CN109143333A - Forward modeling method and computer readable storage medium based on triangulation model - Google Patents
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Abstract
Disclose a kind of forward modeling method and computer readable storage medium based on triangulation model.This method comprises: given disperse node, carries out Delaunay Triangulation for rate pattern；On the basis of rate pattern triangulation, dynamic ray tracing is carried out；Theoretical seismogram is obtained using Gaussian beam propagation operator.Technical solution provided by the invention reduces scattering caused by grid " sawtooth " effect of finite difference modelling, improves the precision of wave-field simulation to the better adaptability of complicated structure；And computational efficiency is high, can directly obtain the earthquake record of removal direct wave.
Description
Technical field
The present invention relates to seismic wave field numerical simulation field, more particularly, to it is a kind of based on triangulation model just
Drill method and computer readable storage medium.
Background technique
Wavefield forward modeling technology is very widely used in seismic prospecting.It can mentioning for new technology by forward simulation
Out, feasibility analysis and application test provide the analogue data of high quality；Acquisition, the place of field seismic data can directly be instructed
Reason and explanation.Numerical simulation can mainly be classified as three categories at present: wave equation numerical solution, integral equation method and ray tracing
Method.Gaussian beam forward simulation is a kind of method of ray-tracing procedure class, and computational efficiency is higher and remains the dynamics of wave letter
Breath.
In seismic prospecting, either wavefield forward modeling or tomographic inversion, model parameterization are the most fundamental problems.When
Preceding mainstream technology is all based on regular grid and divides (common are rectangular mesh subdivision or simple triangular mesh generation), if any
Limit difference forward modeling, back wave chromatography are all based on rectangular mesh.When using rectangle cell parameterization, there are many disadvantages, tools
Body is as follows:
(1) model facetization flexibility is poor, and no matter the uniformity requirements of rectangular mesh all make in construction complexity or simple region
It is divided with same precision；(2) to the description low precision of velocity interface, it is easy to produce " sawtooth " shape boundary；(3) complex die
When type, fine grid blocks is needed to describe rate pattern, it is computationally intensive；Amount of storage is big when (4) being used for tomographic inversion, it is long to calculate the time,
Equation condition is poor, it is difficult to solve.
Therefore, it is necessary to a kind of the Forward Modeling for dividing rate pattern be developed, to overcome rule-based grid mould
Type divides poor, the computationally intensive defect of flexibility.
The information for being disclosed in background of invention part is merely intended to deepen the reason to general background technique of the invention
Solution, and it is known to those skilled in the art existing to be not construed as recognizing or imply that the information is constituted in any form
Technology.
Summary of the invention
The invention proposes a kind of forward modeling method and computer readable storage medium based on triangulation model, can
By Delaunay Triangulation and Gaussian beam forward modeling method, realizes and obtain theoretical seismogram.
According to an aspect of the invention, it is proposed that a kind of forward modeling method based on triangulation model, this method comprises: giving
Determine disperse node, rate pattern is subjected to Delaunay Triangulation；On the basis of rate pattern triangulation, moved
State ray tracing；Theoretical seismogram is obtained using Gaussian beam propagation operator.
According to another aspect of the invention, it is proposed that a kind of computer readable storage medium, is stored thereon with computer journey
Sequence performs the steps of when described program is executed by processor
Step 1, disperse node is given, rate pattern is subjected to Delaunay Triangulation；
Step 2, on the basis of rate pattern triangulation, dynamic ray tracing is carried out；
Step 3, theoretical seismogram is obtained using Gaussian beam propagation operator.
Technical solution provided by the invention reduces the grid of finite difference modelling to the better adaptability of complicated structure
Scattering, improves the precision of wave-field simulation caused by " sawtooth " effect；And computational efficiency is high, can directly obtain removal direct wave
Earthquake record.
Methods and apparatus of the present invention has other characteristics and advantages, these characteristics and advantages are attached from what is be incorporated herein
It will be apparent in figure and subsequent specific embodiment, or will be in the attached drawing and subsequent specific implementation being incorporated herein
It is stated in detail in example, these the drawings and specific embodiments are used together to explain specific principle of the invention.
