transformation to obtain:
Formula (15) and (16) are passed through GREEN function representation and solved and is obtained:
Wherein, G1、G2For GREEN function, the receiving point of formula (17) and (18) on varying depth cable AB is also set up, it may be assumed that
Above-mentioned formula (19) and (20) is write as matrix form to obtain:
UAB1=G1FCD (21)
UAB2=-G2FCD (22)
Formula (21) and (22) are merged and obtain the frequency domain seismic data U containing ghost reflectionAB:
UAB=G1FCD-G2FCD=(G1-G2)FCD (23)
3. a kind of varying depth cable ghost reflection drawing method based on wave equation boundary values inverting as claimed in claim 2, feature
It is, according to the geophone station depth of inputThe GREEN function G of datum level below seawater face is calculated1With datum level phase
For the GREEN function G of the line of symmetry in seawater face2Detailed process are as follows:
In equal medium, the calculation formula of GREEN function are as follows:
Wherein, parameter k=ω/v；Parameter
According to the geophone station depth of inputAnd formula (24) and (25) calculate separately to obtain G1And G2:
4. a kind of varying depth cable ghost reflection drawing method based on wave equation boundary values inverting as claimed in claim 3, feature
It is, according to the obtained frequency domain seismic data U containing ghost reflectionABAnd the G being calculated1And G2, frequencies omega is calculated
The corresponding pressed frequency domain seismic data F of ghost reflectionCDDetailed process are as follows:
In formula (23), G1-G2It is a matrix, G is calculated according to formula (25)~(27)1-G2, according to marine field earthquake
The sinking depth profile of varying depth cable AB obtains geophone station depth when data acquireFCDIt is free from the frequency domain earthquake of ghost reflection
Data, for amount to be asked；UABThe frequency domain seismic data containing ghost reflection obtained when being field earthquake-capturing is known quantity, passes through
The solution of formula (23) obtains the frequency domain seismic data F without containing ghost reflectionCD。
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| CN110967735A (en) * | 2018-09-28 | 2020-04-07 | 中国石油化工股份有限公司 | Self-adaptive ghost wave suppression method and system |
| CN109633752B (en) * | 2019-01-04 | 2020-04-07 | 吉林大学 | Offshore towing cable data self-adaptive ghost wave compression method based on three-dimensional fast Radon transformation |
| CN112578454B (en) * | 2019-09-29 | 2024-03-22 | 中国石油化工股份有限公司 | Method and system for pressing ghost waves of arbitrarily curved towing rope |
| CN111722273B (en) * | 2020-06-12 | 2022-02-11 | 中国海洋大学 | Simulated annealing virtual reflection suppression method and marine seismic exploration system |
| CN111830566B (en) * | 2020-06-12 | 2022-02-11 | 中国海洋大学 | Parameter matching virtual reflection suppression method and marine seismic exploration system |
| CN112835103B (en) * | 2020-12-31 | 2021-10-08 | 北京东方联创地球物理技术有限公司 | Adaptive ghost wave removing and broadband quasi-zero phase deconvolution combined processing method and system |
| CN114624771B (en) * | 2022-02-10 | 2025-08-22 | 中海石油(中国)有限公司海南分公司 | A method and system for estimating static correction of marine oblique cable seismic exploration data |
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