Detailed description of the invention
Exemplary embodiment of the present is described in more detail in conjunction with the accompanying drawings, of the invention is above-mentioned and other
Purpose, feature and advantage will be apparent, wherein in exemplary embodiments of the present invention, identical reference label is usual
Represent same parts.
Fig. 1 shows the flow chart of the step of forward modeling method based on triangulation model according to the present invention a kind of.
Fig. 2 shows the schematic diagrames of two kinds of division modes at four control points according to an embodiment of the invention.
Fig. 3 shows one according to the present invention and applies exemplary rate pattern Delaunay triangulation figure.
Fig. 4 shows the ray tracing path of certain exemplary single-shot of an application according to the present invention.
Fig. 5 shows the theoretical earthquake note of the waveform display mode of the exemplary Gaussian beam of an application according to the present invention
Record.
Fig. 6 shows the gray scale display mode of the time-domain of the exemplary Gaussian beam of an application according to the present invention theoretically
Shake record.
Fig. 7 shows the rectangular mesh division figure of the exemplary theoretical model of an application according to the present invention.
Fig. 8 shows the exemplary theoretical model rectangular mesh of an application according to the present invention and divides what tilted interface generated
" sawtooth " effect figure.
Fig. 9 shows the theoretical seismogram of an application according to the present invention exemplary finite difference method synthesis.
Figure 10 shows the reason that an exemplary Gaussian beam method of application and finite difference method according to the present invention synthesize
By the differential chart of earthquake record.
Specific embodiment
The present invention will be described in more detail below with reference to accompanying drawings.Although showing the preferred embodiment of the present invention in attached drawing,
However, it is to be appreciated that may be realized in various forms the present invention and should not be limited by the embodiments set forth herein.On the contrary, providing
These embodiments are of the invention more thorough and complete in order to make, and can will fully convey the scope of the invention to ability
The technical staff in domain.
Embodiment 1
Fig. 1 shows the flow chart of the step of forward modeling method based on triangulation model according to the present invention a kind of.
In this embodiment, a kind of forward modeling method based on triangulation model according to the present invention, this method comprises: step
Rapid 101, disperse node is given, rate pattern is subjected to Delaunay Triangulation；Step 102, it is cutd open in rate pattern triangle
On the basis of point, dynamic ray tracing is carried out；And step 103, theoretical seismogram is obtained using Gaussian beam propagation operator.
The embodiment is realized by Delaunay Triangulation and Gaussian beam forward modeling method and obtains theoretical seismogram.
The following detailed description of a kind of specific steps of the forward modeling method based on triangulation model according to the present invention.
Step 101, disperse node is given, rate pattern is subjected to Delaunay Triangulation.
Fig. 2 shows the schematic diagrames of two kinds of division modes at four control points according to an embodiment of the invention.
If shown in Fig. 2, the inside of the circumscribed circle of any one Delaunay triangle cannot include other any points.Figure
The circumscribed circle of 2 left side △ BCD includes A point, therefore such division mode is not Delaunay subdivision, division mode on the right side of Fig. 2, and two
The circumscribed circle of a triangle does not all include other control points, belongs to Delaunay subdivision.Classical Delaunay Triangulation Algorithm
There are two main classes: Bowyer/Watson algorithm and local converter technique.Bowyer/Watson algorithm is also known as the cavity Delaunay
Algorithm or method of adding some points add a point, the current triangle algorithm for guaranteeing that each step obtains is office since a triangle every time
Portion's optimization；Face method is changed sides or changed to partial transformation method also known as, as the Delaunay for realizing increment type point set using partial transformation method
When trigonometric ratio, the triangle where new addition point is positioned first, and three new connection triangular apex are then added within a grid
With the side of new summit, finally the side in the regional area of the new point is detected and converted by the method for changing sides again, is tieed up again
The Delaunay property of protective net lattice.
After the subdivision for completing rate pattern, the objects such as slowness, quality factor, density can be filled in each speed block
Reason amount can also set the gradient value of these physical quantitys in the same block.
Step 102, on the basis of rate pattern triangulation, dynamic ray tracing is carried out.
Given shot point coordinate and the minimum angles of the angle of emergence, maximum angle, angle interval, the dynamic for carrying out a shot point are penetrated
Line tracking, by the various variable saves of tracking to file.
In one example, the dynamic ray tracing includes:
Step 1, the triangular mesh where focus is determined；
Step 2, it determines a shooting angle, carries out dynamic ray tracing；
Step 3, the triangular mesh boundary is encountered, the triangular mesh frontier properties are read, determines the institute encountered
If stating triangular mesh boundary is that reflection, transmission perhaps terminate and track the triangular mesh boundary and be reflection or transmit,
It calculates reflection or transmits the influence to amplitude；
Step 4, the variable in each step-length of records center ray path, the variable include central ray position, slowness
Component, dynamic ray tracing parameter；
Preferably, needing to record the variable on the central ray path of preservation in dynamic ray tracing has: in
Heart ray travel when, the XZ coordinate of each central ray segment endpoint, the slowness component in the direction XZ, dynamic ray parameter q1, q2,
P1, p2 (result of formula (2)), Kmah index, the number in the reflecting layer encountered, transmission or reflection to the impact factor of amplitude,
Impact factor, amplitude decay factor etc. of the transmission or reflection to phase.
Step 5, change shooting angle, repeat step 2- step 4, until traversing all shooting angles.
In one example, the dynamic ray tracing includes kinematics ray tracing and kinetics ray-tracing.
In one example, the kinematics ray tracing is carried out by the first-order ordinary differential equation system of formula (1):
Wherein, xiIndicate the coordinate of central ray, piIndicate that the slowness component of central ray, s indicate to integrate along central ray
Arc length, xi(s) coordinate of central ray step-length, p are indicatedi(s) indicate that the slowness component of central ray step-length, V (s) indicate in
The speed of model on heart ray, τ indicate the time step of ray tracing.
Preferably, Runge Kutta method is generallyd use to solve formula (1).
When kinematics ray tracing has been sought the path of Gaussian beam central ray and has been walked.
In one example, the kinetics ray-tracing is carried out by the first-order ordinary differential equation system of formula (2):
Wherein, P (s) and Q (s) is the plural number become along Gaussian beam central ray, and s indicates to integrate arc length, V along central ray
(s) model velocity along central ray is indicated, τ indicates ray-traced time step-length, and n indicates ray center coordinate system perpendicular to penetrating
The coordinate in line direction.
Preferably, Runge Kutta method is generallyd use to solve formula (1).
P (s) and Q (s) characterizes kinetics ray-tracing parameter, the width and wave-front curvature propagated which determine Gaussian beam.
Kinetics ray-tracing combination kinematics ray tracing is formed single Gaussian beam continuation.
Step 103, theoretical seismogram is obtained using Gaussian beam propagation operator.
In one example, described to include: using Gaussian beam propagation operator acquisition theoretical seismogram
Step 1, it is based on a ray and a detector position, the Gaussian beam of all single-frequency is sought using formula (3)
Wave field；
Step 2, step 1 is repeated to all detector positions；
Step 3, to different rays, it is repeated in step 1 and step 2, and then by all rays to all wave detector positions
The contribution accumulation summation set；
Step 4, plural Ricker wavelet is generated, the result summed with the accumulation that step 3 obtains is multiplied, and then carries out inverse
Fourier transformation obtains the theoretical seismogram；
Wherein, the theoretical seismogram is the theoretical seismogram of time-domain.
Wherein, P (s) and Q (s) is the plural number become along Gaussian beam central ray, and s is the integral arc length along central ray, u
(s, n, ω) is the Gaussian beam wave field of single-frequency, and τ (s) is the propagation time at center ray arc length s, and V (s) indicates central ray
Speed, n are the component of ray center coordinate system vertical centre ray, and i is imaginary unit, and ω is angular frequency.
Preferably, plural Ricker wavelet is generated using formula (4),
Wherein indicate that angular frequency, wpeak indicate the dominant frequency of Ricker wavelet, delay indicates the time delay of Ricker wavelet.
In one example, the acquisition of the detector position is included: and is obtained using given geophone station position by interpolation
Equally distributed reception position.
Using example
The present invention provides a kind of forward modeling methods based on triangulation model, this method comprises:
Given disperse node, carries out Delaunay Triangulation for rate pattern；
Fig. 3 shows one according to the present invention and applies exemplary rate pattern Delaunay triangulation figure, wherein horizontal
Axis states distance, unit km, and the longitudinal axis indicates depth, and unit km, solid line is triangular mesh boundary, as shown in figure 3, devising one
The stratified model of a curved interface, model transverse direction 6km, longitudinal 3km, the model are used for subsequent Gaussian beam forward modeling, show in figure
The Delaunay Triangulation result of the model.
On the basis of rate pattern triangulation, dynamic ray tracing is carried out；
Fig. 4 shows the ray tracing path of certain exemplary single-shot of an application according to the present invention, wherein horizontal axis statement
Distance, unit km, the longitudinal axis indicate depth, and unit km, shot point is located at 2.72km, as shown in figure 4, in the triangle based on Fig. 3
Dynamic ray tracing is carried out in grid, it is shown that ray tracing path.
The earthquake record of time-domain is obtained using Gaussian beam propagation operator.
Fig. 5 shows the theoretical earthquake note of the waveform display mode of the exemplary Gaussian beam of an application according to the present invention
Record.As shown in figure 5, display mode is wave based on the theoretical seismogram that Fig. 3 rate pattern and Fig. 4 ray tracing result obtain
Shape is shown.
Fig. 6 shows the theoretical earthquake note of the gray scale display mode of the exemplary Gaussian beam of an application according to the present invention
Record.As shown in fig. 6, display mode is ash based on the theoretical seismogram that Fig. 3 rate pattern and Fig. 4 ray tracing result obtain
Degree display.
Method of the invention is compared with other rate pattern division methods and forward modeling method:
Fig. 7 shows the rectangular mesh division figure of the exemplary theoretical model of an application according to the present invention
(1200x600), as shown in fig. 7, the rectangular mesh that Fig. 7 shows rate pattern identical as Fig. 3 indicates that model is to use rectangle net
Lattice have 1200 mesh points in 1200 expression horizontal directions, there is 600 mesh points in vertical direction come what is indicated, similar word
The line number and columns selected when being inserted into table.
Fig. 8 shows the exemplary theoretical model rectangular mesh of an application according to the present invention and divides what tilted interface generated
" sawtooth " effect figure.As shown in figure 8, carrying out rectangular mesh division to rate pattern, " sawtooth " effect of tilted interface is generated.
Fig. 9 shows the theoretical seismogram of an application according to the present invention exemplary finite difference method synthesis.Such as
Shown in Fig. 9, the rectangular mesh based on rate pattern is divided, the theoretical seismogram obtained using finite difference method, from figure
It can see the significantly diffracted wave lineups due to caused by " sawtooth ".
Figure 10 shows the reason that an exemplary Gaussian beam method of application and finite difference method according to the present invention synthesize
By the differential chart of earthquake record.As shown in Figure 10, theoretical seismogram and finite difference method based on triangulation Gaussian beam
The difference of the theoretical seismogram of synthesis, Gaussian beam method are tracked the ray of direct wave due to not having, are not had in earthquake record
There is direct wave, in addition to this, the result of two methods is that finite difference calculus exists since mesh generation " sawtooth " effect causes
Multiple diffracted waves.
Technical solution provided by the invention reduces the grid of finite difference modelling to the better adaptability of complicated structure
Scattering, improves the precision of wave-field simulation caused by " sawtooth " effect；And computational efficiency is high, can directly obtain removal direct wave
Earthquake record.
It will be understood by those skilled in the art that above to the purpose of the description of the embodiment of the present invention only for illustratively saying
The beneficial effect of bright the embodiment of the present invention is not intended to limit embodiments of the invention to given any example.
Embodiment 2
According to an embodiment of the invention, providing a kind of computer readable storage medium, it is stored thereon with computer program,
It is performed the steps of when described program is executed by processor
Step 1, disperse node is given, rate pattern is subjected to Delaunay Triangulation；
Step 2, on the basis of rate pattern triangulation, dynamic ray tracing is carried out；
Step 3, theoretical seismogram is obtained using Gaussian beam propagation operator.
The embodiment is realized by Delaunay Triangulation and Gaussian beam forward modeling method and obtains theoretical seismogram.
In one example, described to include: using Gaussian beam propagation operator acquisition theoretical seismogram
Step 1, it is based on a ray and a detector position, the Gaussian beam of all single-frequency is sought using formula (3)
Wave field；
Step 2, step 1 is repeated to all detector positions；
Step 3, to different rays, it is repeated in step 1 and step 2, and then by all rays to all wave detector positions
The contribution accumulation summation set；
Step 4, plural Ricker wavelet is generated, the result summed with the accumulation that step 3 obtains is multiplied, and then carries out inverse
Fourier transformation obtains the theoretical seismogram.
Wherein, P (s) and Q (s) is the plural number become along Gaussian beam central ray, and s is the integral arc length along central ray, u
(s, n, ω) is the Gaussian beam wave field of single-frequency, and τ (s) is the propagation time at center ray arc length s, and V (s) indicates central ray
Speed, n are the component of ray center coordinate system vertical centre ray, and i is imaginary unit, and ω is angular frequency.
In one example, the dynamic ray tracing includes:
Step 1, the triangular mesh where focus is determined；
Step 2, it determines a shooting angle, carries out dynamic ray tracing；
Step 3, the triangular mesh boundary is encountered, the triangular mesh frontier properties are read, determines the institute encountered
If stating triangular mesh boundary is that reflection, transmission perhaps terminate and track the triangular mesh boundary and be reflection or transmit,
It calculates reflection or transmits the influence to amplitude；
Step 4, the variable in each step-length of records center ray path, the variable include central ray position, slowness
Component, dynamic ray tracing parameter；
Step 5, change shooting angle, repeat step 2- step 4, until traversing all shooting angles.
Various embodiments of the present invention are described above, above description is exemplary, and non-exclusive, and
It is not limited to disclosed each embodiment.Without departing from the scope and spirit of illustrated each embodiment, for this skill
Many modifications and changes are obvious for the those of ordinary skill in art field.The selection of term used herein, purport
In the principle, practical application or improvement to the technology in market for best explaining each embodiment, or make the art
Other those of ordinary skill can understand each embodiment disclosed herein.
Claims (10)
1. a kind of forward modeling method based on triangulation model, which is characterized in that this method comprises:
Given disperse node, carries out Delaunay Triangulation for rate pattern；
On the basis of rate pattern triangulation, dynamic ray tracing is carried out；
Theoretical seismogram is obtained using Gaussian beam propagation operator.
2. the forward modeling method according to claim 1 based on triangulation model, wherein the dynamic ray tracing includes
Kinematics ray tracing and kinetics ray-tracing.
3. the forward modeling method according to claim 2 based on triangulation model, wherein the kinematics ray tracing is logical
The first-order ordinary differential equation system for crossing formula (1) carries out:
Wherein, xiIndicate the coordinate of central ray, piIndicate that the slowness component of central ray, s indicate to integrate arc along central ray
It is long, xi(s) coordinate of central ray step-length, p are indicatedi(s) indicate that the slowness component of central ray step-length, V (s) are indicated along center
The speed of model on ray, τ indicate the time step of ray tracing.
4. the forward modeling method according to claim 2 based on triangulation model, wherein the kinetics ray-tracing is logical
The first-order ordinary differential equation system for crossing formula (2) carries out:
Wherein, P (s) and Q (s) is the plural number become along Gaussian beam central ray, and s indicates to integrate arc length, V (s) table along central ray
Show the model velocity along central ray, τ indicates ray-traced time step-length, and n indicates ray center coordinate system perpendicular to ray side
To coordinate.
5. the forward modeling method according to claim 1 based on triangulation model, wherein described propagated using Gaussian beam is calculated
Son obtains theoretical seismogram
Step 1, it is based on a ray and a detector position, the Gaussian beam wave field of all single-frequency is sought using formula (3)；
Step 2, step 1 is repeated to all detector positions；
Step 3, to different rays, it is repeated in step 1 and step 2, and then by all rays to all detector positions
Contribution accumulation summation；
Step 4, plural Ricker wavelet is generated, the result summed with the accumulation that step 3 obtains is multiplied, and then carries out in inverse Fu
Leaf transformation obtains the theoretical seismogram；
Wherein, P (s) and Q (s) be the plural number become along Gaussian beam central ray, s for along the integral arc length of central ray, u (s, n,
It is ω) the Gaussian beam wave field of single-frequency, τ (s) is the propagation time at center ray arc length s, and V (s) indicates the speed of central ray,
N is the component of ray center coordinate system vertical centre ray, and i is imaginary unit, and ω is angular frequency.
6. the forward modeling method according to claim 5 based on triangulation model, wherein the acquisition of the detector position
It include: the reception position being evenly distributed by interpolation using given geophone station position.
7. the forward modeling method according to claim 1 based on triangulation model, wherein the dynamic ray tracing packet
It includes:
Step 1, the triangular mesh where focus is determined；
Step 2, it determines a shooting angle, carries out dynamic ray tracing；
Step 3, the triangular mesh boundary is encountered, the triangular mesh frontier properties are read, determines described three encountered
If hexagonal lattice boundary is that perhaps the termination tracking triangular mesh boundary is reflection or transmission for reflection, transmission, calculate
The influence of reflection or transmission to amplitude；
Step 4, the variable in each step-length of records center ray path, the variable include central ray position, slowness component,
Dynamic ray tracing parameter；
Step 5, change shooting angle, repeat step 2- step 4, until traversing all shooting angles.
8. a kind of computer readable storage medium, is stored thereon with computer program, which is characterized in that described program is by processor
It is performed the steps of when execution
Step 1, disperse node is given, rate pattern is subjected to Delaunay Triangulation；
Step 2, on the basis of rate pattern triangulation, dynamic ray tracing is carried out；
Step 3, theoretical seismogram is obtained using Gaussian beam propagation operator.
9. computer readable storage medium according to claim 8, wherein when the acquisition using Gaussian beam propagation operator
Between the earthquake record in domain include:
Step 1, it is based on a ray and a detector position, the Gaussian beam wave field of all single-frequency is sought using formula (3)；
Step 2, step 1 is repeated to all detector positions；
Step 3, to different rays, it is repeated in step 1 and step 2, and then by all rays to all detector positions
Contribution accumulation summation；
Step 4, plural Ricker wavelet is generated, the result summed with the accumulation that step 3 obtains is multiplied, and then carries out in inverse Fu
Leaf transformation obtains the theoretical seismogram；
Wherein, P (s) and Q (s) be the plural number become along Gaussian beam central ray, s for along the integral arc length of central ray, u (s, n,
It is ω) the Gaussian beam wave field of single-frequency, τ (s) is the propagation time at center ray arc length s, and V (s) indicates the speed of central ray,
N is the component of ray center coordinate system vertical centre ray, and i is imaginary unit, and ω is angular frequency.
10. computer readable storage medium according to claim 8, wherein the dynamic ray tracing includes:
Step 1, the triangular mesh where focus is determined；
Step 2, it determines a shooting angle, carries out dynamic ray tracing；
Step 3, the triangular mesh boundary is encountered, the triangular mesh frontier properties are read, determines described three encountered
If hexagonal lattice boundary is that perhaps the termination tracking triangular mesh boundary is reflection or transmission for reflection, transmission, calculate
The influence of reflection or transmission to amplitude；
Step 4, the variable in each step-length of records center ray path, the variable include central ray position, slowness component,
Dynamic ray tracing parameter；
Step 5, change shooting angle, repeat step 2- step 4, until traversing all shooting angles.
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| CN111208567A (en) * | 2020-01-07 | 2020-05-29 | 中国科学院地理科学与资源研究所 | Ore layer imaging method and device and computer readable storage medium |
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| 刘少勇等: "山前带地震数据射线（束）叠前成像方法研究与应用", 《石油物探》 * |
| 蔡杰雄: "高斯束深度偏移的实现与应用研究", 《石油物探》 * |
| 邓飞等: "高斯射线束正演与偏移", 《石油地球物理勘探》 * |
| 高阳等: "三角网格模型剖分方法的研究与应用", 《中国煤炭地质》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111208567A (en) * | 2020-01-07 | 2020-05-29 | 中国科学院地理科学与资源研究所 | Ore layer imaging method and device and computer readable storage medium |
| CN111208567B (en) * | 2020-01-07 | 2020-10-20 | 中国科学院地理科学与资源研究所 | Ore layer imaging method and device and computer readable storage medium |
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